From 3c6a768e5391e6bc8355fe2bc849d2978afef8f6 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 14:03:34 -0500 Subject: [PATCH] Add reviewed phase-coded callers and phase-access theorems --- .../phase-coded-callers/ANNEX-REPLAY.json | 43 + research/phase-coded-callers/CLAIMS.json | 112 + .../phase-coded-callers/DIRECT-SOURCES.json | 264 + .../phase-coded-callers/EXTERNAL-NOTICES.json | 40 + research/phase-coded-callers/NOTICE.md | 77 + .../phase-coded-callers/PACKAGE-SHA256.json | 302 + .../PORTABLE-ADAPTATION.json | 10 + .../PORTABLE-ADAPTATION.patch | 13 + research/phase-coded-callers/PROOF.md | 353 + research/phase-coded-callers/README.md | 120 + research/phase-coded-callers/REPLAY.json | 266 + research/phase-coded-callers/RESULT.json | 145 + research/phase-coded-callers/SOURCES.json | 2529 + research/phase-coded-callers/VALIDATION.md | 66 + .../fixed-code-interface/ANNEX-MANIFEST.json | 74 + 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+# Source credit and license + +This package contains work prepared for Ali Romman's centre-encoding +campaign with substantial OpenAI Codex assistance. It retains separate +agent proofs, implementations, and independent checks. This notice does +not claim human review, maintainer acceptance, or priority over cited +predecessors. New package material is under Apache-2.0. The full +[repository NOTICE](frozen/NOTICE), [LICENSE](frozen/LICENSE), and +[upstream license](frozen/upstream/LICENSE) remain in the package. + +The controller-followthrough lane supplied the phase-coded local word. +The new-core-transfer lane supplied its clean late-exchange predecessor. +The native-escape lane supplied the D25 and D73 callers, the section +geometry, the translation services, and the current-scalar closure. +The bridge-access lane supplied the actual stage views and an independent +section review. The owner-review lane supplied the separate triple phase +engine, the triple review, the source-bound scalar closure review, and +the general-stage proof review. The translation-service and in-place +review lanes supplied independent literal service checks. The +independent-review lane supplied the A8 odd-grid premise. The owner +review found and reported the simultaneous-map error; its correction +remains binding. These are contribution records within one AI-assisted +campaign, not separate human author identities. + +The provider lineage comes from +[PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133) +at `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. The retained source +README credits dcharb78 and earlier contributors. Its byte-equal +provider copies come from Jeremy Diviney's +[PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148) +at `f2927a4b8afcf0701a6b945e14f30de1d94f5176`. This package does not +claim that PR's packing improvement. Both source README files are +retained in `frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/` +and listed in SOURCES.json. + +The exact phase ledger is the historical +[PR #3251](https://github.com/CrocSwap/integer-mult-bounds/pull/3251) input at +`upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json`, +SHA256 `c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa`. +The phase engine also reads the unchanged historical archive +`selected-replay.tar.gz`, SHA256 +`f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6`. +These are exact consumed premises. Neither is updated to the currently +selected construction. + +The exact Clifford implementation comes from +[PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588) +at `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`. The full native-source +[NATIVE-LIFT.md](frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/NATIVE-LIFT.md) +retains the pinned compiler links and the source notices. It credits +Cinna Davis and [PR #2226](https://github.com/CrocSwap/integer-mult-bounds/pull/2226) +for the warp source, and +[PR #458](https://github.com/CrocSwap/integer-mult-bounds/pull/458) +for the wrapper construction. The source files retain their original +author and AI-assistance notices. + +The inherited stream and layout sources are retained as +[02-streams.tex](frozen/upstream/build/sections/02-streams.tex) and +[05-layers.tex](frozen/upstream/build/sections/05-layers.tex), with exact +hashes in SOURCES.json. Source notices can describe historical results +outside this package's scope. Those descriptions do not become new +claims of this extraction. + +Every file in frozen/ is byte-exact. The sole adapted executable changes +only the resolution of five absolute source paths in a frozen service +receipt. Its original bytes, adapted bytes, and complete diff are retained. +No imported module, mathematical check, source hash, or price is changed. + +The fixed-code appendix retains the source-domain lane's general scalar +interface proof and the independent publication agent's proof and graph +check. Its own notice and source manifest remain unchanged. + +The five [external source notices](EXTERNAL-NOTICES.json) are unchanged +copies from the verified historical GitHub file objects retained by the +reciprocal-native-responses package. Their exact hashes and original +commit links are included. They retain the PR #3133 credits and the +Clifford and warp notices from PR #2588 and PR #2226. diff --git a/research/phase-coded-callers/PACKAGE-SHA256.json b/research/phase-coded-callers/PACKAGE-SHA256.json new file mode 100644 index 0000000000..c20510e5ef --- /dev/null +++ b/research/phase-coded-callers/PACKAGE-SHA256.json @@ -0,0 +1,302 @@ +{ + "schema": "phase-coded-callers-package-hashes-v1", + "files": { + "ANNEX-REPLAY.json": "30cb3324cd434a10f5f75fdd0933f4ea6bcc08ecc5940e50989202d6cd2cb2df", + "CLAIMS.json": "e4103e3ab7fa2d6b515e14a73377bf6c16c8531a710ba4380d40d3a8b2310e72", + "DIRECT-SOURCES.json": "eaa698916699ea8d503bc71660b559ed186c7d1db5b20cd45b3e286ff1a73141", + "EXTERNAL-NOTICES.json": "580b28d74bb72ca158ab15599baca2bff0e4b43c7bbc43f787d16307ac975709", + "NOTICE.md": "6a89014ca6b31c21c2d6f0783021e5d9678a557041afc9410542283d3daba5fb", + "PORTABLE-ADAPTATION.json": "63a00d7993f2c75e6642ac377b78a3d3636d2dee7ab6379181e4770f81a83c9f", + "PORTABLE-ADAPTATION.patch": 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a/research/phase-coded-callers/PORTABLE-ADAPTATION.json b/research/phase-coded-callers/PORTABLE-ADAPTATION.json new file mode 100644 index 0000000000..66463bf2f9 --- /dev/null +++ b/research/phase-coded-callers/PORTABLE-ADAPTATION.json @@ -0,0 +1,10 @@ +{ + "schema": "phase-callers-source-path-adaptation-v1", + "original": "frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py", + "portable": "portable/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py", + "runtime_path": "work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py", + "original_sha256": "c638572c6abf5efb6e6a95beca07527d2f806732745455ccdd8eb25e8e22d249", + "portable_sha256": "408965371eff661f69c38c5ab9907872113c75884c8e93c1d6e89b969d2becf2", + "patch": "PORTABLE-ADAPTATION.patch", + "scope": "Resolve five absolute source paths from the unchanged receipt inside the copied repository. All file hashes, imports, arithmetic, and checks remain. No imported module is changed." +} diff --git a/research/phase-coded-callers/PORTABLE-ADAPTATION.patch b/research/phase-coded-callers/PORTABLE-ADAPTATION.patch new file mode 100644 index 0000000000..b13fc05b3f --- /dev/null +++ b/research/phase-coded-callers/PORTABLE-ADAPTATION.patch @@ -0,0 +1,13 @@ +--- frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py ++++ portable/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py +@@ -38,7 +38,9 @@ + receipt = read(SOURCE / "TRANSLATION-SERVICE.json", PINS["TRANSLATION-SERVICE.json"]) + payload = read(SOURCE / "TRANSLATION-SERVICE-PROGRAMS.json.gz", PINS["TRANSLATION-SERVICE-PROGRAMS.json.gz"]) + probe = read(SOURCE / "SCHUR-PROBE.json", PINS["SCHUR-PROBE.json"]) +-primary = {key: read(Path(item["path"]), item["sha256"]) for key, item in receipt["source_pins"].items()} ++origin_root = Path("/Users/aliromman/Projects/IntegerMultiplicationBounds") ++primary = {key: read(HERE.parents[4] / Path(item["path"]).relative_to(origin_root), item["sha256"]) ++ for key, item in receipt["source_pins"].items()} + + + def accumulate(target, key, value): diff --git a/research/phase-coded-callers/PROOF.md b/research/phase-coded-callers/PROOF.md new file mode 100644 index 0000000000..49be103b7f --- /dev/null +++ b/research/phase-coded-callers/PROOF.md @@ -0,0 +1,353 @@ +# Proof contracts and exact scope + +This document states the retained claims and connects them to the full +byte-exact proofs. It does not replace a general proof with finite test +results. Each source path and receipt is hash-bound in +[SOURCES.json](SOURCES.json). [CLAIMS.json](CLAIMS.json) gives the direct +proof and review map. + +## 1. The 16/96 phase-coded local word + +Use the ordered selected ports +`P=(0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23)` and the other 96 +ports R. Let H be the actual 16 by 96 response matrix and `D=-H*`. +Let Q be the positive line operator and `q=Q^-1`, separately on each +physical input port. These operators do not commute through arbitrary +responses. Their source attachment and order must be retained. + +The [local proof](frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/PHASE-CODED.md) starts with the pinned clean late-exchange +word. It removes 592 ordinary cross-bank ADDs, retains the native +kernels, frames, and adapters, and inserts 96 physical unit ADDs before +the input adapters. Its formal maps are + +```text +F_Q(a,u,z,v) = (-z, u, a+Hu, v+Q_R u), +B_Q(a,u,z,v) = (z, u+Dz-q_R v, -a, v). +``` + +For the Q-entry forward contract, physical inputs are `X=Q(a,u)`, +`Y_P=Q_P z`, and `Y_R=v`. The output X bank and selected Y bank are +FULL. Ordinary Y has the stated F9 q_R type. The initial I-entry +variant removes the selected input Q_P and replaces sixteen rank-eight +calls by rank-nine calls. The backward contract uses its declared +inverse orientation. The full proof gives the types at each event. + +Each local word has 1,520 native children. The Q-entry profile is +`{1:1392,2:64,3:48,8:16}`, with mass 1,792. The initial I-entry +profile has sixteen rank-nine children instead of rank-eight children, +with mass 1,808. Each word costs +`1720+1760+384+768=4632` real scalar primitives. No owned or private +field and no odd division is added. + +The [local receipt](frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/final-normal/CHECKS.json) and the fresh package replay check +all 640 independent inputs for both providers and all three local +orientations. They check that all 416 arbitrary helpers return unchanged. +This replay regenerates the literal transcript. The spatial native +kernels and endpoint adapters are inherited exact records; the replay +does not regenerate their dense Clifford compilations. Their native +phase proof remains a separate pinned premise. + +## 2. Three calls, three legal FULL shears, and the D25 terminal + +The [D25 proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/PHYSICAL-ENDPOINT.md) uses the actual orthogonal stage routes G_s. +Set `H_s=G_P H G_R` and `D_s=G_R D G_P` in each current chart. The +routes fix the intrinsic line for their own stage. They do not make H +stage-independent. At the physical entry put +`(a,u)=qX0`, `z=q_P Y0_P`, and `v=Y0_R`. + +Set `alpha=a+H_0u` and `r=D_1 alpha-q_Rv`. The full stage-1 cover +sweep and helper returns occur before the first added shear. At that +cut X_R and X_P are both FULL. Thus + +```text +X_R -= D_1 X_P +``` + +replaces r by `-q_Rv`. After the last local call, the data are + +```text +X = F25(-z,-q_Rv), +Y = F25(alpha-H_2q_Rv,u). +``` + +The two FULL output shears + +```text +Y_P -= H_2 X_R, +Y_P -= H_0 Y_R +``` + +give `X=-F25 qY0`, `Y=F25 qX0`. This proves the endpoint for +arbitrary physical X0 and Y0. It never reads an ordinary hole through +a scalar shear. The [independent proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/REVIEW.md) derives all +224 data columns with a separate phase engine. It verifies all 1,344 +phase identities and all three complete FULL shear matrices. Its +negative controls reject omitted entry translations and the false +ordinary-FULL type. + +The three shears use 648 complex ADDs, at most 6,144 real scalar +primitives, and 448 affine map calls. This is the direct coefficient +invoice; no smaller factored invoice is consumed. Three local calls +and these shears cost 20,040 scalar primitives before terminal wrappers +and map costs. The Q-entry words have 672 explicit local views; these +are distinct from the shear maps and native side maps. + +The direct Q terminal uses 224 positive line calls. Its complete +profile is `{1:4400,2:192,3:144,8:48}` and mass is +`5376+224=5600`. The initial I-entry alternative uses 208 line calls. +Its complete profile is `{1:4384,2:192,3:144,8:32,9:16}` and mass is +`5392+208=5600`. These are two specified constructions. The 224 and +208 line counts are not universal lower bounds for every decoder. +An unsigned output convention adds 112 field signs, priced at 224 +scalar primitives, unless the caller consumes the signed exchange. + +Every positive child rank in either complete profile is below 25. +For `0<=sigma<1`, `r^sigma > r*25^(sigma-1)` at each such rank. +Summing gives a moment strictly above `224*25^sigma`. Thus these paid +profiles do not provide a strict moment improvement. This conclusion +does not rule out a different terminal or a different interface. + +## 3. The actual nine-call D73 chain + +The [chain proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/CHAIN.md) and [general-view proof review](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/GENERAL-VIEWS-REVIEW.md) +use the nine actual routes, grouped as three triples. The route/level +pairs for the shears are +`(1,1),(2,2),(0,2),(4,4),(5,5),(3,5),(7,7),(8,8),(6,8)`. +The shared input line factor remains attached to the original data. +Each corrected triple applies the signed exchange `J(A,B)=(-B,A)` +to those carried variables. It does not apply a new q. Since +`J^3(A,B)=(B,-A)`, the endpoint is + +```text +X = F73 qY0, +Y = -F73 qX0. +``` + +The exact phase check covers 3,584 natural boundary identities and +1,008 FULL shear-view identities. Removing either the entry or exit +translation causes 896 failures. The all-width view argument uses the +quadratic refinement and spectator-axis extension; it is not inferred +from one width. The executable claim concerns these nine routes. + +Nine Q-entry words have profile `{1:12528,2:576,3:432,8:144}` and +mass 16,128. The direct terminal adds 224 positive line calls, so the +complete profile is `{1:12752,2:576,3:432,8:144}` with mass +`16352=224*73`. The same rank argument gives no strict moment gain. +The scalar subtotal is `41688+18432=60120`, before terminal wrappers. +Keep 1,792 shear maps and 3,584 global entry/exit maps separate from +that scalar subtotal and from native side maps. + +Neither caller proves a recursive consumer for q, a global host, a +complete address and stream invoice, or a numerical-grid bound. The +retained [recursive interface note](frozen/work/centre-encoding-campaign-20261014/lanes/coherent-port/recursive-code-interface-20261020/INTERFACE.md) states a possible +contract and its obligations. It does not discharge them. + +## 4. Separate 8/104 section geometry + +This section has a different interface. Select +`A=(0,7,20,27,36,46,57,111)` and let U contain the other 104 ports. +Construct the 8 by 104 matrix B from the pinned response, and put +`D=B*`. Here `BD=13I`, Q is unitary, and `Q^4=I`. +The query is `A_query=BQ`; define `T=BQ^2D`. + +The [geometry proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY.md), [source qualification](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES.md), +[power classification](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/CLASSIFICATION.md), and +[independent review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/REVIEW.md) prove the following at every +positive width. The nine commuting translation involutions split the +space into 512 character sectors. The copy characters combine by XOR, +and every sector is present. In each sector the actual symmetric +8 by 8 matrix has eigenvalues among `±1,±3,±5,±11,±13`; each listed +value occurs. Exact characteristic calculations and the ten-root +annihilator prove the spectrum. This also proves that T is invertible +and gives its exact inverse in the translation algebra. + +There are two useful right sections of A_query: + +```text +K_minus = qD/13, +K_plus = QD T^-1. +``` + +Since `D*D=13I` and Q is unitary, K_minus has norm `1/sqrt(13)` +and is the minimum-norm section. The singular values of K_plus are +`sqrt(13)/abs(lambda)` for lambda in the spectrum of T. Thus its norm +is `sqrt(13)`, its least singular value is `1/sqrt(13)`, and its +condition number is 13. Its oblique projector +`P_plus=K_plus A_query` has norm 13, image `im(QD)`, and kernel +`ker(BQ)`. Hence `im(QD)` complements `ker(BQ)`. + +The normalized cross-Gram matrix for `im(QD)` and `im(qD)` is T/13. +Their principal cosines are `{1,3,5,11,13}/13`. In particular they +intersect; they are not a direct-sum pair. This is different from the +image/kernel complement just stated. + +For the query `B Q^m` with a section constrained to `im(Q^nD)`, the +proof reduces existence to surjectivity of `BQ^(m+n)D`. When m+n is +0 modulo 4, the unique constrained section is `Q^nD/13`. When m+n is +2 modulo 4, it is `Q^nD T^-1`. These statements hold at every positive +width. For odd m+n there is no such section at width at least five, +even if the proposed section is nonlinear: the restricted linear query +is not onto. The explicit width-five character choice +`(1,2,3,6,6)` has null vector `(0,0,1,0,-1,1,0,1)` and a nonzero +leading seven-minor `-73`, so its rank is seven. Spectator extension +proves the larger-width statement. No minimum-width claim follows. + +## 5. Translation services and the corrected one-bank inverse + +The [two-bank service proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/TRANSLATION-SERVICE.md) and +[independent review](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/REVIEW.md) implement the T from Section 4. +They require two existing eight-field FULL banks and one owned C0 field. +The source bank is unchanged and the target bank can have an arbitrary +baseline. The C0 input is discardable, its input contribution is removed, +and its output is zero. No other owner changes. The literal words have +zero native children. Each row in the following table also needs 32 +completed outer-view maps. + +| Service, either sign | Real scalar primitives | Body translation maps | Real odd-division scans | +| --- | ---: | ---: | ---: | +| Add T | 8,530 | 104 | 0 | +| Add T inverse, fewer maps | 166,912 | 2,048 | 16 | +| Add T inverse, fewer scalars | 114,528 | 8,944 | 16 | +| Coded exchange, fewer maps | 183,972 | 2,256 | 16 | +| Coded exchange, fewer scalars | 131,588 | 9,152 | 16 | + +The exchange is the literal three-shear composition +`x+=Ty; y-=T^-1x; x+=Ty`, which gives `(Ty,-T^-1x)`. +The check combines the exact shear programs with the separately proved +all-width inverse. It does not claim a second full sparse replay of the +entire exchange. The exact forward prefix row norm is 53; the inverse +prefix row norm is `9073/715`. These are local bounds. + +The [one-bank inverse proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.md) requires one existing eight-field +bank and one owned C0 field. It uses the free 512-point orbits of the +nine translations, a normalized Walsh transform, the exact inverse in +each character sector, and the inverse Walsh transform. This proves the +word at every positive width. The [literal independent check](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/REVIEW.md) +verifies all nine formal input columns, both inverse orders at all 512 +modes, all 32,768 inverse-kernel coefficients, 144 Walsh-pair blocks, +and 64 completed-level phase identities. It verifies zero C0 output +and removal of the arbitrary C0 input. + +The one-bank word costs 2,080 uniform and 110,284 conditional real scalar +primitives, 144 simultaneous translation maps, sixteen real odd-division +scans, and sixteen outer views. It has zero native children. Its full +word uses nine extra dyadic bits and increases the odd height by one. +The largest mode prefix row norm is 462,848; this gives a local +nineteen-bit guard bound. It is not a full recursive precision invoice. + +The [map-cost correction](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/MAP-COST-CORRECTION.md) withdraws the earlier review's +O(V) shortcut and its fixed-linear whole-body claim at general K. The +selected f bits are interleaved when K>1, so a contiguous complement is +not the physical translation. No extraction view or lowering for that +shortcut was proved. Retain all 144 translation maps at the applicable +packed-map cost, plus sixteen outer maps. The shortcut is valid only +for K=1. The direct conditional marked-counter scans remain valid for +arbitrary selected-bit positions. None of these facts makes the maps +free in a supplier recurrence. + +The rational inverse uses odd denominator 2,145 and sixteen real odd +scans. The frozen translation-service review omits the record count in +one bit-cost sentence. For n complex entries per field, the retained +A8 bound is `64*n*(w_g+1)` arithmetic-head steps, plus stream control, +not `64*(w_g+1)` for an entire service call. The scalar and map invoices +above do not use that typo. The [A8 odd-grid theorem](frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md) is a retained conditional +premise. A child endpoint must satisfy its exact dyadic-grid contract; +a completed parent must cancel the rational endpoint before unscaling. +The services do not supply a global owner lease or a caller terminal. +They are not decoders for Section 2's 16/96 common-q endpoint. + +## 6. Current scalar-code closure + +The [D25 proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/CLOSURE.md), [standalone independent proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/REVIEW.md), +and [corrected source binding](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/BINDING.md) cover invertible scalar +codes C0, C1, C2 in their current fresh charts. Their routed product is + +```text +K = (G2 C2 G2)(G1 C1 G1)C0. +``` + +For a fixed output port p, the route through intermediate ports j,r is +`rho_(2,p) rho_(2,j) rho_(1,j) rho_(1,r)`. The common logical input +with tags `(e2,e1)` separates all 12,544 routes at width f>=2. The +literal affine input `(0,e2,e1)` separates the physical routes at +f>=3. Thus distinct nonzero coefficient products cannot cancel in +that basis column. Invertibility forces every row and column to be +used. A monomial product therefore forces each code to be monomial; +the converse follows from composition of the monomial factors. + +A third Fourier character distinguishes any route that breaks the +intrinsic line. It gives a nonzero Q commutator. Within this current +scalar class, Q commutation therefore holds exactly when all three +codes are diagonal, at f>=3. The full proof states and checks the +line criterion. It does not presume that a small representation has +independent route matrices. + +The proof's regular-cover step uses the explicit covariant lift +`f(d,z)=g(d^-1z)`. Equal support sizes in every fibre show that a full +coordinate monomial which preserves this subspace induces a spatial +monomial. Invariance alone would not suffice. The corrected binding +review checks this step and binds the final source receipt +[bound-normal/CHECKS.json](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/bound-normal/CHECKS.json), SHA256 +`f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a`. +The earlier run-normal and final-normal receipts do not replace it. + +For the eight actual C/C* choices, the review reconstructs all literal +routes and verifies 896 nonmonomial basis witnesses and 896 nonzero +commutator witnesses. The C/C/C route count is 54,976, with at least +18 terms in every output row. The 1,066 nonzeros of scalar C^3 alone +do not certify the whole routed operator. + +The [general-stage proof](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/GENERAL-CLOSURE.md) and its separate +[proof review](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/REVIEW.md) use tags `(e_T,...,e_1)` to recover +all ordered intermediate ports for dimension `9+8T`. With T+1 +invertible current scalar codes, logical monomial closure holds exactly +for monomial codes at f>=T; physical affine closure uses f>=T+1; +Q commutation holds exactly for diagonal codes at f>=T+1. These are +sufficient width bounds, not width optima. The general-T claim is a +proof claim, not a result of the finite replay. + +The theorem excludes old-chart controls, operator-valued coefficients, +changed gathered interfaces, and paid joint decoders. A route count is +not a native child count. The theorem is not a general native decoder +lower bound and does not produce a supplier or kappa improvement. + +## 7. Retained adjacent support + +The phase engine needs the [natural no-reset triple](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/NO-RESET.md) and its +[independent review](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/REVIEW.md). Their exact proof, receipts, and +operator terminal are retained in the closure. That predecessor uses +208 line calls, 16,608 scalar primitives, and 1,344 maps before side +maps and final bank exchange. It is an operator word, not a hosted +native terminal. Its ordinary-hole query differs from the new +phase-coded response. Its costs are not added to the new caller. + +The [historical handoff](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/HANDOFF-PHASE-CALLERS-20261020.md) also describes reciprocal source-cut +readers and other adjacent results. They are not dependencies of the +checks in this package. Their historical presence is not a claim that +this package admits their allocation, record transport, or late erase. +Their publication disposition belongs to their separate packages. + +## 8. One fixed scalar-code interface + +The separate [appendix proof](annexes/fixed-code-interface/PROOF.md) +characterizes preservation of one fixed scalar subspace E. Let P be its +orthogonal projector. Join distinct ports i,j when P_ij is nonzero. +For arbitrary finite-dimensional port operators A_i, the block operator +diag(A_i) preserves E tensor V if and only if A_i=A_j on each component. +The operators need not be invertible or normal. + +Expand the operators in a linearly independent basis. Each resulting +scalar diagonal coefficient matrix must preserve E. Its spectral +projections are polynomials in that diagonal matrix and are orthogonal, +so it also preserves E perpendicular and commutes with P. The entry +equation forces equality along every edge. Conversely, equality along +edges makes the block operator commute with P tensor I and preserves E. + +For the pinned real query R, R R^T=56I. The projector onto ker R is +I-R^T R/56, and its graph is connected on all 112 ports. Thus every +completed port operator must agree for this fixed-code contract. Equal +native ranks alone do not suffice. The [separate review](annexes/fixed-code-interface/REVIEW.md) +accepts this theorem and its exact graph check. Changing the code or +using a joint operator on several arrays remains outside the result. +No native program, free overwrite, or kappa improvement follows. The +source note's later paired-gauge discussion is context only. diff --git a/research/phase-coded-callers/README.md b/research/phase-coded-callers/README.md new file mode 100644 index 0000000000..c656717695 --- /dev/null +++ b/research/phase-coded-callers/README.md @@ -0,0 +1,120 @@ +# Phase-coded callers and exact translation sections + +This package preserves four reviewed local results: phase-coded D25 and +D73 callers, the exact section geometry of the separate eight-row query, +translation services for that query, and closure criteria for current +scalar stage codes. It contains the full source proofs, programs, source +pins, reviews, and a portable replay. These are existing campaign +results. This extraction adds no new research claim. + +The paid D25 and D73 caller profiles have native masses `224*25` and +`224*73`. They do not give a strict moment gain or improve the complete +kappa calculation. A recursive consumer for the common q factor, a +complete host, map costs, owner schedules, and a numerical-grid proof +remain open. The packaging base is +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. The selected PR #4470 at +that base is context only. Historical input pins remain unchanged. + +A separate [fixed-code appendix](annexes/fixed-code-interface/PROOF.md) +gives the projector-graph criterion for one fixed scalar code. Its +112-port consequence and its independent review are separate from the +current changing-stage scalar-code theorem. + +Read the [proof and scope](PROOF.md), [source map](CLAIMS.json), +[replay specification](VALIDATION.md), and [credit](NOTICE.md). +The [map-cost correction](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/MAP-COST-CORRECTION.md) is binding: all 144 simultaneous +translations in the one-bank inverse retain the applicable packed-map +cost, in addition to sixteen outer views. The frozen earlier review +contains a withdrawn O(V) map shortcut. Do not use that shortcut. +The historical translation-service review also omits the record count +in one odd-scan bit-cost sentence. The correct bound is +`64*n*(w_g+1)`, plus stream control, for n complex entries per field. + +## Results and interfaces + +| Result | Exact scope | Remaining boundary | +| --- | --- | --- | +| Phase-coded local word | Both inherited providers; all 640 inputs, including 416 arbitrary helpers; 4,632 real scalar primitives per local call | Native spatial kernels and adapters retain their pinned proof contracts | +| Three-call D25 endpoint | Three FULL shears give `(-F25 q Y0, F25 q X0)` for arbitrary physical inputs | The direct terminal adds 224 rank-one lines for the Q-entry variant, or 208 for the I-entry variant; each complete native mass is 5,600 | +| Nine-call D73 endpoint | The actual nine routes give `(F73 q Y0, -F73 q X0)` with one common q | The direct terminal adds 224 lines; complete native mass is 16,352 | +| Eight-row section geometry | Spectrum `±{1,3,5,11,13}` at every positive width; positive-line right section norm `sqrt(13)` and condition number 13; oblique projector norm 13 | Odd-power obstruction is proved at width at least five; no minimum-width claim | +| Translation services | Exact signed T and T inverse shears, coded exchange, and one-bank T inverse; zero native children under stated bank and C0 contracts | Odd-grid operations, outer views, and all translation maps remain explicit costs | +| Current scalar-code closure | Logical monomial closure at width at least two; physical closure and Q commutation at width at least three; general-stage sufficient bounds T and T+1 | Current invertible scalar codes only; no decoder cost lower bound | + +The caller uses a **16/96 split** and `D=-H*`. The section and translation +services use a **different 8/104 split** and `D=B*`. The symbols belong +to different interfaces. The one-bank section inverse does not decode +the common q endpoint of the phase-coded caller. + +The exact D25 scalar subtotal is `3*4632+6144=20040`, before terminal +wrappers and maps. The nine-call subtotal is `9*4632+18432=60120` with +the same exclusion. The prospective 2,912-scalar local word is not a +source of either claim. Scalar counts, native rank mass, and map counts +are separate quantities. + +## Replay + +Use Python 3.11 or later, the standard library, one worker, and a new +output directory. No Git checkout, source workspace, NumPy, or network +is needed. Keep at least 3 GiB free. + +```sh +python3 -I -B research/phase-coded-callers/replay.py --out /tmp/phase-coded-callers-check +``` + +When this folder is elsewhere, replace only the script path. The default +runs all seven core jobs in normal and optimized Python modes. The final line +is: + +```text +PASS_PHASE_CODED_CALLERS +``` + +The fixed-code appendix has a separate replay. Run it as well for the +full package check: + +```sh +python3 -I -B research/phase-coded-callers/annexes/fixed-code-interface/replay.py --out /tmp/fixed-code-interface-check +``` + +Its final line is `PASS_SCOPED_SUPPORT_PROOF_REPLAY`. + +Each core job runs in a private copy. The source files are hash-checked before +and after the run. The replay checks every output field against its +frozen receipt. It normalizes only repository locations, validated hashes +of generated normalized artifacts, and the recorded self-hash of one +path-only checker adaptation. The local payload and both execution modes +must agree. See [VALIDATION.md](VALIDATION.md) for all checks and limits. + +## Package contents + +[DIRECT-SOURCES.json](DIRECT-SOURCES.json) records all 50 selected +entrypoints. [SOURCES.json](SOURCES.json) records the exact dependency +closure with original paths, byte lengths, and SHA256 hashes. Files in +`frozen/` retain their original bytes and relative repository paths. +The one portable source-path adaptation is documented in +[PORTABLE-ADAPTATION.json](PORTABLE-ADAPTATION.json) and its complete +[diff](PORTABLE-ADAPTATION.patch). No imported module is changed. + +[PACKAGE-SHA256.json](PACKAGE-SHA256.json) binds the package files except +itself. [REPLAY.json](REPLAY.json) records the core packaging replay, and +[ANNEX-REPLAY.json](ANNEX-REPLAY.json) records the separate appendix replay. Full +independent publication review is stored outside this frozen package. +The inherited reviews are separate agent checks, not maintainer approval. + +## Open next questions + +- Can a recursive caller consume the common q endpoint? This would make + the D25 and D73 constructions usable without the direct paid terminal. + A first step is to state one consumer with the exact gathered input + types. A complete endpoint, owner schedule, and recursive cost remain + blockers. The retained interface note does not supply them. +- Can the 144 simultaneous translations be lowered at the actual packed + addresses? A first step is to specify one interleaved selected-bit map + and price its extraction, permutation, and return. The absent lowering + and its cost block the withdrawn general O(V) claim. +- Can a different code interface give a useful terminal? A first step is + to state which code changes between cuts or which joint array operator + is allowed. The current-scalar and fixed-code theorems constrain their + stated classes only. A native program, safe owner use, and a full map + and precision invoice remain necessary. diff --git a/research/phase-coded-callers/REPLAY.json b/research/phase-coded-callers/REPLAY.json new file mode 100644 index 0000000000..8a25435b90 --- /dev/null +++ b/research/phase-coded-callers/REPLAY.json @@ -0,0 +1,266 @@ +{ + "status": "PASS_PHASE_CODED_CALLERS", + "mode": "both", + "only": null, + "source_files": 260, + "source_manifest_sha256": "33946ffb140cf3cbf04ca2a392daca9a5f3e9137a34bcff352cd0d6f8c6c4384", + "replay_sha256": "026a6591ba8aa48218a5989cbbd535b1ebb7e44212f0fb81bac69161e50d9f6c", + "python": "3.14.7 (main, Aug 5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]", + "jobs": [ + { + "id": "local", + "mode": "normal", + "seconds": 2.29, + "outputs": { + "CHECKS.json": { + "sha256": "4479996f8e2ff9d2f83169fe7c519a3e0b9efa5190deeaae1e5943b397c948f7", + "canonical_sha256": "c4a2115bf27dfc42a0bfb0ac3ceb9acc8d187a44d710511339ed03354934856b", + "frozen_byte_equal": false + }, + 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Each child gets a fresh private copy of the frozen repository layout. +The copies are removed after each job. Files produced by old scripts +beside their source paths therefore remain inside the private copy. +No source-workspace path, Git operation, or network call is needed. + +The default command runs these seven jobs twice, once in normal Python +and once with `-O`. Each child also uses `-I -B`. + +| Job | Fresh decisive work | Inherited limit | +| --- | --- | --- | +| local | Regenerate both providers and all three local orientations; check 640 independent inputs and 416 unchanged helpers; reproduce the complete local payload | Spatial native kernels and endpoint adapters remain exact pinned records; no dense native recompilation | +| triple | Independent phase engine; 224 endpoint columns; 1,344 phase identities; all three FULL shears; terminal profiles; negative entry/type controls | Local provider proof and generic native contracts remain premises | +| chain | The actual nine routes; 3,584 boundary and 1,008 shear-view identities; entry/exit omission controls | General-width view proof and common-q recursive consumer are distinct | +| geometry | Reconstruct the actual matrices, 512 character sectors, exact spectrum and odd-power witness | All-width extension uses the retained proof | +| translation | Literal signed T/T inverse shear words, all sixteen live inputs and C0, completed views, exact invoices | Exchange uses exact three-shear composition and the proved inverse; odd-grid theorem is inherited | +| inplace | Nine formal columns; 1,024 mode inverse orders; 32,768 kernel coefficients; 144 Walsh blocks; 64 completed views; exact invoices | Apply MAP-COST-CORRECTION; no general O(V) map lowering | +| closure | Bind the final corrected receipt; reconstruct 12,544 literal affine paths; verify both sets of 896 witnesses | General-T theorem and regular-cover step require the retained proofs; no native decoder replay | + +Each input is checked against SOURCES.json before and after the replay. +Compressed inputs also have their decompressed payload hashes checked +when that hash is recorded. All 50 direct entrypoints remain in the +closure. The checker inputs use the historical pins; packaging base +b58ad9ef4d4e861b0eaa5dba41742bdc072dca51 does not replace those pins. + +The translation-service reviewer originally resolves five absolute +paths from its frozen receipt. The portable copy resolves those same +paths under the copied repository root. All five expected hashes are +unchanged. PORTABLE-ADAPTATION.json and PORTABLE-ADAPTATION.patch bind +and show the complete change. The adaptation does not change an import +or an imported module. + +The output comparison retains every JSON field. It checks generated +output hashes before comparison. It then replaces only the source and +copied repository path prefixes with one marker. For generated artifacts +whose byte hash changes only because of such paths, it compares the +complete normalized artifact and replaces the validated hash by the +artifact's canonical hash. For the adapted translation checker, it +first verifies the actual portable self-hash, then maps that hash to +the original checker hash in the expected receipt. No cost, status, +source hash, matrix, program event, or mathematical field is omitted. +REPLAY.json records byte equality and canonical equality separately. + +The final status is `PASS_PHASE_CODED_CALLERS`. The `--only` and `--mode` +options permit one named job or one Python mode. Such a restricted run +is not the full packaging check. The receipt records both options. + +The output comparison preserves the historical receipts. It does not +endorse the withdrawn O(V) map statement or the service review's missing +record-count factor. PROOF.md states both qualifications. + +The replay does not compile every inherited Clifford kernel, rerun all +historical campaign probes, prove a global owner lease, lower every +packed map, construct the recursive common-q consumer, or recompute the +complete kappa value. The full proofs, exact source contracts, and +independent reviews remain necessary for the all-width claims. + +The fixed-code appendix has its own unmodified runner, source manifest, +exact graph receipt, proof review, and ANNEX-MANIFEST.json. It runs in +normal and optimized Python and compares complete receipt bytes. The +main seven-job replay does not invoke it. Run the second command in +README.md to include it. Its separate review was prepared by the +reciprocal-publication-review agent; no human review is claimed. diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/ANNEX-MANIFEST.json b/research/phase-coded-callers/annexes/fixed-code-interface/ANNEX-MANIFEST.json new file mode 100644 index 0000000000..dffab38f5b --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/ANNEX-MANIFEST.json @@ -0,0 +1,74 @@ +{ + "appendix": "fixed-code-interface", + "files": { + "CHECKS.json": { + "bytes": 535, + "sha256": "f41ad1d3041cda553f129012048d6f468a3bec3f22c5d18bf2457d9fb708531b" + }, + "PROOF.md": { + "bytes": 1906, + "sha256": "c14762025b084a3a54680c8bfd05fdf56b16600eaaebd081f975354564ca9098" + }, + "PUBLICATION.md": { + "bytes": 717, + "sha256": "6b467ba7c62e63de3358edd673c007aecbe4f80b07f57b28e4b3abc05793e78e" + }, + "README.md": { + "bytes": 1104, + "sha256": "ab729911c1add5b5d498115f129a778584d91e42a9d5ce6ee21606d76956ef5f" + }, + "REVIEW.json": { + "bytes": 998, + "sha256": "8dc781deca026398f317a255389c87f9a435172db9a28f9aa1105d89847be315" + }, + "REVIEW.md": { + "bytes": 2841, + "sha256": "f894b5eb3be7681186f2aaddb06c9e5c17cd23f1a05aaae00315fe13c98eb43a" + }, + "SOURCES.json": { + "bytes": 939, + "sha256": "418baabff54c63aafdf00f7f9c286b2e31751783ed5f9f3563ec66c554c99ad0" + }, + "TASK.json": { + "bytes": 450, + "sha256": "503965a1ae0370dd60ce409fd40a330a54f67107f46d68f620054eedbadc2886" + }, + "VALIDATION.json": { + "bytes": 1973, + "sha256": "74a445756ffc90ea64f0f3e321f23f18d6e0453e99239122362bf3e13a3f5772" + }, + "check_graph.py": { + "bytes": 3058, + "sha256": "d5ebf366fb37872b13df1b0bf4a53f9f60e80ad72949122c61aa8c6d4b29e98b" + }, + "frozen/lanes/circuit-interface/INTERFACE.json": { + "bytes": 23232, + "sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + }, + "frozen/lanes/source-domain/CODE-INTERFACE.md": { + "bytes": 5611, + "sha256": "333039ed67aa7661d0ae3a0aa8f2d1fd09fbd542700fdb8afb4b095e76a04166" + }, + "frozen/lanes/source-domain/COVER-REVIEW.json": { + "bytes": 1502, + "sha256": "7cfc5263852b72710f21152b234c5b2ad57ad68120bb6b4f989a442e453b1a25" + }, + "replay.py": { + "bytes": 2891, + "sha256": "c5b6abbe8d9704adfaea980c77f4f34fee78ae2367bf1e2e88bed59ca79b7697" + }, + "validation/normal.log": { + "bytes": 32, + "sha256": "fe56218351644c2780f212ef22c12b2f6bd350496d30bca4fc0079053643899f" + }, + "validation/optimized.log": { + "bytes": 32, + "sha256": "fe56218351644c2780f212ef22c12b2f6bd350496d30bca4fc0079053643899f" + } + }, + "frozen_input_files": 3, + "schema": "accepted-support-proof-appendix-v1", + "scope": "Fixed scalar-code invariance if and only if independent port operators agree on each projector graph component; the pinned ker R graph has one 112-port component.", + "total_bytes_excluding_manifest": 47821, + "total_files_excluding_manifest": 16 +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/CHECKS.json b/research/phase-coded-callers/annexes/fixed-code-interface/CHECKS.json new file mode 100644 index 0000000000..3dee269dbb --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/CHECKS.json @@ -0,0 +1,18 @@ +{ + "code_dimension": 104, + "component_sizes": [ + 112 + ], + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "not_checked": [ + "Native phases", + "Changing codes", + "Joint array operators", + "Recursive admission" + ], + "query_gram": "56 I8", + "scope": "Exact source application. The separate proof review proves the general operator-valued criterion.", + "single_port_operator_leakage_00": "13/196", + "status": "PASS_FIXED_CODE_PROJECTOR_GRAPH", + "undirected_edges": 2912 +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/PROOF.md b/research/phase-coded-callers/annexes/fixed-code-interface/PROOF.md new file mode 100644 index 0000000000..f28e51c849 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/PROOF.md @@ -0,0 +1,36 @@ +# Invariance of one fixed scalar code + +Let E be a complex subspace of C^W. Let P be its orthogonal projection. +Let V be finite-dimensional. Set D=diag(A_1,...,A_W), with operators A_i +on V. Join distinct coordinates i,j when P_ij is nonzero. Then + +```text +D(E tensor V) is contained in E tensor V +if and only if A_i=A_j on each graph component. +``` + +To prove necessity, expand the A_i in a basis B_alpha of their linear +span. Linear independence of B_alpha implies that each scalar diagonal +matrix diag(c_i,alpha) preserves E. For a finite diagonal matrix, each +spectral projection is a polynomial in that matrix. These orthogonal +projections preserve E, so the matrix also preserves E perpendicular. +It commutes with P. Hence (c_i,alpha-c_j,alpha)P_ij=0, which forces the +operator equality on every edge. For sufficiency, the same entry equation +gives [P tensor I,D]=0. The A_i need not be invertible or normal. + +For the pinned real query matrix R, R R^T=56I. Thus the projection onto +ker R is I-R^T R/56. Its graph is connected on all 112 ports. A block of +independent port operators preserves this one fixed code only when all +112 completed operators agree. Equal native ranks do not meet this test. + +This theorem does not exclude changing the code between calls or using a +joint operator on several arrays. The code (u,v,u+v) also shows why full +coordinate projections alone do not prevent compression: a common operator +needs two independent native inputs, followed by scalar reconstruction. +That count does not grant a free overwrite of arbitrary borrowed contents. + +The [original note](frozen/lanes/source-domain/CODE-INTERFACE.md) is unchanged. +The [independent review](REVIEW.md) adopts this criterion and its stated +112-port application. Its later gauge discussion remains source context; +that discussion is already covered by the fixed-word gauge package. +No complete kappa calculation changes. diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/PUBLICATION.md b/research/phase-coded-callers/annexes/fixed-code-interface/PUBLICATION.md new file mode 100644 index 0000000000..3b8cba97aa --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/PUBLICATION.md @@ -0,0 +1,7 @@ +The [fixed-code appendix](PROOF.md) gives an independently reviewed criterion for one fixed scalar code to survive independent native port operators. The operators must agree on each component of the code projector's support graph. The pinned `ker R` graph is connected on all 112 ports, so all completed port operators must agree for that fixed-code contract; equal ranks are insufficient. Changing codes and joint array operators remain outside the result. The exact source graph check passes in normal Python and with `-O`. + +```sh +python3 -I -B research/phase-coded-callers/annexes/fixed-code-interface/replay.py --out /tmp/fixed-code-interface-replay +``` + +Expected final line: `PASS_SCOPED_SUPPORT_PROOF_REPLAY`. diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/README.md b/research/phase-coded-callers/annexes/fixed-code-interface/README.md new file mode 100644 index 0000000000..3c24eeed26 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/README.md @@ -0,0 +1,24 @@ +# Scoped support appendix + +[PROOF.md](PROOF.md) states the accepted result and its limits. +[REVIEW.md](REVIEW.md) gives the separate independent proof review. +The original files under `frozen/` are unchanged and are bound by +[SOURCES.json](SOURCES.json). Historical review status is retained. + +Use Python 3.10 or later and the standard library. Run from this appendix +with a new output directory: + +```sh +python3 -I -B replay.py --out /tmp/fixed-code-interface-replay +``` + +The runner uses fresh copies, one process at a time. It runs normal Python +and Python with `-O`. Both complete receipts must match exact bytes. +The final line is `PASS_SCOPED_SUPPORT_PROOF_REPLAY`. +[VALIDATION.json](VALIDATION.json) records the independent publication run. +The replay does not prove the full native or recursive supplier contract. + +This appendix preserves campaign work and uses substantial OpenAI Codex +assistance. Its new proof review is a separate agent calculation, not an +independent human review. The parent package retains the upstream source +credit and license. This appendix makes no complete kappa claim. diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/REVIEW.json b/research/phase-coded-callers/annexes/fixed-code-interface/REVIEW.json new file mode 100644 index 0000000000..56df08df2c --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/REVIEW.json @@ -0,0 +1,15 @@ +{ + "accepted_proof_wrapper_sha256": "c14762025b084a3a54680c8bfd05fdf56b16600eaaebd081f975354564ca9098", + "claim": "Fixed scalar-code invariance if and only if independent port operators agree on each projector graph component; the pinned ker R graph has one 112-port component.", + "complete_kappa_improvement": false, + "independent_review": "REVIEW.md", + "native_or_recursive_admission": false, + "normal_optimized_complete_receipts_match": true, + "original_inputs_unchanged": true, + "remaining_publication_check": "Coordinator review of actual appendix files, final package link verification, GitHub rendering and readback.", + "review_sha256": "f894b5eb3be7681186f2aaddb06c9e5c17cd23f1a05aaae00315fe13c98eb43a", + "source_manifest_sha256": "418baabff54c63aafdf00f7f9c286b2e31751783ed5f9f3563ec66c554c99ad0", + "status": "ACCEPT_SCOPED_SUPPORT_APPENDIX", + "target_package": "phase-coded-callers", + "validation_sha256": "74a445756ffc90ea64f0f3e321f23f18d6e0453e99239122362bf3e13a3f5772" +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/REVIEW.md b/research/phase-coded-callers/annexes/fixed-code-interface/REVIEW.md new file mode 100644 index 0000000000..ef2c44321c --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/REVIEW.md @@ -0,0 +1,46 @@ +# Independent review of the fixed-code criterion + +Verdict: accept the projector graph criterion and its fixed ker R application +as a scoped appendix. The historical note states that its proof had no +independent review. This file provides that review separately and leaves +the note unchanged. The reviewer read PR-DESCRIPTION-STANDARD.md. + +The necessity proof is valid over the complex numbers. Apply the quotient +map C^W -> C^W/E to D(e tensor v). Expanding A_i in a linearly independent +operator basis gives a zero linear combination in +(C^W/E) tensor End(V). Each diagonal coefficient map therefore preserves E. +A finite diagonal matrix has finitely many distinct eigenvalues. Lagrange +polynomials give its coordinate spectral projections. These projections +are orthogonal, even when the diagonal entries are not real. Their ranges +split E and E perpendicular. Thus invariance implies commutation with P. +This argument does not require any A_i to be normal or invertible. + +The entry equation (c_i-c_j)P_ij=0 forces equality on graph edges and then +on connected components. Conversely, componentwise operator equality makes +D commute with P tensor I and preserves its range. Isolated coordinates, +zero coordinate projections, the full code, and the zero code cause no +exception: each isolated component imposes no relation with another port. + +The source cover checker was read. Its graph test uses the Gram R^T R and +a breadth-first traversal. The new small checker independently forms the +rational projector from the pinned interface, checks R R^T=56I and RP=0, +and uses disjoint-set unions to find its components. The projector formula +then gives P^2=P and dimension 104. It finds one component of size 112. +A scalar operator that acts only on port zero gives a nonzero (I-P)DP +entry and supplies a concrete unequal-operator control. Normal Python and +-O give identical complete receipts. The broader 73-axis cover trace replay +is not needed or repeated here. Its unchanged receipt is retained for the +source lineage only. + +The theorem is useful because it states the precise invariant-code +condition. Full individual coordinate projections do not imply independent +native cost. The example (u,v,u+v) is valid; the independent input dimension +is two. The example (u,u,v,v) correctly permits one common operator on each +pair. Neither example grants free preparation or borrowed-field restoration. + +The later boundary-gauge argument in the original note is consistent with +commutation of the local shear, but it is already covered by the fixed-word +gauge package. It is not an additional result of this appendix. This review +makes no claim of literature-wide novelty. It excludes neither changing +codes nor joint native operators, and it supplies no new native program, +recursive admission, precision result, or complete kappa improvement. diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/SOURCES.json b/research/phase-coded-callers/annexes/fixed-code-interface/SOURCES.json new file mode 100644 index 0000000000..798550b7a9 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/SOURCES.json @@ -0,0 +1,21 @@ +{ + "frozen_files": { + "lanes/circuit-interface/INTERFACE.json": { + "bytes": 23232, + "sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "source": "work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json" + }, + "lanes/source-domain/CODE-INTERFACE.md": { + "bytes": 5611, + "sha256": "333039ed67aa7661d0ae3a0aa8f2d1fd09fbd542700fdb8afb4b095e76a04166", + "source": "work/centre-encoding-campaign-20261014/lanes/source-domain/CODE-INTERFACE.md" + }, + "lanes/source-domain/COVER-REVIEW.json": { + "bytes": 1502, + "sha256": "7cfc5263852b72710f21152b234c5b2ad57ad68120bb6b4f989a442e453b1a25", + "source": "work/centre-encoding-campaign-20261014/lanes/source-domain/COVER-REVIEW.json" + } + }, + "schema": "support-proof-appendix-sources-v1", + "scope": "Unchanged proof and check inputs. Historical receipts retain their original status." +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/TASK.json b/research/phase-coded-callers/annexes/fixed-code-interface/TASK.json new file mode 100644 index 0000000000..9f954ba08d --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/TASK.json @@ -0,0 +1,14 @@ +{ + "arguments": [ + "--source-root", + "{workspace}", + "--out", + "{workspace}/results/CHECKS.json" + ], + "expected": "CHECKS.json", + "id": "fixed-code-interface", + "location": "package", + "receipt": "results/CHECKS.json", + "scope": "Exact 112-port projector graph and a control for unequal port operators. The separate proof review proves the general fixed-code criterion. No native call is replayed.", + "script": "check_graph.py" +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/VALIDATION.json b/research/phase-coded-callers/annexes/fixed-code-interface/VALIDATION.json new file mode 100644 index 0000000000..c099bab98a --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/VALIDATION.json @@ -0,0 +1,43 @@ +{ + "appendix": "fixed-code-interface", + "comparison": "Both complete receipt files match exact bytes.", + "runner_sha256": "c5b6abbe8d9704adfaea980c77f4f34fee78ae2367bf1e2e88bed59ca79b7697", + "runs": [ + { + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-B", + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/support-proof-dispositions/appendices/fixed-code-interface/check_graph.py", + "--source-root", + "/private/tmp/fixed-code-interface-review-20261022-a/normal", + "--out", + "/private/tmp/fixed-code-interface-review-20261022-a/normal/results/CHECKS.json" + ], + "elapsed_seconds": 0.318, + "exit_code": 0, + "mode": "normal", + "receipt_sha256": "f41ad1d3041cda553f129012048d6f468a3bec3f22c5d18bf2457d9fb708531b" + }, + { + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-B", + "-O", + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/support-proof-dispositions/appendices/fixed-code-interface/check_graph.py", + "--source-root", + "/private/tmp/fixed-code-interface-review-20261022-a/optimized", + "--out", + "/private/tmp/fixed-code-interface-review-20261022-a/optimized/results/CHECKS.json" + ], + "elapsed_seconds": 0.317, + "exit_code": 0, + "mode": "optimized", + "receipt_sha256": "f41ad1d3041cda553f129012048d6f468a3bec3f22c5d18bf2457d9fb708531b" + } + ], + "scope": "Exact 112-port projector graph and a control for unequal port operators. The separate proof review proves the general fixed-code criterion. No native call is replayed.", + "source_manifest_sha256": "418baabff54c63aafdf00f7f9c286b2e31751783ed5f9f3563ec66c554c99ad0", + "status": "PASS_SCOPED_SUPPORT_PROOF_REPLAY" +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/check_graph.py b/research/phase-coded-callers/annexes/fixed-code-interface/check_graph.py new file mode 100644 index 0000000000..b146ff06a0 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/check_graph.py @@ -0,0 +1,76 @@ +"""Check the fixed-code projector on the pinned interface.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--source-root", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + source = args.source_root / "lanes/circuit-interface/INTERFACE.json" + raw = source.read_bytes() + require(sha256(raw).hexdigest() == + "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "The interface pin differs") + data = json.loads(raw) + r = [[F(row.get(str(j), 0)) for j in range(112)] for row in data["R"]] + require(len(r) == 8, "The query row count differs") + gram = [[sum(x*y for x, y in zip(a, b)) for b in r] for a in r] + require(gram == [[56*int(i == j) for j in range(8)] for i in range(8)], + "The query Gram differs") + a = [[sum(row[i]*row[j] for row in r) for j in range(112)] + for i in range(112)] + p = [[F(i == j)-a[i][j]/56 for j in range(112)] for i in range(112)] + require(all(p[i][j] == p[j][i] for i in range(112) for j in range(112)), + "The projector is not symmetric") + require(all(sum(r[k][i]*p[i][j] for i in range(112)) == 0 + for k in range(8) for j in range(112)), "The image is not in the kernel") + # The Gram identity gives (R^T R)^2=56 R^T R and proves P^2=P. + require(sum(p[i][i] for i in range(112)) == 104, "The code dimension differs") + parent = list(range(112)) + + def root(i): + while parent[i] != i: + parent[i] = parent[parent[i]] + i = parent[i] + return i + + edges = 0 + for i in range(112): + for j in range(i): + if p[i][j]: + parent[root(i)] = root(j) + edges += 1 + components = {} + for i in range(112): + components.setdefault(root(i), []).append(i) + sizes = sorted(len(v) for v in components.values()) + require(sizes == [112], "The projector graph is not connected") + require(0 < p[0][0] < 1, "The unequal-operator control is absent") + leakage = (1-p[0][0])*p[0][0] + require(leakage != 0, "A single-port scalar projection preserved the code") + result = { + "status": "PASS_FIXED_CODE_PROJECTOR_GRAPH", + "interface_sha256": sha256(raw).hexdigest(), + "query_gram": "56 I8", "code_dimension": 104, + "component_sizes": sizes, "undirected_edges": edges, + "single_port_operator_leakage_00": str(leakage), + "scope": "Exact source application. 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Native endpoint mixing and a changed controller are not admitted.", + "status": "PASS_CENTRE_FREE_SCALAR_INTERFACE", + "target_endpoint": "T_q = F C_q^-1; distinct q have distinct frames", + "word_sha256": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c" +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/frozen/lanes/source-domain/CODE-INTERFACE.md b/research/phase-coded-callers/annexes/fixed-code-interface/frozen/lanes/source-domain/CODE-INTERFACE.md new file mode 100644 index 0000000000..18688b7b67 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/frozen/lanes/source-domain/CODE-INTERFACE.md @@ -0,0 +1,114 @@ +# Fixed scalar codes and recursive interfaces + +A code can reduce the number of native children even when every individual +port has a full input projection. Full coordinate projections do not exclude +that construction. The next theorem gives the actual restriction for a fixed +scalar code. + +## A code closure criterion + +Let `E` be a subspace of `C^W`, with orthogonal projection `P_E`. Let `V` be +a finite-dimensional complex vector space. For operators `A_i` on `V`, put +`D=diag(A_1,...,A_W)` on `C^W tensor V`. Form a graph on the `W` coordinates: +join distinct `i,j` when `(P_E)_(i,j)` is nonzero. Then + +\[ +D(E\otimes V)\subseteq E\otimes V +\] + +holds if and only if `A_i=A_j` on each connected component of this graph. +The operators need not be invertible. + +To prove necessity, choose a basis `B_alpha` of the span of the `A_i` and +write `A_i=sum_alpha c_(i,alpha) B_alpha`. Invariance and linear independence +of the `B_alpha` imply that each diagonal matrix +`diag(c_(i,alpha))` preserves `E`. A finite diagonal normal matrix has +orthogonal spectral projections that are polynomials in that matrix. These +projections preserve `E`, so the matrix also preserves its orthogonal +complement. It therefore commutes with `P_E`. Entry by entry, + +\[ +(c_{i,\alpha}-c_{j,\alpha})(P_E)_{ij}=0. +\] + +Thus the operators agree along every graph edge and on each component. +For sufficiency, the same entrywise formula gives +`(P_E tensor I)D=D(P_E tensor I)`. + +For `E=ker R`, the code projector is `I-R^T R/56`. The independent pinned +source check finds one connected component on all 112 ports. Thus a fixed +`ker R` code survives a block of independent native port operators only if +all 112 completed operators in that block agree. Equality of their ranks +does not suffice. + +This statement concerns one fixed code at the stated block boundary. A +sequence can use different codes between its children. A circuit can also +compute a joint operator on several arrays. Neither possibility is excluded. + +## A positive compression example and its limits + +The code `(u,v,u+v)` has three full coordinate projections. For the common +operator `F`, compute `Fu` and `Fv`, then form their sum. This uses two +native calls for the three physical code coordinates. Its independent input +dimension is two arrays. That dimension, rather than three, enters a recursive +cost denominator. + +The third coordinate in this example is a prescribed redundant value. +An arbitrary borrowed third array has independent old contents. Those contents +must be retained and restored; they cannot be overwritten at no cost. The +code `(u,u,v,v)` also shows why the theorem uses graph components: the first +pair may use one operator and the second pair another. The full space has +singleton components and permits arbitrary port operators. + +For the current supplier, a useful code must therefore do more than remove +the centre syndrome. It must exploit relations among native children, give +the resulting exact joint map, and charge its independent input dimension, +preparation, adapters, arbitrary dirty state, and restoration. The existing +fixed-stock nullspace and equalizer bounds do not rule out such a new contract. + +## Boundary encodings and completed children + +The common-grid argument in the pinned `notes/stopped-product-complex.tex` +does permit one outer encoding. It scales the Gaussian-dyadic inputs and all +dirty auxiliaries by the same scalar power of 21. This scalar encoding +commutes with every linear operation. Each completed child is still exactly +the stipulated tensor `C` and adds no new odd denominator. Only unfinished +calls contribute to the grid height. + +This argument does not itself defer line gauges. With per-role encodings +`T_i`, the logical addition `z_i += c z_j` requires the physical operator +`c T_i T_j^-1` between the two roles. A scalar add has that form only when +the two exact encodings agree. If their preimage frames agree, an actual +rank-zero adapter can reconcile them. Distinct norm-one source lines need +native rank 2 for the direct adapter under the retained frame convention. + +There is a valid boundary freedom for the old exact local shear. Let `S` +be its logical map and let `D` be diagonal on roles. Give each helper the +same right gauge at input and output. Give the four endpoints of each +source/target pair the same right gauge. Then `DS=SD`, for both the forward +shear and its inverse transpose. If the physical endpoint frames are +`B_in,B_out`, the changed endpoint is exactly + +\[ +B_{out} D S D^{-1} B_{in}^{-1} +=B_{out} S B_{in}^{-1}. +\] + +This holds on arbitrary data and helper inputs. It also holds for every +tensor power. Thus paired endpoint gauges can preserve the old local +contract and its global composition. The wire-gauge experiment uses this +freedom. It charges every relative native transition, including any rank-zero +adapter that becomes a rank-one child. A lower local graph objective alone +would still need exact phase lowering, native replay, and a complete finite +invoice before supplier admission. + +If the two data roles receive unequal gauges, the cross term becomes +`D_y D_x^-1 x` and the old shear is lost. If a helper has unequal endpoint +gauges, its arbitrary old value is not restored. These are direct controls +on the boundary argument. + +This note is campaign research. Its code-closure theorem has not yet received +an independent proof review. The source commit is +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The arguments build on the exact +preimage-frame and all-size contracts in the repository. This work used +OpenAI Codex assistance and makes no new supplier or kappa claim. diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/frozen/lanes/source-domain/COVER-REVIEW.json b/research/phase-coded-callers/annexes/fixed-code-interface/frozen/lanes/source-domain/COVER-REVIEW.json new file mode 100644 index 0000000000..396aa5c0f4 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/frozen/lanes/source-domain/COVER-REVIEW.json @@ -0,0 +1,39 @@ +{ + "allowed_codimension_per_replica": "896/73", + "code_projector_graph_component_sizes": [ + 112 + ], + "common_range_upper_bound_per_cover_element": "8/183", + "difference_trace_fourth": "4758/343", + "difference_trace_square": "104/7", + "fixed_stock_moment_if_one_coded_bank_per_replica": "52704/52487", + "full_73d_routes_checked": 896, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "nonidentity_group_product_buckets": 5824, + "not_reviewed": [ + "optional sixth moment", + "native phase implementation", + "new supplier", + "new kappa" + ], + "phase_source_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "rank_bound_excess": "48608/13359", + "rank_lower_bound_per_cover_element": "2912/183", + "review_findings": [ + "Corrected a contradictory index condition in the proof case split; the moment value was unchanged." + ], + "reviewed_files_sha256": { + "PROOF.md": "1d72716fc0dc0e2f9071d0940cec54348da1d12d629eda9432baebccb4a65df4", + "verify_algebra.py": "cb23fdc8a14a6f3ff1e73cdba4e1497a9a95f5ca6d765ecb02fdaa3087782949" + }, + "single_coded_bank_in_all_16_replicas_is_not_excluded_at_zero": "843264/854027", + "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_matrix_rederived": true, + "status": "PASS_INDEPENDENT_73D_COVER_TRACE_REVIEW", + "trace_PQ": "4/7", + "trace_PQPQ": "27/343", + "trivial_representation_control": { + "rank_difference": 0, + "trace_PQ": "8" + } +} diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/replay.py b/research/phase-coded-callers/annexes/fixed-code-interface/replay.py new file mode 100644 index 0000000000..46a081958d --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/replay.py @@ -0,0 +1,72 @@ +"""Replay one support appendix in fresh source copies.""" + +import argparse +from hashlib import sha256 +import json +import os +from pathlib import Path +import shutil +import subprocess +import sys +import time + + +def digest(path): + return sha256(path.read_bytes()).hexdigest() + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + package = Path(__file__).resolve().parent + config = json.loads((package/"TASK.json").read_text()) + manifest = json.loads((package/"SOURCES.json").read_text()) + + def verify(): + for rel, record in manifest["frozen_files"].items(): + path = package/"frozen"/rel + if digest(path) != record["sha256"] or path.stat().st_size != record["bytes"]: + raise ValueError("Frozen source differs: "+rel) + + verify() + output = args.out.resolve() + output.mkdir(parents=True, exist_ok=False) + runs = [] + env = dict(os.environ, OPENBLAS_NUM_THREADS="1", OMP_NUM_THREADS="1", + MKL_NUM_THREADS="1", VECLIB_MAXIMUM_THREADS="1") + for mode in ("normal", "optimized"): + workspace = output/mode + shutil.copytree(package/"frozen", workspace) + (workspace/"results").mkdir(exist_ok=True) + script = (package if config["location"] == "package" else workspace)/config["script"] + command = [sys.executable, "-I", "-B"] + if mode == "optimized": + command.append("-O") + command.append(str(script)) + command.extend(v.format(workspace=str(workspace)) for v in config["arguments"]) + start = time.monotonic() + result = subprocess.run(command, cwd=workspace, env=env, + capture_output=True, text=True) + (output/(mode+".log")).write_text(result.stdout+result.stderr) + if result.returncode: + raise RuntimeError("Child failed: "+mode) + receipt = workspace/config["receipt"] + if receipt.read_bytes() != (package/config["expected"]).read_bytes(): + raise ValueError("Receipt bytes differ: "+mode) + runs.append({"mode": mode, "command": command, "exit_code": 0, + "receipt_sha256": digest(receipt), + "elapsed_seconds": round(time.monotonic()-start, 3)}) + print("PASS", mode, config["id"], flush=True) + verify() + receipt = {"status": "PASS_SCOPED_SUPPORT_PROOF_REPLAY", "appendix": config["id"], + "runs": runs, "source_manifest_sha256": digest(package/"SOURCES.json"), + "runner_sha256": digest(Path(__file__)), + "comparison": "Both complete receipt files match exact bytes.", + "scope": config["scope"]} + (output/"REPLAY.json").write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/validation/normal.log b/research/phase-coded-callers/annexes/fixed-code-interface/validation/normal.log new file mode 100644 index 0000000000..2d147bc271 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/validation/normal.log @@ -0,0 +1 @@ +PASS_FIXED_CODE_PROJECTOR_GRAPH diff --git a/research/phase-coded-callers/annexes/fixed-code-interface/validation/optimized.log b/research/phase-coded-callers/annexes/fixed-code-interface/validation/optimized.log new file mode 100644 index 0000000000..2d147bc271 --- /dev/null +++ b/research/phase-coded-callers/annexes/fixed-code-interface/validation/optimized.log @@ -0,0 +1 @@ +PASS_FIXED_CODE_PROJECTOR_GRAPH diff --git a/research/phase-coded-callers/annexes/phase-access/ANNEX-MANIFEST.json b/research/phase-coded-callers/annexes/phase-access/ANNEX-MANIFEST.json new file mode 100644 index 0000000000..f24ff50d41 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/ANNEX-MANIFEST.json @@ -0,0 +1,366 @@ +{ + "schema": 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"frozen/work/centre-encoding-campaign-20261014/root/GROWING-WALSH.md", + "review": "frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.md", + "scope": "Exact typed rank8/9 transitions and F73 adapters, all positive tensor widths; j0 alternating frame schedule distinct from odd-source j1 transitions." + }, + { + "id": "rational_capture", + "proof": "frozen/work/centre-encoding-campaign-20261014/root/PHASE-CLASS-CAPTURE-20261020.md", + "review": "frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REVIEW.md", + "scope": "56 active fields;4204 scalar units per direction;16 divisions by3 forward and16 multiplications by3 inverse; current common-frame premises remain." + }, + { + "id": "dyadic_capture", + "proof": "frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/DYADIC-CAPTURE.md", + "review": "frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md", + "scope": "Rank16 involution,determinant1,56 active fields,4044 scalar units;1544 additive K/-K words;112H1 conditional on carried rank4W_R; actual W45 fails all56 pair ratios." + } + ], + "new_research_claim": false, + "complete_kappa_improvement": false +} diff --git a/research/phase-coded-callers/annexes/phase-access/CORE-BINDING.json b/research/phase-coded-callers/annexes/phase-access/CORE-BINDING.json new file mode 100644 index 0000000000..125314eca7 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/CORE-BINDING.json @@ -0,0 +1,9 @@ +{ + "schema": "phase-access-unchanged-core-v1", + "manifest": "../../PACKAGE-SHA256.json", + "manifest_sha256": "755bd02a5a69e6d26bfbbb5eead7306252693db19b6be91eceeffe268a50546c", + "files_including_manifest": 298, + "all_original_file_hashes_checked": true, + "annex_is_additional": true, + "core_replay_not_rerun_for_append_only_addition": true +} diff --git a/research/phase-coded-callers/annexes/phase-access/DIRECT-SOURCES.json b/research/phase-coded-callers/annexes/phase-access/DIRECT-SOURCES.json new file mode 100644 index 0000000000..803722af32 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/DIRECT-SOURCES.json @@ -0,0 +1,22 @@ +{ + "schema": "phase-access-entrypoints-v1", + "entrypoints": [ + "work/centre-encoding-campaign-20261014/root/GROWING-WALSH.md", + "work/centre-encoding-campaign-20261014/root/GROWING-WALSH.json", + "work/centre-encoding-campaign-20261014/root/check_growing_walsh.py", + "work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.md", + "work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.json", + "work/centre-encoding-campaign-20261014/lanes/interface-proof/review_walsh_frames.py", + "work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_bridge_operators.py", + "work/centre-encoding-campaign-20261014/lanes/coherent-port/COVARIANCE.json", + "work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json", + "work/centre-encoding-campaign-20261014/root/PHASE-CLASS-CAPTURE-20261020.md", + "work/centre-encoding-campaign-20261014/root/PHASE-CLASS-CAPTURE-FREEZE-20261020.json", + "work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REVIEW.md", + "work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/FREEZE.json", + "work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md", + "work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/FREEZE.json", + "work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/FREEZE.json", + "work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/FREEZE.json" + ] +} diff --git a/research/phase-coded-callers/annexes/phase-access/NOTICE.md b/research/phase-coded-callers/annexes/phase-access/NOTICE.md new file mode 100644 index 0000000000..78bef70849 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/NOTICE.md @@ -0,0 +1,42 @@ +# Source credit and license + +This annex contains existing centre-encoding campaign work prepared for +Ali Romman with substantial OpenAI Codex assistance. New wrapper and +replay material is under Apache-2.0. The full source [NOTICE](frozen/NOTICE), +[LICENSE](frozen/LICENSE), and [upstream license](frozen/upstream/LICENSE) +are retained. No independent human review or maintainer acceptance is +claimed. + +The residual-syndrome lane proposed the fixed even-hyperplane Walsh +representation. The root lane proposed the growing frame. The +interface-proof lane supplied the independent exact phase, child-kernel, +and endpoint proof. The root and independent-review lanes supplied the +ordered phase-class theorem and rational scalar baseline. The +independent-review lane supplied the asymmetric dyadic six-mode +involution. The bridge-review lane supplied its separate sparse-row, +phase-rank, prefix, and common-gauge checks. The low-displacement, +physical pair-code, and shared-root lanes supplied the actual matrix +and frame inputs. These are roles within one AI-assisted campaign. + +The source interface is historical commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Its exact INTERFACE.json +hash is `5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3`. +The packaging base is `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. +Neither base refreshes an older pin or proves applicability to the +current selected construction. The [parent notice](../../NOTICE.md) +retains the full coupled-provider, compiler, and earlier source credit. +This annex consumes exact scalar matrices, programs, and route data; +it does not repeat a complete native supplier admission. + +[PR #1719](https://github.com/CrocSwap/integer-mult-bounds/pull/1719) +at `3ae9a6f3ac74ded022ab3b4872a7357a621af6fb` is related work. Its +[global lift](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/GLOBAL-WALSH.md) +doubles the ambient dimension to 146 and doubles the child ranks. +The retained historical metadata records that distinction. The growing +9-to-73 frame result is a different construction; this annex does not +claim the doubled lift as a new result or consume its global replay. + +All historical source files, scripts, programs, and reviews remain +unchanged. No executable adaptation, import mutation, or revised +historical receipt is used. Earlier pending-review language remains in +the old notes; the later completed peer reviews are included separately. diff --git a/research/phase-coded-callers/annexes/phase-access/PROOF.md b/research/phase-coded-callers/annexes/phase-access/PROOF.md new file mode 100644 index 0000000000..1630cb4cca --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/PROOF.md @@ -0,0 +1,242 @@ +# Exact proofs and interface limits + +The three claims below have separate source proofs and reviews. Their +full arguments are retained in this annex. The finite replay checks the +actual source objects; it does not replace the all-width proofs. Every +source byte is bound in [SOURCES.json](SOURCES.json). + +## 1. Exact growing Walsh frames + +The [root construction](frozen/work/centre-encoding-campaign-20261014/root/GROWING-WALSH.md) and [independent phase proof](frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.md) +use U_s of dimension `n=9+8s`, for `0<=s<=8`. Let omega_n be its +all-ones vector and let `H_n=omega_n-perp`. Since n is odd, H_n is +nondegenerate. Every x has the unique decomposition `a omega_n+h`. +Define G_n as the normalized real Walsh transform on H_n and the +identity on its complement. This exact kernel fixes its scalar phase +and gives `G_n^2=I`. Every orthogonal route supported in U_s fixes +omega_n and preserves the kernel, so it commutes with G_n exactly. + +For the source line `C_q=((1+i)I+(1-i)X_q)/2` and odd q, put +`v=q+omega_n` and `b=x dot v`. Define the monomial L_q by + +```text +L_q |x> = i^b |x+b omega_n>. +``` + +Comparing the two Gaussian coefficients for b=0 and b=1 gives +`G_n C_q G_n=C_omega_n L_q`, with no omitted scalar phase. The L_q +commute with the common line C_omega_n. These exact identities tensor +to every positive tensor size. The common line remains a native +operation. + +For `m=n-8`, the even hyperplanes are nested. Their orthogonal +difference K has basis `k_i=omega_m+e_(m+i)`, `1<=i<=8`, and Gram +matrix `B=I+11^T`, with `B^2=I`. Thus `A_n=G_n G_m` is exactly the +Walsh transform on K. In the address chart A with first eight columns +k_i and ninth column omega_n, let S_8 multiply by i to the weight of +the first eight chart bits. The exact child recipes are + +```text +A_n = P_A P_B S_8 F_8 S_8 P_A^-1, +C_omega_n A_n = P_A P_B S_8 F_9 S_8 P_A^-1. +``` + +Each uses one native child and two composed monomial maps. The right +factor acts first. Even common-line powers are translations; a negative +odd power differs from the positive one by a translation. + +Set `T_n^a=C_omega_n^a G_n`. For integers a,b,j and an admitted +orthogonal route g supported in U_s, the exact ordered identity is + +```text +T_n^a C_q^j P_g (T_m^b)^-1 + = C_omega_n^(a+j-b) L_(q,n)^j P_g L_(omega_m,n)^(-b) A_n. +``` + +The rank is eight when a+j-b is even and nine when it is odd. The +route need not commute with A_n, so the displayed order is required. +For plain frame transport j=0, alternating types 1,0,1,...,1 have +rank-nine transitions. With the initial rank-nine frame, the nine-call +frame schedule has total rank 81 per mode and endpoint rank 73. +If an odd source phase j=1 is inserted, differing types give rank +eight and equal types give rank nine. These are different calculations; +the frame schedule is not a complete source-phase caller invoice. + +Define `D_n|x>=i^(wt(x)-parity(x))|x>`. +Comparing the exact kernels gives + +```text +C_omega_n G_n = D_n F_n D_n +``` + +for n=9+8s. The scalar factor for general odd n is one at these n. +The n=73 endpoint therefore has explicit diagonal F73 adapters. This +acts on arbitrary arrays, but only when the actual mode carries the +stated frame and required contents. It does not restore changed +contents or supply a zero-cost decoder. + +The [receipt](frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.json) checks 61,440 exact common-line +coefficients, all 120 completed odd labels, growing ranks through 73, +65,536 rank-eight kernel entries, 262,144 rank-nine kernel entries, +and the full width-nine endpoint kernel. At larger widths it checks +complete quadratic-phase witnesses. The written kernel proof supplies +the general identity. The full typed transition is proved algebraically; +these counts do not claim a separate full-matrix test for every typed +transition. + +A fixed common chart has rank 17 for the stated cross-stage operators, +and rank one within a stage. That is a statement about the full +operator, not a restriction to a centre image. A local isometry into +`span(omega_m,E_s)` need not extend to the ambient orthogonal cover. +The general linear chart in the child recipe does not grant new scalar +couplings or owner routes. Source access, initial frames, productive +and idle mode schedules, borrowed contents, restoration, monomial +prices, and recursive costs remain separate obligations. + +## 2. Ordered phase classes and the rational baseline + +The [general proof](frozen/work/centre-encoding-campaign-20261014/root/PHASE-CLASS-CAPTURE-20261020.md) and [independent review](frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REVIEW.md) +allow arbitrary invertible spatial phases Q_i on each field. Choose +one anchor Z_g per global phase class. Assume each +`A_i=Q_i Z_g^-1` is an admitted monomial in the current frame. Let Z +repeat Z_g on the class, so Q=AZ. If T preserves classes, then TZ=ZT. +For `C=T^-1 S T`, where S reads and changes only active fields J and +is identity elsewhere, direct multiplication gives + +```text +Q C Q^-1 = A T^-1 [Z_J S_J Z_J^-1 direct-sum I] T A^-1. +``` + +No scalar factor is moved through A. The identity holds on arbitrary +fields and does not require a clean input. The inverse uses S_J^-1 +and the same alignment passes. If each anchor and inverse anchor has +an admitted rank-one implementation, there are `2|J|` anchor children. +Scalar words, alignment maps, and entry and exit frames remain paid. +For any class-supported scalar response K, `QKQ^-1=AKA^-1`; this +identity does not turn an additive use of K into an in-place K inverse. + +A transported inverse has the exact order +`Q C^-1 Q=(Q C^-1 Q^-1)Q^2`. The rightmost Q^2 acts first. It can be +included as the right factor of the first alignment only when that +composed map is admitted. Negative conjugation needs a separate +premise that `Q_i^-1 Z_g` is monomial. The positive premise alone does +not imply it. In the actual directional-phase case the phases commute, +which supplies the inverse alignments. The retained review gives a +noncommuting counterexample to the unjustified general implication. + +The actual response is `E=H^-1 E_mode H`. It has eight signed +six-mode blocks and eight eight-mode blocks `I-dd^T`. The root space +`R=span(30,45,75,384)` gives fourteen classes of eight ports; H +preserves them. In each block choose a class pair and let e equal d +there and zero elsewhere. Set + +```text +u=2e-d, v=2d/k-e/2, S=I+uv^T, k in {6,8}. +``` + +Then `Sd=2e`, `e^T S=(4/k)d^T`, and +`det(S)=1+v^Tu=2(4-k)/k`, which is nonzero. It follows that +`S(I-dd^T)S^-1=I-(k/2)ee^T`, supported within one phase class. +Signed pair sums and differences give a class-preserving P. All +pair differences are passive in this rational construction. With +`T=PH`, the reduced code uses exactly `8*3+8*4=56` active fields. +The passive block is identity and active rows do not read passive data. + +The exact literal forward and inverse words each cost 4,204 old real +scalar primitives. Forward capture also has sixteen real +**division-by-three** scans; inverse capture has sixteen real +**multiplication-by-three** scans. These are separate services. +The prefix row one-norm is twelve. The independent reverse-output +interpreter checks all 640 inputs, all 528 unchanged fields, both +matrix inverse orders, the literal restoration word, response +conjugation, and the exact 56-field reduction. The +[final receipt](frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/verified-normal/CHECKS.json) binds this rational baseline. + +## 3. The separate dyadic capture + +The [dyadic construction](frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/DYADIC-CAPTURE.md) and [distinct peer review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md) +replace the rational six-mode block. For its selected pair p,t set +`a_p=2d_p`, `a_t=0`, `b_p=3d_p`, `b_t=-d_t`, with a,b zero off the +pair. Put `u=a-d`, `v=(d-b)/4`, `S=I+uv^T`. Then +`v^Td=1`, `v^Tu=-2`, `Sd=a`, `b^TS=d^T`, and `b^Ta=6`. +Thus S is an involution with determinant -1, and +`S(I-dd^T)S=I-ab^T`. Its changed pair block is +`[-5,2d_p d_t;0,1]`. + +For an eight-mode block set `u=2e-d`, `v=-u/4`. Then `u^Tu=8` and +`u^Td=-4`, so `S^2=I`, `Sd=2e`, and +`S(I-dd^T)S=I-4ee^T`. Each S-I has rank one. Sixteen disjoint +blocks therefore give `rank(C-I)=16` and `det(C)=1` after conjugation +by H. C remains an involution. + +The actual signed pair rotation uses +`s=d_p x_p+d_t x_t`, `t=-d_p x_p+d_t x_t`. For size six, the active +coordinate is the selected **negative difference**, together with two +other sums. The rank-one vectors there are +`u=(-2,-2,-2)`, `v=(1/2,1/4,1/4)`. For size eight, four sums are +active. There are exactly 56 active coordinates, four in each class. +Every prefix of the pair codes preserves classes, and every reduced +prefix reads and changes active fields only. Endpoint support alone +would not suffice for the later norm bound. + +For a rank-one update with `v^Tu=-2`, a shear that sends u to one +coordinate reduces the update to one row with diagonal -1. The +resulting literal order is `H,P,S_reduced,P^-1,H^-1`. The invoices are + +| Part | Old real scalar primitives | +| --- | ---: | +| H or H inverse | 470 | +| P or P inverse | 1,016 | +| All sixteen reduced blocks | 1,072 | +| C or its literal inverse | 4,044 | +| Either coded additive coupler | 1,544 | + +All scales are signed powers of two. The capture has no odd scan, +CLEAR, owned field, or native child in this scalar chart. The literal +check covers all 640 inputs, 528 unchanged capture fields, and both +full inverse orders. Its prefix row one-norm is ten and its scalar +binary denominator height is three. + +The coded response is `K=CEC`. It is class-supported but not symmetric. +Its determinant is `35^8`; its inverse denominator LCM is 35. Encoding +both banks by C gives `Y+=KX` forward and `X-=KY` backward. The +backward coefficient is -K, not -K transpose. Each additive word has +168 ADDs and costs 1,544 units. This does not implement an in-place +dyadic K inverse. The factors five and seven remain. + +## 4. Actual frame scope + +The [peer review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md) reconstructs the actual W_R and W45 +with an independent binary Pauli interpreter. W_R has Fourier rank +four. All 112 class-anchor ratios in W_R have rank zero, and all +112 anchors have rank one. With `Q'=W_R Q W_R^-1`, the ordered +factorization in Section 2 therefore has 56 inverse and 56 forward +anchor occurrences: a **conditional 112-H1** count. It retains the +4,044 scalar invoice, at most 224 alignment maps, and up to 224 +native side maps. Preparing W_R, removing it, and lowering all maps +are additional obligations. These binary checks establish ranks and +monomial support; they do not emit full phase records or native wrappers. + +The actual rank-one exit is `W45=S_e0 C_45 S_e0`. All 56 proposed +pair ratios in that frame have rank two. It fails the monomial +alignment premise. The conditional 112-H1 count cannot be combined +with its existing one-W45 exit budget. + +The [common-gauge proof](frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/COMMON-GAUGE.md) gives a scoped lower bound. If one +Clifford W makes every pair ratio monomial, let `L=W^-1 Z` and +`U=L intersect X`. Invariance of L under each ratio forces the pair +difference a+b into U. The actual differences span rank four. The +Fourier rank of W is at least dim U, hence at least four. W_R attains +that rank. This is a limit for one common Clifford, not for arbitrary +joint decoders, cross-field mixtures, or changed constructions. + +Under the literal class/active prefix conditions, the unitary anchors +factor out of each input coefficient without changing its cancellation. +Thus the field L2 norm at completed-child boundaries is at most ten +times the largest input field norm. Partial alignment and anchor passes +apply a unitary to a complete field and preserve its norm. Recursive +child interiors are excluded. The scalar binary-height-three bound +does not transfer to the physical word without a separate phase-grid +account. The complete native capture, routed stage matching, source +access, helper progress, terminal output, and recursive invoice remain +open. None of these results changes the complete kappa calculation. diff --git a/research/phase-coded-callers/annexes/phase-access/README.md b/research/phase-coded-callers/annexes/phase-access/README.md new file mode 100644 index 0000000000..2e33fc37e8 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/README.md @@ -0,0 +1,84 @@ +# Growing frames and phase-class access + +This annex preserves three completed local results: the exact growing +Walsh frame theorem, the ordered rational phase-class capture, and its +separately reviewed dyadic peer. It adds no new research claim and gives +no complete kappa improvement. The accepted phase-coded-callers core is +unchanged. This annex has its own proof, source manifest, replay, and +manifest; the core's 298-file manifest remains in force for those files. + +Read the [proof and scope](PROOF.md), [source pins](SOURCES.json), +[claim map](CLAIMS.json), and [source credit](NOTICE.md). The full +historical proofs and reviews remain byte-exact under `frozen/`. + +| Mechanism | Retained result | Required boundary | +| --- | --- | --- | +| Growing Walsh frame | Exact common-line phases, rank-eight and rank-nine child recipes, and diagonal F73 endpoint adapters at every positive tensor width | Source access, mode contents, owner program, legal ambient routes, and complete costs remain open | +| Rational capture | Ordered phase-class identity; 56 active fields; 4,204 old real scalar units in each direction | Forward uses sixteen real division-by-three scans; inverse uses sixteen multiplication-by-three scans | +| Dyadic capture | Rank-16 involution with determinant one; 56 active fields; 4,044 old real scalar units in each direction | The conditional 112-H1 factorization needs carried W_R, its admission, and paid maps | +| Coded additive response | Both directions cost 1,544 old real scalar units; forward uses K and backward uses -K | K is not symmetric; this does not implement an in-place dyadic K inverse | + +**The actual W45 exit does not meet the 112-H1 premise.** Each of its +56 proposed pair ratios has Fourier rank two. The required common W_R +has rank four. Preparing or removing W_R is not free. A lower bound of +four applies only to one common Clifford which makes these pair ratios +monomial, not to an arbitrary joint decoder. + +The growing-frame rank formula is `8 + ((a+j-b) mod 2)`. For frame +transport with `j=0`, alternating types use rank nine at each transition. +For an inserted odd source phase with `j=1`, different input/output +types instead give rank eight. The frame-only schedule has total rank +81 per mode and endpoint rank 73. It is not an odd-source caller invoice. +The endpoint adapters do not restore contents changed by a controller. + +This growing family differs from the doubled global lift in +[PR #1719](https://github.com/CrocSwap/integer-mult-bounds/pull/1719), +whose ambient dimension is 146. That result is comparison material, +not an input to this annex. [RELATED-WORK.json](RELATED-WORK.json) pins +the retained historical description and reviewed commit. + +## Replay + +Use Python 3.11 or later on a Unix-like system, its standard library, +one worker, at least 3 GiB free disk, and a new output directory. No Git, +network, original workspace, or compiler package is needed. + +```sh +python3 -I -B research/phase-coded-callers/annexes/phase-access/replay.py --out /tmp/phase-access-check +``` + +Expected final output: + +```text +PASS_PHASE_ACCESS_ANNEX +``` + +The runner executes three unchanged independent checkers in normal and +optimized Python. Each checker runs in a private copy. Every complete +receipt must match the frozen receipt byte for byte. There is no path +normalization, excluded field, source patch, or import modification. +[REPLAY.json](REPLAY.json) records the packaging check; [VALIDATION.md](VALIDATION.md) +states its coverage and limits. [ANNEX-MANIFEST.json](ANNEX-MANIFEST.json) +binds this annex. [CORE-BINDING.json](CORE-BINDING.json) records the +unchanged accepted core. + +The historical rational source note says that the dyadic review was in +progress. The later, separate [dyadic review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md) is included +and passes. The earlier note remains unchanged as historical evidence. +No independent human review is claimed. + +## Open next questions + +- Can the growing frame carry the required centre contents through actual + source couplings? This determines whether its exact phase theorem can + enter a supplier. A first step is one typed source coupling in the + actual route grammar. The source-access word, owner schedule, and + arbitrary-content restoration remain blockers. +- Can a changed native endpoint carry W_R at a useful complete cost? + A first step is an exact entry, retained-frame, and exit invoice for + one declared caller cut. Current W45 ratios fail, and the full native + phase records and frame costs remain open. +- Can the 56-field factorization support a routed caller? A first step + is to match its input and output types at each actual stage. Alignment + maps, active/passive prefix conditions, helper progress, physical-grid + costs, terminal output, and recursive costs must all be supplied. diff --git a/research/phase-coded-callers/annexes/phase-access/RELATED-WORK.json b/research/phase-coded-callers/annexes/phase-access/RELATED-WORK.json new file mode 100644 index 0000000000..ae04145f8e --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/RELATED-WORK.json @@ -0,0 +1,12 @@ +{ + "schema": "phase-access-related-work-v1", + "comparison_only": true, + "mathematical_dependency": false, + "PR": 1719, + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1719", + "reviewed_commit": "3ae9a6f3ac74ded022ab3b4872a7357a621af6fb", + "retained_metadata": "related-work/PR1719-METADATA.json", + "source_path": "work/centre-encoding-campaign-20261014/upstream-refresh-20261017/publication-state-20261020T192353Z/pr1719/METADATA.json", + "sha256": "4e99a0b556fa801664903e71281d0056d3f299c997258ae3558d88a3deafaa8f", + "distinction": "PR1719 doubles the global supplier from dimension73 to146 and doubles child ranks. This annex concerns growing frames9,17,...,73 with separate source-access and content obligations." +} diff --git a/research/phase-coded-callers/annexes/phase-access/REPLAY.json b/research/phase-coded-callers/annexes/phase-access/REPLAY.json new file mode 100644 index 0000000000..a870b16378 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/REPLAY.json @@ -0,0 +1,60 @@ +{ + "status": "PASS_PHASE_ACCESS_ANNEX", + "source_files": 76, + "source_manifest_sha256": "1218979ade953606cd93809d0374d52b420b24024b95a17278b65894b671a4d0", + "replay_sha256": "77cc713286f3e4868acbed5c0eba8f8f442ffaa3d81ab3ee9f69d6098659cbaf", + "runs": [ + { + "job": "walsh", + "mode": "normal", + "seconds": 1.139, + "receipt_sha256": "d5aa80b2fd1cc78d4d89a0610330b6510c35d5c010f7f432e2237568a8af7cbb", + "receipt": "normal/walsh/WALSH-FRAME-REVIEW.json", + "complete_frozen_receipt_byte_equal": true + }, + { + "job": "rational", + "mode": "normal", + "seconds": 2.286, + "receipt_sha256": "ceaa82288bfd62c9dfe5a784dc3ad20035d39e76d44bd18b60c90dc9b6a3967f", + "receipt": "normal/rational/CHECKS.json", + "complete_frozen_receipt_byte_equal": true + }, + { + "job": "dyadic", + "mode": "normal", + "seconds": 0.55, + "receipt_sha256": "9b4bce6fb5a498901797b76d0a6c25757c1d8f489667fe823c89166047d8a29e", + "receipt": "normal/dyadic/REVIEW.json", + "complete_frozen_receipt_byte_equal": true + }, + { + "job": "walsh", + "mode": "optimized", + "seconds": 1.165, + "receipt_sha256": "d5aa80b2fd1cc78d4d89a0610330b6510c35d5c010f7f432e2237568a8af7cbb", + "receipt": "optimized/walsh/WALSH-FRAME-REVIEW.json", + "complete_frozen_receipt_byte_equal": true + }, + { + "job": "rational", + "mode": "optimized", + "seconds": 2.349, + "receipt_sha256": "ceaa82288bfd62c9dfe5a784dc3ad20035d39e76d44bd18b60c90dc9b6a3967f", + "receipt": "optimized/rational/CHECKS.json", + "complete_frozen_receipt_byte_equal": true + }, + { + "job": "dyadic", + "mode": "optimized", + "seconds": 0.557, + "receipt_sha256": "9b4bce6fb5a498901797b76d0a6c25757c1d8f489667fe823c89166047d8a29e", + "receipt": "optimized/dyadic/REVIEW.json", + "complete_frozen_receipt_byte_equal": true + } + ], + "normal_optimized_byte_equal": true, + "source_files_unchanged": true, + "source_code_adaptations": 0, + "scope": "Exact growing-frame kernels and route ranks; rational and dyadic scalar capture; conditional common-frame geometry. No emitted full native capture, source-access or owner program, recursive supplier, or kappa improvement." +} diff --git a/research/phase-coded-callers/annexes/phase-access/RESULT.json b/research/phase-coded-callers/annexes/phase-access/RESULT.json new file mode 100644 index 0000000000..fd3deac05d --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/RESULT.json @@ -0,0 +1,56 @@ +{ + "schema": "phase-access-result-v1", + "status": "PASS_PHASE_ACCESS_PACKAGING", + "source_files": 76, + "runs": 6, + "normal_optimized_byte_equal": true, + "source_code_adaptations": 0, + "growing_frame": { + "dimensions": [ + 9, + 17, + 25, + 33, + 41, + 49, + 57, + 65, + 73 + ], + "typed_rank": "8+((a+j-b) mod2)", + "alternating_frame_only_j0_rank": 9, + "differing_types_odd_source_j1_rank": 8, + "frame_only_total_native_rank_per_mode": 81, + "endpoint_native_rank": 73, + "contents_restored_by_frame_identity": false + }, + "rational_capture": { + "active_fields": 56, + 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b/research/phase-coded-callers/annexes/phase-access/VALIDATION.md new file mode 100644 index 0000000000..83521b0abc --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/VALIDATION.md @@ -0,0 +1,41 @@ +# Validation scope + +The runner verifies every byte count and SHA256 in SOURCES.json before +and after execution. It checks decompressed hashes when recorded. +Each old checker runs in a separate private repository copy. Scripts +which write beside themselves therefore cannot change frozen inputs. +All three checkers run normally and with `-O`, using `-I -B` and one +worker. Every complete receipt must match its frozen counterpart byte +for byte. No receipt field is normalized or omitted. + +| Check | Fresh work | Proof or implementation boundary | +| --- | --- | --- | +| Walsh review | 61,440 common-line coefficients; actual 120-label route ranks; rank-eight/rank-nine full child kernels; endpoint kernels and quadratic witnesses through dimension73 | Exact typed identities and tensor extension use the written proof; no source-content or owner program | +| Rational review | Independent block formulas and inverse; all640 literal outputs and528 unchanged roles; response conjugation;56-field reduction;4204-unit invoice and sixteen directional odd scans | Common-frame capture is conditional; no physical phase recipes | +| Dyadic peer review | All640 input columns and both inverse orders; rank16/determinant1;4044/1544 invoices; prefix norms/heights;112 alignment and112 anchor ranks; all56 W45 failures | Binary rank/support is not a full phase-wrapper emission; W_R preparation and removal remain unpaid | + +The dyadic checker rejects omission of the selected negative-difference +update. It records a witness that separates K from its transpose, and +checks that K has nonzero off-diagonal entries. The actual W45 ratios +provide a direct failure of the proposed cheaper frame premise. The +rational proof retains the noncommuting counterexample to an unjustified +negative-alignment implication. These controls have different scopes. +The all-width results are not inferred from a bounded matrix sample. + +The Walsh checker imports only basis and route arithmetic from the +unchanged verify_bridge_operators.py. It does not call that module's +archive/Git-loading function. All used route and kernel operations are +local. The rational checker imports a pinned earlier independent matrix +helper; the dyadic peer imports no producer or compiler. The runner +changes no import or source code. + +[REPLAY.json](REPLAY.json) records the six packaging runs. The accepted +298-file core is outside this annex's replay and remains unchanged; +[CORE-BINDING.json](CORE-BINDING.json) records its manifest. The annex's +own manifest excludes only itself. The related PR1719 metadata is +comparison evidence and is not a mathematical replay input. + +This replay does not emit full native phase records for either capture, +prepare or remove W_R, validate new ambient cover routes, restore changed +centre contents, construct a routed owner schedule, price all packed +maps, prove the physical phase grid, or calculate a new complete kappa. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/LICENSE b/research/phase-coded-callers/annexes/phase-access/frozen/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/NOTICE b/research/phase-coded-callers/annexes/phase-access/frozen/NOTICE new file mode 100644 index 0000000000..59d8e0cf31 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/NOTICE @@ -0,0 +1,415 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. + +Partial-gauge extension, 9 October 2026 +Copyright 2026 icekylinx + +The pair-first cube assembly, compatible backward frame enlargement, +partial source-gauge schedule and stopped whole-projector composition are +contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834. + +The physical deferred bit word, reflected event accounting, fan-order +clarification and signed two-stage endpoint are adopted from Zhihao Chen +(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with +Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen +witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38, +with the original Claude disclosure retained. Cyclic interval and core-aware +pair primitives build on Avi Eisenberg (ikeboy), PR #62, +ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance. +Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and +precision credits remain in force. Imported source notices and licenses +are preserved under references/partial-gauge/; see SOURCES.json. + +Three-stage cover extension, 9 October 2026 +Copyright 2026 icekylinx + +The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry, +weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring +fallback, uniform batching, internal row borrowing and exact composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This +repository integration uses Codex assistance and extends +PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86. + +The selected local complex DAG and support/label replay are adopted from +Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf, +with its original Apache-2.0 terms and Claude assistance disclosure. +The unchanged bit physical word retains Zhihao Chen (jacklightChen), +PR #97, and Swapnil Jain's underlying witness and assistance notices. +The prior opposite-bank, stopped ordinary-leaf, copied-center, topology, +semantic/bulk, precision and analytic credits remain applicable. +Original source notices and license bytes are preserved in +references/three-stage-cover/pr117/ and references/partial-gauge/. + +Paired-cube and shared-core extension, 9 October 2026 +Copyright 2026 icekylinx + +The paired-coordinate triple-cube identity, signed overlap channels, +original-source involution, coordinate-star centers, concrete frame/carrier +compiler, chronological source gauges, PR97 gauge-subset selection, +orthogonal cross-stage routing and exact supplier/assembly integration +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. +Repository integration uses Codex assistance and extends PR #130 at +6a9970a530119174507904e23592fd59ede19a5d. + +The substantial completed-core workspace-sharing principle is credited to +an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported +OpenAI Codex assistance. No source code, partition or serialized witness +from that PR is imported. The new routing and paired-motif integration +are described separately and claim no exclusive priority for broad sharing, +paired-coordinate, Fourier or carrier-matching ideas. + +Selected coarse queries restrict the retained eumemic PR #117 positive DAG; +its original Apache-2.0 and Claude assistance notices remain unchanged. +The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil +Jain's frozen witness, notices and historical assistance disclosures. +Earlier generalized Clifford, three-stage, uniform weighted recursion, +ordinary-leaf, semantic/bulk, precision and analytic credits remain in force. +Source-specific license bytes are preserved under references/. + +October 9 recycled-bit integration: +DaysSky (#150), William Porter/hpst3r (#147), Thomas Marchand/Th0rgal (#146), +Rohan Gupta/gupt1156 (#148), James Chang/jamesyc (#124), SovereignSteak (#122). +The original notices and assistance disclosures are retained under research/, +including research/recycled-bit-integration/NOTICE. Andrew Barnes/Bortlesboat +(#101) repairs shared verifiers using rfu08's #64 counterexample. rfu08's +scoped finite and formal-transfer packages are included separately; they do +not establish the full multiplication theorem. Earlier and parallel credits +remain applicable. Douglas Colkitt integrated these with OpenAI Codex assistance. + +SovereignSteak PR151 independently supplies the matching gauge/recycling +composition and the selected 473/10^6 atom refinement; its original package +and assistance disclosure are retained under research/gauge-recycling/. + +October 9 coordinated-frame and completed-entrance-bank integration: +Dugongue PR186, 166a34d75e853e933855f0f7e940fe77c4bb6b8d, builds on +Chafik Boukhalfa/chafreaky's PR181, 7fb2194801e3a10f54772c7f0d5505035a4fc0ad, +and eumemic's PR168 v4, 4a3c769e5c5430e7114c4d3e099ff34664677f17. +The frozen package and prerequisite archive preserve all author, source-license +and assistance notices, including PR175's compiler optimization. DaysSky's +carrier closure, James Chang's terminal substitution and balanced assembly, +geckods' stopping refinements and all preceding framework credits remain. +Rohan Arun's PR185 bootstrap and chafreaky's PR182 bit refinement are reviewed +parallel contributions; their gains are not added to the selected witness. +Douglas Colkitt integrated the package and supplied the bank scheduling +supplement with OpenAI Codex assistance, under Apache-2.0. The all-size +interfaces remain conditional; finite verification is not full formalization. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/upstream/LICENSE b/research/phase-coded-callers/annexes/phase-access/frozen/upstream/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/upstream/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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+ "scale:2": 56 + }, + "events": 172, + "maximum_row_one_norm": "2", + "price": 1016 + }, + "capture_word": { + "binary_height": 3, + "census": { + "add:-1": 200, + "add:-1/2": 16, + "add:1": 200, + "add:1/2": 24, + "scale:-1": 40, + "scale:-1/2": 11, + "scale:-2": 11, + "scale:1/2": 69, + "scale:2": 69 + }, + "events": 640, + "maximum_row_one_norm": "10", + "price": 4044 + }, + "coded_backward_word": { + "binary_height": 0, + "census": { + "add:-1": 108, + "add:-3": 4, + "add:1": 8, + "add:2": 8, + "add:3": 20, + "add:4": 16, + "add:5": 4 + }, + "events": 168, + "maximum_row_one_norm": "10", + "price": 1544 + }, + "coded_forward_word": { + "binary_height": 0, + "census": { + "add:-1": 8, + "add:-2": 8, + "add:-3": 20, + "add:-4": 16, + "add:-5": 4, + "add:1": 108, + "add:3": 4 + }, + "events": 168, + "maximum_row_one_norm": "10", + "price": 1544 + }, + "inverse_word": { + "binary_height": 3, + "census": { + "add:-1": 200, + "add:-1/2": 24, + "add:1": 200, + "add:1/2": 16, + "scale:-1": 40, + "scale:-1/2": 11, + "scale:-2": 11, + "scale:1/2": 69, + "scale:2": 69 + }, + "events": 640, + "maximum_row_one_norm": "10", + "price": 4044 + }, + "reduced_word": { + "binary_height": 1, + "census": { + "add:-1": 40, + "add:-1/2": 16, + "add:1": 40, + "add:1/2": 24, + "scale:-1": 16 + }, + "events": 136, + "maximum_row_one_norm": "2", + "price": 1072 + } + }, + "minimum_common_gauge_rank": 4, + "monomial_alignment_ranks_checked": 112, + "producer_freeze_sha256": "3b7601e537cdd570295cde170a2491de876d7cae7814313b0c4a1f685c199ecd", + "producer_imports": 0, + "rank_one_anchor_checks": 112, + "scalar_input_columns": 640, + "scope": "Exact common-frame scalar word and binary phase geometry. The 112-H1 count is conditional on W_R. No phase recipes, complete routed caller, or supplier admission.", + "source_pins": { + "coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json": "20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701", + "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd", + "controller-followthrough-20261017/shared-root-eight-20261020/v2-normal/PROGRAM.json.gz": "71dec1d8e33625e301c8bfde37d8c08b0019124e1525500555fcc704530bf4a6", + "independent-review-20261017/common-gauge-rank-20261020/FREEZE.json": "9523bfe7aaa2a1430d146727a328b03cf90f0ff4965dfdc2bc2640a58d92de57", + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" + }, + "status": "PASS_INDEPENDENT_DYADIC_PHASE_CLASS_CAPTURE", + "untouched_capture_fields": 528, + "word_level_phase_prefix_premises": true +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md new file mode 100644 index 0000000000..c9c606b84f --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/REVIEW.md @@ -0,0 +1,302 @@ +# Independent review of the dyadic phase-class capture + +The frozen construction passes. The actual response admits a dyadic +involution C with rank(C-I)=16 and determinant one. Both literal +capture words cost 4044 old real scalar primitives. The class-supported +response K=C E C has a 1544-primitive additive word in either direction. +All 640 arbitrary input columns and both capture inverse orders pass. + +The conditional 112-H1 factorization requires the carried rank-four +frame W_R. It does not apply to the current W45 exit. A separate binary +check in this review gives rank two for all 56 proposed pair ratios in +the actual W45 frame. No native phase recipes or complete caller are +admitted by this review. + +## Source binding + +The producer packet is +`independent-review-20261017/phase-class-dyadic-capture-20261020`. +Its freeze SHA256 is +`3b7601e537cdd570295cde170a2491de876d7cae7814313b0c4a1f685c199ecd`. +Only its `verified-normal` and `verified-optimized` outputs are final +evidence. This review verifies every frozen file. + +The actual rank16 response is read from the decompressed v2 +`EXTENSION-PROGRAM.json.gz`, SHA256 +`d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4`. +The cyclic pair geometry has SHA256 +`3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585`. +The actual W_R circuit is read from the shared-root v2 program, +decompressed SHA256 +`71dec1d8e33625e301c8bfde37d8c08b0019124e1525500555fcc704530bf4a6`. +The actual W45 circuit is read from `GAUGE-PROGRAMS.json`, SHA256 +`20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701`. + +The checker imports no producer or compiler code. It constructs the +matrices from the source group signs and port labels. It uses a new +forward sparse-row interpreter for every scalar prefix and a binary +Pauli interpreter for the frame checks. All source paths and pins are +in `REVIEW.json`. + +## Independent algebra + +The source has eight signed groups of size six and eight groups of +size eight. The groups partition all 112 ports. In mode coordinates, +each response is I-dd^T. The actual pair code H gives + + E = H^-1 (direct sum of I-dd^T) H. + +The checker constructs this matrix and compares it entry by entry +with the source response. It also verifies the symmetry of E. + +The root space R=span(30,45,75,384) is a four-dimensional even +isotropic binary space. The actual labels give fourteen q+R classes +of size eight. H preserves each class. A six-mode group meets three +classes in two ports each; an eight-mode group meets four. + +For a six-mode group, let p,t be the selected class pair. Define + + a_p=2d_p, a_t=0, + b_p=3d_p, b_t=-d_t, + u=a-d, v=(d-b)/4, S=I+uv^T, + +with a and b zero off the pair. Direct calculation gives + + v^T d=1, v^T u=-2, S d=a, b^T S=d^T, b^T a=6. + +Thus S^2=I, det S=-1, and + + S(I-dd^T)S = I-ab^T. + +Only the selected class pair occurs in the changed response. The +restriction there is + + [-5, 2d_p d_t; 0, 1]. + +For size eight, let e equal d on the selected pair and zero elsewhere. +Set u=2e-d, v=-u/4. Then u^T u=8 and u^T d=-4. It follows that +S^2=I, S d=2e, and + + S(I-dd^T)S = I-4ee^T. + +Each S-I is nonzero of rank one. The sixteen disjoint blocks therefore +give rank 16, and their determinants multiply to one. Similarity by H +gives the asserted rank and determinant of C=H^-1 S H. Exact +elimination on the independently constructed 112-by-112 matrices +confirms both statements. + +## The active coordinate is a difference + +The actual pair rotation is + + s=d_p x_p+d_t x_t, + t=-d_p x_p+d_t x_t. + +For size six, the transformed u is zero on the selected sum and every +other difference. On the selected negative difference and the two +other sums, the transformed rank-one update is + + u=(-2,-2,-2), v=(1/2,1/4,1/4). + +For size eight, all differences are passive. A valid rescaled +rank-one representation on the four sums is + + u=(1,-1,-1,-1), v=(-1/2,1/2,1/2,1/2). + +There are exactly 56 active fields, four in each global class. +The checker constructs P directly from the source signs and verifies +P S P^-1 against the literal reduced word. A control that removes +updates to a selected difference is rejected. + +Every prefix of H and P preserves phase classes: each ADD has its +source and target in one class. Every prefix of the reduced word +reads and changes active fields only. These are literal gate checks, +not only matrix endpoint checks. + +## Full scalar word and grid + +For a reduced update I+uv^T with v^T u=-2, choose the first active +coordinate p. The shear R given by +x_i -= (u_i/u_p)x_p sends u to u_p e_p. Therefore + + R(I+uv^T)R^-1 = I+u_p e_p v^T R^-1. + +Its only changed row is p. Its diagonal entry is -1; its remaining +entries in that row are u_p v_i. This proves the stated in-place +sequence R, the row update, and R^-1. It uses no extra field. + +The checker verifies the complete chronological factor order + + H, P, S_reduced, P^-1, H^-1. + +It also verifies the literal reverse word. The costs are: + +| Component | Old real scalar primitives | +| --- | ---: | +| H or H^-1 | 470 | +| P or P^-1 | 1016 | +| Six-mode reduced block | 54 | +| Eight-mode reduced block | 80 | +| Sixteen reduced blocks | 1072 | +| Complete C or literal inverse | 4044 | + +The price is derived from each emitted coefficient with the stated +binary ADD tariff. Every scale is a signed power of two. No fixed +odd multiplication, odd division, CLEAR, owned field, or native child +occurs in the scalar word. + +The sparse-row replay starts with 640 independent field variables. +It verifies the complete C map on the first 112 and identity on the +other 528. Both inverse orders are identity on all 640. It computes +the exact maximum prefix row one-norm 10 and maximum binary +denominator height three in both directions. + +Thus arbitrary inputs on a common dyadic grid need at most three +additional binary denominator levels for this scalar word. This is +not a bound on recursive child interiors or on the complete physical +phase implementation. + +## The response is class-supported, not a diagonal unit + +The checker verifies K=C E C entry by entry and checks every nonzero +entry against the global phase classes. K has nonzero off-diagonal +entries and is not symmetric. Its determinant is 35^8. The exact +inverse has denominator LCM 35, with both inverse products checked. +The factors five and seven therefore remain. + +Encoding both banks by the same C changes the forward scalar shear +to Y+=KX. Since the actual source E is symmetric, the backward shear +becomes X-=KY. It is not X-=K^T Y. The checker records an explicit +entry that distinguishes K from K^T. + +The two literal additive words each have 168 ADD events and cost +1544 primitives. Both act correctly on all 640 independent variables; +the 416 fields outside the two data banks remain unchanged. This +does not give an in-place dyadic implementation of K^-1. Their exact +prefix row one-norm is ten, and their binary denominator height is +zero. No odd-grid service is needed for these additive words. + +## Carried-frame scope and the rank-four requirement + +The actual W_R has binary Fourier rank four. For each port choose the +least actual label in its q+R class as anchor. The checker verifies +all 112 ratios + + W_R C_q C_anchor^-1 W_R^-1 + +have Fourier rank zero. Each conjugated anchor has rank one. +These checks bind the abstract phase-class premises to the actual +labels and W_R circuit. They do not emit full monomial records or +rank-one native wrappers. + +Put Q'=W_R Q W_R^-1 and write Q'=A D, with D constant within each +class. Set T=P H. The exact ordered factorization is + + Q' C Q'^-1 + = A T^-1 (D_active S_reduced D_active^-1 direct-sum I) T A^-1. + +It has 56 inverse and 56 forward anchor occurrences. Thus 112 H1 is +the conditional count in this carried frame. It retains 4044 scalar +primitives, at most 224 alignment maps, and up to 224 native side +maps. Preparing W_R, removing it, and lowering all maps are additional +obligations. + +The binary checks suffice for Fourier rank and monomial support. +The ordered identity itself preserves all phases and is valid at +every tensor width. A full native implementation still needs the +actual phase records, legal access, and the inherited compiler and +recursive contracts. + +The actual directional phases commute, and this remains true after +conjugation by W_R. Negative conjugation therefore uses inverse +alignments and anchors. For a transported inverse, the exact identity +is + + Q' C^-1 Q' = (Q' C^-1 Q'^-1) Q'^2. + +The rightmost Q'^2 is a conjugated Pauli translation and is monomial. +It must be retained, either as a separate map or as the explicit +right factor in the first alignment. It is not a free cancellation. + +The exact W45 is S_e0 C_45 S_e0. It has rank one. In this frame all +56 pair ratios have rank two. Therefore the current W45 exit does +not meet the monomial alignment premise. + +There is also a lower bound on a common replacement gauge. For a +ratio C_a C_b^-1, the binary action is (x,z) -> (x+Tz,z), where +T=aa^T+bb^T. If one Clifford W makes every ratio monomial, let +L=W^-1 Z and U=L intersect X. The z-projection of L equals +U-perpendicular. Invariance implies Tz in U, so + + 0=z^T Tz=(a+b) dot z. + +Every edge difference a+b lies in U. The Fourier rank of W is at +least dim U, since L intersect X and L intersect Z are disjoint. +For each actual orthonormal eight-clique, the four disjoint +pair differences are independent. Across all pairs their span +has rank four. Hence any one common Clifford that makes these +pair ratios monomial needs rank at least four. The emitted W_R +attains that rank. + +This bound concerns one common cover gauge. It is not a lower bound +for an arbitrary joint decoder, a circuit with cross-field mixtures, +or a changed productive construction. + +## Prefix norm under the conditional phase factorization + +There is a useful extension of the scalar bound. It requires the +literal prefix conditions verified above: every prefix of T and +T^-1 preserves classes, and every prefix of S_reduced reads and +changes active fields only. Endpoint support alone is insufficient. + +Use the maximum of the field L2 norms. Write A_i for the input +alignment of field i and D_g for its class anchor. After T and the +inverse anchors, each active row has its scalar prefix coefficients +followed by the fixed input factor D_g(i)^-1 A_i^-1. Thus scalar +cancellations for each input field remain exact during the reduced +core. Passive rows are not read. + +After the forward anchors, every row, including each passive row, +has the form + + sum_i l_(r,i) D_g(r) D_g(i)^-1 A_i^-1 x_i, + +where l is the corresponding scalar-prefix matrix. A passive row +has input and output in the same class, so its two D factors cancel. +Each subsequent gate of T^-1 mixes only rows in one class. It +therefore preserves this form and its scalar cancellations. Partial +alignment and anchor passes apply a unitary to one whole field and +do not increase its L2 norm. + +Consequently, the norm at completed-child boundaries is at most the +corresponding scalar row one-norm, hence at most ten times the +maximum input field norm. Recursive child interiors are excluded. +The scalar binary-height-three bound does not transfer to this +physical word without a separate phase-grid account. + +The producing agent independently checked this norm argument and +specified the necessary word-prefix hypotheses. This is a peer +check of the extension, not a second native implementation review. + +## Verification and limits + +Run one process with +`python3 -I -B check_review.py`, then repeat with `-O`. The two +receipts must be byte-identical. Expected output starts with +`PASS_INDEPENDENT_DYADIC_PHASE_CLASS_CAPTURE`. + +No material error was found in the frozen packet. The construction +provides a dyadic scalar capture and an exact conditional phase +factorization. Native phase recipes, rank-four frame preparation, +routed stage matching, helper progress, terminal output, finite map +prices, and the complete recursive invoice remain open. + +The independent-review lane supplied the asymmetric six-mode +involution. The coordinator supplied the phase-class reduction. +The low-displacement, pair-code, and common-gauge packets supply +the actual response and geometry. This review used AI assistance +and is not an independent human review. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/check_review.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/check_review.py new file mode 100644 index 0000000000..460444769c --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/check_review.py @@ -0,0 +1,393 @@ +"""Check the actual dyadic capture without producer imports.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import lcm +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PRODUCER = LANES / "independent-review-20261017/phase-class-dyadic-capture-20261020" +FREEZE_PIN = "3b7601e537cdd570295cde170a2491de876d7cae7814313b0c4a1f685c199ecd" +PINS = { + "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": + "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd", + "controller-followthrough-20261017/shared-root-eight-20261020/v2-normal/PROGRAM.json.gz": + "71dec1d8e33625e301c8bfde37d8c08b0019124e1525500555fcc704530bf4a6", + "coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json": + "20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701", + "independent-review-20261017/common-gauge-rank-20261020/FREEZE.json": + "9523bfe7aaa2a1430d146727a328b03cf90f0ff4965dfdc2bc2640a58d92de57", +} + + +def need(value, reason): + if not value: + raise ValueError(reason) + + +def read(path, digest): + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == digest, "Source hash: " + path.name) + return json.loads(raw) + + +def identity(n): + return [{i: Q(1)} for i in range(n)] + + +def sparse(matrix): + return [{int(j): Q(v) for j, v in row.items() if Q(v)} for row in matrix] + + +def add(left, right, coefficient=Q(1)): + answer = dict(left) + for j, value in right.items(): + answer[j] = answer.get(j, Q(0)) + coefficient * value + if not answer[j]: + del answer[j] + return answer + + +def multiply(left, right): + answer = [] + for row in left: + result = {} + for j, value in row.items(): + result = add(result, right[j], value) + answer.append(result) + return answer + + +def elimination(matrix): + rows = [dict(row) for row in matrix] + rank, determinant = 0, Q(1) + for j in range(len(rows)): + pick = next((i for i in range(rank, len(rows)) if rows[i].get(j)), None) + if pick is None: + continue + if pick != rank: + rows[pick], rows[rank] = rows[rank], rows[pick] + determinant = -determinant + pivot = rows[rank][j] + determinant *= pivot + rows[rank] = {k: v / pivot for k, v in rows[rank].items()} + for i in range(rank + 1, len(rows)): + if rows[i].get(j): + rows[i] = add(rows[i], rows[rank], -rows[i][j]) + rank += 1 + return rank, determinant if rank == len(rows) else Q(0) + + +def put_pair(matrix, inverse, ports, block): + p, t = ports + a, b = map(Q, block[0]) + c, d = map(Q, block[1]) + determinant = a * d - b * c + need(determinant != 0, "Pair unit") + matrix[p], matrix[t] = {p: a, t: b}, {p: c, t: d} + inverse[p], inverse[t] = {p: d / determinant, t: -b / determinant}, {p: -c / determinant, t: a / determinant} + + +def replay(word, n=640): + rows = identity(n) + norm, height, price = Q(1), 0, 0 + census = Counter() + for op, target, source, value in word: + c = Q(value) + numerator, denominator = abs(c.numerator), c.denominator + need(c and denominator & (denominator - 1) == 0 and 0 <= target < 224, "Dyadic scalar gate") + if op == "add": + need(isinstance(source, int) and 0 <= source < 224 and source != target, "Distinct data source") + rows[target] = add(rows[target], rows[source], c) + price += 2 * (1 + numerator.bit_length() + numerator.bit_count() + denominator.bit_length()) + else: + need(op == "scale" and source is None and numerator & (numerator - 1) == 0, "Dyadic unit scale") + rows[target] = {j: c * v for j, v in rows[target].items()} + price += 2 * (abs(numerator.bit_length() - denominator.bit_length()) + int(c < 0)) + norm = max(norm, sum(map(abs, rows[target].values()))) + for value in rows[target].values(): + need(value.denominator & (value.denominator - 1) == 0, "Dyadic prefix coefficient") + height = max(height, value.denominator.bit_length() - 1) + census[op + ":" + str(c)] += 1 + return rows, {"price": price, "maximum_row_one_norm": str(norm), "binary_height": height, + "events": len(word), "census": dict(sorted(census.items()))} + + +def inverse_word(word): + return [[op, target, source, str(-Q(value) if op == "add" else 1 / Q(value))] + for op, target, source, value in reversed(word)] + + +def parity(value): + return value.bit_count() & 1 + + +def span(basis): + result = {0} + for v in basis: + result |= {u ^ v for u in result} + return result + + +def binary_rank(vectors): + pivots = {} + for v in vectors: + while v: + bit = v.bit_length() + if bit in pivots: + v ^= pivots[bit] + else: + pivots[bit] = v + break + return len(pivots) + + +def act(rows, value): + return sum(parity(row & value) << i for i, row in enumerate(rows)) + + +def transpose(rows): + return [sum(((row >> j) & 1) << i for i, row in enumerate(rows)) for j in range(len(rows))] + + +def binary_inverse(rows): + n = len(rows) + left, right = list(rows), [1 << i for i in range(n)] + for j in range(n): + p = next(i for i in range(j, n) if left[i] >> j & 1) + left[j], left[p], right[j], right[p] = left[p], left[j], right[p], right[j] + for i in range(n): + if i != j and left[i] >> j & 1: + left[i] ^= left[j] + right[i] ^= right[j] + need(left == [1 << i for i in range(n)], "Invertible binary address map") + return right + + +def inverse_circuit(word): + result = [] + for gate in reversed(word): + if gate[0] == "P": + result.append(["P", binary_inverse(gate[1])]) + elif gate[0] == "D": + result.append(["D", gate[1], [(-a) % 4 for a in gate[2]]]) + else: + need(gate[0] == "C", "Frame circuit alphabet") + result.append(["C", gate[1], -gate[2]]) + return result + + +def binary_pauli(word, x, z): + for gate in word: + if gate[0] == "P": + x, z = act(gate[1], x), act(transpose(binary_inverse(gate[1])), z) + elif gate[0] == "D": + need(gate[1] == transpose(gate[1]), "Symmetric diagonal phase form") + need(all(((row >> i) & 1) == gate[2][i] % 2 for i, row in enumerate(gate[1])), + "Diagonal phase parity") + z ^= act(gate[1], x) + else: + need(gate[0] == "C", "Pure line operator") + if parity(gate[1] & z): + x ^= gate[1] + return x, z + + +def fourier_rank(word): + return binary_rank([binary_pauli(word, 0, 1 << j)[0] for j in range(9)]) + + +def main(): + freeze = read(PRODUCER / "FREEZE.json", FREEZE_PIN) + for name, pin in freeze["files"].items(): + need(sha256((PRODUCER / name).read_bytes()).hexdigest() == pin, "Frozen producer file") + packet = read(PRODUCER / "verified-normal/CAPTURE-PROGRAM.json", + freeze["files"]["verified-normal/CAPTURE-PROGRAM.json"]) + receipt = read(PRODUCER / "verified-normal/CHECKS.json", freeze["files"]["verified-normal/CHECKS.json"]) + inputs = {name: read(LANES / name, pin) for name, pin in PINS.items()} + for name, pin in receipt["source_pins"].items(): + need(sha256((LANES / name).read_bytes()).hexdigest() == pin, "Other declared source") + common = inputs["independent-review-20261017/common-gauge-rank-20261020/FREEZE.json"] + for name, pin in common["files"].items(): + need(sha256((LANES / "independent-review-20261017/common-gauge-rank-20261020" / name).read_bytes()).hexdigest() + == pin, "Common gauge theorem file") + model = inputs[next(k for k in PINS if k.endswith("EXTENSION-PROGRAM.json.gz"))]["model"] + cyclic = inputs[next(k for k in PINS if k.endswith("CYCLIC-FLAGS.json"))] + geometry = inputs[next(k for k in PINS if k.endswith("GEOMETRY.json"))] + labels = model["ports"] + need(labels == packet["ports"] == cyclic["ports"] == geometry["q_labels"], "Actual port labels") + root = span([30, 45, 75, 384]) + need(len(root) == 16 and all(parity(u) == 0 for u in root), "Four-dimensional even root") + need(root == set(packet["root_space"]) == set(geometry["common_even_isotropic_space"]) + and all(parity(u & v) == 0 for u in root for v in root), "Actual isotropic root space") + classes = [min(q ^ u for u in root) for q in labels] + need(classes == packet["phase_classes"] and Counter(Counter(classes).values()) == {8: 14}, "Actual phase classes") + h, hi, p, pi = (identity(112) for _ in range(4)) + for pair in cyclic["pair_codes"]: + need(len({classes[i] for i in pair["ports"]}) == 1, "H preserves phase classes") + put_pair(h, hi, pair["ports"], pair["matrix"]) + + source_groups = [(a["ordered_carriers_a_b_c"], a["signs"]) for a in model["vertex_assignments"]] + source_groups += [(ports, [1] * 8) for ports in model["small_cliques"]] + need(Counter(i for ports, _ in source_groups for i in ports) == Counter(range(112)), "Disjoint complete groups") + s, e_mode, k_mode, reduced = (identity(112) for _ in range(4)) + active, all_pairs, group_checks = [], [], [] + for group_index, (ports, signs) in enumerate(source_groups): + size = len(ports) + need(size in (6, 8) and all(abs(d) == 1 for d in signs), "Signed actual group") + d = dict(zip(ports, map(Q, signs))) + pairs = [[i for i in ports if classes[i] == g] for g in sorted({classes[i] for i in ports})] + need(all(len(pair) == 2 for pair in pairs), "Pairs within each group class") + selected = pairs[0] + for pair in pairs: + a0, b0 = (d[i] for i in pair) + put_pair(p, pi, pair, [[a0, b0], [-a0, b0]]) + a, b = {i: Q(0) for i in ports}, {i: Q(0) for i in ports} + if size == 6: + a[selected[0]] = 2 * d[selected[0]] + b[selected[0]], b[selected[1]] = 3 * d[selected[0]], -d[selected[1]] + u = {i: a[i] - d[i] for i in ports} + v = {i: (d[i] - b[i]) / 4 for i in ports} + chosen = [selected[1]] + [pair[0] for pair in pairs[1:]] + ru, rv = [-2] * 3, [Q(1, 2), Q(1, 4), Q(1, 4)] + else: + for i in selected: + a[i] = b[i] = 2 * d[i] + u = {i: a[i] - d[i] for i in ports} + v = {i: -u[i] / 4 for i in ports} + chosen = [pair[0] for pair in pairs] + ru, rv = [1, -1, -1, -1], [Q(-1, 2)] + [Q(1, 2)] * 3 + need(sum(v[i] * d[i] for i in ports) == 1 and sum(v[i] * u[i] for i in ports) == -2, "Rank-one involution identities") + need(sum(b[i] * a[i] for i in ports) == size, "Conserved response eigenvalue") + need(all(b[i] + sum(b[j] * u[j] for j in ports) * v[i] == d[i] for i in ports), "Captured query covector") + for i in ports: + s[i] = add(s[i], v, u[i]) + e_mode[i] = add(e_mode[i], d, -d[i]) + k_mode[i] = add(k_mode[i], b, -a[i]) + for i, ui in zip(chosen, ru): + reduced[i] = add(reduced[i], dict(zip(chosen, rv)), ui) + g = packet["groups"][group_index] + need(g["ports"] == ports and g["signs"] == signs and g["pairs"] == pairs + and g["active_ports"] == chosen, "Emitted group and active orientation") + active.extend(chosen) + all_pairs.extend(pairs) + group_checks.append({"size": size, "selected_pair": selected, "active": chosen, + "pair_difference_rank": binary_rank([labels[i] ^ labels[j] for i, j in pairs])}) + + unit = identity(112) + need(multiply(h, hi) == multiply(hi, h) == multiply(p, pi) == multiply(pi, p) == unit, "Both pair inverse orders") + e = multiply(hi, multiply(e_mode, h)) + c = multiply(hi, multiply(s, h)) + k = multiply(hi, multiply(k_mode, h)) + need(e == sparse(model["response"]) == sparse(packet["source_response"]), "Actual physical response") + need(c == sparse(packet["capture"]) and k == sparse(packet["coded_response"]), "Independent capture and response") + need(multiply(c, c) == unit and multiply(c, multiply(e, c)) == k, "Involution and response conjugation") + need(multiply(p, multiply(s, pi)) == reduced, "Selected difference reduction") + need(all(e[i].get(j, 0) == e[j].get(i, 0) for i in range(112) for j in range(112)), "Source symmetry") + need(all(classes[i] == classes[j] for i, row in enumerate(k) for j in row), "K preserves global classes") + need(active == packet["active_ports"] and len(set(active)) == 56 + and Counter(classes[i] for i in active) == {g: 4 for g in set(classes)}, "Exactly four active fields per class") + delta = [add(row, {i: Q(1)}, -1) for i, row in enumerate(c)] + need(elimination(delta)[0] == 16 and elimination(c) == (112, 1), "Displacement rank and determinant") + need(elimination(k) == (112, Q(35**8)), "Non-dyadic-unit coded response") + ei = sparse(model["response_inverse"]) + need(multiply(e, ei) == multiply(ei, e) == unit, "Actual response inverse") + ki = multiply(c, multiply(ei, c)) + need(multiply(k, ki) == multiply(ki, k) == unit, "Both coded response inverse orders") + inverse_denominator = lcm(*(v.denominator for row in ki for v in row.values())) + need(inverse_denominator == 35, "Both odd inverse factors remain") + + word_names = ["H_word", "T_word", "reduced_word", "capture_word", "inverse_word", + "coded_forward_word", "coded_backward_word"] + need(packet["capture_word"] == packet["H_word"] + packet["T_word"] + packet["reduced_word"] + + inverse_word(packet["T_word"]) + inverse_word(packet["H_word"]), + "The complete literal factor order") + need(packet["inverse_word"] == inverse_word(packet["capture_word"]), "The complete literal reverse word") + need(all(op != "add" or classes[target] == classes[source] + for name in ("H_word", "T_word") for op, target, source, _ in packet[name]), + "Every pair-code prefix preserves phase classes") + need(all(target in active and (op != "add" or source in active) + for op, target, source, _ in packet["reduced_word"]), "Every core prefix uses active fields only") + reports, maps = {}, {} + for name in word_names: + maps[name], reports[name] = replay(packet[name]) + extra = [{i: Q(1)} for i in range(112, 640)] + need(maps["H_word"] == h + extra and maps["T_word"] == p + extra, "Literal pair codes") + need(maps["reduced_word"] == reduced + extra, "Literal reduced core") + need(maps["capture_word"] == maps["inverse_word"] == c + extra, "All 640 arbitrary input columns") + need(replay(packet["capture_word"] + packet["inverse_word"])[0] == identity(640) + and replay(packet["inverse_word"] + packet["capture_word"])[0] == identity(640), "Both complete inverse orders") + forward, backward = identity(640), identity(640) + for i, row in enumerate(k): + forward[112 + i] = add(forward[112 + i], row) + backward[i] = add(backward[i], {112 + j: v for j, v in row.items()}, -1) + need(maps["coded_forward_word"] == forward and maps["coded_backward_word"] == backward, + "All 640 arbitrary additive-coupler columns") + need(all(reports[name]["price"] == price for name, price in + [("H_word", 470), ("T_word", 1016), ("reduced_word", 1072), + ("capture_word", 4044), ("inverse_word", 4044), + ("coded_forward_word", 1544), ("coded_backward_word", 1544)]), "Complete scalar invoices") + need(all(reports[name]["maximum_row_one_norm"] == "10" and reports[name]["binary_height"] == 3 + for name in ("capture_word", "inverse_word")), "Exact scalar prefix bounds") + passive = set(range(112)) - set(active) + need(all(reduced[i] == {i: Q(1)} for i in passive), "All passive data remain arbitrary") + need(all(j in active for i in active for j in reduced[i]), "The reduced core does not read passive data") + + # These controls separate the actual interface from two incorrect ones. + selected_difference = packet["groups"][0]["selected_pair"][1] + mutation = [gate for gate in packet["reduced_word"] if gate[1] != selected_difference] + need(replay(mutation)[0] != maps["reduced_word"], "Reject omission of the selected difference") + transpose_witness = next((i, j, str(k[i].get(j, 0)), str(k[j].get(i, 0))) + for i in range(112) for j in range(112) if k[i].get(j, 0) != k[j].get(i, 0)) + need(any(i != j for i, row in enumerate(k) for j in row), "K is not physically diagonal") + + w = inputs[next(k for k in PINS if "shared-root-eight" in k)]["W"] + w45 = inputs[next(k for k in PINS if k.endswith("GAUGE-PROGRAMS.json"))]["W"]["circuit"] + need(w == packet["W"] and fourier_rank(w) == 4 and fourier_rank(w45) == 1, "Actual carried frames") + wi, w45i = inverse_circuit(w), inverse_circuit(w45) + anchors = {g: min(labels[i] for i in range(112) if classes[i] == g) for g in set(classes)} + need({int(g): q for g, q in packet["global_anchors"].items()} == anchors, "One actual global anchor per class") + for i, q in enumerate(labels): + anchor = anchors[classes[i]] + need(q ^ anchor in root and parity(anchor), "Even difference and odd anchor") + need(fourier_rank(wi + [["C", anchor, -1], ["C", q, 1]] + w) == 0, "Alignment is monomial in W_R") + need(fourier_rank(wi + [["C", anchor, 1]] + w) == 1, "Anchor has Fourier rank one") + wrong_ranks = [fourier_rank(w45i + [["C", labels[j], -1], ["C", labels[i], 1]] + w45) + for i, j in all_pairs] + need(wrong_ranks == [2] * 56, "All actual pair ratios have rank two in W45") + need(all(g["pair_difference_rank"] == 4 for g in group_checks if g["size"] == 8), + "The four disjoint pair differences are independent") + need(binary_rank([labels[i] ^ labels[j] for i, j in all_pairs]) == 4, "Exact common-gauge lower-bound rank") + + out = { + "status": "PASS_INDEPENDENT_DYADIC_PHASE_CLASS_CAPTURE", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "producer_freeze_sha256": FREEZE_PIN, "source_pins": PINS, + "producer_imports": 0, "scalar_input_columns": 640, "untouched_capture_fields": 528, + "capture_displacement_rank": 16, "capture_determinant": "1", + "coded_response_determinant": str(35**8), "coded_inverse_denominator_lcm": inverse_denominator, + "K_not_transpose_witness": transpose_witness, + "active_fields": len(active), "global_classes": 14, "group_checks": group_checks, + "literal_scalar_reports": reports, "W_R_rank": 4, "W45_rank": 1, + "word_level_phase_prefix_premises": True, + "monomial_alignment_ranks_checked": 112, "rank_one_anchor_checks": 112, + "W45_pair_ratio_ranks": wrong_ranks, "minimum_common_gauge_rank": 4, + "scope": "Exact common-frame scalar word and binary phase geometry. The 112-H1 count is conditional on W_R. No phase recipes, complete routed caller, or supplier admission.", + } + (HERE / "REVIEW.json").write_text(json.dumps(out, indent=2, sort_keys=True) + "\n") + print("PASS_INDEPENDENT_DYADIC_PHASE_CLASS_CAPTURE: 640 inputs; 4044/1544 scalar costs; W_R rank4; W45 pair ratios rank2") + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json new file mode 100644 index 0000000000..4201e9a04c --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json @@ -0,0 +1,1441 @@ +{ + "D": [ + { + "0": "1/4", + "1": "1/4" + }, + { + "4": "1/4", + "7": "1/4" + }, + {}, + { + "4": "1/4", + "6": "-1/4" + }, + { + "5": "1/4", + "7": "1/4" + }, + { + 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No cheaper encoder or supplier is admitted." +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/coherent-port/coupled-m1-terminal-20261018/AFFINE-GAUGE.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/coherent-port/coupled-m1-terminal-20261018/AFFINE-GAUGE.md new file mode 100644 index 0000000000..3269968cb7 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/coherent-port/coupled-m1-terminal-20261018/AFFINE-GAUGE.md @@ -0,0 +1,112 @@ +# A common gauge for affine port labels + +This note gives a component identity. It does not give a cheaper complete +terminal decoder. + +Let the payload address space be F_2^n. Put + +```text +X_a |x> = |x+a>, +S_b |x> = i^(b.x) |x>, +C_a = ((1+i)I + (1-i)X_a)/2. +``` + +Let A have independent columns a_1,...,a_k. Choose columns b_1,...,b_k +of B such that B^T A=I_k. Define + +```text +W_i = S_(b_i) C_(a_i) S_(b_i), +W = product_i W_i. +``` + +The factors W_i commute. For i different from j, the required identity +is b_i.a_j=0; all diagonal factors commute with one another, and all +translation functions commute with one another. No condition on A^T A, +B^T B, or the offset label is required. + +For any q, set t=B^T q and c=q+A t. Direct Pauli conjugation gives + +```text +W X_q W^-1 = X_c Z_(B t), B^T c=0. (1) +``` + +For one factor, the two cases are + +```text +b.q=0: W(a,b) X_q W(a,b)^-1 = X_q, +b.q=1: W(a,b) X_q W(a,b)^-1 = X_(q+a) Z_b. +``` + +These equations fix the phase, not only the symplectic map. The second +case has no scalar factor. Applying the commuting factors proves (1). + +Now let q range over one affine space q_ref+ran(A). The vector c in (1) +is the same for every q. For two labels q and r, write +t=B^T q, u=B^T r, and e=(t+u).B^T x. Then + +```text +W C_q C_r^-1 W^-1 |x> + = |x>, if e=0, + = -i (-1)^(t.B^T x) |x+c>, if e=1. (2) +``` + +To prove (2), put P=X_c Z_(B t) and R=X_c Z_(B u). +On the indicated address sector, R=(-1)^e P. If e=0, the two +quarter-turn factors cancel. If e=1, their product is -i P. +Since B^T c=0, the translation preserves the sector and its phase. +Thus (2) is an invertible address map with a quadratic phase. + +For tensor width f, apply (2) to each address column. The total phase +is the product of the displayed column phases. The same finite address +map acts on every column. This proves the identity for arbitrary inputs +and every width. It does not replace all column sectors by one sector +of the simultaneous translation. + +## Native rank and a restricted minimum + +The X-from-Z block of W is A A^T and has rank k. Thus W has Fourier +rank k. A native rank-k child with monomial boundary maps can implement +this gauge, subject to the actual child contract and the map cost. + +There is a matching minimum in the following restricted family. +Require one Clifford gauge V, identical on every field in a connected +port component, to make every nonzero edge quotient C_q C_r^-1 +monomial. Write M for the X-from-X block of V and N for its +X-from-Z block. + +The two conjugated translation Paulis commute. Their quarter-turn +product has X-from-Z block + +```text +(M q)(M q)^T + (M r)(M r)^T. +``` + +It is zero exactly when Mq=Mr. Therefore M kills every edge difference. +If these differences span a k-dimensional space U, then +dim ker(M) is at least k. The symplectic identity +M D^T + N C^T=I gives rank(N) at least dim ker(M). +Consequently every such common gauge has Fourier rank at least k. + +For the six actual eight-port components in the pinned geometry, +k=3. Encoding and decoding all eight independent fields with this +common gauge costs 48 units of native rank per component. The direct +two-line mass is 16 per component. This common-gauge construction alone +therefore gives no terminal saving. + +This minimum does not cover coupled field gauges, interleaved native +operations, a changed response, a changed controller, or fusion with +productive native work. It is not a lower bound for the full terminal. + +## Source and scope + +The exact port lists and labels come from +`controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json`, +SHA256 +`21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd`. +The checker uses the actual six components and also checks a rank-four +space whose offset need not be perpendicular to that space. + +No stage route, full-cover scalar pass, child host, terminal cost, or +kappa improvement is inferred. 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Joint field circuits remain outside this theorem.", + "small_exact_symplectic_cases": 2046, + "status": "PASS_EXACT_COMMON_GAUGE_RANK" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/COMMON-GAUGE.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/COMMON-GAUGE.md new file mode 100644 index 0000000000..300dfd6cbc --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/COMMON-GAUGE.md @@ -0,0 +1,155 @@ +# The least rank of a common cover gauge + +Let a family of pure-line ratios be C_a C_b^-1 on n binary cover axes. +The least Bruhat rank of one common cover Clifford W that makes every +ratio monomial is exactly + +```text +dim span{a+b : (a,b) is an edge in the family}. +``` + +This is a separate derivation of the common-gauge minimum already +proved in `coherent-port/coupled-m1-terminal-20261018/AFFINE-GAUGE.md`, +SHA256 +`c287019ae240fbe8ad80f0170f8d90a9964ec6db3050e5a1ea9314a6c270e0ec`. +That packet also gives an exact constructive gauge for affine labels. +The contribution here is a Lagrangian proof, an explicit statement for +arbitrary ratio graphs, and a binding to the new four-owner reduction. + +The result permits arbitrary Clifford phases in W. Thus a more complex +phase choice cannot lower this rank. It concerns one common cover +conjugation. It does not restrict a joint circuit that mixes fields, +uses different interleaved charts, or modifies earlier productive calls. + +For the four-owner terminal from the actual 64-port permutation, the +four lines are orthonormal and the edges form a cycle. Their difference +span has dimension three. A common gauge of rank one or two cannot +make the four cover ratios monomial. + +## Proof of the lower bound + +Use binary Pauli coordinates (x,z). Write X for the subspace z=0 and +Z for the subspace x=0. A pure C_a has symplectic action + +```text +(x,z) -> (x+a(a dot z),z). +``` + +Its inverse has the same binary action. Therefore the ratio for an +edge (a,b) acts by + +```text +(x,z) -> (x+Tz,z), T=aa^T+bb^T. +``` + +Suppose W makes every ratio monomial, and put L=W^-1 Z. A Clifford +is monomial exactly when it preserves computational Z in binary +phase space. Thus L is invariant under each displayed shear. + +Let U={x:(x,0) is in L}, and let Z0 be the projection of L to its +z coordinates. Isotropy of L gives Z0 contained in U-perpendicular. +Both have dimension n-dim(U), so they are equal. + +For any z in Z0, choose (x,z) in L. Invariance gives (Tz,0) in L, +so Tz is in U. Since z is perpendicular to U, + +```text +0 = z^T T z + = (a dot z)^2+(b dot z)^2 + = (a+b) dot z. +``` + +The last equality uses the field F2. Hence a+b is in Z0-perpendicular, +which is U. Let D be the span of all edge differences. Then D is +contained in U. + +The spaces L intersect X and L intersect Z are disjoint subspaces of +L. Consequently + +```text +dim(L intersect Z) <= n-dim(U) <= n-dim(D). +``` + +The Bruhat rank of W is n-dim(W^-1 Z intersect Z). It is therefore +at least dim(D). This proof does not assume that the lines are +orthogonal or that the edge graph is connected. + +## Construction at that rank + +Take U=D and the split Lagrangian + +```text +L = X_U direct_sum Z_(U-perpendicular). +``` + +For z perpendicular to U, every edge satisfies a dot z=b dot z. +Thus Tz=(a dot z)(a+b) is in U, and L is invariant under every ratio. + +Choose a binary address basis G whose first d columns span U. A +partial Walsh transform on those d coordinates, conjugated by the +address permutation G, has inverse image L and Bruhat rank d. It +therefore makes every ratio monomial. + +This Walsh can use the actual Gaussian-dyadic primitive. On one +coordinate, with S=diag(1,i), the product S C_e S is +exp(i*pi/4) times the real Walsh transform. Tensor d such products +and conjugate by G. The scalar phase is common to W and cancels in +W R W^-1. The implemented matrix itself has Gaussian-dyadic entries. +All resulting monomials retain their exact Gaussian-unit phases. + +This proves equality, not only a lower bound or a finite search result. + +## Actual orbit and exact checks + +The checker pins +`bridge-access-20261017/permutation-cycle-20261020/CYCLE64-PROGRAMS.json` +at SHA256 +`e9dadd6bc2aa58065b0079126944dd198238fb91ad55cb992d4ddf574e3989e2`. +For all 32 actual port pairs it verifies the four-line Gram matrix and +the difference rank three. It inherits the producer's reduction from +the routed terminal to these lines. It does not independently replay +the routed owner maps or their full phase equations. + +As an independent exact construction check, it builds the common Walsh +for all nonempty subsets of at most four distinct nonzero directions +in dimensions one through four. It verifies the claimed binary rank +and that every conjugated cycle ratio preserves computational Z. +These cases support the general proof; they do not replace it. + +For the canonical orthonormal quadruple it also uses a separate +Gaussian-integer state interpreter. It checks every column of all +four monomials, including their exact phases. The common gauge uses +three native rank-one calls. The checker does not import a compiler +or a producer module. + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/check_gauge_rank.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/check_gauge_rank.py +``` + +Expected output starts with `PASS_EXACT_COMMON_GAUGE_RANK`. The +receipts must be byte-identical. + +## Meaning for the decoder + +A scheme that applies the same W separately to all four owner fields, +executes the conjugated monomial cycle, and applies W^-1 separately +uses at least 24 native rank units in those eight gauge calls. That +literal scheme is worse than the eight-rank direct decoder. This is +not a lower bound of 24 on a decoder: cancellations, shared fields, +different intermediate charts, and a changed earlier computation +violate the stated scheme. + +In particular, this theorem does not rule out a six-rank joint orbit +implementation. It states what a successful construction must change +if it starts from the common-gauge idea. + +The bridge-access lane supplied the exact four-owner target. The +coherent-port lane supplied the earlier common-gauge construction and +minimum theorem. This lane derived the parallel Lagrangian proof and +the checks above. OpenAI Codex assisted the work. Independent proof +review is requested. No PR +or publication is authorized. Before any PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/FREEZE.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/FREEZE.json new file mode 100644 index 0000000000..98c48956d0 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "CHECKS.json": "72ec3ab4ac563fa1d8ab8f4b0b09cd6343ef589167a40e8d9bc602646add827e", + "COMMON-GAUGE.md": "2987281f974cfaac2cc8d4e4a5371f38de7b3994c98b1f0e8cfa9aec1725a7e9", + "REPRODUCTION.json": "8a609c8db88de6830410a1928d4ef69cf5ec8c731b8b02a26a97b8e516e0caed", + "check_gauge_rank.py": "8cbdd6ef911171c8d364ca60c0b7b4fc5dc00522e092941347ba26104a62d25b" + }, + "scope": "A common cover gauge only; no joint terminal lower bound.", + "status": "PASS_COMMON_GAUGE_GEOMETRY_AND_PHASE" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/REPRODUCTION.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..1ab975ba66 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/REPRODUCTION.json @@ -0,0 +1,15 @@ +{ + "runs": [ + { + "mode": "normal", + "receipt_sha256": "72ec3ab4ac563fa1d8ab8f4b0b09cd6343ef589167a40e8d9bc602646add827e", + "stdout": "PASS_EXACT_COMMON_GAUGE_RANK\nreceipt_sha256=72ec3ab4ac563fa1d8ab8f4b0b09cd6343ef589167a40e8d9bc602646add827e\n" + }, + { + "mode": "optimized", + "receipt_sha256": "72ec3ab4ac563fa1d8ab8f4b0b09cd6343ef589167a40e8d9bc602646add827e", + "stdout": "PASS_EXACT_COMMON_GAUGE_RANK\nreceipt_sha256=72ec3ab4ac563fa1d8ab8f4b0b09cd6343ef589167a40e8d9bc602646add827e\n" + } + ], + "status": "PASS_BYTE_IDENTICAL" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/check_gauge_rank.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/check_gauge_rank.py new file mode 100644 index 0000000000..2e25351897 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-gauge-rank-20261020/check_gauge_rank.py @@ -0,0 +1,178 @@ +#!/usr/bin/env python3 +"""Check common cover gauges and the actual four-line geometry.""" + +from hashlib import sha256 +from itertools import combinations +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / "bridge-access-20261017/permutation-cycle-20261020/CYCLE64-PROGRAMS.json" +SOURCE_SHA = "e9dadd6bc2aa58065b0079126944dd198238fb91ad55cb992d4ddf574e3989e2" +PREDECESSOR = LANES / "coherent-port/coupled-m1-terminal-20261018/AFFINE-GAUGE.md" +PREDECESSOR_SHA = "c287019ae240fbe8ad80f0170f8d90a9964ec6db3050e5a1ea9314a6c270e0ec" + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def basis(values): + pivots, result = {}, [] + for value in values: + x = value + while x: + k = x.bit_length() + if k not in pivots: + pivots[k] = x + result.append(value) + break + x ^= pivots[k] + return result + + +def multiply(columns, x): + answer = 0 + for i, c in enumerate(columns): + if x >> i & 1: + answer ^= c + return answer + + +def inverse(columns): + values = {multiply(columns, x): x for x in range(1 << len(columns))} + need(len(values) == 1 << len(columns), "Invertible address basis") + return [values[1 << i] for i in range(len(columns))] + + +def transpose(columns): + return [sum(((c >> i) & 1) << j for j, c in enumerate(columns)) + for i in range(len(columns))] + + +def common_gauge(n, lines): + differences = [lines[0] ^ q for q in lines[1:]] + u = basis(differences) + columns = basis(u + [1 << i for i in range(n)]) + inv = inverse(columns) + inv_t, columns_t = transpose(inv), transpose(columns) + r = len(u) + mask = (1 << r) - 1 + + def w(item): + x, z = item + x, z = multiply(inv, x), multiply(columns_t, z) + x, z = (x & ~mask) | (z & mask), (z & ~mask) | (x & mask) + return multiply(columns, x), multiply(inv_t, z) + + # This phase-free Walsh has square one in binary phase space. + image_x = [] + for i in range(n): + need(w(w((1 << i, 0))) == (1 << i, 0), "Walsh square on X") + need(w(w((0, 1 << i))) == (0, 1 << i), "Walsh square on Z") + image_x.append(w((0, 1 << i))[0]) + need(len(basis(image_x)) == r, "Common gauge has the claimed rank") + for a, b in zip(lines, lines[1:] + lines[:1]): + for i in range(n): + x, z = w((0, 1 << i)) + x ^= a if (z & a).bit_count() % 2 else 0 + x ^= b if (z & b).bit_count() % 2 else 0 + need(w((x, z))[0] == 0, "Conjugated ratio preserves computational Z") + return columns, r + + +def rotate(pair, power): + a, b = pair + return [(a, b), (-b, a), (-a, -b), (b, -a)][power % 4] + + +def exact_state(events, start): + values, power = {start: (1, 0)}, 0 + for kind, arg, sign in events: + if kind == "P": + values = {multiply(arg, x): c for x, c in values.items()} + elif kind == "S": + values = {x: rotate(c, sign * ((x & arg).bit_count() % 2)) + for x, c in values.items()} + else: + need(kind == "C", "Exact circuit grammar") + new = {} + for x, (a, b) in values.items(): + for y, c in [(x, (a - sign * b, b + sign * a)), + (x ^ arg, (a + sign * b, b - sign * a))]: + old = new.get(y, (0, 0)) + new[y] = old[0] + c[0], old[1] + c[1] + values = {x: c for x, c in new.items() if c != (0, 0)} + power += 1 + while power and all(a % 2 == b % 2 == 0 for a, b in values.values()): + values = {x: (a // 2, b // 2) for x, (a, b) in values.items()} + power -= 1 + return values, power + + +def main(): + need(sha256(PREDECESSOR.read_bytes()).hexdigest() == PREDECESSOR_SHA, + "Parallel minimum-rank proof pin") + raw = SOURCE.read_bytes() + need(sha256(raw).hexdigest() == SOURCE_SHA, "Actual orbit payload pin") + packet = json.loads(raw) + ranks = [] + for record in packet["records"]: + lines = record["cycle_lines"] + need(len(lines) == 4, "Four orbit lines") + need(all((a & b).bit_count() % 2 == (i == j) + for i, a in enumerate(lines) for j, b in enumerate(lines)), + "Actual orthonormal quadruple") + ranks.append(len(basis([lines[0] ^ q for q in lines[1:]]))) + need(ranks == [3] * 32, "All actual difference ranks") + cases = 0 + for n in range(1, 5): + points = list(range(1, 1 << n)) + for size in range(1, min(4, len(points)) + 1): + for chosen in combinations(points, size): + common_gauge(n, list(chosen)) + cases += 1 + columns, r = common_gauge(4, [1, 2, 4, 8]) + need(r == 3, "Canonical rank-three gauge") + events = [("P", inverse(columns), 0)] + for i in range(r): + events.extend([("S", 1 << i, 1), ("C", 1 << i, 1), ("S", 1 << i, 1)]) + events.append(("P", columns, 0)) + adjoint = [(kind, inverse(arg) if kind == "P" else arg, -sign) + for kind, arg, sign in reversed(events)] + monomials = [] + for i in range(4): + a, b = 1 << i, 1 << ((i + 1) % 4) + history = adjoint + [("C", b, -1), ("C", a, 1)] + events + table = [] + for x in range(16): + state, power = exact_state(history, x) + need(power == 0 and len(state) == 1, "Exact monomial column") + y, phase = next(iter(state.items())) + need(phase in [(1, 0), (0, 1), (-1, 0), (0, -1)], "Gaussian-unit phase") + table.append([y, [(1, 0), (0, 1), (-1, 0), (0, -1)].index(phase)]) + need(len({y for y, _ in table}) == 16, "Exact address bijection") + monomials.append(table) + receipt = { + "status": "PASS_EXACT_COMMON_GAUGE_RANK", + "actual_source_sha256": SOURCE_SHA, + "parallel_derivation_sha256": PREDECESSOR_SHA, + "actual_orbits": len(ranks), + "actual_difference_ranks": ranks, + "small_exact_symplectic_cases": cases, + "canonical_gauge_native_rank": r, + "canonical_basis_columns": columns, + "canonical_exact_monomials": monomials, + "scope": "A single common cover Clifford conjugation. Joint field circuits remain outside this theorem.", + } + output = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (HERE / "CHECKS.json").write_bytes(output) + print(receipt["status"]) + print("receipt_sha256=" + sha256(output).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json new file mode 100644 index 0000000000..3924fe2465 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json @@ -0,0 +1,27210 @@ +{ + "affected_ports": [ + 0, + 2, + 7, + 9, + 10, + 11, + 13, + 14, + 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The coded response K=C E C is supported within the +actual q+R phase classes, where R=span(30,45,75,384). + +In a class-preserving pair basis, C acts on only 56 fields and is +identity on the other 56. The capture and its inverse use no odd +division, owned field, or native child inside a common scalar frame. +Their literal cost is 4044 old real scalar units in each direction. + +In the rank-four carried frame W_R, the phase-class reduction gives +an exact factorization of Q C Q^-1 with 112 rank-one phase calls. +This is a conditional factorization count. This packet does not +emit the physical phase recipes or admit the carried frame in a +complete supplier. The current W45 exit is a different frame. + +## Actual response and phase classes + +The source response is E=H^-1 E_mode H. H is the frozen physical +pair code. E_mode is the direct sum of eight signed six-mode blocks +and eight signed eight-mode blocks I-dd^T. + +The actual labels form fourteen q+R classes, each of size eight. +H preserves these classes. Every six-mode block meets three classes +in two ports each. Every eight-mode block meets four classes in two +ports each. The checker verifies these statements from the pinned +source labels and signs. + +Choose the first class of each group in numeric coset order. The +pair order follows the source group's port order. Write its two +ports as p and t. All formulas below use the actual signs d_i. + +## Six-mode block + +Define vectors a and b by + +```text +a_p=2d_p, a_t=0, +b_p=3d_p, b_t=-d_t, +``` + +with all other entries zero. Set + +```text +u=a-d, +v=(d-b)/4, +S=I+u v^T. +``` + +Then + +```text +v^T d=1, v^T u=-2, +S d=a, b^T S=d^T, +b^T a=6. +``` + +The second identity gives S^2=I. All entries are dyadic and +det(S)=-1. Thus S is a unit over Z[1/2]. It follows that + +```text +S(I-dd^T)S = I-ab^T. +``` + +The changed part is wholly inside the chosen phase-class pair. +On that pair it is + +```text +[-5, 2 d_p d_t] +[ 0, 1]. +``` + +The centre information remains available as the within-class +functional b^T(Sx)=d^T x. It is not asserted to be one original +physical field. + +## Eight-mode block + +Let e equal d on the chosen pair and zero elsewhere. Put + +```text +u=2e-d, +v=-u/4, +S=I+u v^T. +``` + +Now u^T u=8, so v^T u=-2 and S^2=I. Also S d=2e. Hence + +```text +S(I-dd^T)S = I-4ee^T. +``` + +This changed part is also confined to the chosen phase-class pair. +It has eigenvalues -7 and 1 on that pair. Again S is a dyadic unit +with determinant -1. + +## Active pair coordinates + +For each same-class pair use the signed rotation coordinates + +```text +s = d_p x_p+d_t x_t, +t = -d_p x_p+d_t x_t. +``` + +This convention makes t the negative signed difference. The pair +matrix is a dyadic unit. Let P be the direct sum of all 56 pair +matrices. + +For a six-mode group, P S P^-1 reads and changes only the chosen +pair's difference and the other two pairs' sums. In that order, + +```text +u_reduced = (-2,-2,-2), +v_reduced = (1/2,1/4,1/4), +S_reduced = I+u_reduced v_reduced^T. +``` + +The chosen pair's sum is passive. Each other difference is passive. +For an eight-mode group, only the four sums are active, with + +```text +u_reduced = (1,-1,-1,-1), +v_reduced = (-1/2,1/2,1/2,1/2). +``` + +All four differences are passive. The total number of active fields +is 8*3+8*4=56. Each global phase class contains four active fields. +The exact active role list is in the payload. + +Put T=P H. Both P and H preserve the global phase classes. The +complete physical code is + +```text +C = H^-1 S H + = T^-1 S_reduced T, +C^-1=C. +``` + +The physical response K=C E C remains supported within the global +phase classes because H preserves them. The complete capture has +rank(C-I)=16 and determinant 1. + +## Literal scalar word + +The reduced blocks have an in-place word with no extra field. +For any of the reduced vectors u and v, choose its first active +field p. Let R perform + +```text +x_i -= (u_i/u_p)x_p for all other active i. +``` + +Then R u=u_p e_p, and + +```text +R S_reduced R^-1 + = I+u_p e_p(v^T R^-1). +``` + +Only its p-th row changes. Its p-th diagonal entry is -1, and +its other entries in that row are u_p v_i. Apply R, multiply +x_p by -1, add u_p v_i x_i into x_p, and apply R^-1. + +The six-mode reduced word has four unit ADDs, two half ADDs, +and one sign SCALE. It costs 4*8+2*10+2=54 old real units. +The eight-mode reduced word has six unit ADDs, three half ADDs, +and one sign SCALE. It costs 6*8+3*10+2=80. + +The complete word executes H, P, the reduced code, P^-1, and +H^-1. Its exact invoice is + +| Part | Old real scalar units | +| --- | ---: | +| H | 470 | +| P | 1016 | +| Reduced code | 1072 | +| Complete capture | 4044 | +| Literal inverse capture | 4044 | + +All event coefficients are dyadic. Every SCALE is a signed power +of two. There are no fixed odd multiplication or division events. +Both complete words have maximum prefix row one-norm 10 and +maximum binary denominator height three. + +The checker verifies all 640 output rows. It leaves the other +528 fields arbitrary and unchanged. It also verifies C^2=I, +the exact conjugation of the actual response, and rank(C-I)=16. +No zero-input, helper, or restoration premise is used. + +The class-supported additive maps + +```text +(X,Y) -> (X,Y+KX), +(X,Y) -> (X-KY,Y) +``` + +each have a complete 1544-unit scalar ADD word. These are different +from applying K in place on one bank. The source E is symmetric, +so encoding both banks by the same C gives these two maps. The +second response is -K, not -K^T. A transpose-dual interface is a +separate choice. + +K itself has determinant 35^8. Its inverse requires the old +response's factors five and seven. This packet does not claim a +dyadic in-place implementation of K^-1. + +## Phase factorization and limits + +Work in the rank-four frame W_R and write Q' for W_R Q W_R^-1. +Choose one global anchor phase D_g in each class. Define + +```text +A_i=Q'_i D_g^-1. +``` + +All A_i are monomial in this frame. The anchor phases have Fourier +rank one. These are consequences of the frozen common-gauge +geometry: q_i+q_anchor lies in R, whereas each anchor is odd and +therefore is not in the even space R. + +Let D repeat the anchor on every field in its class. Then Q'=A D. +Since T preserves classes, + +```text +Q' C Q'^-1 + = A T^-1 [D_active S_reduced D_active^-1 direct-sum I] T A^-1. +``` + +There are exactly 56 inverse anchor calls and 56 forward anchor +calls. Both alignment passes have at most 112 monomial maps. +Each native rank-one factor can require its two side maps; the +corresponding upper bound is 224 side maps. The scalar word keeps +its full 4044-unit invoice. + +No phase is dropped in this identity. The anchor and alignment +operators retain their ordered definitions at every tensor width. +This packet emits their directions and the pinned W circuit, but +does not emit their monomial or native phase recipes. Those +recipes, legal caller access, and recursive child costs must be +checked before this factorization becomes a native caller word. + +The inverse capture has the same active set and the same alignment. +Negative conjugation uses inverse anchors and the corresponding +inverse alignments. These are monomial here because all original +directional phases commute. The statement need not hold for a +general noncommuting phase family without that extra premise. + +For a transported inverse code Q' C^-1 Q', retain the right factor +Q'^2. It can be composed into the first alignment only as an +explicit declared monomial map. It is not an omitted free factor. + +Since K preserves classes, D K=K D and + +```text +Q' K Q'^-1 = A K A^-1. +``` + +Its additive use is therefore native-free in this frame, with the +scalar and monomial maps still charged. + +The current changed supplier uses the rank-one W45 exit. It does +not supply W_R for free. The complete four-pair compression of one +actual orthonormal eight-clique already requires a rank-four common +gauge: its four disjoint pair-difference vectors are independent. +The reviewed common-gauge theorem therefore gives rank at least +four for a gauge that makes all four ratios monomial. This is a +limit of this pair compression, not a general decoder lower bound. + +Preparing or removing W_R, changing native endpoints, routed code +matching, source access, helper progress, terminal output, and the +full recursive cost remain separate. No complete supplier or +kappa improvement is claimed. + +## Evidence and credit + +Run with one CPU from the workspace root: + +```text +python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/emit_capture.py --out NEW_DIRECTORY +python3 -O work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/emit_capture.py --out ANOTHER_NEW_DIRECTORY +``` + +The required status is `PASS_DYADIC_PHASE_CLASS_CAPTURE`. +Both payloads and both receipts must have identical bytes. +Only `verified-normal` and `verified-optimized` are final evidence. +Earlier directories retain the prior difference orientation or a +run made before the explicit source-symmetry check. + +The source pins bind the actual rank-sixteen response, cyclic pair +geometry, and common-root gauge. This construction uses the +coordinator's phase-class reduction, the bridge capture work, and +the campaign's pair-code and gauge results. The asymmetric +six-mode involution and selected-difference reduction were derived +in this lane. This is a producer packet; distinct review remains +required. AI assistance was used. + +No PR, push, commit, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/FREEZE.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/FREEZE.json new file mode 100644 index 0000000000..747ff6c2bd --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "DYADIC-CAPTURE.md": "8837bf1531d215782338db3764c266c36ad129681211ccbd4732542131b4bc42", + "REPRODUCTION.json": "777ecf5a51cf05ae4deb2b9fd450e50f2d4098fbd7fb799ea96761aefa0c7667", + "emit_capture.py": "4fae86c5b2a2f1a607872b866034ec3ad54201f8609537a4af11872dc7ac6b6d", + "verified-normal/CAPTURE-PROGRAM.json": "35f42a141b1ed4bfed08c5ad2c403e57866bf34cf17f354cb92e351b44eb896e", + "verified-normal/CHECKS.json": "9267688504593fe2cf918cde0aa60e1550abdec922db30885d4d3fb042c138ed", + "verified-optimized/CAPTURE-PROGRAM.json": "35f42a141b1ed4bfed08c5ad2c403e57866bf34cf17f354cb92e351b44eb896e", + "verified-optimized/CHECKS.json": "9267688504593fe2cf918cde0aa60e1550abdec922db30885d4d3fb042c138ed" + }, + "independent_review": "required", + "scope": "Actual dyadic capture and class-supported additive response. Conditional112 native phase factorization in W_R; no compiled phase recipes or complete supplier.", + "status": "FROZEN_DYADIC_PHASE_CLASS_CAPTURE_PRODUCER" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/REPRODUCTION.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..4ece7e3024 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/REPRODUCTION.json @@ -0,0 +1,11 @@ +{ + "files": { + "CAPTURE-PROGRAM.json": "35f42a141b1ed4bfed08c5ad2c403e57866bf34cf17f354cb92e351b44eb896e", + "CHECKS.json": "9267688504593fe2cf918cde0aa60e1550abdec922db30885d4d3fb042c138ed" + }, + "final_directories": [ + "verified-normal", + "verified-optimized" + ], + "status": "PASS_BYTE_IDENTICAL_NORMAL_AND_OPTIMIZED" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/emit_capture.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/emit_capture.py new file mode 100644 index 0000000000..8ddf27a4d9 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/emit_capture.py @@ -0,0 +1,298 @@ +#!/usr/bin/env python3 +"""Build a dyadic capture with one active field in each group class.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +OLD = LANES / "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz" +OLD_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" +PINS = { + "independent-review-20261017/route32-capture-review-20261020/check_review.py": + "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89", + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": + "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd", + "independent-review-20261017/common-gauge-rank-20261020/FREEZE.json": + "9523bfe7aaa2a1430d146727a328b03cf90f0ff4965dfdc2bc2640a58d92de57", +} +W_SOURCE = LANES / "controller-followthrough-20261017/shared-root-eight-20261020/v2-normal/PROGRAM.json.gz" +W_PIN = "71dec1d8e33625e301c8bfde37d8c08b0019124e1525500555fcc704530bf4a6" + + +def need(test, label): + if not test: + raise ValueError(label) + + +def encoded(rows): + return [{str(j): str(c) for j, c in sorted(row.items()) if c} for row in rows] + + +def price(word): + total = 0 + for kind, target, origin, text in word: + c = F(text) + a, b = abs(c.numerator), c.denominator + need(c and b & (b - 1) == 0, "Dyadic nonzero gate") + need(0 <= target < 224, "Actual target") + if kind == "add": + need(isinstance(origin, int) and 0 <= origin < 224 and origin != target, + "Distinct actual source") + total += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + else: + need(kind == "scale" and origin is None and a & (a - 1) == 0, + "Power-of-two unit scale") + total += 2 * (abs(a.bit_length() - b.bit_length()) + int(c < 0)) + return total + + +def pair_word(ports, matrix): + p, q = ports + a, b = matrix[0] + c, d = matrix[1] + need(d == -a * b * c and all(abs(v) == 1 for row in matrix for v in row), + "Signed pair factor") + word = [] if a == 1 else [["scale", p, None, str(a)]] + return word + [["add", p, q, str(b)], ["scale", q, None, str(2 * d)], + ["add", q, p, str(c * a)]] + + +def rank_one_word(ports, u, v): + p = ports[0] + need(1 + sum(a * b for a, b in zip(u, v)) == -1, "Rank-one involution") + word = [["add", port, p, str(-a / u[0])] for port, a in zip(ports[1:], u[1:])] + word += [["scale", p, None, "-1"]] + word += [["add", p, port, str(u[0] * b)] for port, b in zip(ports[1:], v[1:])] + word += [["add", port, p, str(a / u[0])] for port, a in zip(ports[1:], u[1:])] + return word + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for path, pin in PINS.items(): + need(sha256((LANES / path).read_bytes()).hexdigest() == pin, "Source pin " + path) + helper_path = LANES / next(p for p in PINS if p.endswith("check_review.py")) + spec = importlib.util.spec_from_file_location("review_algebra", helper_path) + r = importlib.util.module_from_spec(spec) + spec.loader.exec_module(r) + old_raw = gzip.decompress(OLD.read_bytes()) + need(sha256(old_raw).hexdigest() == OLD_PIN, "Rank16 source") + old = json.loads(old_raw)["model"] + w_raw = gzip.decompress(W_SOURCE.read_bytes()) + need(sha256(w_raw).hexdigest() == W_PIN, "Common-root frame") + w_data = json.loads(w_raw) + cyclic = json.loads((LANES / next(p for p in PINS if p.endswith("CYCLIC-FLAGS.json"))).read_text()) + geometry = json.loads((LANES / next(p for p in PINS if p.endswith("GEOMETRY.json"))).read_text()) + q = old["ports"] + need(q == cyclic["ports"] == geometry["q_labels"], "Actual source directions") + root = set(geometry["common_even_isotropic_space"]) + need(root == r.binary_span([30, 45, 75, 384]) and len(root) == 16, "Root space") + classes = [min(v ^ z for z in root) for v in q] + need(Counter(Counter(classes).values()) == {8: 14}, "Fourteen actual classes") + anchors = {c: min(q[p] for p in range(112) if classes[p] == c) for c in set(classes)} + need(all(q[p] ^ anchors[classes[p]] in root and q[p].bit_count() % 2 + for p in range(112)), "Monomial ratio directions and rank-one anchors") + h_word = [] + for pair in cyclic["pair_codes"]: + h_word += pair_word(pair["ports"], pair["matrix"]) + need(len({classes[p] for p in pair["ports"]}) == 1, "H preserves global classes") + + def h_apply(x, inverse=False): + y = list(x) + for item in cyclic["pair_codes"]: + ps, h = item["ports"], item["matrix"] + for i, p in enumerate(ps): + y[p] = sum((F(h[j][i], 2) if inverse else F(h[i][j])) * x[ps[j]] + for j in range(2)) + return y + + source_groups = [(item["ordered_carriers_a_b_c"], item["signs"], "large") + for item in old["vertex_assignments"]] + source_groups += [(ps, [1] * len(ps), "small") for ps in old["small_cliques"]] + groups, t_word, core_word, active = [], [], [], [] + for index, (ps, signs, kind) in enumerate(source_groups): + k = len(ps) + need(k == (6 if kind == "large" else 8), "Group size") + sign = dict(zip(ps, signs)) + pairs = [[p for p in ps if classes[p] == c] for c in sorted({classes[p] for p in ps})] + need(all(len(pair) == 2 for pair in pairs), "Two fields per group class") + for pair in pairs: + a, b = [sign[p] for p in pair] + t_word += pair_word(pair, [[a, b], [-a, b]]) + selected = pairs[0] + a, b = {p: F(0) for p in ps}, {p: F(0) for p in ps} + if k == 6: + a[selected[0]] = 2 * sign[selected[0]] + b[selected[0]] = 3 * sign[selected[0]] + b[selected[1]] = -sign[selected[1]] + u = {p: a[p] - sign[p] for p in ps} + v = {p: (F(sign[p]) - b[p]) / 4 for p in ps} + active_ports = [selected[1]] + [pair[0] for pair in pairs[1:]] + small_u = list(map(F, [-2, -2, -2])) + small_v = [F(1, 2), F(1, 4), F(1, 4)] + else: + for p in selected: + a[p] = 2 * sign[p] + b[p] = 2 * sign[p] + u = {p: (sign[p] if p in selected else -sign[p]) for p in ps} + v = {p: -F(u[p], 4) for p in ps} + active_ports = [pair[0] for pair in pairs] + small_u = list(map(F, [1, -1, -1, -1])) + small_v = [F(-1, 2)] + [F(1, 2)] * 3 + need(sum(v[p] * u[p] for p in ps) == -2, "Actual involution") + need(sum(v[p] * sign[p] for p in ps) == 1, "Actual centre input") + need(all(sign[p] + u[p] == a[p] for p in ps), "Actual centre image") + need(sum(b[p] * a[p] for p in ps) == k, "Correct eigenvalue") + need(all(b[p] + sum(b[t] * u[t] for t in ps) * v[p] == sign[p] for p in ps), + "Actual centre output covector") + local = rank_one_word(active_ports, small_u, small_v) + need(price(local) == (54 if k == 6 else 80), "Reduced scalar cost") + core_word += local + active += active_ports + groups.append({"index": index, "kind": kind, "ports": ps, "signs": signs, + "pairs": pairs, "selected_pair": selected, + "active_ports": active_ports, + "active_selected_type": "negative_signed_difference" if k == 6 else "sum", + "u": {str(p): str(u[p]) for p in ps}, + "v": {str(p): str(v[p]) for p in ps}, + "a": {str(p): str(a[p]) for p in ps if a[p]}, + "b": {str(p): str(b[p]) for p in ps if b[p]}, + "reduced_u": list(map(str, small_u)), "reduced_v": list(map(str, small_v)), + "core_word": local}) + need(len(active) == len(set(active)) == 56, "Exactly56 active fields") + need(Counter(classes[p] for p in active) == {c: 4 for c in set(classes)}, "Four active fields per global class") + passive = sorted(set(range(112)) - set(active)) + hi_word, ti_word = r.inverse_word(h_word), r.inverse_word(t_word) + word = h_word + t_word + core_word + ti_word + hi_word + inverse = r.inverse_word(word) + + def s_apply(x): + y = list(x) + for group in groups: + u, v = {int(p): F(c) for p, c in group["u"].items()}, {int(p): F(c) for p, c in group["v"].items()} + query = sum(v[p] * x[p] for p in group["ports"]) + for p in group["ports"]: + y[p] += u[p] * query + return y + + def capture(x): + return h_apply(s_apply(h_apply(x)), True) + + def k_apply(x): + z = h_apply(x) + y = list(z) + for group in groups: + a, b = {int(p): F(c) for p, c in group["a"].items()}, {int(p): F(c) for p, c in group["b"].items()} + query = sum(c * z[p] for p, c in b.items()) + for p, coefficient in a.items(): + y[p] -= coefficient * query + return h_apply(y, True) + + c_rows = r.rows_from_columns([capture(r.unit(112, j)) for j in range(112)]) + k_rows = r.rows_from_columns([k_apply(r.unit(112, j)) for j in range(112)]) + e_rows = r.sparse(old["response"]) + need(all(e_rows[p].get(t, F(0)) == e_rows[t].get(p, F(0)) + for p in range(112) for t in range(112)), "Original response symmetry") + for j in range(112): + x = r.unit(112, j) + need(capture(capture(x)) == x, "C involution columns") + need(capture(r.apply(e_rows, capture(x))) == k_apply(x), "Exact coded response columns") + need(all(classes[p] == classes[t] for p, row in enumerate(k_rows) for t in row), + "K is supported in global phase classes") + delta = [dict(row) for row in c_rows] + for p, row in enumerate(delta): + r.add(row, p, F(-1)) + need(r.eliminate(delta, 112)[0] == 16, "Rank16 physical capture displacement") + need(r.eliminate(c_rows, 112)[1] == 1, "Physical capture determinant") + for i in range(640): + expected = {(p, 0): coefficient for p, coefficient in c_rows[i].items()} if i < 112 else {(i, 0): F(1)} + need(r.reverse_output(word, i) == r.reverse_output(inverse, i) == expected, + "All640 capture outputs and inverse outputs") + need(r.reverse_output(word + word, i) == {(i, 0): F(1)}, "All640 involution outputs") + if i in passive or i >= 112: + need(r.reverse_output(core_word, i) == {(i, 0): F(1)}, "Passive coordinate identity") + for i in range(112): + original = r.reverse_output(h_word, i) + need(all(classes[p] == classes[i] for p, _ in original), "H literal class support") + original = r.reverse_output(t_word, i) + need(all(classes[p] == classes[i] for p, _ in original), "T literal class support") + selected_differences = {group["selected_pair"][1] for group in groups if group["kind"] == "large"} + need(len(selected_differences) == 8 and selected_differences <= set(active), + "All eight selected differences are active") + mutation = [event for event in core_word if event[1] != min(selected_differences)] + need(any(r.reverse_output(mutation, i) != r.reverse_output(core_word, i) for i in range(112)), + "Reject loss of an active selected difference") + + additive = [["add", 112 + p, t, str(coefficient)] + for p, row in enumerate(k_rows) for t, coefficient in sorted(row.items())] + subtractive = [["add", p, 112 + t, str(-coefficient)] + for p, row in enumerate(k_rows) for t, coefficient in sorted(row.items())] + for i in range(640): + forward = {(i, 0): F(1)} + backward = {(i, 0): F(1)} + if 112 <= i < 224: + forward.update({(p, 0): coefficient for p, coefficient in k_rows[i - 112].items()}) + if i < 112: + backward.update({(112 + p, 0): -coefficient for p, coefficient in k_rows[i].items()}) + need(r.reverse_output(additive, i) == forward and r.reverse_output(subtractive, i) == backward, + "All640 coded additive maps") + bills = {name: price(events) for name, events in + [("H", h_word), ("T", t_word), ("core", core_word), ("capture", word), + ("inverse", inverse), ("coded_forward", additive), ("coded_backward", subtractive)]} + need(bills["capture"] == bills["inverse"] + == 2 * bills["H"] + 2 * bills["T"] + bills["core"], "Complete capture invoice") + bounds = {"capture": r.prefix_bounds(word), "inverse": r.prefix_bounds(inverse)} + packet = { + "schema": "dyadic-phase-class-capture-v1", "ports": q, + "root_basis": [30, 45, 75, 384], "root_space": sorted(root), + "phase_classes": classes, "global_anchors": anchors, "W": w_data["W"], + "groups": groups, "active_ports": active, "passive_ports": passive, + "H_word": h_word, "T_word": t_word, "reduced_word": core_word, + "capture_word": word, "inverse_word": inverse, + "coded_forward_word": additive, "coded_backward_word": subtractive, + "capture": encoded(c_rows), "coded_response": encoded(k_rows), + "source_response": old["response"], "source_inverse": old["response_inverse"], + "invoices": bills, "prefix_bounds": bounds, + "phase_conjugation_contract": { + "gauge": "rank4 W_R", + "active_forward_phase_calls": 56, "active_inverse_phase_calls": 56, + "native_mass": 112, "alignment_maps": 224, + "native_side_map_upper_bound": 224, + "compiled_phase_recipes": False, + "scope": "Exact ordered factorization. This packet does not emit native phase recipes or establish a routed caller.", + }, + } + data = (json.dumps(packet, sort_keys=True, separators=(",", ":")) + "\n").encode() + (args.out / "CAPTURE-PROGRAM.json").write_bytes(data) + receipt = { + "status": "PASS_DYADIC_PHASE_CLASS_CAPTURE", "source_pins": PINS, + "source_response_raw_sha256": OLD_PIN, "W_source_raw_sha256": W_PIN, + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_sha256": sha256(data).hexdigest(), "invoices": bills, + "prefix_bounds": bounds, "arbitrary_field_outputs": 640, "unchanged_fields": 528, + "active_fields": 56, "passive_fields": 56, "physical_capture_displacement_rank": 16, + "capture_determinant": "1", "capture_inverse": "capture", + "global_phase_classes": 14, "phase_native_mass_in_W_R": 112, + "phase_recipes_emitted": False, "odd_divisions_or_multiplications_in_capture": 0, + "scope": "Actual dyadic scalar capture and class-supported coded additive response. Rank4 carried gauge, compiled phase maps, routing, and recursive closure are separate obligations.", + } + raw = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (args.out / "CHECKS.json").write_bytes(raw) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/verified-normal/CAPTURE-PROGRAM.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/verified-normal/CAPTURE-PROGRAM.json new file mode 100644 index 0000000000..993d7310da --- /dev/null +++ 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diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/verified-optimized/CHECKS.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/verified-optimized/CHECKS.json new file mode 100644 index 0000000000..1301b87d73 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-dyadic-capture-20261020/verified-optimized/CHECKS.json @@ -0,0 +1,44 @@ +{ + "W_source_raw_sha256": "71dec1d8e33625e301c8bfde37d8c08b0019124e1525500555fcc704530bf4a6", + "active_fields": 56, + "arbitrary_field_outputs": 640, + "capture_determinant": "1", + "capture_inverse": "capture", + "global_phase_classes": 14, + "invoices": { + "H": 470, + "T": 1016, + "capture": 4044, + "coded_backward": 1544, + "coded_forward": 1544, + "core": 1072, + "inverse": 4044 + }, + "odd_divisions_or_multiplications_in_capture": 0, + "passive_fields": 56, + "payload_sha256": "35f42a141b1ed4bfed08c5ad2c403e57866bf34cf17f354cb92e351b44eb896e", + "phase_native_mass_in_W_R": 112, + "phase_recipes_emitted": false, + "physical_capture_displacement_rank": 16, + "prefix_bounds": { + "capture": { + "binary_height": 3, + "maximum_row_one_norm": "10" + }, + "inverse": { + "binary_height": 3, + "maximum_row_one_norm": "10" + } + }, + "producer_sha256": "4fae86c5b2a2f1a607872b866034ec3ad54201f8609537a4af11872dc7ac6b6d", + "scope": "Actual dyadic scalar capture and class-supported coded additive response. Rank4 carried gauge, compiled phase maps, routing, and recursive closure are separate obligations.", + "source_pins": { + "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd", + "independent-review-20261017/common-gauge-rank-20261020/FREEZE.json": "9523bfe7aaa2a1430d146727a328b03cf90f0ff4965dfdc2bc2640a58d92de57", + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "independent-review-20261017/route32-capture-review-20261020/check_review.py": "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89" + }, + "source_response_raw_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "status": "PASS_DYADIC_PHASE_CLASS_CAPTURE", + "unchanged_fields": 528 +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/FREEZE.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/FREEZE.json new file mode 100644 index 0000000000..aa010c2c0f --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/FREEZE.json @@ -0,0 +1,12 @@ +{ + "files": { + "REPRODUCTION.md": "b0b7d12edf3a48dc25e9e6e7fab85611ca0c56898b28f8b7391e6ff095d4111f", + "REVIEW.md": "f89a17a852489fbf79840f41df72ff7d65fcd6cea44cc21f355de369a0cee99e", + "check_review.py": "c732e8112effaf9293e6c128a9022b9ace2555b11d92cfde0521ec61b23670ed", + "verified-normal/CHECKS.json": "ceaa82288bfd62c9dfe5a784dc3ad20035d39e76d44bd18b60c90dc9b6a3967f", + "verified-optimized/CHECKS.json": "ceaa82288bfd62c9dfe5a784dc3ad20035d39e76d44bd18b60c90dc9b6a3967f" + }, + "normal_optimized_byte_identical": true, + "scope": "General ordered theorem and actual rational scalar baseline. No native phase recipes or complete caller.", + "status": "PASS_INDEPENDENT_PHASE_CLASS_REDUCTION_REVIEW" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REPRODUCTION.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REPRODUCTION.md new file mode 100644 index 0000000000..ba332e2fa1 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REPRODUCTION.md @@ -0,0 +1,23 @@ +# Reproduction + +Run from `/Users/aliromman/Projects/IntegerMultiplicationBounds`. +Use one process at a time. Each output directory must be new. + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/check_review.py --out NEW_NORMAL_DIRECTORY +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/check_review.py --out NEW_OPTIMIZED_DIRECTORY +``` + +Each command must print: + +```text +PASS_INDEPENDENT_PHASE_CLASS_REDUCTION_BASELINE +``` + +The two `CHECKS.json` files must be equal byte for byte. The final +retained runs are `verified-normal` and `verified-optimized`. The earlier +`normal` and `optimized` directories are draft checks before the literal +active-coordinate factorization and the final source freeze were added. + +The checker uses explicit failure conditions. The optimized run does not +remove them. Exact arithmetic uses `fractions.Fraction`. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REVIEW.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REVIEW.md new file mode 100644 index 0000000000..d8c0ce1733 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/REVIEW.md @@ -0,0 +1,136 @@ +# Independent review of the phase-class reduction + +Status: PASS within the stated scope. + +This review binds the root proof to +`PHASE-CLASS-CAPTURE-FREEZE-20261020.json`, SHA-256 +`eab4612fa42657ae663a652d9ea5afdfb8205ce5c17a706d7559c19e31ba0d6c`. +The proof hash is +`dacaf9624bb8ec32fd473570380988bacb7369126c3fe4c9fdf1afd67275ba43`. +The final source change only states the status of the separate dyadic +packet. It does not change the reviewed equations or scalar words. + +## Ordered proof + +Let the field space be a direct sum of copies of an arbitrary spatial +vector space. Use one anchor operator `Z_g` for each global phase class. +Let `Z` repeat that anchor on the class, and put `A=Q Z^-1`. Assume that +each field map in `A` is an admitted monomial map. A scalar matrix `T` +that preserves each class commutes with `Z`. This follows entry by entry: +the left and right anchor on every nonzero entry of `T` are equal. + +For `C=T^-1 S T`, direct multiplication gives + +```text +Q C Q^-1 + = A Z T^-1 S T Z^-1 A^-1 + = A T^-1 (Z S Z^-1) T A^-1. +``` + +If `S` reads and changes only the active set `J`, its passive block is +identity and both off-diagonal blocks are zero. Therefore +`Z S Z^-1 = Z_J S_J Z_J^-1 direct-sum I`. This proves equation (1). +It uses no commutation between `A` and any scalar code. It applies to +arbitrary input fields and does not use an owned zero field. + +The same factorization with `S_J^-1` gives the inverse. It uses the same +alignment maps. If every anchor and inverse anchor has an admitted +rank-one implementation, the factorization has `2|J|` native children. +This statement does not pay for the scalar words, alignment maps, entry +frame, or exit frame. + +If `K` preserves each class, then `ZK=KZ`. Thus +`Q K Q^-1 = A K A^-1`, which proves equation (2). This is an operator +identity. An implementation of `K` still needs a valid arithmetic word. +In particular, an additive coupler and an in-place nonunit matrix are +different services. + +These arguments do not use a spatial dimension. They therefore prove +the stated identities at every width, subject to the same typed map +premises. + +For the transported inverse, the exact order is + +```text +Q C^-1 Q = (Q C^-1 Q^-1) Q^2. +``` + +The rightmost `Q^2` acts first. If it is an admitted translation, the +first alignment can be the ordered product `A^-1 Q^2`. No factor is +moved through another factor in this step. + +## Resolved proof finding + +The original negative-conjugation statement needed an extra premise. +The fact that `Q_i Z_g^-1` is monomial does not in general imply that +`Q_i^-1 Z_g` is monomial. For example, let + +```text +Z = [[1, 1], [1, -1]], A = diag(1, i), Q = A Z. +``` + +Then `Q Z^-1=A` is monomial, but `Q^-1 Z=Z^-1 A^-1 Z` is dense. +The final proof requires the new alignments explicitly. In the actual +directional-phase case the phases commute, so those maps are `A_i^-1`. +The final proof states this restriction. The finding is resolved. + +## Independent scalar check + +The checker imports one pinned matrix helper from an earlier independent +review. It does not import the root producer or its matrix, replay, or +invoice functions. It reads the frozen rank-sixteen response and the +frozen physical pair code. + +From those inputs it reconstructs the eight signed blocks of size six +and the eight blocks of size eight. It also reconstructs the fourteen +actual `q+R` classes for `R=span(30,45,75,384)`. Each class has eight +ports. The physical pair code preserves these classes. + +For each source block the checker forms + +```text +u = 2e-d, v = 2d/k-e/2, S = I+u v^T +``` + +and derives the inverse with the rank-one inverse formula. It checks +`1+v^T u=2(4-k)/k`, both inverse orders, and all 112 columns of the +physical capture and the response conjugation. The coded response has +no nonzero coefficient between distinct phase classes. + +A distinct reverse-output interpreter checks the literal forward and +inverse words on all 640 arbitrary field inputs. It checks all 528 +unchanged roles and the concatenated restoration word. It does not +infer these results from the producer receipt. + +The same interpreter reconstructs the literal reduction `T`, its +inverse, and the reduced word. All 112 columns satisfy +`T C T^-1=S_reduced`. Exactly 56 coordinates are active. The passive +rows are identity, and the active rows do not read a passive input. + +The exact scalar invoices are: + +| Word | Old real scalar units | Extra real scans | Maximum prefix row one-norm | +| --- | ---: | --- | ---: | +| Capture | 4204 | 16 divisions by three | 12 | +| Inverse | 4204 | 16 multiplications by three | 12 | + +The odd scans are separate services. A dyadic matrix entry does not by +itself make a nonunit determinant available from old unit scalings. +The inverse scan invoice is therefore necessary in this baseline. + +## Scope + +The conditional 112-child count uses the rank-four frame for `R`. It +does not apply to the current rank-one `W45` exit. The root note records +the bridge lane's finding that all 56 proposed pair ratios have rank +two in that exit. This review does not repeat that physical phase audit. + +No native recipe, frame preparation, frame removal, helper completion, +routed caller, terminal decoder, or recursive supplier is verified here. +The review establishes the general ordered theorem and the actual +rational scalar baseline. The separate dyadic capture has its own +frozen packet and distinct peer review. + +AI assistance was used. No PR, push, or publication is authorized. +Before any PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/check_review.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/check_review.py new file mode 100644 index 0000000000..1e04349ec7 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/check_review.py @@ -0,0 +1,179 @@ +#!/usr/bin/env python3 +"""Check the rational phase-class baseline with reverse output rows.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +ROOT = LANES.parent / "root" +PINS = { + "PHASE-CLASS-CAPTURE-FREEZE-20261020.json": "eab4612fa42657ae663a652d9ea5afdfb8205ce5c17a706d7559c19e31ba0d6c", + "PHASE-CLASS-CAPTURE-20261020.md": "dacaf9624bb8ec32fd473570380988bacb7369126c3fe4c9fdf1afd67275ba43", + "check_phase_class_capture_20261020.py": "d50e84f8d23ddadee126028998b9cf870aa44f125f2a6bf408ad13515ac53725", + "phase-class-capture-final-normal/PAIRED-CODE.json": "830a19a100763700dfc5142cb9eca1c284d9ad92828c4f4e1fe69bdc84e55b9d", + "phase-class-capture-final-normal/CHECKS.json": "9e90c24848e296d030b329cb3c03884c6ab3022e284a1f7479e5c7f07809f3c6", +} +HELPER = LANES / "independent-review-20261017/route32-capture-review-20261020/check_review.py" +HELPER_PIN = "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89" +OLD = LANES / "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz" +OLD_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" +CYCLIC = LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json" +CYCLIC_PIN = "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + + +def need(test, label): + if not test: + raise ValueError(label) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for name, pin in PINS.items(): + need(sha256((ROOT / name).read_bytes()).hexdigest() == pin, "Root pin " + name) + need(sha256(HELPER.read_bytes()).hexdigest() == HELPER_PIN, "Independent helper pin") + need(sha256(CYCLIC.read_bytes()).hexdigest() == CYCLIC_PIN, "Pair source pin") + raw = gzip.decompress(OLD.read_bytes()) + need(sha256(raw).hexdigest() == OLD_PIN, "Response source pin") + old = json.loads(raw)["model"] + cyclic = json.loads(CYCLIC.read_text()) + source = json.loads((ROOT / "phase-class-capture-final-normal/PAIRED-CODE.json").read_text()) + spec = importlib.util.spec_from_file_location("independent_matrix", HELPER) + r = importlib.util.module_from_spec(spec) + spec.loader.exec_module(r) + groups = [(item["ordered_carriers_a_b_c"], item["signs"]) for item in old["vertex_assignments"]] + groups += [(ps, [1] * len(ps)) for ps in old["small_cliques"]] + need(groups == [(g["ports"], g["signs"]) for g in source["groups"]], "Actual block binding") + space = r.binary_span([30, 45, 75, 384]) + classes = [min(q ^ z for z in space) for q in old["ports"]] + need(source["classes"] == classes, "Actual phase classes") + + def pair(x, inverse=False): + y = list(x) + for record in cyclic["pair_codes"]: + ps, h = record["ports"], record["matrix"] + need(classes[ps[0]] == classes[ps[1]], "Physical pair class") + for i, p in enumerate(ps): + y[p] = sum((F(h[j][i], 2) if inverse else F(h[i][j])) * x[ps[j]] + for j in range(2)) + return y + + def formula(x, inverse=False): + z = pair(x) + y = list(z) + for (ps, d), record in zip(groups, source["groups"]): + selected = set(record["centre_pair"]) + need(len(selected) == 2 and len({classes[p] for p in selected}) == 1, "Centre class pair") + k = len(ps) + u = [F(sign * (2 * (p in selected) - 1)) for p, sign in zip(ps, d)] + v = [F(2 * sign, k) - F(sign * (p in selected), 2) for p, sign in zip(ps, d)] + delta = 1 + sum(a * b for a, b in zip(u, v)) + need(delta == F(2 * (4 - k), k) != 0, "Rank-one determinant") + query = sum(value * z[p] for p, value in zip(ps, v)) + factor = -1 / delta if inverse else 1 + for p, value in zip(ps, u): + y[p] += factor * value * query + return pair(y, True) + + rows = r.rows_from_columns([formula(r.unit(112, j)) for j in range(112)]) + inverse_rows = r.rows_from_columns([formula(r.unit(112, j), True) for j in range(112)]) + need(rows == r.sparse(source["code"]) and inverse_rows == r.sparse(source["inverse_code"]), + "Independent rational rank-one columns") + e, k = r.sparse(old["response"]), r.sparse(source["centre_response"]) + need(all(classes[p] == classes[t] for p, row in enumerate(k) for t in row), "Coded class support") + for j in range(112): + x = r.unit(112, j) + need(formula(formula(x), True) == formula(formula(x, True)) == x, "Both inverse orders") + need(formula(r.apply(e, formula(x, True))) == r.apply(k, x), "Actual response conjugation") + reports = {} + converted = {} + for name, key, expected in [("forward", "scalar_word", rows), + ("inverse", "inverse_scalar_word", inverse_rows)]: + old_units = divides = multiplies = 0 + events = [] + forward_rows = [{p: F(1)} for p in range(112)] + norm = F(1) + for kind, target, origin, text in source[key]: + c = F(text) + need(0 <= target < 112, "Actual target field") + if kind in ("fixed_divide", "fixed_multiply"): + need(origin is None and c == 3, "Fixed odd service") + divides += 2 * (kind == "fixed_divide") + multiplies += 2 * (kind == "fixed_multiply") + c = 1 / c if kind == "fixed_divide" else c + kind = "scale" + else: + a, b = abs(c.numerator), c.denominator + need(c and b & (b - 1) == 0, "Old dyadic event") + if kind == "add": + need(0 <= origin < 112 and origin != target, "Actual source field") + old_units += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + else: + need(kind == "scale" and origin is None and a & (a - 1) == 0, "Old unit scale") + old_units += 2 * (abs(a.bit_length() - b.bit_length()) + int(c < 0)) + events.append([kind, target, origin, str(c)]) + if kind == "scale": + forward_rows[target] = {p: value * c for p, value in forward_rows[target].items()} + else: + for p, value in forward_rows[origin].items(): + r.add(forward_rows[target], p, c * value) + norm = max(norm, sum(map(abs, forward_rows[target].values()), F(0))) + need(old_units == 4204 and norm == 12, "Full old invoice and prefix norm") + need((divides, multiplies) == ((16, 0) if name == "forward" else (0, 16)), "Odd service invoice") + for i in range(640): + want = {(p, 0): value for p, value in expected[i].items()} if i < 112 else {(i, 0): F(1)} + need(r.reverse_output(events, i) == want, "All640 reverse literal outputs") + converted[name] = events + reports[name] = {"old_scalar_units": old_units, "real_division_by_three_scans": divides, + "real_multiplication_by_three_scans": multiplies, "prefix_row_one_norm": str(norm)} + need(all(r.reverse_output(converted["forward"] + converted["inverse"], i) == {(i, 0): F(1)} + for i in range(640)), "All640 literal restoration outputs") + active = set(source["active_sum_carriers"]) + reduced = r.sparse(source["reduced_code"]) + need(len(active) == 56, "Active class sums") + need(all(row == {p: F(1)} for p, row in enumerate(reduced) if p not in active), "Passive identity") + need(all(set(reduced[p]) <= active for p in active), "No passive reads") + reduction_events = source["reduction_word"] + t = [{p: c for (p, mask), c in r.reverse_output(reduction_events, i).items() if mask == 0} + for i in range(112)] + ti = [{p: c for (p, mask), c in r.reverse_output(r.inverse_word(reduction_events), i).items() if mask == 0} + for i in range(112)] + need(t == r.sparse(source["reduction"]), "Literal reduction matrix") + need(all(classes[p] == classes[i] for i, row in enumerate(t) for p in row), + "Actual reduction preserves global classes") + reduced_events = [] + for kind, target, origin, text in source["reduced_code_word"]: + c = F(text) + if kind == "fixed_divide": + kind, c = "scale", 1 / c + elif kind == "fixed_multiply": + kind = "scale" + reduced_events.append([kind, target, origin, str(c)]) + for i in range(112): + want = {(p, 0): c for p, c in reduced[i].items()} + need(r.reverse_output(reduced_events, i) == want, "Literal reduced code") + x = r.unit(112, i) + need(r.apply(t, formula(r.apply(ti, x))) == r.apply(reduced, x), + "Actual active-coordinate factorization") + receipt = {"status": "PASS_INDEPENDENT_PHASE_CLASS_REDUCTION_BASELINE", + "root_pins": PINS, "helper_pin": HELPER_PIN, "old_response_pin": OLD_PIN, + "pair_pin": CYCLIC_PIN, "arbitrary_output_rows": 640, "unchanged_roles": 528, + "reports": reports, "active_fields": 56, + "scope": "General ordered proof and exact rational scalar baseline. No compiled physical phase recipes or caller admission."} + raw = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (args.out / "CHECKS.json").write_bytes(raw) + print(receipt["status"]) + print("receipt_sha256=" + sha256(raw).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/verified-normal/CHECKS.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/verified-normal/CHECKS.json new file mode 100644 index 0000000000..99291b1027 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/verified-normal/CHECKS.json @@ -0,0 +1,31 @@ +{ + "active_fields": 56, + "arbitrary_output_rows": 640, + "helper_pin": "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89", + "old_response_pin": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "pair_pin": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "reports": { + "forward": { + "old_scalar_units": 4204, + "prefix_row_one_norm": "12", + "real_division_by_three_scans": 16, + "real_multiplication_by_three_scans": 0 + }, + "inverse": { + "old_scalar_units": 4204, + "prefix_row_one_norm": "12", + "real_division_by_three_scans": 0, + "real_multiplication_by_three_scans": 16 + } + }, + "root_pins": { + "PHASE-CLASS-CAPTURE-20261020.md": "dacaf9624bb8ec32fd473570380988bacb7369126c3fe4c9fdf1afd67275ba43", + "PHASE-CLASS-CAPTURE-FREEZE-20261020.json": "eab4612fa42657ae663a652d9ea5afdfb8205ce5c17a706d7559c19e31ba0d6c", + "check_phase_class_capture_20261020.py": "d50e84f8d23ddadee126028998b9cf870aa44f125f2a6bf408ad13515ac53725", + "phase-class-capture-final-normal/CHECKS.json": "9e90c24848e296d030b329cb3c03884c6ab3022e284a1f7479e5c7f07809f3c6", + "phase-class-capture-final-normal/PAIRED-CODE.json": "830a19a100763700dfc5142cb9eca1c284d9ad92828c4f4e1fe69bdc84e55b9d" + }, + "scope": "General ordered proof and exact rational scalar baseline. No compiled physical phase recipes or caller admission.", + "status": "PASS_INDEPENDENT_PHASE_CLASS_REDUCTION_BASELINE", + "unchanged_roles": 528 +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/verified-optimized/CHECKS.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/verified-optimized/CHECKS.json new file mode 100644 index 0000000000..99291b1027 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/phase-class-reduction-review-20261020/verified-optimized/CHECKS.json @@ -0,0 +1,31 @@ +{ + "active_fields": 56, + "arbitrary_output_rows": 640, + "helper_pin": "c419f63a47d655c4d2a789cf52f0a00d5186cb7728cdd58aac73ceb21845aa89", + "old_response_pin": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "pair_pin": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "reports": { + "forward": { + "old_scalar_units": 4204, + "prefix_row_one_norm": "12", + "real_division_by_three_scans": 16, + "real_multiplication_by_three_scans": 0 + }, + "inverse": { + "old_scalar_units": 4204, + "prefix_row_one_norm": "12", + "real_division_by_three_scans": 0, + "real_multiplication_by_three_scans": 16 + } + }, + "root_pins": { + "PHASE-CLASS-CAPTURE-20261020.md": "dacaf9624bb8ec32fd473570380988bacb7369126c3fe4c9fdf1afd67275ba43", + "PHASE-CLASS-CAPTURE-FREEZE-20261020.json": "eab4612fa42657ae663a652d9ea5afdfb8205ce5c17a706d7559c19e31ba0d6c", + "check_phase_class_capture_20261020.py": "d50e84f8d23ddadee126028998b9cf870aa44f125f2a6bf408ad13515ac53725", + "phase-class-capture-final-normal/CHECKS.json": "9e90c24848e296d030b329cb3c03884c6ab3022e284a1f7479e5c7f07809f3c6", + "phase-class-capture-final-normal/PAIRED-CODE.json": "830a19a100763700dfc5142cb9eca1c284d9ad92828c4f4e1fe69bdc84e55b9d" + }, + "scope": "General ordered proof and exact rational scalar baseline. No compiled physical phase recipes or caller admission.", + "status": "PASS_INDEPENDENT_PHASE_CLASS_REDUCTION_BASELINE", + "unchanged_roles": 528 +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/CHECKS.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/CHECKS.json new file mode 100644 index 0000000000..12e7d759fe --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/CHECKS.json @@ -0,0 +1,59 @@ +{ + "all_clique_sizes": { + "0": 1, + "1": 64, + "2": 896, + "3": 3584, + "4": 5376, + "5": 3584, + "6": 1792, + "7": 512, + "8": 64 + }, + "correction_rank": 30, + "determinants": { + "full": "33554432", + "ordinary": "2097152", + "selected": "1/16" + }, + "maximal_clique_sizes": { + "4": 896, + "8": 64 + }, + "producer_pins": { + "RESPONSE-FREEZE.json": "59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9", + "RESPONSE.md": "5ea5866231992c389ae2796f1534e0af90ca88bcedfa3fa9758d78f9457d2981", + "check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "run-normal/RESPONSE-CHECKS.json": "7f84440d79200b8c060aad07b910bb96f2bcdde95b07ddb8d41bcea1fcb09d5c", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c" + }, + "response_columns_per_direction": 112, + "scope": "Matrix, scalar words, and actual graph. Native phases and routed terminal are separate.", + "source_pins": { + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + }, + "status": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE", + "word_checks": { + "E": { + "columns": 112, + "prefix_row_norm": "44", + "scalar": 3210 + }, + "inverse_E": { + "columns": 112, + "prefix_row_norm": "44", + "scalar": 3210 + }, + "inverse_transpose_E": { + "columns": 112, + "prefix_row_norm": "14", + "scalar": 3210 + }, + "transpose_E": { + "columns": 112, + "prefix_row_norm": "14", + "scalar": 3210 + } + } +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json new file mode 100644 index 0000000000..a60bd1ddf8 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "CHECKS.json": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97", + "REPRODUCTION.json": "6f67d5ce7a2b8c3764da8134a85464cac5805c1086eed309632f01e74b4491c7", + "REVIEW.md": "e16a0cd145879805481391e9273301d89a88a6b4731ec5efe0e3cf67a38380d8", + "check_review.py": "118088a1b6d7126d50fb4c05a59fc7f69d792a8c0530ddb066d17434c3d9fff2" + }, + "scope": "Native phases, routed terminal, and full supplier price are separate.", + "status": "PASS_INDEPENDENT_MATRIX_SCALAR_AND_GEOMETRY" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..5e36b7c6ba --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json @@ -0,0 +1,15 @@ +{ + "runs": [ + { + "mode": "normal", + "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97", + "stdout": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE\nreceipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97\n" + }, + { + "mode": "optimized", + "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97", + "stdout": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE\nreceipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97\n" + } + ], + "status": "PASS_BYTE_IDENTICAL" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md new file mode 100644 index 0000000000..335ceedf21 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md @@ -0,0 +1,158 @@ +# Independent review of the full rank-thirty response + +The frozen matrix and scalar-code packet passes. It gives an exact +dyadic unit on all 112 ports, with correction rank 30. Both its response +and its inverse retain the specified selected eight-port block. The +ordinary 104-port block has an exact dyadic inverse. All four supplied +common-frame scalar words have the stated map and price. + +No material finding remains in this scope. This review does not certify +the separate native packet, helper progress, a routed cut, a terminal, +or a complete supplier cost. + +## Response and selected interface + +The response on 48 ports is the signed pair conjugate of eight copies +of the root's integer six-mode unit. At each vertex the two modes that +meet selected physical ports occupy the first two a positions. The +sign diagonal gives their two off-diagonal coefficients -alpha_v. +The response and its inverse have the same a-to-a block. These facts +preserve the old selected block in both physical matrices. + +The independent checker derives each vertex assignment from the +pinned mode support and the original selected set. It then acts on +physical basis columns in this order: + +```text +signed pair code, +selected sign diagonal, +rank-one reflection and final coordinate exchange, +selected sign diagonal, +inverse pair code. +``` + +For the inverse it reverses the reflection and exchange. It does not +import the producer or use the producer's matrix to define this action. +All 112 columns in each direction agree with the frozen matrices, +including the disjoint small-port response. Both full inverse orders +are the identity. + +The selected block L is the old block, and L^-1 is the old inverse. +Both multiplication orders are checked. For the ordinary block H, +write the full inverse as + +```text +E^-1 = [[L,N],[P,Q]]. +``` + +The block inverse identity gives H^-1=Q-P L^-1 N. The supplied ordinary +inverse passes both multiplication orders on all 104 columns; every +coefficient is dyadic. The exact determinants are + +```text +det(L)=1/16, det(H)=2^21, det(E)=2^25. +``` + +They also satisfy Jacobi's principal-minor identity +det(H)=det(E) det((E^-1)_SS). No Schur-complement determinant has been +substituted for the ordinary determinant. + +The supplied U and V have ranks 30 and satisfy E-I=UV on every physical +column. The two disjoint parts contribute ranks 16 and 14. Since U is +injective and V is onto its 30-dimensional output, this proves that +the correction rank is exactly 30. + +## The small-port cover and its restricted optimum + +The fourteen cliques partition the 64 small ports. Eleven have size +five and three have size three. The checker verifies each pairwise +binary inner product from the actual q labels. + +On a clique of size k, I-J has eigenvalue 1-k on the constant vector +and eigenvalue one on its complement. Therefore its inverse is +I-J/(k-1), its determinant is 1-k, and its correction rank is one. +For k=3 and k=5 these are dyadic units. The complete small determinant +is (-4)^11(-2)^3=2^25. + +There is a short structural proof that the actual support has no +nine-clique. Every small q satisfies q dot q=1 and q dot z=1 for z=45. +The vector z is nonzero and isotropic. Nine pairwise orthogonal odd +vectors in the nine-dimensional binary space would be an orthonormal +basis. Expanding z in that basis would give z=sum(q_i), and hence +z dot z=1. This contradicts z dot z=0. + +As a separate finite check, this review enumerates all cliques by +increasing vertex extension. This differs from the producer's +pivoted maximal-clique method. It finds exactly the same maximal +cliques: 896 of size four and 64 of size eight. It also compares every +maximal clique, not just the two counts. + +The fourteen-block optimum is valid within the stated disjoint +dyadic rank-one clique model. More generally, if a k by k zero-diagonal +block has rank(A-I)=1, write A=I+u*v. The diagonal equations imply +v*u=-k, so det(A)=1-k. Dyadic invertibility requires k-1 to be a power +of two. The clique-size bound leaves k=2,3,5. Twelve blocks cover at +most sixty ports. Thirteen size-five blocks would cover sixty-five; +replacing a size-five block by size three or two reduces the total by +two or three, and cannot give sixty-four. Fourteen is therefore +necessary and the supplied cover attains it. + +This argument does not apply to an odd-denominator representation, +overlapping blocks, a correction of higher rank within a block, or a +different native encoding. It is not a lower bound for the required +computation. + +## Literal scalar words + +The review executes every supplied gate on each of the 112 independent +input columns. Every input is arbitrary. All target and source indices +are data fields; no initial zero, borrowed helper, or owned scratch is +used. It checks E, E^-1, E^T, and E^-T separately. + +For a signed six-mode block, the in-place reflection code has twelve +unit additions and one negation. The final exchange has three unit +additions and one negation. This costs 124 real scalar primitives per +vertex. The eight blocks cost 992. The physical pair code and inverse +cost 940, so the 48-port scalar code costs 1932. + +For a clique of size k, the three groups of k-1 unit additions and +one scale by -(k-1) implement I-J. Their costs are 102 for k=5 and +52 for k=3. Thus the small code costs 1278 and each full word costs +1932+1278=3210. Reversing or transposing the word preserves this +invoice under the stated tariff. + +The independent column replay also accumulates the absolute row sums +at every changed row. The maximum prefix row norms are 44 for E and +E^-1, and 14 for E^T and E^-T. These bounds concern the scalar code +alone. They do not bound a recursive child's internal state. + +The four words are valid at a common frame. This phrase is a binding +premise. It does not provide access to fields in different hole frames, +or make an accumulated controller chart free to change. + +## Reproduction + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py +``` + +The expected status is `PASS_INDEPENDENT_RANK_THIRTY_RESPONSE`. +The two receipts must be byte-identical. The checker authenticates +the producer proof, checker, payload, receipt, freeze, and the two +underlying input payloads. It does not run or import producer code. +It uses exact integers and fractions. + +The new-core-transfer lane supplied the full response, clique cover, +scalar words, and their producer checks. The root supplied the +reciprocal six-mode construction. The actual pair coordinates and +selected block come from the pinned cyclic and matching packets. +This lane supplied the distinct column replay, clique enumeration, +and the isotropic proof of the clique-size bound. OpenAI Codex +assisted this work. + +No PR, push, or publication is authorized. Before any PR description, +read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py new file mode 100644 index 0000000000..8d27eb2ff8 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py @@ -0,0 +1,233 @@ +#!/usr/bin/env python3 +"""Check the full response with independent columns and clique extension.""" + +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / "new-core-transfer-20261017/low-displacement-20261020" +PINS = { + "RESPONSE-FREEZE.json": "59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9", + "RESPONSE.md": "5ea5866231992c389ae2796f1534e0af90ca88bcedfa3fa9758d78f9457d2981", + "check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c", + "run-normal/RESPONSE-CHECKS.json": "7f84440d79200b8c060aad07b910bb96f2bcdde95b07ddb8d41bcea1fcb09d5c", +} + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def unit(n, j): + return [F(i == j) for i in range(n)] + + +def sparse(rows): + return [{int(k): F(v) for k, v in row.items()} for row in rows] + + +def apply(rows, x): + return [sum((v * x[j] for j, v in row.items()), F(0)) for row in rows] + + +def eliminate(rows, width): + a = [dict(row) for row in rows] + pivot, det = 0, F(1) + for j in range(width): + p = next((i for i in range(pivot, len(a)) if a[i].get(j)), None) + if p is None: + continue + if p != pivot: + a[p], a[pivot] = a[pivot], a[p] + det = -det + value = a[pivot][j] + det *= value + for i in range(pivot + 1, len(a)): + value_i = a[i].get(j, F(0)) / value + if not value_i: + continue + for k, c in a[pivot].items(): + new = a[i].get(k, F(0)) - value_i * c + if new: + a[i][k] = new + else: + a[i].pop(k, None) + pivot += 1 + if pivot == len(a): + break + return pivot, det if pivot == width == len(a) else None + + +def restrict(rows, ports): + return [{j: rows[p][q] for j, q in enumerate(ports) if q in rows[p]} for p in ports] + + +def main(): + for name, digest in PINS.items(): + need(sha256((SOURCE / name).read_bytes()).hexdigest() == digest, "Producer pin") + packet = json.loads((SOURCE / "run-normal/RESPONSE-PROGRAM.json").read_text()) + inputs = {} + for name, digest in packet["source_pins"].items(): + raw = (LANES / name).read_bytes() + need(sha256(raw).hexdigest() == digest, "Inherited source pin") + inputs[Path(name).name] = json.loads(raw) + cyclic = inputs["CYCLIC-FLAGS.json"] + matching = inputs["MATCHED-INVOLUTION-PROGRAM.json"] + selected = matching["selected_ports"] + need(packet["selected_ports"] == selected, "Original selected set") + need(packet["ports"] == cyclic["ports"], "Actual binary directions") + assignments = [] + for v, c in enumerate(cyclic["cyclic_carriers"]): + chosen = [p for p in c if set(map(int, cyclic["mode_rows"][str(p)])) & set(selected)] + need(len(chosen) == 2, "Selected mode count") + assignments.append({"vertex": v, "ordered_carriers_a_b_c": + chosen + [p for p in c if p not in chosen], + "signs": [1, (-1) ** v, 1, 1, 1, 1]}) + need(assignments == packet["vertex_assignments"], "Selected-mode assignment") + + def pair(x, inverse=False): + out = list(x) + for entry in cyclic["pair_codes"]: + ps, h = entry["ports"], entry["matrix"] + for i, p in enumerate(ps): + out[p] = sum((F(h[j][i], 2) if inverse else F(h[i][j])) * x[ps[j]] + for j in range(2)) + return out + + def formula(x, inverse=False, wrong_sign=False): + coded, result = pair(x), list(x) + mixed = list(coded) + for entry in assignments: + ps, d = entry["ordered_carriers_a_b_c"], list(entry["signs"]) + if wrong_sign: + d[1] = 1 + values = [coded[p] * sign for p, sign in zip(ps, d)] + if inverse: + values[-2], values[-1] = values[-1], values[-2] + query = values[-2] - sum(values[:4]) + values = [a + query for a in values[:4]] + [values[-2] + 2 * query, values[-1]] + if not inverse: + values[-2], values[-1] = values[-1], values[-2] + for p, sign, value in zip(ps, d, values): + mixed[p] = sign * value + result = pair(mixed, True) + for c in packet["small_cliques"]: + total = sum(x[p] for p in c) / (len(c) - 1 if inverse else 1) + for p in c: + result[p] = x[p] - total + return result + + e, ei = sparse(packet["response"]), sparse(packet["response_inverse"]) + columns, inverse_columns = [], [] + for j in range(112): + x = unit(112, j) + a, b = formula(x), formula(x, True) + need(a == apply(e, x) and b == apply(ei, x), "Independent response columns") + need(formula(a, True) == formula(b) == x, "Full inverse orders") + columns.append(a) + inverse_columns.append(b) + need(any(formula(unit(112, p), wrong_sign=True) != formula(unit(112, p)) for p in selected), + "Reject omitted selected sign") + old_l = sparse(matching["selected_block"]) + li = sparse(packet["selected_inverse"]) + need(restrict(e, selected) == restrict(ei, selected) == old_l, "Both selected blocks") + need(all(apply(old_l, apply(li, unit(8, j))) == apply(li, apply(old_l, unit(8, j))) == unit(8, j) + for j in range(8)), "Selected inverse orders") + ordinary = sorted(set(range(112)) - set(selected)) + need(ordinary == packet["ordinary_ports"], "Ordinary partition") + h, hi = restrict(e, ordinary), sparse(packet["ordinary_inverse"]) + need(all(c.denominator & (c.denominator - 1) == 0 for row in hi for c in row.values()), + "Dyadic ordinary inverse") + need(all(apply(h, apply(hi, unit(104, j))) == apply(hi, apply(h, unit(104, j))) == unit(104, j) + for j in range(104)), "Ordinary inverse orders") + need(eliminate(old_l, 8)[1] == F(1, 16), "Selected determinant") + need(eliminate(e, 112)[1] == 2 ** 25, "Full determinant") + need(eliminate(h, 104)[1] == 2 ** 21, "Ordinary determinant") + u, v = sparse(packet["correction_U"]), sparse(packet["correction_V"]) + need(eliminate(u, 30)[0] == eliminate(v, 112)[0] == 30, "Factor ranks") + for j in range(112): + x = unit(112, j) + need(apply(u, apply(v, x)) == [a - b for a, b in zip(columns[j], x)], "Correction factor") + + word_receipts = {} + for name, gates in packet["common_frame_words"].items(): + expected = inverse_columns if "inverse" in name else columns + if "transpose" in name: + expected = [list(row) for row in zip(*expected)] + prefix_norms = [F(0)] * len(gates) + price = 0 + parsed = [] + for kind, target, origin, text in gates: + c = F(text) + need(0 <= target < 112 and c != 0, "Literal field and coefficient") + need(c.denominator & (c.denominator - 1) == 0, "Dyadic gate") + a, b = abs(c.numerator), c.denominator + if kind == "add": + need(isinstance(origin, int) and 0 <= origin < 112 and origin != target, + "Arbitrary-input addition") + price += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + else: + need(kind == "scale" and origin is None and a & (a - 1) == 0, "Unit scale") + price += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) + parsed.append((kind, target, origin, c)) + for j in range(112): + x = unit(112, j) + for k, (kind, target, origin, c) in enumerate(parsed): + x[target] = x[target] * c if kind == "scale" else x[target] + c * x[origin] + prefix_norms[k] += abs(x[target]) + need(x == expected[j], "Literal word column " + name) + norm = max([F(1)] + prefix_norms) + need(price == 3210 and norm == (14 if "transpose" in name else 44), "Scalar invoice") + word_receipts[name] = {"columns": 112, "scalar": price, "prefix_row_norm": str(norm)} + + small, q = packet["small_ports"], packet["ports"] + need(sorted(p for c in packet["small_cliques"] for p in c) == small, "Disjoint small cover") + need(Counter(map(len, packet["small_cliques"])) == {3: 3, 5: 11}, "Clique cover sizes") + need(all((q[p] & q[r]).bit_count() % 2 == (p == r) + for c in packet["small_cliques"] for p in c for r in c), "Actual clique cover") + need(all(q[p].bit_count() % 2 == (q[p] & 45).bit_count() % 2 == 1 for p in small) + and (45).bit_count() % 2 == 0, "Affine isotropic obstruction to size nine") + adjacent = [{r for r in small if r != p and (q[p] & q[r]).bit_count() % 2 == 0} + for p in range(112)] + maxima, visited = [], Counter() + + def extend(chosen, options, common): + visited[len(chosen)] += 1 + if not common: + maxima.append(tuple(chosen)) + for i, p in enumerate(options): + extend(chosen + [p], [r for r in options[i + 1:] if r in adjacent[p]], + common & adjacent[p]) + + extend([], small, set(small)) + need(Counter(map(len, maxima)) == {4: 896, 8: 64}, "Separate maximal clique census") + need(sorted(maxima) == sorted(tuple(sorted(c)) for c in packet["maximal_small_cliques"]), + "Every reported maximal clique") + need(max(visited) == 8, "Maximum clique dimension") + receipt = { + "status": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE", + "producer_pins": PINS, + "source_pins": packet["source_pins"], + "response_columns_per_direction": 112, + "correction_rank": 30, + "determinants": {"selected": "1/16", "ordinary": str(2 ** 21), "full": str(2 ** 25)}, + "word_checks": word_receipts, + "all_clique_sizes": dict(sorted(visited.items())), + "maximal_clique_sizes": dict(sorted(Counter(map(len, maxima)).items())), + "scope": "Matrix, scalar words, and actual graph. Native phases and routed terminal are separate.", + } + raw = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (HERE / "CHECKS.json").write_bytes(raw) + print(receipt["status"]) + print("receipt_sha256=" + sha256(raw).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py new file mode 100644 index 0000000000..66ba64bcbf --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/route32-capture-review-20261020/check_review.py @@ -0,0 +1,393 @@ +#!/usr/bin/env python3 +"""Check the route response and capture words from exact input columns.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / "new-core-transfer-20261017/low-displacement-20261020" +PINS = { + "route32/FREEZE.json": "28354cf747adc5c2a10393f02035a936e0e0fa3f666717b419f4eaaeed1814af", + "route32/ROUTE32.md": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28", + "route32/emit_model.py": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711", + "route32/model-normal/ROUTE32-MODEL.json": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52", + "route32/model-normal/CHECKS.json": "69ee6905c99ab4d93f48d828c378f6c902d5e8a9844df68acbc8971158d76502", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c", +} +INHERITED = { + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": + "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd", + "independent-review-20261017/rank-thirty-review-20261020/FREEZE.json": + "15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189", +} +OLD_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" + + +def need(test, label): + if not test: + raise ValueError(label) + + +def sparse(rows): + return [{int(j): F(c) for j, c in row.items() if F(c)} for row in rows] + + +def unit(n, j): + return [F(i == j) for i in range(n)] + + +def apply(rows, x): + return [sum((c * x[j] for j, c in row.items()), F(0)) for row in rows] + + +def rows_from_columns(columns): + return [{j: c for j, c in enumerate(row) if c} for row in zip(*columns)] + + +def eliminate(rows, width): + a = [dict(row) for row in rows] + count, determinant = 0, F(1) + for column in range(width): + found = next((i for i in range(count, len(a)) if a[i].get(column)), None) + if found is None: + continue + if found != count: + a[found], a[count] = a[count], a[found] + determinant = -determinant + pivot = a[count][column] + determinant *= pivot + for i in range(count + 1, len(a)): + factor = a[i].get(column, F(0)) / pivot + if factor: + for j, coefficient in a[count].items(): + value = a[i].get(j, F(0)) - factor * coefficient + if value: + a[i][j] = value + else: + a[i].pop(j, None) + count += 1 + if count == len(a): + break + return count, determinant if count == width == len(a) else None + + +def binary_span(values): + out = {0} + for v in values: + out |= {x ^ v for x in out} + return out + + +def add(row, key, value): + value += row.get(key, F(0)) + if value: + row[key] = value + else: + row.pop(key, None) + + +def reverse_output(word, output): + row = {(output, 0): F(1)} + for kind, target, origin, text in reversed(word): + c = F(text) + terms = [(key, value) for key, value in row.items() if key[0] == target] + if kind == "add": + for (_, mask), value in terms: + add(row, (origin, mask), c * value) + elif kind == "scale": + for key, value in terms: + add(row, key, (c - 1) * value) + else: + need(kind == "translate" and c.denominator == 1, "Translation type") + for key, _ in terms: + del row[key] + for (_, mask), value in terms: + add(row, (target, mask ^ int(c)), value) + return row + + +def inverse_word(word): + return [[kind, target, origin, + str(-F(text) if kind == "add" else 1 / F(text) if kind == "scale" else F(text))] + for kind, target, origin, text in reversed(word)] + + +def word_invoice(word, routes): + price, maps = 0, 0 + for kind, target, origin, text in word: + need(isinstance(target, int) and 0 <= target < 112, "Data field target") + c = F(text) + if kind == "translate": + need(origin is None and c.denominator == 1 and 0 <= c < 512, "Translation label") + maps += 1 + continue + a, b = abs(c.numerator), c.denominator + need(c and b & (b - 1) == 0, "Dyadic nonzero coefficient") + if kind == "add": + need(isinstance(origin, int) and 0 <= origin < 112 and origin != target, + "Data field source") + need(routes[origin] == routes[target], "Every scalar meeting preserves route") + price += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + else: + need(kind == "scale" and origin is None and a & (a - 1) == 0, "Dyadic unit scale") + price += 2 * (abs(a.bit_length() - b.bit_length()) + int(c < 0)) + return {"scalar_units": price, "translation_maps": maps, "native_children": 0, + "owned_fields": 0} + + +def prefix_bounds(word): + rows = [{j: F(1)} for j in range(112)] + norm, height = F(1), 0 + for kind, target, origin, text in word: + c = F(text) + if kind == "scale": + rows[target] = {j: value * c for j, value in rows[target].items()} + else: + need(kind == "add", "Scalar prefix type") + for j, value in rows[origin].items(): + add(rows[target], j, c * value) + norm = max(norm, sum(map(abs, rows[target].values()), F(0))) + for value in rows[target].values(): + b = value.denominator + need(b & (b - 1) == 0, "Dyadic prefix") + height = max(height, b.bit_length() - 1) + return {"maximum_row_one_norm": str(norm), "binary_height": height} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for name, pin in PINS.items(): + need(sha256((SOURCE / name).read_bytes()).hexdigest() == pin, "Producer pin " + name) + for name, pin in INHERITED.items(): + need(sha256((LANES / name).read_bytes()).hexdigest() == pin, "Source pin " + name) + raw = gzip.decompress((SOURCE / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz").read_bytes()) + need(sha256(raw).hexdigest() == OLD_PIN, "Rank-sixteen source pin") + old = json.loads(raw)["model"] + model = json.loads((SOURCE / "route32/model-normal/ROUTE32-MODEL.json").read_text()) + cyclic = json.loads((LANES / next(k for k in INHERITED if k.endswith("CYCLIC-FLAGS.json"))).read_text()) + geometry = json.loads((LANES / next(k for k in INHERITED if k.endswith("GEOMETRY.json"))).read_text()) + rank30 = json.loads((SOURCE / "run-normal/RESPONSE-PROGRAM.json").read_text()) + q = cyclic["ports"] + need(q == model["ports"] == old["ports"] == geometry["q_labels"], "Actual q labels") + root = binary_span([30, 45, 75, 384]) + need(sorted(root) == model["root_space"] == geometry["common_even_isotropic_space"], + "Actual root space") + routes = [min(r for r in root if (r & v).bit_count() % 2) for v in q] + need(routes == model["port_routes"] and Counter(routes) == {30: 64, 45: 32, 75: 16}, + "Actual route labels") + need(model["selected_ports"] == [] and model["ordinary_ports"] == list(range(112)), + "Empty selection") + + def pair(x, inverse=False): + y = list(x) + for record in cyclic["pair_codes"]: + ports, h = record["ports"], record["matrix"] + need(routes[ports[0]] == routes[ports[1]], "Pair route") + for i, p in enumerate(ports): + y[p] = sum((F(h[j][i], 2) if inverse else F(h[i][j])) * x[ports[j]] + for j in range(2)) + return y + + groups = [] + for vertex, carriers in enumerate(cyclic["cyclic_carriers"]): + selected = [p for p in carriers if set(map(int, cyclic["mode_rows"][str(p)])) + & set(old["selected_ports"])] + need(len(selected) == 2, "Original selected modes") + ports = selected + [p for p in carriers if p not in selected] + signs = [1, (-1) ** vertex, 1, 1, 1, 1] + for route in sorted({routes[p] for p in ports}): + group = [(p, d) for p, d in zip(ports, signs) if routes[p] == route] + groups.append(([p for p, _ in group], [d for _, d in group], route, "large")) + for clique in old["small_cliques"]: + need(len(clique) == 8, "Original small clique size") + for route in sorted({routes[p] for p in clique}): + ports = [p for p in clique if routes[p] == route] + groups.append((ports, [1] * len(ports), route, "small")) + need(sorted(p for ps, _, _, _ in groups for p in ps) == list(range(112)), "Mode partition") + need(Counter((kind, len(ps)) for ps, _, _, kind in groups) + == {("large", 4): 8, ("large", 2): 8, ("small", 4): 16}, "Group counts") + relative = Counter() + inside = 0 + for (ps, signs, route, kind), record in zip(groups, model["groups"]): + need((ps, signs, route, kind) == (record["ports"], record["signs"], + record["route"], record["kind"]), "Actual group binding") + need(record["pivot"] == ps[0] and record["centre_multiplier"] == 1 - len(ps), + "Pivot placement") + span = binary_span([q[p] ^ q[ps[0]] for p in ps]) + need(binary_span(record["relative_q_basis"]) == span, "Relative q space") + dim = len(span).bit_length() - 1 + relative[dim] += 1 + inside += span <= root + need(record["relative_q_rank"] == dim + and record["relative_q_in_common_root"] == (span <= root), "Relative q claims") + if kind == "small": + need(all((q[p] & q[t]).bit_count() % 2 == (p == t) for p in ps for t in ps), + "Actual small orthonormal clique") + need(relative == {1: 8, 3: 24} and inside == 8, "Root membership scope") + + def mode_action(x, inverse=False): + y = list(x) + for ps, signs, _, _ in groups: + total = sum(d * x[p] for p, d in zip(ps, signs)) + if inverse: + total /= len(ps) - 1 + for p, d in zip(ps, signs): + y[p] -= d * total + return y + + def response(x, inverse=False): + return pair(mode_action(pair(x), inverse), True) + + e, ei = sparse(model["response"]), sparse(model["response_inverse"]) + u, v = sparse(model["correction_U"]), sparse(model["correction_V"]) + need(len(u) == 112 and len(v) == 32, "Correction dimensions") + for j in range(112): + x = unit(112, j) + a, b = response(x), response(x, True) + need(apply(e, x) == a and apply(ei, x) == b, "Independent response column") + need(response(a, True) == response(b) == x, "Both response inverse orders") + need(apply(u, apply(v, x)) == [a_i - x_i for a_i, x_i in zip(a, x)], "UV correction") + need(apply(sparse(model["mode_response"]), x) == mode_action(x), "Mode response") + need(apply(sparse(model["mode_inverse"]), x) == mode_action(x, True), "Mode inverse") + need(eliminate(u, 32)[0] == eliminate(v, 112)[0] == 32, "Rank32 factors") + need(eliminate(e, 112)[1] == 3 ** 24 == int(model["full_determinant"]), "Full determinant") + need(all(not row.get(p) for p, row in enumerate(e)), "Physical zero diagonal") + need(all(e[p].get(t, F(0)) == e[t].get(p, F(0)) for p in range(112) for t in range(112)), + "Physical response symmetry") + need(all(routes[p] == routes[t] for p, row in enumerate(e) for t in row), "Response route") + old_selected = old["selected_ports"] + need(all(not e[p].get(t) for p in old_selected for t in old_selected), "Old selected block is zero") + need(sparse(model["old_selected_block"]) == [{} for _ in range(8)] + and model["old_selected_determinant"] == "0", "Old selected report") + need(set(c.denominator for row in ei for c in row.values()) <= {1, 2, 3, 6}, + "Only odd inverse denominator three") + diagonal = [F(1)] * 112 + for ps, _, _, _ in groups: + diagonal[ps[0]] = 1 - len(ps) + need(sparse(model["diagonal_response"]) == [{p: c} for p, c in enumerate(diagonal)], + "Actual diagonal response") + + def code_formula(x, reflection=False): + z = pair(x) + result = list(z) + for ps, d, _, _ in groups: + p = ps[0] + if reflection and len(ps) == 4: + s = [-d[0]] + d[1:] + total = sum(s_i * z[t] for t, s_i in zip(ps, s)) / 2 + for t, s_i in zip(ps, s): + result[t] = z[t] - s_i * total + else: + result[p] = sum(d_i * z[t] for t, d_i in zip(ps, d)) + for t, d_i in zip(ps[1:], d[1:]): + result[t] = d_i * z[t] - d[0] * z[p] + return result + + receipts = {} + for name, code in model["codes"].items(): + word, inverse, entry = code["word"], code["inverse_word"], code["entry_word"] + need(inverse == inverse_word(word), "Literal scalar inverse " + name) + need(entry[:112] == [["translate", p, None, str(q[p])] for p in range(112)] + and entry[112:] == word, "Ordered entry code " + name) + expected = rows_from_columns([code_formula(unit(112, j), name == "reflection") for j in range(112)]) + need(expected == sparse(code["code"]), "Formula code " + name) + literal = [{p: c for (p, mask), c in reverse_output(word, i).items() if mask == 0} + for i in range(112)] + need(literal == expected, "Independent reverse scalar outputs " + name) + inverse_rows = [{p: c for (p, mask), c in reverse_output(inverse, i).items() if mask == 0} + for i in range(112)] + need(inverse_rows == sparse(code["inverse_code"]), "Independent reverse inverse outputs") + for j in range(112): + x = unit(112, j) + need(apply(expected, apply(e, apply(inverse_rows, x))) == [diagonal[i] * x[i] for i in range(112)], + "Conjugated centre diagonal") + for order in (word + inverse, inverse + word): + need(all(reverse_output(order, i) == {(i, 0): 1} for i in range(640)), + "All640 literal inverse outputs") + for i in range(640): + want = {(p, q[p]): c for p, c in expected[i].items()} if i < 112 else {(i, 0): F(1)} + need(reverse_output(entry, i) == want, "All640 ordered entry outputs") + need(reverse_output(entry + inverse_word(entry), i) == {(i, 0): 1}, + "All640 spatial inverse outputs") + need(any(reverse_output(word + entry[:112], i) != reverse_output(entry, i) for i in range(112)), + "Reject free Q-square commutation") + mutation = list(word) + mutation.pop(next(i for i, event in enumerate(word) if event[0] == "add")) + need(any(reverse_output(mutation, i) != reverse_output(word, i) for i in range(112)), + "Reject omitted scalar transfer") + invoice, inverse_invoice = word_invoice(word, routes), word_invoice(inverse, routes) + entry_invoice = word_invoice(entry, routes) + need(invoice["scalar_units"] == inverse_invoice["scalar_units"] == (1870 if name == "pivot" else 2486), + "Independent scalar invoice") + need(entry_invoice["translation_maps"] == 112 and entry_invoice["scalar_units"] == invoice["scalar_units"], + "Entry translation invoice") + forward_bounds, backward_bounds = prefix_bounds(word), prefix_bounds(inverse) + need(forward_bounds == {"maximum_row_one_norm": "8", "binary_height": int(name == "reflection")} + and backward_bounds == {"maximum_row_one_norm": "4", "binary_height": 3 - int(name == "reflection")}, + "Exact prefix bounds") + receipts[name] = {"events": len(word), "invoice": invoice, "inverse_invoice": inverse_invoice, + "entry_invoice": entry_invoice, "prefix": forward_bounds, + "inverse_prefix": backward_bounds, "all_output_rows": 640} + + reflection_checks = 0 + for ps, d, _, _ in groups: + if len(ps) != 4: + continue + s = [-d[0]] + d[1:] + matrix = [{j: F(i == j) - F(s[i] * s[j], 2) for j in range(4)} for i in range(4)] + need(apply(matrix, d) == [2 * d[0], 0, 0, 0], "Signed reflection query") + delta = [{j: c - (i == j) for j, c in row.items() if c != (i == j)} for i, row in enumerate(matrix)] + need(eliminate(delta, 4)[0] == 1, "Reflection displacement rank") + for j in range(4): + x = unit(4, j) + need(apply(matrix, apply(matrix, x)) == x, "Reflection involution") + reflection_checks += 1 + + maxima = rank30["maximal_small_cliques"] + need(Counter(map(len, maxima)) == {4: 896, 8: 64}, "Reviewed clique list") + need(all(Counter(routes[p] for p in clique) == {30: 4, 45: 4} + for clique in maxima if len(clique) == 8), "All64 eight-cliques cross routes") + need(max(max(Counter(routes[p] for p in clique).values()) for clique in maxima) == 4, + "Restricted monochromatic clique bound") + route_columns = {} + for stage in (1, 2): + for route in sorted(set(routes)): + direction = (511 ^ route) ^ (1 << (8 + stage)) + need(direction.bit_count() % 2 == 0, "Even transvection direction") + columns = [(1 << j) ^ (direction if (direction >> j) & 1 else 0) for j in range(11)] + need(all((a & b).bit_count() % 2 == (i == j) + for i, a in enumerate(columns) for j, b in enumerate(columns)), "Orthogonal route") + route_columns[f"{stage}:{route}"] = columns + receipt = { + "status": "PASS_INDEPENDENT_ROUTE32_RESPONSE_AND_CAPTURE", + "producer_pins": PINS, "inherited_pins": INHERITED, "rank16_raw_sha256": OLD_PIN, + "response_columns_per_direction": 112, "response_symmetric": True, + "correction_rank": 32, "determinant": str(3 ** 24), + "selection": [], "old_selected_block": "zero", + "centre_multipliers": {"-3": 24, "-1": 8, "1": 80}, + "reflection_blocks": reflection_checks, "code_receipts": receipts, + "relative_q_rank_counts": dict(sorted(relative.items())), "blocks_inside_root": inside, + "route_classes": dict(sorted(Counter(routes).items())), "actual_kappa_columns": route_columns, + "restricted_monochromatic_maximum_clique": 4, + "scope": "Exact response, scalar capture words, and route binding. Native phases and a complete caller have separate reviews.", + } + data = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (args.out / "CHECKS.json").write_bytes(data) + print(receipt["status"]) + print("receipt_sha256=" + sha256(data).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.json new file mode 100644 index 0000000000..ec71dd9a3e --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/WALSH-FRAME-REVIEW.json @@ -0,0 +1,183 @@ +{ + "common_native_child_kernels": [ + { + "basis_matrix_entries": 65536, + "rank": 8 + }, + { + "basis_matrix_entries": 262144, + "rank": 9 + } + ], + "endpoint_identity": "C_omega G_n = D_n F_n D_n for n=9+8s; D_n(x)=(-1)^sum_(i + = 2^(-(n-1)/2) sum_(k in H_n) (-1)^(h dot k) |a omega_n+k>. + +The form on H_n is nondegenerate, so G_n is a real symmetric involution. +It acts as the identity on coordinates outside U_n. Its binary native +rank is n-1. There is no unspecified scalar phase in this definition. + +Let P_g be an orthogonal address map supported in U_n. It fixes omega_n, +since omega_n is the characteristic vector of the dot form. It preserves +H_n and every dot product in the displayed kernel. Hence + + G_n P_g = P_g G_n + +as exact operators, including their phases. + +For an odd q in U_n, put `v=q+omega_n`. The preceding fixed-line proof now +gives `G_n C_q G_n=C_omega_n L_q`. Here, on a physical coordinate x, + + L_q |x> = i^(x dot v) |x+(x dot v) omega_n>. + +This is a monomial map with a linear address map and a quadratic phase +modulo four. It commutes with C_omega_n. + +For `m=n-8`, let `A_n=G_n G_m`. If g is an actual transition route in U_n, +then + + G_n C_q^j P_g G_m + = L_q^j P_g C_omega_n^j A_n. + +The order on the right is part of the statement. P_g need not commute with +A_n. Both P_g and L_q commute with C_omega_n. The last common factor has +rank eight for even j and rank nine for odd j. Thus the label-dependent +part is monomial. The common factor still requires a native child. + +## Exact rank-eight and rank-nine child recipes + +The subspaces H_m and H_n are nested. Their orthogonal difference has the +eight-vector basis + + k_i = omega_m+e_(m+i), 1 <= i <= 8. + +Call this space K. Its Gram matrix in that basis is +`B=I_8+11^T`, with `B^2=I`. The decomposition is + + U_n = H_m orthogonal-sum K orthogonal-sum span(omega_n). + +The operator A_n is precisely the real Walsh transform on K and the +identity on its complement. This follows from the two exact Walsh kernels; +the transforms on H_m cancel with no scalar phase. + +Choose an address chart A whose first eight columns are the k_i, whose +ninth column is omega_n, and whose remaining columns form a basis of H_m. +Let P_B apply B to the first eight chart coordinates. Let S_8 multiply a +chart basis vector by i to the power of its first eight bits' weight. +The native transform is `F_d=product_(i=1)^d C_(e_i)`. Since + + H_8 = S_8 F_8 S_8 + +with exact scalar phase, the two recipes are + + A_n = P_A P_B S_8 F_8 S_8 P_A^-1, + + C_omega_n A_n = P_A P_B S_8 F_9 S_8 P_A^-1. + +The order of these formulas is operator order. The right factor acts first. +Each recipe uses one native child and two composed monomial maps. It acts +on arbitrary input. The same rank-eight construction applies to G_9, with +an even basis of U_9 and complement omega_9. + +Even powers of C_omega_n are translations. Its negative odd power differs +from its positive odd power by a translation. Thus these two recipes also +cover all four phase powers, with a further monomial factor when needed. + +For a fully typed transition, put `T_n^a=C_omega_n^a G_n`. For arbitrary +integers a, b, and j, the exact ordered identity is + + T_n^a C_q^j P_g (T_m^b)^-1 + = C_omega_n^(a+j-b) L_(q,n)^j P_g + L_(omega_m,n)^(-b) A_n. + +To check the order, first move C_omega_m through G_m. Then use +`G_n C_omega_m^-b G_n=C_omega_n^-b L_(omega_m,n)^-b`. +The common line factors can move through all the displayed monomial maps. +This proves equation (3) in the residual-syndrome lane's +`physical-algebra/GROWING-FRAME.md`. It is an algebraic phase review; the +receipt's rank and kernel counts do not claim a separate full-matrix test +of all typed transitions. For the plain transition j=0, the alternating +types `a_s=1-(s mod 2)` have rank nine at all eight later stages. With the +initial rank-nine frame, this is an exact endpoint frame schedule. + +## The exact productive endpoint + +Define the diagonal monomial + + D_n |x> = i^(wt(x)-parity(x)) |x> + = (-1)^(sum_(i. + +For every `n=9+8s`, + + C_omega_n G_n = D_n F_n D_n. + +To prove this, write `a=parity(x)` and `b=parity(y)`. The kernel of the +left side is + + (1+i) 2^(-(n+1)/2) i^(2 x dot y-a-b). + +The kernel of F_n is + + (1+i) 2^(-(n+1)/2) i^(2 x dot y-wt(x)-wt(y)), + +because `n=1 mod 8`. The two diagonal factors give the required kernel. +For a general odd n, an extra scalar `i^((1-n)/2)` is needed; it is one +for the widths used here. In particular, the n=73 endpoint is exactly the +full required native transform with two diagonal adapters. It does not +require a rank-72 decoder. + +This statement is conditional on the actual mode carrying that endpoint +frame with the required contents. If its contents are still changed by the +centre controller, the endpoint identity does not restore them. + +## Verification and remaining obligations + +Run: + +```sh +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/interface-proof/review_walsh_frames.py +``` + +The expected output is `PASS_INDEPENDENT_EXACT_WALSH_FRAMES`. The checker +does not import either proposer script or the Clifford compiler. It uses +the earlier independent selected-route reconstruction. Its checks include: + +- All 61,440 common-line coefficients and all 120 routed port labels. +- Every growing transition from width 9 through width 73, with ranks eight + and nine and the exact kernel-preserving orthogonal route conditions. +- All 65,536 entries of the rank-eight child and all 262,144 entries of the + rank-nine child, as Gaussian integers with their exact denominators. +- All 262,144 entries of the width-nine endpoint and complete quadratic + phase witnesses on both kernel coordinates at every larger width. + +Every check uses an explicit requirement and remains active under `-O`. +The base operator identities tensor to every positive lambda. Scalar +coefficients and address maps must be applied in the same stated order. + +The monomial maps are explicit but are not free. A supplier must price +their phase and address operations, source access, initial frames, active +and idle mode schedules, arbitrary borrowed contents, final restoration, +and all recursive children. This review emits no such controller or owner +program and makes no kappa claim. It does resolve the phase and endpoint +obstacles for the stated growing-frame family. + +There is also an address-group condition. The chart from the local +nine-space to `span(omega_m,E_s)` can be a general linear map. An isometry +between those spaces need not extend to an orthogonal map on the ambient +space. The child recipe is valid as written, but it does not replace an +actual cover route or an owner address without a further proof. + +Prepared with substantial OpenAI Codex assistance and independent agent +review. No independent human review is claimed. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/review_walsh_frames.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/review_walsh_frames.py new file mode 100644 index 0000000000..ea7137eae8 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/review_walsh_frames.py @@ -0,0 +1,236 @@ +"""Check exact common-line Walsh phases, routes, and native child kernels.""" + +from collections import Counter +from hashlib import sha256 +from pathlib import Path +import importlib.util +import json + + +FIXED_CHARTS = {} + + +def require(value, message): + if not value: + raise ValueError(message) + + +def parity(value): + return value.bit_count() & 1 + + +def rank(columns): + pivots = {} + for column in columns: + while column: + bit = column.bit_length() - 1 + if bit not in pivots: + pivots[bit] = column + break + column ^= pivots[bit] + return len(pivots) + + +def apply(columns, value): + result = 0 + for i, column in enumerate(columns): + if value >> i & 1: + result ^= column + return result + + +def inverse(columns): + size = len(columns) + rows = [sum(((column >> i) & 1) << j for j, column in enumerate(columns)) + | (1 << (size + i)) for i in range(size)] + for i in range(size): + pivot = next((j for j in range(i, size) if rows[j] >> i & 1), None) + require(pivot is not None, "Singular address chart") + rows[i], rows[pivot] = rows[pivot], rows[i] + for j in range(size): + if j != i and rows[j] >> i & 1: + rows[j] ^= rows[i] + return [sum(((row >> (size+i)) & 1) << j for j, row in enumerate(rows)) + for i in range(size)] + + +def transpose(columns): + return [sum(((column >> i) & 1) << j for j, column in enumerate(columns)) + for i in range(len(columns))] + + +def fixed_walsh(state, common, size): + key = common, size + if key not in FIXED_CHARTS: + chart = [(1 << i) ^ 256 for i in range(8)] + [common] + chart += [1 << i for i in range(9, size)] + back = inverse(chart) + FIXED_CHARTS[key] = chart, back, transpose(chart), transpose(back) + chart, back, chart_t, back_t = FIXED_CHARTS[key] + x, z = apply(back, state[0]), apply(chart_t, state[1]) + return (apply(chart, (x & ~255) | (z & 255)), + apply(back_t, (z & ~255) | (x & 255))) + + +def growing_walsh(state, size): + x, z = state + omega = (1 << size) - 1 + delta = (x ^ z) & omega + if parity(delta): + delta ^= omega + return x ^ delta, z ^ delta + + +def line(state, label): + x, z = state + return x ^ (label if parity(z & label) else 0), z + + +def multiply(a, b): + return a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0] + + +def rotate(a, power): + x, y = a + return ((x, y), (-y, x), (-x, -y), (y, -x))[power % 4] + + +def native_coefficients(size): + powers_a, powers_b = [(1, 0)], [(1, 0)] + for _ in range(size): + powers_a.append(multiply(powers_a[-1], (1, 1))) + powers_b.append(multiply(powers_b[-1], (1, -1))) + return [multiply(powers_a[size-i], powers_b[i]) for i in range(size+1)] + + +def endpoint_case(size, x, y, coefficients): + a, b = parity(x), parity(y) + exponent = x.bit_count()-a+y.bit_count()-b + actual = rotate(coefficients[(x ^ y).bit_count()], exponent) + wanted = (1, 1) if a == b else (1, -1) + if parity(x & y) ^ (a & b): + wanted = (-wanted[0], -wanted[1]) + scale = 1 << ((size-1)//2) + require(actual == (scale*wanted[0], scale*wanted[1]), + "Exact productive endpoint kernel") + + +def main(): + here = Path(__file__).resolve().parent + spec = importlib.util.spec_from_file_location("independent_routes", here/"verify_bridge_operators.py") + routes = importlib.util.module_from_spec(spec) + spec.loader.exec_module(routes) + source = here.parent/"coherent-port/COVARIANCE.json" + raw = source.read_bytes() + pin = "6466d082f376bcbd8f7d953d8a2625f5e31eb164ffa61f430b1cdf6e6ef30b38" + require(sha256(raw).hexdigest() == pin, "Completed port table pin") + labels = json.loads(raw)["labels"] + require(len(labels) == 120 and all(parity(q) for q in labels), "Odd completed ports") + common = 11 + phase_cases = 0 + for q in labels: + v = q ^ common + require(not parity(v), "Even difference from common line") + for frequency in range(256): + b = parity(frequency & v) + original = [(1, 1), (1, -1) if not b else (-1, 1)] + factored = [rotate((1, 1), b), rotate((1, -1), b)] + if b: + factored.reverse() + require(factored == original, "Common-line exact two-term phase") + phase_cases += 2 + fixed_records = [] + for first, second in ((0, 0), (1, 1), (1, 0), (2, 1)): + size = 9+8*max(first, second) + counts = Counter() + for q in labels: + chart = routes.basis(q) + columns = [] + for i in range(size): + x, z = fixed_walsh((0, 1 << i), common, size) + x, z = (routes.route(x, chart, second), routes.route(z, chart, second)) + x, z = (routes.route(x, chart, first), routes.route(z, chart, first)) + columns.append(fixed_walsh(line((x, z), q), common, size)[0]) + counts[rank(columns)] += 1 + require(counts == {1 if first == second else 17: 120}, "Fixed-chart transition rank") + fixed_records.append({"from_stage": second, "to_stage": first, + "rank_histogram": dict(counts)}) + growing_records = [] + for stage in range(1, 9): + size, previous = 9+8*stage, 1+8*stage + omega = (1 << size)-1 + counts = [Counter(), Counter()] + for q in labels: + chart = routes.basis(q) + rho = [routes.route(1 << i, chart, stage) for i in range(size)] + require(apply(rho, omega) == omega, "Current route fixes the common line") + require(all(parity(a & b) == (i == j) + for i, a in enumerate(rho) for j, b in enumerate(rho)), + "Current route preserves the exact Walsh kernel") + for odd in range(2): + columns = [] + for i in range(size): + x, z = growing_walsh((0, 1 << i), previous) + x, z = routes.route(x, chart, stage-1), routes.route(z, chart, stage-1) + x, z = routes.route(x, chart, stage), routes.route(z, chart, stage) + if odd: + x, z = line((x, z), q) + columns.append(growing_walsh((x, z), size)[0]) + counts[odd][rank(columns)] += 1 + require(counts == [{8: 120}, {9: 120}], "Growing transition ranks") + growing_records.append({"stage": stage, "width": size, + "even_phase_rank": dict(counts[0]), + "odd_phase_rank": dict(counts[1])}) + child_cases = [] + for child_size in (8, 9): + coefficients = native_coefficients(child_size) + count = 0 + for x in range(1 << child_size): + bx = (x & 255) ^ (255 if parity(x & 255) else 0) + moved = bx | (x & 256) + for y in range(1 << child_size): + actual = rotate(coefficients[(moved ^ y).bit_count()], + bx.bit_count()+(y & 255).bit_count()) + sign = -1 if parity(bx & y) else 1 + wanted = (1, 0) if child_size == 8 else ( + (1, 1) if not ((x ^ y) & 256) else (1, -1)) + wanted = tuple(16*sign*a for a in wanted) + require(actual == wanted, "Exact common native child kernel") + count += 1 + child_cases.append({"rank": child_size, "basis_matrix_entries": count}) + endpoint_records = [] + for size in range(9, 74, 8): + coefficients = native_coefficients(size) + if size == 9: + points = ((x, y) for x in range(512) for y in range(512)) + else: + points = ((value & ((1 << size)-1), value >> size) + for value in routes.phase_points(2*size)) + count = 0 + for x, y in points: + endpoint_case(size, x, y, coefficients) + count += 1 + endpoint_records.append({"width": size, "kernel_cases": count, + "complete_quadratic_phase_witness": True}) + report = { + "status": "PASS_INDEPENDENT_EXACT_WALSH_FRAMES", + "root_table_sha256": pin, + "fixed_common_line": common, + "exact_common_line_coefficients": phase_cases, + "fixed_chart_transitions": fixed_records, + "growing_chart_transitions": growing_records, + "common_native_child_kernels": child_cases, + "productive_endpoint_kernels": endpoint_records, + "endpoint_identity": "C_omega G_n = D_n F_n D_n for n=9+8s; D_n(x)=(-1)^sum_(i> i) & 1) + transvection = q ^ (1 << hole) + order = list(range(9)) + order[0], order[hole] = order[hole], order[0] + out = tuple((1 << i) ^ (transvection if (transvection >> i) & 1 else 0) + for i in order) + require(out[0] == q, "Port basis first column") + require(all(parity(a & b) == (i == j) + for i, a in enumerate(out) for j, b in enumerate(out)), "Port basis isometry") + return out + + +def route(value, chart, stage): + if not stage: + return value + start = 9 + 8 * (stage - 1) + out = value & ~(511 | (255 << start)) + out ^= chart[0] if parity(value & chart[0]) else 0 + for i, v in enumerate(chart[1:]): + out ^= (1 << (start + i)) if parity(value & v) else 0 + out ^= v if (value >> (start + i)) & 1 else 0 + return out + + +def phase(terms, frequency): + return sum(sign * parity(axis & frequency) for axis, sign in terms) % 4 + + +def phase_points(n): + return [0] + [1 << i for i in range(n)] + [ + (1 << i) | (1 << j) for i in range(n) for j in range(i)] + + +def equal_phase(left, right, shift, points): + return all((phase(left, value) - phase(right, value) - + 2 * parity(shift & value)) % 4 == 0 for value in points) + + +def scalar_word(rows, inverse=False): + # Earlier row updates leave all later row sums unchanged, since R R^T=56I. + word = [] + for row in rows: + word.append(["clear", 112]) + word.extend(["add", 112, p, int(value)] for p, value in row.items()) + word.append(["quarter", 112]) + if inverse: + word.append(["divide13", 112]) + word.extend(["add", p, 112, -int(value)] for p, value in row.items()) + word.append(["clear", 112]) + return word + + +def scalar_map(word): + rows = [{i: Q(1)} for i in range(113)] + for gate in word: + op, target = gate[:2] + if op == "clear": + rows[target] = {} + elif op in ("quarter", "divide13"): + divisor = 4 if op == "quarter" else 13 + rows[target] = {j: value / divisor for j, value in rows[target].items()} + else: + require(op == "add", "Unknown scalar instruction") + for j, value in list(rows[gate[2]].items()): + result = rows[target].get(j, Q(0)) + gate[3] * value + if result: + rows[target][j] = result + else: + rows[target].pop(j, None) + return rows + + +def divider_certificate(): + # Encode (remainder, input bit) by five bits. Build each valid case once. + # Each indicator uses four AND gates. Five NOT gates supply all literals. + patterns = [[2 * remainder + bit, (2 * remainder + bit) // 13, + (2 * remainder + bit) % 13] + for remainder in range(13) for bit in range(2)] + output_ones = [sum((quotient << 4 | remainder) >> i & 1 + for _, quotient, remainder in patterns) for i in range(5)] + gates = 5 + 4 * len(patterns) + sum(count - 1 for count in output_ones) + require(gates == 161, "Unsigned division gate invoice") + + def transition(remainder, bit): + state = 2 * remainder + bit + output = 0 + for pattern, quotient, next_remainder in patterns: + indicator = all(((state >> i) & 1) == ((pattern >> i) & 1) for i in range(5)) + if indicator: + output |= (quotient << 4) | next_remainder + return output >> 4, output & 15 + + require(all(transition(remainder, bit) == divmod(2 * remainder + bit, 13) + for remainder in range(13) for bit in range(2)), "All division state transitions") + + def conditional_negation(value, negative, width): + carry = negative + result = 0 + for i in range(width): + bit = ((value >> i) & 1) ^ negative + result |= (bit ^ carry) << i + carry &= bit + return result + + def divide_signed(value, width): + bits = value & ((1 << width) - 1) + negative = (bits >> (width - 1)) & 1 + magnitude = conditional_negation(bits, negative, width) + remainder = quotient = 0 + for i in reversed(range(width)): + digit, remainder = transition(remainder, (magnitude >> i) & 1) + quotient = (quotient << 1) | digit + quotient = conditional_negation(quotient, negative, width) + signed = quotient - (1 << width) if (quotient >> (width - 1)) & 1 else quotient + return signed, remainder + + checks = 0 + rejected = 0 + for value in range(-8192, 8192): + quotient, remainder = divide_signed(value, 14) + require(remainder == abs(value) % 13, "Signed division remainder") + if remainder: + rejected += 1 + else: + require(13 * quotient == value, "Exact signed division") + checks += 1 + # Each conditional negation has two XOR gates and one AND per bit. + # Four AND/OR/NOT gates implement each XOR, so two scans cost 18 per bit. + return { + "divisor": 13, + "valid_state_transitions": 26, + "unsigned_AND_OR_NOT_gates_per_numerator_bit": gates, + "signed_AND_OR_NOT_gates_per_numerator_bit": gates + 18, + "scan_order": "Conditional negation from low to high; unsigned division from high to low; conditional negation from low to high", + "extra_finite_control_bits_upper_bound": 32, + "signed_14_bit_inputs_checked": checks, + "nondivisible_inputs_with_nonzero_remainder": rejected, + "exactness_condition": "Input numerator is divisible by 13 under the common odd-grid invariant", + "excluded_costs": ["stream reads and writes", "address routing", "root common-grid conversions"], + } + + +def run(repo, interface): + started = time.monotonic() + raw = interface.read_bytes() + require(sha256(raw).hexdigest() == INTERFACE_HASH, "Interface source pin") + data = json.loads(raw) + phases, template = sources(repo) + ports = data["ports"] + require([entry["q"] for entry in phases["recipes"]] == ports, "Pinned port order") + require(template["exact_data_phase_recipe_sha256"] == PINS[PHASE], "Template phase reference") + require(template["route_semantics"]["data"] == + "physical cover class d*rho(stage,port); rho is the exact orthogonal involution from data_phases.py", + "Template cover route") + require(all(call["owners"][p][1] == [1, call["stage"], p % 112] + for call in template["calls"] for p in range(224)), "Actual data owner routes") + + points = phase_points(17) + entry_exit_checks = 0 + character_checks = 0 + tensor_checks = 0 + controls = Counter() + for entry in phases["recipes"]: + q = entry["q"] + chart = basis(q) + beta = sum((((v.bit_count() - 1) // 2) & 1) << i for i, v in enumerate(chart[1:])) + local_beta = 0 + for i, v in enumerate(chart[1:]): + if (beta >> i) & 1: + local_beta ^= v + moved_local = [(route(1 << i, chart, 1), 1) for i in range(9)] + moved_full = [(route(1 << i, chart, 1), 1) for i in range(17)] + standard_full = [(1 << i, 1) for i in range(17)] + standard_external = [(1 << i, 1) for i in range(9, 17)] + dy = q ^ (beta << 9) + dx = local_beta ^ (beta << 9) + moved_y = moved_local + [(q, -1)] + require(equal_phase(moved_y, standard_external, dy, points), "Complete Y bridge phase") + require(equal_phase(moved_full, standard_full, dx, points), "Complete X bridge phase") + require(equal_phase(moved_local, [(q, 1)] + standard_external, dy, points), + "Complete local source entrance phase") + character_checks += 3 * len(points) + controls["omitted_Y_translation_rejected"] += not equal_phase( + moved_y, standard_external, 0, points) + controls["omitted_X_translation_rejected"] += not equal_phase( + moved_full, standard_full, 0, points) + controls["reversed_Y_route_translation_order_rejected"] += not equal_phase( + moved_y, standard_external, route(dy, chart, 1), points) + # A tensor correction repeats the translation on both address factors. + for a, b in zip(points, reversed(points)): + left = phase(moved_y, a) + phase(moved_y, b) + right = phase(standard_external, a) + phase(standard_external, b) + right += 2 * (parity(dy & a) + parity(dy & b)) + require((left - right) % 4 == 0, "Two-factor Fourier operator phase") + tensor_checks += 1 + for stage, recipe in enumerate(entry["stage_alignment"]): + if not stage: + expected_in = expected_out = 0 + else: + lifted_beta = beta << (9 + 8 * (stage - 1)) + expected_in = q ^ local_beta + expected_out = local_beta ^ lifted_beta + require(route(expected_in, chart, stage) == q ^ lifted_beta, + "Owner-coordinate entry transport") + require(route(expected_out, chart, stage) == expected_out, + "Owner-coordinate exit transport") + require(recipe == dict(entry_X=expected_in, entry_Y=expected_in, + exit_X=expected_out, exit_Y=expected_out), "Actual entry/exit gauge") + entry_exit_checks += 1 + require(all(value == 112 for value in controls.values()), "A phase control was not rejected") + + r = [{int(p): Q(value) for p, value in row.items()} for row in data["R"]] + require(len(r) == 8 and sum(map(len, r)) == 448, "Centre incidence count") + require(all(value in (-1, 1) for row in r for value in row.values()), "Centre coefficient alphabet") + require(all(sum(r[i].get(p, 0) * r[j].get(p, 0) for p in range(112)) == 56 * (i == j) + for i in range(8) for j in range(8)), "Orthogonal centre rows") + scalar = {} + for inverse in (False, True): + word = scalar_word(r, inverse) + result = scalar_map(word) + denominator = 52 if inverse else 4 + expected = [] + for i in range(112): + values = {} + for j in range(112): + value = Q(i == j) - sum(row.get(i, 0) * row.get(j, 0) for row in r) / denominator + if value: + values[j] = value + expected.append(values) + expected.append({}) + require(result == expected, "Complete scalar bridge map, including arbitrary private input") + require(scalar_map(word[1:]) != expected, "Private CLEAR omission control") + if inverse: + changed = list(word) + changed.remove(["divide13", 112]) + require(scalar_map(changed) != expected, "Odd divisor omission control") + counts = Counter(gate[0] for gate in word) + bound = 2 * (4 * counts["add"] + 2 * counts["quarter"] + counts["clear"]) + require(bound == 7232, "Dyadic scalar invoice") + scalar["inverse" if inverse else "forward"] = { + "events": len(word), "macros": dict(counts), "maximum_live_private_arrays": 1, + "dyadic_real_primitive_bound": bound, + "additional_real_divide_by_13_streams": 2 * counts["divide13"], + "native_children": 0, + "full_input_columns_checked": 113, + "private_input_and_output_zero": True, + } + return { + "status": "PASS_EXACT_BRIDGE_OPERATORS_AND_ACTUAL_LOCAL_GAUGE", + "source_base": BASE, "archive_sha256": ARCHIVE_HASH, + "source_pins": PINS, "interface_sha256": INTERFACE_HASH, + "phase_method": "Exact Fourier-character evaluation on all weight-zero, one, and two inputs in the active 17-dimensional space", + "complete_phase_identity_character_checks": character_checks, + "actual_stage_entry_exit_gauges_checked": entry_exit_checks, + "actual_data_owner_routes_checked": len(template["calls"]) * 224, + "two_factor_phase_checks": tensor_checks, + "phase_controls": dict(controls), + "operator_alignment": "A=Z_delta D; A T_boundary=T_common D", + "logical_bridge": "A^-1 J A T_boundary=T_boundary D J D; the same identity holds for J^-1", + "actual_local_shear": "D L(J) D or D U(-J^T) D in the pinned boundary gauges", + "scalar_programs": scalar, + "divide13_finite_bit_circuit": divider_certificate(), + "scope": "Exact native operator and finite scalar macro invoice. Address routing, bit division cost, and a complete controller invoice remain separate.", + "seconds": time.monotonic() - started, + "maximum_resident_bytes": resource.getrusage(resource.RUSAGE_SELF).ru_maxrss, + } + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--repo", type=Path, required=True) + parser.add_argument("--interface", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + result = run(args.repo, args.interface) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + print("phase_gauges=1008 scalar_columns=226 one_private_array=true") + print("forward_real_bound=7232 inverse_extra_real_divide13_streams=16") diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_native_lift.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_native_lift.py new file mode 100644 index 0000000000..fb72255b9c --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_native_lift.py @@ -0,0 +1,336 @@ +"""Check the exact native lift and the finite local bill. + +The checker does not import the emitter or the Clifford compiler. It uses +Pauli conjugation and a separate exact state interpreter. The scalar map is +owned by the independent transpose replay in the adjacent review lane. +""" +from collections import Counter +from fractions import Fraction +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +import resource +import subprocess +import tarfile +import time + +BASE = 'bce54fb3f895cbe5cd4c0eb477c3afeed100190f' +ARCHIVE = 'research/community-frontier1042-audit/selected-replay.tar.gz' +ARCHIVE_HASH = '22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754' +PINS = { + 'CANONICAL-WORD.json.gz': '16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219', + 'LOCAL-PROGRAMS.json.gz': '241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a', + 'CLIFFORD-RECIPES.json': 'd0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731', + 'RESIDUAL-ADAPTERS.json': '383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c', +} + + +def require(condition, label): + if not condition: + raise ValueError(label) + + +def load(repo): + args = ['git', 'show', BASE + ':' + ARCHIVE] + proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE) + digest = sha256() + while chunk := proc.stdout.read(65536): + digest.update(chunk) + require(proc.wait() == 0 and digest.hexdigest() == ARCHIVE_HASH, 'archive pin') + proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE) + values = {} + with tarfile.open(fileobj=proc.stdout, mode='r|gz') as archive: + for entry in archive: + name = entry.name.removeprefix('slots/local/') + if entry.name.startswith('slots/local/') and name in PINS: + raw = archive.extractfile(entry).read() + require(sha256(raw).hexdigest() == PINS[name], name + ' pin') + values[name] = json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw) + require(proc.wait() == 0 and set(values) == set(PINS), 'source extraction') + return values + + +def parity(value): + return value.bit_count() % 2 + + +def mul(matrix, vector): + return sum(parity(row & vector) << i for i, row in enumerate(matrix)) + + +def transpose(matrix): + return tuple(sum(((row >> j) & 1) << i for i, row in enumerate(matrix)) for j in range(len(matrix))) + + +def inverse(matrix): + n = len(matrix) + rows = [row | (1 << (n+i)) for i, row in enumerate(matrix)] + for j in range(n): + pivot = next((i for i in range(j, n) if rows[i] >> j & 1), None) + require(pivot is not None, 'singular binary chart') + rows[j], rows[pivot] = rows[pivot], rows[j] + for i in range(n): + if i != j and rows[i] >> j & 1: + rows[i] ^= rows[j] + require([row & ((1 << n)-1) for row in rows] == [1 << i for i in range(n)], 'binary inverse') + return tuple(row >> n for row in rows) + + +def extend(vectors, n): + columns, pivots = [], {} + for value in tuple(vectors) + tuple(1 << i for i in range(n)): + reduced = value + while reduced: + j = reduced.bit_length()-1 + if j not in pivots: + pivots[j] = reduced + columns.append(value) + break + reduced ^= pivots[j] + require(len(columns) == n, 'frame basis extension') + return tuple(columns) + + +def adjoint(circuit): + out = [] + for gate in reversed(circuit): + if gate[0] == 'P': + out.append(('P', inverse(gate[1]))) + elif gate[0] == 'D': + out.append(('D', gate[1], tuple(-a % 4 for a in gate[2]))) + elif gate[0] == 'C': + out.append(('C', gate[1], -gate[2])) + elif gate[0] == 'phase': + out.append(('phase', -gate[1] % 4)) + else: + require(gate[0] == 'X', 'adjoint gate type') + out.append(gate) + return tuple(out) + + +def fourier(rank): + return tuple(('C', 1 << i, 1) for i in range(rank)) + + +def frame(vectors, n): + rank = len(vectors) + if rank == 0: + return () + if rank == n: + return fourier(n) + matrix = transpose(extend(vectors, n)) + columns = transpose(inverse(matrix)) + quadratic = tuple((1 << i) ^ sum(parity(a & b) << j for j, b in enumerate(columns)) for i, a in enumerate(columns)) + diagonal = tuple((row >> i) & 1 for i, row in enumerate(quadratic)) + chart = (('P', matrix), ('D', quadratic, diagonal)) + return adjoint(chart) + fourier(rank) + chart + + +def monomial(record): + matrix = tuple(record['matrix_rows']) + quadratic = tuple(record['quadratic_rows']) + linear = tuple(record['linear_Z4']) + require(transpose(quadratic) == quadratic, 'quadratic symmetry') + require(len(matrix) == len(quadratic) == len(linear) == 9, 'monomial dimension') + require(all(a % 2 == (quadratic[i] >> i) & 1 for i, a in enumerate(linear)), 'diagonal parity') + inverse(matrix) + return (('D', quadratic, linear), ('P', matrix), ('X', record['offset']), ('phase', record['phase'])) + + +def recipe(record): + rank = record['rank'] + require(isinstance(rank, int) and 0 <= rank <= 9, 'child rank') + if rank == 0: + require(record['right'] is None, 'rank zero right factor') + return monomial(record['left']) + return monomial(record['right']) + fourier(rank) + monomial(record['left']) + + +def tableau(circuit, n=9): + rows = [(1 << i, 0, 0) for i in range(n)] + [(0, 1 << i, 0) for i in range(n)] + for gate in circuit: + tag = gate[0] + out = [] + inverse_transpose = transpose(inverse(gate[1])) if tag == 'P' else None + for x, z, phase in rows: + if tag == 'P': + x, z = mul(gate[1], x), mul(inverse_transpose, z) + elif tag == 'X': + phase += 2 * parity(z & gate[1]) + elif tag == 'C': + if parity(z & gate[1]): + x ^= gate[1] + phase += 3 * gate[2] + elif tag == 'D': + quadratic, linear = gate[1:] + phase += sum(linear[i] for i in range(n) if x >> i & 1) + phase += 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(n) if x >> i & 1) + z ^= mul(quadratic, x) + else: + require(tag == 'phase', 'tableau gate type') + out.append((x, z, phase % 4)) + rows = out + return tuple(rows) + + +@lru_cache(maxsize=512) +def action(gate): + if gate[0] == 'P': + return tuple(mul(gate[1], x) for x in range(512)) + require(gate[0] == 'D', 'state action type') + quadratic, linear = gate[1:] + return tuple((sum(linear[i] for i in range(9) if x >> i & 1) + + 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(9) if x >> i & 1)) % 4 for x in range(512)) + + +def rotate(pair, power): + a, b = pair + return ((a, b), (-b, a), (-a, -b), (b, -a))[power % 4] + + +def state(circuit, basis=0): + value = [(0, 0)] * 512 + value[basis] = (1, 0) + denominator = 0 + for gate in circuit: + tag = gate[0] + if tag == 'P': + moved = [(0, 0)] * 512 + for source, target in enumerate(action(gate)): + moved[target] = value[source] + value = moved + elif tag == 'X': + value = [value[x ^ gate[1]] for x in range(512)] + elif tag == 'D': + value = [rotate(pair, p) for pair, p in zip(value, action(gate))] + elif tag == 'phase': + value = [rotate(pair, gate[1]) for pair in value] + elif tag == 'C': + direction, sign = gate[1:] + moved = [] + for x, (a, b) in enumerate(value): + c, d = value[x ^ direction] + moved.append((a-sign*b+c+sign*d, b+sign*a+d-sign*c)) + value = moved + denominator += 1 + else: + raise ValueError('state gate type') + while denominator and all((a | b) % 2 == 0 for a, b in value): + value = [(a//2, b//2) for a, b in value] + denominator -= 1 + return value, denominator + + +def equal(actual, expected, label): + require(tableau(actual) == tableau(expected), label + ': Pauli action') + require(state(actual) == state(expected), label + ': global phase') + + +def scalar_cost(gate): + if gate[0] in ('copy', 'clear'): + return 1 + value = Fraction(*gate[-2:]) + numerator, denominator = abs(value.numerator), value.denominator + require(numerator > 0 and denominator & (denominator-1) == 0, 'nonzero dyadic scalar') + if gate[0] == 'scale': + require(numerator & (numerator-1) == 0, 'dyadic scale unit') + return abs(numerator.bit_length()-denominator.bit_length()) + (value < 0) + require(gate[0] == 'add', 'scalar type') + return 3 + numerator.bit_length()-1 + numerator.bit_count() + denominator.bit_length()-1 + + +def main(args): + start = time.monotonic() + data = load(args.repo) + word = data['CANONICAL-WORD.json.gz'] + old = data['LOCAL-PROGRAMS.json.gz'] + phase = data['CLIFFORD-RECIPES.json'] + residual = data['RESIDUAL-ADAPTERS.json']['recipes'] + changed_raw = gzip.decompress(args.changed.read_bytes()) + require(sha256(changed_raw).hexdigest() == 'fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877', 'changed payload pin') + changed = json.loads(changed_raw) + require(set(changed) == {'forward', 'backward'}, 'orientation inventory') + native = lambda events: [e for e in events if e[0] in ('climb', 'adapter', 'residual_adapter')] + invoices = {} + for name, events in changed.items(): + require(native(events) == native(old[name]), 'persistent native stream') + require(all(e[0] in ('scalar', 'phase', 'climb', 'adapter', 'residual_adapter') for e in events), 'event grammar') + first = events.index(['phase', 'centre_dirty_correction']) + last = events.index(['phase', 'A']) + prefix = [e[1] for e in events[first+1:last]] + require(all(e[0] == 'scalar' and e[2] == 0 for e in events[first+1:last]), 'correction frame') + scalars = [e[1] for e in events if e[0] == 'scalar'] + paid = Counter(e[5] for e in events if e[0] == 'climb') + invoices[name] = { + 'events': len(events), 'scalar_macros': len(scalars), + 'real_component_primitive_bound': 2*sum(map(scalar_cost, scalars)), + 'prefix_macros': dict(Counter(e[0] for e in prefix)), + 'prefix_real_component_primitive_bound': 2*sum(map(scalar_cost, prefix)), + 'paid_profile': dict(sorted(paid.items())), + 'paid_rank_sum': sum(rank*count for rank, count in paid.items()), + 'persistent_native_events': len(native(events)), + } + used = {(e[3], e[4]) for e in changed['forward'] if e[0] == 'climb'} + children = {(r['old'], r['new']): r for r in phase['children']} + require(len(children) == len(phase['children']) and used <= set(children), 'child recipe binding') + frames = [frame(tuple(vectors), 9) for vectors in word['frames']] + for i, (a, b) in enumerate(sorted(used)): + record = children[a, b] + require(record['rank'] == len(word['frames'][b])-len(word['frames'][a]), 'paid frame difference') + equal(recipe(record), adjoint(frames[a])+frames[b], 'child '+str((a, b))) + if i % 500 == 0: + print('phase edges', i, '/', len(used), flush=True) + endpoints = {(r['role'], r['port']): r for r in phase['endpoint_adapters']} + require(set(endpoints) == {(role, p) for role in ('source', 'target') for p in range(112)}, 'endpoint coverage') + for (role, port), record in endpoints.items(): + q = word['ports'][port] + conventional = (('C', q, 1),) if role == 'source' else (('C', q, -1),)+fourier(9) + expected_frame = word['start'][port] if role == 'source' else word['final'][112+port] + require(record['frame'] == expected_frame and record['rank'] == 0, 'endpoint frame binding') + equal(recipe(record), adjoint(conventional)+frames[expected_frame], 'endpoint '+str((role, port))) + used_residual = set() + for event in changed['forward']: + if event[0] == 'residual_adapter': + _, position, register, entry, *tail = event + terminal = tail[0] if tail else 1 + key = str(entry) if terminal == 1 else str(entry)+':'+str(terminal) + require(key in residual and position in ('pre', 'post'), 'residual binding') + require(entry == word['start'][register] and terminal == word['final'][register], 'residual boundary') + used_residual.add(key) + for key in sorted(used_residual): + record = residual[key] + entry = record['frame'] + terminal = record.get('terminal', 1) + equal(recipe(record), adjoint(frames[entry])+frames[terminal], 'residual '+key) + probe = next(r for r in children.values() if r['left']['phase'] != 0 or r['right'] and r['right']['phase'] != 0) + correct = recipe(probe) + corrupt = tuple(gate for gate in correct if gate[0] != 'phase') + if state(corrupt) == state(correct): + corrupt = correct+(('phase', 1),) + require(tableau(corrupt) == tableau(correct) and state(corrupt) != state(correct), 'global phase negative control') + require(state(corrupt, 1) != state(correct, 1), 'phase control second input') + report = { + 'status': 'PASS_INDEPENDENT_NATIVE_FRAME_LIFT_AND_FINITE_LOCAL_BILL', + 'base': BASE, 'archive_sha256': ARCHIVE_HASH, 'member_sha256': PINS, + 'changed_payload_sha256': sha256(changed_raw).hexdigest(), + 'checked_unique_persistent_edges': len(used), 'checked_endpoint_adapters': len(endpoints), + 'checked_residual_recipes': len(used_residual), 'finite_local_invoice': invoices, + 'exact_operator_method': 'Pauli conjugation and exact Gaussian dyadic zero state; no compiler import', + 'negative_controls': ['wrong global phase with the same Pauli action, on basis inputs 0 and 1'], + 'all_tensor_powers': 'Base operators are exactly equal, so their tensor powers are equal for every positive integer. The common frame conjugation proof gives the full array map.', + 'not_claimed': ['global chart or owner admission', 'recursive supplier admission', 'new kappa', 'fresh all-size compiler proof'], + 'seconds': time.monotonic()-start, 'max_rss_bytes': resource.getrusage(resource.RUSAGE_SELF).ru_maxrss, + } + args.out.write_text(json.dumps(report, indent=2, sort_keys=True)+'\n') + print(report['status'], flush=True) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--repo', type=Path, required=True) + parser.add_argument('--changed', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + main(parser.parse_args()) diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz 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b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE-FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "RESPONSE.md": "5ea5866231992c389ae2796f1534e0af90ca88bcedfa3fa9758d78f9457d2981", + "check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "run-normal/RESPONSE-CHECKS.json": "7f84440d79200b8c060aad07b910bb96f2bcdde95b07ddb8d41bcea1fcb09d5c", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c" + }, + "normal_optimized_byte_identical": true, + "scope": "Native phase and routed terminal review remain open.", + "status": "PASS_EXACT_RESPONSE_AND_SCALAR_CODES" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md new file mode 100644 index 0000000000..0ee7aebbb6 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md @@ -0,0 +1,165 @@ +# A rank-thirty correction on the actual 112 ports + +This packet gives an exact unit response E on the actual 112 data ports. +It has rank(E-I)=30. The previous signed matching has correction rank +56. The new response keeps the useful selected eight-port principal +block L. Both E and E^-1 have selected block L. The ordinary principal +block is also a dyadic unit. + +The packet also gives complete in-place scalar words for E, E^-1, E^T, +and E^-T. Each word costs 3210 real scalar primitives at a common +frame. It uses no owned or borrowed field. These are port-code and +matrix results. Native phase lowering, routed access, the physical +terminal, helper progress, and the complete supplier cost are separate. + +## The 48-port reciprocal part + +The signed pair code H comes from the pinned cyclic family. Its 24 +two-field blocks satisfy H H^T=2I. The six coded fields at each of +eight vertices have their actual carrier labels in the payload. + +Use the root's reciprocal six-mode matrix. Write a=(a0,a1,a2,a3), +s=sum(a), and define + +```text +E6(a,b,c) = (a-s*1+b*1, c, -2s+3b), +E6^-1(a,b,c) = (a-s*1+c*1, -2s+3c, b). +``` + +Both matrices are integer units with determinant one and zero +diagonal. Their correction rank is two. The root proof establishes +the general construction and the sharp rank-two lower bound. + +At each vertex, put its two modes that meet the selected physical +ports in the first two a positions. Fill the other four positions in +the source order. Conjugate the block by the sign diagonal + +```text +D_v = diag(1, alpha_v, 1, 1, 1, 1), +alpha_v = (-1)^v. +``` + +The two selected-mode off-diagonal entries of both D_v E6 D_v and +D_v E6^-1 D_v are -alpha_v. All their diagonal entries are zero. +Consequently the physical selected block is exactly the old L after +the pair code is removed. The full physical 48-port response is +H^-1 (direct_sum_v D_v E6 D_v) H. It has determinant one and +correction rank sixteen. Its inverse is explicitly given by the same +formula with E6^-1. + +This assignment is significant for the existing selected interface: +L^2=I/2 and det(L)=1/16 remain valid. It is not an arbitrary rank-two +block that loses the selected principal unit. + +The mode word uses E6=P R, where P exchanges b and c. The reflection +R is implemented without a scratch field. With d_i the four a signs, +execute + +```text +b -= sum_i d_i a_i +a_i += d_i b for each i +b *= -1 +b += sum_i d_i a_i +exchange b,c +``` + +The exchange is four priced scalar instructions: three unit ADDs and +one negative unit scale. Thus each six-mode word costs 124. The eight +words cost 992. The physical pair code and its inverse cost 940 on +one bank. This gives 1932 for the complete 48-port scalar code. + +The reflection factor alone has nonzero diagonal. Its scalar code +does not prove that it can be used as a free native transfer. + +## A fourteen-block cover of the other 64 ports + +The exact orthogonality graph joins ports p,r when q_p dot q_r=0. +All 64 q labels have odd norm. Exhaustive maximal-clique enumeration +finds 896 maximal cliques of size four and 64 of size eight. In +particular, this fixed support has no nine-clique. + +The payload gives a disjoint cover by eleven five-cliques and three +three-cliques. On a clique of size k use + +```text +C_k = I-J_k, C_k^-1 = I-J_k/(k-1). +``` + +Here J_k is the all-ones matrix. Each C_k is a dyadic unit, has zero +diagonal, and differs from identity by rank one. Thus the 64-port +part has correction rank fourteen and determinant 2^25. + +Fourteen is optimal within disjoint dyadic rank-one clique blocks of +sizes two, three, and five. A cover with at most twelve blocks covers +at most sixty ports. Thirteen five-blocks cover sixty-five ports, and +replacing a size five by size three or two decreases this number by +two or three, never by one. The graph has no size nine block. This is +a lower bound for this stated clique model, not a lower bound for all +native constructions or terminal decoders. + +An in-place word for C_k is + +```text +a += sum(rest) +b -= a for each remaining field b +a *= -(k-1) +a -= sum(rest) +``` + +The word uses 3(k-1) unit ADDs and one dyadic scale. Its cost is 102 +when k=5 and 52 when k=3. The complete small code costs +11*102+3*52=1278. Reverse the word and invert its instructions to +obtain the inverse. The inverse has nonzero diagonal and is not +claimed to belong to the direct native zero-diagonal family. + +## Complete code and principal inverse + +Combine the two disjoint responses. The resulting E has determinant +2^25 and correction rank thirty. The payload gives exact matrices U,V +with 30 columns and rows, respectively, such that E-I=UV. Both U and +V have rank thirty. + +Let S be the old selected eight ports and U0 its complement. Partition +E^-1 as [[L,N],[P,Q]]. Then + +```text +(E_U0,U0)^-1 = Q-P L^-1 N. +``` + +Both multiplication orders are checked on all 104 ordinary columns. +Every inverse coefficient is dyadic. The ordinary determinant is +2^21. The selected determinant is 1/16. + +The combined scalar word costs 1932+1278=3210. Its reverse gives +E^-1. Reverse the instruction order and transpose each elementary +operation to give E^T; apply both operations to give E^-T. Every word +is checked on all 112 columns. The maximum prefix row one-norm is +44 for E and E^-1, and 14 for E^T and E^-T. These are bounds for the +top-level scalar word only. + +The generic five-code controller can use a native forward response +E and raw backward response E^T, provided each common-frame code is +legally bound at its stated cut. Its residual is still the ordered +operator E2 E1^-T E0. The physical terminal sees +Q(E2 E1^-T E0)Q^-1. Rank thirty in one local chart does not provide +free access to those correction coordinates in a routed hole frame. + +## Reproduction and credit + +The checker requires a new output directory and preserves all source +packets. Run it once with ordinary Python and once with optimized +Python, with different output directories. The expected status is +PASS_LOW_DISPLACEMENT_RESPONSE. The two payloads and receipts must +be byte-identical. + +The root supplied the reciprocal rank-two matrix and its proof. The +independent-review lane supplied the complete cyclic zero-diagonal +family. The controller and oblique-native lanes supplied the actual +signed pair coordinates and the selected matching interface. The +encoded-controller lane supplied the legal-cut general-unit +controller and the three-field I-J code. This packet binds the +selected principal units, gives the actual fourteen-clique cover, +and extends the scalar code to five fields. AI assistance was used. + +No PR or publication is authorized. Before any future PR description, +read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py new file mode 100644 index 0000000000..17a70cda41 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py @@ -0,0 +1,339 @@ +#!/usr/bin/env python3 +"""Bind the rank-two response and the small clique cover to actual ports.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": + "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", +} +CLIQUES = [ + [5, 34, 40, 85, 97], [3, 32, 38, 50, 95], [24, 48, 67, 80, 82], + [23, 35, 55, 65, 68], [1, 17, 66, 75, 83], [8, 12, 45, 107, 109], + [29, 49, 54, 56, 108], [26, 30, 64, 73, 96], [4, 33, 69, 74, 88], + [18, 22, 84], [19, 28, 77], [39, 58, 86], [6, 98, 100, 101, 102], + [31, 59, 60, 93, 103], +] + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(relative): + raw = (LANES / relative).read_bytes() + need(sha256(raw).hexdigest() == PINS[relative], "Source pin " + relative) + return json.loads(raw) + + +def identity(n): + return [{i: F(1)} for i in range(n)] + + +def add(target, source, coefficient=F(1)): + for key, value in source.items(): + target[key] = target.get(key, F(0)) + coefficient * value + if not target[key]: + del target[key] + + +def product(a, b): + result = [] + for row in a: + value = {} + for j, coefficient in row.items(): + add(value, b[j], coefficient) + result.append(value) + return result + + +def transpose(a, n): + result = [{} for _ in range(n)] + for i, row in enumerate(a): + for j, value in row.items(): + result[j][i] = value + return result + + +def restrict(a, ports): + index = {p: i for i, p in enumerate(ports)} + return [{index[p]: value for p, value in a[row].items() if p in index} + for row in ports] + + +def rank(rows, columns): + rows = [dict(row) for row in rows] + pivot = 0 + for column in range(columns): + found = next((i for i in range(pivot, len(rows)) if rows[i].get(column)), None) + if found is None: + continue + rows[pivot], rows[found] = rows[found], rows[pivot] + c = rows[pivot][column] + rows[pivot] = {p: v / c for p, v in rows[pivot].items()} + for i in range(pivot + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[pivot], -rows[i][column]) + pivot += 1 + return pivot + + +def determinant(rows): + rows = [dict(row) for row in rows] + result = F(1) + for column in range(len(rows)): + found = next((i for i in range(column, len(rows)) if rows[i].get(column)), None) + if found is None: + return F(0) + if found != column: + rows[column], rows[found] = rows[found], rows[column] + result = -result + c = rows[column][column] + result *= c + for i in range(column + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[column], -rows[i][column] / c) + return result + + +def inverse_word(word): + return [[op, target, origin, str(1 / F(c) if op == "scale" else -F(c))] + for op, target, origin, c in reversed(word)] + + +def transpose_word(word): + return [[op, target if op == "scale" else origin, + origin if op == "scale" else target, c] + for op, target, origin, c in reversed(word)] + + +def replay(word): + state = identity(112) + maximum = F(1) + for op, target, origin, coefficient in word: + c = F(coefficient) + if op == "scale": + state[target] = {p: c * v for p, v in state[target].items() if c * v} + else: + need(op == "add" and target != origin, "Scalar word grammar") + add(state[target], state[origin], c) + maximum = max(maximum, sum(abs(c) for c in state[target].values())) + return state, maximum + + +def price(word): + result = 0 + for op, _, _, coefficient in word: + c = F(coefficient) + a, b = abs(c.numerator), c.denominator + need(a and not b & (b - 1), "Dyadic coefficient") + if op == "scale": + need(not a & (a - 1), "Dyadic unit scale") + result += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) + else: + result += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + return result + + +def maximal_cliques(ports, q): + n = len(ports) + adjacent = [sum(1 << j for j, r in enumerate(ports) + if i != j and not (q[p] & q[r]).bit_count() % 2) + for i, p in enumerate(ports)] + result = [] + + def visit(chosen, possible, excluded): + if not possible and not excluded: + result.append(chosen) + return + options = possible | excluded + pivot = max((i for i in range(n) if options >> i & 1), + key=lambda i: (adjacent[i] & possible).bit_count(), default=0) + todo = possible & ~adjacent[pivot] + while todo: + bit = todo & -todo + i = bit.bit_length() - 1 + todo -= bit + visit(chosen | bit, possible & adjacent[i], excluded & adjacent[i]) + possible -= bit + excluded |= bit + + visit(0, (1 << n) - 1, 0) + return [[ports[i] for i in range(n) if mask >> i & 1] for mask in sorted(result)] + + +def encoded(rows): + return [{str(p): str(c) for p, c in sorted(row.items())} for row in rows] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = read(next(name for name in PINS if "CYCLIC" in name)) + matching = read(next(name for name in PINS if "MATCHED" in name)) + selected, small = matching["selected_ports"], matching["small_ports"] + selected_set = set(selected) + q = cyclic["ports"] + h = identity(112) + codes = [] + for pair in cyclic["pair_codes"]: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + h[a], h[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)} + if aa != 1: + codes.append(["scale", a, None, str(aa)]) + codes.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + hi = transpose(h, 112) + for p in cyclic["affected_ports"]: + hi[p] = {k: v / 2 for k, v in hi[p].items()} + need(product(h, hi) == identity(112), "Actual pair inverse") + mode = identity(112) + mode_inverse = identity(112) + mode_u, mode_v = [{} for _ in range(112)], [] + mode_word, assignments = [], [] + for vertex, group in enumerate(cyclic["cyclic_carriers"]): + chosen = [p for p in group if selected_set.intersection(map(int, cyclic["mode_rows"][str(p)]))] + rest = [p for p in group if p not in chosen] + need(len(chosen) == 2 and len(rest) == 4, "Two selected modes per vertex") + order = chosen + rest + signs = [1, 1 if vertex % 2 == 0 else -1, 1, 1, 1, 1] + e = [{j: F((i == j) - 1) for j in range(4) if i != j} | {4: F(1)} + for i in range(4)] + e += [{5: F(1)}, {0: F(-2), 1: F(-2), 2: F(-2), 3: F(-2), 4: F(3)}] + swap = [0, 1, 2, 3, 5, 4] + ei = [{swap[j]: c for j, c in e[swap[i]].items()} for i in range(6)] + need(product(e, ei) == product(ei, e) == identity(6), "Six-mode reciprocal pair") + for i, p in enumerate(order): + mode[p] = {order[j]: c * signs[i] * signs[j] for j, c in e[i].items()} + mode_inverse[p] = {order[j]: c * signs[i] * signs[j] for j, c in ei[i].items()} + offset = len(mode_v) + local_u = [[1, 0]] * 4 + [[0, 1], [2, -1]] + local_v = [[-1, -1, -1, -1, 1, 0], [0, 0, 0, 0, -1, 1]] + for i, p in enumerate(order): + mode_u[p].update({offset + j: F(value * signs[i]) + for j, value in enumerate(local_u[i]) if value}) + mode_v.extend([{order[j]: F(value * signs[j]) for j, value in enumerate(row) if value} + for row in local_v]) + a, b, c = order[:4], order[4], order[5] + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(-signs[i])]) + for i, p in enumerate(a): + mode_word.append(["add", p, b, str(signs[i])]) + mode_word.append(["scale", b, None, "-1"]) + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(signs[i])]) + mode_word.extend([["add", b, c, "1"], ["add", c, b, "-1"], + ["add", b, c, "1"], ["scale", c, None, "-1"]]) + assignments.append({"vertex": vertex, "ordered_carriers_a_b_c": order, "signs": signs}) + need(replay(mode_word)[0] == mode, "In-place rank-two mode code") + response, response_inverse = product(hi, product(mode, h)), product(hi, product(mode_inverse, h)) + u, v = product(hi, mode_u), product(mode_v, h) + small_word = [] + need(sorted(p for group in CLIQUES for p in group) == sorted(small), "Exact disjoint64 cover") + for group in CLIQUES: + k = len(group) + need(k in (3, 5), "Dyadic clique size") + need(all((q[p] & q[r]).bit_count() % 2 == int(p == r) + for p in group for r in group), "Actual orthonormal clique") + for p in group: + response[p] = {r: F(-1) for r in group if r != p} + response_inverse[p] = {r: F(int(p == r)) - F(1, k - 1) for r in group} + u[p] = {len(v): F(-1)} + v.append({p: F(1) for p in group}) + a, rest = group[0], group[1:] + small_word.extend([["add", a, p, "1"] for p in rest]) + small_word.extend([["add", p, a, "-1"] for p in rest]) + small_word.append(["scale", a, None, str(1 - k)]) + small_word.extend([["add", a, p, "-1"] for p in rest]) + word = codes + mode_word + inverse_word(codes) + small_word + common_words = {"E": word, "inverse_E": inverse_word(word), + "transpose_E": transpose_word(word), + "inverse_transpose_E": transpose_word(inverse_word(word))} + expected = {"E": response, "inverse_E": response_inverse, + "transpose_E": transpose(response, 112), + "inverse_transpose_E": transpose(response_inverse, 112)} + word_receipts = {} + for name, gates in common_words.items(): + actual, maximum = replay(gates) + need(actual == expected[name], "Full112 scalar code " + name) + need(replay(gates + inverse_word(gates))[0] == identity(112), "Both code orders " + name) + word_receipts[name] = {"real_scalar_primitives": price(gates), + "prefix_row_l1_bound": str(maximum), "owned_fields": 0} + need(product(response, response_inverse) == product(response_inverse, response) == identity(112), + "Full112 reciprocal products") + correction = [dict(row) for row in response] + for i in range(112): + add(correction[i], {i: F(-1)}) + need(product(u, v) == correction and rank(u, 30) == rank(v, 112) == 30, + "Exact full rank30 correction factor") + l = restrict(response, selected) + li = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_inverse"]] + old_l = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_block"]] + need(l == restrict(response_inverse, selected) == old_l, "Both selected blocks retain L") + need(product(l, li) == identity(8), "Selected inverse") + ordinary = sorted(set(range(112)) - selected_set) + p = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(selected) + if response_inverse[r].get(s)} for r in ordinary] + n = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(ordinary) + if response_inverse[r].get(s)} for r in selected] + ordinary_inverse = restrict(response_inverse, ordinary) + for row, update in zip(ordinary_inverse, product(product(p, li), n)): + add(row, update, -1) + ordinary_block = restrict(response, ordinary) + need(product(ordinary_block, ordinary_inverse) == product(ordinary_inverse, ordinary_block) + == identity(104), "Both ordinary104 inverse orders") + need(all(not c.denominator & (c.denominator - 1) + for row in ordinary_inverse for c in row.values()), "Dyadic ordinary inverse") + maxima = maximal_cliques(small, q) + histogram = Counter(map(len, maxima)) + need(histogram == {4: 896, 8: 64}, "Exhaustive maximal clique census") + # A separate exhaustive extension pass checks the absence of a ninth vertex. + need(all(not any(p not in clique and all(not (q[p] & q[r]).bit_count() % 2 for r in clique) + for p in small) for clique in maxima), "Each reported clique is maximal") + receipt = { + "status": "PASS_LOW_DISPLACEMENT_RESPONSE", + "source_pins": PINS, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "correction_rank_large48": 16, "correction_rank_small64": 14, "correction_rank_full112": 30, + "selected_determinant": str(determinant(l)), + "full_determinant": str(determinant(response)), + "ordinary104_determinant": str(determinant(ordinary_block)), + "small_clique_sizes": dict(sorted(Counter(map(len, CLIQUES)).items())), + "all_maximal_small_clique_sizes": dict(sorted(histogram.items())), + "common_frame_scalar_codes": word_receipts, + "scope": "Exact port matrices, principal units, scalar codes and geometry. Native phases and terminal access are separate.", + } + payload = { + "source_pins": PINS, "ports": q, "selected_ports": selected, "ordinary_ports": ordinary, + "large_ports": cyclic["affected_ports"], "small_ports": small, + "vertex_assignments": assignments, "mode_response": encoded(mode), + "mode_inverse": encoded(mode_inverse), "small_cliques": CLIQUES, + "response": encoded(response), "response_inverse": encoded(response_inverse), + "correction_U": encoded(u), "correction_V": encoded(v), + "selected_block": encoded(l), "selected_inverse": encoded(li), + "ordinary_inverse": encoded(ordinary_inverse), "common_frame_words": common_words, + "maximal_small_cliques": maxima, + } + raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode() + (args.out / "RESPONSE-PROGRAM.json").write_bytes(raw) + receipt["payload_sha256"] = sha256(raw).hexdigest() + (args.out / "RESPONSE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py new file mode 100644 index 0000000000..532c8709eb --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py @@ -0,0 +1,279 @@ +#!/usr/bin/env python3 +"""Emit and check the native rank-thirty response on the actual ports.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + ("plain", "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"), + "new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json": + ("plain", "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c"), + "new-core-transfer-20261017/low-displacement-20261020/check_response.py": + ("plain", "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"), + "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz": + ("decompressed", "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa"), + "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py": + ("plain", "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"), + "interface-proof/verify_native_lift.py": + ("plain", "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b"), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(relative): + mode, pin = PINS[relative] + raw = (LANES / relative).read_bytes() + if mode == "decompressed": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Source pin " + relative) + return raw + + +def load_module(name, relative): + read(relative) + spec = importlib.util.spec_from_file_location(name, LANES / relative) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +r = load_module("low_response", "new-core-transfer-20261017/low-displacement-20261020/check_response.py") +compiler = load_module("low_compiler", "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py") +phase = load_module("low_phase", "interface-proof/verify_native_lift.py") + + +def basis(vectors): + rows = list(dict.fromkeys(vectors)) + count = 0 + for bit in range(8, -1, -1): + found = next((i for i in range(count, len(rows)) if rows[i] >> bit & 1), None) + if found is None: + continue + rows[count], rows[found] = rows[found], rows[count] + for i in range(len(rows)): + if i != count and rows[i] >> bit & 1: + rows[i] ^= rows[count] + count += 1 + return tuple(rows[:count]) + + +def rows(value): + return [{int(p): F(c) for p, c in row.items()} for row in value] + + +def verify_word(word, response, direction): + current = list(word["start"]) + state = [{i: F(1)} for i in range(len(current))] + maximum = F(1) + scalar_word = [] + for event in word["events"]: + if event[0] == "native": + _, field, old, new, rank, key = event + need(current[field] == old, "Literal native entry frame") + need(len(basis(word["frames"][old] + word["frames"][new])) == len(word["frames"][new]), + "Literal nested native edge") + need(rank == len(word["frames"][new]) - len(word["frames"][old]) + == word["native_recipes"][key]["rank"], "Literal native rank") + current[field] = new + else: + need(event[0] == "scalar", "Literal event grammar") + gate, frame = event[1:] + op, target, origin, coefficient = gate + c = F(coefficient) + need(current[target] == frame, "Literal scalar target frame") + if op == "scale": + state[target] = {p: c * v for p, v in state[target].items() if c * v} + else: + need(op == "add" and target != origin and current[origin] == frame, + "Literal scalar source frame") + r.add(state[target], state[origin], c) + maximum = max(maximum, sum(abs(v) for v in state[target].values())) + scalar_word.append(gate) + expected = [{i: F(1)} for i in range(len(current))] + for target, row in enumerate(response): + if direction == "forward": + r.add(expected[112 + target], row) + else: + for origin, coefficient in row.items(): + r.add(expected[origin], {112 + target: -coefficient}) + need(state == expected and current == word["final"], "All640 columns and final frames") + profile = Counter(event[4] for event in word["events"] if event[0] == "native") + return {"all_input_columns": len(current), "untouched_arbitrary_fields": len(current) - 224, + "owned_fields": 0, "private_fields": 0, "native_profile": dict(sorted(profile.items())), + "native_mass": sum(k * v for k, v in profile.items()), "native_children": sum(profile.values()), + "real_scalar_primitives": r.price(scalar_word), "prefix_row_l1_bound": str(maximum), + "native_side_map_bound": 2 * sum(profile.values()), "endpoint_maps": 224} + + +def make_word(cyclic, model, direction): + frames = deepcopy(cyclic["frames"]) + indices = {tuple(frame): i for i, frame in enumerate(frames)} + small = set(model["small_ports"]) + current = list(cyclic["start"]) + events = [] + mode = rows(model["mode_response"]) + by_parameter = {record["id"]: record for record in cyclic["parameters"]} + transfer_records = [] + for event in cyclic["programs"][direction]: + kind = event[0] + if kind == "native": + _, field, old, new, rank = event + if field % 112 in small: + need(field < 224, "Only data fields receive native progress") + continue + need(current[field] == old, "Pinned cyclic native frame") + current[field] = new + events.append(["native", field, old, new, rank, str(old) + ":" + str(new)]) + elif kind == "parameter_add": + _, target, origin, parameter, sign, frame = event + record = by_parameter[parameter] + carriers = cyclic["cyclic_carriers"][record["vertex"]] + c = sign * mode[carriers[record["row"]]].get(carriers[record["column"]], F(0)) + if c: + transfer_records.append({"part": "large48", "event": len(events), + "coefficient": str(c), "parameter": parameter}) + events.append(["scalar", ["add", target, origin, str(c)], frame]) + else: + need(kind in ("add", "scale"), "Pinned cyclic scalar grammar") + _, target, origin, coefficient, frame = event + events.append(["scalar", [kind, target, origin, coefficient], frame]) + + def frame(vectors): + vectors = basis(vectors) + if vectors not in indices: + indices[vectors] = len(frames) + frames.append(list(vectors)) + return indices[vectors] + + def native(field, new): + old = current[field] + if old == new: + return + need(len(basis(frames[old] + frames[new])) == len(frames[new]), "Clique nested edge") + events.append(["native", field, old, new, len(frames[new]) - len(frames[old]), + str(old) + ":" + str(new)]) + current[field] = new + + q = cyclic["ports"] + for group in model["small_cliques"]: + k = len(group) + for depth in range(1, k): + for i, p in enumerate(group): + native(p, frame(q[group[(i + j) % k]] for j in range(depth))) + native(112 + p, frame(q[group[(i - j) % k]] for j in range(1, depth + 1))) + for i, p in enumerate(group): + target_port = group[(i + depth) % k] + need(current[p] == current[112 + target_port], "Every clique transfer has equal frames") + target, origin, coefficient = ((112 + target_port, p, "-1") if direction == "forward" + else (p, 112 + target_port, "1")) + transfer_records.append({"part": "small64", "event": len(events), + "source_port": p, "target_port": target_port, + "coefficient": coefficient}) + events.append(["scalar", ["add", target, origin, coefficient], current[p]]) + for p in group: + native(p, cyclic["final"][p]) + native(112 + p, cyclic["final"][112 + p]) + need(current == cyclic["final"], "Full native frame completion") + return {"frames": frames, "start": cyclic["start"], "final": cyclic["final"], + "events": events, "transfer_records": transfer_records} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = json.loads(read("independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json")) + model = json.loads(read("new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json")) + core = json.loads(read("new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz")) + for provider, data in core["providers"].items(): + need(data["canonical"]["ports"] == cyclic["ports"], "Pinned provider directions " + provider) + need(len(data["canonical"]["start"]) == 632, "Pinned live-field count " + provider) + words = {direction: make_word(cyclic, model, direction) for direction in ("forward", "backward")} + need(words["forward"]["frames"] == words["backward"]["frames"], "Both directions use the same actual frames") + frames = words["forward"]["frames"] + edge_pairs = sorted({(event[2], event[3]) for word in words.values() + for event in word["events"] if event[0] == "native"}) + recipes = {} + for i, (old, new) in enumerate(edge_pairs): + operation = compiler.canonical_frame(9, tuple(frames[old])).adjoint().then( + compiler.canonical_frame(9, tuple(frames[new]))) + record, _ = compiler.lower_child(operation) + need(record["rank"] == len(frames[new]) - len(frames[old]), "Fresh native rank") + phase.equal(phase.recipe(record), phase.adjoint(phase.frame(frames[old], 9)) + + phase.frame(frames[new], 9), "Fresh native phase " + str((old, new))) + recipes[str(old) + ":" + str(new)] = record + if (i + 1) % 100 == 0: + print("Native phases", i + 1, "/", len(edge_pairs), flush=True) + endpoints = [] + for p, q in enumerate(cyclic["ports"]): + for role in ("source", "target"): + conventional = (compiler.cgate(9, q) if role == "source" + else compiler.cgate(9, q, -1).then(compiler.fourier(9))) + circuit = (("C", q, 1),) if role == "source" else (("C", q, -1),) + phase.fourier(9) + frame = cyclic["start"][p] if role == "source" else cyclic["final"][112 + p] + operation = conventional.adjoint().then(compiler.canonical_frame(9, tuple(frames[frame]))) + record, _ = compiler.lower_child(operation) + need(record["rank"] == 0, "Endpoint adapter is monomial") + phase.equal(phase.recipe(record), phase.adjoint(circuit) + phase.frame(frames[frame], 9), + "Fresh conventional endpoint " + str((role, p))) + endpoints.append({"port": p, "role": role, "frame": frame, **record}) + reports = {} + for direction, word in words.items(): + word["native_recipes"] = recipes + word["endpoint_adapters"] = endpoints + reports[direction] = verify_word(word, rows(model["response"]), direction) + need(reports["forward"]["native_profile"] == {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}, + "Complete profile") + need(reports["forward"]["native_mass"] == 1792 and reports["forward"]["real_scalar_primitives"] == 5288, + "Complete local invoice") + # Deletion of one nonzero transfer must change the complete content map. + bad = deepcopy(words["forward"]) + del bad["events"][bad["transfer_records"][0]["event"]] + try: + verify_word(bad, rows(model["response"]), "forward") + except ValueError: + pass + else: + raise ValueError("The missing transfer control was accepted") + payload = {"schema": "low-displacement-native-v1", "source_pins": PINS, + "response": model["response"], "common_frame_words": model["common_frame_words"], + "selected_ports": model["selected_ports"], "small_cliques": model["small_cliques"], + "providers": {provider: words for provider in core["providers"]}} + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for provider, directions in saved["providers"].items(): + for direction, word in directions.items(): + need(verify_word(word, rows(saved["response"]), direction) == reports[direction], + "Serialized provider replay " + provider + " " + direction) + (args.out / "NATIVE-PROGRAM.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = {"status": "PASS_LOW_DISPLACEMENT_NATIVE", "source_pins": PINS, + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "fresh_native_phase_checks": len(recipes), "fresh_endpoint_phase_checks": len(endpoints), + "reports": reports, "same_geometry_both_providers_checked": True, + "negative_control": "one nonzero transfer omitted and rejected", + "scope": "Complete local data shears and exact phases. Helpers are unchanged; their progress, recursive hosting, routed codes and terminal remain open."} + (args.out / "NATIVE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/native-normal-v2/NATIVE-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..725c71f7ea6f0cc0b316852deaf034ed3d87725f GIT binary patch literal 233723 zcmZ5`V{l|$w03OU&crq*wrzEsOq_`(b~0hdHYc`iPcX4J6P-?xjnt*_g89?zSJo{s~TI7j7}nmPl& zwgs2_-TaMbahi|62L)%OVc~@OKh>gMESBF{zjuyHa`#L+9;a529(vf^i8l#$l4MM> 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b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/pivot-codes/emit_pivot_codes.py new file mode 100644 index 0000000000..a29bb99743 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/pivot-codes/emit_pivot_codes.py @@ -0,0 +1,227 @@ +#!/usr/bin/env python3 +"""Emit an in-place centre code for the exact rank-sixteen response.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +PARENT = HERE.parent +LANES = PARENT.parents[1] +PINS = { + PARENT / "check_response.py": + "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", +} +SOURCE = PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz" +SOURCE_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" + + +def need(test, message): + if not test: + raise ValueError(message) + + +for path, pin in PINS.items(): + need(sha256(path.read_bytes()).hexdigest() == pin, "Source pin " + str(path)) +spec = importlib.util.spec_from_file_location("response_helpers", PARENT / "check_response.py") +r = importlib.util.module_from_spec(spec) +spec.loader.exec_module(r) + + +def inverse(word): + result = [] + for op, target, source, coefficient in reversed(word): + if op == "fixed_multiply": + result.append(["fixed_divide", target, source, coefficient]) + elif op == "fixed_divide": + result.append(["fixed_multiply", target, source, coefficient]) + elif op == "translate": + result.append([op, target, source, coefficient]) + else: + value = F(coefficient) + result.append([op, target, source, str(1 / value if op == "scale" else -value)]) + return result + + +def replay(word, spatial=False): + state = [{(i, 0): F(1)} if spatial else {i: F(1)} for i in range(640)] + norm, binary_height, odd_height = F(1), 0, 0 + for op, target, source, coefficient in word: + need(0 <= target < 112, "Only data targets") + if op == "translate": + need(spatial, "Translation requires the spatial interpreter") + state[target] = {(i, t ^ int(coefficient)): c for (i, t), c in state[target].items()} + elif op == "add": + need(0 <= source < 112 and source != target, "Only distinct data sources") + r.add(state[target], state[source], F(coefficient)) + else: + need(op in ("scale", "fixed_multiply", "fixed_divide"), "Literal scalar grammar") + value = F(coefficient) + if op == "fixed_divide": + value = 1 / value + state[target] = {i: c * value for i, c in state[target].items() if c * value} + norm = max(norm, sum(abs(c) for c in state[target].values())) + for coefficient in state[target].values(): + denominator = coefficient.denominator + binary = odd = 0 + while denominator % 2 == 0: + denominator //= 2 + binary += 1 + while denominator % 3 == 0: + denominator //= 3 + odd += 1 + need(denominator == 1, "Only the declared binary and odd-three grid") + binary_height, odd_height = max(binary_height, binary), max(odd_height, odd) + for i in range(112, 640): + need(state[i] == ({(i, 0): F(1)} if spatial else {i: F(1)}), + "Every other arbitrary input stays unchanged") + return state[:112], { + "maximum_prefix_row_one_norm": str(norm), + "additional_binary_height": binary_height, + "additional_odd_three_height": odd_height, + } + + +def price(word): + old, odd_multiply, odd_divide, translations = 0, 0, 0, 0 + for gate in word: + if gate[0] == "fixed_multiply": + odd_multiply += 2 + elif gate[0] == "fixed_divide": + odd_divide += 2 + elif gate[0] == "translate": + translations += 1 + else: + old += r.price([gate]) + return { + "old_real_scalar_units": old, + "real_fixed_three_multiplication_scans": odd_multiply, + "real_fixed_three_division_scans": odd_divide, + "explicit_translation_maps": translations, + "native_children": 0, + "owned_fields": 0, + } + + +def make_code(model, cyclic): + word = [] + pair_matrix = r.identity(112) + for pair in cyclic["pair_codes"]: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + pair_matrix[a], pair_matrix[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)} + if aa != 1: + word.append(["scale", a, None, str(aa)]) + word.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + groups = [ + {"ports": item["ordered_carriers_a_b_c"], "signs": item["signs"], "kind": "large"} + for item in model["vertex_assignments"] + ] + groups += [{"ports": group, "signs": [1] * 8, "kind": "small"} + for group in model["small_cliques"]] + need(sorted(p for group in groups for p in group["ports"]) == list(range(112)), + "The sixteen mode blocks partition all data fields") + modes = r.identity(112) + diagonal = r.identity(112) + for group in groups: + ports, signs = group["ports"], group["signs"] + pivot, size = ports[0], len(ports) + group["pivot"] = pivot + group["centre_multiplier"] = 1 - size + for p, sign in zip(ports, signs): + if sign == -1: + word.append(["scale", p, None, "-1"]) + for p in ports[1:]: + word.append(["add", p, pivot, "-1"]) + if size == 6: + word.extend([["scale", pivot, None, "2"], + ["fixed_multiply", pivot, None, "3"]]) + else: + need(size == 8, "The exact rank-sixteen block sizes") + word.append(["scale", pivot, None, "8"]) + for p in ports[1:]: + word.append(["add", pivot, p, "1"]) + modes[pivot] = {p: F(sign) for p, sign in zip(ports, signs)} + for p, sign in zip(ports[1:], signs[1:]): + modes[p] = {p: F(sign), pivot: F(-signs[0])} + diagonal[pivot] = {pivot: F(1 - size)} + return word, groups, r.product(modes, pair_matrix), diagonal + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + raw = gzip.decompress(SOURCE.read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_PIN, "Exact native response source") + model = json.loads(raw)["model"] + cyclic = json.loads(next(path.read_bytes() for path in PINS if path.name == "CYCLIC-FLAGS.json")) + word, groups, expected, diagonal = make_code(model, cyclic) + reverse = inverse(word) + code, growth = replay(word) + code_inverse, inverse_growth = replay(reverse) + need(code == expected, "Literal centre sums and complement differences") + need(replay(word + reverse)[0] == replay(reverse + word)[0] == r.identity(112), + "Both literal inverse orders") + response = [{int(p): F(c) for p, c in row.items()} for row in model["response"]] + need(r.product(code, r.product(response, code_inverse)) == diagonal, + "The exact response has sixteen scalar centre actions") + entry = [["translate", p, None, str(q)] for p, q in enumerate(model["ports"])] + word + entry_rows, entry_growth = replay(entry, spatial=True) + want_entry = [{(p, model["ports"][p]): c for p, c in row.items()} for row in code] + need(entry_rows == want_entry, "Each input line square is on the correct side of the code") + need(replay(entry + inverse(entry), spatial=True)[0] + == replay(inverse(entry) + entry, spatial=True)[0] + == [{(p, 0): F(1)} for p in range(112)], "Both literal spatial inverse orders") + wrong = word + entry[:112] + need(replay(wrong, spatial=True)[0] != want_entry, "Wrong-side square control") + need(price(word)["old_real_scalar_units"] == price(reverse)["old_real_scalar_units"] == 2078, + "Literal complete scalar invoice") + payload = { + "source_decompressed_sha256": SOURCE_PIN, + "groups": groups, + "pivots": [group["pivot"] for group in groups], + "code": r.encoded(code), + "code_inverse": r.encoded(code_inverse), + "diagonal_response": r.encoded(diagonal), + "scalar_words": {"code": word, "inverse_code": reverse}, + "entry_square_word": entry, + "entry_square_inverse_word": inverse(entry), + } + data = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode() + (args.out / "PIVOT-CODES.json").write_bytes(data) + checks = { + "status": "PASS_RANK16_EXISTING_PORT_PIVOT_CODE", + "source_decompressed_sha256": SOURCE_PIN, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_sha256": sha256(data).hexdigest(), + "arbitrary_input_columns": 640, + "unchanged_other_fields": 528, + "new_fields": 0, + "code_invoice": price(word), + "inverse_invoice": price(reverse), + "entry_square_invoice": price(entry), + "code_prefix": growth, + "inverse_prefix": inverse_growth, + "entry_prefix": entry_growth, + "both_scalar_inverse_orders": True, + "both_spatial_inverse_orders": True, + "wrong_side_square_rejected": True, + "transport_scope": "The common-entry code is literal. The formal transported code q C q diagonalizes Q E q because its sixteen centre multipliers are scalar. No raw-output decoder or stage transition is supplied.", + } + (args.out / "CHECKS.json").write_text(json.dumps(checks, indent=2, sort_keys=True) + "\n") + print(checks["status"], checks["code_invoice"], checks["code_prefix"], checks["inverse_prefix"]) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json new file mode 100644 index 0000000000..fb98041000 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "ROUTE32.md": "ae02183f0b8e83baab893d9c9db915abe476bf9704edf23e593eef796af3fc28", + "emit_model.py": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711", + "emit_native.py": "f961d989a708b40b26780860caa88bf73b86d451b603add3f254d0d0a7a709ff", + "model-normal/CHECKS.json": "69ee6905c99ab4d93f48d828c378f6c902d5e8a9844df68acbc8971158d76502", + "model-normal/ROUTE32-MODEL.json": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52", + "native-normal/CHECKS.json": "304b30eb8f9810ff36fcf0a4181bd630a0eb041a6fba89a53fbeea227860cae3", + "native-normal/ROUTE32-NATIVE.json.gz": "69342058ffb9128ecc743cf478772896fd037c7aeeac845326d65626d7f3b425" + }, + "normal_optimized_byte_identical": true, + "scope": "Complete raw local native word and exact route-compatible in-place code. The common-root gauge and full productive caller remain separate.", + "status": "PASS_ROUTE32_RESPONSE_CAPTURE_AND_NATIVE" +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md new file mode 100644 index 0000000000..d50856ffc1 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/ROUTE32.md @@ -0,0 +1,209 @@ +# A route-compatible response with a dyadic centre code + +The current shared-root route divides the 112 ports into three +classes. The class label r_p is the first vector r in the ordered +root space with q_p dot r=1. The order is + +```text +0,30,45,51,75,85,102,120,384,414,429,435,459,469,486,504. +``` + +The actual classes have 64, 32, and 16 ports, with labels 30, 45, +and 75. The 64 small ports split equally between classes 30 and 45. +The 48 large ports split into 32 in class 30 and 16 in class 75. + +The rank-sixteen response does not preserve these classes. Each of +its eight small cliques contains four ports from each of the two +small classes. Each large six-mode block contains four modes in +class 30 and two in class 75. A change of construction is required. + +## The response + +Every actual two-port pair code stays within a route class. Apply +the same pair-code matrix H as in the rank-sixteen construction. +At each large vertex, replace the six-mode block by two blocks: + +```text +I_4 - d_4 d_4^T, I_2 - d_2 d_2^T. +``` + +The groups are the four and two modes with the same route label. +Retain their original signs. Split each small eight-clique into its +two four-port route classes, and use I_4-11^T on each part. + +There are eight large four-mode blocks, eight large two-mode blocks, +and sixteen small four-port blocks. These 32 blocks partition all +112 mode labels. If M is their direct sum, set + +```text +E = H^-1 M H. +``` + +The full physical E has zero diagonal. Each nonzero entry E_pt +connects ports with r_p=r_t. Also, + +```text +rank(E-I) = 32, +det(E) = 3^24. +``` + +Each block inverse is I-dd^T/(k-1), where k is two or four. +Thus the full response is a rational unit, and its only odd inverse +denominator is three. The complete inverse is checked in both +orders. The old selected-eight principal block is singular. This +packet uses empty selection: the ordinary response is the entire +112 by 112 unit. + +The source graph cannot keep rank sixteen by choosing another +monochromatic eight-clique cover. All 64 maximal eight-cliques have +four ports from each small route class. The largest monochromatic +clique in the actual graph has size four. This is an exact check +against the independently reviewed complete maximal-clique list. +It is a restriction of this clique construction, not a lower bound +for all possible native responses. + +## Two in-place centre codes + +Apply the actual H pair code. In each signed block choose its first +mode as a pivot. The sum-and-difference code multiplies coordinates +by their signs, subtracts the pivot from every other coordinate, +multiplies the pivot by the block size, and adds all complement +coordinates to it. The pivot then holds the old signed sum. + +This code C and its literal inverse each cost 1,870 old real scalar +units. They use no owned field, no new field, no native child, and +no odd division. The maximum prefix row one-norm is 8 forward and +4 backward. The inverse needs at most three extra binary +fractional bits. + +The exact diagonal form is + +```text +C E C^-1 = diag(-3 I_24, -I_8, I_80), +``` + +with the diagonal entries placed at the actual pivot ports listed +in the payload. The 32 centre coordinates occupy existing data +fields. The other 80 fields retain independent complement data. + +A second code uses a rank-one reflection on each four-mode block. +For its sign vector d, let p be the pivot and let + +```text +s = d - 2 d_p e_p, +S = I - s s^T/2. +``` + +Then S squared is I, rank(S-I)=1, and S d=2 d_p e_p. +Thus S diagonalizes I-dd^T with centre multiplier -3. +Its exact no-scratch word is + +```text +x_i += d_i d_p x_p for all i other than p +x_p *= -2 +x_p += d_i d_p x_i for all i other than p +x_p /= 2 +x_i -= d_i d_p x_p for all i other than p. +``` + +It costs 78 old units per four-mode block. The two-mode blocks use +the preceding pivot code. Including H, this second complete code +and its inverse each cost 2,486 units. They are dyadic and use no +additional field or native child. Their forward and inverse prefix +row one-norms are 8 and 4. Their maximum binary heights are one +and two. + +The reflection code has a smaller block displacement rank. The +pivot code has a smaller scalar invoice. No decoder advantage for +the reflection code is claimed without its physical caller. + +## Route and phase scope + +Both complete physical codes preserve the route labels. Therefore +they commute with every field-diagonal spatial operator of the +form diag(A_(r_p)). This follows entry by entry: every nonzero +scalar coefficient connects two copies of the same A_r. + +For the unshifted shared-root D11 stages, put e=511, v_p=e+r_p, +and u_(s,p)=v_p+e_(8+s), for s=1,2. The actual route has columns + +```text +kappa_(s,p)(e_j) = e_j + (u_(s,p))_j u_(s,p). +``` + +The advance is P_kappa inverse F9 P_kappa; stage zero is F9. +If two route labels agree, their complete column lists, permutation +operators, and ordered advance operators agree. This includes +their phase, since they are the same ordered circuit. Thus the +commutation applies to these actual unshifted advances, rather +than to a nominal label alone. Added field-dependent address views +or phase corrections still require their own checks. Route +preservation does not permit Q to move through C. + +For either code the current entry word C Q^2 is literal: it has +112 explicit input translations followed by the scalar code. +The spatial interpreter retains the ordered translation labels. +The formal transported code q C q, with q=Q^-1, has the same +diagonal response because the centre multipliers are scalar. +This fact does not supply a raw-output decoder or a free transition +to a subsequent input code. + +The relative q-difference spaces have dimension one for the eight +two-mode blocks and dimension three for the other 24 blocks. +Only the eight two-mode spaces lie inside the common root space. +Thus a common-root gauge cost cannot be inferred from route +preservation. It requires the actual native and endpoint operators. + +## Complete raw native word + +The large sector uses the pinned cyclic pair flags. It changes only +the scalar transfer coefficients. The small sector uses the exact +sixteen four-cliques and their cyclic flags. Every nonzero ADD has +equal source and target frames. + +The local map is + +```text +F(x,y,h) = (x, y+E x, h), +B(x,y,h) = (x-E^T y, y, h). +``` + +The input convention is X=Qx, Y=y. The output convention is +X=F9 x' and Y=F9 Q^-1 y'. The native invoice in either direction is + +```text +944 H1 + 48 H3 + 64 H5 + 64 H6, +1120 native children, native mass 1792, +4312 old real scalar primitives, 224 endpoint adapters. +``` + +The native prefix row one-norm is 14 in either direction. +All 640 input columns are independent. The 416 fields outside +the data banks remain unchanged. They receive no productive +advance in this word. + +The emitter checks 297 fresh native operators, including their +global phases. It reuses 752 operators only after exact ordered +frame comparison with the frozen reviewed sources. The 224 +endpoint adapters have the same exact endpoint frames as those +sources. Both complete provider words are serialized, read back, +and replayed. Removal of a nonzero transfer is rejected. + +## Evidence + +`emit_model.py` pins the pair geometry, root space, clique list, +and rank-sixteen predecessor. It checks the response and inverse, +both capture codes, all 640 columns, literal inverse orders, +route preservation, and the spatial entry code. + +`emit_native.py` binds the exact model hash and emits both complete +native directions. Normal and optimized runs must give identical +payloads and receipts. The model and native freezes are separate +from a common-root gauge extension and independent review. + +The construction builds on the root's route-compatible split, +the controller's common-root geometry, the independent cyclic +flags, and the native rank-sixteen word. The four-mode reflection +uses the root's rank-one capture formula. AI assistance was used. +This packet does not claim a complete supplier or kappa bound. +No publication is authorized. diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_model.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_model.py new file mode 100644 index 0000000000..b6dd94d986 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_model.py @@ -0,0 +1,244 @@ +#!/usr/bin/env python3 +"""Build the route-compatible response and its exact in-place codes.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +PARENT = HERE.parent +LANES = PARENT.parents[1] +SOURCE = PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz" +SOURCE_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" +PINS = { + PARENT / "pivot-codes/emit_pivot_codes.py": + "af2f2ab1c5daba0bcd1a8878f2b81b2834e10a4f8ca1a2ef66779d52b30e64b4", + LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + LANES / "controller-followthrough-20261017/matching-geometry-20261018/GEOMETRY.json": + "21e14a24dbe8776038e4deea3181509d23c43fa9314776c4c14c90a5180573fd", + PARENT / "run-normal/RESPONSE-PROGRAM.json": + "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c", +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +for path, pin in PINS.items(): + need(sha256(path.read_bytes()).hexdigest() == pin, "Source pin " + str(path)) +spec = importlib.util.spec_from_file_location("frozen_pivot", PARENT / "pivot-codes/emit_pivot_codes.py") +pivot = importlib.util.module_from_spec(spec) +spec.loader.exec_module(pivot) +r = pivot.r + + +def binary_basis(vectors): + rows = list(dict.fromkeys(vectors)) + used = 0 + for bit in range(8, -1, -1): + found = next((i for i in range(used, len(rows)) if rows[i] >> bit & 1), None) + if found is None: + continue + rows[used], rows[found] = rows[found], rows[used] + for i in range(len(rows)): + if i != used and rows[i] >> bit & 1: + rows[i] ^= rows[used] + used += 1 + return rows[:used] + + +def pair_word(cyclic): + word, matrix = [], r.identity(112) + for pair in cyclic["pair_codes"]: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + matrix[a], matrix[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)} + if aa != 1: + word.append(["scale", a, None, str(aa)]) + word.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + need(pivot.replay(word)[0] == matrix, "Actual pair word") + return word, matrix + + +def capture(groups, pair, reflection): + word = list(pair) + for group in groups: + ports, signs = group["ports"], group["signs"] + p, k = ports[0], len(ports) + if reflection and k == 4: + for t, sign in zip(ports[1:], signs[1:]): + word.append(["add", t, p, str(sign * signs[0])]) + word.append(["scale", p, None, "-2"]) + for t, sign in zip(ports[1:], signs[1:]): + word.append(["add", p, t, str(sign * signs[0])]) + word.append(["scale", p, None, "1/2"]) + for t, sign in zip(ports[1:], signs[1:]): + word.append(["add", t, p, str(-sign * signs[0])]) + else: + for t, sign in zip(ports, signs): + if sign == -1: + word.append(["scale", t, None, "-1"]) + for t in ports[1:]: + word.append(["add", t, p, "-1"]) + word.append(["scale", p, None, str(k)]) + for t in ports[1:]: + word.append(["add", p, t, "1"]) + return word + + +def make_model(old, cyclic, geometry, rank30): + q = old["ports"] + root_space = geometry["common_even_isotropic_space"] + need(root_space == sorted(root_space), "The route enumeration uses numeric order") + need(q == geometry["q_labels"] == cyclic["ports"], "Actual route direction labels") + routes = [next(t for t in root_space if (q[p] & t).bit_count() % 2) for p in range(112)] + need(Counter(routes) == {30: 64, 45: 32, 75: 16}, "Exact route classes") + pair, h = pair_word(cyclic) + hi = pivot.replay(pivot.inverse(pair))[0] + need(all(routes[a] == routes[b] for data in cyclic["pair_codes"] + for a, b in [data["ports"]]), "Every pair code preserves the route") + groups = [] + mode, mode_inverse = r.identity(112), r.identity(112) + mode_u, mode_v = [{} for _ in range(112)], [] + for record in old["vertex_assignments"]: + ports, signs = record["ordered_carriers_a_b_c"], record["signs"] + for route in sorted({routes[p] for p in ports}): + entries = [(p, s) for p, s in zip(ports, signs) if routes[p] == route] + need(len(entries) == (4 if route == 30 else 2), "Large route split") + groups.append({"ports": [p for p, _ in entries], "signs": [s for _, s in entries], + "route": route, "kind": "large", "vertex": record["vertex"]}) + small = [] + for clique in old["small_cliques"]: + for route in sorted({routes[p] for p in clique}): + ports = [p for p in clique if routes[p] == route] + need(len(ports) == 4, "Small route split") + need(all((q[p] & q[t]).bit_count() % 2 == int(p == t) + for p in ports for t in ports), "Actual four-clique") + small.append(ports) + groups.append({"ports": ports, "signs": [1] * 4, "route": route, "kind": "small"}) + need(sorted(p for group in groups for p in group["ports"]) == list(range(112)), + "All32 blocks partition the data modes") + for index, group in enumerate(groups): + ports, signs = group["ports"], group["signs"] + k = len(ports) + group["pivot"] = ports[0] + group["centre_multiplier"] = 1 - k + group["relative_q_basis"] = binary_basis([q[p] ^ q[ports[0]] for p in ports[1:]]) + group["relative_q_rank"] = len(group["relative_q_basis"]) + group["relative_q_in_common_root"] = all(t in root_space for t in group["relative_q_basis"]) + for i, p in enumerate(ports): + mode[p] = {t: F(int(i == j) - signs[i] * signs[j]) + for j, t in enumerate(ports) if i != j} + mode_inverse[p] = {t: F(int(i == j)) - F(signs[i] * signs[j], k - 1) + for j, t in enumerate(ports)} + mode_u[p] = {index: F(-signs[i])} + mode_v.append({p: F(sign) for p, sign in zip(ports, signs)}) + response = r.product(hi, r.product(mode, h)) + response_inverse = r.product(hi, r.product(mode_inverse, h)) + u, v = r.product(hi, mode_u), r.product(mode_v, h) + delta = [dict(row) for row in response] + for p in range(112): + r.add(delta[p], {p: F(-1)}) + need(r.product(u, v) == delta and r.rank(u, 32) == r.rank(v, 112) == 32, + "Actual rank32 response correction") + need(r.product(response, response_inverse) == r.product(response_inverse, response) == r.identity(112), + "Both complete response inverse orders") + need(all(p not in row for p, row in enumerate(response)), "Zero physical diagonal") + need(all(routes[p] == routes[t] for p, row in enumerate(response) for t in row), + "Every response coefficient preserves the actual route") + need(r.determinant(response) == 3 ** 24, "The whole ordinary response is a unit") + complete = rank30["maximal_small_cliques"] + need(Counter(tuple(sorted(Counter(routes[p] for p in clique).items())) + for clique in complete if len(clique) == 8) == {((30, 4), (45, 4)): 64}, + "No actual eight-clique stays inside one route") + need(max(max(Counter(routes[p] for p in clique).values()) for clique in complete) == 4, + "The actual monochromatic clique bound") + model = { + "ports": q, "large_ports": old["large_ports"], "small_ports": old["small_ports"], + "selected_ports": [], "ordinary_ports": list(range(112)), + "root_basis": geometry["common_even_isotropic_basis"], "root_space": root_space, + "port_routes": routes, "groups": groups, "small_cliques": small, + "mode_response": r.encoded(mode), "mode_inverse": r.encoded(mode_inverse), + "response": r.encoded(response), "response_inverse": r.encoded(response_inverse), + "correction_U": r.encoded(u), "correction_V": r.encoded(v), + "full_determinant": str(3 ** 24), "correction_rank": 32, + "old_selected_block": r.encoded(r.restrict(response, old["selected_ports"])), + "old_selected_determinant": str(r.determinant(r.restrict(response, old["selected_ports"]))), + } + diagonal = r.identity(112) + for group in groups: + diagonal[group["pivot"]] = {group["pivot"]: F(group["centre_multiplier"])} + codes, reports = {}, {} + for name, reflection in [("pivot", False), ("reflection", True)]: + word = capture(groups, pair, reflection) + inverse = pivot.inverse(word) + c, growth = pivot.replay(word) + ci, inverse_growth = pivot.replay(inverse) + need(r.product(c, r.product(response, ci)) == diagonal, "Exact diagonal centre action " + name) + need(pivot.replay(word + inverse)[0] == pivot.replay(inverse + word)[0] == r.identity(112), + "Literal code inverse orders " + name) + need(all(routes[p] == routes[t] for p, row in enumerate(c) for t in row), + "The full physical code preserves routes " + name) + entry = [["translate", p, None, str(qp)] for p, qp in enumerate(q)] + word + want = [{(p, q[p]): coefficient for p, coefficient in row.items()} for row in c] + need(pivot.replay(entry, spatial=True)[0] == want, "Exact input-square entry " + name) + need(pivot.replay(entry + pivot.inverse(entry), spatial=True)[0] + == [{(p, 0): F(1)} for p in range(112)], "Exact spatial inverse " + name) + codes[name] = {"word": word, "inverse_word": inverse, "entry_word": entry, + "code": r.encoded(c), "inverse_code": r.encoded(ci)} + reports[name] = {"invoice": pivot.price(word), "inverse_invoice": pivot.price(inverse), + "prefix": growth, "inverse_prefix": inverse_growth} + need(reports["pivot"]["invoice"]["old_real_scalar_units"] == 1870, "Complete pivot invoice") + need(reports["reflection"]["invoice"]["old_real_scalar_units"] == 2486, + "Complete reflection invoice") + model["diagonal_response"] = r.encoded(diagonal) + model["codes"] = codes + return model, reports + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + raw = gzip.decompress(SOURCE.read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_PIN, "Frozen rank16 source") + old = json.loads(raw)["model"] + inputs = {path.name: json.loads(path.read_bytes()) for path in PINS if path.suffix == ".json"} + model, reports = make_model(old, inputs["CYCLIC-FLAGS.json"], inputs["GEOMETRY.json"], + inputs["RESPONSE-PROGRAM.json"]) + data = (json.dumps(model, sort_keys=True, separators=(",", ":")) + "\n").encode() + (args.out / "ROUTE32-MODEL.json").write_bytes(data) + checks = { + "status": "PASS_ROUTE32_RESPONSE_AND_CAPTURE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_sha256": sha256(data).hexdigest(), + "source_decompressed_sha256": SOURCE_PIN, + "reports": reports, + "correction_rank": 32, + "determinant": model["full_determinant"], + "old_selected_determinant": model["old_selected_determinant"], + "relative_q_rank_counts": dict(sorted(Counter(g["relative_q_rank"] for g in model["groups"]).items())), + "blocks_inside_common_root": sum(g["relative_q_in_common_root"] for g in model["groups"]), + "all_blocks": len(model["groups"]), + "arbitrary_inputs_checked": 640, + "old_small_monochromatic_maximum_clique_size": 4, + "scope": "Exact route-compatible unit and dyadic in-place centre codes. Native implementation and the physical moving-code caller have separate checks.", + } + (args.out / "CHECKS.json").write_text(json.dumps(checks, indent=2, sort_keys=True) + "\n") + print(json.dumps(checks, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_native.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_native.py new file mode 100644 index 0000000000..33a8d8197a --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/emit_native.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python3 +"""Emit the complete native data word for the route-compatible response.""" + +import argparse +from copy import deepcopy +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +PARENT = HERE.parent +EMITTER = PARENT / "emit_native.py" +EMITTER_PIN = "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745" +MODEL = HERE / "model-normal/ROUTE32-MODEL.json" +MODEL_PIN = "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52" +SOURCES = { + PARENT / "native-normal-v2/NATIVE-PROGRAM.json.gz": + "e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558", + PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz": + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +need(sha256(EMITTER.read_bytes()).hexdigest() == EMITTER_PIN, "Frozen native emitter") +spec = importlib.util.spec_from_file_location("route32_native_helpers", EMITTER) +n = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = n +spec.loader.exec_module(n) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + need(sha256(MODEL.read_bytes()).hexdigest() == MODEL_PIN, "Frozen route-compatible model") + model = json.loads(MODEL.read_bytes()) + cyclic = json.loads(n.read("independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json")) + inherited = {} + source = None + for path, pin in SOURCES.items(): + raw = gzip.decompress(path.read_bytes()) + need(sha256(raw).hexdigest() == pin, "Native phase source pin") + source = json.loads(raw) + word = source["providers"]["base"]["forward"] + for key, recipe in word["native_recipes"].items(): + old, new = map(int, key.split(":")) + pair = tuple(word["frames"][old]), tuple(word["frames"][new]) + if pair in inherited: + need(inherited[pair] == recipe, "Repeated exact recipe agrees") + inherited[pair] = recipe + base = source["providers"]["base"]["forward"] + words = {direction: n.make_word(cyclic, model, direction) for direction in ("forward", "backward")} + frames = words["forward"]["frames"] + need(frames == words["backward"]["frames"], "Both orientations have identical actual frames") + pairs = sorted({(event[2], event[3]) for word in words.values() + for event in word["events"] if event[0] == "native"}) + recipes, fresh, reused = {}, 0, 0 + for old, new in pairs: + pair = tuple(frames[old]), tuple(frames[new]) + if pair in inherited: + recipe = inherited[pair] + reused += 1 + else: + operation = n.compiler.canonical_frame(9, pair[0]).adjoint().then( + n.compiler.canonical_frame(9, pair[1])) + recipe, _ = n.compiler.lower_child(operation) + n.phase.equal(n.phase.recipe(recipe), n.phase.adjoint(n.phase.frame(pair[0], 9)) + + n.phase.frame(pair[1], 9), "Fresh route32 native phase") + fresh += 1 + if fresh % 100 == 0: + print("Fresh route32 phases", fresh, flush=True) + need(recipe["rank"] == len(pair[1]) - len(pair[0]), "Exact new native rank") + recipes[str(old) + ":" + str(new)] = recipe + reports = {} + for direction, word in words.items(): + word["native_recipes"] = recipes + word["endpoint_adapters"] = base["endpoint_adapters"] + need(word["start"] == base["start"] and word["final"] == base["final"], + "Identical inherited endpoint indices") + need(all(word["frames"][i] == base["frames"][i] for i in word["start"] + word["final"]), + "Identical inherited endpoint bases") + reports[direction] = n.verify_word(word, n.rows(model["response"]), direction) + need(reports[direction]["native_profile"] == {1: 944, 3: 48, 5: 64, 6: 64} + and reports[direction]["native_mass"] == 1792 + and reports[direction]["real_scalar_primitives"] == 4312, "Complete native invoice") + bad = deepcopy(words["forward"]) + del bad["events"][bad["transfer_records"][0]["event"]] + try: + n.verify_word(bad, n.rows(model["response"]), "forward") + except ValueError: + pass + else: + raise ValueError("The missing transfer control was accepted") + payload = {"schema": "route32-native-v1", "model": model, + "providers": {provider: words for provider in source["providers"]}} + data = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(data) + for provider, directions in saved["providers"].items(): + for direction, word in directions.items(): + need(n.verify_word(word, n.rows(saved["model"]["response"]), direction) == reports[direction], + "Serialized complete native replay " + provider + " " + direction) + (args.out / "ROUTE32-NATIVE.json.gz").write_bytes(gzip.compress(data, mtime=0)) + checks = { + "status": "PASS_ROUTE32_COMPLETE_NATIVE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "model_sha256": MODEL_PIN, + "payload_decompressed_sha256": sha256(data).hexdigest(), + "fresh_native_phases": fresh, + "inherited_native_phases": reused, + "inherited_endpoint_phases": 224, + "reports": reports, + "missing_transfer_rejected": True, + "scope": "Complete local native data word. The416 other fields are unchanged. Productive helper progress, common-root conjugation, moving-code transitions and recursive hosting are separate.", + } + (args.out / "CHECKS.json").write_text(json.dumps(checks, indent=2, sort_keys=True) + "\n") + print(json.dumps(checks, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/CHECKS.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/CHECKS.json new file mode 100644 index 0000000000..43a6775d56 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/route32/model-normal/CHECKS.json @@ -0,0 +1,76 @@ +{ + "all_blocks": 32, + "arbitrary_inputs_checked": 640, + "blocks_inside_common_root": 8, + "correction_rank": 32, + "determinant": "282429536481", + "old_selected_determinant": "0", + "old_small_monochromatic_maximum_clique_size": 4, + "payload_sha256": "85d44223697700a916e4cffeb334c8f82179f6535f7b0db64a37eddf37bedf52", + "producer_sha256": "6e93a21f04305c5061c9979acaba3588e3dfbb229471dd9bb780486768d15711", + "relative_q_rank_counts": { + "1": 8, + "3": 24 + }, + "reports": { + "pivot": { + "inverse_invoice": { + "explicit_translation_maps": 0, + "native_children": 0, + "old_real_scalar_units": 1870, + "owned_fields": 0, + "real_fixed_three_division_scans": 0, + "real_fixed_three_multiplication_scans": 0 + }, + "inverse_prefix": { + "additional_binary_height": 3, + "additional_odd_three_height": 0, + "maximum_prefix_row_one_norm": "4" + }, + "invoice": { + "explicit_translation_maps": 0, + "native_children": 0, + "old_real_scalar_units": 1870, + "owned_fields": 0, + "real_fixed_three_division_scans": 0, + "real_fixed_three_multiplication_scans": 0 + }, + "prefix": { + "additional_binary_height": 0, + "additional_odd_three_height": 0, + "maximum_prefix_row_one_norm": "8" + } + }, + "reflection": { + "inverse_invoice": { + "explicit_translation_maps": 0, + "native_children": 0, + "old_real_scalar_units": 2486, + "owned_fields": 0, + "real_fixed_three_division_scans": 0, + "real_fixed_three_multiplication_scans": 0 + }, + "inverse_prefix": { + "additional_binary_height": 2, + "additional_odd_three_height": 0, + "maximum_prefix_row_one_norm": "4" + }, + "invoice": { + "explicit_translation_maps": 0, + "native_children": 0, + "old_real_scalar_units": 2486, + "owned_fields": 0, + "real_fixed_three_division_scans": 0, + "real_fixed_three_multiplication_scans": 0 + }, + "prefix": { + "additional_binary_height": 1, + "additional_odd_three_height": 0, + "maximum_prefix_row_one_norm": "8" + } + } + }, + "scope": "Exact route-compatible unit and dyadic in-place centre codes. 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a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + }, + { + "stage": 2, + "width": 25, + "cross_ranks": { + "0": { + "8": 112 + }, + "1": { + "9": 112 + }, + "2": { + "8": 112 + }, + "3": { + "9": 112 + } + }, + "frame_transition_ranks": { + "0->0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + }, + { + "stage": 3, + "width": 33, + "cross_ranks": { + "0": { + "8": 112 + }, + "1": { + "9": 112 + }, + "2": { + "8": 112 + }, + "3": { + "9": 112 + } + }, + "frame_transition_ranks": { + "0->0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + }, + { + "stage": 4, + "width": 41, + "cross_ranks": { + "0": { + "8": 112 + }, + "1": { + "9": 112 + }, + "2": { + "8": 112 + }, + "3": { + "9": 112 + } + }, + "frame_transition_ranks": { + "0->0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + }, + { + "stage": 5, + "width": 49, + "cross_ranks": { + "0": { + "8": 112 + }, + "1": { + "9": 112 + }, + "2": { + "8": 112 + }, + "3": { + "9": 112 + } + }, + "frame_transition_ranks": { + "0->0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + }, + { + "stage": 6, + "width": 57, + "cross_ranks": { + "0": { + "8": 112 + }, + "1": { + "9": 112 + }, + "2": { + "8": 112 + }, + "3": { + "9": 112 + } + }, + "frame_transition_ranks": { + "0->0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + }, + { + "stage": 7, + "width": 65, + "cross_ranks": { + "0": { + "8": 112 + }, + "1": { + "9": 112 + }, + "2": { + "8": 112 + }, + "3": { + "9": 112 + } + }, + "frame_transition_ranks": { + "0->0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + }, + { + "stage": 8, + "width": 73, + "cross_ranks": { + "0": { + "8": 112 + }, + "1": { + "9": 112 + }, + "2": { + "8": 112 + }, + "3": { + "9": 112 + } + }, + "frame_transition_ranks": { + "0->0": 8, + "0->1": 9, + "1->0": 9, + "1->1": 8 + }, + "typed_cross_ranks": { + "0->0": { + "9": 112 + }, + "0->1": { + "8": 112 + }, + "1->0": { + "8": 112 + }, + "1->1": { + "9": 112 + } + } + } + ], + "final_frame_ranks": { + "0": 72, + "1": 73 + }, + "scope": "Exact binary ranks and commutation only. Full phases, native lowering, arbitrary-mode closure, and a supplier invoice remain separate checks." +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/GROWING-WALSH.md b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/GROWING-WALSH.md new file mode 100644 index 0000000000..a15d4a6fd0 --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/GROWING-WALSH.md @@ -0,0 +1,131 @@ +# A growing Walsh representation for odd source phases + +This note states an exact frame construction. It does not state a decoded +supplier or a kappa improvement. The centre values must still enter and leave +the new mode representation through legal operations. + +Let U_s have dimension m_s=9+8s, for s=0,...,8. Let omega_s be the sum of its +coordinate vectors. The vector omega_s has odd weight. Put + + H_s = omega_s-perp inside U_s, + P_s = I_U_s + omega_s omega_s^T over F_2. + +The subspace H_s is nondegenerate. Every vector has a unique form +`a omega_s+h`, with `a in F_2` and `h in H_s`. Define G_s by + + (G_s f)(a omega_s+h) + = 2^(-(m_s-1)/2) sum_(k in H_s) (-1)^(h dot k) f(a omega_s+k). + +It acts as the identity on unused coordinates. Its kernel fixes its global +phase. It satisfies G_s^2=I. Its binary symplectic action is + + (x,z) -> (x+P_s(x+z), z+P_s(x+z)). + +Every orthogonal route supported in U_s fixes omega_s. It preserves H_s and +the dot product. Thus it commutes with G_s exactly, including the phase. +This statement applies to the old supplier's routes within completed U_s. + +## One common line for every odd phase + +Use the source convention + + C_p = ((1+i)/2) I + ((1-i)/2) X_p. + +For odd p in U_s, put v=p+omega_s and b=v dot x. Define the monomial L_p by + + (L_p f)(x) = i^b f(x+b omega_s). + +The value b is unchanged by adding omega_s. Thus L_p commutes with C_omega_s. +For b=0 and b=1, direct comparison of the two Gaussian coefficients gives + + G_s C_p G_s = C_omega_s L_p. + +There is no omitted scalar phase. Tensor products give the identity for +every positive tensor size. The operator C_p is not replaced by a scalar; +the common C_omega_s factor is still a native operation. + +## Growth across one fresh block + +The subspaces H_(s-1) and H_s are nested. Their orthogonal difference is + + V_s = {parity(z) omega_(s-1)+z : z in E_s}, + +where E_s is the new eight-dimensional coordinate block. Thus +`Delta_s=G_s G_(s-1)` is a Walsh transform of native rank eight. It acts in +the nine-dimensional space `W_s=span(omega_(s-1), E_s)`. + +Let g be an orthogonal route supported in U_s. For integer phase types a,b +and an integer j, the exact identity is + + T_s^a C_p^j g (T_(s-1)^b)^-1 + = C_omega_s^(a+j-b) L_p^j g L_omega_(s-1)^(-b) Delta_s, + +where `T_s^a=C_omega_s^a G_s`. All L operators in this formula use U_s. +This follows by conjugating the old common line through G_s and by using +the exact route commutation above. The monomial factors commute with the +new common line. Therefore the native rank is eight when `a+j-b` is even, +and nine when it is odd. + +The root check uses the old 112 port labels and all eight fresh stages. +It checks the binary operators directly. All 896 routed odd-phase cases +have rank eight when the input and output type parities differ. They have +rank nine when those parities agree. These are exact rank claims. This +root check does not by itself establish the full phases. + +## Explicit full-transform adapters + +On an odd coordinate space of dimension n congruent to 1 modulo 8, set + + D_n f(x) = (-1)^(sum_(i> i) & 1) + v = label ^ (1 << zero) + basis = [] + for i in range(9): + point = 1 << i + if zero and (point & 1) != ((point >> zero) & 1): + point ^= 1 | (1 << zero) + basis.append(point ^ (v if parity(point & v) else 0)) + require(basis[0] == label, "The port basis does not begin at its label.") + offset = 9 + 8 * (stage - 1) + result = value & ~(511 | (255 << offset)) + if parity(value & label): + result ^= label + for i, point in enumerate(basis[1:]): + if parity(value & point): + result ^= 1 << (offset + i) + if (value >> (offset + i)) & 1: + result ^= point + return result + + +def route(state, label, stage): + return tuple(route_vector(value, label, stage) for value in state) + + +def native_rank(operation, width): + return rank([operation((0, 1 << i))[0] for i in range(width)]) + + +def main(): + source = Path(__file__).resolve().parents[1] / "lanes/circuit-interface/INTERFACE.json" + raw = source.read_bytes() + data = json.loads(raw) + labels = data["ports"] + require(len(labels) == 112, "The old port count has changed.") + require(all(parity(q) for q in labels), "A source label is even.") + records = [] + for stage in range(1, 9): + current = 9 + 8 * stage + previous = current - 8 + omega = (1 << current) - 1 + old_omega = (1 << previous) - 1 + for label in labels: + for bit in range(current): + vector = 1 << bit + require(even_projection(even_projection(vector, current), previous) == + even_projection(vector, previous), "The projections do not nest.") + for state in ((vector, 0), (0, vector)): + require(walsh(route(state, label, stage), current) == + route(walsh(state, current), label, stage), + "The growing Walsh frame does not commute with the route.") + def cross(state, label, power): + state = walsh(state, previous) + state = route(state, label, stage - 1) + state = route(state, label, stage) + state = c_line(state, label, power) + return walsh(state, current) + cross_ranks = {str(power): dict(Counter(native_rank( + lambda state, label=label: cross(state, label, power), current) + for label in labels)) for power in (0, 1, 2, 3)} + transition_ranks = {} + typed_cross_ranks = {} + for before in range(2): + for after in range(2): + def transition(state): + state = c_line(state, old_omega, before) + state = walsh(state, previous) + state = walsh(state, current) + return c_line(state, omega, after) + transition_ranks[f"{before}->{after}"] = native_rank(transition, current) + def typed_cross(state, label): + state = c_line(state, old_omega, before) + state = cross(state, label, 1) + return c_line(state, omega, after) + typed_cross_ranks[f"{before}->{after}"] = dict(Counter(native_rank( + lambda state, label=label: typed_cross(state, label), current) + for label in labels)) + records.append({"stage": stage, "width": current, + "cross_ranks": cross_ranks, + "frame_transition_ranks": transition_ranks, + "typed_cross_ranks": typed_cross_ranks}) + final_ranks = {} + for phase in range(2): + final_ranks[str(phase)] = native_rank( + lambda state: c_line(walsh(state, 73), (1 << 73) - 1, phase), 73) + result = {"status": "PASS_BINARY_GROWING_WALSH_GEOMETRY", + "source_sha256": sha256(raw).hexdigest(), "source_base": data["base"], + "records": records, "final_frame_ranks": final_ranks, + "scope": "Exact binary ranks and commutation only. Full phases, native lowering, arbitrary-mode closure, and a supplier invoice remain separate checks."} + Path(__file__).with_name("GROWING-WALSH.json").write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps(result, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/check_phase_class_capture_20261020.py b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/check_phase_class_capture_20261020.py new file mode 100644 index 0000000000..ebf58dee1d --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/check_phase_class_capture_20261020.py @@ -0,0 +1,289 @@ +"""Check paired centre codes on the actual rank-sixteen response.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +ROOT = Path(__file__).resolve().parent +LANES = ROOT.parent / "lanes" +PINS = { + "capture": ( + "bridge-access-20261017/rank16-capture-20261020/run-normal/CAPTURE.json", + "cd6d621140290c73a771e1d6c531d2ffa00ae278e5b4e39b4ad9ff1ae00cc888", + ), + "pairs": ( + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + ), +} + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def source(key): + name, pin = PINS[key] + raw = (LANES / name).read_bytes() + need(sha256(raw).hexdigest() == pin, "Source pin: " + key) + return json.loads(raw) + + +def ident(n): + return [{i: F(1)} for i in range(n)] + + +def add(row, other, coefficient): + for column, value in other.items(): + new = row.get(column, F(0)) + coefficient * value + if new: + row[column] = new + else: + row.pop(column, None) + + +def product(a, b): + result = [] + for row in a: + out = {} + for j, value in row.items(): + add(out, b[j], value) + result.append(out) + return result + + +def encoded(a): + return [{str(j): str(c) for j, c in row.items()} for row in a] + + +def decoded(a): + return [{int(j): F(c) for j, c in row.items()} for row in a] + + +def inverse_word(word): + result = [] + for op, target, source, c in reversed(word): + if op in ("fixed_multiply", "fixed_divide"): + new_op = "fixed_divide" if op == "fixed_multiply" else "fixed_multiply" + result.append([new_op, target, source, c]) + else: + result.append([op, target, source, str(-F(c) if op == "add" else 1 / F(c))]) + return result + + +def replay(word, n=112): + rows = ident(n) + largest = F(1) + for op, target, source, coefficient in word: + coefficient = F(coefficient) + need(0 <= target < 112, "Only the data bank is changed") + if op == "add": + need(source != target and 0 <= source < 112, "An off-diagonal ADD") + add(rows[target], rows[source], coefficient) + else: + need(op in ("scale", "fixed_multiply", "fixed_divide") and coefficient, + "An invertible scalar operation") + if op == "fixed_divide": + coefficient = 1 / coefficient + rows[target] = {j: coefficient * c for j, c in rows[target].items()} + largest = max(largest, sum(map(abs, rows[target].values()))) + return rows, largest + + +def invoice(word): + old = multiply = divide = 0 + for op, _, _, coefficient in word: + if op == "fixed_multiply": + multiply += 2 + elif op == "fixed_divide": + divide += 2 + else: + coefficient = F(coefficient) + a, b = abs(coefficient.numerator), coefficient.denominator + need(a and not b & (b - 1), "A dyadic coefficient") + if op == "scale": + need(not a & (a - 1), "A dyadic unit") + old += 2 * (abs(a.bit_length() - b.bit_length()) + (coefficient < 0)) + else: + old += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + return { + "old_real_scalar_units": old, "real_fixed_three_multiplication_scans": multiply, + "real_fixed_three_division_scans": divide, "owned_fields": 0, + "native_children_inside_common_chart": 0, + } + + +def unit_word(pairs): + result = [] + for pair in pairs: + a, b = pair["ports"] + (aa, ab), (ba, bb) = pair["matrix"] + need(abs(aa) == abs(ab) == abs(ba) == abs(bb) == 1, "Signed pair") + need(aa * bb == -ab * ba, "Hadamard determinant") + if aa != 1: + result.append(["scale", a, None, str(aa)]) + result.extend([ + ["add", a, b, str(ab)], + ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)], + ]) + return result + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + capture, pairs = source("capture"), source("pairs")["pair_codes"] + labels = capture["ports"] + space = [0] + for basis in [30, 45, 75, 384]: + space += [x ^ basis for x in space] + need(len(set(space)) == 16, "The root space has dimension four") + need(all((x & y).bit_count() % 2 == 0 for x in space for y in space), + "The root space is isotropic") + classes = [min(q ^ r for r in space) for q in labels] + need(all(classes[a] == classes[b] for a, b in (p["ports"] for p in pairs)), + "The physical pair code preserves phase classes") + + h_word = unit_word(pairs) + h = replay(h_word)[0] + hi = replay(inverse_word(h_word))[0] + pairing_word, reduced_word, groups = [], [], [] + active = [] + s = ident(112) + k_matrix = ident(112) + for original in capture["groups"]: + ports, signs = original["ports"], original["signs"] + sign = dict(zip(ports, signs)) + partition = {} + for port in ports: + partition.setdefault(classes[port], []).append(port) + same_class_pairs = [sorted(value) for _, value in sorted(partition.items())] + need(all(len(pair) == 2 for pair in same_class_pairs), "Every class has two modes") + local_active = [] + for a, b in same_class_pairs: + # The first output is the signed sum; the second is a difference. + if sign[a] != 1: + pairing_word.append(["scale", a, None, str(sign[a])]) + pairing_word.extend([ + ["add", a, b, str(sign[b])], + ["scale", b, None, str(-2 * sign[b])], + ["add", b, a, "1"], + ]) + local_active.append(a) + m = len(local_active) + p = local_active[0] + active += local_active + for a in local_active[1:]: + reduced_word.append(["add", a, p, "1"]) + reduced_word.append(["scale", p, None, str(-(m - 2))]) + for a in local_active[1:]: + reduced_word.append(["add", p, a, "1"]) + if m == 3: + reduced_word.extend([ + ["fixed_divide", p, None, "3"], + ["scale", p, None, "2"], + ]) + else: + need(m == 4, "Only the actual reduced block sizes") + reduced_word.append(["scale", p, None, "1/2"]) + for a in local_active[1:]: + reduced_word.append(["add", a, p, "-1"]) + selected = set(same_class_pairs[0]) + u = {a: F(sign[a] * (2 * int(a in selected) - 1)) for a in ports} + v = {a: F(2 * sign[a], len(ports)) - F(sign[a] * int(a in selected), 2) + for a in ports} + for a, value in u.items(): + add(s[a], v, value) + for a in selected: + add(k_matrix[a], {b: F(sign[b]) for b in selected}, + -F(len(ports) * sign[a], 2)) + groups.append({ + "ports": ports, "signs": signs, "pairs": same_class_pairs, + "active_sum_carriers": local_active, "centre_pair": sorted(selected), + "block_size": len(ports), "reduced_size": m, + "rank_one_determinant": str(F(8, len(ports)) - 2), + }) + + t_word = h_word + pairing_word + t, _ = replay(t_word) + ti, _ = replay(inverse_word(t_word)) + pmat = replay(pairing_word)[0] + pmi = replay(inverse_word(pairing_word))[0] + reduced = replay(reduced_word)[0] + need(product(pmat, product(s, pmi)) == reduced, "The exact reduction to class sums") + inactive = set(range(112)) - set(active) + need(len(active) == len(inactive) == 56, "The two sets each have 56 coordinates") + need(all(reduced[j] == {j: F(1)} for j in inactive), "All differences are fixed") + need(all(not (set(reduced[j]) & inactive) for j in active), "No difference is read") + + word = t_word + reduced_word + inverse_word(t_word) + inverse = inverse_word(word) + c, growth = replay(word, 640) + ci, inverse_growth = replay(inverse, 640) + need(product(c, ci) == product(ci, c) == ident(640), "Both inverse orders") + need(all(c[j] == ci[j] == {j: F(1)} for j in range(112, 640)), + "All 528 other roles are unchanged") + need(c[:112] == product(hi, product(s, h)), "The physical rank-one code") + response = decoded(capture["response"]) + centre = product(c[:112], product(response, ci[:112])) + need(centre == product(hi, product(k_matrix, h)), "The actual response") + need(all(classes[i] == classes[j] for i, row in enumerate(centre) for j in row), + "The output response stays in each phase class") + need(all(classes[i] == classes[j] for i, row in enumerate(t) for j in row), + "The full reduction stays in each phase class") + + # This is a formal phase test. The exponent difference labels each block. + # Equal class labels make every T coefficient commute with the class phase. + def formal_conjugate(matrix): + return [ + {(j, classes[i], classes[j]): value for j, value in row.items()} + for i, row in enumerate(matrix) + ] + need(formal_conjugate(centre) == [ + {(j, classes[j], classes[j]): value for j, value in row.items()} + for row in centre + ], "The centre action has no nontrivial class-phase ratio") + + payload = { + "source_pins": PINS, "phase_space_basis": [30, 45, 75, 384], + "classes": classes, "groups": groups, "active_sum_carriers": active, + "code": encoded(c[:112]), "inverse_code": encoded(ci[:112]), + "centre_response": encoded(centre), "reduction": encoded(t), + "reduced_code": encoded(reduced), + "scalar_word": word, "inverse_scalar_word": inverse, + "reduction_word": t_word, "reduced_code_word": reduced_word, + } + raw = (json.dumps(payload, sort_keys=True, indent=2) + "\n").encode() + (args.out / "PAIRED-CODE.json").write_bytes(raw) + receipt = { + "status": "PASS_ACTUAL_PHASE_CLASS_CAPTURE", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_sha256": sha256(raw).hexdigest(), "source_pins": PINS, + "arbitrary_columns": 640, "unchanged_other_roles": 528, + "active_class_sums": len(active), + "code_prefix_norm": str(growth), "inverse_prefix_norm": str(inverse_growth), + "literal_scalar_operations": len(word), + "code_invoice": invoice(word), "inverse_invoice": invoice(inverse), + "reduction_invoice": invoice(t_word), + "reduced_code_invoice": invoice(reduced_word), + "conditional_native_phase_calls": 2 * len(active), + "scope": ( + "Exact scalar code and phase-class reduction. The 112-call bound assumes " + "paid monomial phase alignment and rank-one phases in a carried common " + "frame. It does not implement frame preparation/removal or a supplier." + ), + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/phase-class-capture-final-normal/CHECKS.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/phase-class-capture-final-normal/CHECKS.json new file mode 100644 index 0000000000..33e5d52add --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/phase-class-capture-final-normal/CHECKS.json @@ -0,0 +1,51 @@ +{ + "active_class_sums": 56, + "arbitrary_columns": 640, + "checker_sha256": "d50e84f8d23ddadee126028998b9cf870aa44f125f2a6bf408ad13515ac53725", + "code_invoice": { + "native_children_inside_common_chart": 0, + "old_real_scalar_units": 4204, + "owned_fields": 0, + "real_fixed_three_division_scans": 16, + "real_fixed_three_multiplication_scans": 0 + }, + "code_prefix_norm": "12", + "conditional_native_phase_calls": 112, + "inverse_invoice": { + "native_children_inside_common_chart": 0, + "old_real_scalar_units": 4204, + "owned_fields": 0, + "real_fixed_three_division_scans": 0, + "real_fixed_three_multiplication_scans": 16 + }, + "inverse_prefix_norm": "12", + "literal_scalar_operations": 656, + "payload_sha256": "830a19a100763700dfc5142cb9eca1c284d9ad92828c4f4e1fe69bdc84e55b9d", + "reduced_code_invoice": { + "native_children_inside_common_chart": 0, + "old_real_scalar_units": 1040, + "owned_fields": 0, + "real_fixed_three_division_scans": 16, + "real_fixed_three_multiplication_scans": 0 + }, + "reduction_invoice": { + "native_children_inside_common_chart": 0, + "old_real_scalar_units": 1582, + "owned_fields": 0, + "real_fixed_three_division_scans": 0, + "real_fixed_three_multiplication_scans": 0 + }, + "scope": "Exact scalar code and phase-class reduction. The 112-call bound assumes paid monomial phase alignment and rank-one phases in a carried common frame. It does not implement frame preparation/removal or a supplier.", + "source_pins": { + "capture": [ + "bridge-access-20261017/rank16-capture-20261020/run-normal/CAPTURE.json", + "cd6d621140290c73a771e1d6c531d2ffa00ae278e5b4e39b4ad9ff1ae00cc888" + ], + "pairs": [ + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + ] + }, + "status": "PASS_ACTUAL_PHASE_CLASS_CAPTURE", + "unchanged_other_roles": 528 +} diff --git a/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/phase-class-capture-final-normal/PAIRED-CODE.json b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/phase-class-capture-final-normal/PAIRED-CODE.json new file mode 100644 index 0000000000..762f21ea9c --- /dev/null +++ b/research/phase-coded-callers/annexes/phase-access/frozen/work/centre-encoding-campaign-20261014/root/phase-class-capture-final-normal/PAIRED-CODE.json @@ -0,0 +1,16282 @@ +{ + "active_sum_carriers": [ + 0, + 2, + 70, + 13, + 27, + 14, + 11, + 41, + 21, + 43, + 9, + 37, + 16, + 25, + 20, + 7, + 61, + 10, + 44, + 57, + 42, + 62, + 52, + 46, + 1, + 5, + 73, + 19, + 3, + 4, + 60, + 22, + 35, + 38, + 6, + 39, + 45, + 12, + 8, + 108, + 17, + 67, + 58, + 29, + 32, + 65, + 34, + 18, + 24, + 26, + 28, + 96, + 31, + 59, + 23, + 55 + ], + "centre_response": [ + { + "0": "-1/2", + "27": "-3/2", + "76": "-3/2", + "87": "-3/2" + }, + { + "1": "-3", + "82": "-4" + }, + { + "2": "1" + }, + { + "3": "-3", + "80": "-4" + }, + { + "4": "1" + }, + { + "5": "1" + }, + { + "6": "1" + }, + { + "57": "-3/2", + "7": "-1/2", + "81": "-3/2", + "92": "-3/2" + }, + { + "8": "1" + }, + { + "9": "1" + }, + { + "10": "-1/2", + "62": "3/2", + "71": "3/2", + "90": "-3/2" + }, + { + "11": "-1/2", + "63": "3/2", + 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For each old rank-r frame, `Gamma_V = i^-r (H_V tensor H_V)` satisfies `Gamma_V^2 = I` on arbitrary arrays. The actual routed centre queries then admit complementary factors whose cross-stage product is zero. This removes a coefficient-field obstruction to a reusable centre encoder.\n\nThe [proof and finite invoice](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/PROOF.md), [centre application](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/CENTRE-APPLICATION.md), [complete replay receipt](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/evidence/REPLAY.json), and [source manifest](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/SOURCES.json) are pinned to the reviewed commit. The [native proof](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/NATIVE-PROOF.md) and [global binding](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/GLOBAL-WALSH.md) establish the implementation interfaces.\n\nThe construction doubles the ambient dimension from 73 to 146 and every recursive child rank. It retains the 14336 productive families, complete borrowed-helper jobs, invocation order, owner assignment, and diagonal cover-group order. Its paid rank mass is 2082816 and its rank deficit is 10240. Every normalized recursive rank ratio is unchanged, so the pure complex moment and complete kappa calculation do not improve. The twofold lift passes the complete retained finite guards, including the 512-bit prefix and 48-bit local primitive bound. The fourfold comparison fails the local primitive guard.\n\nThe exact base and consumed dependency commit is `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The input is the [historical PR #1094 selection receipt](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1094-audit/ASSEMBLY.json), not a claim about today's selected frontier. The proof retains the all-size native, compiler, whole-call hosting, precision, fixed-tape, and analytic recurrence assumptions. The replay emits local native factors and a complete global operator schedule; it does not flatten an all-size instruction tape or prove the full multiplication theorem. Legal decoder access, changed-word mode hosting, and the complete cost of a cheaper centre supplier remain open.\n\nFrom the repository root, with Python 3.10 or later, Git, and the pinned source commit present, run:\n\n```sh\npython3 -I -B research/involutive-walsh-lift/verify.py\n```\n\nThe expected final line is:\n\n```text\nPASS_INVOLUTIVE_WALSH_LIFT_PACKAGE\n```\n\nAll seven stages passed, including cold replays into fresh output directories. Separate research agents checked the proofs and wrote independent exact reviewers. Coverage includes 1004 full frame adapters, 2896 full child operators, 224 endpoints, 36 helper normalizers, all 712 scalar input columns in both orientations, all 144 selected calls, 69120 complete helper jobs, 7526 idle suffixes, and 14336 productive endpoints. Negative controls reject a missing scalar phase, the singular even-line formula, a wrong helper route, a missing helper job, an incorrect bridge sign, and stale terminal or cover translations. Two exact rational moment engines agree. The final staged source and artifact hashes match the replay. Source assertions are required; do not run the driver with `-O`. The old frontier admission target was not rerun or modified. Independent human review has not yet occurred.\n\nThe [source notices](https://github.com/aliromman/integer-mult-bounds/blob/3ae9a6f3ac74ded022ab3b4872a7357a621af6fb/research/involutive-walsh-lift/NOTICE.md) preserve the full lineage. The consumed local word and gauge are credited to @icekylinx in the [gauge44 notice](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/gauge44-slots/NOTICE.md); the 16-replica assembly is credited to Hao Yan (@FanPUYen) in the [t16 notice](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/gauge44-slots-t16/t16/NOTICE.md). The owner exchanges and invoice use @rohanarun's [PR #1094](https://github.com/CrocSwap/integer-mult-bounds/pull/1094), whose [source README](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/complex-t16-rare-pattern-exchanges/README.md) also credits Jeremy Kothe (@jeremykothe2) for [PR #1087](https://github.com/CrocSwap/integer-mult-bounds/pull/1087). Earlier author and license notices remain intact. New research, code, and verification used substantial OpenAI Codex assistance under the user's direction. 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'work/centre-encoding-campaign-20261014/' +JOBS = [ + ('walsh', 'lanes/interface-proof/review_walsh_frames.py', None, + 'WALSH-FRAME-REVIEW.json', 'WALSH-FRAME-REVIEW.json'), + ('rational', 'lanes/independent-review-20261017/phase-class-reduction-review-20261020/check_review.py', + '--out', 'CHECKS.json', 'verified-normal/CHECKS.json'), + ('dyadic', 'lanes/bridge-review-20261017/dyadic-phase-capture-review-20261020/check_review.py', None, + 'REVIEW.json', 'REVIEW.json'), +] + + +def need(value, message): + if not value: + raise ValueError(message) + + +def digest(raw): + return sha256(raw).hexdigest() + + +def verify(): + manifest = json.loads((HERE / 'SOURCES.json').read_text()) + for item in manifest['files']: + raw = (HERE / item['package_path']).read_bytes() + need(len(raw) == item['bytes'] and digest(raw) == item['sha256'], + 'Frozen source mismatch: ' + item['package_path']) + if 'decompressed_sha256' in item: + need(digest(gzip.decompress(raw)) == item['decompressed_sha256'], + 'Frozen payload mismatch: ' + item['package_path']) + return manifest + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + output = args.out.resolve() + output.mkdir(parents=True, exist_ok=False) + need(shutil.disk_usage(output).free >= 3 * 1024 ** 3, 'Keep at least 3 GiB free') + manifest = verify() + runs = [] + env = dict(os.environ) + env.update({name: '1' for name in ('OPENBLAS_NUM_THREADS', 'OMP_NUM_THREADS', + 'MKL_NUM_THREADS', 'VECLIB_MAXIMUM_THREADS')}) + for optimized in (False, True): + mode = 'optimized' if optimized else 'normal' + for label, script, option, receipt, expected in JOBS: + saved = output / mode / label + saved.mkdir(parents=True) + with tempfile.TemporaryDirectory(prefix='phase-access-', dir=output) as temporary: + repository = Path(temporary) / 'repository' + shutil.copytree(HERE / 'frozen', repository) + executable = repository / BASE / script + generated = Path(temporary) / 'generated' if option else executable.parent + command = [sys.executable, '-I', '-B'] + (['-O'] if optimized else []) + [str(executable)] + if option: + command += [option, str(generated)] + start = time.monotonic() + process = subprocess.run(command, cwd=repository, env=env, text=True, + stdout=subprocess.PIPE, stderr=subprocess.STDOUT, check=False) + (saved / 'stdout.txt').write_text(process.stdout) + need(process.returncode == 0, label + ' failed: ' + str(saved / 'stdout.txt')) + raw = (generated / receipt).read_bytes() + frozen = (HERE / 'frozen' / BASE / Path(script).parent / expected).read_bytes() + need(raw == frozen, 'Complete receipt bytes differ: ' + label) + (saved / receipt).write_bytes(raw) + runs.append({'job': label, 'mode': mode, 'seconds': round(time.monotonic() - start, 3), + 'receipt_sha256': digest(raw), 'receipt': str((saved / receipt).relative_to(output)), + 'complete_frozen_receipt_byte_equal': True}) + print('PASS ' + mode + ' ' + label, flush=True) + for label, *_ in JOBS: + pair = [r['receipt_sha256'] for r in runs if r['job'] == label] + need(len(pair) == 2 and pair[0] == pair[1], 'Normal and optimized receipt mismatch') + verify() + result = {'status': 'PASS_PHASE_ACCESS_ANNEX', 'source_files': len(manifest['files']), + 'source_manifest_sha256': digest((HERE / 'SOURCES.json').read_bytes()), + 'replay_sha256': digest(Path(__file__).read_bytes()), 'runs': runs, + 'normal_optimized_byte_equal': True, 'source_files_unchanged': True, + 'source_code_adaptations': 0, + 'scope': 'Exact growing-frame kernels and route ranks; rational and dyadic scalar capture; conditional common-frame geometry. No emitted full native capture, source-access or owner program, recursive supplier, or kappa improvement.'} + (output / 'REPLAY.json').write_text(json.dumps(result, indent=2) + '\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/phase-coded-callers/frozen/LICENSE b/research/phase-coded-callers/frozen/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/phase-coded-callers/frozen/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. + +Partial-gauge extension, 9 October 2026 +Copyright 2026 icekylinx + +The pair-first cube assembly, compatible backward frame enlargement, +partial source-gauge schedule and stopped whole-projector composition are +contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834. + +The physical deferred bit word, reflected event accounting, fan-order +clarification and signed two-stage endpoint are adopted from Zhihao Chen +(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with +Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen +witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38, +with the original Claude disclosure retained. Cyclic interval and core-aware +pair primitives build on Avi Eisenberg (ikeboy), PR #62, +ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance. +Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and +precision credits remain in force. Imported source notices and licenses +are preserved under references/partial-gauge/; see SOURCES.json. + +Three-stage cover extension, 9 October 2026 +Copyright 2026 icekylinx + +The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry, +weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring +fallback, uniform batching, internal row borrowing and exact composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This +repository integration uses Codex assistance and extends +PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86. + +The selected local complex DAG and support/label replay are adopted from +Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf, +with its original Apache-2.0 terms and Claude assistance disclosure. +The unchanged bit physical word retains Zhihao Chen (jacklightChen), +PR #97, and Swapnil Jain's underlying witness and assistance notices. +The prior opposite-bank, stopped ordinary-leaf, copied-center, topology, +semantic/bulk, precision and analytic credits remain applicable. +Original source notices and license bytes are preserved in +references/three-stage-cover/pr117/ and references/partial-gauge/. + +Paired-cube and shared-core extension, 9 October 2026 +Copyright 2026 icekylinx + +The paired-coordinate triple-cube identity, signed overlap channels, +original-source involution, coordinate-star centers, concrete frame/carrier +compiler, chronological source gauges, PR97 gauge-subset selection, +orthogonal cross-stage routing and exact supplier/assembly integration +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. +Repository integration uses Codex assistance and extends PR #130 at +6a9970a530119174507904e23592fd59ede19a5d. + +The substantial completed-core workspace-sharing principle is credited to +an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported +OpenAI Codex assistance. No source code, partition or serialized witness +from that PR is imported. The new routing and paired-motif integration +are described separately and claim no exclusive priority for broad sharing, +paired-coordinate, Fourier or carrier-matching ideas. + +Selected coarse queries restrict the retained eumemic PR #117 positive DAG; +its original Apache-2.0 and Claude assistance notices remain unchanged. +The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil +Jain's frozen witness, notices and historical assistance disclosures. +Earlier generalized Clifford, three-stage, uniform weighted recursion, +ordinary-leaf, semantic/bulk, precision and analytic credits remain in force. +Source-specific license bytes are preserved under references/. + +October 9 recycled-bit integration: +DaysSky (#150), William Porter/hpst3r (#147), Thomas Marchand/Th0rgal (#146), +Rohan Gupta/gupt1156 (#148), James Chang/jamesyc (#124), SovereignSteak (#122). +The original notices and assistance disclosures are retained under research/, +including research/recycled-bit-integration/NOTICE. Andrew Barnes/Bortlesboat +(#101) repairs shared verifiers using rfu08's #64 counterexample. rfu08's +scoped finite and formal-transfer packages are included separately; they do +not establish the full multiplication theorem. Earlier and parallel credits +remain applicable. Douglas Colkitt integrated these with OpenAI Codex assistance. + +SovereignSteak PR151 independently supplies the matching gauge/recycling +composition and the selected 473/10^6 atom refinement; its original package +and assistance disclosure are retained under research/gauge-recycling/. + +October 9 coordinated-frame and completed-entrance-bank integration: +Dugongue PR186, 166a34d75e853e933855f0f7e940fe77c4bb6b8d, builds on +Chafik Boukhalfa/chafreaky's PR181, 7fb2194801e3a10f54772c7f0d5505035a4fc0ad, +and eumemic's PR168 v4, 4a3c769e5c5430e7114c4d3e099ff34664677f17. +The frozen package and prerequisite archive preserve all author, source-license +and assistance notices, including PR175's compiler optimization. DaysSky's +carrier closure, James Chang's terminal substitution and balanced assembly, +geckods' stopping refinements and all preceding framework credits remain. +Rohan Arun's PR185 bootstrap and chafreaky's PR182 bit refinement are reviewed +parallel contributions; their gains are not added to the selected witness. +Douglas Colkitt integrated the package and supplied the bank scheduling +supplement with OpenAI Codex assistance, under Apache-2.0. The all-size +interfaces remain conditional; finite verification is not full formalization. diff --git a/research/phase-coded-callers/frozen/upstream/LICENSE b/research/phase-coded-callers/frozen/upstream/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/phase-coded-callers/frozen/upstream/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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A step reads and writes at most one cell on each +tape and moves each head by at most one cell. Fixed tracks and finitely +many work tapes change time by a fixed factor. We distinguish moving one +digit in a fixed radix, which needs a bounded number of scans, from +interchanging fields whose numbers of digits grow. The latter permutation +will be realized in Section~\ref{sec:tape-interchange} by computing XOR +combinations of intermediate data streams. The present section supplies +the elementary scans it uses. Every scan includes its counters and the +return of its tape heads. + +\subsection{Array order and elementary scans} + +For a positive integer $a$ write $[a]=\{0,\ldots,a-1\}$. +An array with address set $[a_1]\times\cdots\times[a_t]$ is stored in +lexicographic order, with the first coordinate most significant. Its +entries are bits unless a record width is specified. A trailing record +of $B$ bits can equivalently be regarded as a final address field $[B]$. +An address is implicit in an entry's position in this ordered stream; it +is not stored beside every data bit. +The \emph{logical volume} $V$ is the number of stored data bits. Work +tapes and duplicate streams are charged in time but do not increase $V$ +in recurrences. All the fields discussed below are nonempty. A call +with an empty array is handled directly. + +An address permutation $f$ moves the entry at $x$ to $f(x)$. Thus its +action on an array $A$ is $(fA)(f(x))=A(x)$. Adjacent fields which are +irrelevant to an operation may be replaced by a single field whose length +is their product. In particular, the elementary procedures below have a +fixed number of formal address fields even when a surrounding algorithm +has a growing list of coordinates. Lengths and positions are supplied in +canonical binary on descriptor tapes; no additional tape head is attached to an +address coordinate. Each elementary call receives a fixed number of +collapsed canonical lengths. Constructing them from a longer surrounding +list is work of the caller; recursive calls below construct their own +collapsed descriptors within their stated bounds. + +When one address field is designated as a row field, collapse the fields +before it to a prefix $[P]$ and those after it to a suffix $[B]$. If the +row field has range $[R]$, a \emph{row} at prefix $p$ and row index $r$ +is the complete consecutive block $\{p\}\times\{r\}\times[B]$. +Every row therefore contains $B$ bits in the same suffix order. + +For headers that concatenate a list of positive integer parameters, we use +the self-delimiting code +\begin{equation} + b_v=\lfloor\log_2v\rfloor+1,\qquad + \Gamma(v)=0^{b_v-1}\operatorname{bin}_{b_v}(v),\qquad + |\Gamma(v)|=2b_v-1\quad(v\ge1). + \label{eq:integer-descriptor-code} +\end{equation} +The initial zeroes specify how many further bits follow the first one, +so concatenated codes can be read in order. We use this code when an +interface specifies a header; elementary calls still receive the fixed +number of canonical binary lengths described above. + +\begin{lemma}[Elementary stream operations] +\label{lem:elementary-streams} +Fix a radix $q\ge2$. Each of the following operations on an array of +volume $V$ takes $O(V)$ steps on a fixed number of one-dimensional tapes: +\begin{enumerate} +\item any fixed permutation of the pair of digit values at two specified +radix-$q$ positions, whether or not the positions are adjacent; +\item moving one specified radix-$q$ digit to another position, preserving +the order of the intervening positions; +\item splitting on a specified radix-$q$ digit, applying a fixed +pointwise map to aligned streams, and merging them back; +\item for positive integers $P,R,B$, within each prefix of an array on +$[P]\times[R]\times[B]$, splitting +whole rows cyclically into a fixed number $W$ of streams, and, when $W$ +divides $R$, merging those streams in any fixed order of the row classes. +\end{enumerate} +The bounds include shape preparation, counter initialization and resets, +and returning or clearing the visited portions of work tapes. Their +constants may depend on the fixed radix, the fixed pointwise map, and the +fixed number of row classes. +\end{lemma} + +\begin{proof} +For the first operation split into $q^2$ streams according to the two +specified digits. With these digits fixed, the order of all remaining +digits is unchanged by the permutation. Enumerate output addresses in +their required order and read the stream prescribed by the two preimage +digits. For a digit move use $q$ streams instead. The same observation +shows that splitting on one digit gives streams with the same remaining +address set in the same order. Scan their aligned entries, apply the +fixed pointwise map, and merge according to the output digit; this proves +the third operation. For the fourth, write $r=Wg+w$, where +$0\le w0,\quad 0<\epsilon<1. +\] +The exponents and comparison constants are fixed, and we impose their +further restrictions in Proposition~\ref{prop:simultaneous-layer}. +Two consequences explain the layout. The polynomial length $r$ grows +faster than every fixed power of $p$, so a scan of a record pays for +polynomial work on its address. Also $K/\log p\to\infty$, which will +make the exceptional set in a packed change of address bits small enough +to repair by sorting. We will obtain cost $O(Vd^{\lambda'})$, with +$\lambda'<1$ and $V$ the logical bit volume, whereas separate butterfly +factors would require $D$ whole-array passes. + +We first construct tensor products of the auxiliary two-point kernel +$C$ from Proposition~\ref{prop:complex-motif-interface}. Its phase +frames express a $C$ tensor product using smaller groups of +selected bits, separated by binary changes of basis. We implement those +changes by moving whole address chunks. Splitting complete rows among +the network's wire roles then reduces the volume of each recursive +call. Finally, we bound the intermediate dyadic values and convert the +completed $C$ layer to the normalized $H_0$ layer. The entire layer is +evaluated exactly before one final truncation. + +\subsection{Phase frames for a simultaneous butterfly layer} +\label{subsec:phase-frames} + +Hold the unselected address bits fixed and regard the stored complex +values on one wire role as a function of the selected bits. The phase +identities below express an edge's residual operator as a product of +two-point kernels on selected directions. + +Put +\[ + H_0=\frac12\begin{pmatrix}1&1\\1&-1\end{pmatrix},\qquad + H=\sqrt2 H_0,\qquad \mathsf S=\operatorname{diag}(1,i),\qquad + Z=\operatorname{diag}(1,-1). +\] +For the bit-flip matrix $X=\bigl(\begin{smallmatrix}0&1\\1&0\end{smallmatrix}\bigr)$, +define +\begin{equation}\label{eq:phase-C} + C=H\mathsf SH=aI+bX,\qquad a=\frac{1+i}{2},\quad b=\frac{1-i}{2}. +\end{equation} +Direct multiplication gives +\begin{equation}\label{eq:phase-basic-identities} + H_0=b\mathsf SC\mathsf S,\qquad C^2=X,\qquad C^4=I,\qquad + C^{-1}=bI+aX=-iZCZ. +\end{equation} +In particular, $C=iZC^{-1}Z$. These identities use only Gaussian dyadic +coefficients. The Hadamard matrices in the definition of +$\mathcal C_U$ are used to prove identities; they need not be executed +by the machine. + +Consider an edge from label $U_-$ to label $U_+$, and choose an +orthonormal basis $v_1,\ldots,v_{\rho_{\rm edge}}$ of its residual. +Proposition~\ref{prop:complex-motif-interface} gives the frame change +\[ + \mathcal C_{U_+}\mathcal C_{U_-}^{-1} + =\prod_{j=1}^{\rho_{\rm edge}}(aI+bX_{v_j})^{\epsilon_j}, + \qquad \epsilon_j\in\{1,-1\}. +\] +Here $(X_vf)(x)=f(x+v)$, and we write $C_v=aI+bX_v$. +The number of directional kernels is precisely +$\rho_{\rm edge}$, including on decreasing edges. The next step puts those directions +into coordinate positions without performing a general transpose. + +\paragraph{Implementing an arbitrary residual basis.} +For $M\in\operatorname{GL}(m,\mathbb F_2)$, let $\mathcal P_M$ be the +address permutation that moves the value at $x$ to $Mx$. Thus +$(\mathcal P_Mf)(x)=f(M^{-1}x)$, and +\begin{equation}\label{eq:phase-conjugation} + \mathcal P_MX_v\mathcal P_M^{-1}=X_{Mv}. +\end{equation} +Extend $v_1,\ldots,v_{\rho_{\rm edge}}$ to a basis of $\mathbb F_2^m$ and take these vectors as +the first $\rho_{\rm edge}$ columns of $M$. The displayed edge identity +then becomes +\begin{equation}\label{eq:phase-edge-coordinate} + \mathcal C_{U_+}\mathcal C_{U_-}^{-1} + =\mathcal P_M\left(\prod_{j=1}^{\rho_{\rm edge}}C_{e_j}^{\epsilon_j}\right) + \mathcal P_M^{-1}, +\end{equation} +where $e_j$ is the $j$th standard basis vector. The matrix $M$ need not +preserve the dot product: equation~\eqref{eq:phase-conjugation} only +uses its invertibility. + +For the array layout used below, take a group of $e=mf$ consecutive +axis chunks and divide it into $m$ consecutive slots of $f$ chunks, +numbered in physical order. +Number the chunks within each slot by $j=0,\ldots,f-1$, starting at +its least significant end. Write $x_{h,j}$ for the selected bit in +chunk $j$ of slot $h$, where $1\le h\le m$. Column $j$ is the vector +$(x_{1,j},\ldots,x_{m,j})$. A frame on this group is the tensor +product of the same phase frame +$\mathcal C_U$ of Proposition~\ref{prop:complex-motif-interface} +on these $f$ columns. + +To implement \eqref{eq:phase-edge-coordinate} on the group, first apply +$\mathcal P_M^{-1}$ separately to each column. For each +$1\le h\le\rho_{\rm edge}$, apply $(C^{\epsilon_h})^{\otimes f}$ to the +$f$ bits $x_{h,0},\ldots,x_{h,f-1}$. This is one child operation +on the $f$ axes in slot $h$. Finally apply $\mathcal P_M$ to every +column. A negative directional kernel still requires only one +forward child, because +\begin{equation}\label{eq:phase-inverse-child} + (C^{-1})^{\otimes f} + =(-i)^f Z^{\otimes f}C^{\otimes f}Z^{\otimes f}. +\end{equation} +The rightmost phase is applied first. All inverse wrappers are address +signs and constant fourth-root phases, so they add no recursive calls. + +Gaussian elimination expresses any $M\in\operatorname{GL}(m,\mathbb F_2)$ +as a product of at most $m(m-1)+3m$ elementary row additions: one clears +at most $m-1$ other entries per pivot, and each row swap is three row +additions. Reversing the elimination gives the required product since +each row addition is an involution. The number is a constant because +$m$ is fixed. Adding row $h'$ to row $h$ in every column applies +$x_{h,j}\leftarrow x_{h,j}\mathbin\oplus x_{h',j}$ for every +$0\le j1$, these segments +are disjoint, and the highest one ends immediately below $j_{f-1}$. +Write their initial values in $y$ and $z$ as +\[ + u_i=2g_i+a_i,\qquad w_i=2h_i+b_i, + \qquad a_i,b_i\in\{0,1\}. +\] +The values $g_i,h_i\in\{0,\ldots,2^{K-1}-1\}$ are the guard values. The +control for this pair of segments is the selected bit $c_i=x_{j_i}$. + +Apply each line of \eqref{eq:eight-packed-additions} simultaneously to all +these segment pairs. Physically, a line updating $y$ by sign $\varepsilon$ +and testing parity $b$ of $z$ is the single cyclic shift +\begin{equation} +\label{eq:packed-cyclic-shift} + y\longleftarrow y+ + \varepsilon\sum_{i=0}^{f-2}2^{j_i} + [\,x_{j_i}=1\,][\,z_{j_i}=b\,] + \pmod{2^L}. +\end{equation} +For a line updating $z$, interchange $y$ and $z$ in this formula. +The shift offset never depends on its target chunk, so each line is a +bijection of the rectangle. Let $S_0$ be their composition. It fixes +the spectator coordinates. + +Let $\mathcal B$ consist of the addresses for which +at least one used guard value, in either $y$ or $z$, fails +\begin{equation} +\label{eq:packed-guard-interval} + 10\le g\le 2^{K-1}-11. +\end{equation} +At an address outside $\mathcal B$, each segment initially lies in +$[20,2^K-21]$. Even displacement eight keeps it inside +$[0,2^K-1]$. Inductively, each packed addition therefore agrees with all +the independent segment additions: no segment carries into or borrows +from the next segment. When $f>1$, the bits below $j_0$ and above the +highest used segment are untouched as well. By +\eqref{eq:eight-packed-result}, $S_0$ +then agrees with the ideal permutation $T_0$ that performs the required +XORs at $j_0,\ldots,j_{f-2}$ and fixes all other address coordinates. + +There are exactly twenty excluded values for each guard in +\eqref{eq:packed-guard-interval}. Since its complete range has +$2^{K-1}$ values, the union bound over the $2(f-1)$ guards gives +\begin{equation} +\label{eq:packed-bad-fraction} + |\mathcal B|\le\delta_{\rm bad}M. +\end{equation} +Indeed, the complete $y,z$ ranges give the same guard distribution at +each choice of spectator coordinates. No record value enters this count. + +The ideal map $T_0$ preserves all guard values and therefore preserves +$\mathcal B$. Both $T_0$ and $S_0$ are bijections, and they agree off +$\mathcal B$. Taking complements in the finite rectangle gives +\[ + S_0(\mathcal B^c)=T_0(\mathcal B^c)=\mathcal B^c, + \qquad S_0(\mathcal B)=\mathcal B. +\] +Thus $T_0S_0^{-1}$ fixes $\mathcal B^c$ and permutes $\mathcal B$. +It remains to implement the rotations and this correction on tapes. + +For one rotation, move its target to the rightmost of the three chunk +positions if necessary. Let $P^{\rm sw}$ be the product of the record +field lengths before the earlier exchanged chunk, let $G^{\rm sw}$ +be the product between the exchanged chunks, and let $B^{\rm sw}$ be +$R$ times the product after the later one. Empty products are one. +The bit array has exactly the shape +\[ + [P^{\rm sw}]\times[2^L]\times[G^{\rm sw}] + \times[2^L]\times[B^{\rm sw}]. +\] +The third chunk lies inside one collapsed spectator interval. +Pass only $L$ and these three positive canonical lengths to +Lemma~\ref{lem:chunk-swap}. Each length is at most $V$, so the local +descriptor has $O(A_{\rm rect})$ bits. The swap costs $O(VL^\tau)$, including +its own padding and cleanup. + +The equal chunk lengths leave the field-length list unchanged by a +completed swap. Keep the permutation of the logical names $x,y,z$ in +finite local state. With the target now after its two controls, collapse +the remaining intervals to obtain +\[ + [\Lambda_0]\times[2^L]_{\rm control\,1}\times[\Lambda_1] + \times[2^L]_{\rm control\,2}\times[\Lambda_2] + \times[2^L]_{\rm target}\times[B_{\rm rot}], +\] +where $B_{\rm rot}$ includes the payload and every displayed spectator +length is positive. Their product with the chunk lengths is $V$. +Together with $K,f,\rho$ and the finite name permutation, these fixed +canonical lengths form an $O(A_{\rm rect})$-bit local descriptor. The offset +routine receives the two current $L$-bit logical control values. A scan +of at most $f\le L$ selected positions evaluates +\eqref{eq:packed-cyclic-shift} in $L^{O(1)}$ time, without reading the +target or spectator values. Lemma~\ref{lem:ordered-affine-streams} +therefore gives an $O(V)$ rotation: its offset work is absorbed by the +$2^L$ nonempty target blocks in each fiber. Undo the swap after the +rotation. The local descriptors and name permutation are updated at +completed swap boundaries; the primitives use their own descriptors +inside padded layouts. +There are at most sixteen swaps and eight rotations in $S_0$. + +To implement the correction, scan the stream with a record-rank counter. +All chunk names are back in their original positions. Dividing the +current rank through the fixed seven field lengths recovers the three +chunk values and their mixed-radix record strides. The strides exclude +the $R$ payload bits. All involved integers have $O(A_{\rm rect})$ bits, so +schoolbook arithmetic, descriptor copying, and resets take at most +$O(A_{\rm rect}^3)$ per record. Test membership in $\mathcal B$ and extract just +those records. For a current exceptional address $q$, compute +$q'=T_0(S_0^{-1}(q))$ by reversing the eight modular additions with +negated offsets, then applying the selected XORs directly. Each reversed +mask uses the current controls of that reversed line. There are at most +$f\le L\le A_{\rm rect}$ selected positions, so this calculation also fits +$O(A_{\rm rect}^3)$ time. + +If $q_h,q'_h$ are the current and destination values of chunk +$h\in\{x,y,z\}$ and $\sigma_h$ is its record stride, the fixed +spectator coordinates give +\[ + \operatorname{rank}(q')=\operatorname{rank}(q)+ + \sum_{h\in\{x,y,z\}}(q'_h-q_h)\sigma_h. +\] +The differences are signed. Attach this destination rank, padded to +$\lceil\log_2M\rceil\le A_{\rm rect}$ bits, to the extracted record, and mark its +hole on a fixed track of the full stream. Hold the full stream untouched +while stable binary radix sorting scans only the extracted records and +keys, least significant key bit first. Since $T_0S_0^{-1}$ permutes +$\mathcal B$, these keys are distinct and are exactly the ranks of the +marked holes. One forward full-stream scan reinserts the sorted records. +This implements $T_0$ everywhere. + +Finally apply the two-bit XOR to $x_{j_{f-1}},y_{j_{f-1}}$ by +Lemma~\ref{lem:elementary-streams}, splitting those chunks at the +selected positions and collapsing the other intervals. Its descriptor +again has a fixed number of positive lengths, each at most $V$. +This costs $O(V)$ and supplies the omitted selected position. When +$f=1$, $S_0,T_0$ are identities, $\mathcal B$ is empty, and this last +step is the entire algorithm. + +The movement costs $O(V(L^\tau+1))$. A fixed number of full record scans +costs $O(MA_{\rm rect}^3+V)$, and the at most $A_{\rm rect}$ radix passes cost +$O(|\mathcal B|A_{\rm rect}(R+A_{\rm rect}))$; skip them when the extracted bank is empty. +The initial descriptor has a fixed number of canonical integers of +$O(A_{\rm rect})$ bits, so its preparation is covered by $O(MA_{\rm rect}^3)$. +All counters, positioning, rewinds, and cleanup are included. +Equation~\eqref{eq:packed-bad-fraction} proves +\eqref{eq:packed-rectangle-time} on a fixed number of tapes. +After division by $V=MR$, its additional terms are bounded by +$A_{\rm rect}^3/R$ and +$80(f-1)2^{-K}A_{\rm rect}(1+A_{\rm rect}/R)$. Under the stated family bounds +the first tends to zero, and the second is +$O(p^2 2^{-K}(1+A_{\rm rect}/R))=o(1)$. This proves the final assertion. +\end{proof} + +\paragraph{Application to a fixed binary change of basis.} +An invertible matrix over $\mathbb F_2$ of fixed order $m\ge3$ is a +product of a fixed number of elementary row additions; a row exchange +is three such additions. In one invocation of the finite network on +$e=mf$ axes, slot $h$ consists of $f$ consecutive $K$-bit axis chunks. +It therefore has address-bit width $L=fK$, and its selected bits +$x_{h,j}$ occupy positions $\rho+jK$ for $0\le j1$. +For these fixed choices +there are a cutoff $p_0$, one fixed finite-alphabet multitape procedure, +and an implicit time constant with the following guarantee. The cutoff +and time constant may depend on the fixed rational parameters +and these constants. For every choice of positive integers $p,d,r$ +with $p\ge p_0$ and +\[ + a_dp^\epsilon\le d\le b_dp^\epsilon,\qquad + 2^{a_rp/d}\le r\le 2^{b_rp/d}, +\] +put $K=\lfloor d^c\rfloor$, and let $1\le D\le d$, $P,S\ge1$, and +$0\le\rho@m-q_3xe*Un3qXU0#A^e$U`~T42dl?H;Q?P`8e{psO5Rb$KsD$AA>)N zVqCryEf*aX?WMP*&!?|EJbmY+cE?man|>gCG@L#>IsE;-S`LA)w(nh8D7e{~qMumTB;3`p z86GZy0b_QWZeX@%Q%=!B;ur^FAn|Qa@7=&{iKSfVwixE~B<9Q68?&iw^r1`Q^f+9? zbN|H6ZNHiUvjFipSnxbua+ElopY#;P9O`-=G#wfZA7Xp%2TWo%GbK)TjwjvsPh8yg z+ru$O$DR`0m}zwRiQVhdZDI+`=DpJ{&x6Cv$4l=&ni3mU7)8gT!gUIs&s+_i4QobC~HV8t%4Fd=!qcIW;?N zKiogG_e}Jxn><;nUO(x=1eEM$PM&PEV~#o`FdGFDC+NQLQ8Dw&4g{Zl-5X`~GZQhp zeZ#T~1x^m_Vi>deksI6Q@y@5$`kdy`6kUinMzfzvEapdqw#^frPYt(MlAYgoi9wB$ z$8UA*y=m|l>q?~K?_#h|w&3q#OE9A9C<&b(xwmbe@n&Uo`_st%=sNTWc-uVFd9P0l zXqrqX(DgbYB+orrq}nvuLZAztV5HGek~cr1v2C8~>@aw35916!d*+hPy#yoAj*^D? z5&doRBImtfF{ruVjW*}Cl@e#cQL)<=$$5fZI#8pMj*`#wBbM7M<(1Cqo!s^giAi)u zMjuB;tQ~%rddx{e<{QgN3!OP83*)8Rj^#h6kj_JgulT zGrqe+;>VsceOci=^i?I6nZJSU-sssY`DNFul65i132$MDRAM<}=Tnjep1^I&X6K7DHMrIj-d04d z+hfjTGc^PaOV%@_?DP%tZ4cX?wCQK}?TCGJc9|i4h&fn@*Xc>d99yRxc@AZsdK~w! z6ASOQC)`Yw*gdrN@J>M)ZT6uPokk9GQW)qb#A=+Kwm0UdJDS+>76K^PiRRex7XnC9 zZYHKou^&D`^Gk?13a%VZPq#Kj2e1<>)8DzhkKWio>CgTx7W97z-6rQ@XJMzG;^5;2 zZf}a#U;~-rt4|_x<3rZ=eR}SXV7NBAdAbNS>DT=M-Q`oH985; 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b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/check_bridge_access.py @@ -0,0 +1,399 @@ +"""Check future projection bridges at the actual supplier cuts.""" + +import argparse +from bisect import bisect_left +from collections import Counter, defaultdict +from fractions import Fraction +from functools import cache +from hashlib import sha256 +import gzip +import json +from pathlib import Path +import tarfile + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +ROOT = HERE.parents[3] +ARCHIVE = ROOT / "worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz" +ARCHIVE_PIN = "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" +MEMBERS = { + "template": ("candidate/strict/global/hosted/GLOBAL-TEMPLATE.json.gz", "2acf02b418078e37090495c601fe550448751d4f35912757b13a1f778efc7760"), + "phases": ("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"), + "word": ("candidate/strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz", "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219"), +} +PINS = { + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "cover-algebra/BRIDGES.md": "0db4e1e4589da903e50057b2d8657512c1185159a9ee18e605ad54c027c7dc80", + "interface-proof/BRIDGE-OPERATOR-REVIEW.json": "c905a19d70f34c435c5f5454c6190bbfb1ce4594b1513bf76156acf620d7c6fc", + "interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json": "8b8c4d814b44c2fc42cf9ad995f8451512309fcfc46bea9317ebe4b4d79e8a4d", +} +SELECTED = [0, 7, 20, 27, 36, 46, 57, 111] +ORDINARY = [p for p in range(112) if p not in SELECTED] +UNIT = [1 << j for j in range(73)] +ZERO = (0, 0, 0) + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def owner(replica, pair, side, port): + return 896 * replica + 224 * pair + 112 * side + port + + +def act(columns, vector): + result = 0 + while vector: + low = vector & -vector + result ^= columns[low.bit_length() - 1] + vector ^= low + return result + + +def add_phase(a, b): + return a[0] ^ b[0], a[1] ^ b[1] ^ (a[0] & b[0]), a[2] ^ b[2] + + +def negative(a): + return a[0], a[1] ^ a[0], a[2] + + +@cache +def line(vector, exponent=1): + cross = 0 + for j in range(73): + if vector >> j & 1: + cross ^= (vector & ((1 << j) - 1)) << (j * (j - 1) // 2) + return (vector if exponent & 1 else 0, + vector if exponent & 2 else 0, cross if exponent & 1 else 0) + + +def product(terms): + result = ZERO + for vector, exponent in terms: + result = add_phase(result, line(vector, exponent % 4)) + return result + + +def canonical(q, level, side): + if level == -1: + return line(q) if side == 0 else ZERO + frame = ((1 << (9 + 8 * level)) - 1, 0, 0) + return add_phase(frame, line(q, 3)) if side else frame + + +def chart(q): + hole = next(i for i in range(9) if not q >> i & 1) + v = q ^ (1 << hole) + order = list(range(9)) + order[0], order[hole] = order[hole], order[0] + basis = [(1 << j) ^ (v if v >> j & 1 else 0) for j in order] + UNIT[9:] + need(basis[0] == q and all((a & b).bit_count() % 2 == int(i == j) + for i, a in enumerate(basis) for j, b in enumerate(basis)), "Actual orthogonal port chart") + return basis + + +def route(basis, stage): + columns = list(UNIT) + if stage: + swaps = [basis[j + 1] ^ UNIT[9 + 8 * (stage - 1) + j] for j in range(8)] + columns = [v ^ sum_xor(a for a in swaps if (a & v).bit_count() & 1) for v in columns] + need([act(columns, v) for v in columns] == UNIT, "Stage route is an involution") + return columns + + +def sum_xor(values): + result = 0 + for value in values: + result ^= value + return result + + +def phases_and_views(data): + views, checks, controls = {}, Counter(), Counter() + for p, recipe in enumerate(data["phases"]["recipes"]): + q, basis = recipe["q"], chart(recipe["q"]) + need(basis[1:9] == recipe["idle_children"][0]["orthogonal_axes"][:8], "Source port basis") + beta = sum((((v.bit_count() - 1) // 2) & 1) << j for j, v in enumerate(basis[1:9])) + local_beta = act(basis[1:9], beta) + for t in range(1, 9): + rho = route(basis, t) + lifted_beta = beta << (9 + 8 * (t - 1)) + delta_y = q ^ lifted_beta + delta_x = local_beta ^ lifted_beta + need(act(rho, recipe["stage_alignment"][t]["entry_Y"]) == delta_y, + "Future view has the literal supplier entry translation") + need(recipe["stage_alignment"][t]["exit_X"] == delta_x, + "Past view has the literal supplier exit translation") + for level in range(t): + terms = [(act(rho, e), 1) for e in UNIT[:9 + 8 * level]] + [(q, -1)] + actual = product(terms) + common_axes = list(range(9, 9 + 8 * level)) + list(range(9 + 8 * (t - 1), 9 + 8 * t)) + expected = product([(UNIT[j], 1) for j in common_axes]) + need(add_phase(actual, line(delta_y, 2)) == expected, "Full future-Y phase identity") + checks["future_Y"] += 1 + controls["omitted_Y_translation"] += actual != expected + controls["wrong_Y_translation_order"] += add_phase(actual, line(act(rho, delta_y), 2)) != expected + for level in range(t, 9): + actual = product([(act(rho, e), 1) for e in UNIT[:9 + 8 * level]]) + expected = canonical(q, level, 0) + need(add_phase(actual, line(delta_x, 2)) == expected, "Full past-X phase identity") + checks["past_X"] += 1 + controls["omitted_X_translation"] += actual != expected + views[p, t, "Y"] = dict(port=p, stage=t, side="Y", route_columns=rho, + translation_after_route=delta_y, translation_before_route=act(rho, delta_y)) + views[p, t, "X"] = dict(port=p, stage=t, side="X", route_columns=rho, + translation_after_route=delta_x, translation_before_route=act(rho, delta_x)) + need(checks == {"future_Y": 4032, "past_X": 4032}, "Full cone coverage") + need(controls == {"omitted_Y_translation": 4032, "wrong_Y_translation_order": 4032, + "omitted_X_translation": 4032}, "All exact phase controls fail") + return views, dict(checks), dict(controls) + + +def scalar_word(B, sign): + word = [["add", 112 + p, p, str(sign)] for p in ORDINARY] + word += [["add", 112 + a, p, str(-sign * B[i][j])] + for i, a in enumerate(SELECTED) for j, p in enumerate(ORDINARY) if B[i][j]] + return word + + +def scalar_check(B): + receipts = {} + for sign in (-1, 1): + word = scalar_word(B, sign) + rows = [{j: Fraction(1)} for j in range(224)] + max_norm = Fraction(1) + for _, target, source, coefficient in word: + coefficient = Fraction(coefficient) + need(source < 112 and target >= 112 and source in ORDINARY, "No changed or selected source is read") + for origin, value in rows[source].items(): + rows[target][origin] = rows[target].get(origin, 0) + coefficient * value + max_norm = max(max_norm, sum(abs(x) for x in rows[target].values())) + expected = [{j: Fraction(1)} for j in range(224)] + for p in ORDINARY: + expected[112 + p][p] = Fraction(sign) + for i, a in enumerate(SELECTED): + for j, p in enumerate(ORDINARY): + if B[i][j]: + expected[112 + a][p] = -sign * B[i][j] + need(rows == expected and len(word) == 520 and max_norm == 27, "Exact arbitrary-data U bridge") + need(rows[:112] == [{j: Fraction(1)} for j in range(112)], "Every source is unchanged") + receipts[str(sign)] = dict(program=word, arbitrary_input_columns=224, + unit_adds=104, half_adds=416, real_scalar_bound=4992, + maximum_intermediate_row_one_norm=str(max_norm), native_children=0, + private_fields=0, unchanged_source_rows=112) + return receipts + + +def schedule_audit(data, views, mixed): + template, phases, word = data["template"], data["phases"]["recipes"], data["word"] + events, calls = template["execution_schedule"], template["calls"] + bases = [chart(r["q"]) for r in phases] + positions = {e["time"]: i for i, e in enumerate(events) if e["kind"] == "local_cover_sweep"} + touches, deadline = defaultdict(list), {} + for i, e in enumerate(events): + if e["kind"] == "local_cover_sweep": + c = calls[e["time"]] + touches[c["replica"], c["pair"]].append(i) + elif e["kind"] == "bridge": + for pair in (e["src"], e["dst"]): + touches[e["replica"], pair].append(i) + elif e["kind"] == "idle_cover_sweep": + for side, child in enumerate(e["child_indices"]): + deadline[e["replica"], child] = (i, side) + jobs, suffixes, partition = defaultdict(list), defaultdict(list), defaultdict(set) + for index, job in enumerate(template["hosting"]["pooled_slots"]): + end, side = deadline[job["owner_replica"], job["child"]] + e = events[end] + used = touches[job["owner_replica"], e["pair"]] + offset = bisect_left(used, end) + release = used[offset - 1] if offset else -1 + need(release < positions[job["time"]] < end, "Old complete helper strict window") + family = owner(job["owner_replica"], e["pair"], side, job["port"]) + role = 224 + job["helper"] + width = len(word["frames"][word["final"][role]]) - len(word["frames"][word["start"][role]]) + begin = 8 * (e["from_level"] + 1) + 1 + job["offset"] + axes = list(range(begin, begin + width)) + spectators = [j for j in range(73) if j not in axes][:9 - width] + descriptor = [3, job["child"], job["offset"]] if width == 9 else [4, job["child"], job["offset"], width, spectators] + need(job["family"] == family and job["width"] == width + and calls[job["time"]]["owners"][role] == [family, descriptor], "Literal helper role and route") + key = job["owner_replica"], job["child"], job["port"] + need(not partition[key].intersection(axes), "No helper axis repeats") + partition[key].update(axes) + jobs[job["time"]].append((family, product([(bases[job["port"]][j], 1) for j in axes]))) + for job in template["idle_children"]: + end, side = deadline[job["replica"], job["child"]] + e = events[end] + begin = 8 * (e["from_level"] + 1) + 1 + job["pending_offset"] + stop = 8 * (e["to_level"] + 1) + 1 + axes = list(range(begin, stop)) + family = owner(job["replica"], e["pair"], side, job["port"]) + need(job["family"] == family and len(axes) == job["rank"], "Literal idle suffix") + key = job["replica"], job["child"], job["port"] + need(not partition[key].intersection(axes), "No suffix axis repeats") + partition[key].update(axes) + suffixes[end].append((family, product([(bases[job["port"]][j], 1) for j in axes]))) + for (replica, child), (end, _) in deadline.items(): + e = events[end] + expected = set(range(8 * (e["from_level"] + 1) + 1, 8 * (e["to_level"] + 1) + 1)) + for p in range(112): + need(partition[replica, child, p] == expected, "Every pending axis is used once") + frames = [canonical(phases[f % 112]["q"], -1, (f // 112) % 2) for f in range(14336)] + retired, cuts, counts = set(), [], Counter() + bridge_count = Counter() + + def complete(replica, pair, level): + for side in (0, 1): + for p in range(112): + f = owner(replica, pair, side, p) + expected = canonical(phases[p]["q"], level, side) + if f in retired: + expected = add_phase(expected, line(phases[p]["q"])) + need(frames[f] == expected, "Actual complete bank phase") + + for position, event in enumerate(events): + kind, replica = event["kind"], event.get("replica") + if kind == "local_cover_sweep": + call = calls[event["time"]] + pair, stage = call["pair"], call["stage"] + need(len(call["owners"]) == len({o[0] for o in call["owners"]}) == 704, "No local owner alias") + complete(replica, pair, stage - 1) + for side in (0, 1): + for p in range(112): + f = owner(replica, pair, side, p) + need(call["owners"][112 * side + p] == [f, [1, stage, p]], "Actual active route") + frames[f] = canonical(phases[p]["q"], stage, side) + if mixed and side == 1 and p in SELECTED and stage in (2, 4, 6, 8): + retired.add(f) + frames[f] = add_phase(frames[f], line(phases[p]["q"])) + for f, phase in jobs[event["time"]]: + frames[f] = add_phase(frames[f], phase) + counts["helper_jobs"] += 1 + complete(replica, pair, stage) + counts["local_calls"] += 1 + elif kind == "idle_cover_sweep": + for f, phase in suffixes[position]: + frames[f] = add_phase(frames[f], phase) + counts["idle_suffixes"] += 1 + for side, child in enumerate(event["child_indices"]): + for p in range(112): + f = owner(replica, event["pair"], side, p) + frames[f] = add_phase(frames[f], line(phases[p]["idle_children"][child]["translation_after"], 2)) + complete(replica, event["pair"], event["to_level"]) + counts["idle_events"] += 1 + elif kind == "bridge": + index = bridge_count[replica] + bridge_count[replica] += 1 + if index < 6: + src_pair, dst_pair, side = event["dst"], event["src"], 1 + stage = 2 * dst_pair + 1 + level = 2 * src_pair + 1 + (index % 2) + sign = -event["coefficient"] + need(src_pair + 1 == dst_pair and level < stage, "Future Y bridge order") + counts["future_Y_cuts"] += 1 + else: + src_pair, dst_pair, side = event["src"], event["dst"], 0 + stage, level, sign = 2 * dst_pair + 1, 8, 1 + need(src_pair + 1 == dst_pair and stage <= level, "Past X tail order") + counts["past_X_tail_cuts"] += 1 + families = [owner(replica, src_pair, side, p) for p in ORDINARY] + families += [owner(replica, dst_pair, side, p) for p in range(112)] + need(len(families) == len(set(families)) == 216, "No bridge source/target owner alias") + for p in ORDINARY: + source = owner(replica, src_pair, side, p) + target = owner(replica, dst_pair, side, p) + expected = canonical(phases[p]["q"], level, side) + need(frames[source] == frames[target] == expected, "Exact same-port ordinary bridge phase") + for p in SELECTED: + target = owner(replica, dst_pair, side, p) + need(target not in retired and frames[target] == canonical(phases[p]["q"], level, side), + "Every selected target has the required unmodified phase") + name = "Y" if side else "X" + cuts.append(dict(position=position, source_event=event["source_event"], replica=replica, + source_pair=src_pair, target_pair=dst_pair, side=name, stage=stage, + completed_level=level, sign=sign, + source_ordinary_families=[owner(replica, src_pair, side, p) for p in ORDINARY], + target_families=[owner(replica, dst_pair, side, p) for p in range(112)], + aligned_source_ports=ORDINARY, aligned_target_ports=SELECTED, + scalar_word_key=str(sign), new_affine_view_maps=224, + retained_X_bridge=(index < 6), removed_Y_tail=(index >= 6))) + counts["all_bridge_frame_pairs"] += 224 + elif kind == "terminal_Y_translations": + for pair in range(4): + complete(replica, pair, 8) + counts["preterminal_endpoints"] += 1 + elif kind == "terminal": + counts["terminal_events"] += 1 + else: + need(kind in ("bank_padding_cover_sweep", "translate_every_live_family"), "Known source event") + need(all(v == 9 for v in bridge_count.values()) and len(cuts) == 144, "All new bridge cuts") + need(counts["helper_jobs"] == 69120 and counts["idle_suffixes"] == 7526 + and counts["future_Y_cuts"] == 96 and counts["past_X_tail_cuts"] == 48, "Complete source schedule") + need(len(retired) == (512 if mixed else 0), "Selected FULL exceptions") + return dict(mixed_selected_outputs=mixed, checked_counts=dict(counts), cuts=cuts, + retired_selected_fields_not_read=512 if mixed else 0) + + +def main(args): + raw = ARCHIVE.read_bytes() + need(sha256(raw).hexdigest() == ARCHIVE_PIN, "Selected archive pin") + data = {} + with tarfile.open(ARCHIVE) as stream: + for key, (path, pin) in MEMBERS.items(): + raw = stream.extractfile(path).read() + need(sha256(raw).hexdigest() == pin, "Archive member pin: " + key) + data[key] = json.loads(gzip.decompress(raw) if path.endswith(".gz") else raw) + for path, pin in PINS.items(): + need(sha256((LANES / path).read_bytes()).hexdigest() == pin, "Premise pin: " + path) + interface = json.loads((LANES / "circuit-interface/INTERFACE.json").read_bytes()) + R = [[Fraction(row.get(str(p), "0")) for p in range(112)] for row in interface["R"]] + need(interface["ports"] == [r["q"] for r in data["phases"]["recipes"]], "Actual port order") + need(all(sum(R[k][a] * R[k][b] for k in range(8)) == 4 * int(i == j) + for i, a in enumerate(SELECTED) for j, b in enumerate(SELECTED)), "Selected square minor") + B = [[sum(R[k][a] * R[k][p] for k in range(8)) / 4 for p in ORDINARY] for a in SELECTED] + need(sum(bool(c) for row in B for c in row) == 416 + and all(sum(bool(c) for c in row) == 52 for row in B) + and all(abs(c) == Fraction(1, 2) for row in B for c in row if c), "Exact sparse B matrix") + views, checks, controls = phases_and_views(data) + scalar = scalar_check(B) + uniform, mixed = [schedule_audit(data, views, setting) for setting in (False, True)] + need(uniform["cuts"] == mixed["cuts"], "One program handles both retirement phase policies") + payload = dict(format="future-projection-bridge-v1", views=list(views.values()), + scalar_words={k: v["program"] for k, v in scalar.items()}, cuts=uniform["cuts"], + operation_order=["104 same-port ordinary ADDs", "Align 104 source U and 8 target A fields", + "416 half ADDs", "Undo 112 affine views"], + inverse_view_order="Undo translation, then undo the route; rho is its own inverse") + payload_raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + args.program.write_bytes(gzip.compress(payload_raw, mtime=0)) + for row in scalar.values(): + del row["program"] + receipt = dict(status="PASS_ACTUAL_FUTURE_PROJECTION_BRIDGES", archive_sha256=ARCHIVE_PIN, + source_member_sha256={k: v[1] for k, v in MEMBERS.items()}, premise_sha256=PINS, + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), + payload_sha256=sha256(payload_raw).hexdigest(), phase_checks=checks, phase_controls=controls, + scalar_words=scalar, uniform_schedule=uniform["checked_counts"], mixed_schedule=mixed["checked_counts"], + mixed_retired_selected_fields_not_read=512, new_native_children=0, new_private_fields=0, + unchanged_original_helper_jobs=69120, unchanged_original_idle_suffixes=7526, + complete_T_equals_W_bridge_invoice=dict(U_updates=144, real_scalar_bound=718848, + retained_X_unit_adds=10752, retained_X_real_scalar_bound=86016, + total_real_scalar_bound=804864, new_affine_view_maps=32256, + native_profile_delta={}, live_delta=0, physical_stock_delta=0), + complete_T_zero_bridge_invoice=dict(U_updates=96, real_scalar_bound=479232, + retained_X_real_scalar_bound=86016, total_real_scalar_bound=565248, + new_affine_view_maps=21504, native_profile_delta={}, live_delta=0, physical_stock_delta=0), + tensor_scope="All phase polynomials are exact modulo four and have zero constant. The identities tensor to every positive width.", + scope="Literal source-bound bridge macros and exact phase/owner admission. This is not a complete supplier, precision invoice, or kappa claim.", + open_costs=["Compile affine view maps in the complete finite invoice", "Bind the selected controller and all new local maps", "Price complete controller growth and recursive supplier"]) + args.out.write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n", encoding="utf-8") + print(receipt["status"]) + print(json.dumps(dict(cuts=144, new_native_children=0, scalar=804864, affine_views=32256), sort_keys=True)) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, default=HERE / "ACCESS.json") + parser.add_argument("--program", type=Path, default=HERE / "BRIDGE-PROGRAMS.json.gz") + main(parser.parse_args()) diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py new file mode 100644 index 0000000000..b8c206ea6f --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py @@ -0,0 +1,157 @@ +"""Check one cover response at all nine fresh three-leg cuts.""" + +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import tarfile + + +HERE = Path(__file__).resolve().parent +BRIDGE = HERE.parent +BASE_PIN = "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111" +N = 73 + + +def need(test, label): + if not test: + raise ValueError(label) + + +def load(): + path = BRIDGE / "check_bridge_access.py" + need(sha256(path.read_bytes()).hexdigest() == BASE_PIN, "Phase source pin") + spec = importlib.util.spec_from_file_location("cycle_cover_phase_source", path) + base = importlib.util.module_from_spec(spec) + spec.loader.exec_module(base) + need(sha256(base.ARCHIVE.read_bytes()).hexdigest() == base.ARCHIVE_PIN, "Supplier source archive") + with tarfile.open(base.ARCHIVE) as archive: + name, pin = base.MEMBERS["phases"] + raw = archive.extractfile(name).read() + need(sha256(raw).hexdigest() == pin, "Actual port and entry phase ledger") + phases = json.loads(raw)["recipes"] + return base, phases + + +def transpose(columns): + return [sum(((columns[j] >> i) & 1) << j for j in range(N)) for i in range(N)] + + +def compose(base, left, right): + return [base.act(left, v) for v in right] + + +def phase(base, terms, columns=None): + return base.product([(base.act(columns, v) if columns else v, exponent) for v, exponent in terms]) + + +def difference(base, wanted, given): + gap = base.add_phase(wanted, base.negative(given)) + need(gap[0] == 0 and gap[2] == 0, "The complete phase defect is a translation") + return gap[1] + + +def cut_terms(base, q, v0, stage): + if not stage: + return [(q, 1)], [(v0, 1)] + source = [(v, 1) for v in base.UNIT[:9 + 8 * (stage - 1)]] + target = source + [(q, -1), (base.UNIT[9 + 8 * (stage - 1)], 1)] + return source, target + + +def one_port(base, recipe, port): + q = recipe["q"] + basis = base.chart(q) + need(basis[1:9] == recipe["idle_children"][0]["orthogonal_axes"][:8], "Literal complement chart") + v0 = basis[1] + cycle = [q, v0] + [base.UNIT[9 + 8 * j] for j in range(8)] + need(all((x & y).bit_count() % 2 == int(i == j) + for i, x in enumerate(cycle) for j, y in enumerate(cycle)), "The ten cycle vectors are orthonormal") + columns = [] + for e in base.UNIT: + image = e + for j, v in enumerate(cycle): + if (v & e).bit_count() & 1: + image ^= v ^ cycle[(j + 1) % 10] + columns.append(image) + inverse = transpose(columns) + need(compose(base, columns, inverse) == compose(base, inverse, columns) == base.UNIT, + "The cycle is orthogonal and both inverse orders hold") + need([base.act(columns, v) for v in cycle] == cycle[1:] + cycle[:1], "Exact cycle orientation") + powers = [q] + for _ in range(10): + powers.append(base.act(columns, powers[-1])) + need(powers[-1] == q and len(set(powers[:-1])) == 10, "The cycle has order ten") + cuts = [] + for stage in range(9): + source, target = cut_terms(base, q, v0, stage) + source_phase = phase(base, source) + target_phase = phase(base, target) + transported_target = phase(base, target, inverse) + delta = difference(base, transported_target, source_phase) + need(base.add_phase(source_phase, base.line(delta, 2)) == transported_target, + "The literal translation gives the complete physical transfer") + rho = base.route(basis, stage) + if stage: + entry = base.act(rho, recipe["stage_alignment"][stage]["entry_X"]) + need(recipe["stage_alignment"][stage]["entry_X"] == recipe["stage_alignment"][stage]["entry_Y"], + "Both current entries use the same translation") + else: + entry = 0 + exterior = [(v, 1) for v in base.UNIT[9:9 + 8 * stage]] + need(base.add_phase(phase(base, source, rho), base.line(entry, 2)) + == phase(base, exterior + [(q, 1)]), "Actual source cut is exterior times C_q") + need(base.add_phase(phase(base, target, rho), base.line(entry, 2)) + == phase(base, exterior + [(v0, 1)]), "Actual target cut is exterior times C_v0") + body_route = compose(base, rho, compose(base, inverse, rho)) + need(compose(base, rho, body_route) == compose(base, inverse, rho), "Source-body to target-body equation") + need(compose(base, body_route, transpose(body_route)) == base.UNIT, "The body route is a cover permutation") + cuts.append({"stage": stage, "source_rank": 8 * stage + 1, + "target_rank": 8 * stage + 1, "translation_in_source_cover_coordinates": delta, + "source_body_to_target_body_columns": body_route, + "entry_translation_after_route": entry, + "omitted_translation_fails": source_phase != transported_target}) + full = [(v, 1) for v in base.UNIT] + forward_source_delta = difference(base, phase(base, full, inverse), phase(base, full)) + forward_output_delta = base.act(columns, forward_source_delta) + need(forward_output_delta == difference(base, phase(base, full), phase(base, full, columns)), + "FULL forward source and output conventions agree") + inverse_output_delta = difference(base, phase(base, full), phase(base, full, inverse)) + need(inverse_output_delta == forward_source_delta, "FULL inverse correction") + need(base.act(inverse, q) == cycle[-1], "The decoder source line is the first axis of E8") + return {"port": port, "q": q, "v0": v0, "cycle_vectors": cycle, + "L_columns": columns, "L_inverse_columns": inverse, "stage_cuts": cuts, + "FULL_E_output_translation": forward_output_delta, + "FULL_E_inverse_output_translation": inverse_output_delta, + "terminal_source_line_at_output_h": cycle[-1], "terminal_target_line_at_output_h": q} + + +def main(): + base, phases = load() + records = [one_port(base, recipe, p) for p, recipe in enumerate(phases)] + need(len(records) == 112, "All supplier ports") + payload = {"schema": "common-cycle-cover-response-v1", "phase_source_sha256": BASE_PIN, + "source_phase_member_sha256": base.MEMBERS["phases"][1], + "logical_operator": "(E f)_p(h)=f_p(h L_p)", + "logical_inverse": "(E^-1 f)_p(h)=f_p(h L_p^-1)", + "payload_action_of_logical_code": "identity", "records": records} + raw = (json.dumps(payload, sort_keys=True, indent=2) + "\n").encode() + (HERE / "CYCLE-COVER-PROGRAMS.json").write_bytes(raw) + receipt = {"status": "PASS_COMMON_CYCLE_COVER_RESPONSE", "ports": 112, + "stages_per_port": 9, "complete_translation_phase_checks": 1008, + "entry_frame_checks": 2016, "body_route_bijections": 1008, + "FULL_code_phase_checks": 224, "cycle_order": 10, + "nonzero_cut_translation_controls": sum(c["omitted_translation_fails"] for r in records for c in r["stage_cuts"]), + "native_mass_per_fresh_local_call": 1792, "fresh_child_profile": {"1": 112, "7": 112, "8": 112}, + "new_native_children_for_transfer": 0, "transfer_complex_ADDs": 112, + "terminal_rank_one_children_per_four_pair_replica": 896, + "source_archive_sha256": base.ARCHIVE_PIN, "phase_source_sha256": BASE_PIN, + "program_sha256": sha256(raw).hexdigest(), + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "scope": "Actual cover and complete phase interface. Fresh native leg emission, global schedule, and full price are separate dependencies."} + (HERE / "CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/FREEZE.json new file mode 100644 index 0000000000..b639fc2c4a --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/FREEZE.json @@ -0,0 +1,17 @@ +{ + "PR_description_prerequisite": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "files": { + "GENERAL-VIEWS.md": "5da866eb2802e8a30ea77d2f88877b5005a2eb04632514c897a426e76277db2e", + "check_views.py": "e21245d82f952f5e3c8cd74aaa3d4adc4a8931ab53fc100594568d403f503c0b", + "run-normal/CHECKS.json": "92d2d5c453a8e77edb22784bdbdca4772616305d878dc3d1aebf20d95caeda06", + "run-normal/VIEWS.json": "a1f27d8cb6e93ffbec72f3120433d788c87af7c08bc362e479838ea8fc7b5a60", + "run-optimized/CHECKS.json": "92d2d5c453a8e77edb22784bdbdca4772616305d878dc3d1aebf20d95caeda06", + "run-optimized/VIEWS.json": "a1f27d8cb6e93ffbec72f3120433d788c87af7c08bc362e479838ea8fc7b5a60" + }, + "general_claim": "Proved for every T>=1 by the quadratic-refinement and spectator-axis argument.", + "independent_review": "Requested separately.", + "normal_optimized_byte_equal": true, + "publication": "No PR or publication authorized.", + "schema": "general-stage-view-freeze-v1", + "status": "PASS_EXACT_NORMAL_AND_OPTIMIZED" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md new file mode 100644 index 0000000000..9b57035450 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md @@ -0,0 +1,195 @@ +# Exact stage views in every dimension 9+8T + +The actual D25 and D73 DATA routes are instances of one exact formula. +The formula works for every positive integer T in dimension \(D=9+8T\). +It retains the actual root chart of each of the 112 ports. It gives the +complete payload phase and the regular-cover owner map. + +This result supplies the stage boundary identities needed to carry the +same local nine-dimensional service to later stages. It does not make +the routed response constant. It does not supply a complete caller, +a new recursive host, a finite map cost, or an exponent. + +## Root quadratic refinement + +Fix an actual port with intrinsic unit vector q. The root chart is the +pinned orthonormal basis + +\[ +B=(q,b_1,\ldots,b_8) +\] + +of the first nine coordinates. Its q has Hamming weight 3 or 7. +For any unit vector v, define + +\[ +\beta(v)=\frac{|v|-1}{2}\pmod 2. +\] + +Put \(\beta_j=\beta(b_j)\) and + +\[ +\delta_0=q+\sum_{j=1}^{8}\beta_jb_j. +\tag{1} +\] + +The coefficient of q is one because its weight is 3 or 7. +Let \(C_v\) be the exact line transform with Fourier multiplier +\(i^{v\cdot z}\). Let \(X_v=C_v^2\) be the translation by v. +All these operators commute. If \(F_0\) is FULL on the root axes, then + +\[ +Q\prod_{j=1}^{8}C_{b_j}=X_{\delta_0}F_0,\qquad Q=C_q. +\tag{2} +\] + +To prove (2), compare the Z4 functions +\(\sum_{v\in B}(v\cdot z)\) and \(|z|\). Their difference has zero +quadratic part modulo four because B is orthonormal. Its linear part +is even. Evaluate it at each basis vector \(v\in B\): the value is +\(1-|v|=2\beta(v)\pmod4\). Thus the difference is +\(2\delta_0\cdot z\). This proves the full phase, including its sign. + +## The route and its two translations + +Let \(E_s=(e_{s,1},\ldots,e_{s,8})\) be the fresh coordinate block for +stage s, where \(1\leq s\leq T\). Define \(\rho_s\) to exchange +\(b_j\) with \(e_{s,j}\), for each j, and to fix q and all other fresh +blocks. This is an orthogonal involution. An explicit matrix is + +\[ +\rho_s=I+\sum_{j=1}^{8} + (b_j+e_{s,j})(b_j+e_{s,j})^{\mathsf T}. +\tag{3} +\] + +The eight vectors in the sum are isotropic and pairwise orthogonal. +Equation (3) therefore has the stated action on the complete +orthonormal basis. + +The two physical translations are + +\[ +\delta_{\rm in}(s)=\rho_s\delta_0 + =q+\sum_j\beta_je_{s,j},\qquad +\delta_{\rm out}(s)=\delta_0+\rho_s\delta_0. +\tag{4} +\] + +Let \(P_{\rho_s}\) be the payload address permutation. The entry map is +\(V_{\rm in}=X_{\delta_{\rm in}}P_{\rho_s}\). Its equivalent order is +\(P_{\rho_s}X_{\delta_0}\). The exit map is +\(V_{\rm out}=X_{\delta_{\rm out}}P_{\rho_s}\). +The exit translation is fixed by \(\rho_s\), so the exit map is its +own inverse. + +## Adjacent-stage identities + +Let \(F_\ell\) be FULL on the root and fresh blocks 1 through \(\ell\). +Let \(F_{{\rm ext},s}\) be FULL on fresh blocks 1 through s. +The exact adjacent identities are + +\[ +\begin{aligned} +V_{\rm in}(s)F_{s-1} + &=F_{{\rm ext},s}\,Q\,P_{\rho_s},\\ +V_{\rm in}(s)F_{s-1}q + &=F_{{\rm ext},s}\,P_{\rho_s},\\ +V_{\rm out}(s)F_s + &=F_sP_{\rho_s},\\ +V_{\rm out}(s)F_sq + &=F_sqP_{\rho_s}. +\end{aligned} +\tag{5} +\] + +For the first identity, conjugate (2) by \(P_{\rho_s}\). +The eight root-complement line factors become the fresh block s. +The other completed fresh blocks are fixed. The entry translation +in (4) cancels the translated factor in (2). +The second identity follows because \(\rho_s q=q\) and \(Qq=I\). + +For the third identity, the factors from both the root and fresh +block s are present. Exchanging these factors changes FULL by precisely +\(X_{\delta_0+\rho_s\delta_0}\), which the exit map cancels. +The fourth identity follows again from \(\rho_s q=q\). + +All remaining coordinates are spectators. None of these arguments +depends on T or on the number of preceding completed blocks. + +The same proof gives the complete access cones. A FULL field at level +\(\ell\geq s\) admits the stage-s exit map. A hole field \(F_\ell q\) +at level \(\ell` in +normal Python and in `python3 -O`; both payload and receipt must be +byte equal. + +The root charts, D25 records, and D73 records come from the actual +supplier access calculations. The retained-reader consequence uses +the complete forward service and its emitted inverse-adjoint. All +source hashes are explicit in the payload. This work uses AI assistance +and exact finite-field and Z4 computation. + +No PR or publication is authorized. Before any future PR description, +read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/check_views.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/check_views.py new file mode 100644 index 0000000000..0d57cbe4e0 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/check_views.py @@ -0,0 +1,227 @@ +"""Emit dimension-independent stage views and check their exact phases.""" + +import argparse +from collections import Counter +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PINS = { + "D25": ( + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), + "D73": ( + "bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", + "57e2f089e0dd9f363603fc0278612b8ae8b98956a7422aa41fbd592922213abc", + ), + "complete_dual": ( + "bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json", + "09ad251a968be73fe95eefb05f57b842eb9f55e43822f029505256705120c811", + ), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = (LANES / path).read_bytes() + if path.endswith(".gz"): + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source: " + name) + return json.loads(raw) + + +def xor(values): + result = 0 + for value in values: + result ^= value + return result + + +def act(columns, value): + result = 0 + while value: + bit = value & -value + result ^= columns[bit.bit_length() - 1] + value ^= bit + return result + + +def add(a, b): + return a[0] ^ b[0], a[1] ^ b[1] ^ (a[0] & b[0]), a[2] ^ b[2] + + +def line(vector, exponent=1): + cross = 0 + value = vector + while value: + bit = value & -value + j = bit.bit_length() - 1 + cross ^= (vector & (bit - 1)) << (j * (j - 1) // 2) + value ^= bit + return (vector if exponent & 1 else 0, + vector if exponent & 2 else 0, cross if exponent & 1 else 0) + + +def phase(terms): + result = (0, 0, 0) + for vector, exponent in terms: + result = add(result, line(vector, exponent % 4)) + return result + + +def root_record(q): + need(q < 512 and q.bit_count() in (3, 7), "The actual intrinsic-line family") + hole = next(j for j in range(9) if not (q >> j & 1)) + v = q ^ (1 << hole) + order = list(range(9)) + order[0], order[hole] = order[hole], order[0] + basis = [(1 << j) ^ (v if v >> j & 1 else 0) for j in order] + need(basis[0] == q and all((a & b).bit_count() % 2 == (i == j) + for i, a in enumerate(basis) for j, b in enumerate(basis)), + "The literal root chart is orthonormal") + beta = [((b.bit_count() - 1) // 2) % 2 for b in basis] + need(beta[0] == 1, "The actual q correction is one") + delta = xor(b for b, bit in zip(basis, beta) if bit) + need(add(phase([(1 << j, 1) for j in range(9)]), line(delta, 2)) + == phase([(b, 1) for b in basis]), "The exact root quadratic refinement") + return {"q": q, "root_basis": basis, "beta": beta, + "root_translation": delta} + + +def make_view(q, stage, stages): + need(1 <= stage <= stages, "A stage inside the chosen dimension") + root = root_record(q) + dimension = 9 + 8 * stages + unit = [1 << j for j in range(dimension)] + block = unit[9 + 8 * (stage - 1):9 + 8 * stage] + swaps = [b ^ e for b, e in zip(root["root_basis"][1:], block)] + rho = [e ^ xor(v for v in swaps if (v & e).bit_count() % 2) for e in unit] + entry_before = root["root_translation"] + entry_after = q ^ xor(e for e, bit in zip(block, root["beta"][1:]) if bit) + exit_after = entry_before ^ entry_after + need(act(rho, entry_before) == entry_after and act(rho, q) == q, + "The entry translation and own line have the exact images") + need([act(rho, x) for x in rho] == unit, "The route is an involution") + need(all(act(rho, b) == e and act(rho, e) == b + for b, e in zip(root["root_basis"][1:], block)), + "The route exchanges exactly the eight stated axes") + return { + "dimension": dimension, "stage": stage, "q": q, "route_columns": rho, + "entry_before_route": entry_before, "entry_after_route": entry_after, + "exit_after_route": exit_after, + } + + +def check_view(record, stages, all_levels=False): + q, s, rho = record["q"], record["stage"], record["route_columns"] + unit = [1 << j for j in range(record["dimension"])] + delta_in, delta_out = record["entry_after_route"], record["exit_after_route"] + counts = Counter() + future_levels = range(s) if all_levels else (s - 1,) + past_levels = range(s, stages + 1) if all_levels else (s,) + for level in future_levels: + full = [(v, 1) for v in unit[:9 + 8 * level]] + exterior = [(v, 1) for v in unit[9:9 + 8 * level]] + exterior += [(v, 1) for v in unit[9 + 8 * (s - 1):9 + 8 * s]] + for hole in (False, True): + source = full + ([(q, -1)] if hole else []) + desired = exterior + ([] if hole else [(q, 1)]) + transported = phase([(act(rho, v), n) for v, n in source]) + need(add(transported, line(delta_in, 2)) == phase(desired), + "The complete future or adjacent entry phase") + need(transported != phase(desired), "Omitting the entry translation fails") + counts["future_entry_hole" if hole else "future_entry_full"] += 1 + for level in past_levels: + full = [(v, 1) for v in unit[:9 + 8 * level]] + for hole in (False, True): + source = full + ([(q, -1)] if hole else []) + transported = phase([(act(rho, v), n) for v, n in source]) + need(add(transported, line(delta_out, 2)) == phase(source), + "The complete current or past exit phase") + need(transported != phase(source), "Omitting the exit translation fails") + counts["past_exit_hole" if hole else "past_exit_full"] += 1 + return counts + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + sources = {name: read(name) for name in PINS} + by25 = {(r["stage"], r["port"]): r for r in sources["D25"]["entries"]} + ports = [by25[0, p]["q"] for p in range(112)] + roots = [{"port": p, **root_record(q)} for p, q in enumerate(ports)] + need(len(set(ports)) == 112, "All intrinsic lines are distinct") + bound25 = 0 + for (stage, port), old in by25.items(): + if stage == 0: + need(old["route_columns"] == [1 << j for j in range(25)], + "The stage-zero route is the identity") + continue + new = make_view(ports[port], stage, 2) + align = old["literal_stage_alignment"] + need(new["route_columns"] == old["route_columns"] + and new["entry_before_route"] == align["entry_X"] == align["entry_Y"] + and new["exit_after_route"] == align["exit_X"] == align["exit_Y"], + "All literal D25 route and phase records agree") + bound25 += 1 + bound73 = 0 + for old in sources["D73"]["views"]: + new = make_view(ports[old["port"]], old["stage"], 8) + need(new["route_columns"] == old["route_columns"], "The literal D73 route agrees") + if old["side"] == "Y": + need(new["entry_after_route"] == old["translation_after_route"] + and new["entry_before_route"] == old["translation_before_route"], + "The literal D73 future entry phase agrees") + else: + need(old["side"] == "X" + and new["exit_after_route"] == old["translation_after_route"] + == old["translation_before_route"], "The literal D73 past exit phase agrees") + bound73 += 1 + reports = {} + for stages in (1, 2, 3, 8, 16): + counts = Counter() + for q in ports: + for stage in range(1, stages + 1): + counts.update(check_view(make_view(q, stage, stages), stages, + all_levels=stages <= 8)) + reports[str(9 + 8 * stages)] = dict(counts) + payload = { + "schema": "general-orthogonal-stage-view-v1", "source_pins": PINS, + "root_records": roots, "dimension": "D=9+8T for any positive integer T", + "route": "Swap root_basis[j+1] with e_(9+8*(s-1)+j), for j=0,...,7.", + "entry_before_route": "root_translation", + "entry_after_route": "q XOR sum(beta[j+1]*e_(9+8*(s-1)+j))", + "exit_after_route": "entry_before_route XOR entry_after_route", + "owner": "h=d*rho_(s,p); the route is an orthogonal involution.", + "scope": "Exact ideal field and owner views. Native core, recursive host, " + "map cost, caller closure, and exponent are separate.", + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + receipt = { + "status": "PASS_GENERAL_STAGE_VIEW_SOURCE_BINDING_AND_PHASE_REGRESSIONS", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_sha256": sha256(raw).hexdigest(), + "literal_D25_nonzero_stage_records": bound25, + "literal_D73_side_records": bound73, "regressions": reports, + "proof_scope": "The arbitrary-T result is proved by the quadratic-refinement " + "and spectator-axis argument, not inferred from these tests.", + } + args.output.mkdir(parents=True, exist_ok=False) + (args.output / "VIEWS.json").write_bytes(raw) + (args.output / "CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/run-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..1fb17f042c --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/run-normal/CHECKS.json @@ -0,0 +1,40 @@ +{ + "literal_D25_nonzero_stage_records": 224, + "literal_D73_side_records": 1792, + "payload_sha256": "a1f27d8cb6e93ffbec72f3120433d788c87af7c08bc362e479838ea8fc7b5a60", + "producer_sha256": "e21245d82f952f5e3c8cd74aaa3d4adc4a8931ab53fc100594568d403f503c0b", + "proof_scope": "The arbitrary-T result is proved by the quadratic-refinement and spectator-axis argument, not inferred from these tests.", + "regressions": { + "137": { + "future_entry_full": 1792, + "future_entry_hole": 1792, + "past_exit_full": 1792, + "past_exit_hole": 1792 + }, + "17": { + "future_entry_full": 112, + "future_entry_hole": 112, + "past_exit_full": 112, + "past_exit_hole": 112 + }, + "25": { + "future_entry_full": 336, + "future_entry_hole": 336, + "past_exit_full": 336, + "past_exit_hole": 336 + }, + "33": { + "future_entry_full": 672, + "future_entry_hole": 672, + "past_exit_full": 672, + "past_exit_hole": 672 + }, + "73": { + "future_entry_full": 4032, + "future_entry_hole": 4032, + "past_exit_full": 4032, + "past_exit_hole": 4032 + } + }, + "status": "PASS_GENERAL_STAGE_VIEW_SOURCE_BINDING_AND_PHASE_REGRESSIONS" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/run-normal/VIEWS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/run-normal/VIEWS.json new file mode 100644 index 0000000000..cd3777b892 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/general-stage-views-20261020/run-normal/VIEWS.json @@ -0,0 +1 @@ +{"dimension":"D=9+8T for any positive integer T","entry_after_route":"q XOR sum(beta[j+1]*e_(9+8*(s-1)+j))","entry_before_route":"root_translation","exit_after_route":"entry_before_route XOR entry_after_route","owner":"h=d*rho_(s,p); the route is an orthogonal 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Backward caller, inherited helper hosting and complete supplier remain separate.", + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md new file mode 100644 index 0000000000..587107b820 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/INVOLUTION-READER.md @@ -0,0 +1,204 @@ +# A restored-source query for the routed involution + +The actual dyadic row involution permits a shorter fixed-reader service. +At the completed FULL cut, apply the current involution to X, query +the past reader from X, and apply the involution again. The last step +restores every source field. The target can have an arbitrary baseline. + +The emitted query has 8,440 real scalar primitives, 672 monomial maps, +and no native child or extra field. With the existing carrier prefix, +the complete typed forward service has 14,896 real scalar primitives +and native rank 1,792. This result does not close a backward caller, +the helper host, or the full supplier. + +## The reversible-source query lemma + +Let X be a complete source bank. Let Y be a distinct target bank. +Let T be a unit on X, and let L be a reader from X to Y. Assume that +the following three operations are admitted at their actual frames: + +1. Apply T to X. +2. Add LX to Y. +3. Apply \(T^{-1}\) to X. + +On arbitrary independent x and y, this word gives + +\[ +(x,y)\longmapsto (x,y+LTx). +\tag{1} +\] + +The first operation gives \(Tx\). The second adds \(LTx\) to the +unchanged target baseline. The last restores x. No condition on +\(LJ\), no zero source, and no zero target is needed. In particular, +the selected target records need not be a separate owned workspace. + +If the three words restore their own borrowed fields, the complete +word restores them as well. The price is +\(a(T)+c(L)+a(T^{-1})\), with the actual view and storage costs included. +If both source words cost at most a, this is at most \(2a+c(L)\). +The lemma does not make T or L admissible at a new frame. + +Several target readers can be used between steps 1 and 3 if each +reader preserves X and the other target baselines. In that case the +two source transformations are shared. This is an algebraic extension; +this packet emits one sixteen-row reader. + +## The actual current source unit + +The source is the controller lane's 112-port physical row involution A. +The emitter pins its exact matrix and its 3,276-scalar common-frame +word. It checks both the complete word and \(A^2=I\). + +The pivot set P has sixteen ports. Its complement R has 96 ports. +The source response E and A have exactly the same R rows: + +\[ +A[R,*]=E[R,*]. +\tag{2} +\] + +Thus the frozen carrier prefix for E remains a valid carrier prefix +for A. It emits the ordinary increment \((A_tx)_R\), leaves the selected +records independent, and completes all X and selected Y fields to +FULL. No native transfer or native phase recipe is changed. + +Let \(A_t\) be the current routed operator. Let \(L_s\) be the retained +past reader. Use (1) with \(T=A_t=T^{-1}\) and \(L=L_s\). +The result is the required selected increment \(L_sA_tx\). + +This argument does not replace \(A_t\) by a scalar matrix in the +global chart. It does not commute the reader through the response. +The map \(L_sA_t\) has 3,824 actual owner paths in each checked case. +The implementation does not enumerate those paths as separate ADDs. + +## Literal current and past views + +The three checked pairs are +\((s,t)=(0,1),(0,2),(1,2)\). The physical input level is always \(t-1\). +The label s identifies the carried reader, not that physical level. + +At the completed level t, the current A word has this order: + +1. Apply the literal current FULL view to each of the 112 X fields. +2. Execute the pinned 3,276-scalar A word. +3. Undo those 112 views. + +The word therefore uses 224 map calls and has the exact global action +\(A_t\). The emitter checks every view's complete Z4 phase polynomial. +Each route is orthogonal and fixes every uncompleted axis. +The current view arrays equal the current DATA exit arrays in the +frozen dispatcher. + +For the old reader, write \(L_s=J^{\mathsf T}+B_s\). Use the old FULL +views on 96 ordinary X fields and sixteen selected Y fields. Run +the 1,760-scalar complement reader and undo its views. This costs +224 maps. Then make the sixteen same-port selected copies, at a +cost of 128 scalar primitives and no further map. + +All maps act only on FULL fields. The ordinary Y hole fields are +neither read nor changed by this late query. The second A word uses +the same current views and the same scalar word as the first. + +The exact order is: + +```text +current A on X +past B_s complement query into Y_P +sixteen selected copies into Y_P +current A on X +``` + +The two current A words restore X as a complete routed operator. +They do not restore X by identifying different owner paths. + +## The complete typed forward service + +Use the frozen carrier prefix before the query. It has 2,406 events +and the profile + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H8. +``` + +Its native rank is 1,792, and it has 1,520 native children. Its +scalar price is 6,456. All 416 arbitrary helper fields are restored. +The existing native phase checks and the current DATA phase checks +remain unchanged. + +Let \(F_\ell\) be FULL on the first \(9+8\ell\) axes, and put +\(G_R=\operatorname{diag}(I_P,q_R)\). For independent target records w, +the complete service is + +\[ +(F_{t-1}x,\ F_{t-1}G_Rw) +\longmapsto +(F_tx,\ F_tG_R(w+D_{s,t}x)), +\tag{3} +\] + +where + +\[ +(D_{s,t})_P=L_sA_t,\qquad +(D_{s,t})_R=(A_t)_R. +\] + +If \(w=C_sy\), the selected records after the service are +\(L_s(y+A_tx)\). Thus the reader from stage s is retained. + +The native cover sweep and all DATA exits precede the late query. +The program contains both native provider prefixes, all actual stage +view records, and all six provider/pair invocations. It preserves +the whole-cover barrier in the previous dispatcher. + +The query invoice is: + +| Part | Real scalar primitives | Maps | +| --- | ---: | ---: | +| First current A | 3,276 | 224 | +| Past complement reader | 1,760 | 224 | +| Selected copies | 128 | 0 | +| Second current A | 3,276 | 224 | +| Total | 8,440 | 672 | + +Adding the carrier prefix gives 14,896 scalar primitives. A conservative +bound for this word is 4,384 monomial calls: 448 DATA calls, 224 local +endpoint adapters, at most 3,040 native side maps, and 672 query maps. +This is a call count, not a finite real-operation price for those maps. +Helper acquisition, recursive parking, and the outer caller remain +separate. + +The exact query row-sum maximum at the emitted gate boundaries is +202, and its binary denominator height is at most two. These values +hold for all three pairs. The bound also holds after the complete +carrier prefix. It does not cover internal arithmetic in a lowered +ADD, a native child, or a recursive caller. + +## Checks, scope, and credit + +The emitter uses exact rational coefficients and the pinned route +algebra engine. It checks all 640 formal input columns of the joined +prefix and query. Each coefficient retains its input field and its +complete \(O(25,2)\) owner route. It compares the result with the +direct \(L_sA_t\) product. Every X field, ordinary Y field, and helper +has the required endpoint. + +Omitting the second A word fails. Replacing the past reader by the +current reader also fails. Both controls fail for every checked pair. + +Run `emit_query.py --output ` with normal Python and +with `python3 -O`. The payloads and receipts must be byte equal. +The emitter rejects an existing output directory. + +The reversible-source argument supplies the selected query. It does +not prove that the complete response \(D_{s,t}\) is reciprocal or +stage independent. A backward service, the complete controller, +raw output restoration, recursive hosting, and a final exponent +remain open. + +The work uses the controller lane's dyadic row involution, the native +lane's carrier prefix, and the bridge-access and review lanes' fixed +reader and literal view calculations. OpenAI Codex assisted the work. +No publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/emit_query.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/emit_query.py new file mode 100644 index 0000000000..ec79601de6 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/emit_query.py @@ -0,0 +1,282 @@ +"""Emit a restored-source query for the actual routed involution.""" + +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import argparse +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PINS = { + "involution": ( + "controller-followthrough-20261017/row-involution-20261020/" + "run-normal/ROW-INVOLUTION.json", + "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b", + ), + "capture": ( + "controller-followthrough-20261017/row-capture-20261020/" + "run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7", + ), + "prefix": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz", + "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e", + ), + "view_query": ( + "bridge-access-20261017/row-capture-access-20261020/" + "reuse-normal/REUSE-PROGRAM.json", + "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b", + ), + "dispatcher": ( + "bridge-access-20261017/row-capture-access-20261020/" + "integration-v2-normal/DISPATCHER.json", + "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24", + ), + "dispatcher_freeze": ( + "bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json", + "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331", + ), + "operator_engine": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "fixed-reader-reuse-20261020/emit_routed_query.py", + "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900", + ), +} + + +def need(test, label): + if not test: + raise ValueError(label) + + +def read(name): + path, pin = PINS[name] + raw = (LANES / path).read_bytes() + if path.endswith(".gz"): + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source: " + name) + return raw + + +def load_engine(): + read("operator_engine") + spec = importlib.util.spec_from_file_location( + "involution_reader_engine", LANES / PINS["operator_engine"][0]) + engine = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = engine + spec.loader.exec_module(engine) + return engine + + +def emit_word(engine, pair, involution, capture, pivots): + events, maps, registry, ranges = [], [], {}, {} + stage = pair["service_stage"] + full_axes = engine.UNIT[:9 + 8 * stage] + full = engine.phase.product([(v, 1) for v in full_axes]) + + def register(columns, translation): + columns = tuple(columns) + key = columns, translation + if key not in registry: + inverse = engine.transpose(columns) + need(engine.compose(columns, inverse) == engine.compose(inverse, columns) + == engine.UNIT, "The route is orthogonal") + need(columns[9 + 8 * stage:] == engine.UNIT[9 + 8 * stage:], + "The route fixes all future axes") + transformed = engine.phase.product( + [(engine.act(columns, v), 1) for v in full_axes]) + need(engine.phase.add_phase(transformed, engine.phase.line(translation, 2)) == full, + "The complete FULL phase equation") + registry[key] = len(maps) + maps.append({ + "columns": columns, "translation": translation, + "inverse_columns": inverse, + "inverse_translation": engine.act(inverse, translation), + }) + return registry[key] + + def view(field, record, inverse=False): + route, delta = tuple(record["route_columns"]), record["translation"] + if inverse: + route = engine.transpose(route) + delta = engine.act(route, delta) + events.append(["map", field, register(route, delta)]) + + current = {v["port"]: v for v in pair["current_code_views"]} + old = {v["port"]: v for v in pair["old_reader_views"]} + ordinary = sorted(set(range(112)) - set(pivots)) + + def apply_current(name): + begin = len(events) + for p in range(112): + view(p, current[p]) + for op, target, source, coefficient in involution["common_frame_words"]["A"]: + events.append(["scalar", op, target, source, coefficient]) + for p in reversed(range(112)): + view(p, current[p], inverse=True) + ranges[name] = [begin, len(events)] + + apply_current("apply_current_involution") + begin = len(events) + fields = [(p, p) for p in ordinary] + [(112 + p, p) for p in pivots] + for field, p in fields: + view(field, old[p]) + for op, target, source, coefficient in capture["scalar_word"]: + need(target in pivots and (source is None or source in ordinary), + "The old complement reader is unchanged") + events.append(["scalar", op, 112 + target, source, coefficient]) + for field, p in reversed(fields): + view(field, old[p], inverse=True) + ranges["old_reader_complement"] = [begin, len(events)] + begin = len(events) + for p in pivots: + events.append(["scalar", "add", 112 + p, p, "1"]) + ranges["selected_reader_copy"] = [begin, len(events)] + apply_current("restore_current_involution") + return {"reader_stage": pair["reader_stage"], "service_stage": stage, + "events": events, "maps": maps, "stage_ranges": ranges} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + source = {name: read(name) for name in PINS} + inv, capture, prefix, access, dispatch = ( + json.loads(source[name]) + for name in ("involution", "capture", "prefix", "view_query", "dispatcher")) + engine = load_engine() + pivots = inv["pivots"] + selected = set(pivots) + need(pivots == prefix["selected_ports"] == capture["pivots"] == access["pivots"], + "All packets use the same physical selected ports") + matrix = engine.base.n.rows(inv["response"]) + old_response = engine.base.n.rows(prefix["response"]) + reader = engine.base.n.rows(capture["centre_reader"]) + need(all(matrix[p] == old_response[p] for p in range(112) if p not in selected), + "The retained ordinary native response is exactly A_R") + need(engine.base.n.r.product(matrix, matrix) == engine.base.n.r.identity(112), + "The actual physical response is an involution") + scalar_state = engine.base.n.r.identity(112) + for op, target, origin, value in inv["common_frame_words"]["A"]: + coefficient = F(value) + if op == "add": + engine.base.n.r.add(scalar_state[target], scalar_state[origin], coefficient) + else: + need(op == "scale", "Only scalar ADD and SCALE") + scalar_state[target] = {j: coefficient * v for j, v in scalar_state[target].items()} + need(scalar_state == matrix, "The complete 112-column current scalar A word") + need(engine.base.n.r.price(inv["common_frame_words"]["A"]) == 3276, + "The exact scalar price of A") + prefix_reports = {} + for provider, word in prefix["providers"].items(): + prefix_reports[provider] = engine.base.verify( + word, engine.base.n.r.identity(112), matrix, [{} for _ in range(112)], selected) + words, reports = {}, {} + for pair in access["pairs"]: + s, t = pair["reader_stage"], pair["service_stage"] + key = f"{s}:{t}" + stage_view = dispatch["stage_views"][t - 1] + data_exits = {v["port"]: v for v in stage_view["DATA_exit"] if v["side"] == "X"} + for view in pair["current_code_views"]: + expected = data_exits[view["port"]] + need(view["route_columns"] == expected["route_columns"] + and view["translation"] == expected["translation_after_route"], + "Current query views equal the actual DATA exits") + at = engine.routed(matrix, range(112), pair["current_code_views"]) + ls = engine.routed(reader, pivots, pair["old_reader_views"]) + direct = engine.product(ls, at) + word = emit_word(engine, pair, inv, capture, pivots) + initial = engine.initial_prefix(at, selected) + expected = [dict(row) for row in initial] + for p, row in zip(pivots, direct): + engine.add(expected[112 + p], row) + actual, complete_report = engine.replay( + word["events"], word["maps"], initial, selected) + need(actual == expected, "All 640 columns after the complete native prefix") + query_initial = [{(i, engine.UNIT): F(1)} for i in range(640)] + query_expected = [dict(row) for row in query_initial] + for p, row in zip(pivots, direct): + engine.add(query_expected[112 + p], row) + query_actual, query_report = engine.replay( + word["events"], word["maps"], query_initial, selected) + need(query_actual == query_expected, "All independent FULL query inputs") + need(query_actual[:112] == query_initial[:112] + and query_actual[224:] == query_initial[224:], + "Every source and arbitrary helper is restored") + need(query_report["scalar_primitives"] == 8440 + and query_report["monomial_maps"] == 672, "The complete query invoice") + cutoff = word["stage_ranges"]["restore_current_involution"][0] + bad, _ = engine.replay(word["events"][:cutoff], word["maps"], query_initial, selected) + need(bad != query_expected, "Omitting the source restoration fails") + wrong_pair = deepcopy(pair) + wrong_pair["old_reader_views"] = wrong_pair["current_code_views"] + wrong_word = emit_word(engine, wrong_pair, inv, capture, pivots) + bad, _ = engine.replay(wrong_word["events"], wrong_word["maps"], query_initial, selected) + need(bad != query_expected, "Replacing the old reader by the current reader fails") + words[key] = word + reports[key] = { + "query": query_report, "after_native_prefix": complete_report, + "direct_owner_paths": sum(map(len, direct)), + "negative_controls": ["omitted_restore", "current_reader_substitution"], + } + invocations = deepcopy(dispatch["invocations"]) + for call in invocations: + query_block = call["ordered_blocks"][-1] + need(query_block["op"] == "fixed_past_reader_query", + "The query follows the full native sweep and DATA exits") + query_block.update({ + "source": "queries", + "literal_source": "queries", + "literal_key": f"{call['reader_stage']}:{call['service_stage']}", + "map_calls": 672, + }) + query_block.pop("pair_record") + call["query_key"] = query_block["literal_key"] + call.pop("query_pair_record") + call["scalar_primitives"] = 14896 + call["map_call_bound"]["late_query"] = 672 + call["map_call_bound"]["total"] = 4384 + payload = { + "schema": "involution-fixed-reader-service-v1", "source_pins": PINS, + "pivots": pivots, "response": inv["response"], + "native_prefixes": prefix["providers"], "queries": words, + "stage_views": dispatch["stage_views"], "invocations": invocations, + "physical_contract": { + "input": "(Fprev*x, Fprev*diag(I_P,q_R)*w)", + "output": "(Fnew*x, Fnew*diag(I_P,q_R)*(w+D_st*x))", + "response_rows_P": "L_s*A_t", + "response_rows_R": "(A_t)_R", + "arbitrary_selected_baselines": True, + "physical_input_level": "t-1, independent of reader stage s", + }, + "helper_hosting": dispatch["owner_contract"], + "backward_or_complete_caller_claimed": False, + } + args.output.mkdir(parents=True, exist_ok=False) + raw = (json.dumps(payload, separators=(",", ":"), sort_keys=True) + "\n").encode() + (args.output / "INVOLUTION-READER.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_ACTUAL_INVOLUTION_FIXED_READER_SERVICE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "prefix_reports": prefix_reports, "query_reports": reports, + "query_scalar_primitives": 8440, "query_maps": 672, + "complete_word_scalar_primitives": 14896, + "own_word_monomial_call_bound": 4384, + "native_mass": 1792, "native_children": 1520, + "backward_or_complete_caller_claimed": False, + } + (args.output / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json new file mode 100644 index 0000000000..854518cab3 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/CHECKS.json @@ -0,0 +1,131 @@ +{ + "backward_or_complete_caller_claimed": false, + "complete_word_scalar_primitives": 14896, + "native_children": 1520, + "native_mass": 1792, + "own_word_monomial_call_bound": 4384, + "payload_decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091", + "prefix_reports": { + "base": { + "additional_content_binary_height": 1, + "arbitrary_input_columns": 640, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "fixed_odd_scans": 0, + "maximum_content_prefix_row_one_norm": "22", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "ordinary_hole_targets": 96, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 6456, + "scalar_stage_prices": { + "precode": 0, + "retained_core": 6456, + "selected_line_progress": 0 + }, + "selected_full_targets": 16, + "unchanged_arbitrary_helper_fields": 416, + "unchanged_source_fields": 112 + }, + "extra": { + "additional_content_binary_height": 1, + "arbitrary_input_columns": 640, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "fixed_odd_scans": 0, + "maximum_content_prefix_row_one_norm": "22", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "ordinary_hole_targets": 96, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 6456, + "scalar_stage_prices": { + "precode": 0, + "retained_core": 6456, + "selected_line_progress": 0 + }, + "selected_full_targets": 16, + "unchanged_arbitrary_helper_fields": 416, + "unchanged_source_fields": 112 + } + }, + "producer_sha256": "29afc86c918f428d9562b02e2017a1eebc38b1cf2dcae2b2d6bf53c5473be14b", + "query_maps": 672, + "query_reports": { + "0:1": { + "after_native_prefix": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "202", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "direct_owner_paths": 3824, + "negative_controls": [ + "omitted_restore", + "current_reader_substitution" + ], + "query": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "202", + "monomial_maps": 672, + "scalar_primitives": 8440 + } + }, + "0:2": { + "after_native_prefix": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "202", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "direct_owner_paths": 3824, + "negative_controls": [ + "omitted_restore", + "current_reader_substitution" + ], + "query": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "202", + "monomial_maps": 672, + "scalar_primitives": 8440 + } + }, + "1:2": { + "after_native_prefix": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "202", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "direct_owner_paths": 3824, + "negative_controls": [ + "omitted_restore", + "current_reader_substitution" + ], + "query": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "202", + "monomial_maps": 672, + "scalar_primitives": 8440 + } + } + }, + "query_scalar_primitives": 8440, + "status": "PASS_ACTUAL_INVOLUTION_FIXED_READER_SERVICE" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/INVOLUTION-READER.json.gz b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-20261020/final-normal/INVOLUTION-READER.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..17f67393c05956eec337ee0791797c9134fadee9 GIT binary patch literal 210767 zcmX_m19T+c({?ttZQI7iwry{;Nj95FHnweUY+D=KHa2!LvGLCS{^$GV^z`Yeu3KGI zx9&4lb(&-I~;kUc>;Z!%@m#6ufyZaoU=Zo=@ zoX?%jv+mB?- zPitJxr^X8V94Ws2)_+%$^M34S5%zt4+X-d)Jafwt{&+Y@oz{37cXPiEHTHR1{(QUq zYrN(C^32lxcJ(DlCE54U5%_V^U&EOE==*dqE&K_)^!fOCL%<>n*P2F zQs=D(Xk=c02lf6?@<`(QalH((^X=e06y&v+;P8eew+P?YyS?E@4HoYUWZyr3UT?-z 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It includes the native carrier prefix, all DATA maps, +the whole-cover barrier, and the late query. The old-reader label can be +0 or 1. The current service stage can be 1 or 2. The three pairs are +\((s,t)=(0,1),(0,2),(1,2)\). Both native providers are included. + +The complete word costs 14,896 real scalar primitives and has native +rank 1,792. It has no extra field and no odd division. All 416 borrowed +helper fields can have arbitrary input values and are restored. +The map count is an upper bound of 4,384 calls. This packet does not +give a finite real-operation price for these maps, a new helper host, +a closed caller, or a multiplication exponent. + +## The exact types + +Let P be the pinned set of sixteen selected ports. Let R be its +96-port complement. Put + +\[ +G_R=\operatorname{diag}(I_P,q_R),\qquad +F_\ell=\operatorname{FULL}_{9+8\ell}. +\] + +The physical input level is \(t-1\), independent of the reader label s. +The old reader is the actual routed \(L_s\). The current response is +the actual routed dyadic involution \(A_t\). Define the complete +112-row operator \(D_{s,t}\) by + +\[ +(D_{s,t})_P=L_sA_t,\qquad (D_{s,t})_R=(A_t)_R. +\tag{1} +\] + +The emitted inverse-adjoint service is + +\[ +(F_{t-1}x,\ F_{t-1}G_Rw) +\longmapsto +(F_t(x-D_{s,t}^{*}w),\ F_tG_Rw). +\tag{2} +\] + +The selected records and all ordinary records in w are arbitrary. +The word preserves their logical contents. It does not set a borrowed +baseline to zero. The star includes the inverse owner route of every +coefficient, as well as the matrix transpose. + +For comparison, the frozen forward service has the same physical +types and the content map \((x,w)\mapsto(x,w+D_{s,t}x)\). +Equation (2) is its exact inverse-adjoint, with its unitary input and +output frames retained. + +## Same chronology, complete physical operation + +For chronological gates \(g_1,\ldots,g_n\), the physical operator is +\(U=g_n\cdots g_1\). Then + +\[ +U^{-*}=g_n^{-*}\cdots g_1^{-*}. +\tag{3} +\] + +Thus the chronological order does not change. For each scalar gate: + +- Replace `target += c * source` by `source -= c * target`. +- Replace a real scale c by the scale \(c^{-1}\). + +All coefficients here are real. Every scale is a nonzero signed power +of two. No CLEAR or noninvertible gate occurs. + +Each native child and each physical monomial map is unitary. Therefore +its inverse-adjoint is the same physical operator, with the same global +phase. The emitter retains every native event, phase recipe, input +adapter, output adapter, DATA map, and late map at its original position. +It checks all nine-dimensional monomial matrices for invertibility and +all stored quadratic phases for unit modulus. The exact native recipe +identities are inherited from the pinned independent phase review. +No new native phase recipe is inferred from a binary rank alone. + +At every scalar event, the source and target have the same physical +frame. Transposing that event therefore remains legal. The new replay +checks this equality at every event, with the exact live frame ledger. +It checks all 640 input columns. The native prefix gives + +\[ +x\longmapsto x-(A_t)_R^{*}w_R,\qquad w\longmapsto w. +\tag{4} +\] + +The late word then subtracts \((L_sA_t)^*w_P\) from X. Its maps touch +only X and selected Y fields, which are FULL at that cut. Ordinary Y +fields keep their hole frames and do not enter the late query. +Equations (4) and this final subtraction give (2). + +The complete physical order remains: + +```text +DATA entry +128 native input adapters +complete native carrier cover sweep +96 ordinary output adapters +DATA exit +complete-cover barrier +late inverse-adjoint reader query +``` + +The late map source fields are not relabelled. A former query target +becomes a scalar source, while its physical map stays at the same place +in the word. This distinction is checked in the serialized program. + +The same construction applies to any finite word of unitary field maps +and invertible linear scalar gates. It requires the physical frame and +field at each event, not an inverse of its response matrix. If the +forward endpoint is a lower shear with reader D and is the identity +on arbitrary borrowed fields, the new endpoint is the upper shear with +reader \(-D^*\) and is also the identity on those fields. D can be +rectangular or singular. For composition, apply the rule to the complete +physical gate list in its existing chronological order. A new boundary +conversion is needed only when the original words did not already have +compatible physical types. + +## Actual D25 source and phase binding + +Each field uses the exact regular-cover route +\(h=d\rho_{t,p}\). The route is orthogonal, fixes the port's intrinsic +line, and has the pinned DATA translation. The emitter repeats all +448 entry and 448 exit Z4 identities in the dispatcher. It also checks +the complete Z4 identity and inverse translation of each late FULL map. + +The native input and output types in the current body are + +\[ +\operatorname{diag}(Q,Z),\qquad +\operatorname{diag}(F_9,F_9G_R), +\quad Z=\operatorname{diag}(Q_P,I_R). +\] + +The DATA identities identify these types with the two global boundaries +in (2), with the same common exterior. They apply to the new word +because all its physical frame operators are unchanged. + +For a unitary input frame I and output frame O, a content map C has +physical action \(OCI^{-1}\). Its inverse-adjoint is +\(OC^{-*}I^{-1}\). This proves the direction of the retained physical +boundaries. It does not reverse the stage progression or exchange the +two DATA views. + +The regular-cover replay retains both the input field and the complete +25-axis owner matrix in every coefficient. It lifts the replayed native +prefix through the actual DATA arrays, then executes the literal late +word. For all six provider/pair cases, it equals the direct operator in +(2). Both products with the forward adjoint are the identity on all +640 fields. The actual source-view order is part of this calculation. + +## Full invoice and bounds + +| Part | Real scalar primitives | Map calls | +| --- | ---: | ---: | +| Native carrier prefix | 6,456 | 224 endpoint adapters | +| Late inverse-adjoint query | 8,440 | 672 | +| DATA entry and exit | 0 | 448 | +| Native child side maps | 0 | at most 3,040 | +| Complete word | 14,896 | at most 4,384 | + +The native profile is + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H8. +``` + +There are 1,520 native children and total native rank 1,792. Scalar +transposition and inversion of signed power-of-two scales preserve +the frozen tariff. Native child sizes and physical side maps do not +change. + +The exact coefficient row-sum peak of the native prefix is 12, with +binary denominator height one. The late dual on independent inputs +has peak 30 and height two. After the actual native prefix, the complete +emitted-boundary peak is 40 and height two in all six cases. +These are content bounds at the emitted gate boundaries. They exclude +internal arithmetic in a lowered ADD, a recursive child, or a caller. + +The original helper owner contract is retained. The same helper fields +and native events occur at the same times, and the new 640-column replay +restores every arbitrary helper value. This does not prove a new +recursive parking construction or change the inherited helper count. + +## Verification, scope, and credit + +Run `emit_dual.py --output ` with normal Python and with +`python3 -O`. The payloads and receipts must be byte equal. The emitter +rejects an existing output directory. + +The checks include the complete physical frame ledgers, all 640 native +and routed columns, all 416 helper identities, both inverse product +orders, the 896 DATA phase equations, and all late map phases. +Changing a dual ADD sign fails in both native prefixes and in all three +late queries. The serialized complete words are replayed again. + +The packet uses the controller lane's row involution, the native lane's +carrier prefix, the reviewed fixed-reader forward query, and the +independent native, DATA, and late-dual reviews. Their exact paths and +hashes are in the program and freeze manifest. This work was produced +with AI assistance and exact rational computation. + +This result supplies a complete backward service with the types in +(2). It does not assert that \(D_{s,t}\) is reciprocal, that it is the +same at different stages, or that a complete caller closes. The original +raw-output phases, recursive hosting, finite map costs, and final +supplier calculation remain separate obligations. + +No PR or publication is authorized. Before any future PR description, +read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json new file mode 100644 index 0000000000..a4a2556a48 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/FREEZE.json @@ -0,0 +1,19 @@ +{ + "PR_description_prerequisite": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "all_416_other_fields_untouched_by_emitted_top_level_events": true, + "explicit_top_level_fields_used": 224, + "files": { + "COMPLETE-DUAL.md": "37a3a187acf93cad2048f9147457bf8925cf53ce61836b5e899dd13bc4239c5e", + "emit_dual.py": "4c10ca91f788052bc3e1da43f63d6dde0a84d4b8b1c34e8f64f3912e47a86a32", + "final-normal/CHECKS.json": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84", + "final-normal/COMPLETE-DUAL.json.gz": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1", + "final-optimized/CHECKS.json": "68d4fb6e86f0d4a1798750b447e6c19f0cc4e949ebd45442c71f01ac45781b84", + "final-optimized/COMPLETE-DUAL.json.gz": "c975db3c12e9c5165899835e07317c7bd6d853a772f89c6db69d7cf15a373cd1" + }, + "independent_review": "Requested separately; not claimed by this freeze.", + "normal_optimized_byte_equal": true, + "payload_decompressed_sha256": "f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be", + "publication": "No PR or publication authorized.", + "schema": "complete-inverse-adjoint-reader-freeze-v1", + "status": "PASS_PRODUCER_EXACT_NORMAL_AND_OPTIMIZED" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py new file mode 100644 index 0000000000..3e7c798f7e --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/emit_dual.py @@ -0,0 +1,433 @@ +"""Emit the complete inverse-adjoint routed reader service.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PINS = { + "forward": ( + "bridge-access-20261017/involution-reader-20261020/" + "final-normal/INVOLUTION-READER.json.gz", + "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091", + ), + "forward_freeze": ( + "bridge-access-20261017/involution-reader-20261020/FREEZE.json", + "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6", + ), + "forward_review": ( + "bridge-review-20261017/involution-reader-review-20261020/FREEZE.json", + "b4770cbd56bc8b115728529ab218d60ca2bd1a385896ba78cfdf374f04370c97", + ), + "native_phase_review": ( + "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c", + ), + "dispatcher_freeze": ( + "bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json", + "bbc0e4026b1d003dedc55c78cd6300ef429ee2d95712e55bbab896da2840c331", + ), + "engine": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "fixed-reader-reuse-20261020/emit_routed_query.py", + "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900", + ), + "views": ( + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = (LANES / path).read_bytes() + if path.endswith(".gz"): + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source: " + name) + return raw + + +def load_engine(): + read("engine") + spec = importlib.util.spec_from_file_location( + "complete_reader_dual_engine", LANES / PINS["engine"][0]) + result = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = result + spec.loader.exec_module(result) + return result + + +def scalar_dual(gate): + op, target, source, raw = gate + value = F(raw) + if op == "add": + return [op, source, target, str(-value)] + need(op == "scale" and value, "Every scalar gate is invertible") + return [op, target, None, str(1 / value)] + + +def dual_prefix(original): + word = deepcopy(original) + for old, new in zip(original["events"], word["events"]): + if old[0] == "scalar": + new[1] = scalar_dual(old[1]) + else: + need(old[0] == "native" and new == old, "Native events do not change") + for key in original: + if key != "events": + need(word[key] == original[key], "All native records and adapters stay fixed") + return word + + +def dual_query(original): + word = deepcopy(original) + for index, event in enumerate(original["events"]): + if event[0] == "scalar": + word["events"][index] = ["scalar"] + scalar_dual(event[1:]) + else: + need(event[0] == "map" and word["events"][index] == event, + "Every physical field map stays in the same position") + need(word["maps"] == original["maps"], "All map phases and inverse records stay fixed") + return word + + +def unitary_records(engine, word): + records = [] + for recipe in word["native_recipes"].values(): + need(1 <= recipe["rank"] <= 9, "A normalized native child has positive rank") + records.extend(recipe[key] for key in ("left", "right") if recipe[key] is not None) + for view in word["input_views"]: + need(view["rank"] == 0 and view["right"] is None, "A monomial input adapter") + records.append(view["left"]) + for view in word["output_views"]: + recipe = view["recipe"] + need(recipe["rank"] == 0 and recipe["right"] is None, "A monomial output adapter") + records.append(recipe["left"]) + for record in records: + need(len(record["matrix_rows"]) == 9 + and len(engine.base.n.basis(record["matrix_rows"])) == 9, + "A physical monomial side map is a bijection") + need(0 <= record["offset"] < 512 and 0 <= record["phase"] < 4, + "A physical offset and unit-modulus global phase") + need(len(record["linear_Z4"]) == len(record["quadratic_rows"]) == 9 + and all(0 <= x < 4 for x in record["linear_Z4"]) + and all(0 <= x < 512 for x in record["quadratic_rows"]), + "The complete unit-modulus quadratic phase record") + return len(records) + + +def replay_prefix(engine, word): + current = list(word["start"]) + state = engine.base.n.r.identity(640) + profile = Counter() + maximum, height, price = F(1), 0, 0 + for event in word["events"]: + if event[0] == "native": + _, target, old, new, rank, key = event + need(current[target] == old, "The physical native input frame") + a, b = word["frames"][old], word["frames"][new] + need(len(engine.base.n.basis(a + b)) == len(b), "Nested native frames") + need(len(b) - len(a) == rank == word["native_recipes"][key]["rank"], + "The physical native rank and recipe") + current[target] = new + profile[rank] += 1 + continue + need(event[0] == "scalar", "The complete native event grammar") + gate, frame = event[1:] + op, target, source, raw = gate + value = F(raw) + need(current[target] == frame, "The dual scalar target frame") + if op == "add": + need(source != target and current[source] == frame, + "The dual scalar source has the same physical frame") + engine.base.n.r.add(state[target], state[source], value) + else: + need(op == "scale", "Only ADD and SCALE") + state[target] = {j: value * x for j, x in state[target].items()} + price += engine.base.n.r.price([gate]) + maximum = max(maximum, sum(abs(x) for x in state[target].values())) + for x in state[target].values(): + d = x.denominator + need(d & (d - 1) == 0, "All scalar coefficients are dyadic") + height = max(height, d.bit_length() - 1) + need(current == word["final"], "All 640 final physical frames") + need(state[224:] == engine.base.n.r.identity(640)[224:], + "All 416 arbitrary helper fields are restored") + return state, { + "input_fields": 640, "restored_helper_fields": 416, + "native_profile": dict(sorted(profile.items())), + "native_children": sum(profile.values()), + "native_mass": sum(k * v for k, v in profile.items()), + "scalar_primitives": price, + "coefficient_prefix_row_sum": str(maximum), + "coefficient_binary_height": height, + "input_adapter_maps": len(word["input_views"]), + "output_adapter_maps": len(word["output_views"]), + } + + +def phase_bindings(engine, bundle, views): + records = {(v["stage"], v["port"]): v for v in views["entries"]} + counts = Counter() + for stage in bundle["stage_views"]: + t = stage["service_stage"] + need(stage["physical_input_level"] == t - 1 + and stage["physical_output_level"] == t, "The adjacent physical levels") + before = [(v, 1) for v in engine.UNIT[:9 + 8 * (t - 1)]] + after = [(v, 1) for v in engine.UNIT[:9 + 8 * t]] + exterior = [(v, 1) for v in engine.UNIT[9:9 + 8 * t]] + for key in ("DATA_entry", "DATA_exit"): + need(len(stage[key]) == 224 and {v["field"] for v in stage[key]} == set(range(224)), + "The DATA maps cover every field exactly once") + for view in stage[key]: + p = view["port"] + side = view["side"] + need(view["field"] == p + (112 if side == "Y" else 0), + "The physical field and bank are unchanged") + literal = records[t, p] + rho = literal["route_columns"] + q = literal["q"] + align = literal["literal_stage_alignment"] + need(view["route_columns"] == rho and view["owner_from_body"] == "h=d*rho", + "The exact regular-cover owner view") + need(engine.compose(tuple(rho), engine.transpose(rho)) == engine.UNIT + and engine.act(rho, q) == q, "Orthogonal own-line DATA route") + full = side == "X" or p in bundle["pivots"] + if key == "DATA_entry": + delta = engine.act(rho, align["entry_" + side]) + need(view["translation_before_route"] == align["entry_" + side] + and view["translation_after_route"] == delta, "The literal entry phase") + source = before + ([] if full else [(q, -1)]) + wanted = exterior + ([(q, 1)] if full else []) + else: + exit_key = "exit_X" if full else "exit_Y" + delta = align[exit_key] + need(view["translation_after_route"] == delta + and view["literal_translation_key"] == exit_key, "The literal exit phase") + source = after + ([] if full else [(q, -1)]) + wanted = source + actual = engine.phase.add_phase( + engine.phase.product([(engine.act(rho, v), n) for v, n in source]), + engine.phase.line(delta, 2)) + need(actual == engine.phase.product(wanted), "The complete DATA Z4 identity") + counts[key] += 1 + return dict(counts) + + +def identity(engine): + return [{(i, engine.UNIT): F(1)} for i in range(640)] + + +def adjoint(engine, rows): + result = [{} for _ in rows] + for target, row in enumerate(rows): + for (source, route), value in row.items(): + engine.add(result[source], {(target, engine.transpose(route)): value}) + return result + + +def lift_prefix(engine, local, stage): + rho = {v["field"]: tuple(v["route_columns"]) for v in stage["DATA_exit"]} + result = [] + for target, row in enumerate(local): + if target >= 224: + need(row == {target: F(1)}, "The helper endpoint is the actual identity") + result.append({(target, engine.UNIT): F(1)}) + continue + need(all(source < 224 for source in row), "No borrowed helper enters a data output") + result.append({ + (source, engine.compose(engine.transpose(rho[target]), rho[source])): value + for source, value in row.items() + }) + return result + + +def check_query_maps(engine, word): + t = word["service_stage"] + full_axes = engine.UNIT[:9 + 8 * t] + full = engine.phase.product([(v, 1) for v in full_axes]) + for record in word["maps"]: + route, inverse = tuple(record["columns"]), tuple(record["inverse_columns"]) + need(engine.compose(route, inverse) == engine.compose(inverse, route) == engine.UNIT, + "The late map and its inverse are exact") + need(inverse == engine.transpose(route), "The late route is orthogonal") + need(route[9 + 8 * t:] == engine.UNIT[9 + 8 * t:], "Future axes stay fixed") + need(record["inverse_translation"] == engine.act(inverse, record["translation"]), + "The inverse translation is exact") + actual = engine.phase.add_phase( + engine.phase.product([(engine.act(route, v), 1) for v in full_axes]), + engine.phase.line(record["translation"], 2)) + need(actual == full, "The complete late FULL phase identity") + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + sources = {name: read(name) for name in PINS} + forward = json.loads(sources["forward"]) + views = json.loads(sources["views"]) + engine = load_engine() + selected = set(forward["pivots"]) + response = engine.base.n.rows(forward["response"]) + phase_report = phase_bindings(engine, forward, views) + prefixes, prefix_states, prefix_reports = {}, {}, {} + expected_local = engine.base.n.r.identity(640) + for target, row in enumerate(response): + if target not in selected: + for source, value in row.items(): + engine.base.n.r.add(expected_local[source], {112 + target: -value}) + for provider, original in forward["native_prefixes"].items(): + word = dual_prefix(original) + unitary_count = unitary_records(engine, word) + state, report = replay_prefix(engine, word) + need(state == expected_local, "All 640 local inverse-adjoint columns") + need(report["native_mass"] == 1792 and report["native_children"] == 1520 + and report["scalar_primitives"] == 6456, "The complete native dual invoice") + need(dual_prefix(word) == original, "The gatewise operation is an involution") + bad = deepcopy(word) + index = next(i for i, event in enumerate(bad["events"]) + if event[0] == "scalar" and event[1][0] == "add") + bad["events"][index][1][3] = str(-F(bad["events"][index][1][3])) + altered, _ = replay_prefix(engine, bad) + need(altered != expected_local, "A wrong native-prefix dual sign fails") + report["unitary_monomial_records_checked"] = unitary_count + report["negative_control_wrong_native_prefix_sign"] = True + prefixes[provider], prefix_states[provider], prefix_reports[provider] = word, state, report + query_words, reports, complete_states = {}, {}, {} + unit = identity(engine) + for key, original in forward["queries"].items(): + word = dual_query(original) + need(dual_query(word) == original, "The late gatewise operation is an involution") + check_query_maps(engine, word) + query_forward, _ = engine.replay(original["events"], original["maps"], unit, selected) + query_expected = adjoint(engine, [ + {term: (2 * value if term == (i, engine.UNIT) else F(0)) - value + for term, value in row.items()} + for i, row in enumerate(query_forward) + ]) + actual_query, query_report = engine.replay(word["events"], word["maps"], unit, selected) + need(actual_query == query_expected, "All 640 independent late dual columns") + need(query_report["scalar_primitives"] == 8440 and query_report["monomial_maps"] == 672, + "The exact late dual invoice") + t = word["service_stage"] + stage = forward["stage_views"][t - 1] + per_provider = {} + for provider, local in prefix_states.items(): + initial = lift_prefix(engine, local, stage) + actual, report = engine.replay(word["events"], word["maps"], initial, selected) + local_forward = engine.base.n.r.identity(640) + for p in range(112): + if p not in selected: + engine.base.n.r.add(local_forward[112 + p], response[p]) + forward_initial = lift_prefix(engine, local_forward, stage) + forward_complete, _ = engine.replay( + original["events"], original["maps"], forward_initial, selected) + inverse_forward = [dict(row) for row in unit] + for target in range(112, 224): + for term, value in forward_complete[target].items(): + if term != (target, engine.UNIT): + engine.add(inverse_forward[target], {term: -value}) + expected = adjoint(engine, inverse_forward) + need(actual == expected, "All 640 complete routed inverse-adjoint columns") + complete_states[key, provider] = actual + need(actual[112:] == unit[112:], "All target records and 416 helper fields are restored") + forward_star = adjoint(engine, forward_complete) + need(engine.product(actual, forward_star) == engine.product(forward_star, actual) == unit, + "Both complete content inverse-adjoint products") + need(engine.product(forward_complete, inverse_forward) + == engine.product(inverse_forward, forward_complete) == unit, + "Both complete forward inverse products") + per_provider[provider] = report + bad = deepcopy(word) + index = next(i for i, e in enumerate(bad["events"]) + if e[0] == "scalar" and e[1] == "add" and e[3] >= 112) + bad["events"][index][4] = str(-F(bad["events"][index][4])) + altered, _ = engine.replay(bad["events"], bad["maps"], unit, selected) + need(altered != actual_query, "A wrong transferred source sign fails") + query_words[key] = word + reports[key] = {"late_query": query_report, "complete_word": per_provider, + "all_640_columns": True, "both_inverse_products": True, + "negative_control_wrong_transferred_source_sign": True} + invocations = deepcopy(forward["invocations"]) + expected_order = ["DATA_entry", "native_input_adapters", + "complete_native_carrier_cover_sweep", "ordinary_output_adapters", + "DATA_exit", "complete_cover_barrier", "fixed_past_reader_query"] + for call in invocations: + need([b["op"] for b in call["ordered_blocks"]] == expected_order, + "The complete physical block order stays fixed") + need(call["physical_input_level"] == call["service_stage"] - 1, + "The physical entry level is separate from the old reader label") + need(call["query_key"] in query_words and call["provider"] in prefixes, + "Every invocation resolves to complete emitted words") + call["ordered_blocks"][-1]["op"] = "inverse_adjoint_fixed_past_reader_query" + payload = { + "schema": "complete-inverse-adjoint-involution-reader-v1", + "source_pins": PINS, "pivots": forward["pivots"], "response": forward["response"], + "native_prefixes": prefixes, "queries": query_words, + "stage_views": forward["stage_views"], "invocations": invocations, + "helper_hosting": forward["helper_hosting"], + "physical_contract": { + "input": "(Fprev*x, Fprev*diag(I_P,q_R)*w)", + "output": "(Fnew*(x-D_st^*w), Fnew*diag(I_P,q_R)*w)", + "D_st_rows_P": "L_s*A_t", "D_st_rows_R": "(A_t)_R", + "physical_input_level": "t-1, independent of reader stage s", + "arbitrary_inputs": "All 640 fields; no zero selected baseline.", + }, + "scope": "Complete typed inverse-adjoint service for three D25 pairs and two providers. " + "No complete caller, new helper host, finite map cost, or exponent claim.", + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + need(saved["stage_views"] == forward["stage_views"] + and saved["helper_hosting"] == forward["helper_hosting"], + "Serialized DATA phase records and helper contract are unchanged") + for provider, word in saved["native_prefixes"].items(): + state, report = replay_prefix(engine, word) + need(state == prefix_states[provider] + and all(value == prefix_reports[provider][key] for key, value in report.items()), + "The serialized complete native dual passes") + for key, word in saved["queries"].items(): + stage = saved["stage_views"][word["service_stage"] - 1] + for provider in prefixes: + actual, report = engine.replay(word["events"], word["maps"], + lift_prefix(engine, prefix_states[provider], stage), selected) + need(actual == complete_states[key, provider] + and report == reports[key]["complete_word"][provider], + "The serialized complete routed dual passes") + args.output.mkdir(parents=True, exist_ok=False) + (args.output / "COMPLETE-DUAL.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_COMPLETE_TYPED_INVERSE_ADJOINT_READER", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "prefix_reports": prefix_reports, "query_reports": reports, + "DATA_phase_equations": phase_report, + "all_native_and_endpoint_phase_records_unchanged": True, + "all_late_map_fields_phases_and_positions_unchanged": True, + "all_640_columns_and_416_helpers_checked": True, + "complete_scalar_primitives": 14896, "complete_native_rank": 1792, + "complete_native_children": 1520, "own_word_map_call_bound": 4384, + "scope": payload["scope"], + } + (args.output / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json new file mode 100644 index 0000000000..382247af36 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/involution-reader-dual-20261020/final-normal/CHECKS.json @@ -0,0 +1,134 @@ +{ + "DATA_phase_equations": { + "DATA_entry": 448, + "DATA_exit": 448 + }, + "all_640_columns_and_416_helpers_checked": true, + "all_late_map_fields_phases_and_positions_unchanged": true, + "all_native_and_endpoint_phase_records_unchanged": true, + "complete_native_children": 1520, + "complete_native_rank": 1792, + "complete_scalar_primitives": 14896, + "own_word_map_call_bound": 4384, + "payload_decompressed_sha256": "f307406b952957ebcb2ce847da97e0d3f42c21ff340843755c6aa6de387321be", + "prefix_reports": { + "base": { + "coefficient_binary_height": 1, + "coefficient_prefix_row_sum": "12", + "input_adapter_maps": 128, + "input_fields": 640, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "negative_control_wrong_native_prefix_sign": true, + "output_adapter_maps": 96, + "restored_helper_fields": 416, + "scalar_primitives": 6456, + "unitary_monomial_records_checked": 3150 + }, + "extra": { + "coefficient_binary_height": 1, + "coefficient_prefix_row_sum": "12", + "input_adapter_maps": 128, + "input_fields": 640, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "negative_control_wrong_native_prefix_sign": true, + "output_adapter_maps": 96, + "restored_helper_fields": 416, + "scalar_primitives": 6456, + "unitary_monomial_records_checked": 3150 + } + }, + "producer_sha256": "4c10ca91f788052bc3e1da43f63d6dde0a84d4b8b1c34e8f64f3912e47a86a32", + "query_reports": { + "0:1": { + "all_640_columns": true, + "both_inverse_products": true, + "complete_word": { + "base": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "40", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "extra": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "40", + "monomial_maps": 672, + "scalar_primitives": 8440 + } + }, + "late_query": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "30", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "negative_control_wrong_transferred_source_sign": true + }, + "0:2": { + "all_640_columns": true, + "both_inverse_products": true, + "complete_word": { + "base": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "40", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "extra": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "40", + "monomial_maps": 672, + "scalar_primitives": 8440 + } + }, + "late_query": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "30", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "negative_control_wrong_transferred_source_sign": true + }, + "1:2": { + "all_640_columns": true, + "both_inverse_products": true, + "complete_word": { + "base": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "40", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "extra": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "40", + "monomial_maps": 672, + "scalar_primitives": 8440 + } + }, + "late_query": { + "additional_binary_height": 2, + "exact_prefix_content_one_norm": "30", + "monomial_maps": 672, + "scalar_primitives": 8440 + }, + "negative_control_wrong_transferred_source_sign": true + } + }, + "scope": "Complete typed inverse-adjoint service for three D25 pairs and two providers. 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No new native service, stream-map cost, or supplier claim.", + "source_pins": { + "geometry": "a3d970f070e6aaf67b79bd80d564cd7d653580f1f7fc1daadc3170dbdb9249ff", + "interface": "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746", + "map_correction": "fbf9ef6d0069ab6b5d4ac8ad5daa480a88fdc8bc363cfacb309d47010e3f3c7f", + "phase": "cf39b15752fcb96cc22b9013dce38e13a4399d99b30dc9f53eef788d5ded2bf4", + "source_qualification": "ae8ec52c10c77658190b996a529a405736e377ebc76e9804eaf73e7ff965cc97" + }, + "spectral_occurrence_modes": { + "-13": 320, + "-11": 3, + "-5": 13, + "-3": 7, + "-1": 1, + "1": 1, + "3": 1, + "5": 3, + "11": 13, + "13": 0 + }, + "status": "PASS_INDEPENDENT_PHASE_SECTION_GEOMETRY" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/FREEZE.json new file mode 100644 index 0000000000..7fa76397fa --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/FREEZE.json @@ -0,0 +1,9 @@ +{ + "files": { + "CHECKS.json": "3810b1bf9072a315e36c35f70102d3df9d4cc5867aea196940efa84b3944331d", + "REVIEW.md": "605dd615ce9f1bc97466e0e7a6201e7c3a610dc73809f59d7989ffa0d7c9a300", + "check_review.py": "824ae9452773fda97c82b3f765e125fc7c32777537705f1913608cd35309d038" + }, + "normal_optimized_receipts_identical": true, + "status": "FROZEN_INDEPENDENT_PHASE_SECTION_REVIEW" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/REVIEW.md new file mode 100644 index 0000000000..ca1064028f --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/REVIEW.md @@ -0,0 +1,109 @@ +# Independent review of the phase-section geometry + +The review passes. No material defect was found in the algebra, the +norm bounds, or the stated line-power classification. The result is an +operator theorem. It does not give a complete native scatter or a +supplier cost improvement. + +The reviewed proof is `native-escape-20261017/PHASE-SECTION-GEOMETRY.md`, +SHA256 `a3d970f070e6aaf67b79bd80d564cd7d653580f1f7fc1daadc3170dbdb9249ff`. +Read it with `PHASE-SECTION-GEOMETRY-SOURCES.md`, SHA256 +`ae8ec52c10c77658190b996a529a405736e377ebc76e9804eaf73e7ff965cc97`. +The source qualification preserves the frozen proof and links the map +cost correction. No norm claim uses the withdrawn O(V) translation +shortcut. + +## Independent exact checks + +The checker reads the actual R matrix and the actual 112 line labels. +It forms B from the selected eight-column minor. It does not import +the producer's spectral, classification, or geometry checker. + +- It verifies BD=13I with exact arithmetic. +- It forms all 512 real symmetric character matrices for T=BQ^2D. +- It proves that each matrix is annihilated by the product of the ten + factors with roots -13, -11, -5, -3, -1, 1, 3, 5, 11, and 13. +- It proves that each of these ten roots occurs in at least one matrix. + Since every matrix is real symmetric, these checks give the exact + spectrum without a numerical eigensolver. +- It rebuilds the width-five odd-power mode from characters + (1,2,3,6,6). The stated null vector is nonzero and lies in the kernel. + The leading seven-by-seven minor of S_1 is -73. Thus the mode has + rank seven. Its real phase also applies to S_3. + +At any positive tensor width, the Q^2 sign depends only on the XOR of +the copy characters. All 512 XOR values occur. The ten-value spectrum +therefore holds at each positive width. The odd-power witness extends +to every width at least five by adding zero copy characters. + +## Algebra review + +Set A=BQ, D=B*, q=Q^-1, and T=BQ^2D. The identities BD=13I and +Q^4=I give AK_minus=AK_plus=I for + +```text +K_minus=qD/13, K_plus=QD T^-1. +``` + +Since AA*=13I, K_minus=A*/13 is the minimum-norm right inverse. +Every other solution differs from it by a vector in ker(A), which is +orthogonal to im(A*). The claimed minimum norm follows. + +The identity K_plus* K_plus=13 T^-2 gives the five stated singular +values. The largest is sqrt(13), the smallest is 1/sqrt(13), and their +ratio is 13. The occurrence checks make all three bounds sharp. + +P_plus=K_plus A is idempotent. Its image is im(QD), and its kernel is +ker(A). To check its exact norm, put U=D/sqrt(13). Then U is an +isometry and + +```text +D T^-1 B=13 U T^-1 U*. +``` + +An isometric embedding preserves the norm of the middle operator. +The unitary Q factors also preserve norm. Hence ||P_plus||=13. This +does not assert that P_plus is an orthogonal projection. + +The two isometries qD/sqrt(13) and QD/sqrt(13) have cross-Gram map +T/13. Its singular values give the stated principal-angle cosines. +Cosine one occurs, so the two phase images have a nonzero intersection. +The useful complement is im(QD) plus ker(BQ). + +For an image constrained to im(Q^nD), injectivity of D gives a unique +coefficient map H. The right-inverse equation is S_(m+n) H=I. +Residues zero and two give the stated unique sections. At the singular +odd-power mode, S_(m+n) is not onto. This excludes a section even if +the choice of preimage is nonlinear. The conclusion has the stated +width restriction. It does not assert a minimum singular width. + +Unitary stage routes that commute with their own port lines transport +these identities and norms. This is the route hypothesis used here; +the review does not claim free access between different stage charts. + +## Cost boundary and validation + +The map correction is +`native-escape-20261017/inplace-service-review/MAP-COST-CORRECTION.md`, +SHA256 `fbf9ef6d0069ab6b5d4ac8ad5daa480a88fdc8bc363cfacb309d47010e3f3c7f`. +The 144 simultaneous translations retain their declared packed-map +cost. The interleaved layout does not justify the withdrawn contiguous +bit-field shortcut. This correction does not change the exact inverse +or the geometry above. + +The review ran the checker in normal and optimized Python modes. The +receipts were byte-identical. The command is: + +```text +python3 -I -B check_review.py +PASS_INDEPENDENT_PHASE_SECTION_GEOMETRY +``` + +The optimized command adds `-O`. All final values use exact integer or +rational arithmetic. The checker uses one process. No new source or +target access, borrowed-state restoration, native emission, recursive +hosting, or complete supplier budget was verified in this review. + +OpenAI Codex assisted the review. No PR, commit, or push was made. +Before a future PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/check_review.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/check_review.py new file mode 100644 index 0000000000..60300b7db0 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/phase-section-review-20261018/check_review.py @@ -0,0 +1,115 @@ +"""Check the exact spectral inputs to the phase-section geometry.""" + +from fractions import Fraction as F +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "geometry": ("native-escape-20261017/PHASE-SECTION-GEOMETRY.md", "a3d970f070e6aaf67b79bd80d564cd7d653580f1f7fc1daadc3170dbdb9249ff"), + "source_qualification": ("native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES.md", "ae8ec52c10c77658190b996a529a405736e377ebc76e9804eaf73e7ff965cc97"), + "map_correction": ("native-escape-20261017/inplace-service-review/MAP-COST-CORRECTION.md", "fbf9ef6d0069ab6b5d4ac8ad5daa480a88fdc8bc363cfacb309d47010e3f3c7f"), + "interface": ("new-core-transfer-20261017/INTERFACE.json", "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746"), + "phase": ("bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py", "cf39b15752fcb96cc22b9013dce38e13a4399d99b30dc9f53eef788d5ded2bf4"), +} +ROOTS = [-13, -11, -5, -3, -1, 1, 3, 5, 11, 13] +A = [0, 7, 20, 27, 36, 46, 57, 111] +U = [p for p in range(112) if p not in A] + + +def need(value, label): + if not value: + raise ValueError(label) + + +def det(a): + a = [row[:] for row in a] + n = len(a) + sign, prior = 1, 1 + for k in range(n - 1): + pivot = next((i for i in range(k, n) if a[i][k]), None) + if pivot is None: + return 0 + if pivot != k: + a[k], a[pivot] = a[pivot], a[k] + sign = -sign + for i in range(k + 1, n): + for j in range(k + 1, n): + numerator = a[i][j] * a[k][k] - a[i][k] * a[k][j] + need(numerator % prior == 0, "Exact Bareiss division") + a[i][j] = numerator // prior + prior = a[k][k] + for i in range(k + 1, n): + a[i][k] = 0 + return sign * a[-1][-1] + + +def mm(a, b): + bt = list(zip(*b)) + return [[sum(x * y for x, y in zip(row, col)) for col in bt] for row in a] + + +def main(): + for rel, pin in PINS.values(): + need(sha256((LANES / rel).read_bytes()).hexdigest() == pin, rel + " pin") + phase_path = LANES / PINS["phase"][0] + spec = importlib.util.spec_from_file_location("section_review_phase", phase_path) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + _, ports = phase.load() + q = [p["q"] for p in ports] + source = json.loads((LANES / PINS["interface"][0]).read_text()) + r = [[F(row.get(str(p), 0)) for p in range(112)] for row in source["R"]] + b2 = [[sum(r[j][a] * r[j][p] for j in range(8)) / 2 for p in U] for a in A] + need(all(x.denominator == 1 for row in b2 for x in row), "Twice B is integer") + b2 = [[int(x) for x in row] for row in b2] + need(all(sum(b2[i][k] * b2[j][k] for k in range(104)) == 52 * (i == j) + for i in range(8) for j in range(8)), "BD equals 13I") + seen = {} + for chi in range(512): + signs = [1 - 2 * ((chi & q[p]).bit_count() & 1) for p in U] + t4 = [[sum(b2[i][k] * b2[j][k] * signs[k] for k in range(104)) + for j in range(8)] for i in range(8)] + value = [[int(i == j) for j in range(8)] for i in range(8)] + for root in ROOTS: + factor = [[t4[i][j] - 4 * root * (i == j) for j in range(8)] for i in range(8)] + value = mm(value, factor) + if root not in seen and det(factor) == 0: + seen[root] = chi + need(not any(x for row in value for x in row), "Exact ten-root annihilator") + need(set(seen) == set(ROOTS), "Every claimed spectral value occurs") + copy_characters = (1, 2, 3, 6, 6) + powers = [sum((q[p] & chi).bit_count() & 1 for chi in copy_characters) % 4 for p in U] + need(set(powers) <= {0, 2}, "The odd-power witness is real") + s4 = [[sum(b2[i][k] * b2[j][k] * (1 if powers[k] == 0 else -1) + for k in range(104)) for j in range(8)] for i in range(8)] + null = [0, 0, 1, 0, -1, 1, 0, 1] + need(all(sum(x * y for x, y in zip(row, null)) == 0 for row in s4), "Odd-power null vector") + minor = det([row[:7] for row in s4[:7]]) + need(minor == -73 * 4**7, "Odd-power rank is exactly seven") + singular_squared = sorted({F(13, root * root) for root in ROOTS}) + cosines_squared = sorted({F(root * root, 169) for root in ROOTS}) + need(singular_squared[0] == F(1, 13) and singular_squared[-1] == 13, "Sharp section norm bounds") + result = { + "status": "PASS_INDEPENDENT_PHASE_SECTION_GEOMETRY", + "source_pins": {k: pin for k, (_, pin) in PINS.items()}, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "exact_symmetric_mode_matrices": 512, + "spectral_occurrence_modes": seen, + "positive_section_singular_values_squared": [str(x) for x in singular_squared], + "principal_angle_cosines_squared": [str(x) for x in cosines_squared], + "positive_section_norm_squared": "13", "condition_number_squared": "169", + "oblique_projector_norm_squared": "169", "odd_power_rank": 7, + "odd_power_leading_minor": str(F(minor, 4**7)), + "scope": "Exact spectral inputs and independent algebra review. No new native service, stream-map cost, or supplier claim.", + } + (HERE / "CHECKS.json").write_text(json.dumps(result, sort_keys=True, indent=2) + "\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json new file mode 100644 index 0000000000..b022f3636e --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION-FREEZE.json @@ -0,0 +1,12 @@ +{ + "files": { + "INTEGRATION.md": "7fce1ef14e08963b84bb43f839db280e83879261fc8af950dad072998edcb8a2", + "check_integration.py": "c178c339b0398d7e6f0232d68d681527dfaed70da10941f09bd9db3f141887fb", + "integration-v2-normal/CHECKS.json": "ee6add0c9f4a6330d5180190f29a052f491b1adefef7d9aabb6bc389f4ed057c", + "integration-v2-normal/DISPATCHER.json": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24", + "integration-v2-optimized/CHECKS.json": "ee6add0c9f4a6330d5180190f29a052f491b1adefef7d9aabb6bc389f4ed057c", + "integration-v2-optimized/DISPATCHER.json": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24" + }, + "normal_optimized_byte_identical": true, + "scope": "Exact native-prefix/data-view/query splice; inherited helper hosting and complete supplier remain separate." +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION.md new file mode 100644 index 0000000000..ed2c9ee398 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/INTEGRATION.md @@ -0,0 +1,218 @@ +# The native prefix and the fixed-reader dispatcher + +This packet joins the emitted carrier prefix to the fixed past-reader +query. It gives the exact data interface at the D25 stages 1 and 2. +It preserves the native helper contract as an explicit premise. +It does not give a complete supplier or a multiplication exponent. + +The inputs are the frozen `CARRIER-PREFIX.json.gz`, +`REUSE-PROGRAM.json`, `ROUTED-QUERY.json.gz`, and +`DIMENSION25-VIEWS.json`. The dispatcher records their paths and hashes. +It does not change those files. + +## The physical level and the reader label + +Let P be the fixed sixteen selected ports. Let R be the other 96 ports. +Let \(F_\ell\) be the full transform on the first \(9+8\ell\) axes. +Put + +\[ +G_R=\operatorname{diag}(I_P,q_R). +\] + +Here q is the portwise inverse intrinsic line. Fix a reader stage s +and a service stage t, with \(s` with normal Python +and with `python3 -O`. The two dispatcher files and the two receipts +must be byte equal. The checker rejects an existing output directory. + +The checks bind both providers and the three pairs +\((0,1),(0,2),(1,2)\). They replay the carrier prefix, check every +adjacent data boundary phase, and bind the complete late-query +program. The pinned native integration lane replay covers the 2,064 +literal query maps and its scalar word after this exact prefix. + +This work extends the controller lane's normalized row capture, the +native lane's line-entry carrier, and the earlier D25 view proof. +OpenAI Codex assisted the work. No publication is authorized. Before +any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json new file mode 100644 index 0000000000..f58eb9a9f7 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "REUSE.md": "5038811fc5097ed0e86df6c7d4e5ea147c8b0e977e7ba633499b72528dc28d5d", + "check_reuse.py": "5728ceb5877e3e59ce4d8d4ae21672bb22029944051e6193f9a36b4996b66279", + "reuse-normal/REUSE-CHECKS.json": "1ae1c147f99cf31c7fa6886516e3417417767a08888923bea09afa73dac43729", + "reuse-normal/REUSE-PROGRAM.json": "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b", + "reuse-optimized/REUSE-CHECKS.json": "1ae1c147f99cf31c7fa6886516e3417417767a08888923bea09afa73dac43729", + "reuse-optimized/REUSE-PROGRAM.json": "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b" + }, + "formation_freeze_sha256": "9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11", + "normal_optimized_byte_equal": true, + "schema": "fixed-reader-reuse-freeze-v1", + "scope": "Exact forward fixed-reader query, carrier phases and actual D25 owner views. Complete native integration, backward companion and supplier remain separate." +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE.md new file mode 100644 index 0000000000..f2684a085b --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/REUSE.md @@ -0,0 +1,197 @@ +# A fixed centre reader can be carried through forward services + +The sixteen FULL centre rows need not be converted back to plain target +rows before the next forward service. Their exact next-entry type is +the required intrinsic line. A rank-eight path can carry each row to +the next FULL cut. A dyadic query at that cut updates the same past +reader and restores all source fields. + +This result gives a typed forward-service extension. It does not give +a backward companion or a complete caller. The separate local formation +word has been emitted. The complete reuse native word still needs its +own integration and replay. + +## The carried reader + +Keep the pivot set P and the normalized row readers from `ACCESS.md`. +Let J insert sixteen values at P, and let \(J^{\mathsf T}\) select P. +At stage s, write + +\[ +L_s=J^{\mathsf T}+B_s,\qquad B_sJ=0,\qquad +C_s=I+JB_s. +\] + +Each symbol includes its actual stage routes. In particular, \(B_s\) +and \(B_t\) are different operators when \(s\ne t\). + +Suppose the target bank contains \(L_sy\) on its selected FULL rows +and \(y_R\) on its other hole rows. This is a unit encoding of arbitrary +y. Equivalently, its selected and ordinary input values can be chosen +independently. + +At a later current entry t, the literal views give local target types +\(Q_p\) on P and I on R. Keep the original ordinary target paths. On +each selected carrier, replace the removed path by + +\[ +Q_p\longrightarrow F_9. +\] + +This is the operator \(F_9q_p\), of native rank eight. The program gives +an exact positive H8 recipe for every selected port. It uses the actual +orthogonal port chart, with its eight complementary axes first, and an +explicit output translation. The full Z4 phase polynomial is checked. + +After the retained sweep and these carrier paths, all X fields and +all selected Y fields are FULL. Add \(L_sE_tx\) to the selected target +bank at that cut. The outputs are + +\[ +X_{\rm out}=F_9x,\qquad +Y_{P,\rm out}=F_9L_s(y+E_tx),\qquad +Y_{R,\rm out}=F_9q_R(y+E_tx)_R. +\] + +The same reader \(L_s\) has been retained. No old-stage target read was +used. The input reader was not replaced by \(L_t\). + +## A query through sixteen existing source carriers + +The actual response has \(E_t[P,P]=0\). It also has + +\[ +E_t=I+A_tL_t,\qquad +L_t=J^{\mathsf T}+B_t,\qquad C_t=I+JB_t, +\] + +where \(A_t=(E_t-I)J\). These are routed operator identities. Since +\(L_sJ=I\), direct multiplication gives + +\[ +L_sE_tC_t^{-1} + = B_s-B_t + (L_sE_tJ)J^{\mathsf T}. +\] + +No factor at stage s is commuted through a factor at stage t. Put +\(M_{s,t}=L_sE_tJ\). Use this complete order at the FULL cut: + +1. Add \(B_sX_R\) to \(Y_P\). +2. Add the current \(X_P\) to \(Y_P\). +3. Apply \(C_t\) to X. +4. Subtract the new \(X_P\) from \(Y_P\). +5. Add \(M_{s,t}X_P\) to \(Y_P\). +6. Apply \(C_t^{-1}\) to X. + +Steps 2 and 4 contribute \(-B_tX_R\). The query in step 5 reads the +current centres \(L_tX\) from the existing sixteen X fields. Thus the +complete increment is \(L_sE_tX_{\rm original}\). +Step 6 restores every X field. Every target baseline is retained. +No scratch field or zero input is used. + +This factorization avoids an inverse of E. In particular, it needs no +division by five or seven. Both C words are the emitted dyadic shears +from the normalized row-capture packet. + +## Actual owner paths and phases + +The checker binds the three D25 pairs \((s,t)=(0,1),(0,2),(1,2)\). +For a term with intermediate port j and final source port r, the +complete owner multiplier is + +\[ +A=\rho_{s,p}\rho_{s,j}\rho_{t,j}\rho_{t,r}. +\] + +The coefficient is \(L_{p,j}E_{j,r}\). The full query \(L_sE_t\) has +3,808 such terms. Its selected-source part \(M_{s,t}\) has 696 terms. +Each of the latter reads one of the sixteen selected X fields. +Different owner paths are kept as different terms. + +All factors of A act within the completed prefix at level t. They fix +every uncompleted axis. A is orthogonal. Therefore + +\[ +F_{9+8t}P_AF_{9+8t}^{-1}=X_{\delta_A}P_A. +\] + +The program computes the entire Z4 difference polynomial to obtain +\(\delta_A\). It verifies that its odd and quadratic parts vanish. +It also checks the inverse map, whose route is \(A^{-1}\) and whose +translation is \(A^{-1}\delta_A\). + +The owner read is \(h\mapsto hA\). The payload map \(P_A\) expresses the +source chart in the target chart. Together with the translation, these +are one field/address map. They are not two independent uses of the +source data. + +For each middle-query term, apply that map to its source field, add +the required scalar multiple to the selected Y field, and apply the +inverse map to the source. This restores the full arbitrary source +array before the next term. Right multiplication by A is a cover +bijection, so this procedure is legal on the regular orthogonal cover. + +Step 1 uses the literal past-stage FULL views on 96 source fields and +16 target fields. Steps 3 and 6 use the current-stage FULL views on +all 112 source fields. The checker verifies these full phase equations. +Steps 2 and 4 are same-port copies between FULL fields. + +The checker also expands both sides of the query identity as exact +sums of owner paths. It compares coefficients only after the complete +route matrices agree. This prevents a false cancellation between +different body owners. + +## Invoice and bounds + +The conservative query invoice for each checked pair is: + +| Part | Real scalar primitives | Monomial map calls | +| --- | ---: | ---: | +| Past-reader complement query | 1,760 | 224 | +| Two same-port copies | 256 | 0 | +| Current C and its inverse | 3,520 | 448 | +| Selected-source middle query | 5,632 | 1,392 | +| Total | 11,168 | 2,064 | + +The middle query scales each large target by four, executes its +integer-coefficient additions, then divides that target by four. +The small targets need no such scale. This uses only dyadic units. +The two copies use all sixteen selected ports. + +The query uses no native child and no extra field. A conservative +triangle-inequality bound for every scalar prefix is 972, relative to +unit one-norm inputs at the query entrance. The checker derives this +bound from the literal scalar order. It also bounds the new binary +denominator height by three. These are bounds for one query. They are +not a recursive precision certificate. + +The retained native word has scalar price 6,456. Replacing its selected +paths by sixteen H8 calls gives the prospective local profile + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H8. +``` + +Its native rank is 1,792, equal to the old rank. The retained word plus +the new query has scalar price 17,624. The 2,064 query maps are additional +to native wrappers and ordinary boundary maps. Their finite cost and +the child hosting must still be included in a complete supplier. + +## Reuse scope + +The operator proof applies whenever the later FULL cut admits both +stage routes, the pivot normalization \(L_sJ=I\) holds, and the ordinary +target paths do not read a selected target. These are concrete +conditions. They do not require a common response across stages. + +This packet verifies those conditions for the actual D25 forward +services and all three possible past/current stage pairs. It does not +assert the same input type for a backward service. That service needs +its own dual code and native proof. + +Run `check_reuse.py` normally and with `python3 -O`, with separate output +directories. The two program files and the two receipts must be byte +equal. The immutable formation packet remains unchanged. + +No publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/check_integration.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/check_integration.py new file mode 100644 index 0000000000..3f95ba2894 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/check_integration.py @@ -0,0 +1,341 @@ +"""Bind the native carrier prefix to the actual D25 reuse dispatcher.""" + +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import argparse +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PINS = { + "prefix": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz", + "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e", + ), + "prefix_freeze": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "fixed-reader-reuse-20261020/PREFIX-FREEZE.json", + "fc3cef0e499e5bc85c25bb0fc88f5ecd12e44b66799e3d793dac37de8d88d26e", + ), + "native_phase_review": ( + "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c", + ), + "query": ( + "bridge-access-20261017/row-capture-access-20261020/" + "reuse-normal/REUSE-PROGRAM.json", + "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b", + ), + "query_freeze": ( + "bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json", + "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf", + ), + "literal_query": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz", + "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a", + ), + "literal_query_freeze": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "fixed-reader-reuse-20261020/QUERY-FREEZE.json", + "f111a90f7403f93494e9d1f83ae35dbf7dd72eddc8c9f8bf730d677b4a31402d", + ), + "views": ( + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), + "phase": ( + "bridge-access-20261017/check_bridge_access.py", + "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111", + ), +} +UNIT = [1 << j for j in range(25)] + + +def need(test, label): + if not test: + raise ValueError(label) + + +def raw_source(name): + path, pin = PINS[name] + raw = (LANES / path).read_bytes() + if path.endswith(".gz"): + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source: " + name) + return raw + + +def rank(vectors): + pivots = {} + for value in vectors: + while value: + bit = value.bit_length() - 1 + if bit not in pivots: + pivots[bit] = value + break + value ^= pivots[bit] + return len(pivots) + + +def add(target, source, coefficient): + for column, value in source.items(): + target[column] = target.get(column, F(0)) + coefficient * value + if not target[column]: + del target[column] + + +def price(op, value): + n, d = abs(value.numerator), value.denominator + need(n and d & (d - 1) == 0, "Nonzero dyadic coefficient") + if op == "scale": + need(n & (n - 1) == 0, "The scale is a dyadic unit") + return 2 * (abs(n.bit_length() - d.bit_length()) + (value < 0)) + return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1) + + +def check_prefix(word, response, selected): + live = list(word["start"]) + state = [{p: F(1)} for p in range(640)] + profile = Counter() + scalar_price = 0 + for index, event in enumerate(word["events"]): + if event[0] == "native": + _, target, old, new, mass, key = event + need(live[target] == old, "Native input frame") + left, right = word["frames"][old], word["frames"][new] + need(rank(left + right) == len(right), "Nested native frame") + need(len(right) - len(left) == mass + == word["native_recipes"][key]["rank"], "Native rank") + live[target] = new + profile[mass] += 1 + else: + need(event[0] == "scalar", "Prefix event grammar") + (_, (op, target, source, coefficient), frame) = event + value = F(coefficient) + need(live[target] == frame, "Scalar target frame") + if op == "add": + need(source != target and live[source] == frame, + "Scalar source frame") + need(source not in {112 + p for p in selected}, + "The prefix does not read a selected target") + add(state[target], state[source], value) + else: + need(op == "scale", "Prefix scalar grammar") + state[target] = {j: value * v for j, v in state[target].items()} + scalar_price += price(op, value) + if index == 2389: + need(all(live[p] == 1 for p in range(112)), + "All sources are FULL after the complete retained core") + expected = [{p: F(1)} for p in range(640)] + for p in range(112): + if p not in selected: + add(expected[112 + p], response[p], F(1)) + need(state == expected, "The full 640-column carrier prefix") + need(live == word["final"], "The full prefix frame ledger") + need(all(live[p] == live[112 + p] == 1 for p in selected), + "Every selected query source and target is FULL") + need(all(state[p] == {p: F(1)} for p in range(224, 640)), + "All 416 arbitrary helper fields are restored") + need(len(word["events"]) == 2406 + and word["stage_ranges"]["retained_core"] == [0, 2390] + and word["stage_ranges"]["selected_line_progress"] == [2390, 2406] + and "late_query" not in word["stage_ranges"], "The exact prefix cut") + need(profile == {1: 1392, 2: 64, 3: 48, 8: 16} + and scalar_price == 6456, "The complete prefix invoice") + source_views = {v["port"]: v for v in word["input_views"] if v["role"] == "source"} + selected_views = [v for v in word["input_views"] if v["role"] == "selected_target"] + need(set(source_views) == set(range(112)) and len(selected_views) == 16, + "The complete input adapter stock") + for view in selected_views: + source = source_views[view["port"]] + need(view["field"] == 112 + view["port"] and view["port"] in selected + and view["source_entry_port"] == view["port"], "Selected input adapter field") + need(all(view[key] == source[key] for key in ("frame", "rank", "left", "right")), + "The selected input adapter equals the source adapter") + need({v["port"] for v in word["output_views"]} == set(range(112)) - selected, + "Only ordinary target output adapters remain") + need(len(word["input_views"]) == 128 and len(word["output_views"]) == 96, + "The exact adapter count") + return { + "native_profile": dict(sorted(profile.items())), + "native_rank": sum(k * v for k, v in profile.items()), + "native_children": sum(profile.values()), + "scalar_primitives": scalar_price, + "arbitrary_input_columns": 640, + "restored_arbitrary_helper_fields": 416, + "input_adapters": 128, "ordinary_output_adapters": 96, + "native_phase_review_is_pinned_dependency": True, + } + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + sources = {key: raw_source(key) for key in PINS} + prefix, query, views = (json.loads(sources[key]) for key in ("prefix", "query", "views")) + literal_query = json.loads(sources["literal_query"]) + need(literal_query["native_prefixes"] == prefix["providers"], + "The literal query uses this exact complete native prefix") + need(literal_query["source_pins"]["query"]["sha256"] == PINS["query"][1], + "The literal query uses this exact path program") + spec = importlib.util.spec_from_file_location("reuse_dispatcher_phase", LANES / PINS["phase"][0]) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + selected = set(prefix["selected_ports"]) + need(prefix["selected_ports"] == query["pivots"], "The exact carried pivot set") + response = [{int(j): F(v) for j, v in row.items()} for row in prefix["response"]] + reports = {name: check_prefix(word, response, selected) + for name, word in prefix["providers"].items()} + records = {(v["stage"], v["port"]): v for v in views["entries"]} + stage_programs, counts = [], Counter() + for t in (1, 2): + full_before = [(v, 1) for v in UNIT[:9 + 8 * (t - 1)]] + full_after = [(v, 1) for v in UNIT[:9 + 8 * t]] + exterior = [(v, 1) for v in UNIT[9:9 + 8 * t]] + data_entries, data_exits = [], [] + for side, offset in (("X", 0), ("Y", 112)): + for p in range(112): + record = records[t, p] + rho, q, align = (record[key] for key in + ("route_columns", "q", "literal_stage_alignment")) + need(all((a & b).bit_count() % 2 == int(i == j) + for i, a in enumerate(rho) for j, b in enumerate(rho)), + "Regular-cover orthogonal route") + need([phase.act(rho, v) for v in rho] == UNIT + and phase.act(rho, q) == q, "The route fixes its intrinsic line") + need(rho[9 + 8 * t:] == UNIT[9 + 8 * t:], "No future coordinate is changed") + full_input = side == "X" or p in selected + before = full_before + ([] if full_input else [(q, -1)]) + entry_delta = phase.act(rho, align["entry_" + side]) + actual = phase.add_phase( + phase.product([(phase.act(rho, v), n) for v, n in before]), + phase.line(entry_delta, 2)) + expected = phase.product(exterior + ([(q, 1)] if full_input else [])) + need(actual == expected, "Exact adjacent current entry phase") + counts["entry_phase_equations"] += 1 + after = full_after + ([] if full_input else [(q, -1)]) + exit_key = "exit_X" if full_input else "exit_Y" + exit_delta = align[exit_key] + actual = phase.add_phase( + phase.product([(phase.act(rho, v), n) for v, n in after]), + phase.line(exit_delta, 2)) + need(actual == phase.product(after), "Exact global output phase") + counts["exit_phase_equations"] += 1 + data_entries.append({ + "field": offset + p, "port": p, "side": side, + "owner_from_body": "h=d*rho", + "route_columns": rho, + "translation_before_route": align["entry_" + side], + "translation_after_route": entry_delta, + "intrinsic_input": "Q_p" if full_input else "I", + }) + data_exits.append({ + "field": offset + p, "port": p, "side": side, + "owner_from_body": "h=d*rho", + "route_columns": rho, + "translation_after_route": exit_delta, + "global_output": "FULL" if full_input else "FULL*q_p", + "literal_translation_key": exit_key, + }) + stage_programs.append({ + "service_stage": t, "physical_input_level": t - 1, + "physical_output_level": t, + "common_exterior_axes": [v for v, _ in exterior], + "DATA_entry": data_entries, "DATA_exit": data_exits, + }) + invocations = [] + for number, pair in enumerate(query["pairs"]): + s, t = pair["reader_stage"], pair["service_stage"] + need((s, t) in ((0, 1), (0, 2), (1, 2)) and s < t, + "The checked past/current pair") + need(pair["real_scalar_primitives"] == 11168 + and pair["monomial_map_calls"] == 2064 + and pair["native_children_in_query"] == 0, "The complete routed query invoice") + literal = literal_query["queries"][f"{s}:{t}"] + need(literal["reader_stage"] == s and literal["service_stage"] == t, + "The exact literal query stage labels") + need(sum(event[0] == "map" for event in literal["events"]) == 2064, + "All literal query maps are retained") + need(sum(price(event[1], F(event[4])) for event in literal["events"] + if event[0] == "scalar") == 11168, "The literal scalar query price") + need(all(record["port"] in selected for record in query["carrier_recipes"]), + "Only selected carrier paths are added") + for provider in prefix["providers"]: + invocations.append({ + "provider": provider, "reader_stage": s, "service_stage": t, + "physical_input_level": t - 1, + "physical_output_level": t, + "stage_view_record": t - 1, "query_pair_record": number, + "ordered_blocks": [ + {"op": "DATA_entry", "record": t - 1, "map_calls": 224}, + {"op": "native_input_adapters", "source": "prefix", + "provider": provider, "map_calls": 128}, + {"op": "complete_native_carrier_cover_sweep", "source": "prefix", + "provider": provider, "event_range": [0, 2406]}, + {"op": "ordinary_output_adapters", "source": "prefix", + "provider": provider, "map_calls": 96}, + {"op": "DATA_exit", "record": t - 1, "map_calls": 224}, + {"op": "complete_cover_barrier"}, + {"op": "fixed_past_reader_query", "source": "query", + "pair_record": number, "literal_source": "literal_query", + "literal_key": f"{s}:{t}", "map_calls": 2064}, + ], + "scalar_primitives": 17624, + "map_call_bound": { + "DATA": 448, "local_endpoint_adapters": 224, + "native_side_maps": 3040, "late_query": 2064, + "total": 5776, + }, + }) + need(counts == {"entry_phase_equations": 448, "exit_phase_equations": 448}, + "The complete adjacent D25 boundary census") + payload = { + "schema": "fixed-reader-global-dispatcher-v1", "source_pins": PINS, + "dimension": 25, "selected_ports": prefix["selected_ports"], + "stage_views": stage_programs, "invocations": invocations, + "contract": { + "input": "(Fprev*x, Fprev*diag(I_P,q_R)*w)", + "output": "(Fnew*x, Fnew*diag(I_P,q_R)*(w+A_st*x))", + "response_rows_P": "L_s*E_t", + "response_rows_R": "(E_t)_R", + "reader_label_is_not_physical_level": True, + "arbitrary_independent_selected_records": True, + "full_native_sweep_before_global_query": True, + }, + "owner_contract": { + "cover": "Regular O(25,2)", + "data_partition": "For each field, d -> d*rho_(t,p) is a bijection.", + "native_helpers": "Use the inherited 416-field helper contract; restore it per body.", + "helper_hosting_reproved_here": False, + }, + "native_phase_validation": "Use the pinned independent line-entry review.", + "complete_supplier_claimed": False, + } + args.output.mkdir(parents=True, exist_ok=False) + raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode() + (args.output / "DISPATCHER.json").write_bytes(raw) + receipt = { + "status": "PASS_FIXED_READER_NATIVE_D25_DISPATCHER", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "program_sha256": sha256(raw).hexdigest(), "source_pins": PINS, + "providers": reports, "boundary_checks": dict(counts), + "reader_service_pairs": [[0, 1], [0, 2], [1, 2]], + "scalar_primitives": 17624, "query_map_calls": 2064, + "total_monomial_call_bound": 5776, + "inherited_helper_hosting_still_required": True, + "complete_supplier_claimed": False, + } + (args.output / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/check_reuse.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/check_reuse.py new file mode 100644 index 0000000000..641266ee7f --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/check_reuse.py @@ -0,0 +1,321 @@ +"""Check the fixed-reader query at actual completed D25 cuts.""" + +from collections import defaultdict +from fractions import Fraction as F +from functools import cache +from hashlib import sha256 +import argparse +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +ACCESS_PIN = "48baba6e09b787924c496c8d4ce89c9dd3f77585946516f90ff8803d45adb5cd" +UNIT = tuple(1 << j for j in range(25)) +IDENTITY = UNIT + + +def need(value, message): + if not value: + raise ValueError(message) + + +def module(path, name): + spec = importlib.util.spec_from_file_location(name, path) + out = importlib.util.module_from_spec(spec) + spec.loader.exec_module(out) + return out + + +def act(a, value): + out = 0 + while value: + bit = value & -value + out ^= a[bit.bit_length() - 1] + value ^= bit + return out + + +@cache +def compose(a, b): + return tuple(act(a, value) for value in b) + + +def transpose(a): + return tuple(sum(((a[j] >> i) & 1) << j for j in range(25)) + for i in range(25)) + + +def accumulate(row, key, value): + row[key] += value + if not row[key]: + del row[key] + + +def compose_rows(left, right): + out = [] + for row in left: + acc = defaultdict(F) + for (j, a), value in row.items(): + for (r, b), other in right[j].items(): + accumulate(acc, (r, compose(a, b)), value * other) + out.append(dict(acc)) + return out + + +def price(op, value): + n, d = abs(value.numerator), value.denominator + need(n and d & (d - 1) == 0, "Nonzero dyadic coefficient") + if op == "scale": + need(n & (n - 1) == 0, "Scale is a dyadic unit") + return 2 * (abs(n.bit_length() - d.bit_length()) + (value < 0)) + return 2 * (3 + n.bit_length() - 1 + n.bit_count() + d.bit_length() - 1) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, default=HERE / "reuse-normal") + args = parser.parse_args() + access_path = HERE / "check_access.py" + need(sha256(access_path.read_bytes()).hexdigest() == ACCESS_PIN, + "Frozen formation checker") + source = module(access_path, "fixed_reader_source") + capture = json.loads(source.raw_source("capture")) + native = json.loads(source.raw_source("native")) + views = json.loads(source.raw_source("views")) + source.raw_source("phase") + phase = module(LANES / source.PINS["phase"][0], "fixed_reader_phase") + pset = set(source.PIVOTS) + pindex = {p: i for i, p in enumerate(source.PIVOTS)} + e = source.matrix(capture["response"]) + l = source.matrix(capture["centre_reader"]) + need(all(not (set(e[p]) & pset) for p in pset), "Actual E[P,P] is zero") + rho = {(v["stage"], v["port"]): tuple(v["route_columns"]) + for v in views["entries"]} + records = {(v["stage"], v["port"]): v for v in views["entries"]} + code = capture["scalar_word"] + inverse = capture["inverse_scalar_word"] + need(sum(price(g[0], F(g[3])) for g in code) == 1760, + "Current capture scalar price") + need(sum(price(g[0], F(g[3])) for g in inverse) == 1760, + "Current capture inverse scalar price") + need(all(g[2] not in pset for g in code if g[0] == "add"), + "Current capture reads only complement") + for provider in native["providers"].values(): + retained_price = sum( + price(event[1][0], F(event[1][3])) + for event in provider["forward"]["events"] + if event[0] == "scalar" and event[1][1] not in {112 + p for p in pset}) + need(retained_price == 6456, "Retained scalar word invoice") + carrier_recipes = [] + for p in source.PIVOTS: + q = records[0, p]["q"] + chart = phase.chart(q)[:9] + basis = tuple(chart[1:] + chart[:1]) + UNIT[9:] + need(compose(transpose(basis), basis) == IDENTITY, + "Rank-eight carrier basis") + expected = phase.product([(x, 1) for x in UNIT[:9]] + [(q, -1)]) + head = phase.product([(x, 1) for x in basis[:8]]) + delta = phase.add_phase(expected, phase.negative(head)) + need(delta[0] == delta[2] == 0, "Carrier remainder is a translation") + need(phase.add_phase(head, phase.line(delta[1], 2)) == expected, + "Exact F9 q carrier recipe") + carrier_recipes.append({ + "port": p, "q": q, "rank": 8, "basis_columns": basis, + "inverse_columns": transpose(basis), + "output_translation": delta[1], + "input_frame": "Q_p", "output_frame": "F9", + }) + + def routed(rows, targets, stage): + return [{ + (r, compose(rho[stage, p], rho[stage, r])): value + for r, value in row.items() + } for p, row in zip(targets, rows)] + + def full_view(stage, port, level): + record = records[stage, port] + a = rho[stage, port] + delta = record["literal_stage_alignment"]["exit_X"] + full = [(x, 1) for x in UNIT[:9 + 8 * level]] + actual = phase.add_phase( + phase.product([(act(a, x), n) for x, n in full]), + phase.line(delta, 2)) + need(actual == phase.product(full), "Literal past/current FULL view") + return {"port": port, "route_columns": a, "translation": delta} + + all_pairs = [] + for s, t in ((0, 1), (0, 2), (1, 2)): + ls = routed(l, source.PIVOTS, s) + lt = routed(l, source.PIVOTS, t) + et = routed(e, range(112), t) + direct = compose_rows(ls, et) + middle = [ + {(r, a): v for (r, a), v in row.items() if r in pset} + for row in direct + ] + need(sum(map(len, direct)) == 3808, "Complete direct query census") + need(sum(map(len, middle)) == 696, "Selected-source query census") + lifted_lt = [{} for _ in range(112)] + for p, row in zip(source.PIVOTS, lt): + lifted_lt[p] = row + factored = compose_rows(middle, lifted_lt) + for i, p in enumerate(source.PIVOTS): + row = defaultdict(F, factored[i]) + for key, value in ls[i].items(): + if key[0] not in pset: + accumulate(row, key, value) + for key, value in lt[i].items(): + if key[0] not in pset: + accumulate(row, key, -value) + need(dict(row) == direct[i], + "Full noncommutative owner-path query identity") + full = [(x, 1) for x in UNIT[:9 + 8 * t]] + full_phase = phase.product(full) + routes = {} + route_table = [] + query = [] + scalar_bill = 0 + map_count = 0 + for p, row in zip(source.PIVOTS, middle): + denominator = max(v.denominator for v in row.values()) + if denominator != 1: + query.append(["scale", p, None, str(denominator), None]) + scalar_bill += price("scale", F(denominator)) + for (r, a), value in sorted(row.items()): + need(r in pset and a != IDENTITY, "Selected source, actual route") + need(a[9 + 8 * t:] == UNIT[9 + 8 * t:], + "Route fixes every uncompleted axis") + ai = transpose(a) + need(compose(ai, a) == compose(a, ai) == IDENTITY, + "Composed query route is orthogonal") + if a not in routes: + transformed = phase.product([(act(a, x), n) for x, n in full]) + difference = phase.add_phase(full_phase, phase.negative(transformed)) + need(difference[0] == difference[2] == 0, + "FULL conjugate is a pure translation and address map") + delta = difference[1] + reverse = phase.add_phase( + full_phase, + phase.negative(phase.product([(act(ai, x), n) for x, n in full]))) + need(reverse == phase.line(act(ai, delta), 2), + "Exact inverse source map") + routes[a] = len(route_table) + route_table.append({ + "columns": a, "inverse_columns": ai, + "FULL_translation": delta, + "inverse_FULL_translation": act(ai, delta), + }) + integer = denominator * value + need(integer.denominator == 1, "Normalized query integer") + query.append(["mapped_add_restore", p, r, str(integer), routes[a]]) + scalar_bill += price("add", integer) + map_count += 2 + if denominator != 1: + query.append(["scale", p, None, str(F(1, denominator)), None]) + scalar_bill += price("scale", F(1, denominator)) + need(scalar_bill == 5632 and map_count == 1392, "Middle query invoice") + old_reader_views = [full_view(s, p, t) for p in range(112)] + current_code_views = [full_view(t, p, t) for p in range(112)] + # All view maps preserve row one-norm. Use the triangle inequality + # at each scalar step to obtain a conservative prefix bound. + bounds = [F(1) for _ in range(224)] + grid = [0 for _ in range(224)] + peak = F(1) + peak_grid = 0 + + def apply_bound(op, target, origin, value): + nonlocal peak, peak_grid + if op == "scale": + bounds[target] *= abs(value) + grid[target] = max( + 0, grid[target] + value.denominator.bit_length() + - abs(value.numerator).bit_length()) + else: + bounds[target] += abs(value) * bounds[origin] + grid[target] = max(grid[target], grid[origin] + + value.denominator.bit_length() - 1) + peak = max(peak, bounds[target]) + peak_grid = max(peak_grid, grid[target]) + + for op, p, r, value in code: + apply_bound(op, 112 + p, r, F(value)) + for p in source.PIVOTS: + apply_bound("add", 112 + p, p, F(1)) + for op, p, r, value in code: + apply_bound(op, p, r, F(value)) + for p in source.PIVOTS: + apply_bound("add", 112 + p, p, F(-1)) + for op, p, r, value, _ in query: + apply_bound("add" if op == "mapped_add_restore" else op, + 112 + p, r, F(value)) + for op, p, r, value in inverse: + apply_bound(op, p, r, F(value)) + need(peak_grid == 3, "Additional binary grid bound") + all_pairs.append({ + "reader_stage": s, "service_stage": t, + "chronology": [ + "Y_P += B_s X_R through old_reader_views", + "Y_P += X_P", + "X <- C_t X through current_code_views", + "Y_P -= X_P", + "Y_P += (L_s E_t selector_P) X_P through middle_query", + "X <- C_t^-1 X through current_code_views", + ], + "old_reader_views": old_reader_views, + "old_reader_view_ports": { + "X": sorted(set(range(112)) - pset), "Y": source.PIVOTS}, + "current_code_views": current_code_views, + "middle_routes": route_table, + "middle_query": query, + "direct_owner_paths_checked": 3808, + "selected_source_paths": 696, + "real_scalar_primitives": 11168, + "monomial_map_calls": 2064, + "native_children_in_query": 0, "extra_fields": 0, + "conservative_prefix_one_norm": str(peak), + "additional_binary_grid_levels_at_most": 3, + "odd_divisions": 0, + }) + payload = { + "schema": "fixed-row-reader-reuse-v1", + "formation_checker_sha256": ACCESS_PIN, "source_pins": source.PINS, + "pivots": source.PIVOTS, "carrier_recipes": carrier_recipes, + "pairs": all_pairs, + "input_Y": "Selected Q_p L_s y; complement y_R, in the current body.", + "output_Y": "Selected F9 L_s(y+E_t x); complement F9 q_R(y+E_t x)_R.", + "restored_source_fields": 112, "unchanged_outside_fields": 416, + "reuse_native_profile": {"1": 1392, "2": 64, "3": 48, "8": 16}, + "reuse_native_rank": 1792, + "retained_scalar_primitives": 6456, + "retained_word_plus_query_scalar_primitives": 17624, + "complete_local_emitter_bound_here": False, + "recursive_hosting_bound_here": False, + "backward_companion_bound_here": False, + } + args.output.mkdir(parents=True, exist_ok=True) + raw = (json.dumps(payload, sort_keys=True, indent=2) + "\n").encode() + (args.output / "REUSE-PROGRAM.json").write_bytes(raw) + receipt = { + "status": "PASS_FIXED_READER_D25_REUSE_QUERY", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "program_sha256": sha256(raw).hexdigest(), + "source_pins": source.PINS, + "stage_pairs": [[0, 1], [0, 2], [1, 2]], + "direct_owner_paths_per_pair": 3808, + "selected_source_paths_per_pair": 696, + "query_scalar_primitives": 11168, "query_monomial_maps": 2064, + "carrier_rank8_phase_recipes": 16, + "additional_binary_grid_levels_at_most": 3, + "prefix_one_norm_bounds": [p["conservative_prefix_one_norm"] for p in all_pairs], + "complete_supplier_claimed": False, + } + (args.output / "REUSE-CHECKS.json").write_text( + json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/CHECKS.json new file mode 100644 index 0000000000..27d453f43b --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/CHECKS.json @@ -0,0 +1,100 @@ +{ + "boundary_checks": { + "entry_phase_equations": 448, + "exit_phase_equations": 448 + }, + "checker_sha256": "c178c339b0398d7e6f0232d68d681527dfaed70da10941f09bd9db3f141887fb", + "complete_supplier_claimed": false, + "inherited_helper_hosting_still_required": true, + "program_sha256": "35772f75d983661a21f6a6ba69d06fb7bcdcaaaf20ec7ad838863541a8581e24", + "providers": { + "base": { + "arbitrary_input_columns": 640, + "input_adapters": 128, + "native_children": 1520, + "native_phase_review_is_pinned_dependency": true, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_rank": 1792, + "ordinary_output_adapters": 96, + "restored_arbitrary_helper_fields": 416, + "scalar_primitives": 6456 + }, + "extra": { + "arbitrary_input_columns": 640, + "input_adapters": 128, + "native_children": 1520, + "native_phase_review_is_pinned_dependency": true, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_rank": 1792, + "ordinary_output_adapters": 96, + "restored_arbitrary_helper_fields": 416, + "scalar_primitives": 6456 + } + }, + "query_map_calls": 2064, + "reader_service_pairs": [ + [ + 0, + 1 + ], + [ + 0, + 2 + ], + [ + 1, + 2 + ] + ], + "scalar_primitives": 17624, + "source_pins": { + "literal_query": [ + "new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz", + "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a" + ], + "literal_query_freeze": [ + "new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json", + "f111a90f7403f93494e9d1f83ae35dbf7dd72eddc8c9f8bf730d677b4a31402d" + ], + "native_phase_review": [ + "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c" + ], + "phase": [ + "bridge-access-20261017/check_bridge_access.py", + "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111" + ], + "prefix": [ + "new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz", + "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e" + ], + "prefix_freeze": [ + "new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json", + "fc3cef0e499e5bc85c25bb0fc88f5ecd12e44b66799e3d793dac37de8d88d26e" + ], + "query": [ + "bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-PROGRAM.json", + "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b" + ], + "query_freeze": [ + "bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json", + "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf" + ], + "views": [ + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + ] + }, + "status": "PASS_FIXED_READER_NATIVE_D25_DISPATCHER", + "total_monomial_call_bound": 5776 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json new file mode 100644 index 0000000000..83e7eed134 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/row-capture-access-20261020/integration-v2-normal/DISPATCHER.json @@ -0,0 +1,32749 @@ +{ + "complete_supplier_claimed": false, + "contract": { + "arbitrary_independent_selected_records": true, + "full_native_sweep_before_global_query": true, + "input": "(Fprev*x, Fprev*diag(I_P,q_R)*w)", + "output": "(Fnew*x, Fnew*diag(I_P,q_R)*(w+A_st*x))", + "reader_label_is_not_physical_level": true, + "response_rows_P": "L_s*E_t", + "response_rows_R": "(E_t)_R" + }, + "dimension": 25, + "invocations": [ + { + "map_call_bound": { + "DATA": 448, + "late_query": 2064, + "local_endpoint_adapters": 224, + "native_side_maps": 3040, + "total": 5776 + }, + "ordered_blocks": [ + { + "map_calls": 224, + "op": "DATA_entry", + "record": 0 + }, + { + "map_calls": 128, + "op": "native_input_adapters", + "provider": "base", + "source": "prefix" + }, + { + "event_range": [ + 0, + 2406 + ], + "op": "complete_native_carrier_cover_sweep", + "provider": "base", + "source": "prefix" + }, + { + "map_calls": 96, + "op": "ordinary_output_adapters", + "provider": "base", + "source": "prefix" + }, + { + "map_calls": 224, + "op": "DATA_exit", + "record": 0 + }, + { + "op": "complete_cover_barrier" + }, + { + "literal_key": "0:1", + "literal_source": "literal_query", + "map_calls": 2064, + "op": "fixed_past_reader_query", + "pair_record": 0, + "source": "query" + } + ], + "physical_input_level": 0, + "physical_output_level": 1, + "provider": "base", + "query_pair_record": 0, + "reader_stage": 0, + "scalar_primitives": 17624, + "service_stage": 1, + "stage_view_record": 0 + }, + { + "map_call_bound": { + "DATA": 448, + "late_query": 2064, + "local_endpoint_adapters": 224, + "native_side_maps": 3040, + "total": 5776 + }, + "ordered_blocks": [ + { + "map_calls": 224, + "op": "DATA_entry", + "record": 0 + }, + { + "map_calls": 128, + "op": "native_input_adapters", + "provider": "extra", + "source": "prefix" + }, + { + "event_range": [ + 0, + 2406 + ], + "op": "complete_native_carrier_cover_sweep", + "provider": "extra", + "source": "prefix" + }, + { + "map_calls": 96, + "op": "ordinary_output_adapters", + "provider": "extra", + "source": "prefix" + }, + { + "map_calls": 224, + "op": "DATA_exit", + "record": 0 + }, + { + "op": "complete_cover_barrier" + }, + { + "literal_key": "0:1", + "literal_source": "literal_query", + "map_calls": 2064, + "op": "fixed_past_reader_query", + "pair_record": 0, + "source": "query" + } + ], + "physical_input_level": 0, + "physical_output_level": 1, + "provider": "extra", + "query_pair_record": 0, + "reader_stage": 0, + "scalar_primitives": 17624, + "service_stage": 1, + "stage_view_record": 0 + }, + { + "map_call_bound": { + "DATA": 448, + "late_query": 2064, + "local_endpoint_adapters": 224, + "native_side_maps": 3040, + "total": 5776 + }, + "ordered_blocks": [ + { + "map_calls": 224, + "op": "DATA_entry", + "record": 1 + }, + { + "map_calls": 128, + "op": "native_input_adapters", + "provider": "base", + "source": "prefix" + }, + { + "event_range": [ + 0, + 2406 + ], + "op": "complete_native_carrier_cover_sweep", + "provider": "base", + "source": "prefix" + }, + { + "map_calls": 96, + "op": "ordinary_output_adapters", + "provider": "base", + "source": "prefix" + }, + { + "map_calls": 224, + "op": "DATA_exit", + "record": 1 + }, + { + "op": "complete_cover_barrier" + }, + { + "literal_key": "0:2", + "literal_source": "literal_query", + "map_calls": 2064, + "op": "fixed_past_reader_query", + "pair_record": 1, + "source": "query" + } + ], + "physical_input_level": 1, + "physical_output_level": 2, + "provider": "base", + "query_pair_record": 1, + "reader_stage": 0, + "scalar_primitives": 17624, + "service_stage": 2, + "stage_view_record": 1 + }, + { + "map_call_bound": { + "DATA": 448, + "late_query": 2064, + "local_endpoint_adapters": 224, + "native_side_maps": 3040, + "total": 5776 + }, + "ordered_blocks": [ + { + "map_calls": 224, + "op": "DATA_entry", + "record": 1 + }, + { + "map_calls": 128, + "op": "native_input_adapters", + "provider": "extra", + "source": "prefix" + }, + { + "event_range": [ + 0, + 2406 + ], + "op": "complete_native_carrier_cover_sweep", + "provider": "extra", + "source": "prefix" + }, + { + "map_calls": 96, + "op": "ordinary_output_adapters", + "provider": "extra", + "source": "prefix" + }, + { + "map_calls": 224, + "op": "DATA_exit", + "record": 1 + }, + { + "op": "complete_cover_barrier" + }, + { + "literal_key": "0:2", + "literal_source": "literal_query", + "map_calls": 2064, + "op": "fixed_past_reader_query", + "pair_record": 1, + "source": "query" + } + ], + "physical_input_level": 1, + "physical_output_level": 2, + "provider": "extra", + "query_pair_record": 1, + "reader_stage": 0, + "scalar_primitives": 17624, + "service_stage": 2, + "stage_view_record": 1 + }, + { + "map_call_bound": { + "DATA": 448, + "late_query": 2064, + "local_endpoint_adapters": 224, + "native_side_maps": 3040, + "total": 5776 + }, + "ordered_blocks": [ + { + "map_calls": 224, + "op": "DATA_entry", + "record": 1 + }, + { + "map_calls": 128, + "op": "native_input_adapters", + "provider": "base", + "source": "prefix" + }, + { + "event_range": [ + 0, + 2406 + ], + "op": "complete_native_carrier_cover_sweep", + "provider": "base", + "source": "prefix" + }, + { + "map_calls": 96, + "op": "ordinary_output_adapters", + "provider": "base", + "source": "prefix" + }, + { + "map_calls": 224, + "op": "DATA_exit", + "record": 1 + }, + { + "op": "complete_cover_barrier" + }, + { + "literal_key": "1:2", + "literal_source": "literal_query", + "map_calls": 2064, + "op": "fixed_past_reader_query", + "pair_record": 2, + "source": "query" + } + ], + "physical_input_level": 1, + "physical_output_level": 2, + "provider": "base", + "query_pair_record": 2, + "reader_stage": 1, + "scalar_primitives": 17624, + "service_stage": 2, + "stage_view_record": 1 + }, + { + "map_call_bound": { + "DATA": 448, + "late_query": 2064, + "local_endpoint_adapters": 224, + "native_side_maps": 3040, + "total": 5776 + }, + "ordered_blocks": [ + { + "map_calls": 224, + "op": "DATA_entry", + "record": 1 + }, + { + "map_calls": 128, + "op": "native_input_adapters", + "provider": "extra", + "source": "prefix" + }, + { + "event_range": [ + 0, + 2406 + ], + "op": "complete_native_carrier_cover_sweep", + "provider": "extra", + "source": "prefix" + }, + { + "map_calls": 96, + "op": "ordinary_output_adapters", + "provider": "extra", + "source": "prefix" + }, + { + "map_calls": 224, + "op": "DATA_exit", + "record": 1 + }, + { + "op": "complete_cover_barrier" + }, + { + "literal_key": "1:2", + "literal_source": "literal_query", + "map_calls": 2064, + "op": "fixed_past_reader_query", + "pair_record": 2, + "source": "query" + } + ], + "physical_input_level": 1, + "physical_output_level": 2, + "provider": "extra", + "query_pair_record": 2, + "reader_stage": 1, + "scalar_primitives": 17624, + "service_stage": 2, + "stage_view_record": 1 + } + ], + "native_phase_validation": "Use the pinned independent line-entry review.", + "owner_contract": { + "cover": "Regular O(25,2)", + "data_partition": "For each field, d -> d*rho_(t,p) is a bijection.", + "helper_hosting_reproved_here": false, + "native_helpers": "Use the inherited 416-field helper contract; restore it per body." + }, + "schema": "fixed-reader-global-dispatcher-v1", + "selected_ports": [ + 0, + 27, + 36, + 111, + 20, + 7, + 57, + 46, + 1, + 3, + 6, + 8, + 17, + 18, + 24, + 23 + ], + "source_pins": { + "literal_query": [ + "new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/query-normal/ROUTED-QUERY.json.gz", + "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a" + ], + "literal_query_freeze": [ + "new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json", + "f111a90f7403f93494e9d1f83ae35dbf7dd72eddc8c9f8bf730d677b4a31402d" + ], + 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"retained_word_plus_query_scalar_primitives": 17624, + "reuse_native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "reuse_native_rank": 1792, + "schema": "fixed-row-reader-reuse-v1", + "source_pins": { + "capture": [ + "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7" + ], + "native": [ + "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" + ], + "phase": [ + "bridge-access-20261017/check_bridge_access.py", + "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111" + ], + "views": [ + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + ] + }, + "unchanged_outside_fields": 416 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/FREEZE.json new file mode 100644 index 0000000000..3808f618ad --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/FREEZE.json @@ -0,0 +1,16 @@ +{ + "files": { + "GENERAL-QUERY.md": "cc96ab14ce744b4acf30bc5e8088a35807611a497abc673b11eab225d9bf7993", + "PEER-REVIEW.md": "653372564d82ea8b7c8f7b2b1a76de4cf97f97879864dcd9479f09ca6ceaf86e", + "REPRODUCTION.json": "cbf5cf14b663c1c78f27f4f41ff18dc77eaa99619bf2d5f58373a574dc12a802", + "REVIEW.md": "e8862531740470b3bb4f45b421c0ab100c07f00bed71271b398ee7bdb89d834d", + "check_review.py": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7", + "normal/REVIEW-CHECKS.json": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830", + "optimized/REVIEW-CHECKS.json": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830" + }, + "inherited_service_review_sha256": "ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7", + "payload_decompressed_sha256": "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091", + "producer_freeze_sha256": "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6", + "schema": "independent-routed-involution-reader-review-v1", + "scope": "Six complete forward data services and three late inverse-adjoint queries. The helper host, complete backward caller, and supplier remain separate." +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md new file mode 100644 index 0000000000..9eadd8701f --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/GENERAL-QUERY.md @@ -0,0 +1,105 @@ +# Sharing a restored source across target readers + +Let X be a source module. Let \(Y_1,\ldots,Y_k\) be distinct target +modules. Let T be a unit on X. Assume that these operations are +admitted at their actual physical views: + +1. T and \(T^{-1}\) act in place on X. +2. Reader j adds \(L_jX\) to \(Y_j\). It preserves X and every + other target. +3. Each operation restores its own borrowed fields. + +Then the word + +\[ +T;\quad +(Y_1\mathrel{+}=L_1X);\quad\cdots\quad +(Y_k\mathrel{+}=L_kX);\quad +T^{-1} +\] + +has the exact endpoint + +\[ +(x,y_1,\ldots,y_k) +\longmapsto +(x,y_1+L_1Tx,\ldots,y_k+L_kTx). +\] + +The proof follows the actual order. After the first word the +source is Tx. Each reader leaves that source unchanged and +retains the independent baseline of its own target. The final +word restores x. Thus the source transformations are paid once. +No zero target, inverse reader, or commutation hypothesis is +required. + +The price is + +\[ +a(T)+a(T^{-1})+\sum_{j=1}^k c(L_j), +\] + +before any sharing of physical views. A reader that alters a +source during its literal word is permitted only if that word +restores the source before the next reader. The endpoint +identity does not remove the cost of target storage or access. + +## Actual D25 schedule for one retained reader + +Use the reviewed current involution \(T=A_t\). Assume k distinct +target banks are already available in the completed FULL frame, +with the same retained reader \(L_s=P+B_s\). This is an explicit +availability premise. It is not a new native host construction. + +Use this schedule: + +1. Apply the actual current A word to X, with its current views. +2. Put the 96 ordinary X fields in the old s FULL views. +3. For each target bank, add the sixteen selected X fields to + its selected target fields while those targets remain in + global FULL. Enter its sixteen old s target views, run the + 1,760-scalar complement reader, and restore its target views. +4. Restore the 96 old source views. +5. Apply the actual current A word to X again. + +The selected X fields remain in global FULL throughout step 3. +The complement reader does not need those selected X fields. +Each target therefore receives both the selected copy and +\(B_sA_tx\). Their sum is \(L_sA_tx\), with the full operator +order retained. + +The two current A words cost 6,552 scalar primitives and +448 maps. The k readers cost \(1888k\) scalar primitives. +Their shared ordinary source views cost 192 maps. Their +target views cost \(32k\) maps. Thus the complete query +schedule has + +\[ +\boxed{6552+1888k\text{ scalar primitives},\qquad +640+32k\text{ monomial calls}.} +\] + +For k=1, these are the reviewed literal counts 8,440 and 672. +For k=2, they are 10,328 and 704. The two-target schedule +has not been joined to a native host or supplier in this +packet. No extra fields are treated as free. + +If readers use g different old stages, the same source pair +can still be shared. Group the targets by their old stage, +and enter and restore the 96 ordinary source views for +each group. The scalar count remains \(6552+1888k\); the +map count becomes \(448+192g+32k\). This formula assumes +that each stated old-stage view is admitted at the common +completed cut. + +This theorem isolates a reusable source operation. It does +not make a product \(C_sA_t\) reciprocal or stage independent. +It does not construct a backward caller, a complete recursive +host, or a terminal decoder. + +The bridge-access producer checked the actual one-reader +view schedule and its multi-target count independently. +Its response is recorded in `PEER-REVIEW.md`. + +No publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md new file mode 100644 index 0000000000..cdee425048 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/PEER-REVIEW.md @@ -0,0 +1,26 @@ +# Peer check of the multi-target schedule + +On 2026-10-20, the bridge-access producer checked the proposed +multi-target schedule independently. The producer confirmed +the following points: + +- Keep the 96 ordinary source fields in the old s FULL views + between target queries. Enter and restore them once, for + 192 map calls. +- For each target bank, make the sixteen selected copies in + global FULL before entering its sixteen old target views. + Run the complement query, then restore those target views. + This costs 32 maps per target bank. +- The selected X fields stay in global FULL. They remain + available for the same-port copies. +- The complete query costs \(6552+1888k\) scalar primitives + and \(640+32k\) maps. +- The target banks must be distinct and have paid FULL + hosting. This calculation does not provide that host. + +The peer check concerns the new schedule theorem. It does +not replace the independent replay of the producer's actual +one-target word in `REVIEW.md`. + +No publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..d93b1a0810 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/REPRODUCTION.json @@ -0,0 +1,11 @@ +{ + "commands": [ + "python3 check_review.py --output normal", + "python3 -O check_review.py --output optimized" + ], + "no_producer_files_changed": true, + "normal_optimized_byte_identical": true, + "one_cpu": true, + "receipt_sha256": "280b823b18d35aecaa497e95e6115a6ecb02693c1cbc1232ce2e1a5432b62830", + "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/REVIEW.md new file mode 100644 index 0000000000..5493e5eb7c --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/REVIEW.md @@ -0,0 +1,240 @@ +# Independent review of the routed involution reader + +The frozen forward service passes for both native providers and all +three D25 reader/service pairs. The independent checks found no +material defect. Each complete service has 14,896 real scalar +primitives, native rank 1,792, and at most 4,384 monomial map calls. +All 640 formal input columns are checked. + +This service computes the new involution response A. It changes the +sixteen selected response rows. It is not a cheaper word for the old +E response. The helper host, finite map price, recursive precision, +backward caller, and complete supplier remain separate obligations. + +## Pinned input and independent method + +The producer freeze has SHA-256 +`3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6`. +The decompressed query payload has SHA-256 +`35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091`. +The controller involution payload has SHA-256 +`a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b`. + +This review uses the earlier independent joined-service review, +whose freeze has SHA-256 +`ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7`. +The new checker imports that pinned review's mathematical helpers. +It imports no producer code. + +The earlier review binds the exact native prefix, all 896 DATA +phase equations, all six cover schedules, and the independent +native phase review. The new payload contains the same native +prefixes and DATA records, byte for byte. This review checks that +equality. It does not repeat the earlier large native spatial replay. +It does replay the complete prefix on all 640 formal inputs. + +The new part reconstructs A from the original native U and V. +It checks the full scalar word, the actual routed involutions, +every late map phase, the ordered query, the complete data map, +and each component of the invoice. + +## Independent matrix construction + +Write the original response as \(E=I+UV\). Let P be the actual +sixteen selected ports, and let R be their 96-port complement. +The selected column minor \(V_P\) has determinant 16. It is a +dyadic unit. Keep \(U_R\), and set + +\[ +\widetilde U_P=V_P^{-1}(-2I-V_RU_R), +\qquad +A=I+\widetilde U V. +\] + +The construction gives \(V\widetilde U=-2I\). Hence + +\[ +A^2=I+\widetilde U(2I+V\widetilde U)V=I. +\] + +The checker constructs this matrix before it reads the emitted +response for comparison. All 96 ordinary rows agree with E, and +all sixteen selected rows differ from E. The actual normalized +reader is \(L=V_P^{-1}V\), and \(LA=-L\). + +The full 3,276-scalar `common_frame_words.A` is replayed from the +112-column identity matrix. Its result is exactly A. Its targets +and sources are existing X fields. It uses no extra field and no +odd division. + +The source identity \(A^2=I\) does not imply that A is symmetric +or unitary. It does not make \(C_sA_t\) self-inverse, reciprocal, +or independent of the stage. + +## Exact routed query and arbitrary inputs + +Let \(A_t\) include the actual current owner routes. Let \(L_s\) +be the retained reader. At the completed FULL cut, use + +\[ +X\mathrel{\gets}A_tX,\qquad +Y_P\mathrel{+}=L_sX,\qquad +X\mathrel{\gets}A_tX. +\] + +For arbitrary independent x and y, this word gives + +\[ +(x,y)\longmapsto(x,y+L_sA_tx). +\] + +The second source transform restores X because the routed +operator itself is an involution. No different owner routes +are identified. No reader is commuted through a response. + +For each of \((s,t)=(0,1),(0,2),(1,2)\), the independent checker +builds the actual D25 route matrices from the pinned q vectors. +It checks that each map is orthogonal, that its inverse is exact, +and that it fixes all future axes. Its FULL conjugation phase +is checked as a complete Z4 polynomial, including translation. +The current query views agree with the current DATA exits. + +The native cover sweep and all exits occur before the query. +The physical input level is \(t-1\). In particular, reader pair +\((0,2)\) uses a stage-zero reader carried to physical level one; +it does not skip the stage-one physical advance. + +The literal late word has four parts: + +| Part | Scalar primitives | Monomial calls | +| --- | ---: | ---: | +| Current A on all X | 3,276 | 224 | +| Old complement reader into selected Y | 1,760 | 224 | +| Sixteen same-port selected copies | 128 | 0 | +| Current A on all X | 3,276 | 224 | +| Total | 8,440 | 672 | + +The old complement reader retains its arbitrary target baseline. +The query neither reads nor changes the ordinary Y hole fields. +All source fields return to their initial values at the FULL cut. +The 416 outside fields keep their independent input values. + +Each direct \(L_sA_t\) product has 3,824 distinct field/owner-route +terms. The independent replay keeps their order and compares all +640 input columns. Omitting the second A word fails. Replacing +the old reader by the current reader also fails, for all three pairs. + +## Complete forward map and cost + +The unchanged carrier prefix has the profile + +\[ +1392H_1+64H_2+48H_3+16H_8. +\] + +It has 1,520 children, native rank 1,792, and 6,456 scalar +primitives. Its ordinary output rows remain valid because +\(A[R,*]=E[R,*]\). Its selected records are independent. +All 416 helper values are restored under the inherited helper +supply contract. + +Let \(G_R=\operatorname{diag}(I_P,q_R)\). Let \(F_\ell\) denote +FULL on the first \(9+8\ell\) axes. Define + +\[ +(D_{s,t})_P=L_sA_t,\qquad +(D_{s,t})_R=(A_t)_R. +\] + +The complete forward data service is + +\[ +(F_{t-1}x,F_{t-1}G_Rw) +\longmapsto +(F_tx,F_tG_R(w+D_{s,t}x)). +\] + +The target w is arbitrary. If \(w=C_sy\), the selected output +records are \(L_s(y+A_tx)\). The same reader is retained. +The checker composes the exact routed query with the full +prefix and verifies all 640 input columns for all six +provider/pair invocations. + +The complete scalar count is \(6456+8440=14896\). +The monomial call bound is + +\[ +448+224+3040+672=4384. +\] + +These terms count DATA entry/exit maps, local endpoint adapters, +native side maps, and query maps. This is a map-call count. It +does not price the finite implementation of a map. Identity +maps remain counted where the literal word calls them. + +The native prefix's exact content coefficient bound is 22, +with binary denominator height one. The late query's exact +coefficient row-sum maximum is 202, with height two. These +values hold for all three pairs. + +The query maximum is attained at an emitted boundary. Its +witness has 266 coefficients of magnitude \(1/2\), another +134 of magnitude \(1/2\), and one coefficient of magnitude 2. +Their absolute sum is 202. The receipt also gives a coefficient +of magnitude \(1/4\), so height two is attained. + +At these late boundaries the regular cover gives a sharp +physical sup norm: different routes give different input +owners, and the payload view for a route is its unique FULL +conjugate. Terms with the same field and route have already +been combined. The remaining source values can take the +required signs independently. This argument does not assert +sharpness for a quotient cover. It does not cover primitive +arithmetic interiors, native-child interiors, or the full +recursive caller. + +## Separate late inverse-adjoint check + +The checker also transforms each late scalar ADD to its negative +transpose and each SCALE to its reciprocal. It keeps chronology. +The map events remain unchanged because they are unitary. +This is the gatewise inverse-adjoint word. + +The replay on all 640 inputs gives + +\[ +X\mathrel{-}=A_t^*L_s^*Y_P,\qquad Y_P\mathrel{\gets}Y_P. +\] + +Its price is also 8,440 scalar primitives and 672 maps. Its +exact emitted-boundary coefficient row-sum maximum is 30, +and its binary denominator height is two, for each pair. + +This is a check of the late word. No separately packaged +complete backward native service is emitted or approved +by this review. The transpose of a query is not a reciprocal +caller with the required physical input and output frames. + +## Reproduction, extension, and credit + +Run from this directory: + +```text +python3 check_review.py --output normal +python3 -O check_review.py --output optimized +``` + +Both runs print `PASS_INDEPENDENT_ROUTED_INVOLUTION_READER`. +The two `REVIEW-CHECKS.json` files must be byte equal. +`GENERAL-QUERY.md` gives a separate multi-target schedule theorem. +It does not claim a new target host or native caller. + +The controller lane supplied the row involution. The bridge-access +lane supplied the literal query and D25 binding. The native lanes +supplied the unchanged carrier prefix and its independent phase +review. This lane supplied the independent matrix, route, arbitrary +input, full service, and late dual checks. AI agents prepared these +local research records. + +No publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/check_review.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/check_review.py new file mode 100644 index 0000000000..ec5ba02c71 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/check_review.py @@ -0,0 +1,273 @@ +"""Check the routed involution reader with independent matrix algebra.""" + +import argparse +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +OLD_REVIEW = HERE.parent / "fixed-reader-service-review-20261020" +PRODUCER = LANES / "bridge-access-20261017/involution-reader-20261020" +CONTROLLER = LANES / "controller-followthrough-20261017/row-involution-20261020" +FREEZE_PIN = "3ba792d18fbd57122ab4ae3301a3ff74b81751cf03fd2b7e8f9dc632759364e6" +PAYLOAD_PIN = "35f3735f1e2f9693c1b65aa292736d927dc38cbf0670af5e469097803187f091" +OLD_REVIEW_PIN = "ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7" +A_PIN = "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b" + + +def need(test, message): + if not test: + raise ValueError(message) + + +def digest(raw): + return sha256(raw).hexdigest() + + +def pinned(path, expected, compressed=False): + raw = path.read_bytes() + if compressed: + raw = gzip.decompress(raw) + need(digest(raw) == expected, "Pin: " + str(path)) + return raw + + +def freeze(path, expected): + result = json.loads(pinned(path, expected)) + for name, pin in result["files"].items(): + pinned(path.parent / name, pin) + return result + + +freeze(OLD_REVIEW / "FREEZE.json", OLD_REVIEW_PIN) +spec = importlib.util.spec_from_file_location("independent_service_math", OLD_REVIEW / "check_service.py") +s = importlib.util.module_from_spec(spec) +spec.loader.exec_module(s) +r = s.r + + +def complete_matrix(u, v): + vp = [{j: row[p] for j, p in enumerate(r.PIVOTS) if p in row} for row in v] + vpi, determinant = r.invert(vp) + remaining_u = [{} if p in r.PSET else dict(row) for p, row in enumerate(u)] + residual = r.matmul(v, remaining_u) + requested = [] + for i, row in enumerate(residual): + out = {j: -value for j, value in row.items()} + r.put(out, i, F(-2)) + requested.append(out) + changed_rows = r.matmul(vpi, requested) + changed_u = [dict(row) for row in u] + for p, row in zip(r.PIVOTS, changed_rows): + changed_u[p] = row + need(r.matmul(v, changed_u) == [{i: F(-2)} for i in range(16)], + "Exact rank-sixteen involution certificate") + a = r.eye(112) + for row, correction in zip(a, r.matmul(changed_u, v)): + for j, value in correction.items(): + r.put(row, j, value) + return a, changed_u, r.matmul(vpi, v), determinant + + +def to_operations(word, level): + for record in word["maps"]: + a, ai = tuple(record["columns"]), tuple(record["inverse_columns"]) + need(r.product(a, ai) == r.product(ai, a) == r.UNIT and ai == r.transpose(a), + "The literal map is orthogonal") + need(a[9 + 8 * level:] == r.UNIT[9 + 8 * level:], "Every future axis is fixed") + delta = r.phase_translation(r.add_phase(r.full_phase(level), r.minus_phase(r.full_phase(level, a)))) + need(record["translation"] == delta + and record["inverse_translation"] == r.apply(ai, delta), "Literal FULL phase and inverse") + operations = [] + for event in word["events"]: + if event[0] == "map": + _, field, index = event + operations.append(("map", field, None, tuple(word["maps"][index]["columns"]))) + else: + need(event[0] == "scalar", "Literal query event grammar") + _, op, field, source, coefficient = event + need(op in ("add", "scale"), "Dyadic scalar grammar") + need(source is None or source < 112, "No target record is used as a source") + operations.append((op, field, source, F(coefficient))) + need(field < 112 or field - 112 in r.PSET, "Only FULL query fields are changed") + return operations + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, default=HERE / "normal") + args = parser.parse_args() + producer_freeze = freeze(PRODUCER / "FREEZE.json", FREEZE_PIN) + need(producer_freeze["payload_decompressed_sha256"] == PAYLOAD_PIN, "Payload freeze") + bundle = json.loads(pinned(PRODUCER / "final-normal/INVOLUTION-READER.json.gz", PAYLOAD_PIN, True)) + sources = {} + for name, (path, pin) in bundle["source_pins"].items(): + raw = pinned(LANES / path, pin, path.endswith(".gz")) + if path.endswith(".json") or path.endswith(".json.gz"): + sources[name] = json.loads(raw) + inv = json.loads(pinned(CONTROLLER / "run-normal/ROW-INVOLUTION.json", A_PIN)) + need(inv == sources["involution"], "Exact controller word source") + native_path, native_pin = r.PINS["native"] + native = json.loads(pinned(LANES / native_path, native_pin, True)) + u, v, old_e = (r.sparse(native["model"][key]) + for key in ("correction_U", "correction_V", "response")) + a, changed_u, reader, vp_det = complete_matrix(u, v) + need(a == r.sparse(inv["response"]) == r.sparse(bundle["response"]), + "The emitted response equals the independently completed actual matrix") + need(changed_u == r.sparse(inv["correction_U"]), "The changed factor agrees") + need(r.matmul(a, a) == r.eye(112), "The complete 112-port involution") + need(all(a[p] == old_e[p] for p in range(112) if p not in r.PSET), + "Exactly the old ordinary rows are retained") + need(all(a[p] != old_e[p] for p in r.PIVOTS), "All sixteen selected rows change") + need(reader == r.sparse(sources["capture"]["centre_reader"]), "The retained old reader") + need(r.matmul(reader, a) == [{j: -x for j, x in row.items()} for row in reader], + "The current reader has eigenvalue minus one") + codeword = inv["common_frame_words"]["A"] + need(r.scalar_word(r.eye(112), codeword) == a, "Independent complete scalar A word") + need(sum(r.real_price(op, F(value)) for op, _, _, value in codeword) == 3276, + "Exact source unit price") + need(all(dst < 112 and (src is None or src < 112) for _, dst, src, _ in codeword), + "The source word uses existing X only") + old_payload = json.loads(s.read(*s.PAYLOADS["service"], True)) + need(bundle["native_prefixes"] == old_payload["native_prefixes"] + and bundle["stage_views"] == old_payload["stage_views"] + and bundle["helper_hosting"] == old_payload["owner_contract"], + "The exact reviewed native and DATA components are retained") + need(tuple(bundle["pivots"]) == r.PIVOTS, "The exact selected field order") + prefix_reports = {name: s.prefix_replay(word, a) + for name, word in bundle["native_prefixes"].items()} + ports = native["model"]["ports"] + routes = {(stage, p): r.route(ports[p], stage) for stage in range(3) for p in range(112)} + query_reports = {} + dual_reports = {} + query_parts = { + "apply_current_involution": (3276, 224), + "old_reader_complement": (1760, 224), + "selected_reader_copy": (128, 0), + "restore_current_involution": (3276, 224), + } + for key, word in bundle["queries"].items(): + old_stage, level = word["reader_stage"], word["service_stage"] + need(key == f"{old_stage}:{level}", "Reader and service labels") + operations = to_operations(word, level) + at = r.routed_matrix(a, range(112), level, routes) + identity = [{(p, r.UNIT): F(1)} for p in range(112)] + need(r.multiply_routed(at, at) == identity, "The actual routed source involution") + ls = r.routed_matrix(reader, r.PIVOTS, old_stage, routes) + lt = r.routed_matrix(reader, r.PIVOTS, level, routes) + direct = r.multiply_routed(ls, at) + need(sum(map(len, direct)) == 3824, "Direct selected owner-path census") + end = 0 + part_reports = {} + for label, (expected_scalar, expected_maps) in query_parts.items(): + lo, hi = word["stage_ranges"][label] + need(lo == end and lo <= hi <= len(operations), "Complete ordered query intervals") + part = operations[lo:hi] + price = sum(r.real_price(op, value) for op, _, _, value in part if op != "map") + maps = sum(op == "map" for op, _, _, _ in part) + need((price, maps) == (expected_scalar, expected_maps), "Per-part exact invoice") + if label in ("apply_current_involution", "restore_current_involution"): + scalars = [[op, dst, src, str(value)] for op, dst, src, value in part if op != "map"] + need(scalars == codeword, "Both current words are the pinned A program") + expected_maps_list = ( + [("map", p, None, routes[level, p]) for p in range(112)] + + [("map", p, None, routes[level, p]) for p in reversed(range(112))]) + need([op for op in part if op[0] == "map"] == expected_maps_list, + "The current A uses the exact DATA route views") + part_reports[label] = {"scalar_primitives": price, "maps": maps} + end = hi + need(end == len(operations), "No query event lies outside its complete schedule") + initial = [{(i, r.UNIT): F(1)} for i in range(640)] + expected = [dict(row) for row in initial] + for p, row in zip(r.PIVOTS, direct): + for term, value in row.items(): + r.put(expected[112 + p], term, value) + actual, bill, triangle, grid, exact = r.replay(operations) + need(actual == expected, "All 640 arbitrary query input columns") + need(bill == {"real_scalar": 8440, "maps": 672} + and exact["coefficient_row_sum_peak"] == "202" + and exact["coefficient_binary_height"] == 2, "Query invoice and exact prefixes") + global_prefix = [dict(row) for row in initial] + for p in range(112): + if p not in r.PSET: + for term, value in at[p].items(): + r.put(global_prefix[112 + p], term, value) + complete = r.multiply_routed(actual, global_prefix) + complete_expected = [dict(row) for row in global_prefix] + for p, row in zip(r.PIVOTS, direct): + for term, value in row.items(): + r.put(complete_expected[112 + p], term, value) + need(complete == complete_expected, "All 640 complete service input columns") + cutoff = word["stage_ranges"]["restore_current_involution"][0] + wrong, *_ = r.replay(operations[:cutoff]) + need(wrong != expected and wrong[:112] != initial[:112], "No-restore control fails") + need(r.multiply_routed(lt, at) != direct, "The current reader cannot replace the old reader") + dual, dual_bill, dual_triangle, dual_grid, dual_exact = r.replay(operations, dual=True) + dual_expected = [dict(row) for row in initial] + for p, row in zip(r.PIVOTS, direct): + for (origin, path), value in row.items(): + r.put(dual_expected[origin], (112 + p, r.transpose(path)), -value) + need(dual == dual_expected and dual_bill == bill, + "The literal inverse-adjoint late query on all 640 columns") + need(dual_exact["coefficient_row_sum_peak"] == "30" + and dual_exact["coefficient_binary_height"] == 2, "Exact late dual prefix bounds") + query_reports[key] = { + "input_columns": 640, "direct_paths": 3824, "parts": part_reports, + "invoice": bill, "exact_prefix": exact, "triangle_prefix": str(triangle), + "triangle_binary_height": grid, + "negative_controls": ["omitted_source_restore", "current_reader_substitution"], + } + dual_reports[key] = {"input_columns": 640, "invoice": dual_bill, "exact_prefix": dual_exact, + "triangle_prefix": str(dual_triangle), "triangle_binary_height": dual_grid} + service_reports = [] + for call in bundle["invocations"]: + provider, old_stage, level = call["provider"], call["reader_stage"], call["service_stage"] + old_call = next(c for c in old_payload["services"] if + (c["provider"], c["reader_stage"], c["service_stage"]) == + (provider, old_stage, level)) + need(call["ordered_blocks"][:-1] == old_call["ordered_blocks"][:-1], + "The complete native cover barrier is unchanged") + key = f"{old_stage}:{level}" + late = call["ordered_blocks"][-1] + need(late["op"] == "fixed_past_reader_query" + and late["source"] == late["literal_source"] == "queries" + and late["literal_key"] == call["query_key"] == key + and late["map_calls"] == 672, "The exact new query splice") + need(call["physical_input_level"] == level - 1 and call["physical_output_level"] == level + and call["stage_view_record"] == level - 1, "The adjacent physical stage") + prefix_report = prefix_reports[provider] + scalar = prefix_report["scalar_primitives"] + query_reports[key]["invoice"]["real_scalar"] + need(scalar == call["scalar_primitives"] == 14896 + and call["map_call_bound"] == { + "DATA": 448, "local_endpoint_adapters": 224, "native_side_maps": 3040, + "late_query": 672, "total": 4384}, "The complete new response service invoice") + service_reports.append({"provider": provider, "reader_stage": old_stage, "service_stage": level, + "scalar_primitives": scalar, "native_mass": prefix_report["native_mass"], + "monomial_map_call_bound": 4384, "input_columns": 640}) + need(len(service_reports) == 6 and len(query_reports) == 3, "All six actual services") + result = { + "status": "PASS_INDEPENDENT_ROUTED_INVOLUTION_READER", + "checker_sha256": digest(Path(__file__).read_bytes()), + "producer_freeze_sha256": FREEZE_PIN, "payload_decompressed_sha256": PAYLOAD_PIN, + "inherited_service_review_sha256": OLD_REVIEW_PIN, "actual_A_payload_sha256": A_PIN, + "pivot_minor_determinant": str(vp_det), "rank_certificate": "V U_tilde = -2 I16", + "actual_source_scalar_price": 3276, "changed_selected_rows": 16, "unchanged_ordinary_rows": 96, + "prefix_reports": prefix_reports, "queries": query_reports, "late_dual_queries": dual_reports, + "services": service_reports, "producer_code_imported": False, + "new_native_phase_checks": "The exact reviewed components are unchanged.", + "full_backward_service_emitted": False, "complete_supplier_claimed": False, + } + args.output.mkdir(parents=True, exist_ok=True) + raw = (json.dumps(result, sort_keys=True, indent=2) + "\n").encode() + (args.output / "REVIEW-CHECKS.json").write_bytes(raw) + print(result["status"]) + print(digest(raw)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json new file mode 100644 index 0000000000..7aa6839fde --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/involution-reader-review-20261020/normal/REVIEW-CHECKS.json @@ -0,0 +1,523 @@ +{ + "actual_A_payload_sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b", + "actual_source_scalar_price": 3276, + "changed_selected_rows": 16, + "checker_sha256": "2e6211b88e02d4b03ad1c4072b22dc11cb7a4328ba70f2808b0364084e10cad7", + "complete_supplier_claimed": false, + "full_backward_service_emitted": false, + "inherited_service_review_sha256": "ba06daabfd69759b489f5ae97a75ff68243bd5016a0981508ff529759ac8edd7", + "late_dual_queries": { + "0:1": { + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "30", + "height_witness": { + "coefficient": "1/4", + "event_index": 1276, + "origin": 112, + "route": [ + 3584, + 3086, + 2574, + 1550, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 11, + 7, + 16, + 32, + 64, + 128, + 256, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 25 + }, + "norm_witness": { + "coefficient_census": { + "-1": 1, + "-1/2": 20, + "-4": 1, + "1": 1, + "1/2": 20, + "4": 1 + }, + "coefficient_terms": 44, + "event_index": 1696, + "target": 111 + } + }, + "input_columns": 640, + "invoice": { + "maps": 672, + "real_scalar": 8440 + }, + "triangle_binary_height": 2, + "triangle_prefix": "4717" + }, + "0:2": { + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "30", + "height_witness": { + "coefficient": "1/4", + "event_index": 1276, + "origin": 112, + "route": [ + 917504, + 786446, + 655374, + 393230, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216, + 512, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 11, + 7, + 16, + 32, + 64, + 128, + 256 + ], + "target": 25 + }, + "norm_witness": { + "coefficient_census": { + "-1": 1, + "-1/2": 20, + "-4": 1, + "1": 1, + "1/2": 20, + "4": 1 + }, + "coefficient_terms": 44, + "event_index": 1696, + "target": 111 + } + }, + "input_columns": 640, + "invoice": { + "maps": 672, + "real_scalar": 8440 + }, + "triangle_binary_height": 2, + "triangle_prefix": "4717" + }, + "1:2": { + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "30", + "height_witness": { + "coefficient": "1/4", + "event_index": 1276, + "origin": 112, + "route": [ + 656384, + 787456, + 917504, + 394240, 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= 56 I8", + "P = R^T R/4", + "P^2 = 14 P", + "J = I112-P", + "J^2+12J-13I112=0", + "J^-1 = (12I112+J)/13" + ], + "map": "(x,y,h,c) -> (x, y + J x - R^T H h/4, h, 0)", + "not_claimed": [ + "Native centre-free supplier admission", + "Free endpoint J^-1", + "Changed global controller", + "Kappa improvement" + ], + "ports": [ + 11, + 19, + 35, + 67, + 131, + 259, + 13, + 21, + 37, + 69, + 133, + 261, + 41, + 73, + 137, + 265, + 49, + 81, + 145, + 273, + 161, + 289, + 193, + 321, + 385, + 14, + 22, + 38, + 70, + 134, + 262, + 26, + 74, + 138, + 266, + 50, + 146, + 274, + 98, + 162, + 290, + 194, + 322, + 386, + 28, + 44, + 140, + 268, + 84, + 148, + 276, + 100, + 164, + 292, + 196, + 324, + 388, + 56, + 88, + 152, + 280, + 104, + 168, + 296, + 200, + 328, + 392, + 112, + 176, + 304, + 208, + 336, + 400, + 224, + 352, + 416, + 448, + 508, + 506, + 502, + 494, + 478, + 446, + 382, + 254, + 505, + 501, + 493, + 477, + 445, + 381, + 253, + 499, + 491, + 475, + 443, + 379, + 251, + 487, + 471, + 439, + 375, + 247, + 463, + 431, + 367, + 239, + 415, + 351, + 223, + 319, + 191 + ], + "program_sha256": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3", + "scope": "Exact scalar interface only. Native endpoint mixing and a changed controller are not admitted.", + "status": "PASS_CENTRE_FREE_SCALAR_INTERFACE", + "target_endpoint": "T_q = F C_q^-1; distinct q have distinct frames", + "word_sha256": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/coherent-port/recursive-code-interface-20261020/INTERFACE.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/coherent-port/recursive-code-interface-20261020/INTERFACE.md new file mode 100644 index 0000000000..e3a75fbdad --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/coherent-port/recursive-code-interface-20261020/INTERFACE.md @@ -0,0 +1,411 @@ +# A closed upper code and its recursive access conditions + +The changed terminal has a useful closed code family. On a fixed +selected row set P and its complement R, write + +```text +N(B) = iota_P B pi_R, +C(B) = I+N(B). +``` + +The coefficients of B can be spatial operators. They need not commute. +For all B and D, + +```text +N(B)N(D)=0, +C(B)C(D)=C(B+D), +C(B)^-1=C(-B). (1) +``` + +Thus this code does not acquire products of reader coefficients while +the row partition remains fixed. This is a positive interface result. +It does not, by itself, supply a recursive native implementation. + +The actual next child must receive the right code on its gathered +axes. A change of those axes need not leave a scalar reader. An +actual reader edge below gives a four-line operator after such a +change. Also, a deeper recursive call uses a new row digit. Its +selected projection is not the projection in (1). + +This note separates these two access conditions from the closed +algebra. It does not prove that every possible coded recursion fails. +No new supplier, native saving, or kappa bound is claimed. + +The coordinating and independent-review lanes proposed the changed +terminal and its four-code rule. This note checks their recursive +interface conditions against the actual reader and child contract. + +## Sources and unchanged contracts + +All paths in this note are relative to the campaign lanes directory. +`CHECKS.json` gives the full paths and digests. + +The actual selected set, reader H, and response D come from +`new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz`. +Its decompressed digest is +`7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2`. +There are 16 selected and 96 ordinary ports. The exact checks give + +```text +D=-H^T, +HD=diag(-5 I8,-7 I8). +``` + +H has 160 signed half coefficients and 56 unit coefficients. Its +direct scalar ADD word costs 2,048 old real primitives. + +The clean forward and backward words are the frozen +`CLEAN-LATE-EXCHANGE.json.gz` and `CLEAN-DUAL.json.gz` in that lane. +They have 224 data fields and 416 other fields. The 416 fields are +arbitrary and unchanged. They are not clean storage. + +The routed no-reset terminal is pinned by +`independent-review-20261017/no-reset-terminal-factor-20261020/FREEZE.json`, +digest +`1b1f191e9de1ef20b88aca6d870f93fe68b0923e8b05a87d9ca7d960e0385963`. +Its terminal factor is + +```text +diag(Q_P,Q_R^2,-I) W^-1 L W, +W=diag(I_P,Q_R,I_R). +``` + +This is a decoder on `(beta,h,R)`. It is not a bare supplier code. +The selected-X sign and the final bank exchange are separate. + +The current recursive source, `notes/batched-complex-rows.tex`, keeps +all compact and spectator ranges in a child and gives that child +exactly 1/W of its parent's volume. Its selected axes are gathered +before the call. Each recursive level has a new row digit. The +complete dirty-helper contract in `research/idle-axis-hosting/PROOF.md` +requires the exact pending native operator on arbitrary helper input. +Neither contract grants a joint code on unrelated principal arrays. + +## The changed terminal + +In the pinned terminal, omit only the last shear + +```text +b <- b-H0 t. +``` + +The other seven shears give `(alpha,u,-v)`, where +`alpha=a+H0 u`. After the stated signs and the positive Q on the +112 recovered data fields, the output is + +```text +(F25 Y0, F25 K(H0) X0), +K(B)=Q C(B) q, q=Q^-1. (2) +``` + +Here H0 is the root reader. Its scalar port map has no stage route. +It commutes with the common full transform. The Q operators in (2) +remain on their own fields. + +For one common Q, (1) gives + +```text +K(B)K(D)=K(B+D). +``` + +The omitted shear changes the endpoint claim. It does not delete +the cost of reading H0 from a caller that requires the raw output. + +If the 16 selected positive Q operations are also omitted, the code is + +```text +Khat(B) = [[q_P, B q_R], + [0, I_R ]]. (3) +``` + +The resulting terminal has 192 line operations. This code includes +a selected diagonal phase. It is not a member of the unipotent +family (1). + +## What survives at one row digit + +Let A preserve the P/R row partition, with diagonal blocks A_P and A_R. +The blocks can contain noncommuting spatial or parent-field operators. +Direct multiplication gives + +```text +A C(B) A^-1 = C(A_P B A_R^-1). (4) +``` + +Consequently, all upper defects inserted at one internal row digit +remain one upper defect under a word of such operations. This remains +true if its B block links several parent principal arrays. A native +array advance, an address view that does not change that row digit, +and a scalar parent-field operation all preserve the partition. +Equation (4) is an algebraic statement; the coefficient that it +produces may require native work to read. + +If each principal array instead has its own stored code, an ADD has +an explicit relative-code condition. For stored arrays +`xhat=C(Bx)x` and `yhat=C(By)y`, the semantic ADD `x<-x+c y` requires + +```text +xhat <- xhat+c C(Bx-By)yhat. (5) +``` + +The unchanged ADD is valid only if the relative code acts as the +identity on the source state. The source is arbitrary here. One can +instead track a joint code by (4), but that choice does not make its +eventual removal free. + +## Exact child entrance + +Write Q_U for the port line operator defined by one gathered native +block U. Suppose the stored code is `K_U(B)=Q_U C(B) q_U`. The next +child uses gathered block V and the usual physical input `Q_V x`. +Its logical input code is exactly + +```text +q_V K_U(B) Q_V + = I+iota_P [q_V,P Q_U,P B q_U,R Q_V,R] pi_R. (6) +``` + +When U and V, their row roles, and their views agree, the adjacent +factors cancel and (6) is C(B). This is the useful matched entrance. +For distinct gathered blocks, (6) is still upper, but it need not be +a plain scalar or affine reader. + +The actual H edge from ordinary port 2 to selected port 0 has +coefficient 1/2. Their native labels are respectively 35 and 11. +Use two disjoint equal-width native blocks. At one tensor copy, +the nonconstant coefficient in (6) has the four line directions + +```text +11, 35, 11<<9, 35<<9 +``` + +with signs `(+1,-1,-1,+1)`. They are linearly independent. The exact +Gaussian column of the operator has 16 nonzero entries, each +computed by the checker. Its symplectic Fourier rank is four. +At tensor width f its column support is exactly `16^f`. If the +blocks coincide, the same calculation gives the identity. + +This check does not impose a restriction on all possible new code +services. It shows that the current scalar reader does not certify +this changed entrance. A fixed finite sum of payload monomial reads +cannot equal that coefficient for every width. A word with a growing +number of scalar ADDs, a new native reader, or a different gather can +remain possible; each needs its own cost and source contract. + +The example uses the complete-row child contract to choose disjoint +gathered blocks. It does not claim that a specific two calls in the +latest 640-field global host use those blocks. Such a host has not +been admitted for this new interface. + +## Why the retained left-reader service is not enough + +For a central forward shear with response E, codes on both banks +give the exact typed operation in bank order (X,Y): + +```text +diag(Cx,Cy) [[I,0],[E,I]] diag(Cx,Cy)^-1 + = [[I,0],[Cy E Cx^-1,I]]. (7) +``` + +The retained fixed-reader service supplies `Cy E`. It supplies (7) +when the source code is the identity, or when a separate proved +operation supplies the right factor `Cx^-1`. It does not establish +that factor merely because the next physical entrance contains Q. + +The inverse adjoint of the left-coded response is `E* Cy*`. +For an upper code, `Cy*` is lower. It is generally not `Cy^-1`, +which is upper with its sign changed. Thus the forward service and +its current adjoint are not yet a closed recursive code alphabet. +The missing operation is an actual source-code cancellation or a +different native response with the full block in (7). + +## Fresh row digits + +The same partition cannot be used without change at every depth +under the retained 1/W child-volume contract. The parent role is +fixed within one principal child array. The child's own selected +and ordinary roles belong to a later row digit. + +This distinction is visible without native phases. Restrict to one +actual nonzero H edge and put `C=I+(1/2)e_12`. On d independent row +digits, the corresponding product is `C^tensor d`. Then + +```text +(C^tensor d-I)^(d+1)=0, +(C^tensor d-I)^d != 0. (8) +``` + +For example, d=2 has a nonzero product of the two nilpotent maps. +The checker verifies d=1,2,3,4 exactly. In general the top term is +`d! (C-I)^tensor d`, which is nonzero in characteristic zero. + +Thus the square-zero claim at one row digit does not prove a +depth-independent square-zero claim for the whole recursion. +Equation (8) is not a lower bound on removal cost. A structured +multi-digit code can still have a short description and a separate +algorithm. No such full algorithm is supplied here. + +## A valid four-code identity + +The polynomial `q^3-q^2+q-I` vanishes at the one-copy eigenvalues +1 and -i. It fails at tensor width two: at eigenvalue -1 it equals +-4. Therefore the original alternating-sign four-code proposal +does not apply at all widths. + +There is a corrected identity. Let A be any map from R to P, and +let q act on P with `q^4=I`. Set + +```text +K_(e,s) = [[q^e, s q^(e-1) A], + [0, I ]]. +``` + +Use the chronological sequence + +```text +(e,s) = (1,+1), (3,+1), (1,-1), (3,-1). +``` + +The first two codes have product +`I+N((q^3+q^2)A)`. The last two have its inverse. +Thus the complete product is the identity. No q passes through A. +The checker also uses a noncommuting matrix A and all four phase +eigenvalues as an exact control. + +For (3), A must be the same transported `B q_R` in all four calls, +on the same row partition and with the same q_P. The exponent +change from 1 to 3 is a selected q_P^2 translation. The identity +does not prove those entrance conditions or the reader equality. +In particular, four identical semantic transforms on the same +block give only their fourth power; this is not a new productive +full-transform supplier by itself. + +## The common-q alternative + +The separately frozen phase-coded triple has endpoint + +```text +(-F25 q Y0, F25 q X0) +``` + +on arbitrary physical inputs. Its source is +`native-escape-20261017/phase-coded-triple-20261020/FREEZE.json`, +digest +`0ee32fe22f42cffce2a9673f0dc95496a4b4bb8b11a534f77a11f5fe9c7aeb4b`. +The current proof and complete phase replay are inherited here. + +Each q_p has odd norm in dimension 25 and is not the characteristic +vector. An orthogonal basis can start with q_p. Therefore +`F25 q_p`, up to its exact monomial frame factors, is a rank-24 +native operator. This interpretation has target mass `224*24=5376`. +The actual profile is + +```text +4176 H1 + 192 H2 + 144 H3 + 48 H8. +``` + +It has exactly that mass. If this word is used as an H24 supplier, +then for every 0 r / 24^b. +``` + +The normalized child moment is therefore strictly greater than one. +Relabeling the word as an H24 supplier does not give a positive-b +saving. It can still be useful as a coded H25 operation if a proved +caller consumes the missing q factor. + +## A safe output conversion and the open contract + +For an actual root reader H, a standalone removal of `K(H)` can use +the existing 112 data fields: + +```text +apply q to all 112 fields; +apply C(-H), with its 216 scalar ADDs; +apply Q to all 112 fields. +``` + +This gives the exact inverse code on arbitrary data. It has 224 +rank-one line operations and 2,048 scalar primitives, before line +side maps and whole-stream address costs. No clean accumulator is +used. This is a safe upper bound, not an optimum or a strict saving. + +A useful positive recursive construction must instead bind all of: + +1. the two-sided operation (7), or an equivalent code update; +2. the gathered-axis code in (6) at every child entrance; +3. the code on every borrowed output, with its actual next owner; +4. the multi-digit description and its scalar/address cost; +5. a raw outer output or a priced final conversion. + +The closed upper algebra removes an operator-product problem. It +does not remove these physical access and hosting conditions. + +## A same-block inverse companion + +There is also a positive two-type construction with an explicit +scope. Suppose a reversible supplier has the complete endpoint +`S=C F`, with the identity on every borrowed field. Suppose + +```text +C=W^-1 L W, WF=FW, LZ=ZL, +J=W^-1 Z W is monomial, +Z F^-1 Z=(-i)^e F. +``` + +Here F is the full transform on e selected axes. Z is the sign on +those axes. Then J commutes with C, and + +```text +i^e J S^-1 J^-1 = F C^-1. (9) +``` + +Thus the forward word has type `I -> C`, and its transformed reverse +has type `C -> I`, with positive semantic F in both cases. The +second word after the first gives F^2. The equality holds on every +input, including arbitrary borrowed values. + +For the upper code K(H0), take `W=q`, `L=C(H0)`, and the common +all-axes sign Z. The root reader is a scalar port map, so it commutes +with Z. On an odd line p, at tensor width f, + +```text +Q_p Z q_p = (-i)^f X_p Z. +``` + +Therefore J has one translation, one address sign, and a known +scalar phase on each coded field. It has no new native factor. +Every inverse native kernel in the reversed word can use +`C_axis^-1=X_axis C_axis`; its translation must be included in the +wrapper. This retains the native profile. Scalar inverses, address +passes, and the two J wrappers still have their own costs. + +Equation (9) is a complete endpoint statement only for a supplier +that has the stated S endpoint and borrowed-field contract. The +208-line coded terminal gives such a candidate after its explicit +bank exchange. It already has mass 5,600. This lemma does not turn +that mass into a strict saving, and it does not apply without a new +derivation to the cheaper code Khat. + +For two different gathered blocks, the join contains `C_V^-1 C_U`. +It cancels only when the two transported codes agree. Equation (6) +is the actual condition at that join. Thus (9) gives a useful +same-block type pair, not a complete recursive reuse theorem. + +## Verification + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/coherent-port/recursive-code-interface-20261020/check_interface.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/coherent-port/recursive-code-interface-20261020/check_interface.py +``` + +The checker pins every input. It reads actual source matrices but +imports no source interpreter. 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"final-optimized/PHASE-CODED.json.gz": "68b9d0993a2e31f2f8f41623de9cd5692c1b25f24088f3f6999f82ebfb566d46" + }, + "normal_optimized_byte_identical": true, + "payload_decompressed_sha256": "ffdbe1c84af50e58ee0ab3a9ada15571476146caad1119f55e17d655934f0874", + "scope": "Exact local phase-coded words and ordered caller algebra. The direct208-line terminal gives native mass5600. Routed terminal maps, recursive hosting and numerical-grid costs remain separate. No strict supplier improvement.", + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/PHASE-CODED.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/PHASE-CODED.md new file mode 100644 index 0000000000..122234465d --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/PHASE-CODED.md @@ -0,0 +1,248 @@ +# A phase-coded clean response with a FULL terminal + +The clean native word admits the following changed response: + +```text +F_Q(a,u,z,v) = (-z, u, a+B u, v+Q_R u). +B_Q(a,u,z,v) = (z, u+D z-q_R v, -a, v), D=-B*. +``` + +Each Q-entry word uses native mass 1792 and 4632 real scalar +primitives. It uses no owned field. The I-entry formation word has +native mass 1808 and the same scalar cost. All 416 borrowed helper +fields are restored. + +The three-call word `F_Q0, B_Q1, F_Q2` exposes its data and selected +record in FULL fields. Its direct terminal has 208 positive-line +calls. The total native mass is 5600. This is an exact closure of the +operator algebra. It is not a strict supplier improvement. The +routed terminal invoice, recursive hosting, and numerical grid are +separate obligations. + +## Source and native change + +The source is the frozen clean late exchange in +`new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020`. +Its forward payload has decompressed SHA256 +`b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083`. +Its freeze has SHA256 +`96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc`. +The selected-role inverse-adjoint construction is pinned by +`DUAL-FREEZE.json`, SHA256 +`fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43`. +All paths in this note are relative to the campaign `lanes` directory. + +The local input has physical types + +```text +X = Q(a,u), Y_P = Q_P z, Y_R = v. +``` + +The formation variant has `Y_P=z`. Both variants output X and +selected Y in F9. Ordinary Y has frame `F9 q_R`. + +Delete the 592 ordinary X-to-Y transfer ADDs from the retained core. +Keep every native event, frame, input adapter, and output adapter. +Keep the FULL source code and the signed selected exchange. The +remaining native word has content map + +```text +F_zero(a,u,z,v) = (-z,u,a+B u,v). +``` + +The checker verifies this map on all 640 arbitrary input fields. +In particular, the internal target code and its inverse still cancel +when the cross-bank transfers are absent. + +Before all input adapters, apply 96 physical unit ADDs: + +```text +physical Y_p <- physical Y_p + physical X_p, p in R. +``` + +The physical input on X is Q, while ordinary Y enters in I. Thus this +prefix adds `Q_R u` to v. It is not a same-frame logical addition. +Composition with `F_zero` gives the displayed `F_Q`. + +## The backward word + +Take the same-chronology inverse adjoint of `F_zero`, then conjugate +it by the selected X/Y role exchange. This gives + +```text +B_zero(a,u,z,v) = (z,u+D z,-a,v). +``` + +The native operators and endpoint adapters are unitary. Their inverse +adjoints are the same physical operators. For a scalar ADD, reverse +source and target and negate the coefficient. For a real SCALE, +invert the coefficient. The producer applies these rules in the +original event order. + +The selected input frames are equal in the Q-entry variant. The +selected output frames are also equal. Thus the role conjugation +uses wire labels and adds no boundary swap instructions. + +The inverse adjoint of the physical entry prefix is + +```text +physical X_p <- physical X_p - physical Y_p, p in R. +``` + +Its logical effect is `u <- u-q_R v`. It therefore gives the displayed +`B_Q`. No q operator is moved through B or D. + +## Native and scalar invoice + +The Q-entry profile is + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H8. +``` + +The formation profile replaces the last sixteen H8 calls by H9. +There are 1520 native calls in each word. + +The retained scalar core costs 1720. The FULL source code or its +dual costs 1760. The signed selected exchange costs 384. The physical +entry prefix costs `96*8=768`. Thus the complete scalar cost is + +```text +1720 + 1760 + 384 + 768 = 4632. +``` + +No native recipe is changed. The checker compares the complete +native records and all endpoint adapters with the pinned source. +It checks all 640 body columns, then composes the physical prefix +with Q or q kept on its original input source. This checks all 640 +ordered columns of each complete local map. + +The body prefix bound and the physical entry shear bound are recorded +separately. They are not a complete recursive numerical-grid invoice. + +## Three actual stage contents + +The no-reset boundary theorem is pinned by +`native-escape-20261017/no-reset-triple-20261020/FREEZE.json`, +SHA256 +`089425bdf431d81456e1c988a1fd21a837baca43e510bc92dee98dc2ee571791`. +Its entry and exit identities are independent of the local content +map. Each port route fixes its own Q line. They therefore transport +the changed maps above with the same global Q and q. + +Use I-entry formation at stage 0 and Q-entry words at stages 1 and 2. +Define initial contents by + +```text +a = q_P X0_P, u = q_R X0_R, +z = Y0_P, v = Y0_R. +``` + +Let B0, D1, and B2 be the routed operators at their actual stages. +They need not commute. Set + +```text +alpha = a+B0 u, +R = D1 alpha-q_R v, +beta = alpha+B2 R. +``` + +After the three calls and their declared exit views, the complete +physical output is + +```text +X = F25(-z,R), +Y = F25(beta,u+D1 alpha). +``` + +The ordinary Y output is FULL because its logical content before +the last q exit is `Q_R(u+D1 alpha)`. This cancellation occurs on the +left of the whole expression. It does not commute Q through D1. + +## Ordered terminal + +Apply these four shears after the global exits: + +```text +Y_P <- Y_P-B2 X_R, +X_R <- X_R-D1 Y_P, +Y_R <- Y_R-D1 Y_P, +Y_P <- Y_P-B0 Y_R. +``` + +Their content is + +```text +X = (-z,-q_R v), Y = (a,u). +``` + +All sources and targets are FULL. No ordinary-hole query is used. +Positive Q on the 96 ordinary X fields and on all 112 Y fields gives + +```text +(X,Y) = F25(-Y0,X0). +``` + +The scalar port word for the four shears costs 7040. Their routed +monomial views must also be counted. The 208 positive-line children +and their wrappers must be supplied. + +There is a shorter scalar placement. Immediately after the middle +call, apply the current FULL shear `X_R <- X_R-D1 X_P`. The last +call then outputs + +```text +X = F25(-z,-q_R v), +Y = F25(alpha-B2 q_R v,u). +``` + +Only the final B2 and B0 upper shears remain. This uses three FULL +shears in total and has scalar port cost 5280. It has the same +208-line terminal. + +## Full native-mass limit of this construction + +With formation at stage 0, the complete profile including the direct +terminal is + +```text +4384 H1 + 192 H2 + 144 H3 + 32 H8 + 16 H9. +``` + +Its native mass is + +```text +4384 + 192*2 + 144*3 + 32*8 + 16*9 = 5600 = 224*25. +``` + +For every `0 <= sigma < 1`, all child ranks are below 25. Hence + +```text +sum_h count_h h^sigma > 25^(sigma-1) sum_h count_h h + = 224*25^sigma. +``` + +Thus regrouping the same native mass cannot give a strict positive +moment margin while every child rank remains below 25. A strict +improvement must remove some native mass or change this complete +construction. This statement does not give a lower bound for coupled +field encodings or other native schedules. + +## Verification + +Run the two programs in fresh output directories: + +```sh +python3 -I -B emit_phase_coded.py --out NEW_NATIVE_DIRECTORY +python3 -I -B check_caller.py --out NEW_CALLER_DIRECTORY +``` + +The expected statuses are `PASS_PHASE_CODED_CLEAN_LOCAL` and +`PASS_ORDERED_PHASE_CODED_CALLER`. The caller checker uses a free +operator-word algebra. It cancels only adjacent Q and q factors. +It checks the complete content endpoint, both terminal placements, +and the final original-input phases. 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The source phase theorem admits the mixed boundaries. Exact routed decoder maps, recursive hosting, and numerical-grid costs remain separate. 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The source phase theorem admits the mixed boundaries. Exact routed decoder maps, recursive hosting, and numerical-grid costs remain separate. Native mass5600 is not a strict supplier improvement.", + "source_pins": { + "phase_freeze": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/FREEZE.json", + "sha256": "089425bdf431d81456e1c988a1fd21a837baca43e510bc92dee98dc2ee571791" + } + }, + "status": "PASS_ORDERED_PHASE_CODED_CALLER", + "zero_order_scalar_port_invoice": { + "four_final_FULL_shears": 7040, + "shorter_three_FULL_shear_total": 19176, + "three_local_words": 13896, + "total": 20936 + } +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/check_caller.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/check_caller.py new file mode 100644 index 0000000000..d15d71d7af --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/check_caller.py @@ -0,0 +1,171 @@ +#!/usr/bin/env python3 +"""Check the ordered caller and its remaining phase invoice.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PHASE = LANES / "native-escape-20261017/no-reset-triple-20261020" +PINS = { + "phase_freeze": ( + PHASE / "FREEZE.json", + "089425bdf431d81456e1c988a1fd21a837baca43e510bc92dee98dc2ee571791", + ), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def reduced(word): + result = [] + for letter in word: + if result and (result[-1], letter) in (("Q", "q"), ("q", "Q")): + result.pop() + else: + result.append(letter) + return tuple(result) + + +def add(*terms): + result = {} + for scale, poly in terms: + for word, coefficient in poly.items(): + result[word] = result.get(word, F(0)) + scale * coefficient + if not result[word]: + del result[word] + return result + + +def op(letter, poly): + result = {} + for word, coefficient in poly.items(): + key = reduced((letter,) + word) + result[key] = result.get(key, F(0)) + coefficient + if not result[key]: + del result[key] + return result + + +def neg(poly): + return add((-1, poly)) + + +def forward(state, reader): + a, u, z, v = state + return [neg(z), u, add((1, a), (1, op(reader, u))), + add((1, v), (1, op("Q", u)))] + + +def backward(state, lower): + a, u, z, v = state + return [z, add((1, u), (1, op(lower, z)), (-1, op("q", v))), + neg(a), v] + + +def encoded(poly): + return [[list(word), str(value)] for word, value in sorted(poly.items())] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for name, (path, pin) in PINS.items(): + need(sha256(path.read_bytes()).hexdigest() == pin, + "Pinned route source " + name) + + a, u, z, v = [{(letter,): F(1)} for letter in ("a", "u", "z", "v")] + alpha = add((1, a), (1, op("B0", u))) + state0 = forward([a, u, z, v], "B0") + state1 = backward(state0, "D1") + state2 = forward(state1, "B2") + r = add((1, op("D1", alpha)), (-1, op("q", v))) + beta = add((1, alpha), (1, op("B2", r))) + expected = [neg(z), r, beta, op("Q", add((1, u), (1, op("D1", alpha))))] + need(state2 == expected, "The complete noncommuting content endpoint") + + full = state2[:3] + [op("q", state2[3])] + need(full[3] == add((1, u), (1, op("D1", alpha))), + "The ordinary output has a FULL representation") + + decoded = list(full) + decoded[2] = add((1, decoded[2]), (-1, op("B2", decoded[1]))) + need(decoded[2] == alpha, "The selected record has no borrowed baseline") + decoded[1] = add((1, decoded[1]), (-1, op("D1", decoded[2]))) + decoded[3] = add((1, decoded[3]), (-1, op("D1", decoded[2]))) + decoded[2] = add((1, decoded[2]), (-1, op("B0", decoded[3]))) + need(decoded == [neg(z), neg(op("q", v)), a, u], + "Four ordered FULL shears") + final = [decoded[0], op("Q", decoded[1]), + op("QP", decoded[2]), op("Q", decoded[3])] + need(final == [neg(z), neg(v), op("QP", a), op("Q", u)], + "The canonical signed exchange of the original physical inputs") + + middle = list(state1) + middle[1] = add((1, middle[1]), (-1, op("D1", middle[0]))) + alternate = forward(middle, "B2") + alternate = alternate[:3] + [op("q", alternate[3])] + need(alternate == [ + neg(z), neg(op("q", v)), + add((1, alpha), (-1, op("B2", op("q", v)))), u + ], "A current FULL middle scatter replaces two final scatters") + alternate[2] = add((1, alternate[2]), (-1, op("B2", alternate[1]))) + alternate[2] = add((1, alternate[2]), (-1, op("B0", alternate[3]))) + need(alternate == decoded, "The shorter scalar decoder has the same result") + + bad = list(full) + bad[2] = add((1, bad[2]), (1, op("B2", bad[1]))) + need(bad[2] != alpha, "A wrong selected correction fails") + need(op("Q", op("B2", r)) != op("B2", op("Q", r)), + "The checker does not commute Q through a reader") + + profile = {1: 3 * 1392 + 208, 2: 3 * 64, 3: 3 * 48, 8: 32, 9: 16} + mass = sum(rank * count for rank, count in profile.items()) + need(mass == 25 * 224 == 5600, "The exact native mass reaches the threshold") + receipt = { + "status": "PASS_ORDERED_PHASE_CODED_CALLER", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins": { + name: {"path": str(path), "sha256": pin} + for name, (path, pin) in PINS.items() + }, + "initial_contents": ["a=q_P X0_P", "u=q_R X0_R", + "z=Y0_P", "v=Y0_R"], + "content_endpoint": [encoded(p) for p in state2], + "full_endpoint": [encoded(p) for p in full], + "decoded_full_endpoint": [encoded(p) for p in decoded], + "canonical_endpoint": [encoded(p) for p in final], + "native_profile_with_direct_terminal": profile, + "native_mass_with_direct_terminal": mass, + "direct_terminal_positive_lines": 208, + "zero_order_scalar_port_invoice": { + "three_local_words": 3 * 4632, + "four_final_FULL_shears": 4 * 1760, + "total": 3 * 4632 + 4 * 1760, + "shorter_three_FULL_shear_total": 3 * 4632 + 3 * 1760, + }, + "scope": ( + "The ordered algebra closes the signed exchange after direct " + "phase correction. The source phase theorem admits the mixed " + "boundaries. Exact routed decoder maps, recursive hosting, " + "and numerical-grid costs remain separate. Native mass5600 " + "is not a strict supplier improvement." + ), + } + (args.out / "CALLER.json").write_text( + json.dumps(receipt, indent=2, sort_keys=True) + "\n" + ) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/emit_phase_coded.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/emit_phase_coded.py new file mode 100644 index 0000000000..1fd40efcbd --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/emit_phase_coded.py @@ -0,0 +1,316 @@ +#!/usr/bin/env python3 +"""Check a phase-coded ordinary response in the clean native word.""" + +import argparse +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +SOURCE = LANES / ( + "new-core-transfer-20261017/low-displacement-20261020/" + "clean-late-exchange-20261020" +) +PINS = { + "forward_producer": ( + SOURCE / "emit_clean_exchange.py", + "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc", + ), + "dual_producer": ( + SOURCE / "emit_dual.py", + "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8", + ), + "forward": ( + SOURCE / "run-normal/CLEAN-LATE-EXCHANGE.json.gz", + "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083", + ), + "freeze": ( + SOURCE / "FREEZE.json", + "96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc", + ), + "dual_freeze": ( + SOURCE / "DUAL-FREEZE.json", + "fa8f910fe7f22a696f47513c95e814588723dc8abaaa68061fcba3676c308d43", + ), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source " + name) + return raw + + +def load(name, path): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def poly_add(target, source, coefficient=F(1)): + for key, value in source.items(): + target[key] = target.get(key, F(0)) + coefficient * value + if not target[key]: + del target[key] + + +def poly_identity(): + return [{(i, 0): F(1)} for i in range(640)] + + +def apply_scalar_map(rows, state): + result = [] + for row in rows: + value = {} + for source, coefficient in row.items(): + poly_add(value, state[source], coefficient) + result.append(value) + return result + + +def encoded_polynomials(rows): + return [ + [[source, exponent, str(value)] + for (source, exponent), value in sorted(row.items())] + for row in rows + ] + + +def report_prefix_scope(report): + report["body_content_prefix_row_one_norm"] = report.pop( + "maximum_content_prefix_row_one_norm" + ) + report["physical_entry_prefix_row_one_norm"] = "2" + report["prefix_scope"] = ( + "The body bound uses its declared typed input. The physical " + "prefix is a separate unit shear. This is not a complete " + "recursive numerical-grid invoice." + ) + + +def remove_transfers(original): + word = deepcopy(original) + events, ranges, removed = [], {}, [] + for stage, interval in sorted( + original["stage_ranges"].items(), key=lambda item: item[1][0]): + start = len(events) + for index in range(*interval): + event = original["events"][index] + is_transfer = ( + stage == "retained_core" + and event[0] == "scalar" + and event[1][0] == "add" + and 112 <= event[1][1] < 224 + and 0 <= event[1][2] < 112 + ) + if is_transfer: + removed.append([index, event]) + else: + events.append(deepcopy(event)) + ranges[stage] = [start, len(events)] + word["events"], word["stage_ranges"] = events, ranges + need(len(removed) == 592, "All ordinary source-to-target transfers") + return word, removed + + +def expected_zero(code, selected, identity): + rows = deepcopy(identity) + for p in selected: + rows[p] = {112 + p: F(-1)} + rows[112 + p] = dict(code[p]) + return rows + + +def expected_dual(code, selected, identity): + rows = deepcopy(identity) + for p in selected: + rows[p] = {112 + p: F(1)} + rows[112 + p] = {p: F(-1)} + for j, coefficient in code[p].items(): + if j != p: + rows[j][112 + p] = -coefficient + return rows + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for name in PINS: + read(name) + base = load("phase_clean_source", PINS["forward_producer"][0]) + dual = load("phase_clean_dual", PINS["dual_producer"][0]) + n = base.n + source = json.loads(read("forward")) + pivots = source["selected_ports"] + selected = set(pivots) + ordinary = [p for p in range(112) if p not in selected] + code = n.rows(source["code"]) + identity = n.r.identity(640) + zero_map = expected_zero(code, selected, identity) + dual_map = expected_dual(code, selected, identity) + permutation = list(range(640)) + for p in pivots: + permutation[p], permutation[112 + p] = 112 + p, p + + expected_f = poly_identity() + expected_b = poly_identity() + for p in pivots: + expected_f[p] = {(112 + p, 0): F(-1)} + expected_f[112 + p] = {(j, 0): v for j, v in code[p].items()} + expected_b[p] = {(112 + p, 0): F(1)} + expected_b[112 + p] = {(p, 0): F(-1)} + for p in ordinary: + expected_f[112 + p][p, 1] = F(1) + expected_b[p][112 + p, -1] = F(-1) + for j in pivots: + value = -code[j].get(p, F(0)) + if value: + expected_b[p][112 + j, 0] = value + + providers, reports = {}, {} + for provider, variants in source["providers"].items(): + providers[provider], reports[provider] = {}, {} + for entry in ("I", "Q"): + original = variants[entry] + forward, removed = remove_transfers(original) + report = base.verify(forward, zero_map) + need( + [e for e in original["events"] if e[0] == "native"] + == [e for e in forward["events"] if e[0] == "native"], + "Every native event is unchanged", + ) + need( + all(forward[k] == original[k] for k in + ("frames", "native_recipes", "input_views", "output_views")), + "Every native phase and endpoint adapter is unchanged", + ) + state = poly_identity() + for p in ordinary: + state[112 + p][p, 1] = F(1) + actual = apply_scalar_map(zero_map, state) + need(actual == expected_f, "All640 ordered forward columns") + report["physical_entry_adds"] = 96 + report["complete_scalar_primitives"] = ( + report["real_scalar_primitives"] + 96 * 8 + ) + report["removed_transfer_adds"] = len(removed) + report["formal_Q_order"] = "Q_p remains attached to input source p." + report_prefix_scope(report) + providers[provider]["forward_" + entry] = { + "physical_prefix": [["add", 112 + p, p, "1"] for p in ordinary], + "prefix_location": "Before every inherited input adapter.", + "body": forward, + "removed_transfers": removed, + } + reports[provider]["forward_" + entry] = report + + if entry == "Q": + backward = dual.lower(forward, permutation) + report_b = base.verify(backward, dual_map) + state = poly_identity() + for p in ordinary: + state[p][112 + p, -1] = F(-1) + actual = apply_scalar_map(dual_map, state) + need(actual == expected_b, "All640 ordered backward columns") + report_b["physical_entry_adds"] = 96 + report_b["complete_scalar_primitives"] = ( + report_b["real_scalar_primitives"] + 96 * 8 + ) + report_b["extra_boundary_swaps"] = 0 + report_b["formal_Q_order"] = ( + "q_p remains attached to input source Y_p." + ) + report_prefix_scope(report_b) + providers[provider]["backward_Q"] = { + "physical_prefix": [["add", p, 112 + p, "-1"] + for p in ordinary], + "prefix_location": "Before every inherited input adapter.", + "body": backward, + } + reports[provider]["backward_Q"] = report_b + + forward = providers[provider]["forward_Q"]["body"] + bad = deepcopy(forward) + bad["events"].append(deepcopy( + providers[provider]["forward_Q"]["removed_transfers"][0][1])) + try: + base.verify(bad, zero_map) + except ValueError: + pass + else: + raise ValueError("A retained ordinary transfer was accepted") + + payload = { + "schema": "phase-coded-clean-local-v1", + "source_pins": { + name: {"path": str(path), "sha256": pin} + for name, (path, pin) in PINS.items() + }, + "selected_ports": pivots, + "ordinary_ports": ordinary, + "code": source["code"], + "providers": providers, + "zero_response_content": n.r.encoded(zero_map[:224]), + "zero_response_dual_content": n.r.encoded(dual_map[:224]), + "phase_coded_forward": encoded_polynomials(expected_f[:224]), + "phase_coded_backward": encoded_polynomials(expected_b[:224]), + "contract": { + "input_Q": "X=Q(a,u), Y_P=Q_P z, Y_R=v.", + "input_I": "X=Q(a,u), Y_P=z, Y_R=v.", + "output_frames": "X and Y_P are F9; Y_R is F9 q_R.", + "forward_content": "(-z,u,a+B u,v+Q_R u)", + "backward_content": "(z,u+D z-q_R v,-a,v), D=-B^T", + "prefix": ( + "The physical ordinary ADD is applied before the input " + "views. It is not a same-frame logical ADD." + ), + "scope": ( + "Complete local words. A routed caller and its final " + "original-input phases are separate obligations." + ), + }, + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + (args.out / "PHASE-CODED.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_PHASE_CODED_CLEAN_LOCAL", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "reports": reports, + "arbitrary_input_columns": 640, + "arbitrary_helpers_restored": 416, + "new_native_kernels": 0, + "native_phase_scope": ( + "All native kernels and endpoint adapters are byte-exact " + "inherited records. The physical entry ADD has coefficient " + "one or minus one and no spatial operator." + ), + "scope": payload["contract"]["scope"], + } + (args.out / "CHECKS.json").write_text( + json.dumps(receipt, indent=2, sort_keys=True) + "\n" + ) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/final-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/final-normal/CHECKS.json new file mode 100644 index 0000000000..f971031b03 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/final-normal/CHECKS.json @@ -0,0 +1,220 @@ +{ + "arbitrary_helpers_restored": 416, + "arbitrary_input_columns": 640, + "native_phase_scope": "All native kernels and endpoint adapters are byte-exact inherited records. The physical entry ADD has coefficient one or minus one and no spatial operator.", + "new_native_kernels": 0, + "payload_decompressed_sha256": "ffdbe1c84af50e58ee0ab3a9ada15571476146caad1119f55e17d655934f0874", + "producer_sha256": "28f264dfeb47d5422c58fd51c8316ea69081dfc208831085d2bddf3b13d45baa", + "reports": { + "base": { + "backward_Q": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "body_content_prefix_row_one_norm": "3", + "complete_scalar_primitives": 4632, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "extra_boundary_swaps": 0, + "formal_Q_order": "q_p remains attached to input source Y_p.", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "physical_entry_adds": 96, + "physical_entry_prefix_row_one_norm": "2", + "prefix_scope": "The body bound uses its declared typed input. The physical prefix is a separate unit shear. This is not a complete recursive numerical-grid invoice.", + "private_fields": 0, + "real_scalar_primitives": 3864, + "scalar_stage_prices": { + "retained_core": 1720, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + }, + "forward_I": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "body_content_prefix_row_one_norm": "22", + "complete_scalar_primitives": 4632, + "direct_full_identity_wrapper_children": 16, + "explicit_input_monomial_views": 112, + "explicit_output_monomial_views": 96, + "formal_Q_order": "Q_p remains attached to input source p.", + "native_children": 1520, + "native_mass": 1808, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "9": 16 + }, + "native_side_map_upper_bound": 3008, + "odd_divisions": 0, + "owned_fields": 0, + "physical_entry_adds": 96, + "physical_entry_prefix_row_one_norm": "2", + "prefix_scope": "The body bound uses its declared typed input. The physical prefix is a separate unit shear. This is not a complete recursive numerical-grid invoice.", + "private_fields": 0, + "real_scalar_primitives": 3864, + "removed_transfer_adds": 592, + "scalar_stage_prices": { + "retained_core": 1720, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + }, + "forward_Q": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "body_content_prefix_row_one_norm": "22", + "complete_scalar_primitives": 4632, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "formal_Q_order": "Q_p remains attached to input source p.", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "physical_entry_adds": 96, + "physical_entry_prefix_row_one_norm": "2", + "prefix_scope": "The body bound uses its declared typed input. The physical prefix is a separate unit shear. This is not a complete recursive numerical-grid invoice.", + "private_fields": 0, + "real_scalar_primitives": 3864, + "removed_transfer_adds": 592, + "scalar_stage_prices": { + "retained_core": 1720, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + } + }, + "extra": { + "backward_Q": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "body_content_prefix_row_one_norm": "3", + "complete_scalar_primitives": 4632, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "extra_boundary_swaps": 0, + "formal_Q_order": "q_p remains attached to input source Y_p.", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "physical_entry_adds": 96, + "physical_entry_prefix_row_one_norm": "2", + "prefix_scope": "The body bound uses its declared typed input. The physical prefix is a separate unit shear. This is not a complete recursive numerical-grid invoice.", + "private_fields": 0, + "real_scalar_primitives": 3864, + "scalar_stage_prices": { + "retained_core": 1720, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + }, + "forward_I": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "body_content_prefix_row_one_norm": "22", + "complete_scalar_primitives": 4632, + "direct_full_identity_wrapper_children": 16, + "explicit_input_monomial_views": 112, + "explicit_output_monomial_views": 96, + "formal_Q_order": "Q_p remains attached to input source p.", + "native_children": 1520, + "native_mass": 1808, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "9": 16 + }, + "native_side_map_upper_bound": 3008, + "odd_divisions": 0, + "owned_fields": 0, + "physical_entry_adds": 96, + "physical_entry_prefix_row_one_norm": "2", + "prefix_scope": "The body bound uses its declared typed input. The physical prefix is a separate unit shear. This is not a complete recursive numerical-grid invoice.", + "private_fields": 0, + "real_scalar_primitives": 3864, + "removed_transfer_adds": 592, + "scalar_stage_prices": { + "retained_core": 1720, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + }, + "forward_Q": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "body_content_prefix_row_one_norm": "22", + "complete_scalar_primitives": 4632, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "formal_Q_order": "Q_p remains attached to input source p.", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "physical_entry_adds": 96, + "physical_entry_prefix_row_one_norm": "2", + "prefix_scope": "The body bound uses its declared typed input. 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"-1/2", + "91": "1/2" + } + ], + "schema": "rank16-row-involution-v1", + "source_pins": { + "capture_checker": "ccf661107a790c3d858a3f2bd4d8adc5269f588bfd989bd2e2029e26cbb14081", + "capture_payload": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7", + "native": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "pairs": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + } +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/cover-algebra/BRIDGES.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/cover-algebra/BRIDGES.md new file mode 100644 index 0000000000..fda782ac93 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/cover-algebra/BRIDGES.md @@ -0,0 +1,344 @@ +# Legal native bridges for routed centre operators + +This note continues `PROOF.md`. It uses the same pinned centre matrix and +route charts. The global boundary frames are the frames supplied by the +selected controller and checked by `temporal-reuse/verify_routes.py` against +`DATA-PHASES.json`: + +\[ +X_q:F_{U_s},\qquad Y_q:F_{U_s}C_q^{-1},\qquad +U_s=L\oplus E_1\oplus\cdots\oplus E_s. +\] + +Here `dim(L)=9`, each `dim(E_t)=8`, and `s=0,...,8`. +At the initial boundary, `X_q` has frame `C_q` and `Y_q` has frame zero. +This note checks bridges under these frame formulas. It does not repeat the +complete controller-frame derivation. + +## Full frame conditions + +Let + +\[ +\phi_{X,s}(x)=\sum_{i=0}^{8+8s}(e_i\cdot x)\pmod4, +\] + +\[ +\phi_{Y,s,q}(x)=\phi_{X,s}(x)-(q\cdot x)\pmod4. +\] + +Each dot product in these phase formulas is its binary value, interpreted +as 0 or 1 before reduction modulo 4. The phase value is `i^phi`. +The polar matrices are the orthogonal projections onto `U_s` and + +\[ +H_s(q)=U_s\cap q^\perp, +\] + +respectively. For an orthogonal right route `r`, a bridge from input port +`p` to output port `q` is legal up to an even linear phase exactly when + +\[ +\begin{array}{ll} +X:& rU_s=U_s,\\ +Y:& rH_s(p)=H_s(q). +\end{array} +\] + +Equality of the polar matrices is necessary. It is sufficient because two +quadratic phase forms with the same polar matrix differ by an even linear +form. The resulting translation must be applied; the polar condition alone +does not certify the phase. + +The stronger pair of conditions `rU_s=U_s` and `rp=q` is sufficient for a +Y bridge. It is not necessary. In particular, the actual Y frame does not +distinguish its hole line from the other directions in its radical. + +## A legal exchange with a future direction + +Let `e` be a unit coordinate vector in a future block. The binary +transvection + +\[ +S_{q,e}=I+(q+e)(q+e)^T +\] + +exchanges `q` and `e` and fixes `H_s(q)` pointwise. Thus it is Y-frame legal, +although it does not preserve `U_s` or the line `q`. + +Every selected port has weight 3 or 7. Therefore +`phi_Y(q)=wt(q)-1=2 mod4`, whereas `phi_Y(e)=0`. The full phase defect is + +\[ +\phi_{Y,s,q}(S_{q,e}x)-\phi_{Y,s,q}(x) +=2(q+e)\cdot x\pmod4. +\] + +The correction is exactly the translation vector `q+e`. +The checker verifies this identity as a full quadratic phase form for all +112 ports and all eight boundaries that have a future block. A controller +that forbids these bridges would impose a construction-specific restriction. + +## Future Y access and past X access + +Let `D_t=diag(rho_t(q))` and `K_t=D_t J D_t`, as operators on logical +content. The physical implementation of `D_t` below includes its phase +alignment. A bare cover permutation is not a substitute for that alignment. + +If `s=t`, then every `rho_t(q)` preserves `U_s`. The same argument gives +`K_t` and `K_t^{-1}` on X. At the initial zero Y frame every `D_t` is legal +without a phase defect. Stage 0 has `D_0=I`. + +There are explicit phase corrections for these two alignments. Write +`B_q` for the eight chart columns and set + +\[ +(\beta_q)_i=\frac{\operatorname{wt}((B_q)_i)-1}{2}\pmod2. +\] + +Let `lift_t` put an eight-bit vector in `E_t`. Then + +\[ +\delta_Y(q,t)=q+\operatorname{lift}_t(\beta_q),\qquad s=1`, write `U_prev=L+E_1+...+E_(t-1)`. +If `J_qp` is nonzero, then `p` and `q` are orthogonal. Set +`g=rho_t(q)rho_t(p)`. One has + +\[ +gU_{prev}=q^\perp\text{ in }L +\;\oplus\;E_1\oplus\cdots\oplus E_{t-1} +\;\oplus\;\langle\rho_t(q)p\rangle +\subseteq H_t(q). +\] + +Legal pre-X and post-Y bridges preserve this inclusion. An identity +same-port transfer does not have this property, because `U_prev` contains +the target hole. Hence one forward off-diagonal edge cannot be converted +to the identity transfer by legal endpoint bridges alone. This is a +single-edge statement. It does not exclude multi-call controller paths. + +## Endpoint test for the current full-stage residual + +At the final boundary the rank-zero Y algebra is the line-preserving group +algebra: a group term `g` from port `p` to port `q` must satisfy `gp=q`. +This algebra is closed under composition. The same condition makes +`C_q g C_p^{-1}` have zero polar defect. + +The controller worker is studying the residual + +\[ +E=K_8K_7^{-1}K_6K_5^{-1}\cdots K_1^{-1}K_0. +\] + +In fact, the same conclusion holds for every chronological product of +`K_t` and `K_t^{-1}` that contains at least one `K_t`, with the stages +increasing from right to left. The identity coefficient of `K_t^{-1}` +is `12/13`, and each remaining term has the support of `K_t`. +Before the first off-diagonal term in a product path, the carried initial +port is the current port. At stage 0, an off-diagonal term leaves that +vector in the new port's orthogonal complement, since `J_qp` is supported +only on `p dot q=0`. At a positive stage `t`, the first off-diagonal term +sends that vector into `E_t`, hence into `H_t(q)`. + +Each subsequent term at stage `u>t` maps +`H_(u-1)(p)` to `H_(u-1)(q)`: the two route charts map these spaces to the +same space `E_u + E_1 + ... + E_(u-1)`. An identity term also preserves +this property. Each factor `K_t` has zero port diagonal, so at least one +off-diagonal term must occur in every product path. Therefore every +surviving entry of any such product satisfies `q dot (gp)=0`. No such +entry can satisfy `gp=q`. This includes both orientations of the +alternating normalization word. + +Consequently this residual is outside the final Y rank-zero algebra. Every +nonzero group entry of `C_q E C_p^{-1}` has polar defect rank 2. This does +not prove that two complete rank-one endpoint boundaries are the cheapest +repair. A factored or encoded repair may cost less and remains a research +target. The actual controller word and its full cost are separate obligations. +The statement does not cover arbitrary inserted routers that mix future +blocks or products whose stage order decreases. + +### A stronger statement for arbitrary port support + +The restriction can be proved without the binary-orthogonal support of +`J`. Consider any chronological product + +\[ +E=(D_m A_m D_m)\cdots(D_1 A_1 D_1)A_0, +\] + +where each `A_s` is a scalar port matrix and the block `E_s` is new at stage +`s`. Port labels may repeat. Use the same chart for each occurrence of the +same physical label. On a product path, let `p` and `q` be the input and +output labels of a stage, and let `v` be the carried image of the original +source line before that stage. The vector `v` has no component in `E_s`. +Set `h=p dot v_local`. For `g=rho_s(q)rho_s(p)`, the block formula gives + +\[ +(gv)_{E_s}=h B_q^T p,\qquad q\cdot(gv)=(q\cdot p)h. +\] + +Every later stage fixes `E_s` pointwise. A final line-preserving path must +therefore have zero new external component at each stage and final hole +coefficient one. The hole coefficient cannot change from zero to one under +the displayed recurrence. Thus it is one at every stage, and +`B_q^T p=0`. Since `ker(B_q^T)=span(q)`, this implies `p=q` at every +positive stage. Each such route is the identity. The stage-zero label must +also equal the original label to give the final source line. + +Consequently the line-preserving part of `E` is exactly the product of the +within-label blocks of the scalar matrices. With distinct labels it is + +\[ +\operatorname{diag}_p\left(\prod_{s=0}^m (A_s)_{pp}\right) +\] + +at the identity cover element. This is a statement about a chronological +product. It is not a homomorphism on arbitrary words in the routed algebra. + +For the 120-port completion with its eight distinct centre-normal labels, +the line-preserving part of `M_8...M_0` is exactly +`diag(0_112,13^9 I_8)`. With arbitrary choices of eight additional labels, +at least 104 of the original labels remain singletons. Their diagonal is +zero, so their entire input columns have no line-preserving component in +this normalization word. A duplicate label is allowed by the local native +interface; it does not remove this count. + +There is a further statement that does not require a zero diagonal. Let +the last scalar matrix split as `A_m=A_same+A_change`, according to whether +its input and output physical labels agree. Let `H` be the cover subgroup +that fixes `E_m` pointwise. Every term of the earlier invertible product +`P` and its inverse lies in `H`. The routed `A_same` is supported at the +identity, whereas every routed `A_change` term is outside `H`. Therefore +the two products have disjoint `H` and non-`H` support. The second product +cannot be zero if `A_change` is nonzero, since `P` is invertible. + +For such a last changing term from `p` to `q`, + +\[ +g^{-1}q=\rho_m(p)q +\] + +has a nonzero `E_m` component. No earlier route sends an initial local line +to this vector, because earlier routes preserve `U_(m-1)`. Hence every +surviving coefficient in that second product fails line preservation. Any +nontrivial last label-changing factor leaves a nonfree endpoint component. +This argument was checked independently with the controller worker. It +does not give a lower bound on the cost of a final repair. + +## Reproduction + +From the workspace root, run: + +```sh +python3 -B work/centre-encoding-campaign-20261014/lanes/cover-algebra/verify_bridges.py --interface work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json --out work/centre-encoding-campaign-20261014/lanes/cover-algebra/BRIDGES.json +``` + +The output is `PASS_EXACT_NATIVE_BRIDGE_PHASES`. The code uses exact integer +phase forms, binary matrix operations, and rational matrix coefficients. +It does not certify a complete supplier or a multiplication exponent. + +Open work includes a cheaper residual decoder, legal movement of the +post-X factors on idle bank roles, and full lowering of the new scalar +access pattern. This work used AI assistance and builds on the selected +supplier and the campaign's interface, route, and controller calculations. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json new file mode 100644 index 0000000000..3924fe2465 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json @@ -0,0 +1,27210 @@ +{ + "affected_ports": [ + 0, + 2, + 7, + 9, + 10, + 11, + 13, + 14, + 15, + 16, + 20, + 21, + 25, + 27, + 36, + 37, + 41, + 42, + 43, + 44, + 46, + 47, + 51, + 52, + 53, + 57, + 61, + 62, + 63, + 70, + 71, + 72, + 76, + 78, + 79, + 81, + 87, + 89, + 90, + 91, + 92, + 94, + 99, + 104, + 105, + 106, + 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The current dyadic scalar +emitter does not have this operation, but the retained fixed-tape model +already permits fixed odd divisors on a common exact grid. Thus the +modulo-three obstruction applies to that emitter's coefficient ring. It +is not an obstruction to the required computation. + +This note gives a scalar word for the actual A8 block, its fused upper +correction, and a complete representation rule for recursive use. The +fused word uses one existing private array, 7,008 old real scalar +primitives, and 16 real division-by-three scans. It adds no native child +at a legal common-frame cut. It has odd denominator height one at every +prefix. These are new finite statements about this block. The common +odd-grid method is retained prior work. + +The result does not supply the complete controller, its owners, or its +phase proof. In particular, the fused original-X response still has an +eight-dimensional kernel. The retained selected Y values are necessary +for the complete two-bank map. No new complete kappa value is claimed. + +## Source binding + +The actual interface is `../../new-core-transfer-20261017/INTERFACE.json`, +SHA256 `c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746`. +The checker verifies this pin before it reads R. The clean core, its full +native phase review, and the raw selected boundary convention are reviewed +in the parent directory's `NEW-CORE-LOGICAL-REVIEW.md`, +`NEW-CORE-NATIVE-REVIEW.md`, and `NEW-RAW-REVIEW.md`. + +The source model was fetched again at commit +`6f100d4bb5083f8c35d96fd95a539811c62f245c`. The following files have the +same Git blob identities as the prior rational-decoder source packet: + +- [The fixed-tape model](https://github.com/CrocSwap/integer-mult-bounds/blob/6f100d4bb5083f8c35d96fd95a539811c62f245c/upstream/build/sections/02-streams.tex). +- [The exact recursive contract and guard](https://github.com/CrocSwap/integer-mult-bounds/blob/6f100d4bb5083f8c35d96fd95a539811c62f245c/upstream/build/sections/05-layers.tex). +- [The retained common odd grid](https://github.com/CrocSwap/integer-mult-bounds/blob/6f100d4bb5083f8c35d96fd95a539811c62f245c/notes/stopped-product-complex.tex), in "One exact odd-denominator grid". + +The retained grid proof uses division by 21. It scales all root dyadic +inputs and dirty auxiliaries once. It proves the depth bound from the +Gaussian-dyadic endpoint of each completed child. Its exactness argument +also applies to division by three. + +The local campaign predecessor is +`../../interface-proof/rational-decoder/RATIONAL-DECODER.md`. That note +gives the exact signed scan, a one-accumulator J inverse, and the root-grid +cost. Its independent review is +`../../temporal-reuse/RATIONAL-DECODER-REVIEW.md`. The A8 factor below uses +the same arithmetic method on the actual ordinary block. It does not +claim to introduce fixed odd division or common grids. + +## The actual block and its inverse + +Let + + A = [0,7,20,27,36,46,57,111], U = {0,...,111} minus A. + +The pinned interface gives an 8 by 112 signed matrix R. Each row has 56 +nonzero entries. Write R_U for its 104 ordinary columns, and put + + K = R^T/4, H = I_U - K_U R_U. + +The checker derives, from the pinned entries, + + R_U R_U^T = 52 I_8, R_U K_U = 13 I_8. + +Each row of R_U has 52 entries, each equal to +1 or -1. Hence + + H^-1 = I_U - K_U R_U/12 = I_U - R_U^T R_U/48. (1) + +For P=R_U^T R_U, the identity P^2=52P proves both inverse orders. In fact +the coefficient of P in (I-P/4)(I-P/48) is +`-1/4 -1/48 +52/(4*48)=0`. The same calculation proves the other order. +The eigenvalue on the eight-dimensional query image is -12 for H and +-1/12 for its inverse. The eigenvalue on ker(R_U) is one. + +The failure of H to be a dyadic unit is exact: modulo three, the eight +columns of K_U are independent kernel channels. Equation (1) removes +this obstruction over Z[1/2,1/3]. It does not change the native source +operators or treat an odd division as an admitted old SCALE. + +## One private accumulator + +Use the already owned private C0 array. For each row r_i of R_U, perform +the following steps in order: + + C0 = 0 + C0 += r_i[p] * X_p for each nonzero ordinary entry p + C0 *= 1/16 + C0 /= 3 exact signed numerator division + X_p -= r_i[p] * C0 for each nonzero ordinary entry p + C0 = 0 + +All eight rows use the same array. Distinct rows are orthogonal, so the +rank-one updates have zero cross product. Their product is exactly (1). +All other fields are unchanged. C0 ends at zero and has no dependence on +its arbitrary initial value. This is an owned-array construction. It +does not permit the erasure of an arbitrary borrowed helper. + +To apply H, use the same query and scatter with `C0 *= 1/4`, and omit the +division by three. Its row updates also have zero cross product. + +Suppose that k complete inverse rows have already run. The complete next +query r_i X equals r_i times the module input, since each earlier term +contains r_i r_j^T=0. A partial query can have one new factor of three in +its denominator. The complete query has none. Division occurs only after +the complete query. The new scatter therefore adds at most one factor. +This proves the odd-height-one bound at every prefix, including partial +queries and partial scatters. It holds relative to any existing input +height, including rational inputs from an unfinished parent. + +The same argument bounds the additional binary denominator height by four +for the inverse and by two for H. Partial queries do not receive another +scale until the complete orthogonal cancellation has occurred. + +## Fuse the completed-X upper correction + +The raw selected backward boundary needs, after H^-1 on ordinary X, + + X_A += K_A R_U X_U. + +All these X fields are at the same completed full frame. Since +`R_U H^-1 = -R_U/12`, the combined map on the initial completed X is + + X_U' = X_U - R_U^T R_U X_U/48, + X_A' = X_A - R_A^T R_U X_U/48. (2) + +Thus the inverse loop can scatter through all 56 entries of the full row +R_i, instead of only its 52 ordinary entries. Each query still reads only +ordinary X. Its orthogonality and denominator proof are unchanged. +Selected writes do not enter later queries. + +This order matters. The upper correction uses the final ordinary X, and +(2) is the ordered product of that upper map with H^-1. The checker +verifies this product on all 112 data columns. It does not move a line +operator Q through R, K, or H. + +For the raw backward formula, write the original input as x=(a,u), +y=(b,v), and put q=Q^-1 on selected fields. The retained physical input +convention has selected X=Q a. The raw backward core, before its old +postlower correction, gives + + X_U = u - J_US Q a - H v, + X_A = q b - J_AA Q a - J_AU v, + Y_A = Q a, Y_U = v. + +Apply (2). The borrowed-y response of completed X becomes `diag(q,-I)`. +In particular, arbitrary ordinary borrowed v is restored with coefficient +-I; it need not be zero, divisible by three, or a previously computed +centre. The common-grid conversion below supplies the integer divisibility +for every such input. + +Let E=diag(-I_A,I_U). Apart from the explicit input Q, the fused response +of X to original x is + + A_X = E - K R/12. + +The actual matrix has `R E K=12I_8`. Therefore `A_X E K=0`, and +`E A_X=I-E K R/12` is a rank-104 projector. The nullity is exactly eight. +Division by three does not remove this content kernel. The full two-bank +map still has the selected original content in Y_A. A controller that +requires A_X^-1 cannot use this A8 word. A controller that uses the +retained selected Y must prove that use explicitly. + +## Literal invoice and finite guard + +The old scalar price is used without modification. A complex unit ADD +costs eight real primitives; a positive complex `1/4` SCALE costs four; +`1/16` costs eight; CLEAR costs two. A complex odd division is two separate +real scans. It is not assigned an old primitive price. + +| Factor | Unit ADDs | SCALEs | CLEARs | Old real primitives | Real /3 scans | +| --- | ---: | ---: | ---: | ---: | ---: | +| H | 832 | 8 | 16 | 6720 | 0 | +| H^-1 | 832 | 8 | 16 | 6752 | 16 | +| H^-1 with upper correction | 864 | 8 | 16 | 7008 | 16 | + +All three rows use no new native child. The H input word is legal on the +ordinary Y fields at frame I. The inverse and fused words are legal on +completed X at FULL. C0 must be cleared and assigned the same frame before +its query; all operations in one factor then use that frame. No nonzero +private value is relabelled. The scalar packet contains no native frame +transition. A complete transferred word must check these lifetime facts. + +An exact Fraction-row calculation covers all 113 input columns: +112 data fields and arbitrary C0. It obtains the following maximum row +1-norms over every stored scalar prefix: + +| Factor | Maximum row 1-norm | New binary height | New odd height | +| --- | ---: | ---: | ---: | +| H | 121 | 2 | 0 | +| H^-1 | 52 | 4 | 1 | +| Fused inverse | 52 | 4 | 1 | + +The row norms bound stored magnitudes relative to the maximum input field +magnitude. Primitive unit ADD temporaries are bounded by twice the larger +operand bound. The SCALEs and exact division decrease magnitude. Thus +256 times the input bound suffices for H scalar arithmetic, and 128 times +the input bound suffices for either inverse. The signed division carry is +at most two. These are finite factor bounds. They do not assert that the +old complete supplier's precision constant is unchanged. + +When added to the independently reviewed 164514-scalar core, the two +selected exchanges for F cost 416 and the one selected exchange for B +costs 208. Clearing the seven other owned fields costs 14. Thus the +predicted complete local bills are + + balanced F: 171664 old real primitives, + fused B: 171744 old real primitives plus 16 real /3 scans. + +Both retain native mass 5073. These sums are predictions for the literal +transfer. This packet does not claim to have replayed those complete new +words. Their emitter, helpers, phase bindings, and frame checks remain a +separate verification step. + +## Exact signed division and root preparation + +Use one signed w-bit two's-complement numerator. Starting at its least +significant bit, read b, write a, and update the finite carry c by + + a = (b-c) mod 2, c' = (c+3a-b)/2, c starts at 0. + +The six possible input-bit/carry transitions preserve `0 <= c < 3`. +Summation gives `3 Q_unsigned = N_unsigned + 2^w c_final`. With input +and output sign bits s_N,s_Q, the signed quotient is exact precisely when + + c_final = 3 s_Q - s_N. + +This condition rejects nonmultiples. On a valid division the quotient +cannot overflow. The numerator is overwritten in place. Carry and sign +flags need only finite control. There is no second numerical array. +At most `4(w+1)` arithmetic-head steps cover a move to the low end, the +computation traversal, delimiters, and return. Retained descriptor and +record-counter work is an additional O(w+1) per record. The coefficient +four is not claimed for that separate layer. + +Multiplication by three writes `(3b+c) mod 2` and updates +`c'=floor((3b+c)/2)`. Its signed final test is +`c_final=3s_N-s_output`. The preallocated guard prevents overflow. The +same arithmetic-head scan bound applies. Both algorithms preserve the +common record format. The checker exhausts all signed inputs at widths +one through twelve, as a check of the general invariant, and rejects the +unscaled numerator one. + +## Recursive common-grid theorem + +Assume a fixed finite parent word has M inverse-factor occurrences. Assume +all other local operations are Gaussian dyadic. Replace each completed +recursive child by its exact linear endpoint on every data and arbitrary +helper column. Assume each such endpoint is Gaussian dyadic. Let D bound +the number of recursive edges in any live call chain. Put + + K_3 = M(D+1), S = 3^K_3, common grid = 2^-P/S. (3) + +P is a binary guard for the new complete word. At the outer boundary, +multiply the padded integer numerator of every physical numeric stream by +S. This includes arbitrary borrowed data, helpers, and numeric work +streams. Private zeros remain zero. Address fields, tags, and descriptors +are not numeric payloads and are not scaled. Any numeric literal must be +written in the same representation. The factors here write only zero. + +No denominator tag is added. No stream changes format at a local +division, recursive entry, or return. A common scalar S commutes with +every exact linear native operator, so the encoded computation represents +the same operator. This statement does not apply to an unproved rounded +version of that operator. + +Each finite parent prefix adds at most M to the odd denominator height. +The height-one factor proof allows this count per inverse occurrence, +instead of eight counts for its eight divisions. Gaussian-dyadic +operations cannot add odd height. A completed Gaussian-dyadic child also +cannot add odd height, even when its input already has an odd denominator. +Only unfinished calls add height. Their chain has at most D+1 nodes. Thus +all intermediates lie on (3), and every /3 scan receives an integer +numerator divisible by three. + +This proof starts with arbitrary dyadic root values scaled by S. It does +not start with arbitrary integer numerators on the finest grid. The latter +claim would be false, as numerator one shows. It also does not permit a +completed recursive child to retain an uncancelled rational normalization. +Repeated completed children with endpoint x/3 can increase odd height +beyond any bound that counts only active depth. Such a construction needs +a different global denominator bound. + +At the completed outer return, require the exact intended +Gaussian-dyadic endpoint on all physical roles. Every numerator is then +divisible by S. Divide all physical numeric streams by three K_3 times. +This restores the original encoding of arbitrary borrowed values under +their stipulated endpoint operation. There is no new approximation error +and no new tolerance premise. The inherited final truncation occurs only +after this exact unscaling. + +If N counts all real numeric records and w_g is the guarded common width, +both outer conversions together cost at most + + 8 N K_3 (w_g+1) + +arithmetic-head steps. Descriptor and counter work adds +`O(N K_3 (w_g+1))`. The additional numerator width is at most `2K_3` bits, +since `3^K_3 < 2^(2K_3)` for positive K_3. One local inverse factor on n +complex entries per field adds at most `64 n (w_g+1)` arithmetic-head +steps for its sixteen real scans, plus the retained linear stream work. +Its old scalar invoice is separate and remains in the table above. + +For the retained 73-axis recurrence with largest child at most 48e/73, +`2*48^2 < 73^2` gives `D <= 2 ceil(log2(d+1))`. Fixed M therefore adds +O(log d) bits and O(V log d) outer work. The local scans add O(V) finite +node work. The same positive complex-power slack absorbs the outer log +factor. This statement preserves a strict exponent once its complete +supplier moment is proved; it does not supply that missing moment. + +A full guard can be constructed as in the retained proof. Give each local +scalar primitive a finite magnitude and denominator-height charge, and +use the exact bound above for each factor. Completed u-axis children add +at most u binary denominator bits and a factor `2^u` in row norm. A +finite parent with total child rank s and largest child ratio rho<1 has +a prefix bound of the form + + A(e) <= A(rho e) + a e + b, + +where a and b are explicit constants from its complete event list. For +e>=1, `(a+b)e/(1-rho)` is a linear inductive majorant, with a fixed base +allowance. The additional `2K_3` numerator bits in (3) are logarithmic. +Thus O(p) records suffice in the retained parameter family. The complete +controller must calculate its own a,b and binary P. A cancellation-based +bound for a different old whole word cannot be copied without that check. + +Replacing /3 by a dyadic approximation alone is not this extension. The +checker replaces it by 85/256 and proves that composition with H does not +restore arbitrary inputs exactly. This rejects that direct substitution. +It does not exclude a separately proved reversible rounded construction. + +## What the recent Newton-code results do and do not require + +[PR3423](https://github.com/CrocSwap/integer-mult-bounds/pull/3423) and +[PR3406](https://github.com/CrocSwap/integer-mult-bounds/pull/3406) were +refreshed and their pinned proof files were read. Exact heads, paths, and +Git blob identities are in `sources/GITHUB-PINS.json`. Their executable +suites were not rerun for this audit. + +Their actual P104 code is `B_9=E Z[i]^512`, where +`E=[[1,0],[1,1+i]]^tensor9`. The proved source Clifford alphabet preserves +this module. The signed-floor pair is exact on its stated domain. The +real initial Y banks must also satisfy the appropriate fourfold +divisibility before quarter reads. These are source-domain obligations, +not free preparation of arbitrary dirty payloads. + +The [PR3423 consumer proof](https://github.com/CrocSwap/integer-mult-bounds/blob/15d28c4de37dc47ea07cd7173c8b318fca7a4d75/research/p104-newton-interfaces/CONSUMER.md) +states the resulting coefficient map as `E^-1 A E`, and checks a case +where it differs from A. A caller must bind that changed interface. The +common scalar grid in (3) has `S^-1 A S=A` for every exact linear A. It +therefore avoids that non-scalar interface change, but pays root scaling, +extra width, exact scans, and all unchanged native operations. Neither +Newton theorem imposes a ban on odd rational intermediates in the retained +exact machine model. Their fixed P104 bill also does not replace the bill +for the changed PR3133 core used here. + +## Reproduction and remaining work + +Run one process from the workspace root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-grid-a8-20261017/check_a8_odd_grid.py --out /tmp/A8-ODD-GRID-REPLAY.json +``` + +Expected status: `PASS_A8_EXACT_ODD_GRID_NORMALIZATION`. +The checker writes the boundary words next to its chosen receipt. Compare +both files to the frozen packet. It verifies all formal input columns, +both H inverse orders, the fused order, every prefix denominator bound, +all local bills, the exact X-content kernel, and signed record arithmetic. +Controls reject an omitted division, an approximate inverse, and a root +numerator outside the stated representation contract. + +The next required check is the literal transfer onto both new native +providers, with all helper and private columns, legal frames, and native +phase pins. A complete supplier must then use the retained selected +content, bind the controller, host all private state, prove every owner +endpoint, and calculate the complete moment and precision. These tasks +are not certified by this local packet. An independent reviewer must also +review this new factor and its grid argument; the producing lane's older +independent reviews do not review its own new construction. + +The actual raw selected mechanism and minor block identities come from +the native-escape and new-core-transfer lanes. The scalar scan and grid +method come from the credited retained sources and prior rational-decoder +work. OpenAI Codex assisted the derivation, implementation, and source +audit. No human review, maintainer selection, PR, push, or publication +commit is claimed. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/BRIDGE-OPERATOR-REVIEW.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/BRIDGE-OPERATOR-REVIEW.json new file mode 100644 index 0000000000..bdd8781819 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/BRIDGE-OPERATOR-REVIEW.json @@ -0,0 +1,73 @@ +{ + "actual_data_owner_routes_checked": 32256, + "actual_local_shear": "D L(J) D or D U(-J^T) D in the pinned boundary gauges", + "actual_stage_entry_exit_gauges_checked": 1008, + "archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754", + "complete_phase_identity_character_checks": 51744, + "divide13_finite_bit_circuit": { + "divisor": 13, + "exactness_condition": "Input numerator is divisible by 13 under the common odd-grid invariant", + "excluded_costs": [ + "stream reads and writes", + "address routing", + "root common-grid conversions" + ], + "extra_finite_control_bits_upper_bound": 32, + "nondivisible_inputs_with_nonzero_remainder": 15123, + "scan_order": "Conditional negation from low to high; unsigned division from high to low; conditional negation from low to high", + "signed_14_bit_inputs_checked": 16384, + "signed_AND_OR_NOT_gates_per_numerator_bit": 179, + "unsigned_AND_OR_NOT_gates_per_numerator_bit": 161, + "valid_state_transitions": 26 + }, + "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "logical_bridge": "A^-1 J A T_boundary=T_boundary D J D; the same identity holds for J^-1", + "maximum_resident_bytes": 182386688, + "operator_alignment": "A=Z_delta D; A T_boundary=T_common D", + "phase_controls": { + "omitted_X_translation_rejected": 112, + "omitted_Y_translation_rejected": 112, + "reversed_Y_route_translation_order_rejected": 112 + }, + "phase_method": "Exact Fourier-character evaluation on all weight-zero, one, and two inputs in the active 17-dimensional space", + "scalar_programs": { + "forward": { + "additional_real_divide_by_13_streams": 0, + "dyadic_real_primitive_bound": 7232, + "events": 920, + "full_input_columns_checked": 113, + "macros": { + "add": 896, + "clear": 16, + "quarter": 8 + }, + "maximum_live_private_arrays": 1, + "native_children": 0, + "private_input_and_output_zero": true + }, + "inverse": { + "additional_real_divide_by_13_streams": 16, + "dyadic_real_primitive_bound": 7232, + "events": 928, + "full_input_columns_checked": 113, + "macros": { + "add": 896, + "clear": 16, + "divide13": 8, + "quarter": 8 + }, + "maximum_live_private_arrays": 1, + "native_children": 0, + "private_input_and_output_zero": true + } + }, + "scope": "Exact native operator and finite scalar macro invoice. Address routing, bit division cost, and a complete controller invoice remain separate.", + "seconds": 4.192791291999583, + "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_pins": { + "t16/global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "t16/global/hosted/GLOBAL-TEMPLATE.json.gz": "73f47a1e60b1e4ea66dbca9a497c411c8e6adc7984e276a437a10a9a7a13b47a" + }, + "status": "PASS_EXACT_BRIDGE_OPERATORS_AND_ACTUAL_LOCAL_GAUGE", + "two_factor_phase_checks": 17248 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json new file mode 100644 index 0000000000..d727682fc3 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json @@ -0,0 +1,117 @@ +{ + "checked_counts": { + "all_bridge_frame_pairs": 32256, + "all_live_cover_correction_events": 1, + "applied_complete_idle_phase_slots": 35840, + "bridges": 144, + "helper_jobs": 69120, + "idle_events": 160, + "idle_suffixes": 7526, + "local_calls": 144, + "ordinary_terminal_events": 16, + "retained_terminal_Y_translation_events": 16 + }, + "controls": { + "omitted_cover_correction": [ + { + "character": 1, + "delta": 15, + "port": 0 + } + ], + "omitted_idle_translation": "Exact phase frame mismatch at event 5, family 224", + "owner_vs_invocation_coordinates": { + "endpoint": "entry_X", + "invocation_translation": 3595, + "owner_translation": 15, + "port": 0, + "stage": 1 + }, + "wrong_incoming_line": [ + { + "port": 1, + "wrong_incoming_residual_translation": 19 + }, + { + "port": 6, + "wrong_incoming_residual_translation": 13 + }, + { + "port": 21, + "wrong_incoming_residual_translation": 289 + }, + { + "port": 22, + "wrong_incoming_residual_translation": 193 + }, + { + "port": 87, + "wrong_incoming_residual_translation": 493 + }, + { + "port": 92, + "wrong_incoming_residual_translation": 499 + }, + { + "port": 109, + "wrong_incoming_residual_translation": 223 + }, + { + "port": 110, + "wrong_incoming_residual_translation": 319 + } + ] + }, + "direct_character_cross_checks": 4096, + "doubled_native_premise": false, + "endpoint_children": 1024, + "exact_boundary": "Retain old Y translation; before decoder apply C_(gq)^-1 to Y modes, then after logical restoration apply C_(gq) to X modes", + "exact_owner_phase_states": 14336, + "geometry_payload_sha256": "498d85807dd3032de01b5da72a67717f02ee0ecf068e8c47f67d4f21034cd896", + "halving_margin": 721, + "idle_phase_polynomials": 2240, + "idle_suffixes": 7526, + "independent_loader_sha256": "1b043bf941f079d48bab69bfab9bd9376a1c2c3a957093486b497859689c37bb", + "independent_local_review_sha256": "4d565d17a78e74d4a2adf6f7be01192a11541875fad84cdcb37d0117b10597e4", + "live": 14336, + "local_payload_sha256": "66901cb2887208deae3c97aefb831ce5a54e00129b4b4487c9b3fa03d4ed67c0", + "local_scalar_subtotal": 29124000, + "maximum_child": 48, + "mode_swap_complex_adds": 4608, + "mode_swap_complex_signs": 1536, + "mode_swaps": 1536, + "nonzero_stage_translations": 3584, + "original_complex_word": true, + "original_phase_member_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "paid_profile": { + "1": 351780, + "2": 60192, + "3": 62585, + "4": 20448, + "5": 11808, + "7": 7, + "48": 4866 + }, + "paid_rank": 1034368, + "physical": 14826, + "producer_imported": false, + "productive_rank": 1046528, + "rank_deficit": 12160, + "reviewed_input_sha256": { + "ORIGINAL-COMPLEX-MODE-PHASES.json": "307b6c94b29210d2bb28b5d6cad1f841a4d44edb14214a775d13ac7006087621", + "ORIGINAL-COMPLEX-MODE-PHASES.md": "84198917093bc88c699da9bee309491b650bc7565cea436f0f6a002d94bd97b2", + "ORIGINAL-FRAME-MODE-HISTORY.json": "56617c72449e841855a474a1906be9665681f0a4eaa29fbc423c5f4e7082ecf7", + "ORIGINAL-FRAME-MODE-HISTORY.md": "f3141b2312ebbf62156299467d68d1bde6cc392e4fe608e9d0f6da8c8ce8159b", + "original_complex_mode_phases.py": "308c0f2ed368ee83cc251ffd8f27d410a492019d2980ed5ae57c6943aaa59f0a", + "original_frame_mode_history.py": "86bb00291089ef6d96051f0ac63eafcb02e22881262908a7fef27b3263ad455a" + }, + "scope": "Original complex local word, complete selected arbitrary-owner phase history, mode swaps and64-line boundary repair per replica. No logical decoder implementation, complete finite invoice, recursive supplier, or kappa claim", + "source_archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "source_schedule_events": 482, + "stage_phase_polynomials": 4032, + "status": "PASS_INDEPENDENT_ORIGINAL_COMPLEX_MODE_PHASES_AND_OWNERS", + "strict_idle_windows": 160, + "tensor_scope": "All operator equalities retain the zero-character phase and tensor for every positive multiplicity", + "terminal_line_phases": 112, + "whole_helper_jobs": 69120 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_native_lift.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_native_lift.py new file mode 100644 index 0000000000..fb72255b9c --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_native_lift.py @@ -0,0 +1,336 @@ +"""Check the exact native lift and the finite local bill. + +The checker does not import the emitter or the Clifford compiler. It uses +Pauli conjugation and a separate exact state interpreter. The scalar map is +owned by the independent transpose replay in the adjacent review lane. +""" +from collections import Counter +from fractions import Fraction +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +import resource +import subprocess +import tarfile +import time + +BASE = 'bce54fb3f895cbe5cd4c0eb477c3afeed100190f' +ARCHIVE = 'research/community-frontier1042-audit/selected-replay.tar.gz' +ARCHIVE_HASH = '22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754' +PINS = { + 'CANONICAL-WORD.json.gz': '16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219', + 'LOCAL-PROGRAMS.json.gz': '241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a', + 'CLIFFORD-RECIPES.json': 'd0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731', + 'RESIDUAL-ADAPTERS.json': '383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c', +} + + +def require(condition, label): + if not condition: + raise ValueError(label) + + +def load(repo): + args = ['git', 'show', BASE + ':' + ARCHIVE] + proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE) + digest = sha256() + while chunk := proc.stdout.read(65536): + digest.update(chunk) + require(proc.wait() == 0 and digest.hexdigest() == ARCHIVE_HASH, 'archive pin') + proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE) + values = {} + with tarfile.open(fileobj=proc.stdout, mode='r|gz') as archive: + for entry in archive: + name = entry.name.removeprefix('slots/local/') + if entry.name.startswith('slots/local/') and name in PINS: + raw = archive.extractfile(entry).read() + require(sha256(raw).hexdigest() == PINS[name], name + ' pin') + values[name] = json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw) + require(proc.wait() == 0 and set(values) == set(PINS), 'source extraction') + return values + + +def parity(value): + return value.bit_count() % 2 + + +def mul(matrix, vector): + return sum(parity(row & vector) << i for i, row in enumerate(matrix)) + + +def transpose(matrix): + return tuple(sum(((row >> j) & 1) << i for i, row in enumerate(matrix)) for j in range(len(matrix))) + + +def inverse(matrix): + n = len(matrix) + rows = [row | (1 << (n+i)) for i, row in enumerate(matrix)] + for j in range(n): + pivot = next((i for i in range(j, n) if rows[i] >> j & 1), None) + require(pivot is not None, 'singular binary chart') + rows[j], rows[pivot] = rows[pivot], rows[j] + for i in range(n): + if i != j and rows[i] >> j & 1: + rows[i] ^= rows[j] + require([row & ((1 << n)-1) for row in rows] == [1 << i for i in range(n)], 'binary inverse') + return tuple(row >> n for row in rows) + + +def extend(vectors, n): + columns, pivots = [], {} + for value in tuple(vectors) + tuple(1 << i for i in range(n)): + reduced = value + while reduced: + j = reduced.bit_length()-1 + if j not in pivots: + pivots[j] = reduced + columns.append(value) + break + reduced ^= pivots[j] + require(len(columns) == n, 'frame basis extension') + return tuple(columns) + + +def adjoint(circuit): + out = [] + for gate in reversed(circuit): + if gate[0] == 'P': + out.append(('P', inverse(gate[1]))) + elif gate[0] == 'D': + out.append(('D', gate[1], tuple(-a % 4 for a in gate[2]))) + elif gate[0] == 'C': + out.append(('C', gate[1], -gate[2])) + elif gate[0] == 'phase': + out.append(('phase', -gate[1] % 4)) + else: + require(gate[0] == 'X', 'adjoint gate type') + out.append(gate) + return tuple(out) + + +def fourier(rank): + return tuple(('C', 1 << i, 1) for i in range(rank)) + + +def frame(vectors, n): + rank = len(vectors) + if rank == 0: + return () + if rank == n: + return fourier(n) + matrix = transpose(extend(vectors, n)) + columns = transpose(inverse(matrix)) + quadratic = tuple((1 << i) ^ sum(parity(a & b) << j for j, b in enumerate(columns)) for i, a in enumerate(columns)) + diagonal = tuple((row >> i) & 1 for i, row in enumerate(quadratic)) + chart = (('P', matrix), ('D', quadratic, diagonal)) + return adjoint(chart) + fourier(rank) + chart + + +def monomial(record): + matrix = tuple(record['matrix_rows']) + quadratic = tuple(record['quadratic_rows']) + linear = tuple(record['linear_Z4']) + require(transpose(quadratic) == quadratic, 'quadratic symmetry') + require(len(matrix) == len(quadratic) == len(linear) == 9, 'monomial dimension') + require(all(a % 2 == (quadratic[i] >> i) & 1 for i, a in enumerate(linear)), 'diagonal parity') + inverse(matrix) + return (('D', quadratic, linear), ('P', matrix), ('X', record['offset']), ('phase', record['phase'])) + + +def recipe(record): + rank = record['rank'] + require(isinstance(rank, int) and 0 <= rank <= 9, 'child rank') + if rank == 0: + require(record['right'] is None, 'rank zero right factor') + return monomial(record['left']) + return monomial(record['right']) + fourier(rank) + monomial(record['left']) + + +def tableau(circuit, n=9): + rows = [(1 << i, 0, 0) for i in range(n)] + [(0, 1 << i, 0) for i in range(n)] + for gate in circuit: + tag = gate[0] + out = [] + inverse_transpose = transpose(inverse(gate[1])) if tag == 'P' else None + for x, z, phase in rows: + if tag == 'P': + x, z = mul(gate[1], x), mul(inverse_transpose, z) + elif tag == 'X': + phase += 2 * parity(z & gate[1]) + elif tag == 'C': + if parity(z & gate[1]): + x ^= gate[1] + phase += 3 * gate[2] + elif tag == 'D': + quadratic, linear = gate[1:] + phase += sum(linear[i] for i in range(n) if x >> i & 1) + phase += 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(n) if x >> i & 1) + z ^= mul(quadratic, x) + else: + require(tag == 'phase', 'tableau gate type') + out.append((x, z, phase % 4)) + rows = out + return tuple(rows) + + +@lru_cache(maxsize=512) +def action(gate): + if gate[0] == 'P': + return tuple(mul(gate[1], x) for x in range(512)) + require(gate[0] == 'D', 'state action type') + quadratic, linear = gate[1:] + return tuple((sum(linear[i] for i in range(9) if x >> i & 1) + + 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(9) if x >> i & 1)) % 4 for x in range(512)) + + +def rotate(pair, power): + a, b = pair + return ((a, b), (-b, a), (-a, -b), (b, -a))[power % 4] + + +def state(circuit, basis=0): + value = [(0, 0)] * 512 + value[basis] = (1, 0) + denominator = 0 + for gate in circuit: + tag = gate[0] + if tag == 'P': + moved = [(0, 0)] * 512 + for source, target in enumerate(action(gate)): + moved[target] = value[source] + value = moved + elif tag == 'X': + value = [value[x ^ gate[1]] for x in range(512)] + elif tag == 'D': + value = [rotate(pair, p) for pair, p in zip(value, action(gate))] + elif tag == 'phase': + value = [rotate(pair, gate[1]) for pair in value] + elif tag == 'C': + direction, sign = gate[1:] + moved = [] + for x, (a, b) in enumerate(value): + c, d = value[x ^ direction] + moved.append((a-sign*b+c+sign*d, b+sign*a+d-sign*c)) + value = moved + denominator += 1 + else: + raise ValueError('state gate type') + while denominator and all((a | b) % 2 == 0 for a, b in value): + value = [(a//2, b//2) for a, b in value] + denominator -= 1 + return value, denominator + + +def equal(actual, expected, label): + require(tableau(actual) == tableau(expected), label + ': Pauli action') + require(state(actual) == state(expected), label + ': global phase') + + +def scalar_cost(gate): + if gate[0] in ('copy', 'clear'): + return 1 + value = Fraction(*gate[-2:]) + numerator, denominator = abs(value.numerator), value.denominator + require(numerator > 0 and denominator & (denominator-1) == 0, 'nonzero dyadic scalar') + if gate[0] == 'scale': + require(numerator & (numerator-1) == 0, 'dyadic scale unit') + return abs(numerator.bit_length()-denominator.bit_length()) + (value < 0) + require(gate[0] == 'add', 'scalar type') + return 3 + numerator.bit_length()-1 + numerator.bit_count() + denominator.bit_length()-1 + + +def main(args): + start = time.monotonic() + data = load(args.repo) + word = data['CANONICAL-WORD.json.gz'] + old = data['LOCAL-PROGRAMS.json.gz'] + phase = data['CLIFFORD-RECIPES.json'] + residual = data['RESIDUAL-ADAPTERS.json']['recipes'] + changed_raw = gzip.decompress(args.changed.read_bytes()) + require(sha256(changed_raw).hexdigest() == 'fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877', 'changed payload pin') + changed = json.loads(changed_raw) + require(set(changed) == {'forward', 'backward'}, 'orientation inventory') + native = lambda events: [e for e in events if e[0] in ('climb', 'adapter', 'residual_adapter')] + invoices = {} + for name, events in changed.items(): + require(native(events) == native(old[name]), 'persistent native stream') + require(all(e[0] in ('scalar', 'phase', 'climb', 'adapter', 'residual_adapter') for e in events), 'event grammar') + first = events.index(['phase', 'centre_dirty_correction']) + last = events.index(['phase', 'A']) + prefix = [e[1] for e in events[first+1:last]] + require(all(e[0] == 'scalar' and e[2] == 0 for e in events[first+1:last]), 'correction frame') + scalars = [e[1] for e in events if e[0] == 'scalar'] + paid = Counter(e[5] for e in events if e[0] == 'climb') + invoices[name] = { + 'events': len(events), 'scalar_macros': len(scalars), + 'real_component_primitive_bound': 2*sum(map(scalar_cost, scalars)), + 'prefix_macros': dict(Counter(e[0] for e in prefix)), + 'prefix_real_component_primitive_bound': 2*sum(map(scalar_cost, prefix)), + 'paid_profile': dict(sorted(paid.items())), + 'paid_rank_sum': sum(rank*count for rank, count in paid.items()), + 'persistent_native_events': len(native(events)), + } + used = {(e[3], e[4]) for e in changed['forward'] if e[0] == 'climb'} + children = {(r['old'], r['new']): r for r in phase['children']} + require(len(children) == len(phase['children']) and used <= set(children), 'child recipe binding') + frames = [frame(tuple(vectors), 9) for vectors in word['frames']] + for i, (a, b) in enumerate(sorted(used)): + record = children[a, b] + require(record['rank'] == len(word['frames'][b])-len(word['frames'][a]), 'paid frame difference') + equal(recipe(record), adjoint(frames[a])+frames[b], 'child '+str((a, b))) + if i % 500 == 0: + print('phase edges', i, '/', len(used), flush=True) + endpoints = {(r['role'], r['port']): r for r in phase['endpoint_adapters']} + require(set(endpoints) == {(role, p) for role in ('source', 'target') for p in range(112)}, 'endpoint coverage') + for (role, port), record in endpoints.items(): + q = word['ports'][port] + conventional = (('C', q, 1),) if role == 'source' else (('C', q, -1),)+fourier(9) + expected_frame = word['start'][port] if role == 'source' else word['final'][112+port] + require(record['frame'] == expected_frame and record['rank'] == 0, 'endpoint frame binding') + equal(recipe(record), adjoint(conventional)+frames[expected_frame], 'endpoint '+str((role, port))) + used_residual = set() + for event in changed['forward']: + if event[0] == 'residual_adapter': + _, position, register, entry, *tail = event + terminal = tail[0] if tail else 1 + key = str(entry) if terminal == 1 else str(entry)+':'+str(terminal) + require(key in residual and position in ('pre', 'post'), 'residual binding') + require(entry == word['start'][register] and terminal == word['final'][register], 'residual boundary') + used_residual.add(key) + for key in sorted(used_residual): + record = residual[key] + entry = record['frame'] + terminal = record.get('terminal', 1) + equal(recipe(record), adjoint(frames[entry])+frames[terminal], 'residual '+key) + probe = next(r for r in children.values() if r['left']['phase'] != 0 or r['right'] and r['right']['phase'] != 0) + correct = recipe(probe) + corrupt = tuple(gate for gate in correct if gate[0] != 'phase') + if state(corrupt) == state(correct): + corrupt = correct+(('phase', 1),) + require(tableau(corrupt) == tableau(correct) and state(corrupt) != state(correct), 'global phase negative control') + require(state(corrupt, 1) != state(correct, 1), 'phase control second input') + report = { + 'status': 'PASS_INDEPENDENT_NATIVE_FRAME_LIFT_AND_FINITE_LOCAL_BILL', + 'base': BASE, 'archive_sha256': ARCHIVE_HASH, 'member_sha256': PINS, + 'changed_payload_sha256': sha256(changed_raw).hexdigest(), + 'checked_unique_persistent_edges': len(used), 'checked_endpoint_adapters': len(endpoints), + 'checked_residual_recipes': len(used_residual), 'finite_local_invoice': invoices, + 'exact_operator_method': 'Pauli conjugation and exact Gaussian dyadic zero state; no compiler import', + 'negative_controls': ['wrong global phase with the same Pauli action, on basis inputs 0 and 1'], + 'all_tensor_powers': 'Base operators are exactly equal, so their tensor powers are equal for every positive integer. The common frame conjugation proof gives the full array map.', + 'not_claimed': ['global chart or owner admission', 'recursive supplier admission', 'new kappa', 'fresh all-size compiler proof'], + 'seconds': time.monotonic()-start, 'max_rss_bytes': resource.getrusage(resource.RUSAGE_SELF).ru_maxrss, + } + args.out.write_text(json.dumps(report, indent=2, sort_keys=True)+'\n') + print(report['status'], flush=True) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--repo', type=Path, required=True) + parser.add_argument('--changed', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + main(parser.parse_args()) diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/HANDOFF-PHASE-CALLERS-20261020.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/HANDOFF-PHASE-CALLERS-20261020.md new file mode 100644 index 0000000000..15c49b273d --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/HANDOFF-PHASE-CALLERS-20261020.md @@ -0,0 +1,344 @@ +# Native caller handoff + +No PR, commit, push, or publication is authorised. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. +Preserve all frozen packets. Use one CPU in this lane. + +The phase-coded caller removes the centre-dependent terminal correction. +It leaves a common portwise q factor on both original input banks. +The same common q remains after three such triples through D73. +No recursive consumer for that factor has been admitted. + +The current follow-up concerns a different unitary centre code. The +three current scalar stage codes cannot close to a monomial unless +each is monomial. They cannot commute with Q unless each is diagonal. +These statements now have direct common-input spatial witnesses. The +old unverified small-representation independence argument is not used. +Read the closure section below for the precise width and code limits. + +## Current phase-coded caller + +Read `phase-coded-triple-20261020/PHYSICAL-ENDPOINT.md`. +Its source is the controller lane's frozen phase-coded native word. +For the Q-entry variant, three legal FULL shears give + +```text +X = -F25 q Y0, +Y = F25 q X0. +``` + +Both X0 and Y0 are arbitrary physical inputs. The first shear is +`X_R-=D1 X_P` after the complete stage-1 sweep. The last two are +`Y_P-=H2 X_R` and `Y_P-=H0 Y_R` after stage 2. The middle and +stage-2 shears use the literal FULL affine views and translations. +No ordinary hole is read by a scalar shear. + +The normal and optimized checks pass all 224 data columns and all +1,344 phase identities. The endpoint has exactly 224 stored operator +terms after the shears. The source native replay covers all 640 +local columns, including 416 arbitrary helpers; that local replay +is inherited rather than repeated in this caller check. + +```text +phase-coded-triple-20261020/FREEZE.json +0ee32fe22f42cffce2a9673f0dc95496a4b4bb8b11a534f77a11f5fe9c7aeb4b +PHYSICAL-ENDPOINT.md +5eb5eba5d3bed38faf9e411ca4a9a6f8e67765966011e93dec96f2300613756f +check_phase_coded_triple.py +82a36b9f258d1aa2d95830502b336eb8aae9e7beff643b1f854c3d87451098f6 +run-normal/CHECKS.json +44a1c03836ba47af92965dc7d2bb716d0f94d03dd54cb3122eeaa9f1d08a3cc3 +``` + +The local Q-entry native mass is 5,376. It needs 224 positive +line operations for the direct terminal. The initial I-entry mass +is 5,392 and it needs 208 lines. Both totals are +`5600=224*25`. The three added shears have a direct upper bound +of 6,144 scalar primitives and 448 affine field-map calls. +The existing factored scalar code can give a smaller scalar bound, +but this caller packet uses only the direct coefficient bound. + +The signed output convention is explicit. An unsigned convention +adds 112 field signs, at 224 scalar primitives, unless the caller +uses the signed exchange directly. + +The independent child review passed with a separate phase engine. +It is in a separate packet; the frozen producer files are unchanged. + +```text +owner-review/phase-coded-triple-review-20261020/FREEZE.json +700415b75d8f9d20225ee67371adac8d8d7716369171927612690d0e6a7716b9 +REVIEW.md +8342f508f9c2432a01ef196820d5c94b98df012c63f21d560940c8799e337c0c +CHECKS.json +ccdcf2033f575921fc3222017b57bbadcca7f4575cb42139f388718bfb266bb1 +``` + +The coherent-port lane owns the recursive common-q interface. +The new-core lane owns a prospective direct native implementation +of the same local phase-coded map. The current source is the +4,632-scalar local word; do not replace its cost with a prospective +2,912-scalar word before that word is emitted and reviewed. + +## Nine-call D73 chain + +Read `phase-coded-chain-20261020/CHAIN.md`. Nine calls, grouped as +three triples with their three FULL shears, give + +```text +X = F73 q Y0, +Y = -F73 q X0. +``` + +The q factor does not accumulate once per triple. The native mass is +16,128, and the direct terminal adds 224 lines, for 16,352=224*73. +This is not a strict moment gain. The checker verifies 3,584 natural +boundary phase identities and 1,008 FULL-shear view identities. +The normal and optimized outputs agree. + +```text +phase-coded-chain-20261020/FREEZE.json +dd982cc272aa204f8a3d0d82069b7263c21077e03a472a44e59e2bec6fcce47e +CHAIN.md +123ba331ea24a23c0fb775b6e6e3bec2409acdacc938d45f026c54ec0d3bbfa2 +GENERAL-VIEWS-REVIEW.md +9e8c73d3bfaade6d9d06f8c472b88ad52cce624fe2e602c143cd1705c8f662b0 +``` + +The general-view review checks the quadratic-refinement proof and +the spectator-axis extension. It does not turn the current response +into a stage-independent scalar matrix or prove a recursive host. + +## Current scalar-code closure + +Read `unitary-code-closure-20261020/CLOSURE.md` and +`GENERAL-CLOSURE.md`. The exact D25 source and the actual unitary +code are pinned in the checker. There is no native code-C service +or recursive join claim in this packet. + +For three invertible scalar codes C0,C1,C2 in their current charts, +the path through j,r has route + +```text +M = rho_(2,p) rho_(2,j) rho_(1,j) rho_(1,r). +``` + +The common logical input `(e2,e1)` separates all 12,544 paths at +width f at least 2. The common physical input `(0,e2,e1)` separates +their literal affine versions at f at least 3. A third Fourier +character gives an exact nonzero Q-commutator witness for any path +that breaks the intrinsic line. + +Thus monomial closure holds only when all three scalar codes are +monomial. Q commutation holds only when all are diagonal. Every row +of all eight actual C/C* variants has an explicit nonmonomial basis +witness and a nonzero commutator witness. Both sets have 896 entries. +The bound-normal and bound-optimized outputs are byte-identical. + +The direct spatial proof does not assume independent regular owners. +Its covariant lift to the declared regular cover is explicit. No +f=1 conclusion follows from this proof. The separate cover lane has +an additional owner-isolation proof under the full-cover premise. + +The general-stage extension uses tags `(e_T,...,e_1)` to recover +all intermediate ports. Logical monomial closure needs f at least T; +physical affine closure and Q commutation use f at least T+1. These +are sufficient bounds, not width optima. + +The standalone independent representation review is frozen: + +```text +owner-review/unitary-code-closure-review-20261020/FREEZE.json +b3fc9ddc6fdc4cc6c2226b3b9fa101abdb21d22e50ceb3d6c9cefa9280062deb +REVIEW.md +f5bc725b9f14032e5a61341ed73306b45797b90612e256e6e3caa52e6360a3dc +``` + +The final producer, literal affine binding, and general-stage proof +review are frozen: + +```text +unitary-code-closure-20261020/FREEZE.json +ec5d251c2c183fe2fcf5fd51bc9c4806bff6ca0129e08ebaffd4a017503eb160 +CLOSURE.md +63c0deeb7e13b359ca410dfb085e1a89866aa87383d6bd1cec02cba688a4ce3e +GENERAL-CLOSURE.md +a9bc32fc805b83c6317cc62b8c5982dee2d15d73a4065a50ab4e797e3c85826a +bound-normal/CHECKS.json +f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a +owner-review/unitary-code-closure-binding-20261020/FREEZE.json +7e572942617d880931f52f47849b23174b903f57a199a99134b96ed5cac21ea6 +owner-review/general-scalar-closure-review-20261020/FREEZE.json +6f5fbbf6565d2a6078b8ec627722c52c8f94fe0690ae6da1a543e7c3f767022d +``` + +Do not treat the earlier `run-normal` or `final-normal` receipts as +the final source-bound receipt. The current checker is bound by +`bound-normal/CHECKS.json`. The final review recomputed all literal +affine paths and all 1,792 basis and commutator witnesses. The +general-stage review is a separate proof read, with no new path +enumeration or native cost claim. + +The theorem permits different coefficients at each stage and also +permits diagonal terms. It does not cover old-chart controls, +operator-valued codes, changed gathered interfaces, or a paid joint +decoder. Route counts are not native child counts. The root and +coherent-port lanes are investigating a recursive coded consumer. + +## Reciprocal response: three actual reader cuts + +The actual response E=P R has sixteen-row reflection factor +R-I=U ell. Current-I pre-Y P and raw-FULL post-X P give the +common-P forward and reciprocal backward shears. Keep the +stage order. With + +```text +t=y+R0 x, +w=x-(P0^-1 R1 P0)t, +``` + +the three required readers are + +```text +c0=ell0 x, +c1=ell1 P0 t, +c2=ell2(P1 P0)w. +``` + +Their stored arguments are present at the actual source cuts: +c0 and c2 use raw FULL X before post-P; c1 uses current-I Y +before pre-P1 and all native input adapters. The accumulated +P factors require no extra old-stage query. + +The returned record types are F9, F9 q_anchor, and F25. The +middle record is a hole record. Do not call it FULL or omit +its remaining line progression. + +Each conditional read has 136 complex signed ADDs, or 1,088 +real scalar units, into sixteen independent accumulators in +the stated body frame. The accumulators can be arbitrary, +but their old values remain present. The local prefix row +one-norm is eleven and the word adds no coefficient denominator. +All three formations cost 3,264 units only if those typed +accumulators are supplied. + +```text +reciprocal-reader-cuts-20261020/FREEZE.json +4442f8dba6a6940bbc63e52ec17bce96fdcc4879dd5113e0a9ea06067d986992 +reciprocal-reader-cuts-20261020/SOURCE-CUTS.md +0da0fb811c2c2841ac63b77ea678fa973000b79408cc2d4d825167d721bf5c02 +reciprocal-reader-cuts-20261020/bound-normal/CHECKS.json +bf1722a6ee21a5c14f50db6b848972a4bbc9fc56ec69c301357103cdc02e6c9b +reciprocal-reader-cuts-20261020/bound-normal/READERS.json.gz +decompressed f0a3eb19e09f425fc87e3563af72a7879f9cf64799fee0dcbd059bd297bc8045 +owner-review/reciprocal-source-cut-review-20261020/FREEZE.json +03e045189845e0e0bf8722e54cc180f3083d32f752d98f900cfbce9647bc46cc +``` + +The producer checks all 656 local input columns and 672 exact +phase identities. The separate review reconstructs the model +from mode and pair data, checks 1,792 exact phase identities, +and binds all serialized reader and immediate inverse instructions. +Both normal and optimized outputs match. The independent review +found no material error. + +The native source is the frozen reciprocal word with decompressed +hash f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e. +The source-cut checker pins its complete entry and exit metadata; +it does not replay that native word. The native contract remains +a separate dependency. Internal unused-cut coalescing does not +change these complete-word source cuts. + +No safe accumulator allocation, zero baseline, owner lease, +record transport, or late erase is supplied. An immediate inverse +read restores arbitrary accumulators only while its source stays +unchanged. The complete reciprocal decoder also needs its Q-coded +X scatter. These obligations remain open. + +## Earlier clean natural triple + +The natural clean F/Bswap/F word is fully checked as a physical +endpoint. It has a direct 208-positive-line operator terminal. +It retains a sixteen-row query through ordinary Y holes before +that terminal. The new phase-coded word changes the local response +and escapes that particular query. + +```text +no-reset-triple-20261020/FREEZE.json +089425bdf431d81456e1c988a1fd21a837baca43e510bc92dee98dc2ee571791 +owner-review/no-reset-triple-review-20261020/FREEZE.json +65b7bd0119e4dc189a428d604c65dd94cf458ba3a7618d4fb0bb979ade7dd62c +``` + +The independent review contains a literal operator terminal: + +```text +owner-review/no-reset-triple-review-20261020/TERMINAL-WORD.json +e0b356266c026455ddd81e869ff1270fdbe00e342367aac8173026afb446fa88 +``` + +It uses LINE, MAP, ADD, and NEG events. It is not a hosted native +recipe. It costs 208 positive line operations, 16,608 scalar +primitives, and 1,344 affine map calls, before line side maps and +the final bank exchange. Do not emit a duplicate scalar terminal. + +The other independent-review lane factors this same terminal as + +```text +diag(Q_P,Q_R^2,-I) W^-1 L W, +W = diag(I,Q_R,I). +``` + +This acts on `(beta,h,R)`, where `h=q_R r`. +Selected X signs and the final bank exchange are separate. +The dyadic unit L has an eight-shear word and a displacement +factor through at most 48 field arrays. No cheaper native +lowering of this conjugation is known. + +```text +independent-review-20261017/no-reset-terminal-factor-20261020/FREEZE.json +1b1f191e9de1ef20b88aca6d870f93fe68b0923e8b05a87d9ca7d960e0385963 +owner-review/no-reset-terminal-factor-proof-review-20261020/FREEZE.json +80cd2d0c033ba4fa44b78b3335742038d40f71e79ae615d1010874ca2a53bab8 +``` + +Both independent proof reviews found no material error. + +## Earlier reset two-call result + +The clean F/reset/Bswap word puts the original data in one FULL +bank, but only as `F17 q X0`. Its other bank still has an arbitrary +borrowed baseline. This is not an original-input Fourier endpoint. + +```text +coupled-data-split-20261020/FREEZE.json +9ffcc73fe0a8afc34c3a16aec400ab4cdcaa4904213716f48e91c7c79527c308 +independent-review-20261017/coupled-two-call-review-20261020/FREEZE.json +4cc4d8ca3c6c63c8c5a77e0e01a613a56910d968c95dc2c5c402ef2526077659 +``` + +The earlier access concern is resolved. Gamma in this packet means +only the literal orthogonal rho. It never means `F0 q`. The +literal translations prove the entry and exit identities. + +## Other retained results and limits + +The current-I-Y joint reader obstruction, the reset-defect +factorisation, and the exact rational code services remain in +their separate frozen packets. Their scopes do not automatically +apply to the changed phase-coded local response. + +The previous `HANDOFF-20261020.md` records the rational code +services. The rank-thirty in-place translation compiler described +there remains an unexecuted draft. It is not a validated service. + +An exact FULL-only null family was calculated for the old clean +triple. It uses a sixteen-column ordinary right inverse of H0, +with determinant one eighth and integral inverse. This witness +has not been frozen in a separate packet. The new phase-coded +response escapes it. Do not treat the unfinished witness as a +general native lower bound. + +No complete supplier, recursive host, numerical-grid proof, or +complete kappa gain is claimed by these caller results. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-FREEZE.json new file mode 100644 index 0000000000..106c7a3d64 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-FREEZE.json @@ -0,0 +1,9 @@ +{ + "method": "Algebraic consequence of the pinned exact spectrum and coherent-power classification; no new numerical search.", + "proof_sha256": "a3d970f070e6aaf67b79bd80d564cd7d653580f1f7fc1daadc3170dbdb9249ff", + "source_pins": { + "inplace-service-review/REVIEW.md": "d0315887769ec9bc12527a4bdb255b7804b0675b7638767a19062587b41e89cf", + "schur-power-classification/CLASSIFICATION.md": "9f06ddba79bb14cb88c3a19000d1ed1bb41a9fbbe8149d35b7e2854b4593feb6", + "schur-review/REVIEW.md": "2402984a028bef456df8ca4a5e46dd45bbd3ed68611a558f77196f63b66996a5" + } +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES-FREEZE.json new file mode 100644 index 0000000000..7116e5858d --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES-FREEZE.json @@ -0,0 +1,5 @@ +{ + "PHASE-SECTION-GEOMETRY-SOURCES.md": "ae8ec52c10c77658190b996a529a405736e377ebc76e9804eaf73e7ff965cc97", + "PHASE-SECTION-GEOMETRY.md": "a3d970f070e6aaf67b79bd80d564cd7d653580f1f7fc1daadc3170dbdb9249ff", + "inplace-service-review/MAP-COST-CORRECTION.md": "fbf9ef6d0069ab6b5d4ac8ad5daa480a88fdc8bc363cfacb309d47010e3f3c7f" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES.md new file mode 100644 index 0000000000..ca23386e87 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY-SOURCES.md @@ -0,0 +1,15 @@ +# Source qualification for the phase-section geometry + +The frozen PHASE-SECTION-GEOMETRY.md has SHA256 +a3d970f070e6aaf67b79bd80d564cd7d653580f1f7fc1daadc3170dbdb9249ff. +Its algebra and norm conclusions do not use a stream-map complexity +bound. When its one-bank service is used as construction evidence, +read `inplace-service-review/REVIEW.md` with +`inplace-service-review/MAP-COST-CORRECTION.md`, SHA256 +fbf9ef6d0069ab6b5d4ac8ad5daa480a88fdc8bc363cfacb309d47010e3f3c7f. + +The correction withdraws the O(V) shortcut for the 144 simultaneous +translations in the general interleaved layout. Their declared map +invoice and applicable packed-map cost remain. The exact inverse, +one-bank owner contract, native-child count, and scalar invoice are +unchanged. No geometry assertion depends on the withdrawn shortcut. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY.md new file mode 100644 index 0000000000..f6acb5ed57 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/PHASE-SECTION-GEOMETRY.md @@ -0,0 +1,152 @@ +# Exact conditioning of the positive-line centre section + +The reviewed squared-line code gives more than an algebraic right +inverse. It gives a uniformly bounded complement to the actual query +kernel at every tensor width. This note states its exact conditioning +and identifies the line-power classes in which such a section exists. +These are operator norms for the coefficient Hilbert space. They do +not replace the stored-field and arithmetic guards of a native word. + +Use the actual B, D=B^*, and BD=13I. Let Q be the diagonal ordinary +native line operator. It is unitary and Q^4=I. Put + +```text +A = BQ, T = BQ^2D, +K_minus = qD/13, K_plus = QD T^-1, q=Q^-1. +``` + +The independent spectral review proves that T is self-adjoint and that +its exact spectrum, across the complete address space at every positive +width, is + +```text +{ -13,-11,-5,-3,-1,1,3,5,11,13 }. +``` + +All these values occur. T^-1 now has a literal one-bank implementation +with one C0, as reviewed in `inplace-service-review/REVIEW.md`. Its odd +grid, conditional scan cost, and physical view contract remain part of +every use below. + +## A bounded complement to the query kernel + +The identities + +```text +A K_minus = I, A K_plus = I +``` + +follow from BD=13I and T T^-1=I. Since AA^*=13I, K_minus=A^*/13 is +the minimum-norm right inverse. For each centre c, every solution of +Ay=c has the orthogonal decomposition + +```text +y = K_minus c + z, z in ker(A). +``` + +Thus its norm is at least ||c||/sqrt(13). The positive-line section +instead has + +```text +K_plus^* K_plus = 13 T^-2. +``` + +Its exact singular values are + +```text +sqrt(13), sqrt(13)/3, sqrt(13)/5, sqrt(13)/11, 1/sqrt(13). +``` + +Hence ||K_plus||=sqrt(13), its smallest singular value is 1/sqrt(13), +and its condition number is 13, independently of tensor width. The +right inverse can use the positive-line image im(QD), at a bounded +conditioning cost. This image is a direct complement to ker(BQ), not +an additional independent field bank. + +The associated oblique projector is + +```text +P_plus = K_plus A = QD T^-1 BQ. +``` + +It has P_plus^2=P_plus, image im(QD), and kernel ker(BQ). Its exact +norm is 13: multiplication by Q on either side does not change norm, +while D/sqrt(13) is an isometry and B/sqrt(13) is its adjoint. Thus +||D T^-1 B||=13||T^-1||=13. The canonical projector K_minus A is +orthogonal and has norm one. + +## The two phase images + +Let U_plus=QD/sqrt(13) and U_minus=qD/sqrt(13). They are isometries. +Their cross-Gram operator is + +```text +U_minus^* U_plus = T/13. +``` + +Therefore the exact principal-angle cosines between their images are + +```text +1/13, 3/13, 5/13, 11/13, 1. +``` + +The cross-Gram map is uniformly invertible. The two images are not a +direct-sum pair: cosine one occurs. The useful direct-sum statement is +the complement of ker(BQ) above. This distinction prevents an incorrect +claim that the positive- and inverse-line centre images are disjoint. + +In contrast, the unsquared operator BQD is singular at every width at +least five. The frozen exact witness uses copy characters (1,2,3,6,6) +and centre vector (0,0,1,0,-1,1,0,1). Thus the unchanged image im(D) +contains no right inverse for BQ at those widths. The squared-line code +changes the admissible image rather than inverting that singular map. + +## All coherent line-power sections + +More generally, let A_m=BQ^m and require a section with image in +im(Q^nD). Such a section has the unique form Q^nD H, if it exists, +because D is injective. Its query response is + +```text +A_m Q^nD H = S_(m+n) H, S_k=BQ^kD. +``` + +The reviewed coherent-power classification gives the exact uniform +answer: + +| m+n modulo four | Right inverse with this image | +| --- | --- | +| 0 | Q^nD/13 at every positive width | +| 2 | Q^nD T^-1 at every positive width | +| 1 or 3 | No such right inverse at any width at least five | + +The negative statement holds even for a nonlinear choice of H. At the +singular mode, some centre outputs are outside the response range. +The positive statements provide the unique section in the stated image. +For residue zero its norm is 1/sqrt(13). For residue two its norm is +sqrt(13), with condition number 13. All stage routes preserve these +claims because they are unitary and commute with their own port lines. + +## Construction boundary and evidence + +The positive-line section is a concrete interface opportunity: its +centre correction T^-1 now needs one existing eight-field bank and one +owned C0. The Q^nD scatter still needs a legal source, physical target +frames, complete cost, and restoration. This note does not supply those +operations or a complete decoder. The Hilbert norm bounds do not +remove the native word's local guard, root scaling, or owner leases. + +This note depends on these frozen packets: + +- `schur-review/REVIEW.md`, SHA256 + `2402984a028bef456df8ca4a5e46dd45bbd3ed68611a558f77196f63b66996a5`. +- `schur-power-classification/CLASSIFICATION.md`, SHA256 + `9f06ddba79bb14cb88c3a19000d1ed1bb41a9fbbe8149d35b7e2854b4593feb6`. +- `inplace-service-review/REVIEW.md`, SHA256 + `d0315887769ec9bc12527a4bdb255b7804b0675b7638767a19062587b41e89cf`. + +The algebra above is a consequence of those exact identities; it does +not use a new numerical search. OpenAI Codex assisted the work. No +supplier, native-child saving, or kappa claim is made. No PR, commit, +or push was made. Before a future PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/coupled-data-split-20261020/check_typed_split.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/coupled-data-split-20261020/check_typed_split.py new file mode 100644 index 0000000000..288a5de490 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/coupled-data-split-20261020/check_typed_split.py @@ -0,0 +1,303 @@ +"""Check the coupled two-call types with the literal D25 phase maps.""" + +from fractions import Fraction as F +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "views": ( + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), + "row_code": ( + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz", + "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2", + ), + "clean_forward": ( + "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz", + "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083", + ), + "clean_backward": ( + "new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz", + "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c", + ), +} +UNIT = tuple(1 << i for i in range(25)) +ID = (UNIT, ()) + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def act(matrix, vector): + out = 0 + while vector: + low = vector & -vector + out ^= matrix[low.bit_length() - 1] + vector ^= low + return out + + +def add_line(phase, vector, coefficient): + bits = [i for i in range(25) if vector >> i & 1] + for i in bits: + phase[i, i] = (phase.get((i, i), 0) + coefficient) % 4 + for k, i in enumerate(bits): + for j in bits[k + 1:]: + phase[i, j] = (phase.get((i, j), 0) - 2 * coefficient) % 4 + + +def frozen(phase): + return tuple(sorted((i, j, c % 4) for (i, j), c in phase.items() if c % 4)) + + +def phases(terms): + phase = {} + for vector, coefficient in terms: + add_line(phase, vector, coefficient) + return UNIT, frozen(phase) + + +def route(columns): + return tuple(columns), () + + +@lru_cache(maxsize=30000) +def multiply(left, right): + rho, p = left + sigma, q = right + phase = {(i, j): c for i, j, c in p} + for i, j, c in q: + if i == j: + add_line(phase, rho[i], c) + else: + need(c == 2, "Even quadratic phase coefficient") + for a in range(25): + if rho[i] >> a & 1: + for b in range(25): + if rho[j] >> b & 1: + key = (min(a, b), max(a, b)) + phase[key] = (phase.get(key, 0) + c) % 4 + return tuple(act(rho, col) for col in sigma), frozen(phase) + + +def add(*terms): + out = {} + for coefficient, row in terms: + for key, value in row.items(): + out[key] = out.get(key, F(0)) + coefficient * value + return {key: value for key, value in out.items() if value} + + +def operated(op, row): + out = {} + for (column, old), value in row.items(): + key = (column, multiply(op, old)) + out[key] = out.get(key, F(0)) + value + return {key: value for key, value in out.items() if value} + + +def linear(matrix, rows): + return [add(*((value, rows[j]) for j, value in row.items())) + for row in matrix] + + +def zipped(a, b, ca=F(1), cb=F(1)): + return [add((ca, x), (cb, y)) for x, y in zip(a, b)] + + +def sparse(matrix): + return [{int(j): F(c) for j, c in row.items() if F(c)} for row in matrix] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + source = {} + for name, (relative, expected) in PINS.items(): + path = LANES / relative + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == expected, name + " pin") + source[name] = json.loads(raw) + records = {(row["stage"], row["port"]): row for row in source["views"]["entries"]} + q = [records[0, p]["q"] for p in range(112)] + rho = [tuple(records[1, p]["route_columns"]) for p in range(112)] + code = source["row_code"] + p = code["selected_ports"] + r = code["ordinary_ports"] + need(len(p) == 16 and len(r) == 96 and sorted(p + r) == list(range(112)), "Port partition") + c, e = sparse(code["code"]), sparse(code["response"]) + h = [{j: c[a].get(b, F(0)) for j, b in enumerate(r) if c[a].get(b, F(0))} + for a in p] + d = [{j: e[a].get(b, F(0)) for j, b in enumerate(p) if e[a].get(b, F(0))} + for a in r] + need(all(d[j].get(i, F(0)) == -h[i].get(j, F(0)) for i in range(16) for j in range(96)), + "Actual D=-H transpose") + identity_code = [{a: F(1)} for a in range(112)] + for i, a in enumerate(p): + identity_code[a].update({r[j]: value for j, value in h[i].items()}) + need(c == identity_code, "Actual row code fixes all ordinary rows") + ffresh = phases([(1 << i, 1) for i in range(9, 17)]) + ffresh_inverse = phases([(1 << i, -1) for i in range(9, 17)]) + f9 = phases([(1 << i, 1) for i in range(9)]) + f17 = phases([(1 << i, 1) for i in range(17)]) + entry, exit_view = [], [] + entry_checks = exit_checks = 0 + for a in range(112): + record = records[1, a] + alignment = record["literal_stage_alignment"] + need(alignment["entry_X"] == alignment["entry_Y"] and + alignment["exit_X"] == alignment["exit_Y"], "Matched X/Y literal views") + need(tuple(act(rho[a], col) for col in rho[a]) == UNIT and act(rho[a], q[a]) == q[a], + "Route is an involution and fixes its own line") + entry.append(multiply(phases([(act(rho[a], alignment["entry_X"]), 2)]), route(rho[a]))) + exit_view.append(multiply(phases([(alignment["exit_X"], 2)]), route(rho[a]))) + need(multiply(entry[-1], f9) == + multiply(multiply(ffresh, phases([(q[a], 1)])), route(rho[a])), + "Literal one-sided entry") + need(multiply(exit_view[-1], f17) == multiply(f17, route(rho[a])), "Literal FULL exit") + entry_checks += 1 + exit_checks += 1 + + def fields(rows): + return ([rows[a] for a in p], [rows[a] for a in r], + [rows[112 + a] for a in p], [rows[112 + a] for a in r]) + + def joined(ap, ur, zp, vr): + rows = [None] * 224 + for ports, values, offset in ((p, ap, 0), (r, ur, 0), (p, zp, 112), (r, vr, 112)): + for a, value in zip(ports, values): + rows[offset + a] = value + return rows + + def local(rows, variant, backward): + ap, ur, zp, vr = fields(rows) + if not backward: + alpha = zipped(ap, linear(h, ur)) + lower = zipped(ur, linear(d, alpha)) + if variant == "clean": + return joined([add((-1, z)) for z in zp], ur, alpha, zipped(vr, lower)) + return joined(zipped(zp, alpha, cb=-1), lower, alpha, zipped(vr, lower)) + if variant == "clean": + return joined(zipped(zp, linear(h, vr)), zipped(zipped(ur, linear(d, zp)), vr, cb=-1), + [add((-1, a)) for a in ap], vr) + return joined(zipped(zipped(ap, zp), linear(h, zipped(ur, linear(d, zp)))), + zipped(zipped(ur, linear(d, zp)), vr, cb=-1), ap, vr) + + def input_inverse(rows): + return [operated(phases([(q[a % 112], -1)]), row) + if a < 112 or a - 112 in p else row for a, row in enumerate(rows)] + + def output_frame(rows): + return [operated(multiply(f9, phases([(q[a % 112], -1)])), row) + if a >= 112 and a - 112 in r else operated(f9, row) + for a, row in enumerate(rows)] + + unit_rows = [{(a, ID): F(1)} for a in range(224)] + for backward, key, matrix in ( + (False, "clean_forward", source["clean_forward"]["content_map"]), + (True, "clean_backward", source["clean_backward"]["content_maps"]["selected_swap_conjugate"])): + expected = [{(j, ID): coefficient for j, coefficient in row.items()} for row in sparse(matrix)] + need(local(unit_rows, "clean", backward) == expected, key + " exact stored content map") + initial = input_inverse(unit_rows) + initial_a, initial_u, initial_z, initial_v = fields(initial) + initial_alpha = zipped(initial_a, linear(h, initial_u)) + expected_data = [{(a, multiply(f17, phases([(q[a], -1)]))): F(1)} for a in range(112)] + + def replay(variant, omit_entry_translation=False): + rows = output_frame(local(initial, variant, False)) + rows = [operated(phases([(q[a], 2)]), rows[112 + a]) for a in range(112)] + [ + add((-1, row)) for row in rows[:112]] + views = [route(g) for g in rho] if omit_entry_translation else entry + rows = [operated(multiply(ffresh_inverse, views[a % 112]), row) + for a, row in enumerate(rows)] + rows = input_inverse(rows) + rows = output_frame(local(rows, variant, True)) + rows = [operated(multiply(exit_view[a % 112], ffresh), row) for a, row in enumerate(rows)] + y = rows[112:] + yp = [operated(phases([(q[a], 2)]), y[a]) for a in p] + yr = [add((-1, y[a])) for a in r] + if variant == "clean": + yp = [add((-1, row)) for row in yp] + else: + yr = zipped(yr, linear(d, yp), cb=-1) + yp = zipped(yp, linear(h, yr), cb=-1) + decoded = [None] * 112 + for ports, values in ((p, yp), (r, yr)): + for a, row in zip(ports, values): + decoded[a] = row + return rows, decoded + + passes = {} + for variant in ("original", "clean"): + rows, decoded = replay(variant) + need(decoded == expected_data, variant + " decoded physical data on all 224 columns") + wrong, bad_data = replay(variant, True) + rejected = sum(a != b for a, b in zip(bad_data, expected_data)) + need(rejected > 0, variant + " omitted-translation control") + passes[variant] = { + "arbitrary_input_columns": 224, + "data_output_rows": 112, + "omitted_entry_translation_rejected_rows": rejected, + "full_endpoint_terms": sum(map(len, rows)), + } + if variant == "clean": + gq_u = [operated(multiply(route(rho[a]), phases([(q[a], 1)])), row) + for a, row in zip(r, initial_u)] + h1q_u = [operated(route(rho[a]), row) for a, row in zip(p, linear(h, gq_u))] + expected_s = zipped(initial_z, h1q_u, cb=-1) + gz = [operated(route(rho[a]), row) for a, row in zip(p, initial_z)] + d1z = [operated(route(rho[a]), row) for a, row in zip(r, linear(d, gz))] + pre_r = zipped(zipped(initial_v, initial_u, cb=2), linear(d, initial_alpha)) + expected_r = zipped([operated(phases([(q[a], 1)]), row) for a, row in zip(r, pre_r)], d1z) + for ports, values in ((p, expected_s), (r, expected_r)): + for a, row in zip(ports, values): + need(rows[a] == operated(f17, row), "Clean arbitrary source-bank endpoint") + scalar_price = 0 + for row in h: + for value in row.values(): + numerator, denominator = abs(value.numerator), value.denominator + need(denominator & (denominator - 1) == 0, "Dyadic H coefficient") + scalar_price += 2 * (3 + numerator.bit_length() - 1 + numerator.bit_count() + + denominator.bit_length() - 1) + receipt = { + "status": "PASS_ACTUAL_D25_COUPLED_TWO_CALL_TYPES", + "source_pins": {key: {"path": str(LANES / path), "payload_sha256": digest} + for key, (path, digest) in PINS.items()}, + "literal_entry_identities": entry_checks, + "literal_FULL_exit_identities": exit_checks, + "variants": passes, + "clean_data_decoder": { + "H_nonzero_coefficients": sum(map(len, h)), + "H_real_scalar_primitives": scalar_price, + "selected_translation_map_calls": 16, + "sign_fields": 112, + "new_native_children": 0, + "new_fields": 0, + }, + "physical_decoded_data": "F17 q X0", + "arbitrary_source_bank_restored": False, + "local_native_contract_replayed": False, + "stored_clean_content_maps_bound": True, + "complete_supplier_claimed": False, + "scope": "The local coupled F/B types are premises. Literal D25 entry/exit phases and all 224 arbitrary data columns are checked. No final Q cleanup or borrowed restoration is inferred.", + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + print(json.dumps(receipt["variants"], sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/CORRECTION-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/CORRECTION-FREEZE.json new file mode 100644 index 0000000000..23000d49dd --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/CORRECTION-FREEZE.json @@ -0,0 +1,6 @@ +{ + "MAP-COST-CORRECTION.md": "fbf9ef6d0069ab6b5d4ac8ad5daa480a88fdc8bc363cfacb309d47010e3f3c7f", + "REVIEW.json": "1691a9a796fc92e5ca7f1ec622cbd34c125115c331e8689359260db64df256b7", + "REVIEW.md": "d0315887769ec9bc12527a4bdb255b7804b0675b7638767a19062587b41e89cf", + "layout_source_sha256": "20cfc8d12099d4e4ed9e3e7eeb6162edd9b6e0e076f24693364cd24377252594" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/FREEZE.json new file mode 100644 index 0000000000..62db0baf69 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/FREEZE.json @@ -0,0 +1,5 @@ +{ + "REVIEW.json": "1691a9a796fc92e5ca7f1ec622cbd34c125115c331e8689359260db64df256b7", + "REVIEW.md": "d0315887769ec9bc12527a4bdb255b7804b0675b7638767a19062587b41e89cf", + "check_inplace_review.py": "9e811410469b2eb8f58c5239aad68bfe3e8e33745c0536ab419f3e58cd1f231d" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/MAP-COST-CORRECTION.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/MAP-COST-CORRECTION.md new file mode 100644 index 0000000000..9936135040 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/MAP-COST-CORRECTION.md @@ -0,0 +1,45 @@ +# Scope correction for the simultaneous translation cost + +This addendum corrects the map-cost statement in the frozen REVIEW.md, +SHA256 d0315887769ec9bc12527a4bdb255b7804b0675b7638767a19062587b41e89cf. +The earlier file is preserved as evidence. Read it with this correction. + +The claim that all 144 Walsh translations have a direct O(V) lowering +as complements of one contiguous f-bit address field is withdrawn for +the general retained layout. The resulting claim that the whole body +has fixed linear stream cost is also withdrawn. + +The primary source `upstream/build/sections/05-layers.tex` puts one +selected bit at offset rho inside each K-bit chunk. There are f chunks +in each slot. A simultaneous shift g_j flips the selected bits in one +slot and leaves its other bits unchanged. For K>1, these f selected +bits are interleaved with unselected bits. Collapsing the prefix and +suffix does not make them one contiguous f-bit address field. Therefore +the proposed map y -> -1-y modulo 2^f is not that physical map. + +The shortcut is valid when K=1. At general K it would need an explicit +packed extraction view and its cost, or a separate lowering of the +interleaved complement. Neither was proved in the frozen review. + +Retain the producer's original invoice of 144 simultaneous translation +maps and the cost of the applicable packed-map backend. Retain the +sixteen outer view maps. Do not price any of these maps as a single bit +operation or use the withdrawn O(V) shortcut in a supplier recurrence. +The producer's frozen proof did not make that shortcut. + +The following independently checked results are unchanged: every +literal arithmetic map, both inverse orders at all 512 modes, all nine +formal input columns, zero owned output, the complete scalar invoice, +the exact translation-kernel coefficients, all 64 completed-level phase +identities, the one-C0 owner contract, and the zero native-child count +of the declared word. The direct marked-counter conditional scans are +also unchanged. Their marks can be placed at the actual selected-bit +positions; the proof applies to arbitrary positions. + +The one-bank code remains a useful local construction with explicit +map obligations. It is not a complete new supplier or kappa bound. +The owner-review lane found the layout error while extending the word +to a forward encoder. The coordinating agent was informed immediately. +OpenAI Codex assisted the check. No PR, commit, or push was made. Before +any future PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/REVIEW.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/REVIEW.json new file mode 100644 index 0000000000..66df2a2da5 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/REVIEW.json @@ -0,0 +1,83 @@ +{ + "active_mode_operations": 120372, + "arbitrary_owned_input_removed": true, + "checker_sha256": "9e811410469b2eb8f58c5239aad68bfe3e8e33745c0536ab419f3e58cd1f231d", + "completed_level_full_phase_checks": 64, + "counts": { + "ADD": 10743, + "CLEAR": 152, + "COPY": 152, + "DIVIDE_ODD": 8, + "NEG": 2902, + "SCALE2": 10004, + "TRANSLATE": 144, + "conditional_complex_instructions": 23345, + "conditional_scalar_primitives": 110284, + "double": 5010, + "halve": 4994, + "real_odd_division_scans": 16, + "scalar_primitives": 112364, + "translation_maps": 144, + "uniform_scalar_primitives": 2080 + }, + "full_word_extra_dyadic_bits": 9, + "inverse_kernel_coefficients": 32768, + "maximum_completed_mode_row_norm": "1", + "maximum_mode_prefix_coefficient": 225280, + "maximum_mode_prefix_row_norm": 462848, + "mode_extra_dyadic_bits": 0, + "mode_input_columns": 9, + "mode_inverse_orders": 1024, + "odd_height_increase": 1, + "owned_fields": 1, + "owned_output_zero": true, + "scope": "Literal one-bank inverse, conditional-scan backend proof, and inherited completed-view contract. No global lease, full decoder, supplier, or kappa claim.", + "sources": { + "interface": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/INTERFACE.json", + "sha256": "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746" + }, + "layer_source": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/upstream/build/sections/05-layers.tex", + "sha256": "20cfc8d12099d4e4ed9e3e7eeb6162edd9b6e0e076f24693364cd24377252594" + }, + "odd_grid": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md", + "sha256": "e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01" + }, + "phase_ledger": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + "producer_checker": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/check_inplace_service.py", + "sha256": "ec38a9db9d7542eb076def53d8df4af2ede586cc110835014ca1ab8219cc4e56" + }, + "producer_proof": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.md", + "sha256": "46adf0f78165489bd87401fc781b4a5d9505c4998c068800c72dfbc780dd49c6" + }, + "producer_receipt": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.json", + "sha256": "9e568a68279c6aa126d25a593baa9775f39646977968a0391732cae538fea2d8" + }, + "program": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-PROGRAM.json.gz", + "sha256": "e4015617dbb55c2e943eb7762766e9854b6e7d61fbccd905dbfbfcb9cc338a8b" + }, + "spectrum": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/SCHUR-PROBE.json", + "sha256": "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024" + }, + "stream_source": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/upstream/build/sections/02-streams.tex", + "sha256": "606c80db61cad13aa0c3b6060dc4b88dbbe7ac60cdd831aa93f28d908fd09dab" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", + "sha256": "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f" + } + }, + "status": "PASS_INDEPENDENT_INPLACE_TRANSLATION_INVERSE", + "walsh_pair_blocks": 144 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/REVIEW.md new file mode 100644 index 0000000000..a998bdc874 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/inplace-service-review/REVIEW.md @@ -0,0 +1,213 @@ +# Independent review of the one-bank translation inverse + +The literal inverse of T=B Q_U^2 B^T passes independent review. It uses +one existing eight-field centre bank, one owned C0, and zero native +children. The body has fixed linear stream cost at every positive +tensor width. The physical call has the sixteen stated outer view maps. +The result removes the need for a second eight-field bank in this +centre normalization. It does not supply the ordinary source query or +the final ordinary scatter of a complete decoder. + +## Independent arithmetic and physical checks + +The checker imports no producer code. It reads the literal compressed +program, the actual R matrix and phase ledger, and the frozen inverse +kernel. It computes each of the 512 integer matrices directly as + +```text +T_chi = sum_(p in U) B_p B_p^T (-1)^(chi dot q_p). +``` + +It replays only the emitted instructions, with nine formal inputs: +eight arbitrary live fields and arbitrary C0. Integer rows are used +before the eight final divisions. Every source halving has an even +numerator in every formal input column. The output numerator matrix N +satisfies both N T_chi=2145I and T_chi N=2145I. C0 has zero output, and +its input has zero coefficient in every live output. Thus the review +does not assume C0 is initially zero. + +The review also checks each of the 144 literal Walsh blocks on the two +orbit addresses and both arbitrary scratch records. It obtains the +two-by-two maps H/2 and H, respectively, where H has rows (1,1) and +(1,-1). It checks the selector tables, the complete order of the three +word parts, and all 32,768 inverse-kernel positions by a separate +integer Walsh butterfly calculation. These checks include every live +input column; they are not sampled numerical tests. + +The 64 selected completed-X views equal the pinned serialized source +views. The review verifies every linear and quadratic phase coefficient +at the actual completed level s, whose transformed coordinates are the +first 9+8s coordinates. Each view fixes all future coordinates and has +its translation in the completed subspace. The review checks every +entry wrapper and inverse exit wrapper. The physical contract is +V_s^-1 T^-1 V_s. It is not identified with T^-1 in raw owner coordinates. + +The middle word can leave FULL at intermediate instructions. No native +child runs there. Its completed operator is a translation convolution, +so it commutes with the common FULL transform. This proves the stated +final frame without an unproved intermediate-frame invariant. + +## Why the finite mode proof applies at every width + +At tensor width f, let g_j flip coordinate j in every copy, for j=0,...,8. +Let ell_j read coordinate j in the first copy. Then ell_j(g_k)=delta_jk. +The subgroup generated by the nine g_j has size 512 for every positive +f. Its action by translations is free. Each orbit has a unique element +whose nine first-copy bits are zero. + +On each orbit the literal W is the normalized 512-point Walsh matrix. +It sends translation by g_delta to the diagonal sign +(-1)^(chi dot delta). This proves + +```text +W T W^-1 = diag_chi(T_chi), +W^-1 diag_chi(T_chi^-1) W = T^-1. +``` + +The argument concerns one nine-generator translation group. It does not +treat T as a tensor power of an eight-by-eight matrix. The all-width +claim therefore follows from the free-orbit decomposition and the 512 +exact matrix checks. + +## Direct stream implementation and a sharper map bound + +The marked-counter implementation is valid in the pinned fixed-tape +model. Place nine marks on a fixed extra track of the existing address +counter. A finite 512-state register holds their values. Every carry +that flips a marked bit updates that state. For N consecutive records, +the total counter-head travel is O(N+p), including initialization and +returns, where p is the address width. This follows by summing the +O(1+N/2^j) visits to each bit. A selector lookup uses that finite state +and does not rescan the full address. + +For each conditional instruction, scan every source and target record. +The inactive case leaves the target unchanged and still traverses both +streams. The active case uses the retained exact arithmetic scan. A +record reversal can use O(w) temporary bits for a guarded width w; it +does not require another field array. The marked counter uses O(p) +bits. Thus the conditional arithmetic has its stated arithmetic charge +plus O(N+p) control work per real pass. The finite mode selectors remain +fixed when f increases. + +The 144 Walsh translations have a stronger bound than an arbitrary +packed basis map. In the retained column layout, g_j complements one +entire f-bit chart coordinate. On that address field it is exactly + +```text +y -> -1-y modulo 2^f. +``` + +Collapse the other fields into one prefix and one suffix. The retained +ordered-affine stream lemma applies with the fixed unit -1 and fixed +offset -1. Each such complement has O(V) cost, including descriptor +work, tape returns, and cleanup. No packed row-addition exponent is +needed for these 144 maps. The sixteen outer views still use their +inherited route implementation. Work tapes used by the map backend +remain part of that backend; the one-C0 statement counts numeric owner +roles, not an absence of all machine work tapes. + +The checker verifies the literal finite word. The counter bound, +ordered-affine implementation, and orbit proof are source-based +mathematical arguments. This review does not execute a full Turing +machine trace for arbitrary widths. + +## Complete invoice and common-grid contract + +The independent literal count agrees with every entry of the producer +invoice: + +| Part | Uniform scalar units | Conditional scalar units | Coordinate complements | Real odd scans | +| --- | ---: | ---: | ---: | ---: | +| Forward Walsh | 1008 | 144 | 72 | 0 | +| Mode inverse | 208 | 109996 | 0 | 16 | +| Inverse Walsh | 864 | 144 | 72 | 0 | +| Whole body | 2080 | 110284 | 144 | 16 | + +There are 23,345 conditional complex instructions. A physical call adds +eight entry views and eight inverse exit views. No source preparation +outside the stated completed bank and C0 contract is included. + +The scalar units are arithmetic scan units, not exact machine steps. +The conditional units have their extra marked-counter cost. One bound +for that control is a fixed multiple of 110284(N+p), in addition to +the data-record scans. Each of the 144 complements is O(V). The view +costs and odd-division costs are separate. No fraction of inactive modes +is used to reduce the invoice. + +All mode prefixes before the final divisions have integer coefficients. +The complete word increases odd denominator height by at most one. +Its forward Walsh needs nine additional dyadic fractional bits. The +mode word introduces no further dyadic bits, and the inverse Walsh +has no halving. The exact largest mode-prefix row norm is 462,848; +the completed mode inverse has row norm at most one. The normalized +forward transform has row norm one, with unhalved sums at most two; +inverse prefixes have row norm at most 512. Thus 462,848 bounds the +whole stored-field word. Nineteen bits cover this stored-field growth. +The arithmetic backend's temporary-operand guard must also be retained. +This is a local bound, not the complete supplier precision calculation. + +For a fixed odd divisor d, the retained signed division scan uses +a=(b-c) mod 2 and c'=(c+d a-b)/2, with 0<=c= 3 * 2**30, "At least 3 GiB free") +loaded = {key: read(key) for key in PINS} +program, interface, ledger, spectrum = [loaded[key] for key in ("program", "interface", "phase_ledger", "spectrum")] +producer = loaded["producer_receipt"] +need(producer["checker_sha256"] == PINS["producer_checker"][1], "Producer checker pin") +need(producer["payload_compressed_sha256"] == PINS["program"][1], "Producer payload pin") +need(program["live_fields"] == list(range(8)) and program["owned"] == 8, "One-bank ownership") +selected = [0, 7, 20, 27, 36, 46, 57, 111] +need(program["selected_ports"] == selected, "Actual selected minor") +ordinary = [p for p in range(112) if p not in selected] +R = [[F(row.get(str(p), 0)) for p in range(112)] for row in interface["R"]] +B = [[sum(R[i][a] * R[i][p] for i in range(8)) / 4 for p in ordinary] for a in selected] +q = [ledger["recipes"][p]["q"] for p in ordinary] +need(multiply(B, list(map(list, zip(*B)))) == [[13 * x for x in row] for row in identity(8)], "Actual BD=13I") +matrices = [] +for mode in range(512): + matrix = [[sum(B[i][p] * B[j][p] * (-1 if (mode & q[p]).bit_count() % 2 else 1) + for p in range(104)) for j in range(8)] for i in range(8)] + need(all(x.denominator == 1 for row in matrix for x in row), "Integral mode matrix") + matrices.append([[int(x) for x in row] for row in matrix]) + +selectors = {key: frozenset(values) for key, values in program["selectors"].items()} +need(all(len(values) == len(program["selectors"][key]) and values <= set(range(512)) + for key, values in selectors.items()), "Canonical selector table") +for bit in range(9): + need(selectors["bit_" + str(bit)] == {mode for mode in range(512) if mode >> bit & 1}, "First-copy sign selector") +mode_word = program["mode_word"] +need(mode_word[-8:] == [["DIVIDE_ODD", None, i, 2145] for i in range(8)], "Only final uniform odd divisions") +need(all(g[0] != "DIVIDE_ODD" for g in mode_word[:-8]), "One odd-height increment") +maximum, maximum_coefficient, final_maximum = 1, 1, F(0) +numerators = [] +active_operations = 0 +for mode in range(512): + state = identity(9) + for kind, selector, target, *args in mode_word[:-8]: + if selector is not None and mode not in selectors[selector]: + continue + active_operations += 1 + if kind == "ADD": + source, coefficient = args + need(source != target and coefficient in (-1, 1), "Unit ADD on distinct fields") + state[target] = [a + coefficient * b for a, b in zip(state[target], state[source])] + elif kind == "NEG": + state[target] = [-x for x in state[target]] + elif kind == "SCALE2": + if args == [1]: + state[target] = [2 * x for x in state[target]] + else: + need(args == [-1] and all(x % 2 == 0 for x in state[target]), "No new mode denominator") + state[target] = [x // 2 for x in state[target]] + elif kind == "COPY": + need(target == 8 and 0 <= args[0] < 8, "Copy overwrites only owned C0") + state[target] = state[args[0]][:] + else: + need(kind == "CLEAR" and target == 8 and not args, "Only owned C0 is cleared") + state[target] = [0] * 9 + maximum = max(maximum, sum(map(abs, state[target]))) + maximum_coefficient = max(maximum_coefficient, *map(abs, state[target])) + need(not any(state[8]) and not any(row[8] for row in state[:8]), "Arbitrary scratch is removed and cleared") + result = [row[:8] for row in state[:8]] + expected = [[2145 * x for x in row] for row in identity(8)] + need(multiply(result, matrices[mode]) == expected == multiply(matrices[mode], result), "Both exact mode inverse orders") + numerators.append(result) + final_maximum = max(final_maximum, *(F(sum(map(abs, row)), 2145) for row in result)) + +# The local pair replay includes both arbitrary scratch records. +pair_checks = 0 +for name, word in program["walsh_words"].items(): + step = 6 if name == "forward" else 5 + need(len(word) == 72 * step, "Nine Walsh directions on each live field") + seen = set() + for start in range(0, len(word), step): + gates = word[start:start + step] + target = gates[0][3] + shift = gates[1][3] + need(shift in [1 << bit for bit in range(9)] and target < 8, "One simultaneous generator") + bit = shift.bit_length() - 1 + expected = [["COPY", None, 8, target], ["TRANSLATE", None, 8, shift], + ["NEG", "bit_" + str(bit), target], ["ADD", None, target, 8, 1]] + if name == "forward": + expected.append(["SCALE2", None, target, -1]) + expected.append(["CLEAR", None, 8]) + need(gates == expected and (target, bit) not in seen, "Literal Walsh block") + seen.add((target, bit)) + state = [[F(x) for x in row] for row in identity(4)] + state[2:4] = [state[0][:], state[1][:]] + state[2], state[3] = state[3], state[2] + state[1] = [-x for x in state[1]] + state[0] = [x + y for x, y in zip(state[0], state[2])] + state[1] = [x + y for x, y in zip(state[1], state[3])] + if name == "forward": + state[:2] = [[x / 2 for x in row] for row in state[:2]] + state[2:4] = [[F(0)] * 4 for _ in range(2)] + scale = F(1, 2) if name == "forward" else F(1) + need(state == [[scale, scale, 0, 0], [scale, -scale, 0, 0], [0] * 4, [0] * 4], "Walsh map and arbitrary scratch columns") + pair_checks += 1 + +need(program["body"] == program["walsh_words"]["forward"] + mode_word + program["walsh_words"]["inverse"], "Complete program order") +kernel = {(delta, i, j): F(c) for delta, i, j, c in spectrum["kernels"]["inverse"]["entries"]} +for i in range(8): + for j in range(8): + values = [numerators[mode][i][j] for mode in range(512)] + block = 1 + while block < 512: + for start in range(0, 512, 2 * block): + for offset in range(block): + a, b = values[start + offset], values[start + block + offset] + values[start + offset], values[start + block + offset] = a + b, a - b + block *= 2 + need(all(F(value, 512 * 2145) == kernel.get((delta, i, j), 0) + for delta, value in enumerate(values)), "All inverse translation coefficients") + +counts = invoice(program["body"]) +need(counts["translation_maps"] == 144 and counts["real_odd_division_scans"] == 16, "Complete non-scalar invoice") +need(counts["uniform_scalar_primitives"] == 2080 and counts["conditional_scalar_primitives"] == 110284, "Complete scalar invoice") +need(counts["conditional_complex_instructions"] == 23345, "Conditional scan count") +need(counts == producer["counts"]["complete"], "All invoice entries agree") +need(maximum == 462848 and final_maximum == 1, "Exact prefix and final norms") + +# Check the full quadratic phase at each actual completed level s. +actual_views = {(v["stage"], v["port"]): v for v in loaded["views"]["views"] + if v["side"] == "X" and v["port"] in selected} +need(len(actual_views) == 64, "All selected completed views") +need({(v["stage"], v["port"]): v for v in program["completed_views"]} == actual_views, "Literal source views") +for (stage, port), view in actual_views.items(): + rho, delta = view["route_columns"], view["translation_after_route"] + dimension = 9 + 8 * stage + mask = (1 << dimension) - 1 + need(delta & ~mask == 0, "View translation lies in completed coordinates") + need(all(rho[j] == 1 << j for j in range(dimension, 73)), "View fixes future coordinates") + for j in range(73): + need(((rho[j] & mask).bit_count() + 2 * ((delta >> j) & 1) - (j < dimension)) % 4 == 0, + "Completed-level linear phase") + for k in range(j): + need((-2 * (rho[j] & rho[k] & mask).bit_count()) % 4 == 0, "Completed-level quadratic phase") + for j in range(73): + image = 0 + for k in range(73): + if rho[j] >> k & 1: + image ^= rho[k] + need(image == 1 << j, "View route is an involution") +for stage in range(1, 9): + expected = {"enter": [["VIEW", i, stage, selected[i], False] for i in range(8)], + "leave": [["VIEW", i, stage, selected[i], True] for i in reversed(range(8))]} + need(program["stage_wrappers"][str(stage)] == expected, "All entry and inverse exit views") + +receipt = { + "status": "PASS_INDEPENDENT_INPLACE_TRANSLATION_INVERSE", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "sources": {k: {"path": str(p), "sha256": h} for k, (p, h) in PINS.items()}, + "mode_inverse_orders": 1024, "mode_input_columns": 9, + "active_mode_operations": active_operations, "walsh_pair_blocks": pair_checks, + "inverse_kernel_coefficients": 32768, "counts": counts, + "maximum_mode_prefix_row_norm": maximum, + "maximum_mode_prefix_coefficient": maximum_coefficient, + "maximum_completed_mode_row_norm": str(final_maximum), + "mode_extra_dyadic_bits": 0, "full_word_extra_dyadic_bits": 9, + "odd_height_increase": 1, "owned_fields": 1, + "arbitrary_owned_input_removed": True, "owned_output_zero": True, + "completed_level_full_phase_checks": 64, + "scope": "Literal one-bank inverse, conditional-scan backend proof, and inherited completed-view contract. No global lease, full decoder, supplier, or kappa claim.", +} +(HERE / "REVIEW.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") +print(receipt["status"]) +print(json.dumps({"modes": 512, "prefix_norm": maximum, "native_children": 0, "owned_fields": 1})) diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/FREEZE.json new file mode 100644 index 0000000000..b872c50169 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "NO-RESET.md": "e968dd64f34f8dd4422145ccea847d329886657e9e209682a49964d7faf60f3c", + "check_no_reset.py": "8612732e02b68495d6b0b95cbd216d1d0df43be2ffdd29cc7fc9033518ab1c48", + "run-terminal-normal/CHECKS.json": "24741af6fabff0e09bc13518f79477a80f32f88bb49aabaf31f40afa070aa543", + "run-terminal-optimized/CHECKS.json": "24741af6fabff0e09bc13518f79477a80f32f88bb49aabaf31f40afa070aa543" + }, + "normal_optimized_byte_identical": true, + "scope": "Actual D25 natural mixed-frame F/Bswap/F endpoint and208-positive-line operator terminal on224 arbitrary data columns. Native terminal recipes,global helper host,complete recursive invoice and precision are not supplied.", + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/NO-RESET.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/NO-RESET.md new file mode 100644 index 0000000000..0b702317cd --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/NO-RESET.md @@ -0,0 +1,270 @@ +# The natural clean forward-backward-forward word + +Use the clean exchange at stage 0, its selected-swap inverse adjoint +at stage 1, and the clean exchange at stage 2. Do not put a physical +bank reset between these calls. The actual D25 views preserve the +declared mixed types. The endpoint has a dyadic content inverse and +a remaining sixteen-row phase query. + +This packet gives the routed physical endpoint and a complete operator +terminal with 208 positive line operations. It does not emit native +recipes or a host for those line operations. It does not treat the +96 ordinary Y fields as FULL before their stated normalization. + +## Sources and types + +The checker binds the same literal D25 views and clean native payloads +as `../coupled-data-split-20261020/TYPED-SPLIT.md`. It imports only +the exact phase-ring and sparse-row functions from that checker. +It reads the stored forward and backward content matrices from their +pinned payloads. It does not derive those matrices from the endpoint +claimed here. + +Use the same selected set P, ordinary set R, and matrices H and D. +Thus `D=-H*`. Define + +```text +G_s = diag(R_(rho_(s,p))), +H_s = G_(s,P) H G_(s,R), +D_s = G_(s,R) D G_(s,P), +G_0 = I. +``` + +Every G is only a portwise orthogonal route. It is not a Fourier +prefix. Let `Fprev_s=F_(9+8(s-1))` and let Fext_s act on axes +9 through `9+8s-1`. The literal entry and exit views obey + +```text +Ventry_s Fprev_s = Fext_s Q G_s, +Vexit_s F_(9+8s) = F_(9+8s) G_s. +``` + +At a natural boundary, the global types are + +```text +X = Fprev x, +Y_P = Fprev z, +Y_R = Fprev q_R v. +``` + +The next physical input, after the literal views, is therefore + +```text +X = Fext Q G_s x, +Y_P = Fext Q_P G_(s,P) z, +Y_R = Fext G_(s,R) v. +``` + +This is exactly the Q-entry clean type with common exterior Fext. +No Q passes through H or D. The decoded contents change only by G_s. + +At stage 0, use the already emitted I-entry formation variant. +Let the original physical inputs be + +```text +X0 = Q(a,u), +Y0 = (z,v). +``` + +All 224 data fields can be arbitrary. These equations define the +initial local contents; they are not extra gates. The I-entry variant +costs sixteen more units of native mass than the Q-entry variant. +It avoids an initial selected q on z. + +## Actual routed endpoint + +Put + +```text +alpha = a+H_0 u, +K = v+u+D_0 alpha. +``` + +After the first clean call the content is + +```text +X = (-z,u), +Y = (alpha,K). +``` + +X and selected Y are FULL at F9. Ordinary Y has frame `F9 q_R`. +The actual stage-1 call has decoded local input +`G_1(-z,u,alpha,K)`. After Bswapclean and its literal exits, the +global content is + +```text +X = (alpha+H_1 K, W), +Y = (z,K), +W = -v+(D_1-D_0)alpha. +``` + +The same natural boundary rule applies at stage 2. The final physical +endpoint is + +```text +X_P = -F25 z, +X_R = F25 W, +Y_P = F25 beta, +Y_R = F25 q_R r, + +beta = alpha+H_1 K+H_2 W, +r = u+D_1 alpha+D_2 beta. +``` + +This formula includes every original borrowed input. The selected +borrowed fields are restored by a sign. The ordinary borrowed fields +still contain the centre correction `(D_1-D_0)alpha`. + +## Exact content inverse and the physical obligation + +Since `K=r-D_2 beta-W`, the old centre can be written as + +```text +alpha = beta-H_1(r-D_2 beta-W)-H_2 W + = (I+H_1 D_2)beta-H_1 r+(H_1-H_2)W. +``` + +Then + +```text +u = r-D_1 alpha-D_2 beta, +a = alpha-H_0 u, +v = -W+(D_1-D_0)alpha. +``` + +All these content maps are dyadic. No inverse of E, odd division, +or additional independent centre bank occurs in these equations. +The checker verifies the inverse as a content identity. This does +not make the physical access free. + +The final W and beta are in FULL fields. Therefore the terms +`(I+H_1 D_2)beta` and `(H_1-H_2)W` use legal past FULL views. +The term `H_1 r` reads the ordinary Y holes, whose physical content +is `q_R r`. A phase-aware query service is still required for this +term. It cannot be replaced by a scalar read of those fields. + +For the desired original data, the ordinary output is `Q_R u`. +The free translation L_R changes the final `q_R r` baseline to +`Q_R r`. The required correction is then + +```text +Q_R D_1 alpha + Q_R D_2 beta. +``` + +The selected original data are `Q_P a`. A complete terminal must +produce this selected output, make the ordinary correction, restore +v, and preserve all borrowed fields. A low-rank factorization is +not a native implementation of those tasks. + +The reader and scatter occur as a joint problem. The content inverse +above can be used to test a phase code without assuming a free query +or a free final normalization. + +## A complete operator terminal with 208 positive line operations + +There is a direct baseline that uses no extra field. It first puts +ordinary Y in FULL. It then uses a sequence of dyadic shears. This +sequence does not require `I+H_1 D_2` to be a unit. + +Starting from the displayed physical endpoint, use these operations: + +```text +1. Apply Q_R to the 96 ordinary Y fields. +2. Y_R <- Y_R-D_2 Y_P. +3. Y_P <- Y_P-H_1 Y_R. +4. Y_P <- Y_P+(H_1-H_2)X_R. +5. X_R <- -X_R+(D_1-D_0)Y_P. +6. Y_R <- Y_R-D_1 Y_P. +7. Y_P <- Y_P-H_0 Y_R. +8. X_P <- -X_P. +9. Apply Q to all 112 Y fields. +``` + +In steps 2 through 8, all fields are in the common F25 FULL frame. +The H and D expressions denote their legal FULL affine views, with +the literal translations. They are not bare current-chart shears. +After step 2, ordinary Y is `t=r-D_2 beta`. After step 4, selected Y +is alpha. Step 5 restores v. Steps 6 and 7 give u and a. Therefore +the exact physical result is + +```text +X = F25 Y0, +Y = F25 X0. +``` + +The bank exchange is stated explicitly. A final exchange can put the +data in the designated bank if the complete caller requires it. +This result uses the initial I-entry variant. With initial selected +Q entry, restoration of `Y0_P=Q_P z` has a further sixteen-line cost. + +The checker composes this terminal on all 224 input columns. It checks +that each routed H or D shear is an affine FULL view. This gives a +complete operator terminal with 208 positive line operations. It does +not include a serialized native recipe or a global host for those +line operations. + +The direct coefficient implementation has eight H or D shears, each +with the same 216 coefficients and a cost of 2,048 old real primitives. +The 112 signs add 224 primitives. Thus a direct scalar upper bound +is 16,608 primitives. Six routed shears use at most 1,344 per-field +affine map calls in total. These counts do not include the side maps +of the 208 line recipes or the final bank permutation. No map is +priced as a constant-time operation on a complete stream. + +This is a baseline for a joint improvement. No claim is made that +208 line operations fit the complete supplier budget. + +## Local bill and remaining assembly + +The initial I-entry clean call has native profile + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H9. +``` + +Each later Q-entry call has + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H8. +``` + +The sum is native mass 5,392. The three local scalar invoices sum to +25,800 real primitives. These prices include the native local words +and their local adapters. Adding the direct terminal gives 208 more +positive line operations and at most 16,608 more real primitives. +The literal global stage views, terminal views, line side maps, and +bank permutation have their own stream and address costs. No reset +or extra field is added. + +The route proof is exact in dimension 25 and tensors over all spatial +columns. The complete cover sweep must finish before the next stage. +The inherited helper restoration is supplied by the local native +packets. This checker does not replay the global helper host, the +recursive bill, or the full precision proof. + +## Verification + +Run each command with a new output directory: + +```text +python3 -B check_no_reset.py --out +python3 -O -B check_no_reset.py --out +``` + +The normal and optimized receipts are byte-identical. Both initial +entry variants pass all 224 arbitrary input columns and all 224 +physical output rows. The final operator matrix has 176,144 nonzero +input-operator terms. The direct terminal passes on the I-entry +variant. The checker also verifies all 896 natural-boundary phase +identities, all 224 terminal FULL-view identities, and the dyadic +content inverse. + +The first two exploratory runs were interrupted before they produced +a receipt. They used a slower phase substitution. The final checker +uses the same exact polynomial rule with sparse bit iteration. +It compares that rule with the original dense rule on all 224 +actual terminal view/line combinations. + +No PR, commit, or publication is authorized. Read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md` +before any future PR description. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/check_no_reset.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/check_no_reset.py new file mode 100644 index 0000000000..d1920fa640 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/check_no_reset.py @@ -0,0 +1,269 @@ +"""Check the natural three-call word on the actual D25 phase ring.""" + +from fractions import Fraction as F +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +LIBRARY = HERE.parent / "coupled-data-split-20261020/check_typed_split.py" +spec = importlib.util.spec_from_file_location("typed_phase_ring", LIBRARY) +lib = importlib.util.module_from_spec(spec) +spec.loader.exec_module(lib) +need, add, linear, zipped = lib.need, lib.add, lib.linear, lib.zipped +phases, route, sparse = lib.phases, lib.route, lib.sparse + + +@lru_cache(maxsize=None) +def bits(vector): + out = [] + while vector: + low = vector & -vector + out.append(low.bit_length() - 1) + vector ^= low + return tuple(out) + + +@lru_cache(maxsize=30000) +def mapped_phase(rho, phase): + out = {} + for i, j, coefficient in phase: + if i == j: + lib.add_line(out, rho[i], coefficient) + else: + need(coefficient == 2, "Even quadratic coefficient") + for a in bits(rho[i]): + for b in bits(rho[j]): + key = (min(a, b), max(a, b)) + out[key] = (out.get(key, 0) + coefficient) % 4 + return lib.frozen(out) + + +@lru_cache(maxsize=30000) +def multiply(left, right): + if left == lib.ID: + return right + if right == lib.ID: + return left + rho, p = left + sigma, q = right + if rho == lib.UNIT: + phase = {(i, j): c for i, j, c in p} + for i, j, c in q: + phase[i, j] = (phase.get((i, j), 0) + c) % 4 + return sigma, lib.frozen(phase) + if not q: + return tuple(lib.act(rho, col) for col in sigma), p + phase = {(i, j): c for i, j, c in p} + for i, j, coefficient in mapped_phase(rho, q): + phase[i, j] = (phase.get((i, j), 0) + coefficient) % 4 + return tuple(lib.act(rho, col) for col in sigma), lib.frozen(phase) + + +def operated(op, row): + out = {} + for (column, old), value in row.items(): + key = (column, multiply(op, old)) + out[key] = out.get(key, F(0)) + value + return {key: value for key, value in out.items() if value} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + sources = {} + pins = {} + for name, (relative, expected) in lib.PINS.items(): + path = LANES / relative + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == expected, name + " exact source") + sources[name] = json.loads(raw) + pins[name] = {"path": str(path), "sha256": expected} + pins["phase_library"] = {"path": str(LIBRARY), "sha256": sha256(LIBRARY.read_bytes()).hexdigest()} + records = {(row["stage"], row["port"]): row for row in sources["views"]["entries"]} + p = sources["row_code"]["selected_ports"] + r = sources["row_code"]["ordinary_ports"] + c, e = sparse(sources["row_code"]["code"]), sparse(sources["row_code"]["response"]) + h = [{j: c[a].get(b, F(0)) for j, b in enumerate(r) if c[a].get(b, F(0))} for a in p] + d = [{j: e[a].get(b, F(0)) for j, b in enumerate(p) if e[a].get(b, F(0))} for a in r] + q = [records[0, a]["q"] for a in range(112)] + g = {(s, a): tuple(records[s, a]["route_columns"]) for s in range(3) for a in range(112)} + forward = sparse(sources["clean_forward"]["content_map"]) + backward = sparse(sources["clean_backward"]["content_maps"]["selected_swap_conjugate"]) + f9 = phases([(1 << i, 1) for i in range(9)]) + f25 = phases([(1 << i, 1) for i in range(25)]) + unit_rows = [{(i, lib.ID): F(1)} for i in range(224)] + entry, exit_view, exterior = {}, {}, {} + route_checks = 0 + for s in (1, 2): + exterior[s] = phases([(1 << i, 1) for i in range(9, 9 + 8 * s)]) + fprev = phases([(1 << i, 1) for i in range(9 + 8 * (s - 1))]) + fnext = phases([(1 << i, 1) for i in range(9 + 8 * s)]) + for a in range(112): + alignment = records[s, a]["literal_stage_alignment"] + need(alignment["entry_X"] == alignment["entry_Y"] and + alignment["exit_X"] == alignment["exit_Y"], "Literal paired views") + entry[s, a] = multiply(phases([(lib.act(g[s, a], alignment["entry_X"]), 2)]), route(g[s, a])) + exit_view[s, a] = multiply(phases([(alignment["exit_X"], 2)]), route(g[s, a])) + need(multiply(entry[s, a], fprev) == + multiply(multiply(exterior[s], phases([(q[a], 1)])), route(g[s, a])), + "Natural X and selected Y entry") + need(multiply(multiply(entry[s, a], fprev), phases([(q[a], -1)])) == + multiply(exterior[s], route(g[s, a])), "Natural ordinary Y entry") + need(multiply(exit_view[s, a], fnext) == multiply(fnext, route(g[s, a])), + "Natural FULL exit") + need(multiply(multiply(exit_view[s, a], fnext), phases([(q[a], -1)])) == + multiply(multiply(fnext, phases([(q[a], -1)])), route(g[s, a])), + "Natural hole exit") + route_checks += 4 + + def input_inverse(rows, selected_type): + return [operated(phases([(q[a % 112], -1)]), row) + if a < 112 or selected_type == "Q" and a - 112 in p else row + for a, row in enumerate(rows)] + + def output_frame(rows): + return [operated(multiply(f9, phases([(q[a % 112], -1)])), row) + if a >= 112 and a - 112 in r else operated(f9, row) + for a, row in enumerate(rows)] + + def hs(s, rows): + before = [operated(route(g[s, a]), row) for a, row in zip(r, rows)] + return [operated(route(g[s, a]), row) for a, row in zip(p, linear(h, before))] + + def ds(s, rows): + before = [operated(route(g[s, a]), row) for a, row in zip(p, rows)] + return [operated(route(g[s, a]), row) for a, row in zip(r, linear(d, before))] + + def full_view(s, a): + return lib.ID if s == 0 else exit_view[s, a] + + def hs_full(s, rows): + before = [operated(full_view(s, a), row) for a, row in zip(r, rows)] + return [operated(full_view(s, a), row) for a, row in zip(p, linear(h, before))] + + def ds_full(s, rows): + before = [operated(full_view(s, a), row) for a, row in zip(p, rows)] + return [operated(full_view(s, a), row) for a, row in zip(r, linear(d, before))] + + for s in (1, 2): + for a in range(112): + need(multiply(exit_view[s, a], f25) == multiply(f25, route(g[s, a])), + "Actual F25 affine view for a terminal shear") + need(multiply(exit_view[s, a], exit_view[s, a]) == lib.ID, "FULL view involution") + need(multiply(exit_view[s, a], phases([(q[a], 1)])) == + lib.multiply(exit_view[s, a], phases([(q[a], 1)])), + "Independent dense and sparse phase substitutions agree") + variants = {} + for selected_type in ("I", "Q"): + initial = input_inverse(unit_rows, selected_type) + a0, u0 = [initial[a] for a in p], [initial[a] for a in r] + z0, v0 = [initial[112 + a] for a in p], [initial[112 + a] for a in r] + alpha = zipped(a0, hs(0, u0)) + k = zipped(zipped(v0, u0), ds(0, alpha)) + w = zipped(zipped(ds(1, alpha), ds(0, alpha), cb=-1), v0, cb=-1) + beta = zipped(zipped(alpha, hs(1, k)), hs(2, w)) + final_r = zipped(zipped(u0, ds(1, alpha)), ds(2, beta)) + rows = output_frame(linear(forward, initial)) + print("formed stage 0, initial " + selected_type, flush=True) + for s, matrix in ((1, backward), (2, forward)): + exterior_inverse = phases([(1 << i, -1) for i in range(9, 9 + 8 * s)]) + rows = [operated(multiply(exterior_inverse, entry[s, a % 112]), row) + for a, row in enumerate(rows)] + rows = output_frame(linear(matrix, input_inverse(rows, "Q"))) + rows = [operated(multiply(exit_view[s, a % 112], exterior[s]), row) + for a, row in enumerate(rows)] + print("formed stage " + str(s) + ", initial " + selected_type, flush=True) + expected = [None] * 224 + for ports, values, offset, sign, hole in ( + (p, z0, 0, -1, False), (r, w, 0, 1, False), + (p, beta, 112, 1, False), (r, final_r, 112, 1, True)): + for a, row in zip(ports, values): + op = multiply(f25, phases([(q[a], -1)])) if hole else f25 + expected[offset + a] = operated(op, add((sign, row))) + need(rows == expected, "Complete actual routed endpoint, initial " + selected_type) + recovered_k = zipped(zipped(final_r, ds(2, beta), cb=-1), w, cb=-1) + recovered_alpha = zipped(zipped(beta, hs(1, recovered_k), cb=-1), hs(2, w), cb=-1) + recovered_u = zipped(zipped(final_r, ds(1, recovered_alpha), cb=-1), ds(2, beta), cb=-1) + recovered_a = zipped(recovered_alpha, hs(0, recovered_u), cb=-1) + recovered_v = zipped(zipped(ds(1, recovered_alpha), ds(0, recovered_alpha), cb=-1), w, cb=-1) + need((recovered_alpha, recovered_u, recovered_a, recovered_v) == (alpha, u0, a0, v0), + "Exact dyadic content inverse, initial " + selected_type) + terminal_checked = False + if selected_type == "I": + stored_w = [rows[a] for a in r] + stored_beta = [rows[112 + a] for a in p] + exposed_r = [operated(phases([(q[a], 1)]), rows[112 + a]) for a in r] + t = zipped(exposed_r, ds_full(2, stored_beta), cb=-1) + actual_alpha = zipped(zipped(zipped(stored_beta, hs_full(1, t), cb=-1), + hs_full(1, stored_w)), hs_full(2, stored_w), cb=-1) + actual_v = zipped(zipped(ds_full(1, actual_alpha), ds_full(0, actual_alpha), cb=-1), + stored_w, cb=-1) + actual_u = zipped(t, ds_full(1, actual_alpha), cb=-1) + actual_a = zipped(actual_alpha, hs_full(0, actual_u), cb=-1) + for ports, values in ((p, actual_a), (r, actual_u)): + for a, row in zip(ports, values): + need(operated(phases([(q[a], 1)]), row) == operated(f25, unit_rows[a]), + "208-line terminal restores original physical data under F25") + for a, row in zip(r, actual_v): + need(row == operated(f25, unit_rows[112 + a]), + "208-line terminal restores arbitrary ordinary borrowed input under F25") + for a in p: + need(add((-1, rows[a])) == operated(f25, unit_rows[112 + a]), + "208-line terminal restores arbitrary selected borrowed input under F25") + terminal_checked = True + print("checked 208-line terminal", flush=True) + variants[selected_type] = { + "checked_arbitrary_columns": 224, + "checked_physical_output_rows": 224, + "complete_endpoint_operator_terms": sum(map(len, rows)), + "content_inverse": "PASS", + "208_line_terminal_checked": terminal_checked, + "initial_selected_original_Y": "z" if selected_type == "I" else "Q_P z", + } + shear_price = sum(2 * (3 + abs(c.numerator).bit_length() - 1 + + abs(c.numerator).bit_count() + c.denominator.bit_length() - 1) + for row in h for c in row.values()) + need(shear_price == 2048, "Direct H and transposed D scalar price") + need(sum(map(len, h)) == 216, "Actual H coefficient count") + receipt = { + "status": "PASS_ACTUAL_D25_NATURAL_CLEAN_TRIPLE", + "source_pins": pins, + "literal_route_phase_identities": route_checks, + "variants": variants, + "local_profile_initial_I": {"H1": 4176, "H2": 192, "H3": 144, "H8": 32, "H9": 16}, + "local_native_mass_initial_I": 5392, + "local_scalar_initial_I": 25800, + "new_owned_fields": 0, + "remaining_reader": "H_1 r, with physical ordinary Y equal to F25 q_R r", + "remaining_ordinary_scatter": "Q_R D_1 alpha + Q_R D_2 beta", + "final_physical_target": "F25 X0 and F25 Y0 under the inherited common-FULL contract, with any stated bank permutation", + "terminal_operator_word": { + "positive_line_operations": 208, + "extra_fields": 0, + "direct_scalar_upper_bound": 8 * shear_price + 2 * 112, + "routed_shear_affine_map_calls": 6 * 2 * 112, + "native_line_side_maps_included": False, + "final_bank_permutation_included": False, + "serialized_native_recipes_supplied": False, + }, + "complete_native_terminal_claimed": False, + "global_helper_host_replayed": False, + "scope": "Exact physical composition of the pinned local content contracts and literal D25 views. The terminal, global helper host, recursive invoice and precision proof remain open.", + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + print(json.dumps(variants, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/run-terminal-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/run-terminal-normal/CHECKS.json new file mode 100644 index 0000000000..9cbe28a54c --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/run-terminal-normal/CHECKS.json @@ -0,0 +1,69 @@ +{ + "complete_native_terminal_claimed": false, + "final_physical_target": "F25 X0 and F25 Y0 under the inherited common-FULL contract, with any stated bank permutation", + "global_helper_host_replayed": false, + "literal_route_phase_identities": 896, + "local_native_mass_initial_I": 5392, + "local_profile_initial_I": { + "H1": 4176, + "H2": 192, + "H3": 144, + "H8": 32, + "H9": 16 + }, + "local_scalar_initial_I": 25800, + "new_owned_fields": 0, + "remaining_ordinary_scatter": "Q_R D_1 alpha + Q_R D_2 beta", + "remaining_reader": "H_1 r, with physical ordinary Y equal to F25 q_R r", + "scope": "Exact physical composition of the pinned local content contracts and literal D25 views. The terminal, global helper host, recursive invoice and precision proof remain open.", + "source_pins": { + "clean_backward": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz", + "sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c" + }, + "clean_forward": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz", + "sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083" + }, + "phase_library": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/coupled-data-split-20261020/check_typed_split.py", + "sha256": "70ca9ce2dff5256644f35ef65344c7e0dd9f78e3fb48c18436e9e5c20b4f9109" + }, + "row_code": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz", + "sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + } + }, + "status": "PASS_ACTUAL_D25_NATURAL_CLEAN_TRIPLE", + "terminal_operator_word": { + "direct_scalar_upper_bound": 16608, + "extra_fields": 0, + "final_bank_permutation_included": false, + "native_line_side_maps_included": false, + "positive_line_operations": 208, + "routed_shear_affine_map_calls": 1344, + "serialized_native_recipes_supplied": false + }, + "variants": { + "I": { + "208_line_terminal_checked": true, + "checked_arbitrary_columns": 224, + "checked_physical_output_rows": 224, + "complete_endpoint_operator_terms": 176144, + "content_inverse": "PASS", + "initial_selected_original_Y": "z" + }, + "Q": { + "208_line_terminal_checked": false, + "checked_arbitrary_columns": 224, + "checked_physical_output_rows": 224, + "complete_endpoint_operator_terms": 176144, + "content_inverse": "PASS", + "initial_selected_original_Y": "Q_P z" + } + } +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/run-terminal-optimized/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/run-terminal-optimized/CHECKS.json new file mode 100644 index 0000000000..9cbe28a54c --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/run-terminal-optimized/CHECKS.json @@ -0,0 +1,69 @@ +{ + "complete_native_terminal_claimed": false, + "final_physical_target": "F25 X0 and F25 Y0 under the inherited common-FULL contract, with any stated bank permutation", + "global_helper_host_replayed": false, + "literal_route_phase_identities": 896, + "local_native_mass_initial_I": 5392, + "local_profile_initial_I": { + "H1": 4176, + "H2": 192, + "H3": 144, + "H8": 32, + "H9": 16 + }, + "local_scalar_initial_I": 25800, + "new_owned_fields": 0, + "remaining_ordinary_scatter": "Q_R D_1 alpha + Q_R D_2 beta", + "remaining_reader": "H_1 r, with physical ordinary Y equal to F25 q_R r", + "scope": "Exact physical composition of the pinned local content contracts and literal D25 views. 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"counts": { + "ADD": 832, + "CLEAR": 105, + "TRANSLATE": 104, + "half_adds": 832, + "scalar_primitives": 8530, + "translation_maps": 104 + }, + "maximum_intermediate_row_one_norm": "53" + }, + "T_plus": { + "counts": { + "ADD": 832, + "CLEAR": 105, + "TRANSLATE": 104, + "half_adds": 832, + "scalar_primitives": 8530, + "translation_maps": 104 + }, + "maximum_intermediate_row_one_norm": "53" + }, + "exchange_few_maps_minus": { + "counts": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2256, + "real_odd_division_scans": 16, + "scalar_primitives": 183972, + "translation_maps": 2256 + }, + "maximum_intermediate_row_one_norm_upper_bound": "472511/715" + }, + "exchange_few_maps_plus": { + "counts": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2256, + "real_odd_division_scans": 16, + "scalar_primitives": 183972, + "translation_maps": 2256 + }, + "maximum_intermediate_row_one_norm_upper_bound": "472511/715" + }, + "exchange_few_scalars_minus": { + "counts": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 9152, + "real_odd_division_scans": 16, + "scalar_primitives": 131588, + "translation_maps": 9152 + }, + "maximum_intermediate_row_one_norm_upper_bound": "472511/715" + }, + "exchange_few_scalars_plus": { + "counts": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 9152, + "real_odd_division_scans": 16, + "scalar_primitives": 131588, + "translation_maps": 9152 + }, + "maximum_intermediate_row_one_norm_upper_bound": "472511/715" + }, + "few_maps_minus": { + "counts": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2048, + "double": 13168, + "halve": 13120, + "real_odd_division_scans": 16, + "scalar_primitives": 166912, + "translation_maps": 2048, + "unit_adds": 14288 + }, + "maximum_intermediate_row_one_norm": "9073/715" + }, + "few_maps_plus": { + "counts": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2048, + "double": 13168, + "halve": 13120, + "real_odd_division_scans": 16, + "scalar_primitives": 166912, + "translation_maps": 2048, + "unit_adds": 14288 + }, + "maximum_intermediate_row_one_norm": "9073/715" + }, + "few_scalars_minus": { + "counts": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 8944, + "double": 80, + "halve": 16, + "real_odd_division_scans": 16, + "scalar_primitives": 114528, + "translation_maps": 8944, + "unit_adds": 14288 + }, + "maximum_intermediate_row_one_norm": "9073/715" + }, + "few_scalars_plus": { + "counts": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 8944, + "double": 80, + "halve": 16, + "real_odd_division_scans": 16, + "scalar_primitives": 114528, + "translation_maps": 8944, + "unit_adds": 14288 + }, + "maximum_intermediate_row_one_norm": "9073/715" + } + }, + "checker_sha256": "18cae3387c3a83c716ce2a43e47ec082ce72904e1a2516944278ab032c5de2a8", + "completed_phase_views_checked": 64, + "completed_view_maps_per_call": 32, + "controls": { + "omit_binary_halves": true, + "omit_odd_division": true, + "omit_translations": true + }, + "exchange_inverse_orders_checked": 2, + "exchange_power": 4, + "exchange_proof": "Exact checked shear bodies compose in the Laurent ring with T T^-1 = T^-1 T = I from the pinned all-width kernel proof.", + "inverse_kernel_unit_adds": 14288, + "inverse_real_odd_division_scans": 16, + "maximum_odd_denominator_height_increase_per_shear_or_exchange": 1, + "native_wrapper_maps": 0, + "odd_divisor": 2145, + "owned_zero_outputs": true, + "payload_compressed_sha256": "7566388bfb2167b21a5632cd12f4f71004df9c95d5d823f2f0604a6d0847d0e5", + "payload_raw_sha256": "eb303ec22bf77e438c722dd3cfe9a41c5cfc05d38cb31560f2108868dad087f0", + "probe_receipt_sha256": "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024", + "rank_one_children": 0, + "scope": "Local centre services on two existing FULL selected banks and one owned field. The exact odd-grid backend and its bit cost remain supplier obligations. This does not invert B Q_U D or complete a decoder.", + "shear_inverse_orders_checked": 6, + "source_minor_receipt_sha256": "8839f7aa1b8bb273e747b9a2ed21de2fd5f8e185ad92cae7a9d0cfe9f85f9745", + "source_pins": { + "interface": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/INTERFACE.json", + "sha256": "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746" + }, + "line_contract": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/paired-package-review/upstream-followthrough-20261015/current-query-encoder/UNIFORM-SIGNED.json", + "sha256": "9f3939f2eb2d60e187508331b7ab99d6748f73142b5b90bb9ad0c6a4736b3f10" + }, + "phases": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + "view_proof": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.json", + "sha256": "33944a0fe4587aa1ae939dd9861ad7d4c2b7c523dcf05f88fc404e4eeff8c7e8" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", + "sha256": "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f" + } + }, + "status": "PASS_ONE_OWNED_TRANSLATION_SERVICE" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/TRANSLATION-SERVICE.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/TRANSLATION-SERVICE.md new file mode 100644 index 0000000000..30b18f8b47 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/TRANSLATION-SERVICE.md @@ -0,0 +1,262 @@ +# Centre translation services with one owned field + +The actual translation operator `T=B Q_U^2 D` and its inverse give +centre-to-centre additive services with no native children. Each service +uses two existing eight-field FULL centre banks and one owned field C0. +The source bank is unchanged. C0 can have arbitrary input and is zero +at the output. All other data and borrowed fields are unchanged. + +The inverse service needs 16 real division-by-2145 scans. Two literal +schedules give different scalar and translation costs. The exact odd +grid and its bit cost must be supplied when this word is placed in a +supplier. This packet does not give an inverse of `B Q_U D`. + +## Pinned operator + +The frozen `SCHUR-PROBE.json` has SHA-256 +`ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024`. +It proves, for the actual selected set and graph, + +```text +A = [0,7,20,27,36,46,57,111], +U = {0,...,111} minus A, +B = R_A^T R_U/4, D = B^T, +T = B Q_U^2 D, +V = T^-1 = sum_delta K_delta tau_delta. +``` + +The inverse kernel has 4,544 nonzero scalar coefficients and 256 +translation shifts. Every shift has odd weight. Its common denominator +is `8580=4*2145`. For each source component j there are exactly 256 +source/shift groups. The integers + +```text +w_(delta,i,j) = 8580 K_(delta,i,j) +``` + +are stored exactly through the pinned rational kernel. They have a +total of 14,288 nonzero binary digits, counted with multiplicity over +all coefficients. Their largest absolute value is 1,533. + +At every width lambda, tau_delta applies the same nine-bit translation +delta in every tensor copy. The remaining 64 coordinates in each copy +are unchanged. The frozen XOR-character proof establishes this same +kernel for every positive width. No tensor power of an eight-by-eight +inverse matrix is substituted for the kernel. + +## One-field inverse construction + +Let x be the source centre bank and y the target centre bank. For each +source component j, in order: + +1. Copy x_j to C0. Divide C0 by 2145. Halve C0 twice. It now holds + `x_j/8580`. +2. Apply the required translations to C0. For each kernel numerator, + add its signed binary digits to the corresponding target y_i. + A binary digit uses a signed unit ADD from the current scaled C0. +3. Clear C0 after the last contribution from source component j. + +This gives `y <- y+Vx`. Change the sign of each target ADD to obtain +`y <- y-Vx`. The eight source fields stay available throughout the +word, so C0 can process them in series. Only eight owned COPYs and +eight owned CLEARs are needed. The eight complex odd divisions are +16 real scans. No ninth field or additional centre bank is used. + +This construction applies to any finite rational translation kernel +with a common denominator `2^a d`, where d is odd. One owned field can +hold one divided source component across all shifts and all target +broadcasts. The finite kernel controls the count; it need not be a +small count. + +### Schedule with fewer translations + +For each j, visit its 256 shifts in increasing order. If the old shift +is delta_old and the next shift is delta_new, apply the translation +`delta_old XOR delta_new`. Thus there is one map per group. Process +the numerator bits from low to high and double C0 between bit levels. +Restore the starting power of two after the group, except at the last +group, where CLEAR follows. The translation itself need not be undone. + +There are 2,048 translation maps. The sum of the largest bit indices +over the 2,048 groups is 13,168. The sum for the final group of each +source component is 64. Thus the complete scalar price is + +```text +8*14288 + 2*(13168 + 13168-64) + 32 + 32 = 166912. +``` + +The two final terms charge the 16 initial halves and the eight COPYs +plus eight CLEARs. Every source coefficient is included. + +### Schedule with fewer scalar operations + +For each j, visit all needed shifts at one binary level, then advance +to the next level. Keep the current scale and shift across transitions. +There are 80 doubles in total and no power restoration before CLEAR. +There are 8,944 nonempty bit/shift groups. Each transition has a nonzero +XOR shift, so all 8,944 maps are charged. The scalar price is + +```text +8*14288 + 2*80 + 32 + 32 = 114528. +``` + +The source bank is unchanged in both schedules. Neither schedule needs +all eight owned core fields at once. + +## Forward translation service + +The forward operator has a shorter direct word. Clear C0. For each +ordinary port p: + +```text +C0 += sum_j D_(p,j) x_j +C0 <- tau_(q_p) C0 +y_i += B_(i,p) C0 for each nonzero B_(i,p) +CLEAR C0 +``` + +Every ordinary graph column has four signed-half entries. This word +has 832 half ADDs, 105 CLEARs, and 104 translations. Its scalar price +is `832*10+105*2=8530`. The exact replay agrees with every coefficient +of the frozen forward kernel. Negating only the target ADDs gives +the inverse shear `y <- y-Tx`. + +## Completed physical views + +The service acts on two existing selected centre banks with FULL frame +F at the selected completed cut. The payload uses abstract rows 0 to 7 +for x, 8 to 15 for y, and row 16 for C0. Rows 17 to 24 are arbitrary +borrowed test fields. The bank owners must be distinct. Each component +corresponds to its port in A. + +For a selected stage, enter the actual serialized completed-X view on +both banks. Its forward order is route rho, then translation delta. +Leave with the inverse translation, then inverse route. Reverse the +owner order on exit. This gives 16 entering and 16 leaving view maps. + +The checker verifies all 64 selected port-and-stage views. The exact +FULL phase polynomial is + +```text +weight(rho^T f) + 2 delta.f - weight(f) modulo 4. +``` + +Every linear and quadratic coefficient vanishes. The zero constant +also vanishes. The stored inverse order and the orthogonal route are +checked. Omitting the translation fails in every case. Thus both banks +join the same FULL chart with the required phase. The word acts on +their contents in that chart. The source bank returns to its physical +input after the inverse view. The target returns to its prescribed +FULL frame with the stated content update. + +The payload stores each literal body and all eight pairs of stage +wrappers. Its complete word is the concatenation `enter + body + leave`. +There are no omitted arithmetic instructions in that concatenation. +Translations within a body act only on C0. All other live owners are +outside the target set of every instruction. + +No native child is called, so this service adds no recursive helper +endpoint obligation. It still requires one available owned field with +the stated discardable-input contract at the chosen cut. The packet +does not supply a new global ownership schedule. + +## Coded centre exchange + +Three complete additive shears give + +```text +x += T y +y -= V x +x += T y + +(x,y) -> (T y, -V x), V=T^-1. +``` + +For example, after the middle shear, +`y = y_old - V(x_old+T y_old) = -V x_old`. +The last shear therefore leaves `x=T y_old`. +The inverse changes all three shear signs and sends +`(x,y)` to `(-T y,V x)`. The square is `-I`, and the fourth power is I. + +The checker verifies the exact operator products in the Laurent ring +generated by T and V, using both inverse orders from the pinned kernel +proof. The emitted exchange bodies contain the actual three checked +shear words with the source and target bank indices exchanged where +required. One pair of physical view wrappers surrounds the whole word. + +These outputs have their FULL physical frames. Their contents carry +the explicit codes T and V. This is a coded exchange, with its inverse +priced below. It is not a raw exchange or a completed decoder. + +## Complete local invoice + +The retained prices are eight real scalar primitives for a complex +signed unit ADD, ten for a signed-half ADD, and two for a COPY, CLEAR, +or one complex doubling or halving. Odd division is listed separately. + +| Word, either sign | Real scalar primitives | Body translations | Real odd scans | Completed views | Native children | +| --- | ---: | ---: | ---: | ---: | ---: | +| Add T x | 8530 | 104 | 0 | 32 | 0 | +| Add V x, fewer maps | 166912 | 2048 | 16 | 32 | 0 | +| Add V x, fewer scalars | 114528 | 8944 | 16 | 32 | 0 | +| Coded exchange, fewer maps | 183972 | 2256 | 16 | 32 | 0 | +| Coded exchange, fewer scalars | 131588 | 9152 | 16 | 32 | 0 | + +The body translations and completed views are separate charged map +applications. They are not included in the scalar column. No native +wrapper maps are needed. The fixed-odd charge is exactly 16 real +division-by-2145 scans for an inverse shear or an exchange. It is not +16 dyadic primitives. The accepted odd-grid backend must supply the +bit cost of these scans. + +DIVIDE_ODD means exact rational division on an explicit grid with odd +factor 2145. It does not assert that an arbitrary integer numerator is +divisible by 2145. The coefficient ring is `Z[i,1/2,1/2145]`. Starting +on an input grid of odd height h, one shear or one exchange increases +the required prefix height by at most one. The inverse word divides +copies of eight unchanged source fields; it does not divide a value +which a preceding divided copy has modified. The first exchange shear +uses only dyadic arithmetic, and the last also uses only dyadic +arithmetic. No height bound for an arbitrary sequence of calls is +claimed here. + +The exact maximum intermediate formal row one-norm is 53 for the +forward shear and 9073/715 for either inverse-kernel schedule. The +exchange has the proved upper bound 472511/715. For that bound, the +first source update has norm at most 53; the middle target update has +norm at most `1+53*(8358/715)`; its completed value has norm 8358/715; +the last update has norm at most `53+52*(8358/715)`. +This is a local coefficient bound, not a complete supplier precision +bound. + +## Checks and scope + +Run with one process: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/check_translation_service.py +``` + +The first line is `PASS_ONE_OWNED_TRANSLATION_SERVICE`. + +The exact sparse replay checks every coefficient for all 16 arbitrary +live inputs, one arbitrary owned input, and eight arbitrary borrowed +inputs. It checks both signs and both inverse orders for all three +shear bodies. It checks every literal invoice and all completed view +phases. Removing the odd division, translations, or initial halves +fails the claimed inverse-kernel output. Exchange correctness is a +separate exact composition proof from the checked full shear maps. + +The frozen spectral packet, the minor service receipt, and all five +original source byte hashes are checked before use. The source hashes +and frozen spectral receipt are checked again after emission. The +payload has deterministic compressed and uncompressed hashes. +Normal Python and Python with `-O` produced byte-identical receipts +and compressed program payloads. + +This local construction does not invert `B Q_U D`, supply a controller, +admit a complete supplier, or improve kappa. No owner-fill or interior +forward scan was run. Independent review of the new word is pending. +OpenAI Codex assisted the construction and exact checks. No PR, push, +or commit was made. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/check_translation_service.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/check_translation_service.py new file mode 100644 index 0000000000..781178cf42 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-probe/check_translation_service.py @@ -0,0 +1,334 @@ +"""Emit and check centre translation shears with one owned field.""" + +from collections import Counter, defaultdict +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json +import shutil + +HERE = Path(__file__).resolve().parent +PROBE_PIN = "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024" +MINOR_PIN = "8839f7aa1b8bb273e747b9a2ed21de2fd5f8e185ad92cae7a9d0cfe9f85f9745" +A = [0, 7, 20, 27, 36, 46, 57, 111] +U = [p for p in range(112) if p not in A] +C0 = 16 +BORROWED = list(range(17, 25)) +UNIT = [1 << i for i in range(73)] + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def pinned(path, pin): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == pin, "Source pin: " + str(path)) + return json.loads(gzip.decompress(raw) if path.suffix == ".gz" else raw) + + +def initial(): + return [{(i, 0): F(1)} for i in range(25)] + + +def add(row, source, coefficient): + norm_change = F(0) + for key, value in source.items(): + old = row.get(key, F(0)) + new = old + coefficient * value + norm_change += abs(new) - abs(old) + if new: + row[key] = new + else: + row.pop(key, None) + return norm_change + + +def run(state, word): + norms = [sum(map(abs, row.values())) for row in state] + maximum = max(norms) + counts = Counter() + for gate in word: + kind, target = gate[:2] + need(target == C0 or 8 <= target < 16, "Only target centres and C0 can change") + if kind == "ADD": + source, coefficient = gate[2], F(gate[3]) + need(source != target and abs(coefficient) in (1, F(1, 2)), "Unit or half ADD") + norms[target] += add(state[target], state[source], coefficient) + counts["unit_adds" if abs(coefficient) == 1 else "half_adds"] += 1 + counts["scalar_primitives"] += 8 if abs(coefficient) == 1 else 10 + elif kind == "COPY": + need(target == C0 and gate[2] < 8, "Owned source copy") + state[target] = dict(state[gate[2]]) + norms[target] = norms[gate[2]] + counts["scalar_primitives"] += 2 + elif kind == "CLEAR": + need(target == C0, "Only the owned field can be cleared") + state[target], norms[target] = {}, F(0) + counts["scalar_primitives"] += 2 + elif kind == "SCALE2": + need(target == C0 and gate[2] in (-1, 1), "One binary scale on C0") + coefficient = F(2) ** gate[2] + state[target] = {key: coefficient * value for key, value in state[target].items()} + norms[target] *= coefficient + counts["scalar_primitives"] += 2 + counts["double" if gate[2] == 1 else "halve"] += 1 + elif kind == "DIVIDE_ODD": + need(target == C0 and gate[2] == 2145, "One explicit fixed odd divisor") + state[target] = {key: value / 2145 for key, value in state[target].items()} + norms[target] /= 2145 + counts["real_odd_division_scans"] += 2 + else: + need(kind == "TRANSLATE" and target == C0 and 0 < gate[2] < 512, "Nine-coordinate translation on C0") + state[target] = {(origin, delta ^ gate[2]): value for (origin, delta), value in state[target].items()} + counts["translation_maps"] += 1 + counts[kind] += 1 + maximum = max(maximum, norms[target]) + need(not state[C0], "Owned output is zero") + need(all(state[p] == {(p, 0): F(1)} for p in list(range(8)) + BORROWED), "Source and borrowed fields are unchanged") + return dict(counts), str(maximum) + + +def gate_add(target, source, coefficient): + return ["ADD", target, source, str(coefficient)] + + +def forward_word(B, q): + word = [["CLEAR", C0]] + for p in U: + for j, coefficient in B[p].items(): + word.append(gate_add(C0, j, coefficient)) + word.append(["TRANSLATE", C0, q[p]]) + for i, coefficient in B[p].items(): + word.append(gate_add(8 + i, C0, coefficient)) + word.append(["CLEAR", C0]) + return word + + +def inverse_word(groups, schedule): + word = [] + for source in range(8): + word += [["COPY", C0, source], ["DIVIDE_ODD", C0, 2145], + ["SCALE2", C0, -1], ["SCALE2", C0, -1]] + current_shift = 0 + shifts = sorted(delta for j, delta in groups if j == source) + if schedule == "few_maps": + for position, delta in enumerate(shifts): + word.append(["TRANSLATE", C0, current_shift ^ delta]) + current_shift = delta + coefficients = groups[source, delta] + last_bit = max(abs(c).bit_length() - 1 for c in coefficients.values()) + for bit in range(last_bit + 1): + for target, coefficient in sorted(coefficients.items()): + if abs(coefficient) >> bit & 1: + word.append(gate_add(8 + target, C0, 1 if coefficient > 0 else -1)) + if bit < last_bit: + word.append(["SCALE2", C0, 1]) + if position + 1 < len(shifts): + word += [["SCALE2", C0, -1] for _ in range(last_bit)] + else: + need(schedule == "few_scalars", "Known schedule") + last_bit = max(abs(c).bit_length() - 1 for delta in shifts for c in groups[source, delta].values()) + for bit in range(last_bit + 1): + for delta in shifts: + coefficients = groups[source, delta] + if not any(abs(c) >> bit & 1 for c in coefficients.values()): + continue + offset = current_shift ^ delta + if offset: + word.append(["TRANSLATE", C0, offset]) + current_shift = delta + for target, coefficient in sorted(coefficients.items()): + if abs(coefficient) >> bit & 1: + word.append(gate_add(8 + target, C0, 1 if coefficient > 0 else -1)) + if bit < last_bit: + word.append(["SCALE2", C0, 1]) + word.append(["CLEAR", C0]) + return word + + +def negative(word): + return [[*gate[:3], str(-F(gate[3]))] if gate[0] == "ADD" and 8 <= gate[1] < 16 else list(gate) for gate in word] + + +def expected(entries, sign=1): + result = initial() + result[C0] = {} + for delta, target, source, coefficient in entries: + add(result[8 + target], {(source, delta): F(coefficient)}, F(sign)) + return result + + +def exchange(word_T, word_inverse): + def swap_banks(word): + result = [] + for gate in word: + gate = list(gate) + gate[1] = gate[1] ^ 8 if gate[1] < 16 else gate[1] + if gate[0] in ("ADD", "COPY"): + gate[2] = gate[2] ^ 8 if gate[2] < 16 else gate[2] + result.append(gate) + return result + return swap_banks(word_T) + negative(word_inverse) + swap_banks(word_T) + + +def invoice(word): + counts = Counter() + for gate in word: + kind = gate[0] + counts[kind] += 1 + if kind == "ADD": + counts["scalar_primitives"] += 8 if abs(F(gate[3])) == 1 else 10 + elif kind in ("COPY", "CLEAR", "SCALE2"): + counts["scalar_primitives"] += 2 + elif kind == "DIVIDE_ODD": + counts["real_odd_division_scans"] += 2 + else: + need(kind == "TRANSLATE", "Literal instruction") + counts["translation_maps"] += 1 + return dict(counts) + + +def act(columns, vector): + result = 0 + while vector: + bit = vector & -vector + result ^= columns[bit.bit_length() - 1] + vector ^= bit + return result + + +def transpose(columns): + return [sum(((v >> i) & 1) << j for j, v in enumerate(columns)) for i in range(len(columns))] + + +need(shutil.disk_usage(HERE).free >= 3 * 2**30, "At least 3 GiB free") +probe = pinned(HERE / "SCHUR-PROBE.json", PROBE_PIN) +minor = pinned(HERE.parent / "minor-collective-service/MINOR-COLLECTIVE-SERVICE.json", MINOR_PIN) +need(probe["source_pins"] == minor["source_pins"], "Same five source pins") +sources = {key: pinned(Path(pin["path"]), pin["sha256"]) for key, pin in probe["source_pins"].items()} +rows = [{int(p): F(c) for p, c in row.items()} for row in sources["interface"]["R"]] +q = [r["q"] for r in sources["phases"]["recipes"]] +B = {p: {j: sum(row.get(a, 0) * row.get(p, 0) for row in rows) / 4 for j, a in enumerate(A)} for p in U} +B = {p: {j: c for j, c in row.items() if c} for p, row in B.items()} +need(all(len(row) == 4 and all(abs(c) == F(1, 2) for c in row.values()) for row in B.values()), "Actual graph columns") +groups = defaultdict(dict) +for delta, target, source, coefficient in probe["kernels"]["inverse"]["entries"]: + integer = 8580 * F(coefficient) + need(integer.denominator == 1, "Exact integer kernel numerator") + groups[source, delta][target] = integer.numerator +need(len(groups) == 2048, "All source-shift groups") +positive = {"T": forward_word(B, q)} +positive.update({name: inverse_word(groups, name) for name in ("few_maps", "few_scalars")}) +words, results = {}, {} +identity = initial() +identity[C0] = {} +for name, word in positive.items(): + kernel = probe["kernels"]["translation" if name == "T" else "inverse"]["entries"] + for sign, suffix in ((1, "plus"), (-1, "minus")): + label = name + "_" + suffix + actual_word = word if sign == 1 else negative(word) + words[label] = actual_word + state = initial() + counts, maximum = run(state, actual_word) + need(state == expected(kernel, sign), "Exact kernel service: " + label) + need(all(counts[k] == value for k, value in invoice(actual_word).items()), "Independent instruction invoice") + results[label] = dict(counts=counts, maximum_intermediate_row_one_norm=maximum) + for first, second in ((word, negative(word)), (negative(word), word)): + state = initial() + run(state, first) + run(state, second) + need(state == identity, "Both shear inverse orders: " + name) +need(results["T_plus"]["counts"]["scalar_primitives"] == 8530, "Forward scalar invoice") +need(results["few_maps_plus"]["counts"]["scalar_primitives"] == 166912, "Few-map scalar invoice") +need(results["few_scalars_plus"]["counts"]["scalar_primitives"] == 114528, "Few-scalar invoice") +need(results["few_maps_plus"]["counts"]["translation_maps"] == 2048, "Few-map translation invoice") +need(results["few_scalars_plus"]["counts"]["translation_maps"] == 8944, "Few-scalar translation invoice") +for name in ("few_maps", "few_scalars"): + for sign, suffix in ((1, "plus"), (-1, "minus")): + label = "exchange_" + name + "_" + suffix + words[label] = exchange(positive["T"] if sign == 1 else negative(positive["T"]), + positive[name] if sign == 1 else negative(positive[name])) + results[label] = dict(counts=invoice(words[label]), maximum_intermediate_row_one_norm_upper_bound="472511/715") + +# Check the composition on formal operator symbols. The pinned kernel proof gives T V = V T = I. +def operator_product(a, b): + out = [[defaultdict(F) for _ in range(2)] for _ in range(2)] + for i in range(2): + for j in range(2): + for k in range(2): + for left, c in a[i][k].items(): + for right, d in b[k][j].items(): + out[i][j][left + right] += c * d + return [[{k: v for k, v in cell.items() if v} for cell in row] for row in out] + + +unit, zero = {0: F(1)}, {} +identity2 = [[unit, zero], [zero, unit]] +upper = [[unit, {1: F(1)}], [zero, unit]] +lower = [[unit, zero], [{-1: F(-1)}, unit]] +J = operator_product(upper, operator_product(lower, upper)) +need(J == [[zero, {1: F(1)}], [{-1: F(-1)}, zero]], "Exact coded exchange") +minus_J = [[{k: -v for k, v in cell.items()} for cell in row] for row in J] +need(operator_product(J, minus_J) == operator_product(minus_J, J) == identity2, "Both exchange inverse orders") +need(operator_product(operator_product(J, J), operator_product(J, J)) == identity2, "Fourth power") + +views = [v for v in sources["views"]["views"] if v["side"] == "X" and v["port"] in A] +need({(v["stage"], v["port"]) for v in views} == {(s, p) for s in range(1, 9) for p in A}, "All selected completed views") +for view in views: + rho, delta = view["route_columns"], view["translation_after_route"] + rt = transpose(rho) + need([act(rho, x) for x in rho] == UNIT and rho == rt, "Actual orthogonal involution") + need(act(rho, delta) == view["translation_before_route"], "Exact view order") + linear = [(v.bit_count() + 2 * ((delta >> i) & 1) - 1) % 4 for i, v in enumerate(rt)] + quadratic = [(-2 * (a & b).bit_count()) % 4 for i, a in enumerate(rt) for b in rt[i + 1:]] + need(not any(linear + quadratic), "FULL phase endpoint") + need(any((v.bit_count() - 1) % 4 for v in rt), "Translation is necessary") +wrappers = {} +for stage in range(1, 9): + enter = [["VIEW", row, stage, A[row % 8], False] for row in range(16)] + leave = [["VIEW", row, stage, A[row % 8], True] for row in reversed(range(16))] + wrappers[str(stage)] = dict(enter=enter, leave=leave) + +controls = {} +for label, changed in ( + ("omit_odd_division", [g for g in positive["few_scalars"] if g[0] != "DIVIDE_ODD"]), + ("omit_translations", [g for g in positive["few_maps"] if g[0] != "TRANSLATE"]), + ("omit_binary_halves", [g for g in positive["few_scalars"] if g[0] != "SCALE2" or g[2] != -1]), +): + state = initial() + run(state, changed) + need(state != expected(probe["kernels"]["inverse"]["entries"]), "Control must fail: " + label) + controls[label] = True + +payload = dict(schema="one-owned-centre-translation-service-v1", selected_ports=A, + rows=dict(source=list(range(8)), target=list(range(8, 16)), owned=C0, borrowed=BORROWED), + bodies=words, stage_wrappers=wrappers, completed_views=views, + assembly="For a stage and body, concatenate enter, body, and leave. No instruction is omitted.", + view_order="Forward: route, then translation. Inverse: undo translation, then inverse route.", + translation_rule="Repeat the nine-bit shift in every tensor copy; the other coordinates are unchanged.", + odd_division_contract="Exact rational division on the explicit 2145 odd grid, charged as two real scans.") +raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() +program_path = HERE / "TRANSLATION-SERVICE-PROGRAMS.json.gz" +program_path.write_bytes(gzip.compress(raw, mtime=0)) +for key, pin in probe["source_pins"].items(): + need(sha256(Path(pin["path"]).read_bytes()).hexdigest() == pin["sha256"], "Source unchanged: " + key) +need(sha256((HERE / "SCHUR-PROBE.json").read_bytes()).hexdigest() == PROBE_PIN, "Frozen probe unchanged") +receipt = dict(status="PASS_ONE_OWNED_TRANSLATION_SERVICE", cases=results, controls=controls, + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), probe_receipt_sha256=PROBE_PIN, + source_minor_receipt_sha256=MINOR_PIN, source_pins=probe["source_pins"], + payload_raw_sha256=sha256(raw).hexdigest(), payload_compressed_sha256=sha256(program_path.read_bytes()).hexdigest(), + arbitrary_live_columns=16, arbitrary_owned_input_columns=1, arbitrary_borrowed_columns=8, + owned_zero_outputs=True, completed_phase_views_checked=64, completed_view_maps_per_call=32, + rank_one_children=0, native_wrapper_maps=0, shear_inverse_orders_checked=6, + exchange_inverse_orders_checked=2, exchange_power=4, + inverse_kernel_unit_adds=14288, odd_divisor=2145, inverse_real_odd_division_scans=16, + maximum_odd_denominator_height_increase_per_shear_or_exchange=1, + exchange_proof="Exact checked shear bodies compose in the Laurent ring with T T^-1 = T^-1 T = I from the pinned all-width kernel proof.", + scope="Local centre services on two existing FULL selected banks and one owned field. The exact odd-grid backend and its bit cost remain supplier obligations. This does not invert B Q_U D or complete a decoder.") +(HERE / "TRANSLATION-SERVICE.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n", encoding="utf-8") +print(receipt["status"]) +print(json.dumps({name: dict(scalar=item["counts"]["scalar_primitives"], maps=item["counts"]["translation_maps"], + real_odd_scans=item["counts"].get("real_odd_division_scans", 0)) for name, item in results.items()}, sort_keys=True)) diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/SINGULAR-WITNESS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/SINGULAR-WITNESS.json new file mode 100644 index 0000000000..23c89d5e74 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/SINGULAR-WITNESS.json @@ -0,0 +1,322 @@ +{ + "actual_port_phase_counts": { + "0": 54, + "2": 50 + }, + "characters": [ + 1, + 2, + 3, + 6, + 6 + ], + "checker_sha256": "8ddb01debc65ae9d7c401a868f3c25cf9e86d3b0fceb79e817aff916649b0641", + "label_phase_checks": 512, + "leading_seven_by_seven_minor_determinant": "-73", + "null_vector": [ + 0, + 0, + 1, + 0, + -1, + 1, + 0, + 1 + ], + "ordinary_mode_squared_norm": "52", + "ordinary_mode_support": 49, + "ordinary_ports": [ + 1, + 2, + 3, + 4, + 5, + 6, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 21, + 22, + 23, + 24, + 25, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 37, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 47, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + 66, + 67, + 68, + 69, + 70, + 71, + 72, + 73, + 74, + 75, + 76, + 77, + 78, + 79, + 80, + 81, + 82, + 83, + 84, + 85, + 86, + 87, + 88, + 89, + 90, + 91, + 92, + 93, + 94, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 103, + 104, + 105, + 106, + 107, + 108, + 109, + 110 + ], + "padding": "Append zero characters. The same Schur matrix occurs at every width at least five.", + "phase": "2*(q0*q1+q0+q2) modulo 4", + "rank": 7, + "scope": "S=B Q_U D is singular at the stated mode. This rules out an inverse on arbitrary centres at widths at least five. It is not a minimum-width claim or a native lower bound.", + "selected_ports": [ + 0, + 7, + 20, + 27, + 36, + 46, + 57, + 111 + ], + "source_minor_receipt_sha256": "8839f7aa1b8bb273e747b9a2ed21de2fd5f8e185ad92cae7a9d0cfe9f85f9745", + "source_pins": { + "interface": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/INTERFACE.json", + "sha256": "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746" + }, + "line_contract": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/paired-package-review/upstream-followthrough-20261015/current-query-encoder/UNIFORM-SIGNED.json", + "sha256": "9f3939f2eb2d60e187508331b7ab99d6748f73142b5b90bb9ad0c6a4736b3f10" + }, + "phases": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + "view_proof": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.json", + "sha256": "33944a0fe4587aa1ae939dd9861ad7d4c2b7c523dcf05f88fc404e4eeff8c7e8" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", + "sha256": "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f" + } + }, + "source_probe_receipt_sha256": "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024", + "spectator_character_coordinates": [ + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 23, + 24, + 25, + 26, + 27, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 36, + 37, + 38, + 39, + 40, + 41, + 42, + 43, + 44, + 45, + 46, + 47, + 48, + 49, + 50, + 51, + 52, + 53, + 54, + 55, + 56, + 57, + 58, + 59, + 60, + 61, + 62, + 63, + 64, + 65, + 66, + 67, + 68, + 69, + 70, + 71, + 72 + ], + "status": "PASS_DIRECT_SOURCE_SCHUR_SINGULAR_WITNESS", + "twice_S": [ + [ + 1, + -1, + -4, + 7, + -4, + 0, + -5, + 0 + ], + [ + -1, + 5, + 0, + -5, + -4, + -4, + 3, + 0 + ], + [ + -4, + 0, + -3, + 4, + -1, + 3, + 0, + -1 + ], + [ + 7, + -5, + 4, + 1, + 0, + -4, + -5, + 0 + ], + [ + -4, + -4, + -1, + 0, + 1, + 3, + 0, + -1 + ], + [ + 0, + -4, + 3, + -4, + 3, + 1, + 0, + -1 + ], + [ + -5, + 3, + 0, + -5, + 0, + 0, + 1, + 0 + ], + [ + 0, + 0, + -1, + 0, + -1, + -1, + 0, + 1 + ] + ], + "width": 5 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/SINGULAR-WITNESS.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/SINGULAR-WITNESS.md new file mode 100644 index 0000000000..31676e4fd1 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/SINGULAR-WITNESS.md @@ -0,0 +1,105 @@ +# A singular actual centre Schur mode at width five + +The actual operator `S=B Q_U D` is singular at width five. The character +tuple is `(1,2,3,6,6)`, with each integer written in the first nine +coordinates of its tensor copy. All other character coordinates are +zero. Its eight-by-eight Schur matrix has rank seven and the null vector + +```text +v = (0,0,1,0,-1,1,0,1). +``` + +Appending zero characters preserves the matrix. Thus the full operator +has a nonzero kernel at every width at least five. This is a direct +source witness, rather than an inference from the failure of `I+alpha S`. + +## Actual source and phase + +Use the pinned source matrix R and phase labels from DATA-PHASES: + +```text +A = [0,7,20,27,36,46,57,111], +U = {0,...,111} minus A, +B = R_A^T R_U/4, D=B^T, BD=13I. +``` + +In a completed chart, the intrinsic line Q_p has eigenvalue +`i^(sum_j parity(q_p.chi_j))` at a tensor character tuple. This is the +same phase convention as the pinned minor service and Schur probe. +Those packets bind the actual line recipes and completed physical views. + +Write q_k for bit k of a label q. The five characters give + +```text +parity(q.1) + parity(q.2) + parity(q.3) + 2 parity(q.6) + = 2(q0*q1 + q0 + q2) modulo 4. +``` + +The checker verifies this identity for all 512 nine-bit labels. It also +follows by expanding each parity modulo four. The phase is real: + +```text +i^(sum_j parity(q.chi_j)) = (-1)^(q0*q1+q0+q2). +``` + +The source columns give 54 positive and 50 negative phases. No random +matrix or reconstructed root model is substituted for the actual graph. + +## Exact matrix and null vector + +The checker rebuilds the following matrix directly from all 104 source +columns and their exact Gaussian phases: + +```text + [ 1 -1 -4 7 -4 0 -5 0 ] + [-1 5 0 -5 -4 -4 3 0 ] + [-4 0 -3 4 -1 3 0 -1 ] +2 S = [ 7 -5 4 1 0 -4 -5 0 ] + [-4 -4 -1 0 1 3 0 -1 ] + [ 0 -4 3 -4 3 1 0 -1 ] + [-5 3 0 -5 0 0 1 0 ] + [ 0 0 -1 0 -1 -1 0 1 ]. +``` + +Direct multiplication gives `S v=0`. The leading seven-by-seven minor +of S has determinant `-73`. Therefore S has rank exactly seven. The +ordinary source mode is also nonzero: `||D v||^2=52`, and Dv has 49 +nonzero coordinates. The null vector does not come from discarding a +zero source mode. + +Tensor the displayed centre vector with the stated spatial character. +This gives a nonzero vector in the kernel of the full operator. A zero +character in an added copy contributes no line phase, which proves the +same failure at every width at least five. + +## Check and scope + +Run with one process: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/check_singular_witness.py +``` + +The first line is `PASS_DIRECT_SOURCE_SCHUR_SINGULAR_WITNESS`. + +The checker uses exact integer and rational arithmetic. It checks the +five retained source byte hashes, all 512 label phases, the direct +Gaussian sum, every null-vector coordinate, the exact minor determinant, +and the nonzero ordinary mode. No floating-point tolerance is used. +Normal Python and Python with `-O` produced byte-identical receipts. + +The receipt is independent of the exploratory search scripts. The +search first found the quadratic form `q0*q1+q0+q2`; the five-character +identity above is the certificate used here. + +This witness prevents an inverse of S on arbitrary centre inputs at +widths at least five. It does not rule out a larger joint invertible +unit, an additive shear, a restricted-input inverse, or a service that +retains the missing information elsewhere. The separate translation +operator `B Q_U^2 D` remains invertible as proved in its frozen packet. + +No minimum singular width is claimed. The bounded width-two and +width-three results belong to a separate supplement. No native lower +bound, complete controller, supplier admission, or kappa improvement is +claimed. No PR, push, or commit was made. Before any future PR description, +read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/check_singular_witness.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/check_singular_witness.py new file mode 100644 index 0000000000..9119a6fa48 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/centre-schur-singularity/check_singular_witness.py @@ -0,0 +1,116 @@ +"""Check a width-five Schur null vector directly from the source columns.""" + +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import json +import shutil + +HERE = Path(__file__).resolve().parent +PROBE_PIN = "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024" +MINOR_PIN = "8839f7aa1b8bb273e747b9a2ed21de2fd5f8e185ad92cae7a9d0cfe9f85f9745" +A = [0, 7, 20, 27, 36, 46, 57, 111] +U = [p for p in range(112) if p not in A] +CHARACTERS = [1, 2, 3, 6, 6] +VECTOR = [0, 0, 1, 0, -1, 1, 0, 1] +TWICE_S = [ + [1, -1, -4, 7, -4, 0, -5, 0], + [-1, 5, 0, -5, -4, -4, 3, 0], + [-4, 0, -3, 4, -1, 3, 0, -1], + [7, -5, 4, 1, 0, -4, -5, 0], + [-4, -4, -1, 0, 1, 3, 0, -1], + [0, -4, 3, -4, 3, 1, 0, -1], + [-5, 3, 0, -5, 0, 0, 1, 0], + [0, 0, -1, 0, -1, -1, 0, 1], +] + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def pinned(path, pin): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == pin, "Source pin: " + str(path)) + return json.loads(raw) + + +def determinant(matrix): + matrix = [[F(c) for c in row] for row in matrix] + value = F(1) + n = len(matrix) + for j in range(n): + pivot = next((i for i in range(j, n) if matrix[i][j]), None) + if pivot is None: + return F(0) + if pivot != j: + matrix[j], matrix[pivot] = matrix[pivot], matrix[j] + value = -value + divisor = matrix[j][j] + value *= divisor + for i in range(j + 1, n): + coefficient = matrix[i][j] / divisor + for k in range(j + 1, n): + matrix[i][k] -= coefficient * matrix[j][k] + return value + + +need(shutil.disk_usage(HERE).free >= 3 * 2**30, "At least 3 GiB free") +probe = pinned(HERE.parent / "centre-schur-probe/SCHUR-PROBE.json", PROBE_PIN) +minor = pinned(HERE.parent / "minor-collective-service/MINOR-COLLECTIVE-SERVICE.json", MINOR_PIN) +need(probe["source_pins"] == minor["source_pins"], "Retained source pins") +sources = {} +for key, pin in probe["source_pins"].items(): + raw = Path(pin["path"]).read_bytes() + need(sha256(raw).hexdigest() == pin["sha256"], "Current source: " + key) + if key in ("interface", "phases"): + sources[key] = json.loads(raw) +rows = [{int(p): int(c) for p, c in row.items()} for row in sources["interface"]["R"]] +q = [item["q"] for item in sources["phases"]["recipes"]] +columns = {} +for p in U: + numerator = [sum(row.get(a, 0) * row.get(p, 0) for row in rows) for a in A] + need(all(c % 2 == 0 for c in numerator), "Integral twice-normalized source column") + columns[p] = [c // 2 for c in numerator] +need(all(sum(v[i] * v[j] for v in columns.values()) == 52 * (i == j) + for i in range(8) for j in range(8)), "B D = 13 I") +for label in range(512): + phase = sum((label & chi).bit_count() % 2 for chi in CHARACTERS) % 4 + target = 2 * (((label & 1) * ((label >> 1) & 1) + (label & 5).bit_count()) % 2) + need(phase == target, "Exact quadratic phase identity") +real, imaginary = [[0] * 8 for _ in range(8)], [[0] * 8 for _ in range(8)] +phase_counts = {0: 0, 2: 0} +for p, column in columns.items(): + phase = sum((q[p] & chi).bit_count() % 2 for chi in CHARACTERS) % 4 + real_unit, imaginary_unit = ((1, 0), (0, 1), (-1, 0), (0, -1))[phase] + need(phase in phase_counts, "Real phase on each actual ordinary port") + phase_counts[phase] += 1 + for i in range(8): + for j in range(8): + real[i][j] += real_unit * column[i] * column[j] + imaginary[i][j] += imaginary_unit * column[i] * column[j] +need(not any(c for row in imaginary for c in row), "Zero imaginary part") +need(real == [[2 * c for c in row] for row in TWICE_S], "Direct source Gaussian matrix") +need(any(VECTOR) and all(sum(c * v for c, v in zip(row, VECTOR)) == 0 for row in real), "Exact nonzero null vector") +minor_determinant = determinant([[F(c, 2) for c in row[:7]] for row in TWICE_S[:7]]) +need(minor_determinant == -73, "Exact rank-seven minor") +ordinary = [F(sum(c * v for c, v in zip(column, VECTOR)), 2) for column in columns.values()] +need(sum(c * c for c in ordinary) == 52, "The ordinary source mode is nonzero") +for key, pin in probe["source_pins"].items(): + need(sha256(Path(pin["path"]).read_bytes()).hexdigest() == pin["sha256"], "Source unchanged: " + key) +receipt = dict(status="PASS_DIRECT_SOURCE_SCHUR_SINGULAR_WITNESS", + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), + source_probe_receipt_sha256=PROBE_PIN, source_minor_receipt_sha256=MINOR_PIN, + source_pins=probe["source_pins"], selected_ports=A, ordinary_ports=U, + width=5, characters=CHARACTERS, spectator_character_coordinates=list(range(9, 73)), + phase="2*(q0*q1+q0+q2) modulo 4", label_phase_checks=512, + actual_port_phase_counts={str(k): v for k, v in phase_counts.items()}, + twice_S=TWICE_S, null_vector=VECTOR, rank=7, + leading_seven_by_seven_minor_determinant=str(minor_determinant), + ordinary_mode_squared_norm="52", ordinary_mode_support=sum(c != 0 for c in ordinary), + padding="Append zero characters. The same Schur matrix occurs at every width at least five.", + scope="S=B Q_U D is singular at the stated mode. This rules out an inverse on arbitrary centres at widths at least five. It is not a minimum-width claim or a native lower bound.") +(HERE / "SINGULAR-WITNESS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n", encoding="utf-8") +print(receipt["status"]) +print(json.dumps(dict(characters=CHARACTERS, rank=7, null_vector=VECTOR, minor_determinant=str(minor_determinant)), sort_keys=True)) diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/CHECKS.json new file mode 100644 index 0000000000..be8caa9db5 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/CHECKS.json @@ -0,0 +1,12 @@ +{ + "T_at_least": 1, + "kappa_claim": false, + "logical_minimum_sufficient_width": "T", + "material_findings": 0, + "method": "Independent ordered induction and exact source hash binding. No new enumeration.", + "native_replay": false, + "physical_and_Q_minimum_sufficient_width": "T+1", + "source_hashes_checked": 5, + "source_manifest_sha256": "e69db793cf08369685457a0aa104151942cd535186fbeed049ebb892005659e7", + "status": "PASS_BOUNDED_GENERAL_CLOSURE_PROOF_REVIEW" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/FREEZE.json new file mode 100644 index 0000000000..59687e514e --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/FREEZE.json @@ -0,0 +1,9 @@ +{ + "files": { + "CHECKS.json": "823db93229d579200635781237f93f1ec453c91235a69028810094b2b3aeeb7d", + "REVIEW.md": "620aa9e6f1457e5add2a74140eabeaf6f187ee56a4f9dcad7ad710299f37bbb4", + "SOURCE-MANIFEST.json": "e69db793cf08369685457a0aa104151942cd535186fbeed049ebb892005659e7" + }, + "scope": "Proof-only audit of arbitrary-T current-chart scalar closure, with exact frozen source dependencies. No finite search inference or native decoder lower bound.", + "status": "FROZEN_GENERAL_CLOSURE_PROOF_REVIEW" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/REVIEW.md new file mode 100644 index 0000000000..37ba4c34b8 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/REVIEW.md @@ -0,0 +1,114 @@ +# Proof review of closure through T fresh stages + +The general-stage extension is correct under its stated hypotheses. +No material finding remains. It is an induction on the exact route +formula, not an inference from the D25 tests. + +For D=9+8T, T at least 1, and invertible constant scalar matrices +C0,...,CT on the actual 112 ports: + +- Logical monomial closure holds if and only if every C_t is + monomial, at every payload width f at least T. +- The physical affine version has the same criterion at every + f at least T+1. +- At every f at least T+1, Q commutes with the product if and + only if every C_t is diagonal. + +These are sufficient width bounds. They do not assert that the +bounds are optimal. + +## Ordered recovery of the path + +Fix the output port i_T=p. Put + +```text +B_t = rho_(t,i_t) rho_(t,i_(t-1)), +M = B_T ... B_1, +L_(>t) = B_T ... B_(t+1). +``` + +Suppose i_T,...,i_t have been recovered. The prefix L_(>t) is +then known. Every earlier stage fixes the fresh vector e_t. +The exact identity is + +```text +rho_(t,i_t) L_(>t)^-1 M e_t = Omega+q_(i_(t-1)). +``` + +The operator order in this equation matters. It first removes +the known left prefix, then removes the known stage-t factor. +There is no commutation of different routes. Distinct root +labels recover i_(t-1). Descending induction therefore recovers +all T intermediate ports from the single common input +`(e_T,...,e_1)`. + +Its output tuples are distinct, so a linear combination of the +path operators cannot vanish on that input unless all coefficients +vanish. For an affine path, the additional leading zero column +records its translation. Subtraction then gives the same linear +images. This proves the stated logical and physical width bounds, +including the T=1 case. + +Products of nonzero Gaussian scalar coefficients are nonzero. +For each input/output block, the common input therefore rules +out cancellation among paths. Two paths in one block violate +the coordinate-column condition for a monomial operator. Two +single-path blocks in one port row violate its coordinate-row +condition. The nonzero-row and invertibility argument then +forces C_T, C_(T-1),...,C0 to be monomial in that order. +The converse follows by composition. + +## Pulled lines and the phase witness + +Starting at the final stage, cancel every pair whose intermediate +port equals p. At the first mismatch, say stage t, the pulled +line acquires a nonzero component in fresh block t. Every +remaining transpose factor belongs to an earlier stage and +fixes that block. It cannot remove this component. Thus + +```text +M^T q_p = q_k +``` + +holds exactly when every intermediate port and k equal p. + +The T fresh-vector character columns separate all path outputs, +since each route is orthogonal. If one nonzero path breaks the +line, append zero when its phase difference on those tags is +already nonzero modulo 4. Otherwise append a unit character +that distinguishes M^T q_p from q_k. The appended difference +is 1 or -1. The selected branch has a unique output tuple and +a nonzero commutator coefficient. Affine translations multiply +both sides by the same nonzero sign. + +Consequently Q commutation permits only line-preserving nonzero +paths. Every nonzero last-stage entry has a nonzero continuation. +It must therefore be diagonal. Its diagonal entries are nonzero, +so the argument applies successively to every earlier matrix. +Diagonal scalar matrices commute with each port's routes and Q, +which proves the converse. + +## Cover and scope + +The covariant lift and equal-fiber-support argument from the +frozen D25 binding apply without change to O(D,2). Their proof +uses only the finite complete cover and the stated owner action. +It does not use the value D=25. Thus the spatial failure also +excludes a monomial full-cover product in this scalar-code class. + +This review binds the general-stage view theorem and its freeze, +the corrected D25 closure proof, and the general closure proof. +Their exact paths and hashes are in `SOURCE-MANIFEST.json`. +The companion binding freeze is +`7e572942617d880931f52f47849b23174b903f57a199a99134b96ed5cac21ea6`. + +This is a proof-only review. No additional path enumeration, +native replay, recursive host, map-price calculation, or precision +test was run. The theorem does not cover operator-valued +coefficients, extra old-chart controls, or a changed access +interface. It gives no general native lower bound or kappa gain. + +No frozen source is changed. Before any future PR description, +read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. +No PR, commit, push, or publication is authorized. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/SOURCE-MANIFEST.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..51c89ceb51 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/SOURCE-MANIFEST.json @@ -0,0 +1,22 @@ +{ + "D25_binding_freeze": { + "path": 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b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.json new file mode 100644 index 0000000000..5e2630c0ef --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.json @@ -0,0 +1,136 @@ +{ + "all_width_operator": "W^-1 diag(T_chi^-1) W = T^-1, with simultaneous shifts and first-copy selectors.", + "all_width_prefix_row_norm_bound": "462848", + "arbitrary_live_fields": 8, + "backend_source_pins": { + "upstream/build/sections/02-streams.tex": "606c80db61cad13aa0c3b6060dc4b88dbbe7ac60cdd831aa93f28d908fd09dab", + "upstream/build/sections/05-layers.tex": "20cfc8d12099d4e4ed9e3e7eeb6162edd9b6e0e076f24693364cd24377252594" + }, + "character_inverse_orders_checked": 1024, + "checker_sha256": "ec38a9db9d7542eb076def53d8df4af2ede586cc110835014ca1ab8219cc4e56", + "classes": 172, + "completed_view_maps_per_call": 16, + "completed_views_checked": 64, + "conditional_backend": "Direct in-place marked-counter scans; no array split.", + "counts": { + "complete": { + "ADD": 10743, + "CLEAR": 152, + "COPY": 152, + "DIVIDE_ODD": 8, + "NEG": 2902, + "SCALE2": 10004, + "TRANSLATE": 144, + "conditional_complex_instructions": 23345, + "conditional_scalar_primitives": 110284, + "double": 5010, + "halve": 4994, + "real_odd_division_scans": 16, + "scalar_primitives": 112364, + "translation_maps": 144, + "uniform_scalar_primitives": 2080 + }, + "mode": { + "ADD": 10599, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "NEG": 2758, + "SCALE2": 9932, + "conditional_complex_instructions": 23201, + "conditional_scalar_primitives": 109996, + "double": 5010, + "halve": 4922, + "real_odd_division_scans": 16, + "scalar_primitives": 110204, + "uniform_scalar_primitives": 208 + }, + "walsh_forward": { + "ADD": 72, + "CLEAR": 72, + "COPY": 72, + "NEG": 72, + "SCALE2": 72, + "TRANSLATE": 72, + "conditional_complex_instructions": 72, + "conditional_scalar_primitives": 144, + "halve": 72, + "scalar_primitives": 1152, + "translation_maps": 72, + "uniform_scalar_primitives": 1008 + }, + "walsh_inverse": { + "ADD": 72, + "CLEAR": 72, + "COPY": 72, + "NEG": 72, + "TRANSLATE": 72, + "conditional_complex_instructions": 72, + "conditional_scalar_primitives": 144, + "scalar_primitives": 1008, + "translation_maps": 72, + "uniform_scalar_primitives": 864 + } + }, + "diagonal_types": { + "[1, 1, 1, 1, 1, 1, 1, 1]": 2, + "[1, 1, 1, 1, 1, 1, 3, 3]": 48, + "[1, 1, 1, 1, 1, 3, 3, 39]": 16, + "[1, 1, 1, 1, 1, 5, 5, 55]": 8, + "[1, 1, 1, 1, 3, 3, 3, 165]": 96, + "[13, 13, 13, 13, 13, 13, 13, 13]": 1, + "[3, 3, 3, 3, 3, 3, 3, 3]": 1 + }, + "exact_character_word_checks": 512, + "extra_dyadic_fractional_bits": 9, + "inverse_walsh_kernel_entries_checked": 32768, + "marked_counter_checks": { + "carry_bit_visits": 5380, + "cases": 40, + "checked_addresses": 2600, + "scope": "Finite checks of the marked-counter recurrence. The linear bound follows from the binary carry proof." + }, + "maximum_integer_add": 132, + "maximum_odd_height_increase": 1, + "missing_odd_division_control": true, + "mode_bounds": { + "maximum_dyadic_denominator_exponent": 0, + "maximum_final_row_one_norm": "1", + "maximum_intermediate_dyadic_numerator": 225280, + "maximum_intermediate_row_one_norm": "462848" + }, + "mode_replay_formal_input_columns": 9, + "native_children": 0, + "other_fields_unchanged": true, + "owned_arbitrary_input": true, + "owned_fields": 1, + "owned_output_zero": true, + "payload_compressed_sha256": "e4015617dbb55c2e943eb7762766e9854b6e7d61fbccd905dbfbfcb9cc338a8b", + "payload_raw_sha256": "806f2f6d90bd03db075b5199fd63339b0720c77e51daf2dbc9bb77bd0baf07f2", + "scope": "One completed selected bank, one owned field, explicit conditional scans, and the fixed 2145 odd grid. No global lease or decoder claim.", + "smith_row_column_gates": 5802, + "source_pins": { + "interface": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/INTERFACE.json", + "sha256": "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746" + }, + "line_contract": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/paired-package-review/upstream-followthrough-20261015/current-query-encoder/UNIFORM-SIGNED.json", + "sha256": "9f3939f2eb2d60e187508331b7ab99d6748f73142b5b90bb9ad0c6a4736b3f10" + }, + "phases": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + }, + "view_proof": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.json", + "sha256": "33944a0fe4587aa1ae939dd9861ad7d4c2b7c523dcf05f88fc404e4eeff8c7e8" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", + "sha256": "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f" + } + }, + "source_probe_sha256": "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024", + "status": "PASS_INPLACE_TRANSLATION_INVERSE" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.md new file mode 100644 index 0000000000..b088b8930f --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/INPLACE-SERVICE.md @@ -0,0 +1,317 @@ +# In-place inverse of the centre translation operator + +The actual operator `T=B Q_U^2 D` has an in-place inverse on one +existing eight-field selected bank. The word uses one owned field C0 +and no native children. C0 can have arbitrary input. It is zero at the +output. The eight live input fields are arbitrary. Every other field +is unchanged. + +This construction uses new address-conditioned scalar scans. These +scans are not instructions of the old uniform ADD alphabet. The direct +stream implementation below uses a marked address counter. It does not +split a field into full temporary streams. + +The complete common-chart word has 2,080 uniform real scalar units, +110,284 conditional real scalar units, 144 simultaneous translation +maps, and 16 real division-by-2145 scans. A physical completed-X call +also has 16 view maps. The odd-grid format and the bit cost of its +division scan remain explicit supplier obligations. This result does +not invert `B Q_U D`, supply a global lease, or complete a decoder. + +## Actual operator and source contract + +Use the retained selected ports and the actual source matrix: + +```text +A = [0,7,20,27,36,46,57,111], +U = {0,...,111} minus A, +B = R_A^T R_U/4, D = B^T, +T = B Q_U^2 D. +``` + +The frozen `SCHUR-PROBE.json` has SHA-256 +`ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024`. +Its five source pins are retained in this receipt. The checker reads +the source R and q arrays again. It forms every actual character matrix +directly and checks both inverse orders against the frozen kernel. + +At width lambda, each address has lambda copies of the 73-coordinate +chart. Let `g_delta` put delta in the first nine coordinates of every +copy and put zero in the other coordinates. Write `tau_delta` for +translation by this vector. Then + +```text +Q_p^2 = tau_(q_p), +T_chi = sum_(p in U) B_p B_p^T (-1)^(q_p dot chi). +``` + +All 512 matrices `T_chi` are invertible integer matrices. Their inverse +entries have common denominator 2145. These statements concern the +simultaneous translation group, for every positive lambda. They do not +replace T by a tensor power of an eight-by-eight matrix. + +For a physical call, take the eight selected physical X owners at a +completed local B output, where their frame is FULL. Supply one owned +C slot. The local word also accepts arbitrary C-slot contents because +its first instruction overwrites those contents. Apply the eight +actual completed-X views at the chosen stage before the common-chart +word. Apply their inverses after it. + +If `V_s` is this diagonal set of views, the physical operator is + +```text +V_s^-1 T^-1 V_s. +``` + +The common-chart operator is `T^-1`. These two descriptions are kept +separate. The entry view applies its route and then its translation. +The exit view undoes the translation and then applies the inverse +route. All 64 selected stage/port views are checked from their actual +serialized columns. The checker verifies their inverse direction and +the complete FULL phase identity. No global ownership or chronology +claim follows from this local cut contract. + +## Walsh transform on nine global directions + +For `0 <= j < 9`, let `g_j=g_(2^j)`. Let `ell_j(x)` be bit j in the +first copy of x. Then `ell_j(g_k)` is one when j equals k and zero +otherwise. In particular, the nine directions are independent at +every positive width. The addresses with all nine first-copy bits +zero form a transversal of the translation orbits. + +Let `Z_j f(x)=(-1)^ell_j(x) f(x)` and `X_j=tau_(2^j)`. Define + +```text +H_j = (Z_j+X_j)/2. +``` + +Here `Z_j X_j=-X_j Z_j`, while operators with distinct indices commute. +It follows that `H_j^2=I/2`, `H_j^-1=2H_j`, and +`H_j X_j H_j^-1=Z_j`. + +The following literal word applies `H_j` to one live field x: + +```text +COPY x to C0 +TRANSLATE C0 by g_j +NEGATE x only where ell_j is one +ADD x += C0 +HALVE x +CLEAR C0 +``` + +On an orbit pair, with the first address selected by `ell_j=0`, this is + +```text +(a,b) -> ((a+b)/2,(a-b)/2). +``` + +Omit HALVE to apply the inverse. No final multiplication by two is +needed. Each step overwrites C0 before use and clears it after use. +The copied field is translated; the live field stays in place. + +Apply all nine forward steps to each of the eight fields. Call this +operator W. On each orbit, + +```text +(W f)(z+g_chi) = (1/512) sum_h (-1)^(chi dot h) f(z+g_h). +W tau_delta W^-1 = multiplication by (-1)^(chi dot delta). +``` + +Thus the required inverse is + +```text +T^-1 = W^-1 diag_chi(T_chi^-1) W. +``` + +The inverse Walsh steps use the reverse direction order. The identity +is an all-width operator proof. It uses the selector duality above, +not a sample at width one. The checker also reconstructs all 32,768 +scalar kernel positions from the emitted inverse Walsh pair rule. + +## Exact scalar mode word + +The actual character matrices give 172 distinct matrices up to sign. +For each class, choose its sign so that the first nonzero entry is +positive. Exact integer row and column operations give + +```text +L J R = diag(d_0,...,d_7), +T_chi = epsilon_chi J, +T_chi^-1 = (epsilon_chi/2145) R diag(2145/d_j) L. +``` + +L and R are unimodular integer matrices. The seven diagonal types are + +```text +[1,1,1,1,1,1,1,1] 2 classes +[1,1,1,1,1,1,3,3] 48 classes +[1,1,1,1,1,3,3,39] 16 classes +[1,1,1,1,1,5,5,55] 8 classes +[1,1,1,1,3,3,3,165] 96 classes +[3,3,3,3,3,3,3,3] 1 class +[13,13,13,13,13,13,13,13] 1 class. +``` + +Every divisor divides 2145. No new odd prime is used. The payload has +all factors, all elementary row words, and the mode-to-class table. +The checker verifies `L J R=D` and the Smith divisor chain. It also +checks the order used to apply R to a column vector. Column operations +are converted to vector row operations in reverse order. + +There are 5,802 integer factor gates. The largest absolute integer ADD +coefficient is 132. Each integer ADD is expanded into signed unit ADDs, +doublings of its source, and matching halvings. The source is restored +before the next factor gate. A swap uses three signed unit ADDs and one +sign change. Every expanded instruction has an explicit mode selector. + +The diagonal multiplier `m_j(chi)=2145/d_j(chi)` uses one C0. Copy x_j +to C0. Double C0 through binary levels 1 through 11. At level k, add +C0 to x_j only in modes where bit k of `m_j(chi)-1` is one. Clear C0. +The multiplier is odd, so bit zero is zero. This gives the exact +integer multiplication without clearing the live field. Its selector +tables are finite and are stored in the payload. + +Apply the right factors, then the required class sign. Finally divide +each of the eight live fields by 2145. All preceding mode arithmetic +is integral on integral inputs. This arrangement avoids additions +between fields with different mode-dependent odd grids. It gives one +common increase in odd height. + +The checker replays the complete emitted mode word on nine formal +input columns at all 512 modes: eight live inputs and arbitrary C0. +It checks the exact inverse matrix, absence of the C0 input from each +live output, and zero C0 output each time. The first COPY in the full +word overwrites C0 before any instruction reads it. Both operator inverse orders are checked +against the directly rebuilt T matrix. No random matrix is substituted. + +## Direct conditioned-stream backend + +Two exact source files are pinned in the receipt: + +- `upstream/build/sections/02-streams.tex`: the machine model, elementary + stream operations, binary counter proof, and exact fixed-point scans. +- `upstream/build/sections/05-layers.tex`: the column layout, address + sign wrappers, and the individual selected-bit kernel. + +The first source permits a fixed pointwise map selected by specified +address bits. The second source applies exact arithmetic at a selected +bit. Their split/map/merge constructions show this capability, but this +word does not use their full-stream splits for a conditional scalar gate. + +Use the existing binary record-address counter. On a second fixed +track, mark the nine first-copy positions. Keep their current values +in a finite 512-state control register. When an increment changes a +marked counter bit, change the corresponding register bit. The selector +tables then select a gate without rereading the complete address. + +The markers can be placed in one pass over the counter after the nine +positions are prepared. This takes O(p) work for a p-bit address. The +source already charges descriptor preparation and head returns. In N +consecutive counts, bit j changes O(1+N/2^j) times. Increment carries +and counter-head returns therefore take O(N+p) work. No O(p) lookup is +performed for each record. The finite counter checks in the receipt +test the stated update rule at separated selected positions and across +carries; the sum above proves the general bound. + +The data scan changes only the target coefficient record. If the +selector is false, it leaves that record unchanged. If the selector is +true, it performs the same exact arithmetic as the unconditioned gate. +For example, a two's-complement sign change complements the bits and +adds one with a one-bit carry. A signed unit addition uses the aligned +source record and a bounded carry. A power-of-two step shifts within +the guarded record. The source's fixed-point conventions include all +record reversals and head returns. + +The additional storage is the marked O(p)-bit counter and bounded +arithmetic control. If the record order requires a record reversal, its +temporary record has O(p) bits and is cleared locally. No additional +field array is used. The existing aligned source and target streams +are the actual live fields. Each masked real scan has cost +`O(Nw+N+p)` for N records of guarded width w. This is O(V) under the +source record and descriptor contract. The constant is fixed because +the mode table has 512 entries. + +The new mask control does not make the conditional gates old uniform +ADD instructions. Their arithmetic and their counter work are charged +here as a separate extension. Each of the 23,345 conditional complex +instructions scans all its addressed records, including inactive +entries. Source and target heads traverse inactive records too. No +cost reduction is taken from the small fraction of active modes. + +Each instruction has a fixed number of real arithmetic passes. Across +the word, the counter term is at most a fixed multiple of +`110284*(N+p)`, in addition to those arithmetic passes. This bound +charges marked-counter control for every pass of all 23,345 +instructions. It is not a new native-child charge. + +## Complete local invoice and precision + +Retain the source arithmetic prices: a complex signed unit ADD is +eight real scalar units; a COPY, CLEAR, sign change, doubling, or +halving is two. Conditional units have the same arithmetic price plus +the counter work just stated. These units are not exact machine-step +counts. Odd division and address maps are separate. + +| Part | Uniform scalar units | Conditional scalar units | Translation maps | Real odd scans | +| --- | ---: | ---: | ---: | ---: | +| Forward Walsh | 1008 | 144 | 72 | 0 | +| Mode inverse | 208 | 109996 | 0 | 16 | +| Inverse Walsh | 864 | 144 | 72 | 0 | +| Complete common-chart word | 2080 | 110284 | 144 | 16 | + +There are 23,345 conditional complex instructions. Of the conditional +scalar units, 288 are the Walsh selector-sign scans. The 144 simultaneous +translations use the existing map backend and its packed-layout cost; +they are not silently priced as single bit operations. A physical call +adds eight entry and eight exit view maps. It has zero native children +and zero native inverse wrappers. + +DIVIDE_ODD means exact rational division on an explicit grid over +`Z[i,1/2,1/2145]`. It does not say that an arbitrary integer numerator +is divisible by 2145. This word requires 16 real scans of that backend. +Its bit cost must be inserted when the supplier's exact-grid format is +chosen. No free odd division is claimed. + +If the input has odd height h, every prefix has height at most h+1. +The normalized forward Walsh needs nine extra dyadic fractional bits. +The mode word has integral prefixes before its final odd divisions, +and the inverse Walsh has no halving. Thus nine extra dyadic fractional +bits suffice for this word on its explicit odd grid. + +The exact largest mode-prefix row one-norm is 462,848. The largest +completed mode-inverse row one-norm is one. A completed forward Walsh +has row norm one; its unhalved intermediate sum has norm at most two. +An inverse Walsh has prefix row norm at most 512. The complete word +therefore has row one-norm at most 462,848, including C0. Nineteen +integer guard bits suffice for this local growth factor. These are +local coefficient bounds, not a complete supplier precision theorem. + +Intermediate live frames can differ from FULL. There are no native +calls in the word. Its final common-chart operator is a finite +translation kernel, which commutes with the common FULL frame. The +actual entry and exit views preserve FULL. The physical output is +therefore FULL, with the explicit centre operator stated above. No +ordinary source frame or extra centre-bank code is left unpriced. + +## Verification and boundary + +Run one process: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/check_inplace_service.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/check_inplace_service.py +``` + +Both commands must print `PASS_INPLACE_TRANSLATION_INVERSE`. Their +receipt and compressed literal payload must be byte-identical. The +checker uses explicit failures, not Python assertions. A control that +omits the odd divisions must fail. + +The checker verifies the finite arithmetic and view identities. The +marked-counter and orbit arguments prove the width-independent stream +construction. This is not an executed end-to-end Turing-machine trace. +Integration must still bind an actual completed bank and C0 lease, +the fixed-odd format and cost, and all uses in the changed controller. +The singular `B Q_U D` operator is a separate problem. No complete +kappa value, child saving for a whole supplier, or decoder is claimed. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/check_inplace_service.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/check_inplace_service.py new file mode 100644 index 0000000000..d319be0de5 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/inplace-translation-service/check_inplace_service.py @@ -0,0 +1,453 @@ +"""Emit and check an in-place inverse of the centre translation operator.""" + +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json +import shutil + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[5] +PROBE = HERE.parent / "centre-schur-probe" +A = [0, 7, 20, 27, 36, 46, 57, 111] +U_PORTS = [p for p in range(112) if p not in A] +I = [[int(i == j) for j in range(8)] for i in range(8)] +C0 = 8 +BACKEND = { + "upstream/build/sections/02-streams.tex": "606c80db61cad13aa0c3b6060dc4b88dbbe7ac60cdd831aa93f28d908fd09dab", + "upstream/build/sections/05-layers.tex": "20cfc8d12099d4e4ed9e3e7eeb6162edd9b6e0e076f24693364cd24377252594", +} + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def read_pin(path, digest): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == digest, "Source pin: " + str(path)) + return json.loads(gzip.decompress(raw) if path.suffix == ".gz" else raw) + + +def multiply(a, b): + return [[sum(a[i][k] * b[k][j] for k in range(8)) for j in range(8)] for i in range(8)] + + +def row_gate(a, gate): + kind, target = gate[:2] + if kind == "ADD_INTEGER": + source, coefficient = gate[2:] + a[target] = [x + coefficient * y for x, y in zip(a[target], a[source])] + elif kind == "SWAP": + a[target], a[gate[2]] = a[gate[2]], a[target] + else: + need(kind == "NEG", "Integer row gate") + a[target] = [-x for x in a[target]] + + +def smith(a): + a = [row[:] for row in a] + left, right = [row[:] for row in I], [row[:] for row in I] + row_ops, column_ops = [], [] + + def row(gate): + row_gate(a, gate) + row_gate(left, gate) + row_ops.append(gate) + + def column(gate): + for matrix in (a, right): + transposed = list(map(list, zip(*matrix))) + row_gate(transposed, gate) + matrix[:] = list(map(list, zip(*transposed))) + column_ops.append(gate) + + for k in range(8): + candidates = [(abs(a[i][j]), i, j) for i in range(k, 8) for j in range(k, 8) if a[i][j]] + need(candidates, "Full rank pivot") + _, i, j = min(candidates) + if i != k: + row(["SWAP", i, k]) + if j != k: + column(["SWAP", j, k]) + while True: + for i in range(k + 1, 8): + if a[i][k]: + quotient = a[i][k] // a[k][k] + if quotient: + row(["ADD_INTEGER", i, k, -quotient]) + if a[i][k]: + row(["SWAP", i, k]) + break + else: + for j in range(k + 1, 8): + if a[k][j]: + quotient = a[k][j] // a[k][k] + if quotient: + column(["ADD_INTEGER", j, k, -quotient]) + if a[k][j]: + column(["SWAP", j, k]) + break + else: + bad = next(((i, j) for i in range(k + 1, 8) for j in range(k + 1, 8) + if a[i][j] % a[k][k]), None) + if bad is None: + break + row(["ADD_INTEGER", k, bad[0], 1]) + if a[k][k] < 0: + row(["NEG", k]) + diagonal = [a[k][k] for k in range(8)] + need(all(a[i][j] == (diagonal[i] if i == j else 0) for i in range(8) for j in range(8)), "Smith diagonal") + need(all(diagonal[i + 1] % diagonal[i] == 0 for i in range(7)), "Smith divisor chain") + vector_right = [] + for gate in reversed(column_ops): + if gate[0] == "ADD_INTEGER": + vector_right.append([gate[0], gate[2], gate[1], gate[3]]) + else: + vector_right.append(gate[:]) + check = [row[:] for row in I] + for gate in vector_right: + row_gate(check, gate) + need(check == right, "Column factor vector order") + return dict(left=left, right=right, diagonal=diagonal, left_word=row_ops, right_word=vector_right) + + +def load_data(): + probe = read_pin(PROBE / "SCHUR-PROBE.json", "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024") + sources = {key: read_pin(Path(pin["path"]), pin["sha256"]) for key, pin in probe["source_pins"].items()} + rows = [{int(p): int(c) for p, c in row.items()} for row in sources["interface"]["R"]] + q = [recipe["q"] for recipe in sources["phases"]["recipes"]] + b2 = {} + for p in U_PORTS: + products = [sum(row.get(a, 0) * row.get(p, 0) for row in rows) for a in A] + need(all(x % 2 == 0 for x in products), "Integral doubled B column") + b2[p] = [x // 2 for x in products] + matrices = [] + for chi in range(512): + numerator = [[sum((-1 if (q[p] & chi).bit_count() % 2 else 1) * b2[p][i] * b2[p][j] + for p in U_PORTS) for j in range(8)] for i in range(8)] + need(all(x % 4 == 0 for row in numerator for x in row), "Integral actual character matrix") + matrices.append([[x // 4 for x in row] for row in numerator]) + inverse_kernel = {(delta, i, j): F(value) for delta, i, j, value in probe["kernels"]["inverse"]["entries"]} + inverse_entries = [[[(delta, value) for (delta, row, column), value in inverse_kernel.items() + if row == i and column == j] for j in range(8)] for i in range(8)] + inverses = [] + for chi in range(512): + matrix = [[sum(value * (-1 if (delta & chi).bit_count() % 2 else 1) + for delta, value in inverse_entries[i][j]) + for j in range(8)] for i in range(8)] + need(multiply(matrix, matrices[chi]) == multiply(matrices[chi], matrix) == I, "Actual inverse in both orders") + inverses.append(matrix) + return probe, sources, matrices, inverses + + +def expand_row(gate, selector): + kind, target = gate[:2] + if kind == "NEG": + return [["NEG", selector, target]] + source = gate[2] + if kind == "SWAP": + return [["ADD", selector, target, source, 1], ["ADD", selector, source, target, -1], + ["ADD", selector, target, source, 1], ["NEG", selector, source]] + need(kind == "ADD_INTEGER" and target != source and gate[3], "Integer ADD input") + coefficient = gate[3] + length = abs(coefficient).bit_length() - 1 + word = [] + for bit in range(length + 1): + if (abs(coefficient) >> bit) & 1: + word.append(["ADD", selector, target, source, 1 if coefficient > 0 else -1]) + if bit < length: + word.append(["SCALE2", selector, source, 1]) + word += [["SCALE2", selector, source, -1] for _ in range(length)] + return word + + +def walsh_word(inverse): + word = [] + for target in range(8): + for bit in (reversed(range(9)) if inverse else range(9)): + word += [["COPY", None, C0, target], ["TRANSLATE", None, C0, 1 << bit], + ["NEG", "bit_" + str(bit), target], ["ADD", None, target, C0, 1]] + if not inverse: + word.append(["SCALE2", None, target, -1]) + word.append(["CLEAR", None, C0]) + return word + + +def build_mode_word(classes, lookup, selectors): + word = [] + for item in classes: + label = "class_" + str(item["index"]) + selectors[label] = [chi for chi, (index, sign) in enumerate(lookup) if index == item["index"]] + for gate in item["left_word"]: + word += expand_row(gate, label) + for target in range(8): + multipliers = [2145 // classes[index]["diagonal"][target] for index, sign in lookup] + word.append(["COPY", None, C0, target]) + for bit in range(1, max(multipliers).bit_length()): + word.append(["SCALE2", None, C0, 1]) + label = "diagonal_" + str(target) + "_" + str(bit) + selectors[label] = [chi for chi, value in enumerate(multipliers) if ((value - 1) >> bit) & 1] + if selectors[label]: + word.append(["ADD", label, target, C0, 1]) + word.append(["CLEAR", None, C0]) + for item in classes: + for gate in item["right_word"]: + word += expand_row(gate, "class_" + str(item["index"])) + selectors["negative"] = [chi for chi, (index, sign) in enumerate(lookup) if sign < 0] + word += [["NEG", "negative", target] for target in range(8)] + word += [["DIVIDE_ODD", None, target, 2145] for target in range(8)] + return word + + +def invoice(word): + count = Counter() + for gate in word: + kind, selector = gate[:2] + count[kind] += 1 + if kind == "TRANSLATE": + count["translation_maps"] += 1 + elif kind == "DIVIDE_ODD": + count["real_odd_division_scans"] += 2 + else: + price = 8 if kind == "ADD" else 2 + need(kind in ("ADD", "COPY", "CLEAR", "SCALE2", "NEG"), "Priced scalar gate") + category = "uniform_scalar_primitives" if selector is None else "conditional_scalar_primitives" + count[category] += price + if selector is not None: + count["conditional_complex_instructions"] += 1 + count["scalar_primitives"] += price + if kind == "SCALE2": + count["double" if gate[3] == 1 else "halve"] += 1 + return dict(count) + + +def check_modes(word, selectors, inverses): + membership = {key: set(values) for key, values in selectors.items()} + maximum, final_maximum = F(1), F(0) + maximum_integer = 0 + maximum_dyadic_denominator_exponent = 0 + for chi in range(512): + state = [[F(c) for c in row] + [F(0)] for row in I] + [[F(0)] * 8 + [F(1)]] + for gate in word: + kind, selector, target = gate[:3] + if selector is not None and chi not in membership[selector]: + continue + need(0 <= target <= C0, "Only live bank and owned field") + if kind == "ADD": + source, coefficient = gate[3:] + need(source != target and coefficient in (-1, 1), "Literal unit ADD") + state[target] = [x + coefficient * y for x, y in zip(state[target], state[source])] + elif kind == "SCALE2": + need(gate[3] in (-1, 1), "One power-of-two step") + state[target] = [x * F(2) ** gate[3] for x in state[target]] + elif kind == "NEG": + state[target] = [-x for x in state[target]] + elif kind == "COPY": + need(target == C0 and gate[3] < 8, "Copy into one owned field") + state[target] = state[gate[3]][:] + elif kind == "CLEAR": + need(target == C0, "Only the owned field is cleared") + state[target] = [F(0)] * 9 + else: + need(kind == "DIVIDE_ODD" and target < 8 and gate[3] == 2145, "One common output division") + state[target] = [x / 2145 for x in state[target]] + maximum = max(maximum, sum(map(abs, state[target]))) + if kind != "DIVIDE_ODD": + for value in state[target]: + need(value.denominator == 1, "Integral mode prefix before the final divisions") + if value.denominator & (value.denominator - 1) == 0: + maximum_dyadic_denominator_exponent = max(maximum_dyadic_denominator_exponent, value.denominator.bit_length() - 1) + maximum_integer = max(maximum_integer, abs(value.numerator)) + need(state[:8] == [row + [F(0)] for row in inverses[chi]] and not any(state[C0]), "Exact emitted character inverse and zero owned output") + final_maximum = max(final_maximum, *(sum(map(abs, row)) for row in state[:8])) + return dict(maximum_intermediate_row_one_norm=str(maximum), maximum_final_row_one_norm=str(final_maximum), + maximum_dyadic_denominator_exponent=maximum_dyadic_denominator_exponent, + maximum_intermediate_dyadic_numerator=maximum_integer) + + +def pair_matrix(inverse): + rows = [[F(1), F(0)], [F(0), F(1)]] + copied = [row[:] for row in rows] + copied.reverse() + rows[1] = [-x for x in rows[1]] + rows = [[x + y for x, y in zip(row, copy)] for row, copy in zip(rows, copied)] + return rows if inverse else [[x / 2 for x in row] for row in rows] + + +def check_walsh(words): + forward, inverse = pair_matrix(False), pair_matrix(True) + need(forward == [[F(1, 2), F(1, 2)], [F(1, 2), F(-1, 2)]], "Exact H0 pair") + need(inverse == [[1, 1], [1, -1]], "Exact inverse pair") + for a, b in ((forward, inverse), (inverse, forward)): + need([[sum(a[i][k] * b[k][j] for k in range(2)) for j in range(2)] for i in range(2)] == [[1, 0], [0, 1]], "Both pair inverse orders") + for name, word in words.items(): + step_size = 6 if name == "forward" else 5 + need(len(word) == 72 * step_size, "All eight fields and nine directions") + for offset in range(0, len(word), step_size): + gates = word[offset:offset + step_size] + target, shift = gates[0][3], gates[1][3] + bit = shift.bit_length() - 1 + want = [["COPY", None, C0, target], ["TRANSLATE", None, C0, shift], + ["NEG", "bit_" + str(bit), target], ["ADD", None, target, C0, 1]] + if name == "forward": + want.append(["SCALE2", None, target, -1]) + want.append(["CLEAR", None, C0]) + need(gates == want and shift == 1 << bit, "Literal pair order") + for j in range(9): + for k in range(9): + need(((1 << k) >> j) & 1 == int(j == k), "First-copy selector duality") + + +def check_counter(): + cases, visits = 0, 0 + for copies in (1, 2, 3, 7): + positions = [copies * bit for bit in range(9)] + width = positions[-1] + 2 + marks = {position: bit for bit, position in enumerate(positions)} + starts = [0] + [max(0, (1 << position) - 17) for position in positions] + for start in starts: + bits = [(start >> bit) & 1 for bit in range(width)] + mode = sum(bits[position] << bit for bit, position in enumerate(positions)) + local_visits = 0 + for value in range(start, start + 65): + need(mode == sum(((value >> position) & 1) << bit for bit, position in enumerate(positions)), "Marked counter mode") + if value == start + 64: + break + position = 0 + while True: + bits[position] ^= 1 + local_visits += 1 + if position in marks: + mode ^= 1 << marks[position] + if bits[position]: + break + position += 1 + need(local_visits <= 128 + width, "Amortized counter visits") + visits += local_visits + cases += 1 + return dict(cases=cases, checked_addresses=65 * cases, carry_bit_visits=visits, + scope="Finite checks of the marked-counter recurrence. The linear bound follows from the binary carry proof.") + + +def check_walsh_kernel(inverses, probe): + expected = {(delta, i, j): F(value) for delta, i, j, value in probe["kernels"]["inverse"]["entries"]} + for i in range(8): + for j in range(8): + values = [matrix[i][j] / 512 for matrix in inverses] + for bit in reversed(range(9)): + copied = values[:] + values = [(-copied[h] if (h >> bit) & 1 else copied[h]) + copied[h ^ (1 << bit)] + for h in range(512)] + need(values == [expected.get((delta, i, j), F(0)) for delta in range(512)], "Literal inverse Walsh reconstructs the complete kernel") + + +def act(columns, vector): + result = 0 + while vector: + bit = vector & -vector + result ^= columns[bit.bit_length() - 1] + vector ^= bit + return result + + +def check_views(sources): + views = [v for v in sources["views"]["views"] if v["side"] == "X" and v["port"] in A] + need({(v["stage"], v["port"]) for v in views} == {(s, p) for s in range(1, 9) for p in A}, "All selected completed views") + for view in views: + rho, delta = view["route_columns"], view["translation_after_route"] + transpose = [sum(((v >> i) & 1) << j for j, v in enumerate(rho)) for i in range(73)] + need([act(rho, x) for x in rho] == [1 << i for i in range(73)] and rho == transpose, "Actual orthogonal involution") + need(act(rho, delta) == view["translation_before_route"], "Actual route then translation") + linear = [(v.bit_count() + 2 * ((delta >> i) & 1) - 1) % 4 for i, v in enumerate(transpose)] + quadratic = [(-2 * (a & b).bit_count()) % 4 for i, a in enumerate(transpose) for b in transpose[i + 1:]] + need(not any(linear + quadratic), "Completed FULL phase endpoint") + wrappers = {str(stage): dict(enter=[["VIEW", row, stage, A[row], False] for row in range(8)], + leave=[["VIEW", row, stage, A[row], True] for row in reversed(range(8))]) + for stage in range(1, 9)} + return views, wrappers + + +def main(): + need(shutil.disk_usage(HERE).free >= 3 * 2**30, "At least 3 GiB free") + probe, sources, matrices, inverses = load_data() + for path, digest in BACKEND.items(): + need(sha256((ROOT / path).read_bytes()).hexdigest() == digest, "Exact stream source pin") + classes, lookup = {}, [] + for matrix in matrices: + first = next(value for row in matrix for value in row if value) + sign = 1 if first > 0 else -1 + key = tuple(sign * value for row in matrix for value in row) + if key not in classes: + canonical = [list(key[i:i + 8]) for i in range(0, 64, 8)] + factor = smith(canonical) + diagonal = [[factor["diagonal"][i] * I[i][j] for j in range(8)] for i in range(8)] + need(multiply(multiply(factor["left"], canonical), factor["right"]) == diagonal, "Actual Smith factors") + need(all(2145 % d == 0 for d in factor["diagonal"]), "No new odd divisor") + classes[key] = dict(index=len(classes), matrix=canonical, **factor) + lookup.append([classes[key]["index"], sign]) + classes = list(classes.values()) + need(len(classes) == 172, "All actual sign classes") + selectors = {"bit_" + str(bit): [chi for chi in range(512) if (chi >> bit) & 1] for bit in range(9)} + mode_word = build_mode_word(classes, lookup, selectors) + mode_bounds = check_modes(mode_word, selectors, inverses) + walsh_words = dict(forward=walsh_word(False), inverse=walsh_word(True)) + check_walsh(walsh_words) + check_walsh_kernel(inverses, probe) + counter = check_counter() + try: + check_modes([gate for gate in mode_word if gate[0] != "DIVIDE_ODD"], selectors, inverses) + except ValueError as error: + need(str(error) == "Exact emitted character inverse and zero owned output", "Expected control failure") + else: + raise ValueError("Missing odd division must fail") + views, wrappers = check_views(sources) + body = walsh_words["forward"] + mode_word + walsh_words["inverse"] + counts = {name: invoice(word) for name, word in dict(walsh_forward=walsh_words["forward"], mode=mode_word, + walsh_inverse=walsh_words["inverse"], complete=body).items()} + need(counts["walsh_forward"]["uniform_scalar_primitives"] == 1008, "Forward uniform invoice") + need(counts["walsh_inverse"]["uniform_scalar_primitives"] == 864, "Inverse uniform invoice") + need(counts["complete"]["translation_maps"] == 144, "Complete translation invoice") + need(counts["complete"]["real_odd_division_scans"] == 16, "One division per complex output") + payload = dict(schema="inplace-centre-translation-inverse-v1", selected_ports=A, live_fields=list(range(8)), owned=C0, + selectors=selectors, classes=classes, mode_lookup=lookup, walsh_words=walsh_words, + mode_word=mode_word, body=body, stage_wrappers=wrappers, completed_views=views, + instruction_order="Each instruction is [operation, selector, target, arguments]. A null selector means all addresses.", + translation_rule="Repeat the nine-bit shift in every tensor copy. Leave the other coordinates unchanged.", + selector_rule="The selector table uses the nine first-copy address bits. These bits are held in a finite control register.", + view_rule="Enter by route then translation. Leave by inverse translation then inverse route.") + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + program_path = HERE / "INPLACE-PROGRAM.json.gz" + program_path.write_bytes(gzip.compress(raw, mtime=0)) + receipt = dict(status="PASS_INPLACE_TRANSLATION_INVERSE", source_pins=probe["source_pins"], backend_source_pins=BACKEND, + source_probe_sha256="ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024", + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), counts=counts, mode_bounds=mode_bounds, + payload_raw_sha256=sha256(raw).hexdigest(), payload_compressed_sha256=sha256(program_path.read_bytes()).hexdigest(), + classes=len(classes), diagonal_types=dict(Counter(str(x["diagonal"]) for x in classes)), + maximum_integer_add=max(abs(gate[3]) for x in classes for gate in x["left_word"] + x["right_word"] if gate[0] == "ADD_INTEGER"), + smith_row_column_gates=sum(len(x["left_word"]) + len(x["right_word"]) for x in classes), + all_width_operator="W^-1 diag(T_chi^-1) W = T^-1, with simultaneous shifts and first-copy selectors.", + all_width_prefix_row_norm_bound=str(max(F(2), F(mode_bounds["maximum_intermediate_row_one_norm"]), + 512 * F(mode_bounds["maximum_final_row_one_norm"]))), + native_children=0, completed_view_maps_per_call=16, owned_fields=1, owned_arbitrary_input=True, + owned_output_zero=True, arbitrary_live_fields=8, other_fields_unchanged=True, + mode_replay_formal_input_columns=9, + maximum_odd_height_increase=1, conditional_backend="Direct in-place marked-counter scans; no array split.", + marked_counter_checks=counter, missing_odd_division_control=True, + extra_dyadic_fractional_bits=9, inverse_walsh_kernel_entries_checked=32768, + exact_character_word_checks=512, character_inverse_orders_checked=1024, completed_views_checked=64, + scope="One completed selected bank, one owned field, explicit conditional scans, and the fixed 2145 odd grid. No global lease or decoder claim.") + for path, digest in BACKEND.items(): + need(sha256((ROOT / path).read_bytes()).hexdigest() == digest, "Stream source unchanged") + for key, pin in probe["source_pins"].items(): + need(sha256(Path(pin["path"]).read_bytes()).hexdigest() == pin["sha256"], "Source unchanged: " + key) + (HERE / "INPLACE-SERVICE.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n", encoding="utf-8") + print(receipt["status"]) + print(json.dumps(dict(counts=counts, mode_bounds=mode_bounds, prefix_bound=receipt["all_width_prefix_row_norm_bound"]), sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/BLOCK-PROOF.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/BLOCK-PROOF.json new file mode 100644 index 0000000000..e5dd397f37 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/BLOCK-PROOF.json @@ -0,0 +1,1236 @@ +{ + "endpoint": [ + [ + { + "coefficient": "-1", + "source_group": 2, + "word": [] + } + ], + [ + { + "coefficient": "-1", + "source_group": 0, + "word": [ + "D0" + ] + }, + { + "coefficient": "1", + "source_group": 0, + "word": [ + "D1" + ] + }, + { + "coefficient": "-1", + "source_group": 1, + "word": [ + "D0", + "H0" + ] + }, + { + "coefficient": "1", + "source_group": 1, + "word": [ + "D1", + "H0" + ] + }, + { + "coefficient": "-1", + "source_group": 3, + "word": [] + } + ], + [ + { + "coefficient": "1", + "source_group": 0, + "word": [] + }, + { + "coefficient": "1", + "source_group": 0, + "word": [ + "H1", + "D0" + ] + }, + { + "coefficient": "-1", + "source_group": 0, + "word": [ + "H2", + "D0" + ] + }, + { + "coefficient": "1", + "source_group": 0, + "word": [ + "H2", + "D1" + ] + }, + { + "coefficient": "1", + "source_group": 1, + "word": [ + "H0" + ] + }, + { + "coefficient": "1", + "source_group": 1, + "word": [ + "H1" + ] + }, + { + "coefficient": "1", + "source_group": 1, + "word": [ + "H1", + "D0", + "H0" + ] + }, + { + "coefficient": "-1", + "source_group": 1, + "word": [ + "H2", + "D0", + "H0" + ] + }, + { + "coefficient": "1", + "source_group": 1, + "word": [ + "H2", + "D1", + "H0" + ] + }, + { + "coefficient": "1", + "source_group": 3, + "word": [ + "H1" + ] + }, + { + "coefficient": "-1", + "source_group": 3, + "word": [ + "H2" + ] + } + ], + [ + { + "coefficient": "1", + "source_group": 0, + "word": [ + "D1" + ] + }, + { + "coefficient": "1", + "source_group": 0, + "word": [ + "D2" + ] + }, + { + "coefficient": "1", + "source_group": 0, + "word": [ + "D2", + "H1", + "D0" + ] + }, + { + "coefficient": "-1", + "source_group": 0, + "word": [ + "D2", + "H2", + "D0" + ] + }, + { + "coefficient": "1", + 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"BLOCK-PROOF.json": "8c1b9b293eb3237da82671f286e4a1cec1377d2c836b6e4ad0270cbcb4da410f", + "CHECKS.json": "60f5abd1bcf6e93cbd8c3f82e7965427ca96819e10050e14c719dfd13c6b9b87", + "FRAME-CERTIFICATE.json": "a350e2b9a8be1c3a7aa62c6070d7c556a69fc591b5c83092131bd6f221e22a30", + "REVIEW.md": "f86f2ef95cb9168418f1e67ec3e6e1826106393ace8ecc048ab0369d8a478a72", + "SOURCE-MANIFEST.json": "658e43b1c678723baedaaf0898f8f3b50af1fea1e5836960011a85d3893ebb9b", + "TERMINAL-WORD.json": "e0b356266c026455ddd81e869ff1270fdbe00e342367aac8173026afb446fa88", + "check_review.py": "daef106365651360926f41e82cfa5bac291433ea87ba154c1d75e6fe4ce04186" + }, + "normal_optimized_byte_identical": [ + "CHECKS.json", + "SOURCE-MANIFEST.json", + "FRAME-CERTIFICATE.json", + "BLOCK-PROOF.json", + "TERMINAL-WORD.json" + ], + "producer_freeze_sha256": "089425bdf431d81456e1c988a1fd21a837baca43e510bc92dee98dc2ee571791", + "schema": "independent-natural-triple-review-freeze-v1", + "scope": "Actual local source maps, literal D25 mixed frames, free-operator natural triple and content inverse, and 208-positive-line operator terminal. No serialized native terminal recipe, global helper host, recursive supplier bill, or precision theorem." +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/REVIEW.md new file mode 100644 index 0000000000..7791ad3f50 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/REVIEW.md @@ -0,0 +1,287 @@ +# Independent review of the natural D25 clean triple + +The stated no-reset endpoint is correct. The 208-positive-line operator +terminal is also correct on arbitrary data inputs, with the stated bank +exchange. There is no material local finding. + +This review binds the actual local forward and inverse-adjoint content +maps, and the literal D25 phase views. It does not import either producer +checker. It uses a compact frame proof and a separate free-operator +composition. It does not repeat the producer's large expanded global +column replay or the inherited native child replay. + +The producer proof has SHA256 +`e968dd64f34f8dd4422145ccea847d329886657e9e209682a49964d7faf60f3c`. +The bound producer freeze has SHA256 +`089425bdf431d81456e1c988a1fd21a837baca43e510bc92dee98dc2ee571791`. +The completed `run-terminal-normal/CHECKS.json` has SHA256 +`24741af6fabff0e09bc13518f79477a80f32f88bb49aabaf31f40afa070aa543`. +`SOURCE-MANIFEST.json` also binds the imported phase library by its exact +bytes, although this review does not execute that library. + +## Actual local maps + +Let P be the selected set in its serialized order, and R its complement. +Their sizes are 16 and 96. The selected set is + +```text +[0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23]. +``` + +The review reads H from the P,R block of the row code and D from the +R,P block of the actual response. It checks + +```text +C = [[I,H],[0,I]], +D = -H^T, +E_R(a,u) = u + D(a+H u). +``` + +The row code, response, selected set, and port order agree across the +forward and dual payloads. The port labels also agree with the D25 +views. + +On all 224 independent local data columns, the stored forward map is + +```text +F(a,u,z,v) = (-z,u,alpha,v+u+D alpha), +alpha = a+H u. +``` + +The review derives its inverse from these equations and checks both +product orders. It then transposes that inverse and applies the actual +selected-wire permutation to both sides. The result agrees with every +column of the stored selected-swap inverse-adjoint: + +```text +B(a,u,z,v) = (z+H v,u+D z-v,-a,v). +``` + +Thus B is bound to the native dual source. It is not an assumed inverse +of the response E. + +The I-entry forward word has input `(Q(a,u),z,v)`. The later Q-entry +words have input `(Q(a,u),Q_P z,v)`. Both forward variants have the same +content map. Their physical input types and native invoices differ. + +## The natural boundary is a route change + +Write `G_s=diag(R_(rho_s,p))`. Every pinned rho is an orthogonal +involution and fixes its own line q_p. At stage zero, G is the identity. +The actual entry and exit views are + +```text +Ventry_s,p = T_(rho_s,p(entry_X)) R_(rho_s,p), +Vexit_s,p = T_(exit_X) R_(rho_s,p). +``` + +The pinned X and Y translations agree. The review checks, at every port +of stages 1 and 2, + +```text +Ventry_s Fprev_s = Fext_s Q G_s, +Ventry_s Fprev_s q = Fext_s G_s, +Vexit_s Fnext_s = Fnext_s G_s, +Vexit_s Fnext_s q = Fnext_s q G_s. +``` + +There are 896 such identities. The phase checker applies the operator +word from right to left, in input-character coordinates. It reconstructs +the exact degree-two polynomial modulo 4 from its values on the 25 +basis vectors and 300 pairs. This is an identity check, not a sampled +character test. The route matrices are checked as well. The result +tensors over every spatial column. + +Suppose a previous output has physical type + +```text +X=Fprev x, Y_P=Fprev z, Y_R=Fprev q_R v. +``` + +The next entry views give + +```text +X=Fext Q G_s x, +Y_P=Fext Q_P G_(s,P) z, +Y_R=Fext G_(s,R) v. +``` + +Removal of the common exterior and the declared Q-entry input type +therefore leaves exactly G_s times the previous decoded contents. +The exit identities apply G_s to the local output contents. The +complete stage consequently replaces H and D by + +```text +H_s = G_(s,P) H G_(s,R), +D_s = G_(s,R) D G_(s,P). +``` + +No Q is moved through H or D. Only the port's own Q commutes with its +route. In particular, the ordinary Y holes are not treated as FULL. + +Omission of the literal entry translations fails all 224 entry +controls. Removal of the ordinary-Y hole from the input type fails +all 192 ordinary-port controls. + +## Ordered three-call calculation + +Define the initial contents by `X0=Q(a,u)` and `Y0=(z,v)`. These +equations do not add gates. All original physical inputs are arbitrary. + +The first call gives + +```text +alpha = a+H0 u, +K = v+u+D0 alpha, +Fclean0(a,u,z,v) = (-z,u,alpha,K). +``` + +Use the actual routed B formula at stage 1. Its output is + +```text +(alpha+H1 K, u+D1 alpha-K, z, K) + = (alpha+H1 K, W, z, K), + +W = -v+(D1-D0)alpha. +``` + +The final forward call gives + +```text +(-z,W,beta,K+W+D2 beta), +beta = alpha+H1 K+H2 W. +``` + +Since `K+W=u+D1 alpha`, put `r=u+D1 alpha+D2 beta`. The exact +physical endpoint is therefore + +```text +X_P = -F25 z, +X_R = F25 W, +Y_P = F25 beta, +Y_R = F25 q_R r. +``` + +`BLOCK-PROOF.json` records a separate calculation in which all six +operators H0,H1,H2,D0,D1,D2 are free symbols. It checks the first, +second, and final stage endpoints and the inverse. It uses no +commutation relation between these operators. + +For the inverse, set `t=r-D2 beta=K+W`. Then + +```text +alpha = beta-H1 t+(H1-H2)W, +u = t-D1 alpha, +a = alpha-H0 u, +v = -W+(D1-D0)alpha. +``` + +These are ordered dyadic formulas. They do not require a unit +`I+H1 D2`, an odd division, or an extra independent centre bank. + +## The 208-line terminal + +The first 96 positive line operations change `F25 q_R r` to `F25 r`. +All fields are then in the common FULL frame. The following in-place +content updates recover the two original contents: + +```text +Y_R <- Y_R-D2 Y_P # t +Y_P <- Y_P-H1 Y_R +Y_P <- Y_P+(H1-H2)X_R # alpha +X_R <- -X_R+(D1-D0)Y_P # v +Y_R <- Y_R-D1 Y_P # u +Y_P <- Y_P-H0 Y_R # a +X_P <- -X_P # z +``` + +The final 112 positive line operations on Y restore Q(a,u). Thus + +```text +X=F25 Y0, Y=F25 X0. +``` + +This is a bank exchange. A caller that requires the opposite assignment +must include its final permutation. With initial selected Q entry, +the original selected borrowed value is Q_P z. Its restoration needs +16 further positive lines; the 208 count uses initial I entry. + +The review checks all 208 line-frame identities. The wrong negative +line on the first ordinary normalization fails at all 96 ports. + +For every nonzero stage and every port, the review also checks + +```text +Vexit_s,p F25 = F25 R_(rho_s,p), +Vexit_s,p^2 = I. +``` + +These 224 FULL views include the literal exit translations. They differ +from the J views in the separate reset-defect packet. No reset-packet +translation is substituted here. + +`TERMINAL-WORD.json` contains the complete operator word with LINE, +MAP, ADD, and NEG events. It expands every H or D shear into its exact +coefficients and the required FULL views. Each of the eight physical +shear subwords is checked on all 224 independent input symbols. The +free-operator proof then checks their in-place composition. Sources +are restored after each shear; no scratch field or clean baseline is +used. + +The exact direct invoice is + +```text +positive line operations 208 +H or D coefficient ADDs 1728 +field negations 112 +old real scalar units 16608 +FULL affine map calls 1344 +extra fields 0 +odd divisions 0. +``` + +Each H or D has 216 coefficients and costs 2,048 scalar units under the +inherited tariff. There are eight shears and 112 complex negations. +Six shears have a nonzero route stage and use at most 224 field maps +each. The two stage-zero shears need no route maps. + +The LINE events specify exact positive operators. This review does not +provide their serialized native recipes or their host. The invoice also +omits their side maps and the final bank permutation. Every MAP retains +its stream and address cost. + +## Native event invoices and scope + +The review recounts native ranks and scalar prices from every stored +local event list, for both providers. This is an invoice check, not +another native replay. + +The I-entry F word has mass 1,808. Each Q-entry F or selected-swap B +word has mass 1,792. Each costs 8,600 scalar units. Thus the three-call +local total is mass 5,392 and 25,800 scalar units, with profile + +```text +4176 H1 + 192 H2 + 144 H3 + 32 H8 + 16 H9. +``` + +The local source packets supply restoration of the 416 arbitrary +auxiliary fields. This review inherits that local contract. It does +not replay the global helper host, establish a complete routed native +caller, or prove the recursive precision and supplier costs. + +The producer checker uses the correct route product and quadratic +phase substitution. Its physical input decoding and output framing +match the source contracts. Its terminal calculation agrees with the +literal in-place operator word above. The completed producer receipt +is consistent with the independent checks. + +Run from the repository root with fresh output directories: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/check_review.py --out /private/tmp/no-reset-review-normal +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/check_review.py --out /private/tmp/no-reset-review-optimized +``` + +Both runs must report `PASS_INDEPENDENT_NATURAL_TRIPLE_REVIEW`. +Their five JSON outputs must agree byte for byte. All input hashes are +checked again at exit. No frozen producer file is changed. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/SOURCE-MANIFEST.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..44c6657232 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/no-reset-triple-review-20261020/SOURCE-MANIFEST.json @@ -0,0 +1,50 @@ +{ + "dual": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz", + "payload_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c", + "sha256": 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pathlib import Path +import shutil + + +HERE = Path(__file__).resolve().parent +LANE = HERE.parents[1] +LANES = LANE.parent +PRODUCER = LANE / "no-reset-triple-20261020" +NATIVE = LANES / "new-core-transfer-20261017/low-displacement-20261020" +UNIT = tuple(1 << j for j in range(25)) +ID = (UNIT, 0) +SOURCES = { + "views": ( + LANES / "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), + "row_code": ( + NATIVE / "row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz", + "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2", + ), + "forward": ( + NATIVE / "clean-late-exchange-20261020/run-normal/CLEAN-LATE-EXCHANGE.json.gz", + "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083", + ), + "dual": ( + NATIVE / "clean-late-exchange-20261020/dual-normal/CLEAN-DUAL.json.gz", + "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c", + ), +} +PRODUCER_PINS = { + "producer_proof": "e968dd64f34f8dd4422145ccea847d329886657e9e209682a49964d7faf60f3c", + "producer_checker": "8612732e02b68495d6b0b95cbd216d1d0df43be2ffdd29cc7fc9033518ab1c48", + "producer_phase_library": "70ca9ce2dff5256644f35ef65344c7e0dd9f78e3fb48c18436e9e5c20b4f9109", + "producer_checks": "24741af6fabff0e09bc13518f79477a80f32f88bb49aabaf31f40afa070aa543", + "producer_freeze": "089425bdf431d81456e1c988a1fd21a837baca43e510bc92dee98dc2ee571791", +} + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def digest(raw): + return sha256(raw).hexdigest() + + +def act(columns, vector): + result = 0 + for j, column in enumerate(columns): + if vector & (1 << j): + result ^= column + return result + + +def transposed(columns, vector): + return sum(((column & vector).bit_count() & 1) << j + for j, column in enumerate(columns)) + + +def compose(left, right): + return tuple(act(left, column) for column in right) + + +def normal(word): + """Apply the word from right to left and use input character coordinates.""" + matrix = UNIT + terms = Counter() + for kind, value, power in reversed(word): + if kind == "R": + matrix = compose(value, matrix) + else: + need(kind == "P", "Known phase operator") + terms[transposed(matrix, value)] += power + terms = [(v, c % 4) for v, c in terms.items() if c % 4] + linear = tuple(sum(c * ((v >> j) & 1) for v, c in terms) % 4 for j in range(25)) + quadratic = [] + for i in range(25): + for j in range(i + 1, 25): + sample = (1 << i) | (1 << j) + value = (sum(c * ((v & sample).bit_count() & 1) for v, c in terms) - + linear[i] - linear[j]) % 4 + if value: + need(value == 2, "Even quadratic coefficient") + quadratic.append((i, j, value)) + return matrix, linear, tuple(quadratic) + + +def route(columns): + return [("R", tuple(columns), 0)] + + +def line(vector, power): + return [("P", vector, power)] + + +def fourier(start, stop, power=1): + return [("P", 1 << j, power) for j in range(start, stop)] + + +def plus(*terms): + result = {} + for coefficient, row in terms: + for key, value in row.items(): + total = result.get(key, F(0)) + coefficient * value + if total: + result[key] = total + else: + result.pop(key, None) + return result + + +def linear(matrix, rows): + return [plus(*((c, rows[j]) for j, c in row.items())) for row in matrix] + + +def sparse(rows): + return [{int(j): F(c) for j, c in row.items() if F(c)} for row in rows] + + +def transpose(matrix, columns): + result = [{} for _ in range(columns)] + for i, row in enumerate(matrix): + for j, value in row.items(): + result[j][i] = value + return result + + +def eye(size): + return [{j: F(1)} for j in range(size)] + + +def add_price(value): + a, b = abs(value.numerator), value.denominator + need(a and b & (b - 1) == 0, "Nonzero dyadic ADD") + return 2 * (3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1) + + +def local_invoice(item): + profile = Counter() + scalar = 0 + for event in item["events"]: + if event[0] == "native": + profile[event[4]] += 1 + else: + need(event[0] == "scalar", "Known native word event") + gate = event[1] + value = F(gate[3]) + if gate[0] == "add": + scalar += add_price(value) + else: + need(gate[0] == "scale", "Known native scalar event") + a, b = abs(value.numerator), value.denominator + need(a & (a - 1) == b & (b - 1) == 0, "Signed dyadic unit scale") + scalar += 2 * (abs(a.bit_length() - b.bit_length()) + (value < 0)) + return {"profile": dict(sorted(profile.items())), "native_mass": sum(r * n for r, n in profile.items()), + "native_children": sum(profile.values()), "real_scalar_primitives": scalar} + + +def source_matrix_checks(source, selected, ordinary, h, d): + basis = eye(224) + a, u = [basis[p] for p in selected], [basis[p] for p in ordinary] + z, v = [basis[112 + p] for p in selected], [basis[112 + p] for p in ordinary] + + def joined(ap, ur, zp, vr): + result = [None] * 224 + for ports, rows, offset in ((selected, ap, 0), (ordinary, ur, 0), + (selected, zp, 112), (ordinary, vr, 112)): + for p, row in zip(ports, rows): + result[offset + p] = row + return result + + alpha = [plus((1, x), (1, y)) for x, y in zip(a, linear(h, u))] + lower = [plus((1, x), (1, y), (1, z0)) for x, y, z0 in zip(v, u, linear(d, alpha))] + forward = joined([plus((-1, row)) for row in z], u, alpha, lower) + need(forward == sparse(source["forward"]["content_map"]), "All 224 forward content columns") + inverse = joined([plus((1, x), (-1, y)) for x, y in zip(z, linear(h, u))], u, + [plus((-1, row)) for row in a], + [plus((1, x), (-1, y), (-1, z0)) for x, y, z0 in zip(v, u, linear(d, z))]) + need(inverse == sparse(source["forward"]["inverse_content_map"]), "Stored forward inverse") + need(linear(forward, inverse) == basis and linear(inverse, forward) == basis, "Forward inverse both orders") + inverse_adjoint = transpose(inverse, 224) + need(inverse_adjoint == sparse(source["dual"]["content_maps"]["inverse_adjoint"]), "Actual inverse transpose") + permutation = list(range(224)) + for p in selected: + permutation[p], permutation[112 + p] = 112 + p, p + conjugate = [{permutation[j]: value for j, value in inverse_adjoint[permutation[i]].items()} + for i in range(224)] + beta = [plus((1, x), (1, y)) for x, y in zip(z, linear(h, v))] + middle = [plus((1, x), (1, y), (-1, z0)) for x, y, z0 in zip(u, linear(d, z), v)] + backward = joined(beta, middle, [plus((-1, row)) for row in a], v) + need(backward == conjugate == sparse(source["dual"]["content_maps"]["selected_swap_conjugate"]), + "All 224 selected-swap inverse-adjoint columns") + return forward, backward + + +def abstract_check(): + """Keep H0,H1,H2,D0,D1,D2 free and preserve every product order.""" + a, u, z, v = [{(i, ()): F(1)} for i in range(4)] + + def op(name, row): + return {(source, (name,) + word): coefficient for (source, word), coefficient in row.items()} + + def forward(s, state): + ap, ur, zp, vr = state + alpha = plus((1, ap), (1, op("H" + str(s), ur))) + return [plus((-1, zp)), ur, alpha, + plus((1, vr), (1, ur), (1, op("D" + str(s), alpha)))] + + def backward(s, state): + ap, ur, zp, vr = state + return [plus((1, zp), (1, op("H" + str(s), vr))), + plus((1, ur), (1, op("D" + str(s), zp)), (-1, vr)), plus((-1, ap)), vr] + + first = forward(0, [a, u, z, v]) + second = backward(1, first) + endpoint = forward(2, second) + alpha = plus((1, a), (1, op("H0", u))) + k = plus((1, v), (1, u), (1, op("D0", alpha))) + w = plus((-1, v), (1, op("D1", alpha)), (-1, op("D0", alpha))) + beta = plus((1, alpha), (1, op("H1", k)), (1, op("H2", w))) + r = plus((1, u), (1, op("D1", alpha)), (1, op("D2", beta))) + need(first == [plus((-1, z)), u, alpha, k], "First stage endpoint") + need(second == [plus((1, alpha), (1, op("H1", k))), w, z, k], "Second stage endpoint") + need(endpoint == [plus((-1, z)), w, beta, r], "Third stage endpoint") + recovered_k = plus((1, r), (-1, op("D2", beta)), (-1, w)) + recovered_alpha = plus((1, beta), (-1, op("H1", recovered_k)), (-1, op("H2", w))) + recovered_u = plus((1, r), (-1, op("D1", recovered_alpha)), (-1, op("D2", beta))) + recovered_a = plus((1, recovered_alpha), (-1, op("H0", recovered_u))) + recovered_v = plus((-1, w), (1, op("D1", recovered_alpha)), (-1, op("D0", recovered_alpha))) + need([recovered_alpha, recovered_a, recovered_u, recovered_v] == [alpha, a, u, v], "Ordered content inverse") + state = list(endpoint) + trace = [list(state)] + # The first 96 positive lines change the ordinary Y frame to FULL. + state[3] = plus((1, state[3]), (-1, op("D2", state[2]))) + trace.append(list(state)) + state[2] = plus((1, state[2]), (-1, op("H1", state[3]))) + trace.append(list(state)) + state[2] = plus((1, state[2]), (1, op("H1", state[1])), (-1, op("H2", state[1]))) + trace.append(list(state)) + state[1] = plus((-1, state[1]), (1, op("D1", state[2])), (-1, op("D0", state[2]))) + trace.append(list(state)) + state[3] = plus((1, state[3]), (-1, op("D1", state[2]))) + trace.append(list(state)) + state[2] = plus((1, state[2]), (-1, op("H0", state[3]))) + trace.append(list(state)) + state[0] = plus((-1, state[0])) + trace.append(list(state)) + need(state == [z, v, a, u], "In-place terminal content and bank order") + # The final 112 positive lines restore Q(a,u) on Y. + def encode(rows): + return [[{"source_group": source, "word": list(word), "coefficient": str(value)} + for (source, word), value in sorted(row.items())] for row in rows] + return {"initial_groups": ["a", "u", "z", "v"], "first": encode(first), + "second": encode(second), "endpoint": encode(endpoint), + "terminal_trace_after_ordinary_Q": [encode(rows) for rows in trace], + "endpoint_holes": "Only Y_R has the exterior q_R.", + "operator_relations_used": "None between H_s and D_t; no inverse of I+H1 D2."} + + +def affine_product(left, right): + matrix, shift = left + other, translation = right + return compose(matrix, other), shift ^ act(matrix, translation) + + +def terminal_shear(matrix, source_fields, target_fields, stage, sign, views): + events = [] + if stage: + for field in source_fields + target_fields: + rho, shift = views[stage, field % 112] + events.append(["MAP", field, list(rho), shift]) + for i, row in enumerate(matrix): + for j, coefficient in sorted(row.items()): + events.append(["ADD", target_fields[i], source_fields[j], str(sign * coefficient)]) + if stage: + for field in target_fields + source_fields: + rho, shift = views[stage, field % 112] + events.append(["MAP", field, list(rho), shift]) + state = [{(j, UNIT, 0): F(1)} for j in range(224)] + invoice = Counter() + for event in events: + invoice[event[0]] += 1 + if event[0] == "MAP": + target, view = event[1], (tuple(event[2]), event[3]) + state[target] = {(source, new[0], new[1]): value + for (source, old, translation), value in state[target].items() + for new in [affine_product(view, (old, translation))]} + else: + target, source, coefficient = event[1], event[2], F(event[3]) + state[target] = plus((1, state[target]), (coefficient, state[source])) + invoice["scalar_units"] += add_price(coefficient) + expected = [{(j, UNIT, 0): F(1)} for j in range(224)] + for i, row in enumerate(matrix): + target = target_fields[i] + left = views[stage, target % 112] if stage else ID + for j, coefficient in row.items(): + source = source_fields[j] + right = views[stage, source % 112] if stage else ID + product = affine_product(left, right) + expected[target][source, product[0], product[1]] = sign * coefficient + need(state == expected, "Literal FULL shear on all 224 columns") + return events, dict(sorted(invoice.items())) + + +def write_json(path, value): + raw = (json.dumps(value, indent=2, sort_keys=True) + "\n").encode() + path.write_bytes(raw) + return digest(raw) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + parser.add_argument("--producer-run", default="run-terminal-normal") + args = parser.parse_args() + need(shutil.disk_usage(HERE).free >= 3 * 1024**3, "At least 3 GiB free") + args.out.mkdir(parents=True, exist_ok=False) + source, manifest = {}, {} + for name, (path, pin) in SOURCES.items(): + raw = path.read_bytes() + decoded = gzip.decompress(raw) if path.suffix == ".gz" else raw + need(digest(decoded) == pin, "Pinned source " + name) + manifest[name] = {"path": str(path), "sha256": digest(raw), "payload_sha256": pin} + source[name] = json.loads(decoded) + extra = { + "forward_proof": NATIVE / "clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md", + "dual_proof": NATIVE / "clean-late-exchange-20261020/CLEAN-DUAL.md", + "producer_proof": PRODUCER / "NO-RESET.md", + "producer_checker": PRODUCER / "check_no_reset.py", + "producer_phase_library": LANE / "coupled-data-split-20261020/check_typed_split.py", + "producer_checks": PRODUCER / args.producer_run / "CHECKS.json", + "producer_freeze": PRODUCER / "FREEZE.json", + } + for name, path in extra.items(): + pin = digest(path.read_bytes()) + if name in PRODUCER_PINS: + need(pin == PRODUCER_PINS[name], "Pinned " + name) + manifest[name] = {"path": str(path), "sha256": pin} + producer = json.loads(extra["producer_checks"].read_bytes()) + records = {(x["stage"], x["port"]): x for x in source["views"]["entries"]} + need(len(source["views"]["entries"]) == 336 and + set(records) == {(s, p) for s in range(3) for p in range(112)}, "Complete D25 view set") + p, r = source["row_code"]["selected_ports"], source["row_code"]["ordinary_ports"] + need(len(p) == 16 and len(r) == 96 and sorted(p + r) == list(range(112)), "Actual partition") + for name in ("forward", "dual"): + need(source[name]["selected_ports"] == p and source[name]["ports"] == source["row_code"]["ports"], + "Native selected set and port order") + need(source[name]["code"] == source["row_code"]["code"] and + source[name]["response"] == source["row_code"]["response"], "Native response and row-code equality") + q = [records[0, a]["q"] for a in range(112)] + need(q == source["row_code"]["ports"], "Actual route port labels") + c, e = sparse(source["row_code"]["code"]), sparse(source["row_code"]["response"]) + h = [{j: c[a][b] for j, b in enumerate(r) if b in c[a]} for a in p] + d = [{j: e[a][b] for j, b in enumerate(p) if b in e[a]} for a in r] + expected_c = eye(112) + for i, a in enumerate(p): + expected_c[a].update({r[j]: value for j, value in h[i].items()}) + need(c == expected_c, "C has the exact row-only form") + need(d == [{i: -value for i, value in row.items()} for row in transpose(h, 96)], "D=-H transpose") + dh = linear(d, h) + for i, a in enumerate(r): + expected = {p[j]: value for j, value in d[i].items()} + for j, value in dh[i].items(): + expected[r[j]] = value + expected = plus((1, expected), (1, {a: F(1)})) + need(expected == e[a], "Actual ordinary response row is u+D(a+Hu)") + source_matrix_checks(source, p, r, h, d) + invoices = {} + for name in ("forward", "dual"): + for provider, variants in source[name]["providers"].items(): + for variant, item in variants.items(): + bill = local_invoice(item) + need(bill["real_scalar_primitives"] == 8600 and bill["native_children"] == 1520, + "Native scalar and child counts") + expected_profile = {1: 1392, 2: 64, 3: 48, 9 if variant == "I" else 8: 16} + need(bill["profile"] == expected_profile, "Native profile") + invoices[name + ":" + provider + ":" + variant] = bill + views, counts, certificates = {}, Counter(), [] + identity_normal = normal([]) + for s in range(3): + for a in range(112): + row = records[s, a] + matrix = tuple(row["route_columns"]) + need(row["q"] == q[a] and act(matrix, q[a]) == q[a], "Route fixes the matching line") + need(compose(matrix, matrix) == UNIT and + all(transposed(matrix, matrix[j]) == (1 << j) for j in range(25)), + "Orthogonal involution") + if s == 0: + need(matrix == UNIT, "Stage zero route") + continue + alignment = row["literal_stage_alignment"] + need(alignment["entry_X"] == alignment["entry_Y"] and + alignment["exit_X"] == alignment["exit_Y"], "Matched physical bank views") + delta = act(matrix, alignment["entry_X"]) + entry = line(delta, 2) + route(matrix) + exit_view = line(alignment["exit_X"], 2) + route(matrix) + fprev = fourier(0, 9 + 8 * (s - 1)) + fnext = fourier(0, 9 + 8 * s) + fext = fourier(9, 9 + 8 * s) + checks = [ + (entry + fprev, fext + line(q[a], 1) + route(matrix)), + (entry + fprev + line(q[a], -1), fext + route(matrix)), + (exit_view + fnext, fnext + route(matrix)), + (exit_view + fnext + line(q[a], -1), fnext + line(q[a], -1) + route(matrix)), + ] + for left, right in checks: + need(normal(left) == normal(right), "Natural mixed frame identity") + counts["natural_frame_identities"] += 1 + full_result = normal(exit_view + fourier(0, 25)) + need(full_result == normal(fourier(0, 25) + route(matrix)), "Past FULL view") + need(normal(exit_view + exit_view) == identity_normal, "Physical FULL view is an involution") + need(normal(exit_view + line(q[a], 1)) == normal(line(q[a], 1) + exit_view), "View commutes with its own Q") + counts["past_FULL_views"] += 1 + counts["physical_view_inverse_orders"] += 1 + counts["omitted_entry_translation_rejected"] += normal(route(matrix) + fprev) != normal(checks[0][1]) + if a in r: + counts["ordinary_Y_wrong_FULL_type_rejected"] += normal(entry + fprev) != normal(fext + route(matrix)) + view = matrix, alignment["exit_X"] + views[s, a] = view + certificates.append({"stage": s, "port": a, "entry_translation_after_route": delta, + "FULL_translation_after_route": alignment["exit_X"], + "route_columns": list(matrix), "FULL_input_character_normal": full_result}) + full = fourier(0, 25) + for a in range(112): + need(normal(line(q[a], 1) + full) == normal(full + line(q[a], 1)), + "Positive final line preserves the common FULL exterior") + counts["terminal_positive_line_frame_checks"] += 1 + if a in r: + need(normal(line(q[a], 1) + full + line(q[a], -1)) == normal(full), + "Positive ordinary line removes its hole") + counts["terminal_positive_line_frame_checks"] += 1 + counts["negative_ordinary_line_rejected"] += ( + normal(line(q[a], -1) + full + line(q[a], -1)) != normal(full)) + abstract = abstract_check() + xp, xr = p, r + yp, yr = [112 + a for a in p], [112 + a for a in r] + specs = [ + ("minus_D2", d, yp, yr, 2, -1), + ("minus_H1", h, yr, yp, 1, -1), + ("plus_H1_W", h, xr, yp, 1, 1), + ("minus_H2_W", h, xr, yp, 2, -1), + ("plus_D1_alpha", d, yp, xr, 1, 1), + ("minus_D0_alpha", d, yp, xr, 0, -1), + ("minus_D1_alpha", d, yp, yr, 1, -1), + ("minus_H0", h, yr, yp, 0, -1), + ] + word = [["LINE", field, q[field % 112], 1] for field in yr] + shear_invoices = {} + for index, (name, matrix, sources, targets, stage, sign) in enumerate(specs): + if index == 4: + word.extend([["NEG", field] for field in xr]) + events, bill = terminal_shear(matrix, sources, targets, stage, F(sign), views) + word.extend(events) + shear_invoices[name] = bill + word.extend([["NEG", field] for field in xp]) + word.extend([["LINE", 112 + a, q[a], 1] for a in range(112)]) + word_counts = Counter(event[0] for event in word) + need(word_counts == {"LINE": 208, "MAP": 1344, "ADD": 1728, "NEG": 112}, "Literal terminal counts") + scalar = sum(bill["scalar_units"] for bill in shear_invoices.values()) + 2 * word_counts["NEG"] + need(scalar == 16608 and all(bill["scalar_units"] == 2048 for bill in shear_invoices.values()), + "Actual terminal scalar count") + need(producer["status"] == "PASS_ACTUAL_D25_NATURAL_CLEAN_TRIPLE", "Completed producer receipt") + need(producer["literal_route_phase_identities"] == counts["natural_frame_identities"] == 896, + "Producer route count") + need(producer["terminal_operator_word"]["positive_line_operations"] == 208 and + producer["terminal_operator_word"]["direct_scalar_upper_bound"] == scalar and + producer["terminal_operator_word"]["routed_shear_affine_map_calls"] == 1344, + "Producer terminal invoice") + for variant in ("I", "Q"): + need(producer["variants"][variant]["content_inverse"] == "PASS" and + producer["variants"][variant]["checked_arbitrary_columns"] == 224, "Completed producer variants") + need(producer["variants"]["I"]["208_line_terminal_checked"], "Producer terminal passed") + need(producer["local_native_mass_initial_I"] == 1808 + 2 * 1792 == 5392 and + producer["local_scalar_initial_I"] == 3 * 8600 == 25800, "Producer local sum") + need(all(digest(Path(item["path"]).read_bytes()) == item["sha256"] for item in manifest.values()), + "Every source remains unchanged") + pins = { + "SOURCE-MANIFEST.json": write_json(args.out / "SOURCE-MANIFEST.json", manifest), + "FRAME-CERTIFICATE.json": write_json(args.out / "FRAME-CERTIFICATE.json", certificates), + "BLOCK-PROOF.json": write_json(args.out / "BLOCK-PROOF.json", abstract), + "TERMINAL-WORD.json": write_json(args.out / "TERMINAL-WORD.json", word), + } + receipt = { + "status": "PASS_INDEPENDENT_NATURAL_TRIPLE_REVIEW", + "output_sha256": pins, + "phase_checks": dict(sorted(counts.items())), + "local_content_columns": 224, + "local_inverse_both_orders": True, + "inverse_adjoint_and_selected_swap_verified": True, + "global_operator_proof": "Four-block free-operator composition plus exact natural-frame conjugation.", + "expanded_global_column_replay_repeated": False, + "H_coefficient_histogram": dict(sorted(Counter(str(x) for row in h for x in row.values()).items())), + "local_invoices_from_literal_events": invoices, + "terminal_counts": dict(sorted(word_counts.items())), + "terminal_scalar_units": scalar, + "terminal_shear_invoices": shear_invoices, + "terminal_local_shear_columns": 224, + "terminal_output": "X=F25 Y0, Y=F25 X0 for initial selected I entry.", + "extra_selected_Q_entry_restoration_lines": 16, + "new_fields": 0, + "odd_divisions": 0, + "native_line_recipes_or_global_host_supplied": False, + "complete_supplier_or_kappa_claim": False, + } + write_json(args.out / "CHECKS.json", receipt) + print(receipt["status"]) + print(json.dumps({"phase_checks": receipt["phase_checks"], "terminal_counts": receipt["terminal_counts"], + "scalar_units": scalar}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/BLOCK-PROOF.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/BLOCK-PROOF.json new file mode 100644 index 0000000000..b04154137d --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/BLOCK-PROOF.json @@ -0,0 +1,428 @@ +{ + "Q_reader_commutation_not_used": true, + "before_final_shears_under_F25": [ + [ + { + "coefficient": "-1", + "source_group": 2, + "word": [] + } + ], + [ + { + "coefficient": "-1", + "source_group": 3, + "word": [ + [ + "Q", + 3 + ] + ] + } + ], + [ + { + "coefficient": "1", + "source_group": 0, + 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121, + 122, + 123, + 124, + 125, + 126, + 127, + 128, + 131, + 133, + 134, + 137, + 138, + 140, + 141, + 142, + 143, + 144, + 145, + 146, + 147, + 149, + 150, + 151, + 152, + 153, + 154, + 155, + 156, + 157, + 159, + 160, + 161, + 162, + 163, + 164, + 165, + 166, + 167, + 168, + 170, + 171, + 172, + 173, + 174, + 175, + 176, + 177, + 178, + 179, + 180, + 181, + 182, + 183, + 184, + 185, + 186, + 187, + 188, + 189, + 190, + 191, + 192, + 193, + 194, + 195, + 196, + 197, + 198, + 199, + 200, + 201, + 202, + 203, + 204, + 205, + 206, + 207, + 208, + 209, + 210, + 211, + 212, + 213, + 214, + 215, + 216, + 217, + 218, + 219, + 220, + 221, + 222 + ], + "target_fields": [ + 112, + 139, + 148, + 223, + 132, + 119, + 169, + 158, + 113, + 115, + 118, + 120, + 129, + 130, + 136, + 135 + ] + } +] diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/REVIEW.md new file mode 100644 index 0000000000..b2e1d0f101 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/REVIEW.md @@ -0,0 +1,276 @@ +# Independent review of the actual phase-coded triple + +The stated physical endpoint is correct. The three FULL shears give + +```text +X = -F25 q Y0, Y = F25 q X0 +``` + +for Q entry on the selected borrowed fields. For initial I entry, only +the sixteen selected X outputs omit q. There is no material local +finding. The residual q is an actual operator. This review does not +admit it as a free terminal or a recursive input type. + +The review binds the producer proof with SHA256 +`5eb5eba5d3bed38faf9e411ca4a9a6f8e67765966011e93dec96f2300613756f`, +the producer freeze with SHA256 +`0ee32fe22f42cffce2a9673f0dc95496a4b4bb8b11a534f77a11f5fe9c7aeb4b`, +and the completed producer receipt with SHA256 +`44a1c03836ba47af92965dc7d2bb716d0f94d03dd54cb3122eeaa9f1d08a3cc3`. +The local controller freeze has SHA256 +`284e6239ae3287bb139497fe610e67def239ad50697f230b61ac7c7280fb4b75`. +`SOURCE-MANIFEST.json` gives all exact paths and source hashes. + +The checker imports only the frozen independent phase engine from +the preceding owner review. It imports no producer checker. It does +not repeat the native 640-column transcript or the producer's expanded +global matrix. Instead, it checks the local data matrices, proves the +ordered block composition, and checks the actual D25 frame identities. + +## Binding to the stored local maps + +The ordered selected set P has sixteen ports: + +```text +[0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23]. +``` + +R is the sorted complement of 96 ports. The local source and the actual +row-code source have the same selected set, ordinary set, and code. +The line labels agree with the D25 view source. From those matrices, +the checker obtains + +```text +C = [[I,H],[0,I]], D = -H^T. +``` + +It reconstructs all 224 independent data columns of the zero-transfer +forward body: + +```text +F_zero(a,u,z,v) = (-z,u,a+H u,v). +``` + +It derives the inverse, checks both inverse product orders, and takes +its transpose with the actual selected-wire conjugation. This gives +all stored columns of + +```text +B_zero(a,u,z,v) = (z,u+D z,-a,v). +``` + +The physical forward prefix is `Y_R += X_R`, before every input +adapter. Since physical X has type Q and ordinary Y has type I, +this adds `Q_R u` to v. The backward prefix is `X_R -= Y_R`; +it changes u to `u-q_R v`. Composition with the two zero bodies gives +the stored operator rows + +```text +F_Q(a,u,z,v) = (-z,u,a+H u,v+Q_R u), +B_Q(a,u,z,v) = (z,u+D z-q_R v,-a,v). +``` + +All 224 rows and columns agree exactly with the serialized maps. Each +of the 96 nonconstant line terms remains attached to its original +input port. The checker does not replace Q or q by a scalar. + +The native source receipt checks both providers, all 640 independent +local inputs, and all 416 arbitrary helper returns. This review binds +that receipt and all files in its freeze. Native helper restoration is +an inherited premise, not a second native replay. + +## Literal route and phase proof + +Let `G_s=diag(rho_s,p)` contain only the orthogonal routes. Every actual +route is an involution and fixes its own q_p. All local line labels +lie in the root nine axes. The literal physical views are + +```text +Ventry_s,p = T_(rho_s,p(entry_X)) rho_s,p, +Vexit_s,p = T_(exit_X) rho_s,p. +``` + +The X and Y translations agree. At each port of stages 1 and 2, the +checker verifies these six identities: + +```text +Ventry_s Fprev_s = Fext_s Q G_s, +Ventry_s Fprev_s q = Fext_s G_s, +Vexit_s Fnext_s = Fnext_s G_s, +Vexit_s Fnext_s q = Fnext_s q G_s, +Vexit_s F25 = F25 G_s, +Vexit_s Vexit_s = I. +``` + +There are 1,344 identities. The checker applies each word from right +to left and records phases in the input-character coordinates. For +binary x, a parity has the exact expansion + +```text +parity(v dot x) = +sum_i v_i x_i - 2 sum_(i= 112 or port in r or variant == "Q" + row = full + (line(q[port], -1) if hole else []) + corrected = (line(q[port], 1) if field in line_fields else []) + row + need(normal(corrected) == normal(full), "Every terminal physical phase") + if hole: + need(normal(row) != normal(full), "Remaining q is not a free identity") + signed_rows.append({"output": field, "input": (field + 112) % 224, + "sign": -1 if field < 112 else 1, "has_q": hole}) + need(len(line_fields) == (208 if variant == "I" else 224), "Terminal positive-line count") + terminal[variant] = {"positive_line_fields": line_fields, "shortened_physical_rows": signed_rows} + return q, views, certificates, dict(counts), terminal + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + need(shutil.disk_usage(HERE).free >= 3 * 1024**3, "At least 3 GiB free") + args.out.mkdir(parents=True, exist_ok=False) + source, manifest = {}, {} + for name, (path, pin) in PINS.items(): + raw = path.read_bytes() + payload = gzip.decompress(raw) if path.suffix == ".gz" else raw + need(digest(payload) == pin, "Pinned " + name) + manifest[name] = {"path": str(path), "sha256": digest(raw), "payload_sha256": pin} + if path.suffix in (".json", ".gz"): + source[name] = json.loads(payload) + for key, directory in (("local_freeze", CONTROLLER), ("producer_freeze", PRODUCER)): + for relative, pin in source[key]["files"].items(): + path = directory / relative + need(digest(path.read_bytes()) == pin, "Every frozen file " + relative) + manifest[key + ":" + relative] = {"path": str(path), "sha256": pin} + code, local = source["row_code"], source["local"] + p, r = code["selected_ports"], code["ordinary_ports"] + need(p == [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23] and + r == sorted(set(range(112)) - set(p)), "Actual ordered partition") + need(p == local["selected_ports"] and r == local["ordinary_ports"] and local["code"] == code["code"], + "Native row-code source equality") + c, e = sparse(code["code"]), sparse(code["response"]) + h = [{j: c[a][b] for j, b in enumerate(r) if b in c[a]} for a in p] + d = [{j: e[a][b] for j, b in enumerate(p) if b in e[a]} for a in r] + expected = engine.eye(112) + for i, a in enumerate(p): + expected[a].update({r[j]: value for j, value in h[i].items()}) + need(c == expected and d == [{i: -value for i, value in row.items()} + for row in engine.transpose(h, 96)], "Actual H and D=-H transpose") + local_result = local_rows(local, p, r, h, d) + invoices = {} + for provider, variants in local["providers"].items(): + for variant, item in variants.items(): + bill = engine.local_invoice(item["body"]) + prefix = ([["add", a, 112 + a, "-1"] for a in r] if variant == "backward_Q" else + [["add", 112 + a, a, "1"] for a in r]) + need(item["physical_prefix"] == prefix, "All physical entry ADDs") + need(item["prefix_location"] == "Before every inherited input adapter.", "Physical prefix position") + expected_profile = {1: 1392, 2: 64, 3: 48, 9 if variant == "forward_I" else 8: 16} + need(bill["profile"] == expected_profile and bill["native_children"] == 1520 and + bill["real_scalar_primitives"] == 3864, "Literal local invoice") + bill["physical_prefix_scalar_units"] = sum(engine.add_price(F(gate[3])) for gate in prefix) + bill["complete_scalar_units"] = bill["real_scalar_primitives"] + bill["physical_prefix_scalar_units"] + need(bill["complete_scalar_units"] == 4632, "Complete scalar invoice") + bill["explicit_input_views"] = len(item["body"]["input_views"]) + bill["explicit_output_views"] = len(item["body"]["output_views"]) + need(bill["explicit_input_views"] == (112 if variant == "forward_I" else 128) and + bill["explicit_output_views"] == 96, "Literal endpoint adapter count") + report = source["local_checks"]["reports"][provider][variant] + need(bill["native_mass"] == report["native_mass"] and + bill["complete_scalar_units"] == report["complete_scalar_primitives"] and + bill["explicit_input_views"] == report["explicit_input_monomial_views"] and + bill["explicit_output_views"] == report["explicit_output_monomial_views"], + "Local receipt agrees") + need(report["unchanged_arbitrary_helpers"] == 416 and report["all_independent_input_fields"] == 640, + "Inherited native replay contract") + if variant != "backward_Q": + need(len(item["removed_transfers"]) == 592, "Deleted transfer count") + invoices[provider + ":" + variant] = bill + q, views, certificate, phase_counts, terminal = frame_proof(source["views"], p, r) + need(q == code["ports"], "Actual phase labels and row-code ports agree") + blocks = block_proof() + specs = [ + ("middle_D1_after_complete_stage1_sweep", d, p, r, 1, 17), + ("final_H2", h, r, [112 + a for a in p], 2, 25), + ("final_H0", h, [112 + a for a in r], [112 + a for a in p], 0, 25), + ] + shears, shear_counts = [], Counter() + for name, matrix, sources, targets, stage, full_dimension in specs: + events, bill = engine.terminal_shear(matrix, sources, targets, stage, F(-1), views) + need(bill["ADD"] == 216 and bill["scalar_units"] == 2048, "Exact direct coefficient cost") + shear_counts.update(bill) + shears.append({"name": name, "input_and_output_frame": "F" + str(full_dimension), + "source_fields": sources, "target_fields": targets, "events": events, + "checked_arbitrary_columns": 224, "invoice": bill}) + need(shear_counts == {"ADD": 648, "MAP": 448, "scalar_units": 6144}, "Three-shear total") + producer = source["producer_checks"] + need(producer["status"] == "PASS_ACTUAL_D25_PHASE_CODED_TRIPLE" and + producer["phase_identities"] == phase_counts["phase_identities"] == 1344, + "Completed physical producer receipt") + variants = {} + for kind in ("I", "Q"): + keys = ["forward_" + kind, "backward_Q", "forward_Q"] + selected = [invoices["base:" + key] for key in keys] + profile = Counter() + for bill in selected: + profile.update(bill["profile"]) + mass = sum(rank * count for rank, count in profile.items()) + positive_lines = len(terminal[kind]["positive_line_fields"]) + profile[1] += positive_lines + need(mass + positive_lines == sum(rank * count for rank, count in profile.items()) == 5600, + "Complete direct-terminal native mass") + need(producer["variants"][kind]["native_mass_before_terminal"] == mass and + producer["variants"][kind]["direct_terminal_positive_lines"] == positive_lines and + producer["variants"][kind]["native_mass_with_direct_terminal"] == 5600, + "Producer native invoice agrees") + variants[kind] = {"native_mass_before_terminal": mass, "positive_terminal_lines": positive_lines, + "complete_native_mass": 5600, "complete_native_profile": dict(sorted(profile.items())), + "local_scalar_units": sum(bill["complete_scalar_units"] for bill in selected), + "local_explicit_endpoint_views": sum(bill["explicit_input_views"] + + bill["explicit_output_views"] for bill in selected), + "added_shear_affine_maps": shear_counts["MAP"], + "scalar_units_with_three_shears": 20040, + "extra_scalar_units_for_unsigned_X": 224} + need(variants[kind]["local_scalar_units"] + shear_counts["scalar_units"] == 20040, + "Scalar subtotal before terminal wrappers") + need(all(digest(Path(item["path"]).read_bytes()) == item["sha256"] for item in manifest.values()), + "Every source remains unchanged") + outputs = { + "SOURCE-MANIFEST.json": manifest, + "FRAME-CERTIFICATE.json": certificate, + "BLOCK-PROOF.json": blocks, + "FULL-SHEARS.json": shears, + "TERMINAL-PHASES.json": terminal, + } + pins = {name: write_json(args.out / name, value) for name, value in outputs.items()} + receipt = {"status": "PASS_INDEPENDENT_PHASE_CODED_TRIPLE_REVIEW", "output_sha256": pins, + "phase_checks": phase_counts, "local_rows": local_result, + "literal_local_invoices": invoices, "three_FULL_shears": dict(shear_counts), + "variants": variants, "native_640_column_replay_repeated": False, + "producer_sparse_global_replay_repeated": False, + "middle_boundary": "After the full stage-1 sweep and all local helper returns.", + "remaining_obligations": ["global owner hosting", "map stream and address cost", + "terminal line hosting and wrappers", "recursive common-q matching", + "complete numerical precision proof"], + "new_owned_fields": 0, "odd_divisions": 0, "kappa_claim": False} + write_json(args.out / "CHECKS.json", receipt) + print(receipt["status"]) + print(json.dumps({"phases": phase_counts, "shears": dict(shear_counts), "variants": variants}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/phase-coded-triple-review-20261020/final-normal/BLOCK-PROOF.json 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a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/BINDING.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/BINDING.md new file mode 100644 index 0000000000..1309a0e306 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/BINDING.md @@ -0,0 +1,109 @@ +# Final binding of the corrected D25 closure proof + +The corrected producer proof passes this review. Its representation +argument has no remaining gap within the stated scalar-code class. +Logical monomial closure requires f at least 2. Physical affine +closure and the Q-commutation criterion require f at least 3. +The result does not give a native decoder lower bound. + +This binding preserves the standalone review freeze +`b3fc9ddc6fdc4cc6c2226b3b9fa101abdb21d22e50ceb3d6c9cefa9280062deb`. +The final producer pins are: + +```text +CLOSURE.md +63c0deeb7e13b359ca410dfb085e1a89866aa87383d6bd1cec02cba688a4ce3e + +check_closure.py +45d1e215c4dc6f7735deaed0d9df57cf3efa83a0bc4e354c43375187cbe7f01e + +bound-normal/CHECKS.json +f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a +``` + +The checker imports only the frozen independent review module. It +imports no producer module. It compares all corrected producer +artifacts with their optimized copies. It then: + +- Applies the four literal affine views, in order, to all 12,544 + three-column common inputs and compares their stored outputs. +- Reconstructs both nonzero Gaussian coefficients and both output + tuples in each of the 896 monomial-obstruction witnesses. +- Matches all 896 character witnesses to the independent review, + then computes each literal affine sign and complete nonzero + commutator coefficient. +- Compares all eight exact route-support profiles. + +## Cover lift and action convention + +Let L map a spatial function g to + +```text +(L g)(d,z) = g(d^-1 z). +``` + +The same d acts on every spatial column. This map is injective: +evaluation at the identity owner recovers g. For the stated owner +view, substitution gives + +```text +M_(h,delta) Lg(d,z) + = Lg(dh,z+d delta) + = g(h^-1(d^-1 z+delta)) + = L(T_delta P_h g)(d,z). +``` + +Here `P_h g(x)=g(h^-1 x)` and `T_delta g(x)=g(x+delta)`. +These are exactly the function forms of the stated position +convention. No inverse order is changed. + +A translation by the owner-dependent line d q_p gives +`g(d^-1 z+q_p)`. Therefore the intrinsic Q at that owner also +intertwines with the spatial Q_p. Scalar port matrices preserve +the lifted subspace. Spatial non-equality thus gives non-equality +on the declared arbitrary-input cover. + +## Why a cover monomial would induce a spatial monomial + +A covariant point basis function has one nonzero coordinate at +each owner. Its support has size |G|. These supports, including +the input-port label, are pairwise disjoint and partition the +full coordinate set. + +A full-coordinate monomial is a weighted coordinate permutation +with all weights nonzero. It preserves support size. If it +preserves the covariant subspace, the image of one covariant +point basis function must be a union of complete fibers, each +with size |G|. Its support size is still |G|, so that union +contains exactly one fiber. The induced spatial operator sends +each basis vector to a nonzero multiple of one basis vector. +Its invertibility makes it monomial. + +This is the needed justification for restriction to the covariant +subspace. Invariance alone would not justify a general statement +about monomiality on an arbitrary subspace. + +The corrected coordinate row/column argument also passes. Two +paths in one p,k block give two outputs from one input basis +coordinate. If two terms instead lie in distinct input-port +blocks, each affine term is a bijection onto the entire output +fiber. Every output coordinate in that port has two input +coordinates. Either case contradicts full-coordinate monomiality. + +## Verification and limits + +Both commands return `PASS_CORRECTED_PRODUCER_BINDING`: + +```text +python3 -B check_binding.py --out run-normal +python3 -O -B check_binding.py --out run-optimized +``` + +Their two JSON outputs are byte-identical. Source hashes are +checked again at the end. No frozen source is changed. + +No native word, recursive host, implementation cost, precision +bound, or complete supplier is certified here. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. +No PR, commit, push, or publication is authorized. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/CHECKS.json new file mode 100644 index 0000000000..1cb28a6314 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/CHECKS.json @@ -0,0 +1,13 @@ +{ + "basis_column_witnesses_checked": 896, + "cover_lift_and_monomial_restriction": "Proved in BINDING.md.", + "general_decoder_lower_bound": false, + "literal_affine_paths_checked": 12544, + "native_word_replayed": false, + "physical_commutator_witnesses_checked": 896, + "producer_checker_sha256": "45d1e215c4dc6f7735deaed0d9df57cf3efa83a0bc4e354c43375187cbe7f01e", + "producer_proof_sha256": "63c0deeb7e13b359ca410dfb085e1a89866aa87383d6bd1cec02cba688a4ce3e", + "producer_receipt_sha256": "f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a", + "source_manifest_sha256": "bd7ec4f2cdd05167beba7459fa58cc790e95ea9770d17c716f21c909520c1271", + "status": "PASS_CORRECTED_PRODUCER_BINDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/FREEZE.json new file mode 100644 index 0000000000..bc058c5472 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/FREEZE.json @@ -0,0 +1,15 @@ +{ + "files": { + "BINDING.md": "3fb52ed0a563e2e4cb16f773f55f546284ceb6b77406444873bdf34db9569edf", + "CHECKS.json": "11576d3cdc4163ea49bc7b98a6879173d31f70979ef42a707f2d1ea69303cfcf", + "SOURCE-MANIFEST.json": "bd7ec4f2cdd05167beba7459fa58cc790e95ea9770d17c716f21c909520c1271", + "check_binding.py": "363740ef56dab003785b38a7da1c45f50440520b99c9f8722564b9ccf4795089", + "run-normal/CHECKS.json": "11576d3cdc4163ea49bc7b98a6879173d31f70979ef42a707f2d1ea69303cfcf", + "run-normal/SOURCE-MANIFEST.json": "bd7ec4f2cdd05167beba7459fa58cc790e95ea9770d17c716f21c909520c1271", + "run-optimized/CHECKS.json": "11576d3cdc4163ea49bc7b98a6879173d31f70979ef42a707f2d1ea69303cfcf", + "run-optimized/SOURCE-MANIFEST.json": "bd7ec4f2cdd05167beba7459fa58cc790e95ea9770d17c716f21c909520c1271" + }, + "normal_optimized_byte_identical": true, + "scope": "Corrected D25 scalar-code closure proof, covariant cover lift, coordinate monomial argument, all12544 affine paths and1792 exact witnesses. No native lower bound or supplier.", + "status": "FROZEN_FINAL_PRODUCER_BINDING_PASS" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/SOURCE-MANIFEST.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..3fad6465a7 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/SOURCE-MANIFEST.json @@ -0,0 +1,27 @@ +{ + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + 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"/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/unitary-v2-normal/UNITARY-COMPLETION.json.gz": "ab0b61e8e1f530769b6e2f70c1d37798b23f0d5ccb2ea2f6a905bf235938ae58" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/check_binding.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/check_binding.py new file mode 100644 index 0000000000..c3f36c0c81 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/check_binding.py @@ -0,0 +1,156 @@ +"""Bind the corrected producer and check its finite affine witnesses.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +REVIEW = HERE.parent / "unitary-code-closure-review-20261020" +PRODUCER = HERE.parents[1] / "unitary-code-closure-20261020" +PINS = { + REVIEW / "FREEZE.json": "b3fc9ddc6fdc4cc6c2226b3b9fa101abdb21d22e50ceb3d6c9cefa9280062deb", + REVIEW / "check_review.py": "c86a3655dcc6104be95845422a97407e0c389f1cac83c504d25b10cac7c7de03", + PRODUCER / "CLOSURE.md": "63c0deeb7e13b359ca410dfb085e1a89866aa87383d6bd1cec02cba688a4ce3e", + PRODUCER / "check_closure.py": "45d1e215c4dc6f7735deaed0d9df57cf3efa83a0bc4e354c43375187cbe7f01e", + PRODUCER / "bound-normal/CHECKS.json": "f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a", + PRODUCER / "bound-normal/PATH-SIGNATURES.json.gz": "053b09b693cef52a33b7f15ccb0c5697466bd123f3b4e0bbb0318fe2e674ed46", + PRODUCER / "bound-normal/WIDTH-THREE-WITNESSES.json.gz": "09f5ba960ecf9eb965e1ccb94848fcbc36e1d68319502b9378d94c27a7401eca", +} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def digest(raw): + return sha256(raw).hexdigest() + + +def write_json(path, value): + raw = (json.dumps(value, indent=2, sort_keys=True) + "\n").encode() + path.write_bytes(raw) + return digest(raw) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + manifest = {} + + def read(path, pin=None): + raw = path.read_bytes() + if pin is not None: + need(digest(raw) == pin, "Pinned file " + path.name) + manifest[str(path)] = digest(raw) + return raw + + for path, pin in PINS.items(): + read(path, pin) + freeze = json.loads((REVIEW / "FREEZE.json").read_bytes()) + for relative, pin in freeze["files"].items(): + read(REVIEW / relative, pin) + spec = importlib.util.spec_from_file_location("independent_representation_review", REVIEW / "check_review.py") + lib = importlib.util.module_from_spec(spec) + spec.loader.exec_module(lib) + ours = json.loads((REVIEW / "CHECKS.json").read_bytes()) + our_witnesses = json.loads((REVIEW / "COMMUTATOR-WITNESSES.json").read_bytes()) + our_witnesses = {("/".join(w["variant"]), w["output_port"]): w for w in our_witnesses} + our_signatures = json.loads((REVIEW / "TWO-TAG-SIGNATURES.json").read_bytes()) + source = {} + for name, (path, pin) in lib.PINS.items(): + raw = read(path) + decoded = gzip.decompress(raw) if path.suffix == ".gz" else raw + need(digest(decoded) == pin, "Exact source payload") + source[name] = json.loads(decoded) + data = {} + for name in ("CHECKS.json", "PATH-SIGNATURES.json.gz", "WIDTH-THREE-WITNESSES.json.gz"): + raw = read(PRODUCER / "bound-normal" / name) + need(raw == read(PRODUCER / "bound-optimized" / name), "Normal and optimized producer bytes") + data[name] = json.loads(gzip.decompress(raw) if name.endswith(".gz") else raw) + report = data["CHECKS.json"] + need(report["checker_sha256"] == PINS[PRODUCER / "check_closure.py"] and + report["status"] == "PASS_ACTUAL_FRESH_STAGE_PATH_SEPARATION", "Completed corrected producer") + paths = data["PATH-SIGNATURES.json.gz"] + need([row[:4] for row in paths] == our_signatures, "Every route signature agrees with the independent proof") + records = {(row["stage"], row["port"]): row for row in source["views"]["entries"]} + rho = {key: row["route_columns"] for key, row in records.items()} + delta = {key: row["literal_stage_alignment"]["exit_X"] for key, row in records.items() if key[0]} + + def point(p, j, r, value, include_outer=True): + stages = [(1, r), (1, j), (2, j)] + ([(2, p)] if include_outer else []) + for key in stages: + value = lib.act(rho[key], value) ^ delta[key] + return value + + for j, r, image2, image1, inner_shift, outputs in paths: + need(inner_shift == point(0, j, r, 0, False), "Inner affine translation") + need(outputs == [point(0, j, r, x) for x in (0, lib.E2, lib.E1)], + "Literal ordered affine path on the common input") + need(len(paths) == 12544 and report["single_physical_input_affine_outputs"] == 12544, + "All physical paths") + families = {"C": lib.sparse(source["unitary"]["code"]), + "Cstar": lib.sparse(source["unitary"]["inverse_and_adjoint"])} + witnesses = data["WIDTH-THREE-WITNESSES.json.gz"] + for witness in witnesses["basis_witnesses"]: + p, k = witness["output_port"], witness["input_port"] + c0, c1, c2 = [families[name] for name in witness["variant"].split("/")] + need(witness["input_columns"] == [0, lib.E2, lib.E1], "Common physical basis input") + need(len(witness["outputs"]) == 2, "Two selected nonzero outputs") + for item in witness["outputs"]: + j, r = item["path"] + coefficient = lib.mul(c2[p][j], lib.mul(c1[j][r], c0[r][k])) + need(tuple(map(F, item["coefficient"])) == coefficient != lib.ZERO, "Actual Gaussian path coefficient") + need(item["output"] == [point(p, j, r, x) for x in witness["input_columns"]], + "Actual physical output coordinates") + need(witness["outputs"][0]["output"] != witness["outputs"][1]["output"], "Distinct output coordinates") + powers = (lib.ONE, (F(0), F(1)), (F(-1), F(0)), (F(0), F(-1))) + for witness in witnesses["commutator_witnesses"]: + own = our_witnesses[witness["variant"], witness["output_port"]] + pairs = {"input_port": "input_port", "path": "intermediate_ports", "coefficient": "coefficient", + "input_characters": "input_characters", "output_characters": "output_characters", + "output_line_pulled": "pulled_output_line", + "output_exponent": "left_i_power", "input_exponent": "right_i_power"} + need(all(witness[a] == own[b] for a, b in pairs.items()), "Independent commutator witness agrees") + p = witness["output_port"] + j, r = witness["path"] + shift = point(p, j, r, 0) + sign = (-1) ** sum(lib.dot(shift, x) for x in witness["output_characters"]) + difference = lib.add(powers[witness["output_exponent"]], + tuple(-x for x in powers[witness["input_exponent"]])) + coefficient = lib.mul(tuple(map(F, witness["coefficient"])), lib.mul((F(sign), F(0)), difference)) + need(witness["affine_shift"] == shift and witness["affine_sign"] == sign and + tuple(map(F, witness["physical_commutator_coefficient"])) == coefficient != lib.ZERO, + "Literal affine commutator coefficient") + need(len(witnesses["basis_witnesses"]) == len(witnesses["commutator_witnesses"]) == 896, + "All eight variants and every output row") + for variant, profile in report["routed_variant_profiles"].items(): + need(profile["operator_terms"] == ours["actual_profiles"][variant]["total_terms"] and + profile["row_term_histogram"] == ours["actual_profiles"][variant]["row_term_histogram"], + "Exact support profile agreement") + need(report["logical_path_separation_minimum_width"] == 2 and + report["physical_path_and_commutator_minimum_width"] == 3, "Exact width limits") + need(all(digest(Path(path).read_bytes()) == pin for path, pin in manifest.items()), "All files unchanged") + pin = write_json(args.out / "SOURCE-MANIFEST.json", manifest) + receipt = {"status": "PASS_CORRECTED_PRODUCER_BINDING", "source_manifest_sha256": pin, + "producer_proof_sha256": PINS[PRODUCER / "CLOSURE.md"], + "producer_checker_sha256": PINS[PRODUCER / "check_closure.py"], + "producer_receipt_sha256": manifest[str(PRODUCER / "bound-normal/CHECKS.json")], + "literal_affine_paths_checked": len(paths), + "basis_column_witnesses_checked": len(witnesses["basis_witnesses"]), + "physical_commutator_witnesses_checked": len(witnesses["commutator_witnesses"]), + "cover_lift_and_monomial_restriction": "Proved in BINDING.md.", + "native_word_replayed": False, "general_decoder_lower_bound": False} + write_json(args.out / "CHECKS.json", receipt) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/run-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..1cb28a6314 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/run-normal/CHECKS.json @@ -0,0 +1,13 @@ +{ + "basis_column_witnesses_checked": 896, + "cover_lift_and_monomial_restriction": "Proved in BINDING.md.", + "general_decoder_lower_bound": false, + "literal_affine_paths_checked": 12544, + "native_word_replayed": false, + "physical_commutator_witnesses_checked": 896, + "producer_checker_sha256": "45d1e215c4dc6f7735deaed0d9df57cf3efa83a0bc4e354c43375187cbe7f01e", + "producer_proof_sha256": "63c0deeb7e13b359ca410dfb085e1a89866aa87383d6bd1cec02cba688a4ce3e", + "producer_receipt_sha256": "f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a", + "source_manifest_sha256": "bd7ec4f2cdd05167beba7459fa58cc790e95ea9770d17c716f21c909520c1271", + "status": "PASS_CORRECTED_PRODUCER_BINDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/run-normal/SOURCE-MANIFEST.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/run-normal/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..3fad6465a7 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/run-normal/SOURCE-MANIFEST.json @@ -0,0 +1,27 @@ +{ 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--- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/FREEZE.json @@ -0,0 +1,21 @@ +{ + "files": { + "CHECKS.json": "c8e88c6bea32727822a00d62a25529c82be625af56c05f57ac164d217fff600c", + "COMMUTATOR-WITNESSES.json": "39328e50ec3ddbd0e64a9142aea7646cd94ad015d0c430252f7f460b95604bcc", + "REVIEW.md": "f5bc725b9f14032e5a61341ed73306b45797b90612e256e6e3caa52e6360a3dc", + "SOURCE-MANIFEST.json": "0c8acff469641fa9313454d1b91b3479bf7d990a548f87975257eca1629c88bb", + "TWO-TAG-SIGNATURES.json": "a0db5141b26c3d7b638b27c39e7ff91e2f1fa65cc15dbd49d20da00bd990a774", + "check_review.py": "c86a3655dcc6104be95845422a97407e0c389f1cac83c504d25b10cac7c7de03", + "final-normal/CHECKS.json": "c8e88c6bea32727822a00d62a25529c82be625af56c05f57ac164d217fff600c", + "final-normal/COMMUTATOR-WITNESSES.json": "39328e50ec3ddbd0e64a9142aea7646cd94ad015d0c430252f7f460b95604bcc", + 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Common-input logical path independence for f>=2; physical affine path independence and Q-commutation iff three scalar matrices are diagonal for f>=3. 896 exact witnesses in eight actual C/Cstar triples. Final corrected producer binding is separate. No native decoder lower bound.", + "status": "FROZEN_INDEPENDENT_REPRESENTATION_PROOF" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/REVIEW.md new file mode 100644 index 0000000000..eda47e6c93 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/REVIEW.md @@ -0,0 +1,258 @@ +# Common-input proof for the actual unitary-code routes + +The representation gap has an exact repair. The logical path operators +are linearly independent at every tensor width f at least 2. The +physical affine paths have the same property at every f at least 3. +These statements use one common spatial basis input for all paths. +They do not assume a faithful regular action on a separate owner set. + +There is also an exact Q-commutator result at every f at least 3. +For the three invertible scalar codes in the stated current charts, + +```text +Q K = K Q if and only if C0, C1, and C2 are diagonal. +``` + +In particular, every row of all eight actual C/C* triples has a +nonzero commutator. The checker supplies 896 exact witnesses. +No commutator claim is made for f=1 or f=2. None of these results +is a lower bound on a general native decoder. + +The producer packet was not frozen when this review began. This +packet binds the source matrices and route data. A separate +binding must identify the final corrected producer text and receipt. + +## Sources and conventions + +The review reads the actual D25 view source, SHA256 +`125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473`, +and the actual unitary-completion payload, decompressed SHA256 +`fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428`. +`SOURCE-MANIFEST.json` gives their exact paths. No producer module +is imported. + +All 112 q_p are distinct nonzero vectors in the root nine axes. +The unitary source and all three route stages use the same +physical port order. +The checker verifies every route's orthogonality, involution, +own-line condition, and fresh-block identities. It verifies the +stored adjoint and both unitary product orders. The native word +is not replayed. + +Use the position convention `P_A |x> = |A x>`. Define the +unnormalized Fourier character + +```text +|chi> = sum_x (-1)^(chi dot x) |x>. +``` + +Then `P_A |chi> = |A^(-T) chi>`. Every path matrix A here is +orthogonal, so `A^(-T)=A`. Thus the same matrix A acts on +position coordinates and on Fourier-character labels. A physical +translation after the route gives + +```text +T_t P_A |chi> = (-1)^(t dot A chi) |A chi>. +``` + +The intrinsic positive line operator has + +```text +Q_p |chi> = i^parity(q_p dot chi) |chi>. +``` + +On f columns its exponent is the sum of the f parities. These +conventions fix the operator order in the proof below. + +## One common input separates the logical paths + +Let Omega be the sum of the nine root axes. Let e1 and e2 be +the sums of fresh blocks 1 and 2. The actual route identities are + +```text +rho_(1,p) e1 = Omega+q_p, +rho_(2,p) e2 = Omega+q_p. +``` + +Each route fixes the other fresh block pointwise. The ordered +path from input k through r and j to output p is + +```text +M_(p,j,r) = rho_(2,p) rho_(2,j) rho_(1,j) rho_(1,r). +``` + +Fix p. Remove its known invertible left factor rho_(2,p) and +write the remaining product as N_(j,r). Then + +```text +N_(j,r) e2 = Omega+q_j, +N_(j,r) e1 = rho_(2,j) rho_(1,j) (Omega+q_r). +``` + +The first image gives j. Application of +`rho_(1,j) rho_(2,j)` to the second image gives `Omega+q_r`, +which gives r. The checker reconstructs both indices from all +12,544 actual image pairs. + +Now apply every logical path to the SAME position basis input +with columns `(e2,e1)`. Their output pairs are distinct. A linear +combination of these path operators, applied to that one input, +is therefore a linear combination of distinct basis vectors. +It can vanish only when every coefficient vanishes. This proves +linear independence in the actual width-two spatial representation. +It is stronger than matrix distinctness alone. Zero columns extend +the witness to every f at least 2. + +## Physical affine paths + +Let a physical path be the affine map `x -> M x+t`, applied in +each column. Its linear part is the actual M above. Apply every +path to the SAME three-column position input + +```text +(0,e2,e1). +``` + +The output is + +```text +(t, M e2+t, M e1+t). +``` + +The first output gives t. Its differences from the other two +give M e2 and M e1. Thus no two paths have the same output. +This proves physical affine path independence for f at least 3, +for any literal translations t. A nonzero scalar phase on a path +does not change this conclusion. + +This review does not duplicate the producer's affine-translation +enumeration. The argument needs only its stated affine form and +the verified linear parts. The actual FULL-view identities are +separately checked in the frozen phase-coded triple review. + +## Monomial closure + +The coefficient from input port k to output port p is + +```text +sum_(j,r) C2[p,j] C1[j,r] C0[r,k] P_(M_(p,j,r)). +``` + +For fixed k, distinct paths have distinct outputs on the common +input above. For different k, the sources are different input +coordinates. Hence the exact nonzero term count in row p is + +```text +sum_(j in supp C2[p,:]) sum_(r in supp C1[j,:]) |supp C0[r,:]|. +``` + +This counts paths after all allowed cancellations, not only +formal matrix products. A monomial operator must have one +nonzero source and one nonzero output basis position in a row. +The common-input test rules out even a new monomial output view +that is not in the listed path set. + +Since all three matrices are invertible, each row is nonzero. +One term in every output row first forces C2 to be monomial. +Its permutation reaches every row of C1, so C1 must be monomial. +The same argument then forces C0 to be monomial. The converse +holds by composition. + +The resulting criterion is valid in logical coordinates for +f at least 2, and for the literal physical affine maps for f +at least 3. The argument does not establish a width-one result. + +## A common character witness for the Q commutator + +Fix p, k and a nonzero path coefficient +`c=C2[p,j] C1[j,r] C0[r,k]`. Put `A=M_(p,j,r)`. On character +columns `(chi_1,...,chi_f)`, the contribution to `QK-KQ` is + +```text +c * [i^L - i^R] |A chi_1,...,A chi_f>, + +L = sum_l parity(q_p dot A chi_l), +R = sum_l parity(q_k dot chi_l). +``` + +For a physical affine path, multiply this coefficient by the +nonzero sign `(-1)^sum_l(t dot A chi_l)`. The sign is the same +on both sides of the commutator. Thus translations cannot remove +a nonzero phase difference. + +Use e2 and e1 as the first two character columns. Their output +labels separate all paths in this p,k matrix entry, by the +previous certificate. Suppose the chosen path breaks the line: + +```text +A^T q_p != q_k. +``` + +Compute the exponent difference d on those first two columns +modulo 4. If d is nonzero, use 0 as the third column. If d is +zero, choose a unit vector w on which `A^T q_p` and q_k differ. +The third-column parity difference is then 1 or -1. In both +cases, the three-column phase difference is nonzero. + +The chosen path has a unique output character tuple. No other +path can cancel its coefficient. Therefore `QK-KQ` is nonzero +in the actual width-three representation. Zero character +columns preserve the phase difference and give the result for +every greater width. + +This argument checks a common input for the complete path sum. +It does not infer independence merely because two Clifford +operators or two route matrices are unequal. + +## Which paths preserve the line + +The pulled output line is + +```text +M_(p,j,r)^T q_p = rho_(1,r) rho_(1,j) rho_(2,j) q_p. +``` + +If j differs from p, `rho_(2,j) q_p` has a nonzero fresh2 +component. Both stage-1 factors preserve that component. +The result cannot equal any root line q_k. + +If j=p, the expression reduces to `rho_(1,r) q_p`. If r +differs from p, it has a nonzero fresh1 component and again +cannot equal a root line. If j=r=p, the path is the identity, +and distinctness of the port lines gives equality only for k=p. +Consequently + +```text +M_(p,j,r)^T q_p = q_k if and only if j=r=k=p. +``` + +The checker verifies all 12,544 fresh2 tests and all 12,544 +fresh1 tests from the literal route matrices. + +If Q commutes with K at f at least 3, every nonzero path must +preserve the line by the common-character argument. Every row +of C1 and C0 is nonzero, so any nonzero C2[p,j] has a nonzero +continuation. It follows that j=p, and C2 is diagonal. +Invertibility gives nonzero diagonal entries. The same argument +then forces C1 and C0 to be diagonal. Conversely, all three +diagonal scalar matrices commute with the routes and with Q. +This proves the stated criterion. + +## Actual unitary-code witnesses and scope + +The actual C and C* have zero diagonal and nonempty rows. For +each of the eight stage choices, the checker selects one +nonzero path in every output row. All 896 paths have j different +from p and hence break the line. `COMMUTATOR-WITNESSES.json` +stores the input port, intermediate ports, nonzero Gaussian +coefficient, three input characters, output characters, and +the two distinct powers of i. + +All normal and optimized outputs are byte-identical. Source +hashes are checked before and after each run. No frozen source +is changed. This packet supplies no native word, owner host, +recursive interface, cost saving, or numerical-grid proof. + +No PR, commit, push, or publication is authorized. 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import sha256 +import gzip +from itertools import product +import json +from pathlib import Path +import shutil + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[2] +PINS = { + "views": ( + LANES / "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), + "unitary": ( + LANES / "new-core-transfer-20261017/low-displacement-20261020/" + "metric-completion-20261020/unitary-v2-normal/UNITARY-COMPLETION.json.gz", + "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428", + ), +} +ZERO, ONE = (F(0), F(0)), (F(1), F(0)) +UNITS = tuple(1 << j for j in range(25)) +OMEGA = sum(UNITS[:9]) +E1, E2 = sum(UNITS[9:17]), sum(UNITS[17:25]) + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def digest(raw): + return sha256(raw).hexdigest() + + +def act(columns, vector): + value = 0 + for bit, column in enumerate(columns): + if vector & (1 << bit): + value ^= column + return value + + +def dot(x, y): + return (x & y).bit_count() & 1 + + +def add(a, b): + return a[0] + b[0], a[1] + b[1] + + +def mul(a, b): + return a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0] + + +def sparse(raw): + return [{int(j): tuple(map(F, value)) for j, value in row.items()} for row in raw] + + +def matmul(a, b): + result = [] + for row in a: + out = {} + for j, c in row.items(): + for k, d in b[j].items(): + out[k] = add(out.get(k, ZERO), mul(c, d)) + result.append({k: value for k, value in out.items() if value != ZERO}) + return result + + +def write_json(path, value): + raw = (json.dumps(value, indent=2, sort_keys=True) + "\n").encode() + path.write_bytes(raw) + return digest(raw) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + need(shutil.disk_usage(HERE).free >= 3 * 1024**3, "At least 3 GiB free") + args.out.mkdir(parents=True, exist_ok=False) + source, manifest = {}, {} + for name, (path, pin) in PINS.items(): + raw = path.read_bytes() + decoded = gzip.decompress(raw) if path.suffix == ".gz" else raw + need(digest(decoded) == pin, "Exact input " + name) + source[name] = json.loads(decoded) + manifest[name] = {"path": str(path), "sha256": digest(raw), "payload_sha256": pin} + records = {(row["stage"], row["port"]): row for row in source["views"]["entries"]} + need(len(source["views"]["entries"]) == 336 and + set(records) == {(s, p) for s in range(3) for p in range(112)}, "All actual D25 routes") + q = [records[0, p]["q"] for p in range(112)] + need(len(set(q)) == 112 and all(0 < v < 512 for v in q), "Distinct nonzero root lines") + need(q == source["unitary"]["ports"] and + all(records[s, p]["q"] == q[p] for s in range(3) for p in range(112)), + "Unitary code and every route use the same physical port order") + rho = {key: tuple(row["route_columns"]) for key, row in records.items()} + for p in range(112): + need(rho[0, p] == UNITS, "Root-stage identity") + for s in (1, 2): + matrix = rho[s, p] + need(all(act(matrix, matrix[j]) == UNITS[j] for j in range(25)), "Involution") + need(all(dot(matrix[i], matrix[j]) == (i == j) for i in range(25) for j in range(25)), + "Orthogonal route and Fourier action convention") + need(act(matrix, q[p]) == q[p], "Own line fixed") + need(act(rho[1, p], E1) == OMEGA ^ q[p] and + act(rho[2, p], E2) == OMEGA ^ q[p], "Fresh characteristic images") + need(all(act(rho[1, p], v) == v for v in UNITS[17:25]) and + all(act(rho[2, p], v) == v for v in UNITS[9:17]), "Other fresh block fixed pointwise") + + def tail(j, r, vector): + return act(rho[2, j], act(rho[1, j], act(rho[1, r], vector))) + + def path(p, j, r, vector): + return act(rho[2, p], tail(j, r, vector)) + + def dual_path(p, j, r, vector): + return act(rho[1, r], act(rho[1, j], act(rho[2, j], act(rho[2, p], vector)))) + + by_line = {vector: p for p, vector in enumerate(q)} + signatures, signature_rows = {}, [] + for j in range(112): + for r in range(112): + images = tail(j, r, E2), tail(j, r, E1) + need(images not in signatures, "One two-column input separates every path") + recovered_j = by_line[images[0] ^ OMEGA] + recovered_r = by_line[OMEGA ^ act(rho[1, recovered_j], act(rho[2, recovered_j], images[1]))] + need((recovered_j, recovered_r) == (j, r), "Both tags recover the path") + signatures[images] = j, r + signature_rows.append([j, r, *images]) + counts = Counter() + for p in range(112): + for j in range(112): + image2, image1 = act(rho[2, j], q[p]), act(rho[1, j], q[p]) + need(bool(image2 & E2) == (p != j), "Final off-diagonal edge has a fresh2 line component") + need(bool(image1 & E1) == (p != j), "Earlier off-diagonal edge has a fresh1 line component") + counts["fresh2_line_tests"] += 1 + counts["fresh1_line_tests"] += 1 + c = sparse(source["unitary"]["code"]) + star = sparse(source["unitary"]["inverse_and_adjoint"]) + want_star = [{} for _ in range(112)] + for p, row in enumerate(c): + need(row and p not in row, "Actual forward code has a nonempty off-diagonal row") + for j, coefficient in row.items(): + need(coefficient != ZERO, "Stored coefficient is nonzero") + want_star[j][p] = coefficient[0], -coefficient[1] + need(star == want_star, "Actual adjoint") + identity = [{p: ONE} for p in range(112)] + need(matmul(c, star) == matmul(star, c) == identity, "Both unitary orders") + families = {"C": c, "Cstar": star} + witnesses, profiles = [], {} + for names in product(families, repeat=3): + c0, c1, c2 = [families[name] for name in names] + row_sizes = [sum(len(c0[r]) for j in c2[p] for r in c1[j]) for p in range(112)] + need(min(row_sizes) > 1, "Actual path expansion has multiple terms in every row") + profiles["/".join(names)] = {"total_terms": sum(row_sizes), + "row_term_histogram": dict(sorted(Counter(row_sizes).items()))} + for p in range(112): + j = min(c2[p]) + r = min(c1[j]) + k = min(c0[r]) + need(j != p, "Actual final edge is off diagonal") + coefficient = mul(c2[p][j], mul(c1[j][r], c0[r][k])) + need(coefficient != ZERO, "Witness path coefficient") + pulled_line = dual_path(p, j, r, q[p]) + need(pulled_line & E2 and pulled_line != q[k], "Witness path breaks the intrinsic line") + prefix = [E2, E1] + difference = sum(dot(q[p], path(p, j, r, x)) - dot(q[k], x) for x in prefix) % 4 + separating = pulled_line ^ q[k] + extra = 0 if difference else separating & -separating + columns = prefix + [extra] + images = [path(p, j, r, x) for x in columns] + left_power = sum(dot(q[p], x) for x in images) % 4 + right_power = sum(dot(q[k], x) for x in columns) % 4 + need(left_power != right_power, "Exact nonzero three-column commutator phase") + recovered_signature = tuple(act(rho[2, p], x) for x in images[:2]) + need(signatures[recovered_signature] == (j, r), "No other path reaches the witness output") + witnesses.append({"variant": list(names), "output_port": p, "input_port": k, + "intermediate_ports": [j, r], "coefficient": list(map(str, coefficient)), + "input_characters": columns, "output_characters": images, + "left_i_power": left_power, "right_i_power": right_power, + "pulled_output_line": pulled_line}) + need(len(witnesses) == 896, "One witness in every row of all eight actual variants") + need(all(digest(Path(item["path"]).read_bytes()) == item["sha256"] for item in manifest.values()), + "Inputs remain unchanged") + pins = {"SOURCE-MANIFEST.json": write_json(args.out / "SOURCE-MANIFEST.json", manifest), + "TWO-TAG-SIGNATURES.json": write_json(args.out / "TWO-TAG-SIGNATURES.json", signature_rows), + "COMMUTATOR-WITNESSES.json": write_json(args.out / "COMMUTATOR-WITNESSES.json", witnesses)} + result = {"status": "PASS_COMMON_INPUT_REPRESENTATION_REVIEW", "output_sha256": pins, + "logical_path_separation_minimum_width": 2, + "physical_affine_monomial_obstruction_minimum_width": 3, + "commutator_witness_minimum_width": 3, + "distinct_path_pairs": len(signatures), "line_tests": dict(counts), + "actual_physical_port_order_checked": True, + "actual_commutator_witnesses": len(witnesses), "actual_profiles": profiles, + "physical_affine_translations_recomputed": False, + "native_word_replayed": False, "width_one_or_two_commutator_claim": False, + "general_decoder_lower_bound": False} + write_json(args.out / "CHECKS.json", result) + print(json.dumps({"status": result["status"], "paths": len(signatures), + "commutator_witnesses": len(witnesses)}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/final-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/final-normal/CHECKS.json new file mode 100644 index 0000000000..d53bb9af67 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/final-normal/CHECKS.json @@ -0,0 +1,96 @@ +{ + "actual_commutator_witnesses": 896, + "actual_physical_port_order_checked": true, + "actual_profiles": { + "C/C/C": { + "row_term_histogram": { + "18": 32, + "36": 32, + "768": 16, + "1024": 16, + "1536": 16 + }, + "total_terms": 54976 + }, + "C/C/Cstar": { + "row_term_histogram": { + "30": 64, + "1024": 16, + "1280": 32 + }, + "total_terms": 59264 + }, + "C/Cstar/C": { + "row_term_histogram": { + "20": 32, + "40": 32, + "512": 16, + "1280": 16, + "2560": 16 + }, + "total_terms": 71552 + }, + "C/Cstar/Cstar": { + "row_term_histogram": { + "30": 64, + "1152": 32, + "1280": 16 + }, + "total_terms": 59264 + }, + "Cstar/C/C": { + "row_term_histogram": { + "18": 32, + "36": 32, + "640": 16, + "1280": 16, + "1536": 16 + }, + "total_terms": 57024 + }, + "Cstar/C/Cstar": { + "row_term_histogram": { + "30": 64, + "512": 16, + "1920": 32 + }, + "total_terms": 71552 + }, + "Cstar/Cstar/C": { + "row_term_histogram": { + "18": 32, + "36": 32, + "768": 16, + "896": 16, + "1792": 16 + }, + "total_terms": 57024 + }, + "Cstar/Cstar/Cstar": { + "row_term_histogram": { + "27": 64, + "896": 16, + "1216": 32 + }, + "total_terms": 54976 + } + }, + "commutator_witness_minimum_width": 3, + "distinct_path_pairs": 12544, + "general_decoder_lower_bound": false, + "line_tests": { + "fresh1_line_tests": 12544, + "fresh2_line_tests": 12544 + }, + "logical_path_separation_minimum_width": 2, + "native_word_replayed": false, + "output_sha256": { + "COMMUTATOR-WITNESSES.json": "39328e50ec3ddbd0e64a9142aea7646cd94ad015d0c430252f7f460b95604bcc", + "SOURCE-MANIFEST.json": "0c8acff469641fa9313454d1b91b3479bf7d990a548f87975257eca1629c88bb", + "TWO-TAG-SIGNATURES.json": "a0db5141b26c3d7b638b27c39e7ff91e2f1fa65cc15dbd49d20da00bd990a774" + }, + "physical_affine_monomial_obstruction_minimum_width": 3, + "physical_affine_translations_recomputed": false, + "status": "PASS_COMMON_INPUT_REPRESENTATION_REVIEW", + "width_one_or_two_commutator_claim": false +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/final-normal/COMMUTATOR-WITNESSES.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/final-normal/COMMUTATOR-WITNESSES.json new file mode 100644 index 0000000000..56c66867f7 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/final-normal/COMMUTATOR-WITNESSES.json @@ -0,0 +1,26882 @@ +[ + { + "coefficient": [ + "1/64", + "1/64" + ], + "input_characters": [ + 33423360, + 130560, + 0 + ], 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b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/CHAIN.md @@ -0,0 +1,197 @@ +# The common-q type persists through the nine DATA stages + +The phase-coded triple can be repeated at the actual DATA stage +views. After nine local calls and nine FULL scalar shears, it gives + +```text +X = F73 q Y0, +Y = -F73 q X0. +``` + +Both original input banks are arbitrary. The same q factor remains +on both banks. It does not accumulate with the number of triples. +This is a closure result for the data type at the actual stage +boundaries. It does not prove a recursive gathered-axis interface, +a complete helper host, or a multiplication bound. + +## Fixed source and views + +Use the reviewed phase-coded triple from +`../phase-coded-triple-20261020/PHYSICAL-ENDPOINT.md`. +Its freeze SHA256 is +`0ee32fe22f42cffce2a9673f0dc95496a4b4bb8b11a534f77a11f5fe9c7aeb4b`. +The independent review is +`../owner-review/phase-coded-triple-review-20261020/REVIEW.md`, +SHA256 +`8342f508f9c2432a01ef196820d5c94b98df012c63f21d560940c8799e337c0c`. + +The full stage view source is +`bridge-access-20261017/check_bridge_access.py`, +SHA256 +`9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111`. +It binds the actual 73-axis DATA phase ledger in the selected source +archive. The checker verifies the archive and member hashes before +using any recipe. It checks all 112 ports at stages 1 through 8. + +As before, G_s means the portwise orthogonal route rho_s. Define +`H_s=G_(s,P) H G_(s,R)` and `D_s=G_(s,R) D G_(s,P)`. +The literal entry and exit identities are + +```text +Ventry_s Fprev_s = Fext_s Q G_s, +Vexit_s Fnext_s = Fnext_s G_s. +``` + +The checker verifies the FULL and hole forms of both identities: +3,584 phase identities in total. Every route fixes its own q line. +Omitting the actual entry or exit translation fails at all 896 +respective port-stage pairs. + +There are nine added shears, at these route and execution levels: + +```text +(route 1, level 1), (route 2, level 2), (route 0, level 2), +(route 4, level 4), (route 5, level 5), (route 3, level 5), +(route 7, level 7), (route 8, level 8), (route 6, level 8). +``` + +Level s has common FULL frame `F_(9+8s)`. For each listed shear, +the checker verifies the exact FULL affine-view identity and its +involution at all 112 ports. This gives 1,008 further phase checks. +The stage-0 view is the identity. + +## The type lemma + +At a natural boundary, write the physical state as + +```text +X = Fprev(a,u), +Y_P = Fprev z, +Y_R = Fprev q_R v. +``` + +The literal entry views give the declared Q-entry local type. +The three routed local content maps are the F_Q, B_Q, and F_Q +maps of the reviewed triple. At the end of the middle call, apply +`X_R-=D_(s+1) X_P`. At the end of the last call, apply +`Y_P-=H_(s+2) X_R` and `Y_P-=H_s Y_R`. + +The same ordered calculation as in the reviewed triple gives + +```text +X = Fnext(-z,-q_R v), +Y = Fnext(a,u). +``` + +The middle shear occurs after the complete middle cover sweep. +The last two occur after the complete last sweep. Every local +helper return must finish before these scalar maps start. + +Now assume the input has one common-q code: + +```text +X = Fprev q A, +Y = Fprev q B. +``` + +Its natural contents are + +```text +(a,u)=q A, z=q_P B_P, v=B_R. +``` + +Substitution gives + +```text +X = -Fnext q B, +Y = Fnext q A. +``` + +Thus each corrected triple preserves the same code and applies +the signed bank exchange `J(A,B)=(-B,A)`. There is no extra q +factor. In particular, treating ordinary Y as FULL at the next +entry would give the wrong contents: its natural ordinary +coordinate is Q times its stored FULL coordinate. + +This argument uses the order of Q and q. It never moves a line +operator through H or D. The checker uses free noncommuting +operators with only adjacent inverse cancellations. + +The lemma applies to any further stage block with the stated +entry, exit, and FULL-view identities. The literal application +proved here stops at the actual nine source stages. No arbitrary +dimension compiler is supplied. + +## Actual nine-stage word + +The first three calls are F_Q0, B_Q1, F_Q2 with the three +corrections of the reviewed packet. They give the common-q type +under F25 from arbitrary original physical inputs. + +Use the type lemma for calls F_Q3, B_Q4, F_Q5, then for +F_Q6, B_Q7, F_Q8. The three block signs are J, J^2, and J^3. +Since `J^3(A,B)=(B,-A)`, the final result is the endpoint +stated at the start. The checker verifies each intermediate +operator row and the final sign. + +The local word order is an explicit choice for this new data +caller. The old global helper allocation is not thereby proved +to host the changed words. Local arbitrary-helper restoration +and global chronological hosting are separate obligations. + +## Invoice and limits + +All nine local words use Q entry. Their total native profile is + +```text +12528 H1 + 576 H2 + 432 H3 + 144 H8. +``` + +The native mass is `16128=224*72`. The nine local scalar +invoices sum to 41,688 primitives. The nine direct coefficient +shears add at most 18,432 primitives and 1,792 affine field-map +calls. They add no native child or owned field. + +The eight transitions retain 3,584 global entry and exit field-map +calls. Those maps are separate from the local invoices and the +added shear views. Every map retains its stream and address cost. +Native side maps retain their inherited cost as well. + +Applying one positive Q line operation to each of the 224 final +data fields gives + +```text +X = F73 Y0, +Y = -F73 X0. +``` + +The total native mass is then `16352=224*73`. There is no strict +native-mass gain. The common-q code must be matched to an actual +consumer to avoid that terminal cost. This packet proves +within-chain stage matching only. It does not prove matching +across recursive gathered-axis views. + +The source local numerical bounds do not supply a complete +recursive precision proof. The global owner host, terminal native +recipes, final bank convention, and complete kappa calculation +remain open. + +## Verification + +Run with fresh output directories: + +```text +python3 -B check_chain.py --out +python3 -O -B check_chain.py --out +``` + +The normal and optimized receipts are byte-identical. The checks +use the literal DATA ledger and all listed phase identities, +then a separate free-operator induction for the three corrected +blocks. The 224-column local operator checks are inherited from +the reviewed D25 packet. This checker does not repeat a dense +73-axis input matrix expansion. + +No PR, commit, push, or publication is authorized. Read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md` +before any future PR description. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/FREEZE.json new file mode 100644 index 0000000000..3e096dc166 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/FREEZE.json @@ -0,0 +1,12 @@ +{ + "files": { + "CHAIN.md": "123ba331ea24a23c0fb775b6e6e3bec2409acdacc938d45f026c54ec0d3bbfa2", + "GENERAL-VIEWS-REVIEW.md": "9e8c73d3bfaade6d9d06f8c472b88ad52cce624fe2e602c143cd1705c8f662b0", + "check_chain.py": "37aba6c97f5733ba104146fad423c46e0ed42f3c500236b8ad799b026411af4e", + "run-normal/CHECKS.json": "31609236f6e3eaddbcf9290191d6b6cf2a0728dd32b475d9c8062e2518b83673", + "run-optimized/CHECKS.json": "31609236f6e3eaddbcf9290191d6b6cf2a0728dd32b475d9c8062e2518b83673" + }, + "normal_optimized_byte_identical": true, + "scope": "Actual D73 common-q data-type closure through nine stages and mathematical peer review of general-D adjacent stage views. Recursive gathered-axis matching, global hosting and precision remain open.", + "status": "FROZEN_PRODUCER_PASS_WITH_GENERAL_VIEW_PROOF_REVIEW" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/GENERAL-VIEWS-REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/GENERAL-VIEWS-REVIEW.md new file mode 100644 index 0000000000..57afa0bf64 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/GENERAL-VIEWS-REVIEW.md @@ -0,0 +1,76 @@ +# Peer review of the general stage views + +The proof in +`bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md` +has no material error for the adjacent-stage and access-cone +identities used by the phase-coded caller. + +The reviewed proof SHA256 is +`5da866eb2802e8a30ea77d2f88877b5005a2eb04632514c897a426e76277db2e`. +Its source freeze SHA256 is +`b6539737b3144d73c0ca313984573fe1493f9736205ab0d885ebd69d88d27c4d`. +This review checks the mathematical proof. It does not rerun the +producer's arbitrary-dimension generator. + +Let B be the actual root orthonormal basis. The function + +```text +f(z) = sum_(v in B) (v dot z) - |z| mod 4 +``` + +has no quadratic term: its coefficient at a pair of distinct +standard coordinates is minus two times their scalar product +under the orthogonal basis matrix. Every linear coefficient is +even. Thus f is twice a binary linear form. + +For a basis vector v, orthonormality gives +`f(v)=1-|v|=2 beta(v) mod 4`. It follows that this form is +`delta0=sum_(v in B) beta(v) v`. The actual q has weight three +or seven, so its coefficient is one. This proves the source +formula `delta0=q+sum_j beta(b_j)b_j`, including the phase sign. + +The route exchanges each b_j with its fresh unit vector e_j. +The eight vectors b_j+e_j are isotropic and pairwise orthogonal. +The displayed matrix for rho therefore acts as the claimed +exchange, fixes q, and is an orthogonal involution. + +Conjugating the root phase identity by rho gives + +```text +P_rho Froot = X_(rho delta0) Q Ffresh P_rho. +``` + +The entry translation cancels this phase. The old completed +fresh blocks are spectators. This gives the first adjacent +identity; multiplication by q gives the ordinary-hole identity +because rho fixes q. + +When both the root and the current fresh block are FULL, their +exchange has phase `X_(delta0+rho delta0)`. The source exit +translation is exactly that phase. It is fixed by rho, so the +affine exit map is an involution. Old or future spectator blocks +do not change the calculation. This proves the claimed access +cones for every finite number of fresh blocks. + +The owner map is right multiplication by a fixed orthogonal +element on the regular cover. It is a bijection. This permits +the complete-cover view used in the proof; it does not identify +different stages without their owner and payload maps. + +The separate `check_chain.py` in this folder binds the literal +selected D73 archive and verifies all eight natural boundaries +and all nine FULL shears used by the repeated phase-coded caller. +Its phase primitive is inherited from the earlier pinned bridge +checker. The reviewed D25 caller uses a separate phase-ring +implementation. These are source and finite-consistency checks; +the arbitrary-dimension conclusion follows from the proof above. + +The general theorem supports the repeated-triple type lemma +whenever the same local words are available. It does not make +the matrices G_s C G_s independent of s. It does not close a +recursive gathered-axis interface or supply a global helper +host, map-stream invoice, or precision proof. + +No PR, commit, push, or publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/check_chain.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/check_chain.py new file mode 100644 index 0000000000..94e01e93db --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/check_chain.py @@ -0,0 +1,228 @@ +"""Check the common-q type through the actual nine-stage DATA views.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import tarfile + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +BRIDGE = LANES / "bridge-access-20261017/check_bridge_access.py" +BRIDGE_PIN = "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111" +TRIPLE = HERE.parent / "phase-coded-triple-20261020/FREEZE.json" +TRIPLE_PIN = "0ee32fe22f42cffce2a9673f0dc95496a4b4bb8b11a534f77a11f5fe9c7aeb4b" + + +def need(test, message): + if not test: + raise ValueError(message) + + +def reduced(word): + inverse = {"Qp": "qp", "qp": "Qp", "Qr": "qr", "qr": "Qr"} + result = [] + for letter in word: + if result and inverse.get(letter) == result[-1]: + result.pop() + else: + result.append(letter) + return tuple(result) + + +def add(*terms): + out = {} + for scale, row in terms: + for word, value in row.items(): + out[word] = out.get(word, F(0)) + scale * value + return {word: value for word, value in out.items() if value} + + +def op(letter, row): + out = {} + for word, value in row.items(): + key = reduced((letter,) + word) + out[key] = out.get(key, F(0)) + value + return {word: value for word, value in out.items() if value} + + +def forward(state, stage): + a, u, z, v = state + return [add((-1, z)), u, add((1, a), (1, op("H" + str(stage), u))), + add((1, v), (1, op("Qr", u)))] + + +def backward(state, stage): + a, u, z, v = state + return [z, add((1, u), (1, op("D" + str(stage), z)), (-1, op("qr", v))), + add((-1, a)), v] + + +def corrected_triple(state, first): + state = forward(state, first) + state = backward(state, first + 1) + state[1] = add((1, state[1]), (-1, op("D" + str(first + 1), state[0]))) + state = forward(state, first + 2) + state[3] = op("qr", state[3]) + state[2] = add((1, state[2]), (-1, op("H" + str(first + 2), state[1]))) + state[2] = add((1, state[2]), (-1, op("H" + str(first), state[3]))) + return state + + +def encoded(row): + return [[list(word), str(value)] for word, value in sorted(row.items())] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + need(sha256(BRIDGE.read_bytes()).hexdigest() == BRIDGE_PIN, "Phase source pin") + need(sha256(TRIPLE.read_bytes()).hexdigest() == TRIPLE_PIN, "Local triple pin") + spec = importlib.util.spec_from_file_location("chain_source_phase", BRIDGE) + base = importlib.util.module_from_spec(spec) + spec.loader.exec_module(base) + need(sha256(base.ARCHIVE.read_bytes()).hexdigest() == base.ARCHIVE_PIN, + "Selected supplier archive") + with tarfile.open(base.ARCHIVE) as archive: + name, data_pin = base.MEMBERS["phases"] + raw = archive.extractfile(name).read() + need(sha256(raw).hexdigest() == data_pin, "Literal DATA phase member") + ports = json.loads(raw)["recipes"] + need(len(ports) == 112, "All supplier ports") + checks = { + "natural_FULL_entry": 0, "natural_hole_entry": 0, + "natural_FULL_exit": 0, "natural_hole_exit": 0, + "full_shear_views": 0, "own_line_fixed": 0, + } + negative = {"omitted_entry_translation": 0, "omitted_exit_translation": 0} + used_shears = [ + (1, 1), (2, 2), (0, 2), + (4, 4), (5, 5), (3, 5), + (7, 7), (8, 8), (6, 8), + ] + for port, recipe in enumerate(ports): + q = recipe["q"] + basis = base.chart(q) + need(basis[1:9] == recipe["idle_children"][0]["orthogonal_axes"][:8], + "Actual complement basis") + routes = {s: base.route(basis, s) for s in range(9)} + for s in range(1, 9): + rho = routes[s] + alignment = recipe["stage_alignment"][s] + need(alignment["entry_X"] == alignment["entry_Y"] and + alignment["exit_X"] == alignment["exit_Y"], "Paired entry and exit") + need(base.act(rho, q) == q, "Own line") + checks["own_line_fixed"] += 1 + delta_in = base.act(rho, alignment["entry_X"]) + delta_out = alignment["exit_X"] + before = base.UNIT[:9 + 8 * (s - 1)] + after = base.UNIT[:9 + 8 * s] + exterior = base.UNIT[9:9 + 8 * s] + raw_entry = base.product([(base.act(rho, e), 1) for e in before]) + entry = base.add_phase(raw_entry, base.line(delta_in, 2)) + wanted_entry = base.product([(e, 1) for e in exterior] + [(q, 1)]) + need(entry == wanted_entry, "Literal natural FULL entry") + need(base.add_phase(entry, base.line(q, -1)) == + base.product([(e, 1) for e in exterior]), "Literal natural hole entry") + checks["natural_FULL_entry"] += 1 + checks["natural_hole_entry"] += 1 + negative["omitted_entry_translation"] += raw_entry != wanted_entry + raw_exit = base.product([(base.act(rho, e), 1) for e in after]) + exit_phase = base.add_phase(raw_exit, base.line(delta_out, 2)) + wanted_exit = base.product([(e, 1) for e in after]) + need(exit_phase == wanted_exit, "Literal natural FULL exit") + need(base.add_phase(exit_phase, base.line(q, -1)) == + base.product([(e, 1) for e in after] + [(q, -1)]), + "Literal natural hole exit") + checks["natural_FULL_exit"] += 1 + checks["natural_hole_exit"] += 1 + negative["omitted_exit_translation"] += raw_exit != wanted_exit + for stage, level in used_shears: + rho = routes[stage] + delta = recipe["stage_alignment"][stage]["exit_X"] if stage else 0 + axes = base.UNIT[:9 + 8 * level] + actual = base.add_phase( + base.product([(base.act(rho, e), 1) for e in axes]), + base.line(delta, 2)) + need(actual == base.product([(e, 1) for e in axes]), + "The actual shear view is FULL at its execution level") + need(base.act(rho, delta) == delta, "The FULL affine view is an involution") + checks["full_shear_views"] += 1 + need(all(checks[k] == 896 for k in checks if k != "full_shear_views") and + checks["full_shear_views"] == 1008, "Complete phase coverage") + need(negative == { + "omitted_entry_translation": 896, "omitted_exit_translation": 896, + }, "All omitted-translation controls fail") + + a, u, z, v = [{(name,): F(1)} for name in ("a", "u", "z", "v")] + initial = [op("qp", a), op("qr", u), op("qp", z), v] + state = corrected_triple(initial, 0) + expected = [add((-1, op("qp", z))), add((-1, op("qr", v))), + op("qp", a), op("qr", u)] + need(state == expected, "First actual block has the common-q signed type") + endpoints = {"25": [encoded(row) for row in state]} + for first, dimension in ((3, 49), (6, 73)): + entered = state[:3] + [op("Qr", state[3])] + state = corrected_triple(entered, first) + expected = [add((-1, expected[2])), add((-1, expected[3])), + expected[0], expected[1]] + need(state == expected, "The common-q type is preserved by the next block") + endpoints[str(dimension)] = [encoded(row) for row in state] + want = [op("qp", z), op("qr", v), add((-1, op("qp", a))), + add((-1, op("qr", u)))] + need(state == want, "The nine-stage endpoint includes the exact sign") + terminal = [op("Qp" if i % 2 == 0 else "Qr", row) for i, row in enumerate(state)] + need(terminal == [z, v, add((-1, a)), add((-1, u))], + "A direct positive line terminal restores the original physical inputs") + need(op("Qr", op("D4", a)) != op("D4", op("Qp", a)), + "The algebra does not commute a line through a scatter") + + profile = {"1": 9 * 1392, "2": 9 * 64, "3": 9 * 48, "8": 9 * 16} + mass = sum(int(rank) * count for rank, count in profile.items()) + need(mass == 224 * 72 == 16128 and mass + 224 == 224 * 73, + "Exact nine-stage native mass") + receipt = { + "status": "PASS_ACTUAL_D73_COMMON_Q_CHAIN", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins": { + "phase_source": {"path": str(BRIDGE), "sha256": BRIDGE_PIN}, + "supplier_archive": {"path": str(base.ARCHIVE), "sha256": base.ARCHIVE_PIN}, + "supplier_member": {"name": name, "sha256": data_pin}, + "local_triple": {"path": str(TRIPLE), "sha256": TRIPLE_PIN}, + }, + "phase_checks": checks, + "negative_controls": negative, + "free_operator_endpoints": endpoints, + "physical_endpoint": "X=F73 q Y0; Y=-F73 q X0", + "native_profile": profile, + "native_mass": mass, + "direct_terminal_positive_lines": 224, + "native_mass_with_direct_terminal": mass + 224, + "local_scalar_primitives": 9 * 4632, + "nine_direct_FULL_shear_primitives": 9 * 2048, + "added_FULL_affine_map_calls": 1792, + "unchanged_global_stage_entry_exit_map_calls": 8 * 448, + "owned_fields": 0, + "scope": ( + "The exact common-q data type composes through the actual nine " + "DATA stages. Local helper restoration is inherited; a complete " + "owner host, recursive gathered-axis join, and numerical-grid " + "invoice are not proved. The direct terminal has no strict " + "native-mass improvement." + ), + } + (args.out / "CHECKS.json").write_text( + json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps({ + "status": receipt["status"], "phase_checks": checks, + "native_mass": mass, "native_mass_with_direct_terminal": mass + 224, + }, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/run-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..7dc88b7cce --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/run-normal/CHECKS.json @@ -0,0 +1,166 @@ +{ + "added_FULL_affine_map_calls": 1792, + "checker_sha256": "37aba6c97f5733ba104146fad423c46e0ed42f3c500236b8ad799b026411af4e", + "direct_terminal_positive_lines": 224, + "free_operator_endpoints": { + "25": [ + [ + [ + [ + "qp", + "z" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "v" + ], + "-1" + ] + ], + [ + [ + [ + "qp", + "a" + ], + "1" + ] + ], + [ + [ + [ + "qr", + "u" + ], + "1" + ] + ] + ], + "49": [ + [ + [ + [ + "qp", + "a" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "u" + ], + "-1" + ] + ], + [ + [ + [ + "qp", + "z" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "v" + ], + "-1" + ] + ] + ], + "73": [ + [ + [ + [ + "qp", + "z" + ], + "1" + ] + ], + [ + [ + [ + "qr", + "v" + ], + "1" + ] + ], + [ + [ + [ + "qp", + "a" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "u" + ], + "-1" + ] + ] + ] + }, + "local_scalar_primitives": 41688, + "native_mass": 16128, + "native_mass_with_direct_terminal": 16352, + "native_profile": { + "1": 12528, + "2": 576, + "3": 432, + "8": 144 + }, + "negative_controls": { + "omitted_entry_translation": 896, + "omitted_exit_translation": 896 + }, + "nine_direct_FULL_shear_primitives": 18432, + "owned_fields": 0, + "phase_checks": { + "full_shear_views": 1008, + "natural_FULL_entry": 896, + "natural_FULL_exit": 896, + "natural_hole_entry": 896, + "natural_hole_exit": 896, + "own_line_fixed": 896 + }, + "physical_endpoint": "X=F73 q Y0; Y=-F73 q X0", + "scope": "The exact common-q data type composes through the actual nine DATA stages. Local helper restoration is inherited; a complete owner host, recursive gathered-axis join, and numerical-grid invoice are not proved. The direct terminal has no strict native-mass improvement.", + "source_pins": { + "local_triple": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/FREEZE.json", + "sha256": "0ee32fe22f42cffce2a9673f0dc95496a4b4bb8b11a534f77a11f5fe9c7aeb4b" + }, + "phase_source": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/check_bridge_access.py", + "sha256": "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111" + }, + "supplier_archive": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz", + "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" + }, + "supplier_member": { + "name": "candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + } + }, + "status": "PASS_ACTUAL_D73_COMMON_Q_CHAIN", + "unchanged_global_stage_entry_exit_map_calls": 3584 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/run-optimized/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/run-optimized/CHECKS.json new file mode 100644 index 0000000000..7dc88b7cce --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-chain-20261020/run-optimized/CHECKS.json @@ -0,0 +1,166 @@ +{ + "added_FULL_affine_map_calls": 1792, + "checker_sha256": "37aba6c97f5733ba104146fad423c46e0ed42f3c500236b8ad799b026411af4e", + "direct_terminal_positive_lines": 224, + "free_operator_endpoints": { + "25": [ + [ + [ + [ + "qp", + "z" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "v" + ], + "-1" + ] + ], + [ + [ + [ + "qp", + "a" + ], + "1" + ] + ], + [ + [ + [ + "qr", + "u" + ], + "1" + ] + ] + ], + "49": [ + [ + [ + [ + "qp", + "a" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "u" + ], + "-1" + ] + ], + [ + [ + [ + "qp", + "z" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "v" + ], + "-1" + ] + ] + ], + "73": [ + [ + [ + [ + "qp", + "z" + ], + "1" + ] + ], + [ + [ + [ + "qr", + "v" + ], + "1" + ] + ], + [ + [ + [ + "qp", + "a" + ], + "-1" + ] + ], + [ + [ + [ + "qr", + "u" + ], + "-1" + ] + ] + ] + }, + "local_scalar_primitives": 41688, + "native_mass": 16128, + "native_mass_with_direct_terminal": 16352, + "native_profile": { + "1": 12528, + "2": 576, + "3": 432, + "8": 144 + }, + "negative_controls": { + "omitted_entry_translation": 896, + "omitted_exit_translation": 896 + }, + "nine_direct_FULL_shear_primitives": 18432, + "owned_fields": 0, + "phase_checks": { + "full_shear_views": 1008, + "natural_FULL_entry": 896, + "natural_FULL_exit": 896, + "natural_hole_entry": 896, + "natural_hole_exit": 896, + "own_line_fixed": 896 + }, + "physical_endpoint": "X=F73 q Y0; Y=-F73 q X0", + "scope": "The exact common-q data type composes through the actual nine DATA stages. Local helper restoration is inherited; a complete owner host, recursive gathered-axis join, and numerical-grid invoice are not proved. The direct terminal has no strict native-mass improvement.", + "source_pins": { + "local_triple": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/FREEZE.json", + "sha256": "0ee32fe22f42cffce2a9673f0dc95496a4b4bb8b11a534f77a11f5fe9c7aeb4b" + }, + "phase_source": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/check_bridge_access.py", + "sha256": "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111" + }, + "supplier_archive": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz", + "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" + }, + "supplier_member": { + "name": "candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json", + "sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" + } + }, + "status": "PASS_ACTUAL_D73_COMMON_Q_CHAIN", + "unchanged_global_stage_entry_exit_map_calls": 3584 +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/FREEZE.json new file mode 100644 index 0000000000..763e7dcd15 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "PHYSICAL-ENDPOINT.md": "5eb5eba5d3bed38faf9e411ca4a9a6f8e67765966011e93dec96f2300613756f", + "check_phase_coded_triple.py": "82a36b9f258d1aa2d95830502b336eb8aae9e7beff643b1f854c3d87451098f6", + "run-normal/CHECKS.json": "44a1c03836ba47af92965dc7d2bb716d0f94d03dd54cb3122eeaa9f1d08a3cc3", + "run-optimized/CHECKS.json": "44a1c03836ba47af92965dc7d2bb716d0f94d03dd54cb3122eeaa9f1d08a3cc3" + }, + "normal_optimized_byte_identical": true, + "scope": "Actual D25 phase-coded F/B/F, three FULL shears, and a common-q signed exchange. Direct line terminal has total native mass5600. No recursive common-q admission, global hosting, or complete numerical invoice.", + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/PHYSICAL-ENDPOINT.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/PHYSICAL-ENDPOINT.md new file mode 100644 index 0000000000..82a528fb95 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/PHYSICAL-ENDPOINT.md @@ -0,0 +1,266 @@ +# A phase-coded triple has one common line factor + +The actual D25 forward-backward-forward word has a simple physical +endpoint after three scalar shears. With Q entry on the selected +borrowed fields, the result is + +```text +X = -F25 q Y0, +Y = F25 q X0. +``` + +Here X0 and Y0 are the original physical inputs. Both can be arbitrary. +The line operator q acts at each port. The word has no remaining centre +correction. It still has q on both banks. The result does not admit +that factor as a free terminal or as a free recursive interface. + +The I-entry variant removes q from the sixteen selected borrowed +outputs. Its direct terminal then uses 208 positive line operations. +The Q-entry variant uses 224. In both cases the native mass, including +this direct terminal, is 5,600. This is not a strict supplier improvement. + +## Sources and local types + +The local source is the phase-coded clean word from +`controller-followthrough-20261017/phase-coded-clean-20261020`. +Its freeze SHA256 is +`284e6239ae3287bb139497fe610e67def239ad50697f230b61ac7c7280fb4b75`. +The decompressed `final-normal/PHASE-CODED.json.gz` SHA256 is +`ffdbe1c84af50e58ee0ab3a9ada15571476146caad1119f55e17d655934f0874`. + +That source removes the 592 ordinary cross-bank transfer ADDs from +the earlier clean word. It puts a physical ordinary ADD before the +inherited input views. Its replay covers all 640 independent local +input columns, both providers, and all 416 arbitrary helper fields. +The native kernels, frames, and endpoint adapters are inherited +without a change. The present checker binds the stored operator-valued +content rows. It does not repeat that native transcript replay. + +The selected set is + +```text +P = [0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23]. +``` + +R contains the other 96 ports. The actual row code gives +`H=code[P,R]` and `D=response[R,P]=-H*`. These are the same +matrices as in the preceding natural clean triple. + +The local Q-entry input type is + +```text +X = Q(a,u), Y_P = Q_P z, Y_R = v. +``` + +The output type is FULL on X and selected Y, and `F9 q_R` on +ordinary Y. In those types the stored local maps are + +```text +F_Q(a,u,z,v) = (-z,u,a+H u,v+Q_R u), +B_Q(a,u,z,v) = (z,u+D z-q_R v,-a,v). +``` + +The Q in the forward map stays on its source ordinary field. +The q in the backward map stays on its source borrowed field. +Neither operator is commuted through H or D. + +At stage 0, the I-entry variant uses `Y_P=z` instead. The same +displayed content map then has sixteen more units of native mass. + +## Actual stage access + +Use the literal D25 views from +`bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json`, +SHA256 +`125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473`. +Define G_s to be only the portwise orthogonal route rho_s. It is not +the accumulated Fourier prefix. Set + +```text +H_s = G_(s,P) H G_(s,R), +D_s = G_(s,R) D G_(s,P). +``` + +Every G_s is an involution and fixes its own port line. The exact +entry and exit identities are + +```text +Ventry_s Fprev_s = Fext_s Q G_s, +Vexit_s Fnext_s = Fnext_s G_s. +``` + +Their translations are the literal source translations. At a natural +boundary, X and selected Y have frame Fprev, while ordinary Y has +frame `Fprev q_R`. Thus the next local call has exactly its declared +input type with a common Fext exterior. The logical contents change +only by G_s. No additional native line operation is inserted. + +The checker verifies these identities, their ordinary-hole forms, +the final F25 FULL views, and the involution property of each FULL +view. There are 1,344 checked phase identities. Each identity tensors +over the spatial columns. + +## The unmodified three-call word + +Write the initial Q-entry contents as + +```text +X0 = Q(a,u), Y0 = (Q_P z,v), +alpha = a+H_0 u. +``` + +Apply F_Q at stage 0, B_Q at stage 1, and F_Q at stage 2. +Do not insert a physical bank reset. The first two global content +states are + +```text +after stage 0: +X = (-z,u), Y = (alpha,v+Q_R u), + +after stage 1: +X = (alpha,R), Y = (z,v+Q_R u), +R = D_1 alpha-q_R v. +``` + +The final physical fields are + +```text +X_P = -F25 z, +X_R = F25 R, +Y_P = F25 beta, +Y_R = F25(u+D_1 alpha), + +beta = alpha+H_2 R. +``` + +In the last line for ordinary Y, the local q output frame cancels +an explicit Q in its computed content. Therefore this ordinary +output is FULL. This cancellation is checked as an operator identity. +It is not inferred from a dependency on original data. + +All the data can be recovered by four FULL shears: + +```text +Y_P <- Y_P-H_2 X_R, +X_R <- X_R-D_1 Y_P, +Y_R <- Y_R-D_1 Y_P, +Y_P <- Y_P-H_0 Y_R. +``` + +The result is `X=(-z,-q_R v)` and `Y=(a,u)` under F25. +The next section gives a shorter placement of the same correction. + +## Three FULL shears + +After stage 1, X_P is alpha and X_R is R in the common F17 +frame. Apply + +```text +X_R <- X_R-D_1 X_P. +``` + +This changes X_R to `-q_R v`. Use the literal stage-1 FULL +views on the source and target fields, with their translations. +The ordinary Y bank is not accessed by this shear. + +Then perform the stage-2 F_Q call. Its endpoint is + +```text +X = F25(-z,-q_R v), +Y = F25(alpha-H_2 q_R v,u). +``` + +Apply the two final FULL shears + +```text +Y_P <- Y_P-H_2 X_R, +Y_P <- Y_P-H_0 Y_R. +``` + +The first uses the stage-2 FULL views. The second is a scalar +port map in the global common FULL frame. This gives + +```text +X = F25(-z,-q_R v), +Y = F25(a,u). +``` + +In Q entry, `z=q_P Y0_P` and `(a,u)=q X0`. Consequently the +complete result is the common-q signed exchange stated at the start. +In I entry, `z=Y0_P`, so the selected borrowed output already has +the required F25 frame. + +The checker reads all the operator-valued local rows from the native +source payload. It composes each call with the literal entry and exit +views. It inserts the middle shear on the actual physical state, +then checks the two final shears on that state. This is done for all +224 independent data inputs and both initial entry variants. Before +the shears, the final matrix has 22,160 stored input-operator terms. +After the shears, it has exactly 224. + +## Cost and the remaining obligation + +The three native local words have these total profiles: + +```text +Q entry: 4176 H1 + 192 H2 + 144 H3 + 48 H8, +I entry: 4176 H1 + 192 H2 + 144 H3 + 32 H8 + 16 H9. +``` + +Their native masses are 5,376 and 5,392. Each local word has +4,632 scalar primitives in the producer invoice, for a sum of +13,896. No odd division or owned field is introduced. + +A direct coefficient implementation of each added H or D shear has +216 ADDs and 2,048 scalar primitives under the inherited tariff. +The three shears therefore add at most 6,144 scalar primitives. +The two routed shears use 448 affine field-map calls. All map calls +retain their stream and address cost. This direct bound does not +consume the smaller factored scalar code from the producer. + +The signed endpoint is intentional. An unsigned output convention +requires the stated signs or an equivalent signed bank exchange in +the caller. If signs are added directly, they cost 224 scalar +primitives on the 112 X fields. No such signs are hidden in the +three-shear invoice. + +The direct terminal applies Q to all 112 Y fields. It also applies +Q to the 96 ordinary X fields, and to the sixteen selected X fields +in the Q-entry variant. The result is + +```text +X = -F25 Y0, +Y = F25 X0. +``` + +The checker verifies this terminal as an operator on arbitrary +physical inputs. It has 208 positive line operations in I entry +and 224 in Q entry. In both cases the total native mass is +`5600=224*25`. The line side maps, global helper host, bank routing, +complete recursive invoice, and numerical precision proof are not +supplied here. + +An intended recursive consumer must accept the literal common-q +endpoint, including its port directions and gathered-axis views. +A match of formal code names is insufficient. This packet provides +the exact physical endpoint for that test. It does not prove that +the next consumer accepts it. + +## Verification + +Run with two new output directories: + +```text +python3 -B check_phase_coded_triple.py --out +python3 -O -B check_phase_coded_triple.py --out +``` + +The normal and optimized receipts are byte-identical. The checks +include all 224 input columns, both initial entry types, all 1,344 +phase identities, the direct line terminal, and two negative +controls. The wrong middle sign fails. Omission of the remaining +q correction fails. + +No PR, commit, push, or publication is authorized. Read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md` +before any future PR description. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/check_phase_coded_triple.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/check_phase_coded_triple.py new file mode 100644 index 0000000000..85cb3fb897 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/check_phase_coded_triple.py @@ -0,0 +1,281 @@ +"""Check the phase-coded triple with the literal D25 views.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +RING_PATH = HERE.parent / "no-reset-triple-20261020/check_no_reset.py" +RING_PIN = "8612732e02b68495d6b0b95cbd216d1d0df43be2ffdd29cc7fc9033518ab1c48" +BASE_RING_PIN = "70ca9ce2dff5256644f35ef65344c7e0dd9f78e3fb48c18436e9e5c20b4f9109" +PINS = { + "views": ( + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), + "row_code": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz", + "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2", + ), + "phase_coded": ( + "controller-followthrough-20261017/phase-coded-clean-20261020/" + "final-normal/PHASE-CODED.json.gz", + "ffdbe1c84af50e58ee0ab3a9ada15571476146caad1119f55e17d655934f0874", + ), + "phase_coded_freeze": ( + "controller-followthrough-20261017/phase-coded-clean-20261020/FREEZE.json", + "284e6239ae3287bb139497fe610e67def239ad50697f230b61ac7c7280fb4b75", + ), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +need(sha256(RING_PATH.read_bytes()).hexdigest() == RING_PIN, "Exact phase library") +spec = importlib.util.spec_from_file_location("natural_phase_ring", RING_PATH) +ring = importlib.util.module_from_spec(spec) +spec.loader.exec_module(ring) +need(sha256(ring.LIBRARY.read_bytes()).hexdigest() == BASE_RING_PIN, + "Exact base phase library") +lib = ring.lib +add, linear, zipped = lib.add, lib.linear, lib.zipped +operated, multiply = ring.operated, ring.multiply +phases, route = lib.phases, lib.route + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + source, pins = {}, {} + for name, (relative, pin) in PINS.items(): + path = LANES / relative + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Exact source " + name) + source[name] = json.loads(raw) + pins[name] = {"path": str(path), "sha256": pin} + pins["phase_library"] = {"path": str(RING_PATH), "sha256": RING_PIN} + pins["base_phase_library"] = { + "path": str(ring.LIBRARY), "sha256": BASE_RING_PIN, + } + records = {(row["stage"], row["port"]): row + for row in source["views"]["entries"]} + code = source["row_code"] + p, r = code["selected_ports"], code["ordinary_ports"] + need(p == source["phase_coded"]["selected_ports"] and + r == source["phase_coded"]["ordinary_ports"], "Actual port partition") + c, e = lib.sparse(code["code"]), lib.sparse(code["response"]) + h = [{j: c[a][b] for j, b in enumerate(r) if b in c[a]} for a in p] + d = [{j: e[a][b] for j, b in enumerate(p) if b in e[a]} for a in r] + need(all(d[j].get(i, F(0)) == -h[i].get(j, F(0)) + for i in range(16) for j in range(96)), "D is minus H transpose") + q = [records[0, a]["q"] for a in range(112)] + g = {(s, a): tuple(records[s, a]["route_columns"]) + for s in range(3) for a in range(112)} + forward = source["phase_coded"]["phase_coded_forward"] + backward = source["phase_coded"]["phase_coded_backward"] + f9 = phases([(1 << i, 1) for i in range(9)]) + f25 = phases([(1 << i, 1) for i in range(25)]) + units = [{(i, lib.ID): F(1)} for i in range(224)] + entry, exit_view, exterior = {}, {}, {} + phase_checks = 0 + for s in (1, 2): + exterior[s] = phases([(1 << i, 1) for i in range(9, 9 + 8 * s)]) + fprev = phases([(1 << i, 1) for i in range(9 + 8 * (s - 1))]) + fnext = phases([(1 << i, 1) for i in range(9 + 8 * s)]) + for a in range(112): + alignment = records[s, a]["literal_stage_alignment"] + need(alignment["entry_X"] == alignment["entry_Y"] and + alignment["exit_X"] == alignment["exit_Y"], "Paired views") + need(lib.act(g[s, a], q[a]) == q[a], "The route fixes its own line") + entry[s, a] = multiply( + phases([(lib.act(g[s, a], alignment["entry_X"]), 2)]), + route(g[s, a])) + exit_view[s, a] = multiply( + phases([(alignment["exit_X"], 2)]), route(g[s, a])) + need(multiply(entry[s, a], fprev) == + multiply(multiply(exterior[s], phases([(q[a], 1)])), + route(g[s, a])), "Natural FULL entry") + need(multiply(multiply(entry[s, a], fprev), + phases([(q[a], -1)])) == + multiply(exterior[s], route(g[s, a])), "Natural hole entry") + need(multiply(exit_view[s, a], fnext) == + multiply(fnext, route(g[s, a])), "Natural FULL exit") + need(multiply(multiply(exit_view[s, a], fnext), + phases([(q[a], -1)])) == + multiply(multiply(fnext, phases([(q[a], -1)])), + route(g[s, a])), "Natural hole exit") + need(multiply(exit_view[s, a], f25) == + multiply(f25, route(g[s, a])), "Final FULL shear view") + need(multiply(exit_view[s, a], exit_view[s, a]) == lib.ID, + "The FULL view is an involution") + phase_checks += 6 + + def input_inverse(rows, selected_type): + return [operated(phases([(q[i % 112], -1)]), row) + if i < 112 or selected_type == "Q" and i - 112 in p else row + for i, row in enumerate(rows)] + + def output_frame(rows): + return [operated(multiply(f9, phases([(q[i % 112], -1)])), row) + if i >= 112 and i - 112 in r else operated(f9, row) + for i, row in enumerate(rows)] + + def local(matrix, rows): + return [add(*((F(value), + operated(phases([(q[j % 112], power)]), rows[j])) + for j, power, value in row)) + for row in matrix] + + def hs(s, rows, physical=False): + view = (lambda a: exit_view[s, a]) if physical and s else ( + lambda a: route(g[s, a])) + before = [operated(view(a), row) for a, row in zip(r, rows)] + return [operated(view(a), row) for a, row in zip(p, linear(h, before))] + + def ds(s, rows, physical=False): + view = (lambda a: exit_view[s, a]) if physical and s else ( + lambda a: route(g[s, a])) + before = [operated(view(a), row) for a, row in zip(p, rows)] + return [operated(view(a), row) for a, row in zip(r, linear(d, before))] + + def call(rows, stage, matrix): + ext_inverse = phases([(1 << i, -1) for i in range(9, 9 + 8 * stage)]) + entered = [operated(multiply(ext_inverse, entry[stage, i % 112]), row) + for i, row in enumerate(rows)] + result = output_frame(local(matrix, input_inverse(entered, "Q"))) + return [operated(multiply(exit_view[stage, i % 112], exterior[stage]), row) + for i, row in enumerate(result)] + + def field_line(ports, rows, power): + return [operated(phases([(q[a], power)]), row) + for a, row in zip(ports, rows)] + + def joined(ap, ur, zp, vr): + rows = [None] * 224 + for ports, values, offset in ((p, ap, 0), (r, ur, 0), + (p, zp, 112), (r, vr, 112)): + for a, row in zip(ports, values): + rows[offset + a] = row + return rows + + variants = {} + for selected_type in ("I", "Q"): + initial = input_inverse(units, selected_type) + a0, u0 = [initial[a] for a in p], [initial[a] for a in r] + z0, v0 = [initial[112 + a] for a in p], [initial[112 + a] for a in r] + alpha = zipped(a0, hs(0, u0)) + residual = zipped(ds(1, alpha), field_line(r, v0, -1), cb=-1) + beta = zipped(alpha, hs(2, residual)) + final_u = zipped(u0, ds(1, alpha)) + stage0 = output_frame(local(forward, initial)) + stage1 = call(stage0, 1, backward) + ordinary = call(stage1, 2, forward) + expected = joined([add((-1, row)) for row in z0], residual, beta, final_u) + expected = [operated(f25, row) for row in expected] + need(ordinary == expected, "The actual unmodified F_Q triple endpoint") + + middle = list(stage1) + correction = ds(1, [middle[a] for a in p], physical=True) + for a, row in zip(r, correction): + middle[a] = add((1, middle[a]), (-1, row)) + shortened = call(middle, 2, forward) + for a, row in zip(p, hs(2, [shortened[a] for a in r], physical=True)): + shortened[112 + a] = add((1, shortened[112 + a]), (-1, row)) + for a, row in zip(p, hs(0, [shortened[112 + a] for a in r], physical=True)): + shortened[112 + a] = add((1, shortened[112 + a]), (-1, row)) + expected_short = joined( + [add((-1, row)) for row in z0], + [add((-1, row)) for row in field_line(r, v0, -1)], a0, u0) + expected_short = [operated(f25, row) for row in expected_short] + need(shortened == expected_short, "Three legal FULL shears give the short endpoint") + need(all(shortened[a] == operated( + multiply(f25, phases([(q[a], -1)])), + add((-1, units[112 + a]))) for a in r), "Ordinary borrowed q type") + need(all(shortened[112 + a] == operated( + multiply(f25, phases([(q[a], -1)])), units[a]) for a in range(112)), + "The data output is F25 q X0") + if selected_type == "Q": + need(all(shortened[a] == operated( + multiply(f25, phases([(q[a], -1)])), + add((-1, units[112 + a]))) for a in p), "Common q on both banks") + else: + need(all(shortened[a] == operated(f25, add((-1, units[112 + a]))) + for a in p), "I entry restores selected borrowed fields") + + terminal = list(shortened) + for a in range(112): + terminal[112 + a] = operated(phases([(q[a], 1)]), terminal[112 + a]) + for a in r + (p if selected_type == "Q" else []): + terminal[a] = operated(phases([(q[a], 1)]), terminal[a]) + want = [operated(f25, add((-1, units[112 + a]))) for a in range(112)] + want += [operated(f25, units[a]) for a in range(112)] + need(terminal == want, "The direct terminal gives the signed physical exchange") + need(shortened != want, "Omission of the remaining q correction fails") + wrong = list(stage1) + for a, row in zip(r, correction): + wrong[a] = add((1, wrong[a]), (1, row)) + need(call(wrong, 2, forward) != call(middle, 2, forward), + "The wrong middle correction fails") + variants[selected_type] = { + "all_arbitrary_input_columns": 224, + "all_physical_output_rows": 224, + "unmodified_endpoint_terms": sum(map(len, ordinary)), + "shortened_endpoint_terms": sum(map(len, shortened)), + "shortened_endpoint": ( + "X=-F25 q Y0; Y=F25 q X0" if selected_type == "Q" else + "X_P=-F25 Y0_P; X_R=-F25 q_R Y0_R; Y=F25 q X0"), + "new_native_children_for_three_shears": 0, + "direct_terminal_positive_lines": 224 if selected_type == "Q" else 208, + "native_mass_before_terminal": 5376 if selected_type == "Q" else 5392, + "native_mass_with_direct_terminal": 5600, + } + print("checked actual D25 phase-coded triple, initial " + selected_type, flush=True) + + scalar_price = sum( + 2 * (3 + abs(value.numerator).bit_length() - 1 + + abs(value.numerator).bit_count() + value.denominator.bit_length() - 1) + for row in h for value in row.values()) + need(sum(map(len, h)) == 216 and scalar_price == 2048, "Direct scalar tariff") + receipt = { + "status": "PASS_ACTUAL_D25_PHASE_CODED_TRIPLE", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins": pins, + "phase_identities": phase_checks, + "variants": variants, + "three_direct_FULL_shears": { + "scalar_primitives": 3 * scalar_price, + "affine_map_calls": 448, + "owned_fields": 0, + "native_children": 0, + }, + "scope": ( + "The actual D25 physical endpoint is verified on arbitrary data. " + "The native local helper contracts are inherited. The direct " + "remaining line terminal is checked as an operator, not as a " + "hosted recursive word. Common q is not a free terminal." + ), + } + (args.out / "CHECKS.json").write_text( + json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps({ + "status": receipt["status"], "phase_identities": phase_checks, + "variants": variants, + }, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/run-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..6695433af8 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/run-normal/CHECKS.json @@ -0,0 +1,62 @@ +{ + "checker_sha256": "82a36b9f258d1aa2d95830502b336eb8aae9e7beff643b1f854c3d87451098f6", + "phase_identities": 1344, + "scope": "The actual D25 physical endpoint is verified on arbitrary data. The native local helper contracts are inherited. The direct remaining line terminal is checked as an operator, not as a hosted recursive word. Common q is not a free terminal.", + "source_pins": { + "base_phase_library": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/coupled-data-split-20261020/check_typed_split.py", + "sha256": "70ca9ce2dff5256644f35ef65344c7e0dd9f78e3fb48c18436e9e5c20b4f9109" + }, + "phase_coded": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/final-normal/PHASE-CODED.json.gz", + "sha256": "ffdbe1c84af50e58ee0ab3a9ada15571476146caad1119f55e17d655934f0874" + }, + "phase_coded_freeze": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/FREEZE.json", + "sha256": "284e6239ae3287bb139497fe610e67def239ad50697f230b61ac7c7280fb4b75" + }, + "phase_library": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/check_no_reset.py", + "sha256": "8612732e02b68495d6b0b95cbd216d1d0df43be2ffdd29cc7fc9033518ab1c48" + }, + "row_code": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz", + "sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + } + }, + "status": "PASS_ACTUAL_D25_PHASE_CODED_TRIPLE", + "three_direct_FULL_shears": { + "affine_map_calls": 448, + "native_children": 0, + "owned_fields": 0, + "scalar_primitives": 6144 + }, + "variants": { + "I": { + "all_arbitrary_input_columns": 224, + "all_physical_output_rows": 224, + "direct_terminal_positive_lines": 208, + "native_mass_before_terminal": 5392, + "native_mass_with_direct_terminal": 5600, + "new_native_children_for_three_shears": 0, + "shortened_endpoint": "X_P=-F25 Y0_P; X_R=-F25 q_R Y0_R; Y=F25 q X0", + "shortened_endpoint_terms": 224, + "unmodified_endpoint_terms": 22160 + }, + "Q": { + "all_arbitrary_input_columns": 224, + "all_physical_output_rows": 224, + "direct_terminal_positive_lines": 224, + "native_mass_before_terminal": 5376, + "native_mass_with_direct_terminal": 5600, + "new_native_children_for_three_shears": 0, + "shortened_endpoint": "X=-F25 q Y0; Y=F25 q X0", + "shortened_endpoint_terms": 224, + "unmodified_endpoint_terms": 22160 + } + } +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/run-optimized/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/run-optimized/CHECKS.json new file mode 100644 index 0000000000..6695433af8 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/phase-coded-triple-20261020/run-optimized/CHECKS.json @@ -0,0 +1,62 @@ +{ + "checker_sha256": "82a36b9f258d1aa2d95830502b336eb8aae9e7beff643b1f854c3d87451098f6", + "phase_identities": 1344, + "scope": "The actual D25 physical endpoint is verified on arbitrary data. The native local helper contracts are inherited. The direct remaining line terminal is checked as an operator, not as a hosted recursive word. Common q is not a free terminal.", + "source_pins": { + "base_phase_library": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/coupled-data-split-20261020/check_typed_split.py", + "sha256": "70ca9ce2dff5256644f35ef65344c7e0dd9f78e3fb48c18436e9e5c20b4f9109" + }, + "phase_coded": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/final-normal/PHASE-CODED.json.gz", + "sha256": "ffdbe1c84af50e58ee0ab3a9ada15571476146caad1119f55e17d655934f0874" + }, + "phase_coded_freeze": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/phase-coded-clean-20261020/FREEZE.json", + "sha256": "284e6239ae3287bb139497fe610e67def239ad50697f230b61ac7c7280fb4b75" + }, + "phase_library": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/no-reset-triple-20261020/check_no_reset.py", + "sha256": "8612732e02b68495d6b0b95cbd216d1d0df43be2ffdd29cc7fc9033518ab1c48" + }, + "row_code": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz", + "sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + } + }, + "status": "PASS_ACTUAL_D25_PHASE_CODED_TRIPLE", + "three_direct_FULL_shears": { + "affine_map_calls": 448, + "native_children": 0, + "owned_fields": 0, + "scalar_primitives": 6144 + }, + "variants": { + "I": { + "all_arbitrary_input_columns": 224, + "all_physical_output_rows": 224, + "direct_terminal_positive_lines": 208, + "native_mass_before_terminal": 5392, + "native_mass_with_direct_terminal": 5600, + "new_native_children_for_three_shears": 0, + "shortened_endpoint": "X_P=-F25 Y0_P; X_R=-F25 q_R Y0_R; Y=F25 q X0", + "shortened_endpoint_terms": 224, + "unmodified_endpoint_terms": 22160 + }, + "Q": { + "all_arbitrary_input_columns": 224, + "all_physical_output_rows": 224, + "direct_terminal_positive_lines": 224, + "native_mass_before_terminal": 5376, + "native_mass_with_direct_terminal": 5600, + "new_native_children_for_three_shears": 0, + "shortened_endpoint": "X=-F25 q Y0; Y=F25 q X0", + "shortened_endpoint_terms": 224, + "unmodified_endpoint_terms": 22160 + } + } +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/CHECKS.json new file mode 100644 index 0000000000..bad1d5c415 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/CHECKS.json @@ -0,0 +1,129 @@ +{ + "characters": [ + 1, + 2, + 3, + 6, + 6 + ], + "checker_sha256": "058afef01abad26ff10faa0b697f15a09157357d6a640c6f19f489fbd13fcaeb", + "classification_mod4": { + "0": "13I at every width", + "1": "Singular at every width at least five", + "2": "All-width invertible translation operator with reviewed finite kernel", + "3": "Singular at every width at least five" + }, + "leading_minor": "-73", + "minimum_singular_width_claimed": false, + "null_vector": [ + 0, + 0, + 1, + 0, + -1, + 1, + 0, + 1 + ], + "ordinary_image_squared_norm": "52", + "rank": 7, + "selected_ports": [ + 0, + 7, + 20, + 27, + 36, + 46, + 57, + 111 + ], + "singular_matrix": [ + [ + "1/2", + "-1/2", + "-2", + "7/2", + "-2", + "0", + "-5/2", + "0" + ], + [ + "-1/2", + "5/2", + "0", + "-5/2", + "-2", + "-2", + "3/2", + "0" + ], + [ + "-2", + "0", + "-3/2", + "2", + "-1/2", + "3/2", + "0", + "-1/2" + ], + [ + "7/2", + "-5/2", + "2", + "1/2", + "0", + "-2", + "-5/2", + "0" + ], + [ + "-2", + "-2", + "-1/2", + "0", + "1/2", + "3/2", + "0", + "-1/2" + ], + [ + "0", + "-2", + "3/2", + "-2", + "3/2", + "1/2", + "0", + "-1/2" + ], + [ + "-5/2", + "3/2", + "0", + "-5/2", + "0", + "0", + "1/2", + "0" + ], + [ + "0", + "0", + "-1/2", + "0", + "-1/2", + "-1/2", + "0", + "1/2" + ] + ], + "source_pins": { + "SINGULAR-WITNESS.json": "fda1f40ef3f9f80af736570394260c21abbf737c31fe3228ca6883bd29812401", + "SINGULAR-WITNESS.md": "bb3685f88876c941d2340a4e22f5622d844fb78ed33b0588017af40ad0e91368", + "check_singular_witness.py": "8ddb01debc65ae9d7c401a868f3c25cf9e86d3b0fceb79e817aff916649b0641" + }, + "status": "PASS_COHERENT_POWER_SCHUR_CLASSIFICATION", + "supplier_decoder_claimed": false +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/CLASSIFICATION.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/CLASSIFICATION.md new file mode 100644 index 0000000000..2504e51d92 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/CLASSIFICATION.md @@ -0,0 +1,166 @@ +# Coherent line powers in the actual centre Schur operator + +The actual graph has a sharp distinction between odd and even coherent +line powers. Put + +```text +S_k = B Q_U^k D, D=B^T, BD=13I. +``` + +The same integer k acts at all 104 ordinary ports. The native line has +fourth power I. At every positive tensor width, `S_0=13I`, and `S_2` +has the reviewed finite translation inverse. Each odd-power operator +is singular at every width at least five. Thus replacing an odd-power +Schur inverse by the squared-line Schur inverse changes an impossible +uniform inverse into an available one. The replacement has explicit +odd arithmetic and implementation costs. + +| k modulo four | Uniform conclusion | +| --- | --- | +| 0 | `S_k=13I` at every width | +| 1 | Singular at every width at least five | +| 2 | Invertible at every width; inverse has a fixed finite translation kernel | +| 3 | Singular at every width at least five | + +This table concerns invertibility over the rational or complex field. +It does not say that the even cases have dyadic inverses. The inverse +of `13I` needs division by 13. The squared-line inverse has odd +denominator 2,145 in its character matrices. + +## A direct actual-source obstruction + +Use selected ports `A=[0,7,20,27,36,46,57,111]` and their ordinary +complement U. In this order, `B=R_A^T R_U/4`. For the five tensor-copy +characters + +```text +(1,2,3,6,6), +``` + +the native phase at label q is + +```text +i^(parity(q.1)+parity(q.2)+parity(q.3)+2 parity(q.6)) + = (-1)^(q0*q1+q0+q2). +``` + +The checker verifies all 512 label values directly. The phase is real, +so it is the same for Q and Q^-1. The actual 104 columns give the +following matrix, with no model replacement: + +```text + [ 1 -1 -4 7 -4 0 -5 0 ] + [-1 5 0 -5 -4 -4 3 0 ] + [-4 0 -3 4 -1 3 0 -1 ] +2 S_1 = [ 7 -5 4 1 0 -4 -5 0 ] + [-4 -4 -1 0 1 3 0 -1 ] + [ 0 -4 3 -4 3 1 0 -1 ] + [-5 3 0 -5 0 0 1 0 ] + [ 0 0 -1 0 -1 -1 0 1 ]. +``` + +Its null vector is `v=(0,0,1,0,-1,1,0,1)`. Its leading seven-by-seven +minor is exactly `-73`. Hence its rank is exactly seven. Also, +`||Dv||^2=52`, and `Q Dv` lies in the kernel of B. A nonzero centre +direction has moved into the unobserved ordinary subspace. + +Append zero characters to obtain the same matrix at each larger width. +The real phase also gives the same matrix for `S_3`. Finally, `Q^4=I` +reduces every integer k to one of the four cases in the table. No +minimum singular width is claimed. + +The independent checker imports no producer code. It pins the frozen +singular witness and reconstructs the graph, phases, null vector, +rank certificate, and ordinary image from the primary R and q files. +It also binds the positive result to the independent all-width +translation review. + +## The squared-line inverse and its physical scope + +For `T=S_2`, the exact spectra at all widths are contained in +`{+-1,+-3,+-5,+-11,+-13}`. All values occur. The character of Q squared +depends only on the XOR of the tensor-copy characters, so 512 exact +eight-by-eight checks cover every width. The finite inverse has 256 +simultaneous translation shifts, 4,544 nonzero coefficients, and common +denominator `8580=4*2145`. + +The independently reviewed local service applies `y += T^-1 x` to +two distinct existing FULL centre banks, with one owned field C0. It +uses zero native children. One schedule costs 114,528 scalar primitives, +8,944 body translations, sixteen real division-by-2,145 scans, and +32 completed-view maps. The alternative trades more scalar operations +for fewer maps. The source bank is unchanged; all target baselines are +arbitrary; C0 has zero output. A three-shear coded exchange is also +available. These are complete local words, not full supplier decoders. + +The stage content routes give + +```text +B_s = rho_A^-1 B rho_U, +D_s = rho_U^-1 D rho_A. +``` + +Each port route fixes its own native direction, so it commutes with +that port's Q. Thus `S_(k,s)=rho_A^-1 S_k rho_A`. The classification +and the nonzero null modes transfer to every actual stage. The physical +view translations remain part of the implementation; they are already +included in the reviewed service. This algebra does not remove those +translations from an emitted word. + +## A precise positive-line section + +Let the required query be `A_query=BQ_U`. A completion confined to the +unchanged image of D would have form `D H`. Its query response is +`S_1 H`. At the displayed mode S_1 is not surjective, so no H can make +that response the identity on arbitrary centre values. This also +excludes a nonlinear choice of H with values in that fixed image: a +centre value outside the range of S_1 has no preimage there. + +The positive-line image instead gives the exact section + +```text +K_plus = Q_U D T^-1, +A_query K_plus = I. +``` + +The known inverse-line section is `K_minus=q_U D/13`. Their relation is + +```text +K_plus = Q_U^2 K_minus (13 T^-1). +``` + +The ordinary factor Q squared is a translation, and the centre factor +has the finite service above. This proves a uniform change of section +with an explicit centre code. It does not make a dense scatter free. +An additive scatter must apply the ordinary translation to the update, +or conjugate its target bank before and after that scatter. A complete +construction must also provide the centre owners needed to form the +encoded source. The two-bank additive inverse service does not by itself +give an in-place inverse on a single centre bank. + +This distinction identifies the next useful construction problem: +implement the squared-line code at a cut with available centre owners, +then carry it through the physical data endpoint. A larger joint unit, +an additive shear, a restricted-input inverse, or a code that retains +the lost direction elsewhere remains outside the odd-power obstruction. + +## Reproduction and scope + +Run with one process from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/check_classification.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/check_classification.py +``` + +Both runs print `PASS_COHERENT_POWER_SCHUR_CLASSIFICATION` and produce +the same receipt bytes. The separate spectral and literal-service +reviews supply their own reproduction commands and source pins. +The complete supplier's root grid, ownership, recursive accounting, +and final physical decoder remain separate obligations. No native lower +bound, complete supplier admission, or kappa improvement is claimed. +The work builds on the campaign's native graph, phase-access proof, +singular-mode search, and translation service. OpenAI Codex assisted +the calculation and proof. No PR, push, or commit was made. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/FREEZE.json new file mode 100644 index 0000000000..9e90d43c11 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/FREEZE.json @@ -0,0 +1,9 @@ +{ + "files": { + "CHECKS.json": "2d85475317b969c47501d0ed9e57be3254d624472906eab8021ee5892c65447f", + "CLASSIFICATION.md": "9f06ddba79bb14cb88c3a19000d1ed1bb41a9fbbe8149d35b7e2854b4593feb6", + "check_classification.py": "058afef01abad26ff10faa0b697f15a09157357d6a640c6f19f489fbd13fcaeb" + }, + "normal_and_optimized_runs": "byte-identical receipt", + "status": "PASS_COHERENT_POWER_SCHUR_CLASSIFICATION" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/check_classification.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/check_classification.py new file mode 100644 index 0000000000..5d1988c607 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-power-classification/check_classification.py @@ -0,0 +1,92 @@ +"""Check the actual singular mode and the coherent-power Schur classification.""" + +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import json + +HERE = Path(__file__).resolve().parent +BASE = HERE.parent +SOURCE = BASE / "owner-review/centre-schur-singularity" +PINS = { + "SINGULAR-WITNESS.md": "bb3685f88876c941d2340a4e22f5622d844fb78ed33b0588017af40ad0e91368", + "SINGULAR-WITNESS.json": "fda1f40ef3f9f80af736570394260c21abbf737c31fe3228ca6883bd29812401", + "check_singular_witness.py": "8ddb01debc65ae9d7c401a868f3c25cf9e86d3b0fceb79e817aff916649b0641", +} + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def read(path, pin): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == pin, "Pinned source: " + str(path)) + return json.loads(raw) + + +for name, pin in PINS.items(): + need(sha256((SOURCE / name).read_bytes()).hexdigest() == pin, "Frozen singular witness") +spectral = read(BASE / "owner-review/centre-schur-probe/SCHUR-PROBE.json", + "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024") +review = read(BASE / "schur-review/REVIEW.json", "574007db390991f2eeb058e22d733bef4238a739e545318eeff229909a2bd36b") +need(review["status"] == "PASS_INDEPENDENT_SCHUR_REVIEW", "Independent all-width inverse proof") +original = {} +for name in ("interface", "phases"): + pin = spectral["source_pins"][name] + original[name] = read(Path(pin["path"]), pin["sha256"]) +R = [[F(row.get(str(p), 0)) for p in range(112)] for row in original["interface"]["R"]] +q = [row["q"] for row in original["phases"]["recipes"]] +A = [0, 7, 20, 27, 36, 46, 57, 111] +U = [p for p in range(112) if p not in A] +B = [[sum(row[a] * row[p] for row in R) / 4 for p in U] for a in A] +need(all(sum(B[i][p] * B[j][p] for p in range(104)) == 13 * int(i == j) for i in range(8) for j in range(8)), "Actual BD=13I") +characters = (1, 2, 3, 6, 6) +for label in range(512): + phase = sum((label & character).bit_count() % 2 for character in characters) % 4 + x, y, z = [(label >> j) & 1 for j in range(3)] + need(phase == (2 * (x * y + x + z)) % 4, "Exact width-five quadratic phase") + need(phase == 3 * phase % 4, "The same witness has inverse-line orientation") +signs = [1 if sum((q[p] & character).bit_count() % 2 for character in characters) % 4 == 0 else -1 for p in U] +S = [[sum(B[i][p] * B[j][p] * signs[p] for p in range(104)) for j in range(8)] for i in range(8)] +null = [0, 0, 1, 0, -1, 1, 0, 1] +need(all(sum(coefficient * value for coefficient, value in zip(row, null)) == 0 for row in S), "Exact nonzero null vector") + + +def determinant(matrix): + matrix = [row[:] for row in matrix] + result = F(1) + for j in range(len(matrix)): + pivot = next((i for i in range(j, len(matrix)) if matrix[i][j]), None) + if pivot is None: + return F(0) + if pivot != j: + matrix[j], matrix[pivot] = matrix[pivot], matrix[j] + result = -result + value = matrix[j][j] + result *= value + matrix[j] = [entry / value for entry in matrix[j]] + for i in range(j + 1, len(matrix)): + factor = matrix[i][j] + matrix[i] = [entry - factor * above for entry, above in zip(matrix[i], matrix[j])] + return result + + +minor = determinant([row[:7] for row in S[:7]]) +need(minor == -73 and determinant(S) == 0, "Exact rank seven") +ordinary = [sum(B[i][p] * null[i] for i in range(8)) for p in range(104)] +need(sum(value**2 for value in ordinary) == 52, "The lost ordinary image is nonzero") +need(all(sum(B[i][p] * signs[p] * ordinary[p] for p in range(104)) == 0 for i in range(8)), "The line image lies in the query kernel") +need(signs.count(1) == 54 and signs.count(-1) == 50, "Actual phase partition") +result = dict(status="PASS_COHERENT_POWER_SCHUR_CLASSIFICATION", source_pins=PINS, + characters=list(characters), selected_ports=A, null_vector=null, + singular_matrix=[[str(value) for value in row] for row in S], + leading_minor=str(minor), rank=7, ordinary_image_squared_norm="52", + classification_mod4={"0": "13I at every width", "1": "Singular at every width at least five", + "2": "All-width invertible translation operator with reviewed finite kernel", + "3": "Singular at every width at least five"}, + minimum_singular_width_claimed=False, supplier_decoder_claimed=False, + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest()) +(HERE / "CHECKS.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n", encoding="utf-8") +print(result["status"]) diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/REVIEW.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/REVIEW.json new file mode 100644 index 0000000000..1a015a8bd2 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/REVIEW.json @@ -0,0 +1,97 @@ +{ + "all_width_scope": "Translation Schur T has the same 512 character matrices at every width, indexed by XOR of the copy characters.", + "bad_norms": { + "(-1, -2)": [ + 40, + 52 + ], + "(-1, 2)": [ + 40, + 52 + ], + "(-3, 0)": [ + 100 + ], + "(0, -1)": [ + 10, + 10 + ], + "(0, 1)": [ + 10, + 10 + ], + "(1, -2)": [ + 52, + 40 + ], + "(1, 2)": [ + 52, + 40 + ], + "(3, 0)": [ + 100 + ] + }, + "checker_sha256": "16462b9ec0c114c986aa59e658524afd007d070d6039174b75602713d9ee9701", + "gaussian_dyadic_feedback_candidates": [ + [ + -3, + 0 + ], + [ + -1, + -2 + ], + [ + -1, + 2 + ], + [ + 0, + -1 + ], + [ + 0, + 0 + ], + [ + 0, + 1 + ], + [ + 1, + -2 + ], + [ + 1, + 2 + ], + [ + 3, + 0 + ] + ], + "inverse_character_orders": 1024, + "kernel_checks": { + "inverse": { + "coefficients": 4544, + "denominator": 8580, + "shifts": 256 + }, + "translation": { + "coefficients": 1664, + "denominator": 4, + "shifts": 104 + } + }, + "no_full_supplier_claim": true, + "no_native_factor_for_S": true, + "root_formula_cases": 512, + "source_pins": { + "SCHUR-PROBE.json": "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024", + "SCHUR-PROBE.md": "1de7ddbc3bf60246883631bf57e50d22d24f94311af649e325d5297d021bdf04", + "check_schur.py": "eb7f8f53bf195dbb7e534d1bc835560a8240adfe771ce11ee2f927fe6f1b7c55" + }, + "spectral_power_sum_checks": 4096, + "status": "PASS_INDEPENDENT_SCHUR_REVIEW" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/REVIEW.md new file mode 100644 index 0000000000..742a26980c --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/REVIEW.md @@ -0,0 +1,145 @@ +# Independent review of the translation Schur inverse + +The frozen translation Schur result passes an independent exact check. +For the actual supplier graph, the operator + +```text +T = B Q_U^2 D, D=B^T, BD=13I +``` + +has the same ten possible eigenvalues at every positive tensor width: +`-13,-11,-5,-3,-1,1,3,5,11,13`. It has the stated inverse translation +kernel with 256 shifts, 4,544 nonzero coefficients, and common denominator +8,580. This review also proves that no nonzero Gaussian-dyadic constant +alpha gives a uniform Gaussian-dyadic inverse for `I+alpha B Q_U D`. +The latter operator is different from T. + +## Independent method and source scope + +`check_schur_review.py` does not import the producer checker. It reads the +pinned primary R matrix and native q labels, then forms each graph column +in the selected basis. It adds the eight missing directions to obtain +the complete 120-root table. It checks every entry of the complete-root +Fourier identity for all 512 characters. + +For each actual eight-by-eight T character matrix, the checker computes +the first eight power sums by integer matrix multiplication. It compares +them with the claimed spectral multiset. The first eight power sums +determine the degree-eight characteristic polynomial by Newton's +identities in characteristic zero. Each matrix is real symmetric. Thus +the multiset determines its spectrum with multiplicity, and the stated +ten-root polynomial annihilates it. The checker also verifies the inverse +polynomial at each of those ten roots. + +The review then reads the literal rational translation kernels. It uses +direct character sums, without the producer's Walsh inversion. For each +character it verifies both matrix products with the inverse numerator. +Both products are exactly `8580 I`. It also verifies the forward kernel +and the stated row one-norms. There are 1,024 inverse-order checks. + +For any width, the eigenvalue of `Q_p^2` is + +```text +(-1)^(q_p . XOR_j chi_j). +``` + +All 512 characters occur, and every character tuple maps to one of them. +Thus the finite check proves the same identity at every positive width. +Each kernel translation applies its nine-bit shift in every tensor +copy. This is not a tensor power of a width-one matrix inverse. + +The producer proof, receipt, and checker hashes are checked before and +after the review. The receipt records the primary source pins and the +review checker hash. The review does not change the frozen sources. + +## A stronger constant-feedback obstruction + +Let `R=Z[i,1/2]` and `S=B Q_U D`. At width two, take both spatial +characters equal. Direct evaluation of the actual graph gives + +```text +chi=71: S=-I, chi=204: S=I, +chi=30: S=-3I, chi=460: S=3I. +``` + +Zero characters in the other copies extend these witnesses to each +width at least two. Suppose `I+alpha S` has an inverse over R in every +case, where alpha is a constant in R. The first two witnesses imply +that `u=1+alpha` and `v=1-alpha` are units of R, with `u+v=2`. + +Write `pi=1+i`. Each unit of R is `epsilon pi^k`, where k is an integer +and `epsilon` is one of `1,-1,i,-i`. The pi-adic valuation of 2 is 2. +If u and v have different valuations, their smaller valuation must be +2. Divide the sum by `pi^2`. The larger remaining power of pi is a +difference of two fourth roots of unity. A nonzero such difference has +valuation 1 or 2. Hence the two original valuations are 2 and either +3 or 4. + +If the valuations are equal to k, the sum of their two unit factors is +nonzero. Its valuation is 1 or 2. Thus k is 1 or 0. These two cases +prove that it is enough to check `epsilon pi^k` for `0<=k<=4`; negative +valuations cannot occur. Exact enumeration then gives + +```text +alpha in {0, i, -i, 3, -3, 1+2i, 1-2i, -1+2i, -1-2i}. +``` + +Every nonzero candidate fails at one of `S=3I` and `S=-3I`. The norm of +the corresponding `1+alpha S` scalar has an odd factor: the rejecting +norms are among 10, 40, 52, and 100. An element of R is a unit only if +its nonzero norm is a power of two, with an integer exponent. This +contradiction proves the claim for every nonzero constant alpha in R. + +The checker verifies the finite unit equation and every rejecting norm. +This is a uniform ring-invertibility obstruction. It is not a native +child lower bound. It does not exclude an exact odd-grid inverse where +the operator is nonsingular, an operator-valued feedback coefficient, +or a joint unit on data and centre fields. + +## A constructive consequence with a precise limit + +The translation inverse gives an exact right inverse with positive line +orientation. Define + +```text +A = B Q_U, +K_plus = Q_U D T^-1. +``` + +Then `A K_plus = B Q_U^2 D T^-1 = I`. Also, + +```text +K_plus = Q_U^2 (q_U D) T^-1, q_U=Q_U^-1. +``` + +The extra ordinary factor `Q_U^2` is a translation. The centre factor +`T^-1` has a finite translation implementation with fixed odd +arithmetic. Thus this is a precise operator conversion between a +dense inverse-line scatter and a dense positive-line right inverse. +It does not provide the scatter for free. A physical construction must +still give the selected cut, available centre owners, legal source +access, complete local prices, and the final data and helper endpoint. + +The operator S also has the stated nonnormal witness. The review forms +its real and imaginary parts directly from the q labels at width-two +characters `(1,2)`. Their commutator entry `(0,1)` is `1/2`; hence the +same entry of `S* S-S S*` is i. This excludes a single unitary conjugate +of a diagonal phase operator. It does not exclude products of factors. + +## Reproduction and status + +Run with one process from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/check_schur_review.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/schur-review/check_schur_review.py +``` + +Both runs print `PASS_INDEPENDENT_SCHUR_REVIEW`. Their receipts are +byte-identical. This review covers the spectral theorem, the exact +kernels, the two scoped obstructions, and the algebraic right inverse. +The new literal translation-service word has a separate review. No +complete controller, supplier admission, or kappa improvement is +claimed here. OpenAI Codex assisted this review and its exact checker. +No PR, push, or commit was made. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/FREEZE.json new file mode 100644 index 0000000000..ded451ca0a --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/FREEZE.json @@ -0,0 +1,9 @@ +{ + "files": { + "REVIEW.json": "7d9f3f9eccf3629ac97e693d2e2afbc869ba8cf154a15cc1d08cfbf3e94eb1d9", + "REVIEW.md": "0bf7d8470f5d6fb42df098d3e150b0129e2570f418bf70ae17d8a3ec6e25ccac", + "check_service_review.py": "c638572c6abf5efb6e6a95beca07527d2f806732745455ccdd8eb25e8e22d249" + }, + "normal_and_optimized_runs": "byte-identical receipt", + "status": "PASS_INDEPENDENT_TRANSLATION_SERVICE_REVIEW" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/REVIEW.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/REVIEW.json new file mode 100644 index 0000000000..db2283d541 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/REVIEW.json @@ -0,0 +1,151 @@ +{ + "all_live_columns": 16, + "arbitrary_owned_inputs": 1, + "body_checks": { + "T_minus": { + "invoice": { + "ADD": 832, + "CLEAR": 105, + "TRANSLATE": 104, + "scalar_primitives": 8530, + "translation_maps": 104 + }, + "maximum_row_norm": "53" + }, + "T_plus": { + "invoice": { + "ADD": 832, + "CLEAR": 105, + "TRANSLATE": 104, + "scalar_primitives": 8530, + "translation_maps": 104 + }, + "maximum_row_norm": "53" + }, + "exchange_few_maps_minus": { + "invoice": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2256, + "real_odd_division_scans": 16, + "scalar_primitives": 183972, + "translation_maps": 2256 + } + }, + "exchange_few_maps_plus": { + "invoice": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2256, + "real_odd_division_scans": 16, + "scalar_primitives": 183972, + "translation_maps": 2256 + } + }, + "exchange_few_scalars_minus": { + "invoice": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 9152, + "real_odd_division_scans": 16, + "scalar_primitives": 131588, + "translation_maps": 9152 + } + }, + "exchange_few_scalars_plus": { + "invoice": { + "ADD": 15952, + "CLEAR": 218, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 9152, + "real_odd_division_scans": 16, + "scalar_primitives": 131588, + "translation_maps": 9152 + } + }, + "few_maps_minus": { + "invoice": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2048, + "real_odd_division_scans": 16, + "scalar_primitives": 166912, + "translation_maps": 2048 + }, + "maximum_row_norm": "9073/715" + }, + "few_maps_plus": { + "invoice": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 26288, + "TRANSLATE": 2048, + "real_odd_division_scans": 16, + "scalar_primitives": 166912, + "translation_maps": 2048 + }, + "maximum_row_norm": "9073/715" + }, + "few_scalars_minus": { + "invoice": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 8944, + "real_odd_division_scans": 16, + "scalar_primitives": 114528, + "translation_maps": 8944 + }, + "maximum_row_norm": "9073/715" + }, + "few_scalars_plus": { + "invoice": { + "ADD": 14288, + "CLEAR": 8, + "COPY": 8, + "DIVIDE_ODD": 8, + "SCALE2": 96, + "TRANSLATE": 8944, + "real_odd_division_scans": 16, + "scalar_primitives": 114528, + "translation_maps": 8944 + }, + "maximum_row_norm": "9073/715" + } + }, + "checker_sha256": "c638572c6abf5efb6e6a95beca07527d2f806732745455ccdd8eb25e8e22d249", + "completed_view_checks": 64, + "exchange_method": "Literal three-shear decomposition plus independently checked all-width T inverse", + "full_supplier_admission": false, + "odd_grid_source": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md", + "sha256": "e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01" + }, + "source_pins": { + "SCHUR-PROBE.json": "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024", + "TRANSLATION-SERVICE-PROGRAMS.json.gz": "7566388bfb2167b21a5632cd12f4f71004df9c95d5d823f2f0604a6d0847d0e5", + "TRANSLATION-SERVICE.json": "45273e561954139ece2c40697cc2d419aabc4db01c2013a38ef5379f35cc6599", + "TRANSLATION-SERVICE.md": "57d38fd23aae563b107f4924250fb975f2d4f9b6bcc5357735943ff10527a0d0", + "check_translation_service.py": "18cae3387c3a83c716ce2a43e47ec082ce72904e1a2516944278ab032c5de2a8" + }, + "status": "PASS_INDEPENDENT_TRANSLATION_SERVICE_REVIEW", + "untouched_borrowed_fields": "Every owner outside 0..16" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/REVIEW.md new file mode 100644 index 0000000000..d9dfae4195 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/REVIEW.md @@ -0,0 +1,133 @@ +# Independent review of the one-field translation service + +The literal service passes an independent exact review. It implements +`y += T x` or `y += T^-1 x` on two distinct existing eight-field centre +banks, with one owned field C0 and no native children. Both signs pass. +The source bank is unchanged, the target baseline is arbitrary, and C0 +has zero output for every owned input. Every other owner is untouched. + +Here `T=B Q_U^2 D` is the actual supplier translation operator. This +review uses the separately reviewed all-width inverse kernel. It does +not substitute an inverse of `B Q_U D`. + +## Exact checks + +The review checker imports no producer code. It pins the proof, receipt, +emitter, compressed payload, spectral receipt, and five original source +files. It reads the literal payload as a restricted instruction stream. +Only C0 and the eight target owners can change. Source reads, COPY, +CLEAR, binary scales, odd division, and translations have explicit +separate cases. The checker reconstructs each target's complete affine +translation kernel from the ordered instructions. + +Each of the six shear words agrees with its exact kernel on all sixteen +arbitrary live input fields. The arbitrary C0 input has zero coefficient +at every output, and C0 is zero at the end. This proves the complete +linear endpoint, rather than testing sample values. The two signs are +opposites on the target update, so both inverse orders are the identity +on all live fields. The owned C0 endpoint remains zero. + +For each of the four exchange words, the checker verifies that the +literal payload is exactly the concatenation of the three checked shear +words, with the required bank exchange and signs. With `V=T^-1`, the +positive word is + +```text +x += T y +y -= V x +x += T y +``` + +It sends `(x,y)` to `(T y,-V x)`. The negative word sends `(x,y)` to +`(-T y,V x)`. Both inverse orders follow from `TV=VT=I`, which the +independent spectral review checks at all 512 character matrices. The +square is `-I`, so the fourth power is I. This is an exact composition +proof from the literal shear bodies. It is not a claim that a second +full sparse replay of the concatenated exchange was run. + +The physical wrapper is also checked independently. For all 64 selected +port-and-stage views, the route is an orthogonal involution, and the two +stored translation orders agree. The FULL phase difference is zero on +the zero character, all 73 basis characters, and all pairs of basis +characters. A binary linear address map has a phase polynomial of degree +at most two modulo four, so these checks prove the full phase identity. +The emitted entry and exit wrappers match those pinned views for both +banks. Their complete count is 32 maps per call. + +The internal translations act only on C0 and use the same nine-bit +shift in every tensor copy. They commute with the common FULL native +frame. Thus the service returns each bank to its prescribed physical +frame, with the stated content operation. C0 can obtain that frame by +COPY or by its initial zero and subsequent source additions. No live +source is assumed zero. + +## Local cost and coefficient growth + +The independent instruction count gives: + +| Word, either sign | Scalar primitives | Body maps | Real odd scans | +| --- | ---: | ---: | ---: | +| Add T x | 8,530 | 104 | 0 | +| Add T^-1 x, fewer maps | 166,912 | 2,048 | 16 | +| Add T^-1 x, fewer scalars | 114,528 | 8,944 | 16 | +| Coded exchange, fewer maps | 183,972 | 2,256 | 16 | +| Coded exchange, fewer scalars | 131,588 | 9,152 | 16 | + +Each row also has 32 completed-view maps and zero native children. +The scalar column excludes maps and odd scans. Each inverse word uses +eight complex divisions by 2,145, hence sixteen real scans. The source +component is divided once, then held in C0 across its translations and +target broadcasts. Eight COPYs and eight CLEARs suffice for that word. + +The exact maximum prefix row one-norm is 53 for the forward shear and +`9073/715` for either inverse schedule. The checker reconstructs these +bounds from every literal instruction. For the exchange, the proved +upper bound is `472511/715`: the first update has bound 53, the middle +update has bound `1+53*(8358/715)`, and its completed output has bound +`8358/715`. The last update therefore has bound +`53+52*(8358/715)`. This is a local bound only. + +## Exact-grid and ownership boundary + +The inverse word is rational over `Z[i,1/2,1/2145]`. It is not a map on +arbitrary integer numerators at a fixed finest dyadic grid. The caller +must use an explicit common odd grid. One shear or one exchange raises +the required prefix odd height by at most one. Each inverse copy reads +an unchanged source component; in the exchange, the preceding source +update uses only dyadic operations. + +The exact odd-grid source is +`lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md`, +with SHA-256 +`e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01`. +The checker verifies this source pin. That reviewed backend can perform each real scan in +at most `4*(w_g+1)` arithmetic-head steps, with the separate descriptor +and counter cost. Thus the sixteen scans add at most +`64*(w_g+1)` such steps per service call. The complete supplier must +still give its stream width, common root scale, conversion costs, and +precision bound. A rational local endpoint must cancel inside the +complete parent endpoint before the depth-only grid theorem can apply +to a completed recursive child. This review does not admit that global +composition. + +The service needs two distinct existing FULL centre banks and one owned +field with a discardable-input contract at the selected cut. Its body +does not borrow any other field. The local payload does not establish a +new owner schedule or create an additional centre bank. + +## Reproduction and status + +Run with one process from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py +``` + +Both runs print `PASS_INDEPENDENT_TRANSLATION_SERVICE_REVIEW` and produce +the same receipt bytes. No material local defect was found. The review +covers the complete emitted local words and the stated phase wrappers. +It does not complete a controller, admit a supplier, or improve kappa. +OpenAI Codex assisted the proof review and exact checker. No PR, push, +or commit was made. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py new file mode 100644 index 0000000000..900f1f389a --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/translation-service-review/check_service_review.py @@ -0,0 +1,180 @@ +"""Review the literal one-field translation service without producer imports.""" + +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parent / "owner-review/centre-schur-probe" +PINS = { + "TRANSLATION-SERVICE.md": "57d38fd23aae563b107f4924250fb975f2d4f9b6bcc5357735943ff10527a0d0", + "TRANSLATION-SERVICE.json": "45273e561954139ece2c40697cc2d419aabc4db01c2013a38ef5379f35cc6599", + "check_translation_service.py": "18cae3387c3a83c716ce2a43e47ec082ce72904e1a2516944278ab032c5de2a8", + "TRANSLATION-SERVICE-PROGRAMS.json.gz": "7566388bfb2167b21a5632cd12f4f71004df9c95d5d823f2f0604a6d0847d0e5", + "SCHUR-PROBE.json": "ebff70f4ff3d28c345080a4d7b1d90cd952a6208b7f6449037b96dbf3531c024", +} +A = [0, 7, 20, 27, 36, 46, 57, 111] +ODD_PATH = HERE.parents[1] / "independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md" +ODD_PIN = "e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01" + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def read(path, pin): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == pin, "Source hash: " + str(path)) + return json.loads(gzip.decompress(raw) if path.suffix == ".gz" else raw) + + +for name, pin in PINS.items(): + need(sha256((SOURCE / name).read_bytes()).hexdigest() == pin, "Frozen producer input") +need(sha256(ODD_PATH.read_bytes()).hexdigest() == ODD_PIN, "Exact odd-grid backend source") +receipt = read(SOURCE / "TRANSLATION-SERVICE.json", PINS["TRANSLATION-SERVICE.json"]) +payload = read(SOURCE / "TRANSLATION-SERVICE-PROGRAMS.json.gz", PINS["TRANSLATION-SERVICE-PROGRAMS.json.gz"]) +probe = read(SOURCE / "SCHUR-PROBE.json", PINS["SCHUR-PROBE.json"]) +primary = {key: read(Path(item["path"]), item["sha256"]) for key, item in receipt["source_pins"].items()} + + +def accumulate(target, key, value): + result = target.get(key, F(0)) + value + if result: + target[key] = result + else: + target.pop(key, None) + + +def body_kernel(word): + # Only C0 has an address code. The eight sources stay unchanged. + scratch = {(16, 0): F(1)} + outputs = [{(8 + i, 0): F(1)} for i in range(8)] + invoice = Counter() + maximum = F(1) + for gate in word: + kind, target = gate[:2] + need(target == 16 or 8 <= target < 16, "Only C0 and target bank can change") + invoice[kind] += 1 + if kind == "ADD": + source, coefficient = gate[2], F(gate[3]) + need(abs(coefficient) in (1, F(1, 2)), "Admitted scalar ADD") + invoice["scalar_primitives"] += 8 if abs(coefficient) == 1 else 10 + if target == 16: + need(0 <= source < 8, "A source read for C0") + accumulate(scratch, (source, 0), coefficient) + else: + need(source == 16, "Every target update uses C0") + for key, value in scratch.items(): + accumulate(outputs[target - 8], key, coefficient * value) + elif kind == "COPY": + need(target == 16 and 0 <= gate[2] < 8, "Copy one unchanged source") + scratch = {(gate[2], 0): F(1)} + invoice["scalar_primitives"] += 2 + elif kind == "CLEAR": + need(target == 16, "Only owned C0 is clearable") + scratch = {} + invoice["scalar_primitives"] += 2 + elif kind == "SCALE2": + need(target == 16 and gate[2] in (-1, 1), "One binary scale on C0") + scratch = {key: F(2)**gate[2] * value for key, value in scratch.items()} + invoice["scalar_primitives"] += 2 + elif kind == "DIVIDE_ODD": + need(target == 16 and gate[2] == 2145, "Exact fixed odd division") + scratch = {key: value / 2145 for key, value in scratch.items()} + invoice["real_odd_division_scans"] += 2 + else: + need(kind == "TRANSLATE" and target == 16 and 0 < gate[2] < 512, "A literal native-zero translation") + scratch = {(origin, delta ^ gate[2]): value for (origin, delta), value in scratch.items()} + invoice["translation_maps"] += 1 + row = scratch if target == 16 else outputs[target - 8] + maximum = max(maximum, sum(map(abs, row.values()))) + need(not scratch, "Owned zero endpoint") + need(not any(origin == 16 for row in outputs for origin, delta in row), "Arbitrary owned input does not reach data") + return outputs, dict(invoice), str(maximum) + + +words = payload["bodies"] +checked = {} +for kind in ("T", "few_maps", "few_scalars"): + entries = probe["kernels"]["translation" if kind == "T" else "inverse"]["entries"] + for sign, suffix in ((1, "plus"), (-1, "minus")): + name = kind + "_" + suffix + expected = [{(8 + i, 0): F(1)} for i in range(8)] + for delta, target, source, value in entries: + accumulate(expected[target], (source, delta), sign * F(value)) + actual, invoice, maximum = body_kernel(words[name]) + need(actual == expected, "All arbitrary live and owned columns: " + name) + wanted = receipt["cases"][name] + need(all(wanted["counts"][key] == value for key, value in invoice.items()), "Literal complete invoice: " + name) + need(maximum == wanted["maximum_intermediate_row_one_norm"], "Prefix coefficient bound: " + name) + checked[name] = dict(invoice=invoice, maximum_row_norm=maximum) + + +def exchange_banks(word): + result = [] + for instruction in word: + instruction = list(instruction) + if instruction[1] < 16: + instruction[1] = (instruction[1] + 8) % 16 + if instruction[0] in ("ADD", "COPY") and instruction[2] < 16: + instruction[2] = (instruction[2] + 8) % 16 + result.append(instruction) + return result + + +for kind in ("few_maps", "few_scalars"): + for suffix, opposite in (("plus", "minus"), ("minus", "plus")): + first = exchange_banks(words["T_" + suffix]) + middle = words[kind + "_" + opposite] + name = "exchange_" + kind + "_" + suffix + need(words[name] == first + middle + first, "Literal exchange has exactly the three checked shears") + counts = Counter(checked["T_" + suffix]["invoice"]) + counts.update(checked[kind + "_" + opposite]["invoice"]) + counts.update(checked["T_" + suffix]["invoice"]) + need(dict(counts) == receipt["cases"][name]["counts"], "Exchange invoice includes every instruction") + checked[name] = dict(invoice=dict(counts)) + + +def apply(columns, vector): + result = 0 + for i, column in enumerate(columns): + if vector >> i & 1: + result ^= column + return result + + +view_table = {(view["stage"], view["port"]): view for view in primary["views"]["views"] if view["side"] == "X" and view["port"] in A} +need(len(view_table) == 64, "All selected completed views") +for (stage, port), view in view_table.items(): + columns, delta = view["route_columns"], view["translation_after_route"] + need(len(columns) == 73, "Native address dimension") + transpose = [sum(((column >> i) & 1) << j for j, column in enumerate(columns)) for i in range(73)] + need([apply(columns, column) for column in columns] == [1 << i for i in range(73)], "Route inverse") + need(columns == transpose, "Orthogonal symmetric route") + need(apply(columns, view["translation_before_route"]) == delta, "Correct affine order") + def phase(character): + return (apply(transpose, character).bit_count() + 2 * (delta & character).bit_count() - character.bit_count()) % 4 + need(phase(0) == 0, "Zero phase constant") + need(all(phase(1 << i) == 0 for i in range(73)), "All linear phase coefficients") + need(all(phase((1 << i) | (1 << j)) == 0 for i in range(73) for j in range(i)), "All quadratic phase coefficients") +for stage in range(1, 9): + enter = [["VIEW", row, stage, A[row % 8], False] for row in range(16)] + leave = [["VIEW", row, stage, A[row % 8], True] for row in reversed(range(16))] + need(payload["stage_wrappers"][str(stage)] == dict(enter=enter, leave=leave), "Exact complete physical wrapper") + +need(receipt["rank_one_children"] == receipt["native_wrapper_maps"] == 0, "No omitted native calls") +need(receipt["completed_view_maps_per_call"] == 32, "All physical view maps charged") +for name, pin in PINS.items(): + need(sha256((SOURCE / name).read_bytes()).hexdigest() == pin, "Frozen producer input unchanged") +result = dict(status="PASS_INDEPENDENT_TRANSLATION_SERVICE_REVIEW", source_pins=PINS, + odd_grid_source=dict(path=str(ODD_PATH), sha256=ODD_PIN), + all_live_columns=16, arbitrary_owned_inputs=1, untouched_borrowed_fields="Every owner outside 0..16", + completed_view_checks=64, body_checks=checked, + exchange_method="Literal three-shear decomposition plus independently checked all-width T inverse", + full_supplier_admission=False, checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest()) +(HERE / "REVIEW.json").write_text(json.dumps(result, indent=2, sort_keys=True) + "\n", encoding="utf-8") +print(result["status"]) diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/CLOSURE.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/CLOSURE.md new file mode 100644 index 0000000000..a497550bb4 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/CLOSURE.md @@ -0,0 +1,313 @@ +# Exact closure limits for three current-chart scalar codes + +Three invertible scalar codes in the actual D25 charts have a monomial +global product only if all three scalar codes are monomial. In addition, +their global product commutes with the intrinsic line operator Q only if +all three scalar codes are diagonal. These conclusions apply at every +payload tensor width f at least 3. + +The proof uses one common basis input to separate all paths. It does not +infer operator independence from distinct route matrices. No claim is +made for width one. The logical monomial result also holds at width two. + +The actual unitary centre code C and its adjoint C* fail both closure +conditions for all eight choices at the three stages. This removes one +proposed free terminal. It does not give a native decoder lower bound or +an improvement in the complete kappa calculation. + +## The code and representation + +Let C0, C1, and C2 be constant invertible scalar matrices on the 112 +physical ports. Scalars can be Gaussian dyadic numbers. In global +logical coordinates, their stage maps are + +```text +A_s = G_s C_s G_s, +G_s = diag(P_(rho_(s,p))), +G_0 = I, +K = A_2 A_1 A_0. +``` + +Each G_s is only the portwise orthogonal route. The stage entry and exit +maps include their literal translations. They do not include an unpaid +native transform. The proposed all-hole caller has end codes `Q K q` +and K, where `q=Q^-1`. That caller is a separate construction. + +Use the position convention `P_A |x> = |A x>`. At width f, the same +route acts on each of f payload columns. A monomial operator has exactly +one nonzero coefficient in each coordinate row and column. It can use +any coordinate permutation, not only a route listed in this packet. + +The declared D25 caller uses the full regular owner cover. The tests +below also hold in the spatial representation with the stated tensor +widths. This representation is a permitted covariant subspace of the +regular cover: set + +```text +f(d; z_1,...,z_f) = g(d^-1 z_1,...,d^-1 z_f). +``` + +For the accepted owner view +`M_(h,delta) f(d,z)=f(dh,z+d delta)`, the induced position map on g is +`T_delta P_h`. The intrinsic line at owner d is `d q_p`, so its induced +line on g is q_p. Thus a spatial operator failure is also a failure on +the declared arbitrary-input cover. The direct witnesses below do not +need independence of different owner coordinates. + +The covariant point basis has disjoint supports of equal size, namely +the number of owners. A full weighted coordinate permutation preserves +the size of each support. If it preserves the covariant subspace, its +image is a union of complete supports of that same size, so it contains +exactly one. Thus a full-cover monomial induces a spatial monomial. +The spatial monomial obstruction therefore also applies to the declared +full cover, including arbitrary coordinate permutations. + +## Exact route signatures + +Let Omega be the sum of the first nine unit vectors. Let e1 and e2 be +the sums of the eight unit vectors in fresh blocks 1 and 2. + +At port p, the intrinsic line q_p and its eight ordered root-complement +vectors form an orthonormal basis of the first nine coordinates. Their +characteristic-vector identity gives + +```text +sum_l b_(p,l) = Omega+q_p. +``` + +The stage-s route exchanges this complement with fresh block s. It +fixes q_p and the other fresh block. Hence + +```text +rho_(1,p) e1 = Omega+q_p, +rho_(2,p) e2 = Omega+q_p, +rho_(1,p) e2 = e2, +rho_(2,p) e1 = e1. +``` + +All 112 q_p are distinct. The checker verifies these statements against +every literal D25 route. It also checks orthogonality and involution. + +For fixed output port p, a path through intermediate ports j and r has +the ordered matrix + +```text +M_(p,j,r) = rho_(2,p) rho_(2,j) rho_(1,j) rho_(1,r). +``` + +Remove the known left factor rho_(2,p), and call the result N_(j,r). +Then + +```text +N_(j,r) e2 = Omega+q_j, +N_(j,r) e1 = rho_(2,j) rho_(1,j) (Omega+q_r). +``` + +The first image gives j. Apply `rho_(1,j) rho_(2,j)` to the second +image to obtain `Omega+q_r`. This gives r. The checker stores all +12,544 signatures and reconstructs both indices from each signature. + +Now use ONE position basis input with columns `(e2,e1)` for all paths. +The resulting output pairs are distinct. A linear combination of the +path operators can therefore vanish only if every coefficient vanishes. +This proves logical path independence at f=2. Zero columns extend this +result to larger widths. + +## Literal physical affine paths + +At a common completed FULL cut, the stage-s view at port p is + +```text +W_(s,p) = T_(delta_(s,p)) P_(rho_(s,p)), +delta_(s,p) = literal_stage_alignment.exit_X. +``` + +The checker verifies that each W is an involution. The physical path is + +```text +W_(2,p) W_(2,j) W_(1,j) W_(1,r). +``` + +Its linear part is M_(p,j,r). Write its translation as t. The checker +calculates t from the four literal translations in their ordered +composition. It does not omit the physical phase correction. + +Use ONE position basis input with columns `(0,e2,e1)`. Its output is + +```text +(t, M e2+t, M e1+t). +``` + +The first output gives t. Taking its differences from the other two +gives the two separating linear images. Thus all paths have distinct +outputs on this common input. This proves physical path independence +at f=3. The checker verifies all 12,544 affine output triples for p=0. +Every other p is a common invertible left view, so the result holds for +all output ports. A scalar phase on a path cannot change its support. + +## Monomial closure criterion + +The input-k to output-p block is + +```text +K_(p,k) = + sum_(j,r) (C2)_(p,j) (C1)_(j,r) (C0)_(r,k) P_(M_(p,j,r)). +``` + +For fixed p and k, the common input separates all nonzero path terms. +Different input ports are different source coordinates. The exact +number of route terms in port row p is therefore + +```text +sum_(j in supp row_p C2) + sum_(r in supp row_j C1) |supp row_r C0|. +``` + +If a p,k block has two terms, the common input produces at least two +output coordinates from one input coordinate. This excludes a +monomial operator. If every block has at most one term but port row p +has two terms, they come from different input ports. Every output +coordinate then has two source coordinates, which also excludes a +monomial operator. Thus a monomial product has one term per port row. + +Each row of C1 and C0 is nonzero. The support formula first forces each +row of C2 to have one entry. Invertibility makes C2 a scalar monomial +matrix. Its port permutation reaches every row of C1, so C1 is +monomial. The same argument gives C0 monomial. The converse follows +by composition. Therefore + +```text +K is monomial if and only if C0, C1, and C2 are monomial. +``` + +This holds at logical width f at least 2 and physical width f at least +3. It permits different matrices at each stage, diagonal phases, signs, +and scalar port permutations. It does not require zero diagonals. + +## Exact Q-commutator criterion + +Define the Fourier character `|chi>=sum_x (-1)^(chi dot x)|x>`. +An orthogonal A acts on its label by A. An affine path acts by + +```text +T_t P_A |chi> = (-1)^(t dot A chi) |A chi>, +Q_p |chi> = i^parity(q_p dot chi) |chi>. +``` + +Choose a nonzero path coefficient c in block p,k and put A=M_(p,j,r). +For f character columns, its contribution to `QK-KQ` has coefficient + +```text +c (-1)^sum_l(t dot A chi_l) [i^L-i^R], +L = sum_l parity(q_p dot A chi_l), +R = sum_l parity(q_k dot chi_l). +``` + +Use e2,e1 as the first two character columns. They separate every path +output. If `A^T q_p != q_k`, there is a third character that makes the +bracket nonzero. If the exponent difference on the first two columns +is nonzero modulo four, take the third character to be zero. Otherwise, +take a unit vector on which `A^T q_p` and q_k differ. The third parity +difference is then 1 or -1. The chosen path has a unique output, so no +other path cancels it. Literal affine signs are nonzero and are equal +on both sides of the commutator. + +It remains to identify the line-preserving paths. The pulled line is + +```text +M_(p,j,r)^T q_p = rho_(1,r) rho_(1,j) rho_(2,j) q_p. +``` + +If j differs from p, `rho_(2,j) q_p` has a nonzero fresh2 component. +Indeed, a root vector has zero fresh2 image under rho_(2,j) only if it +is in the span of q_j; distinct nonzero q_p is not in that span. +Both stage-1 factors fix this component. The result cannot be q_k. + +If j=p, the expression is `rho_(1,r) q_p`. If r differs from p, the +same argument gives a nonzero fresh1 component. If j=r=p, the path is +the identity and its line equals q_k only if k=p. Thus + +```text +M_(p,j,r)^T q_p = q_k if and only if j=r=k=p. +``` + +If Q commutes with K, every nonzero path must satisfy this condition. +Every nonzero entry of C2 has a nonzero continuation through C1 and C0, +so C2 must be diagonal. Its diagonal entries are nonzero. The same +argument then forces C1 and C0 diagonal. Conversely, diagonal scalar +matrices commute with all portwise routes and lines. Hence, for f at +least 3, + +```text +Q K = K Q if and only if C0, C1, and C2 are diagonal. +``` + +The same result holds for the physical code `F K F^-1`: F commutes +with Q, and the checker also includes the literal affine signs. No +claim is made for f=1 or f=2. + +## Actual unitary code and consequences + +The unitary source is +`new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/unitary-v2-normal/UNITARY-COMPLETION.json.gz`, +with decompressed SHA256 +`fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428`. +The checker reads `code` and `inverse_and_adjoint`, verifies the +adjoint relation, and verifies both unitary product orders. + +The physical rows of C have lengths 2, 4, 8, or 16. The rows of C* +have lengths 3, 8, or 12. All eight three-stage choices fail monomial +closure and Q commutation in every output row. For each row of each +choice, the checker stores a common-input two-output basis witness and +an exact three-character commutator witness, including its affine sign. +There are 896 witnesses of each type. + +For C/C/C, the exact route count is 54,976, with at least eighteen +terms in each port row. The scalar constant-sector matrix C^3 has +1,066 nonzero entries. This smaller calculation does not certify +closure of the full routed product. + +The original sixteen centre readers use all 112 input ports. A scalar +monomial code only permutes and rescales individual inputs. Thirty-two +selected output ports omit an input on which a reader depends. Thus +such a code cannot retain all these readers in those outputs. A new +construction that does not require this retention is outside this +conclusion. + +The theorem leaves open a proved consumer for the nonmonomial endpoint, +a native implementation of its conjugated decoder, an operator-valued +code with admitted extra access, and a changed owner or gathered-axis +interface. Route counts are not native child counts. + +## Verification, credit, and limits + +The route source is +`bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json`, +SHA256 +`125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473`. +The new-core lane supplied C and C*. The cover lane supplied the +conditional all-hole caller and the fresh-edge line test. The bridge +lane supplied the literal views. The independent owner-review lane +checked the common-input argument and the diagonal criterion without +importing this checker. Its standalone proof is +`owner-review/unitary-code-closure-review-20261020/REVIEW.md`, +SHA256 `f5bc725b9f14032e5a61341ed73306b45797b90612e256e6e3caa52e6360a3dc`. +This work used AI assistance. + +Run with fresh output directories: + +```text +python3 -B check_closure.py --out +python3 -O -B check_closure.py --out +``` + +The final normal and optimized outputs must be byte-identical. Checks +cover source hashes, all route signatures, literal affine paths, both +unitary orders, all eight support profiles, both sets of 896 witnesses, +and the 112-port reader support. The general criteria are proved above; +they are not inferred from the eight finite cases. + +No native decoder, recursive host, precision bound, or complete supplier +is claimed. No PR, commit, push, or publication is authorized. Before +any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/FREEZE.json new file mode 100644 index 0000000000..f7f487c666 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/FREEZE.json @@ -0,0 +1,48 @@ +{ + "files": { + "CLOSURE.md": "63c0deeb7e13b359ca410dfb085e1a89866aa87383d6bd1cec02cba688a4ce3e", + "GENERAL-CLOSURE.md": "a9bc32fc805b83c6317cc62b8c5982dee2d15d73a4065a50ab4e797e3c85826a", + "bound-normal/CHECKS.json": "f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a", + "bound-normal/PATH-SIGNATURES.json.gz": "053b09b693cef52a33b7f15ccb0c5697466bd123f3b4e0bbb0318fe2e674ed46", + "bound-normal/WIDTH-THREE-WITNESSES.json.gz": "09f5ba960ecf9eb965e1ccb94848fcbc36e1d68319502b9378d94c27a7401eca", + "bound-optimized/CHECKS.json": "f1e418155b89f8add0f066c80da2ab3a1120e6d78f047753e7e0698daf506a3a", + "bound-optimized/PATH-SIGNATURES.json.gz": "053b09b693cef52a33b7f15ccb0c5697466bd123f3b4e0bbb0318fe2e674ed46", + "bound-optimized/WIDTH-THREE-WITNESSES.json.gz": "09f5ba960ecf9eb965e1ccb94848fcbc36e1d68319502b9378d94c27a7401eca", + "check_closure.py": "45d1e215c4dc6f7735deaed0d9df57cf3efa83a0bc4e354c43375187cbe7f01e" + }, + "future_PR_description_standard": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "independent_review_freezes": { + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/general-scalar-closure-review-20261020/FREEZE.json": "6f5fbbf6565d2a6078b8ec627722c52c8f94fe0690ae6da1a543e7c3f767022d", + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-binding-20261020/FREEZE.json": "7e572942617d880931f52f47849b23174b903f57a199a99134b96ed5cac21ea6", + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/owner-review/unitary-code-closure-review-20261020/FREEZE.json": "b3fc9ddc6fdc4cc6c2226b3b9fa101abdb21d22e50ceb3d6c9cefa9280062deb" + }, + "publication": "No PR, commit, push, or publication is authorized.", + "reproduction": "Run check_closure.py in normal Python and python3 -O with fresh --out directories; compare every output byte.", + "schema": "current-scalar-code-closure-freeze-v1", + "scope": { + "D25_logical_monomial_minimum_sufficient_width": 2, + "D25_physical_monomial_and_commutator_minimum_sufficient_width": 3, + "complete_supplier": false, + "constant_scalar_current_chart_codes": true, + "general_stage_proof": "Logical width at least T; affine and Q witnesses at least T+1. Sufficient bounds only.", + "kappa_gain": false, + "native_cost_lower_bound": false + }, + "source_pins": { + "unitary": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/unitary-v2-normal/UNITARY-COMPLETION.json.gz", + "sha256": "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428" + }, + "views": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + } + }, + "status": "PASS_EXACT_CHECKS_AND_INDEPENDENT_PROOF_REVIEWS", + "superseded_unfrozen_runs": [ + "run-normal", + "run-optimized", + "final-normal", + "final-optimized" + ] +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/GENERAL-CLOSURE.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/GENERAL-CLOSURE.md new file mode 100644 index 0000000000..51b5570465 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/GENERAL-CLOSURE.md @@ -0,0 +1,144 @@ +# Extension to any number of fresh stages + +The D25 closure proof extends to every dimension D=9+8T with T at +least one. It uses the actual general-stage routes. It does not +require an enumeration of all paths. + +Let C0,...,CT be invertible constant scalar matrices on the same 112 +ports. Put + +```text +K = (Gamma_T C_T Gamma_T) ... (Gamma_1 C_1 Gamma_1) C_0, +Gamma_t = diag(P_(rho_(t,p))). +``` + +The root labels q_p are distinct and remain the same at every stage. +Each rho_(t,p) exchanges the root complement of q_p with fresh block +t, fixes q_p, and fixes all other fresh blocks. This is the exact +route from the general-stage view theorem. + +For logical payload width f at least T, K is monomial if and only if +every C_t is monomial. For literal physical affine paths the same +criterion holds at f at least T+1. At f at least T+1, K commutes with +the intrinsic line Q if and only if every C_t is diagonal. + +These width bounds are sufficient. No smaller-width optimum is +claimed. The matrices C_t may differ at every stage. + +## One input separates every path + +Let e_t be the sum of the eight unit vectors in fresh block t. +Let Omega be the sum of the nine root unit vectors. As in D25, + +```text +rho_(t,p) e_t = Omega+q_p. +``` + +Fix output port p and write i_T=p. A path has intermediate ports +i_(T-1),...,i_0 and ordered route + +```text +M = (rho_(T,i_T) rho_(T,i_(T-1))) + ... + (rho_(1,i_1) rho_(1,i_0)). +``` + +Apply every path to the same T-column position input + +```text +(e_T,e_(T-1),...,e_1). +``` + +The first image is +`rho_(T,p)(Omega+q_(i_(T-1)))`, because all earlier stages fix e_T. +It gives i_(T-1). + +Suppose i_T,...,i_t are known. Remove the corresponding known left +route pairs from M e_t. Then remove rho_(t,i_t). Earlier stages fix +e_t, so the result is `Omega+q_(i_(t-1))`. The distinct root labels +give i_(t-1). Descending induction recovers the complete path. + +Thus all intermediate-port paths have distinct outputs on this +one input. Their operators are linearly independent at f=T. Zero +columns extend the test to larger f. + +For a physical affine path `x -> Mx+b`, use the single input + +```text +(0,e_T,e_(T-1),...,e_1). +``` + +Its first output gives b. Subtract it from the others to obtain all +linear images. Thus the same separation holds at f=T+1 for arbitrary +literal path translations. Nonzero scalar phases do not affect it. + +## Monomial product + +For fixed input and output ports, different paths cannot cancel. +Products of nonzero scalar edge coefficients are nonzero. A block +with two paths sends the common basis input to two output coordinates. +If a port row has two blocks with one path each, each output coordinate +has two input coordinates. Either case excludes a monomial operator. + +Every row of each C_t is nonzero. One path per output row therefore +forces C_T to have one entry in each row. Invertibility makes it a +monomial matrix and makes its port permutation reach every row of +C_(T-1). Repeat this argument through C0. The converse follows by +composition. + +The covariant lift and equal-support argument in `CLOSURE.md` carry +this spatial criterion to the declared full regular owner cover. + +## Q commutation + +The pulled output line is M^T q_p. If i_(T-1) differs from p, its +stage-T factor gives a nonzero component in fresh block T. All +remaining transpose factors are from earlier stages and preserve +that component. It cannot equal any root input line q_k. + +If i_(T-1)=p, the stage-T pair cancels. Apply the same argument at +stage T-1. This gives + +```text +M^T q_p = q_k if and only if +i_(T-1)=...=i_0=k=p. +``` + +Use `(e_T,...,e_1)` as the first T Fourier-character columns. They +separate all path outputs, because the routes are orthogonal. For a +path that breaks the line, calculate the Q exponent difference on +these tags modulo four. If it is nonzero, append a zero character. +Otherwise, append a unit vector on which M^T q_p and q_k differ. +The resulting exponent difference is nonzero. + +This branch has a unique output tuple. No other path can cancel it. +A literal affine translation only supplies the same nonzero sign +on both sides of the commutator. Thus a nonzero line-breaking path +makes `QK-KQ` nonzero at f=T+1. + +Every nonzero entry of C_T has a nonzero continuation. Q commutation +therefore forces C_T diagonal. Its diagonal entries are nonzero. +Induction then forces all earlier C_t diagonal. Conversely, diagonal +scalar matrices commute with the portwise routes and with Q. + +## Sources and limits + +The exact general-stage view theorem is +`bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md`, +SHA256 +`5da866eb2802e8a30ea77d2f88877b5005a2eb04632514c897a426e76277db2e`. +Its freeze is +`b6539737b3144d73c0ca313984573fe1493f9736205ab0d885ebd69d88d27c4d`. +The literal D25 instance and all eight C/C* products are checked in +the companion packet. The arbitrary-T result is the induction above, +not an inference from a finite sample. + +This theorem concerns constant scalar codes in their current fresh +charts. It does not include additional old-chart controls, general +operator coefficients, a changed gathered-axis interface, or a paid +decoder. It gives no native cost lower bound and no complete kappa +gain. The complete caller and recursive owner host remain separate. + +This work used AI assistance. No PR, commit, push, or publication is +authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/bound-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/bound-normal/CHECKS.json new file mode 100644 index 0000000000..dfede19cbf --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/unitary-code-closure-20261020/bound-normal/CHECKS.json @@ -0,0 +1,129 @@ +{ + "actual_selected_output_coordinates": 32, + "adjoint_row_counts": { + "3": 64, + "8": 16, + "12": 32 + }, + "basis_column_witnesses": 896, + "checker_sha256": "45d1e215c4dc6f7735deaed0d9df57cf3efa83a0bc4e354c43375187cbe7f01e", + "code_row_counts": { + "2": 32, + "4": 32, + "8": 32, + "16": 16 + }, + "constant_sector_C_cube_terms": 1066, + "distinct_intermediate_path_pairs": 12544, + "distinct_intrinsic_lines": 112, + "exact_affine_commutator_witnesses": 896, + "logical_path_separation_minimum_width": 2, + "original_centre_reader_source_support": 112, + "physical_path_and_commutator_minimum_width": 3, + "root_complement_basis_checks": 224, + "routed_variant_profiles": { + "C/C/C": { + "maximum_row_terms": 1536, + "minimum_row_terms": 18, + "operator_terms": 54976, + "row_term_histogram": { + "18": 32, + "36": 32, + "768": 16, + "1024": 16, + "1536": 16 + } + }, + "C/C/Cstar": { + "maximum_row_terms": 1280, + "minimum_row_terms": 30, + "operator_terms": 59264, + "row_term_histogram": { + "30": 64, + "1024": 16, + "1280": 32 + } + }, + "C/Cstar/C": { + "maximum_row_terms": 2560, + "minimum_row_terms": 20, + "operator_terms": 71552, + "row_term_histogram": { + "20": 32, + "40": 32, + "512": 16, + "1280": 16, + "2560": 16 + } + }, + "C/Cstar/Cstar": { + "maximum_row_terms": 1280, + "minimum_row_terms": 30, + "operator_terms": 59264, + "row_term_histogram": { + "30": 64, + "1152": 32, + "1280": 16 + } + }, + "Cstar/C/C": { + "maximum_row_terms": 1536, + "minimum_row_terms": 18, + "operator_terms": 57024, + "row_term_histogram": { + "18": 32, + "36": 32, + "640": 16, + "1280": 16, + "1536": 16 + } + }, + "Cstar/C/Cstar": { + "maximum_row_terms": 1920, + "minimum_row_terms": 30, + "operator_terms": 71552, + "row_term_histogram": { + "30": 64, + "512": 16, + "1920": 32 + } + }, + "Cstar/Cstar/C": { + "maximum_row_terms": 1792, + "minimum_row_terms": 18, + "operator_terms": 57024, + "row_term_histogram": { + "18": 32, + "36": 32, + "768": 16, + "896": 16, + "1792": 16 + } + }, + "Cstar/Cstar/Cstar": { + "maximum_row_terms": 1216, + "minimum_row_terms": 27, + "operator_terms": 54976, + "row_term_histogram": { + "27": 64, + "896": 16, + "1216": 32 + } + } + }, + "scope": "Three constant scalar current-chart codes with the actual D25 routes. One common width-three basis input separates the literal affine paths. Exact Fourier-character witnesses show Q noncommutation. 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zn-fRtx+)fBYm?&&1qyB$X4rP$@Cc3(-vvN%84_0;vSh}`4+~$0+WuT4GU4%9$Z$d1 zIQ~fg=X;l?r#01Ot-H2Ubct_6u2{5=V@{W%j+jV>|=*JUeEacgGpOwti4P=iD6R9!VT~>Uy z$jPcN;4U@y*1~D|ziA?uM@aQkd$0a|av=l3Hx>{RgC-ksK>S@$>D&?39ndIMJn=d5 zutac!Z3R)6tCh6n{_-d6=>?B2oFGv4j;?dry8D1*HtDzQ@#o3ef#L$phx1*PFC6m0 ziiZR!9K@(<=m>^mgTu_P*ZIonuLo;3Lo>N5e6@4h=cM24hIr;{yWC#BYGrrLsC+L7 zSIJFlnYQ!%-Y{L*-1@UqNeD;%(uQ2+FaHhT)1k+&Hqdp>g#n3qQ6A)vv02*{&ZazA_S3mlQ7}Kl zm7xFUyz}NP2v(=uxT=Hf@ju2-3e=~Um!Q{3xlTKI1}pZ`32^a-sW^U z7P5hMw8C*y$Q`Tt 1, "Every routed output row is nonmonomial") + profiles["/".join(names)] = { + "operator_terms": sum(row_counts), + "minimum_row_terms": min(row_counts), + "maximum_row_terms": max(row_counts), + "row_term_histogram": dict(sorted(Counter(row_counts).items())), + } + for p in range(112): + paths = {} + for j, a2 in sorted(c2[p].items()): + for r, a1 in sorted(c1[j].items()): + for k, a0 in sorted(c0[r].items()): + paths.setdefault(k, []).append((j, r, times(a2, times(a1, a0)))) + k = next(k for k, records in paths.items() if len(records) >= 2) + point_outputs = [] + for j, r, coefficient in paths[k][:2]: + def image(vector): + for s, port in ((1, r), (1, j), (2, j), (2, p)): + vector = act(routes[s, port], vector) + return vector + shift = shifts[2, p] ^ act(routes[2, p], inner_shifts[j, r]) + point_outputs.append({ + "path": [j, r], "coefficient": serialized(coefficient), + "output": [shift, shift ^ image(fresh2), shift ^ image(fresh1)], + }) + need(point_outputs[0]["output"] != point_outputs[1]["output"], + "One input column has at least two nonzero output coordinates") + basis_witnesses.append({ + "variant": "/".join(names), "output_port": p, "input_port": k, + "input_columns": [0, fresh2, fresh1], "outputs": point_outputs, + }) + + j, a2 = next(iter(sorted(c2[p].items()))) + r, a1 = next(iter(sorted(c1[j].items()))) + k, a0 = next(iter(sorted(c0[r].items()))) + coefficient = times(a2, times(a1, a0)) + + def image(vector): + for s, port in ((1, r), (1, j), (2, j), (2, p)): + vector = act(routes[s, port], vector) + return vector + + pulled = q[p] + for s, port in ((2, p), (2, j), (1, j), (1, r)): + pulled = act(routes[s, port], pulled) + need(pulled != q[k], "The chosen path does not preserve the intrinsic line") + chars = [fresh2, fresh1] + phase_difference = ( + sum((q[p] & image(x)).bit_count() % 2 for x in chars) - + sum((q[k] & x).bit_count() % 2 for x in chars)) % 4 + chars.append(0 if phase_difference else (pulled ^ q[k]) & -(pulled ^ q[k])) + outputs = [image(x) for x in chars] + exponent_out = sum((q[p] & x).bit_count() % 2 for x in outputs) % 4 + exponent_in = sum((q[k] & x).bit_count() % 2 for x in chars) % 4 + phase = plus(I_POWER[exponent_out], + (-I_POWER[exponent_in][0], -I_POWER[exponent_in][1])) + need(phase != ZERO, "The isolated Fourier branch has a nonzero phase difference") + shift = shifts[2, p] ^ act(routes[2, p], inner_shifts[j, r]) + sign = (-1) ** sum((shift & x).bit_count() % 2 for x in outputs) + physical_coefficient = times(times(coefficient, (F(sign), F(0))), phase) + need(physical_coefficient != ZERO, "The affine phase does not cancel the witness") + commutator_witnesses.append({ + "variant": "/".join(names), "output_port": p, "input_port": k, + "path": [j, r], "coefficient": serialized(coefficient), + "input_characters": chars, "output_characters": outputs, + "output_line_pulled": pulled, "input_line": q[k], + "output_exponent": exponent_out, "input_exponent": exponent_in, + "affine_shift": shift, "affine_sign": sign, + "physical_commutator_coefficient": serialized(physical_coefficient), + }) + + # Scalar multiplication can cancel coefficients when the stage routes are removed. + scalar_cube = matmul(c, matmul(c, c)) + scalar_count = sum(map(len, scalar_cube)) + routed_count = profiles["C/C/C"]["operator_terms"] + need(scalar_count < routed_count, "The constant-sector product is not the routed product") + selected = source["unitary"]["selected_full_ports"] + readers = matrix(source["unitary"]["original_centre_readers"]) + need(len(selected) == 32 and len(readers) == 16, "Actual centre interface sizes") + need(len({j for row in readers for j in row}) == 112, + "Every input port occurs in the original centre readers") + raw_certificate = (json.dumps(certificate, separators=(",", ":")) + "\n").encode() + (args.out / "PATH-SIGNATURES.json.gz").write_bytes(gzip.compress(raw_certificate, mtime=0)) + witnesses = { + "basis_witnesses": basis_witnesses, + "commutator_witnesses": commutator_witnesses, + } + witness_raw = (json.dumps(witnesses, separators=(",", ":"), sort_keys=True) + "\n").encode() + (args.out / "WIDTH-THREE-WITNESSES.json.gz").write_bytes(gzip.compress(witness_raw, mtime=0)) + receipt = { + "status": "PASS_ACTUAL_FRESH_STAGE_PATH_SEPARATION", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins": pins, + "distinct_intrinsic_lines": len(set(q)), + "root_complement_basis_checks": basis_checks, + "distinct_intermediate_path_pairs": len(signatures), + "single_physical_input_affine_outputs": len(affine_signatures), + "signature_decompressed_sha256": sha256(raw_certificate).hexdigest(), + "witness_decompressed_sha256": sha256(witness_raw).hexdigest(), + "basis_column_witnesses": len(basis_witnesses), + "exact_affine_commutator_witnesses": len(commutator_witnesses), + "logical_path_separation_minimum_width": 2, + "physical_path_and_commutator_minimum_width": 3, + "code_row_counts": dict(sorted(Counter(map(len, c)).items())), + "adjoint_row_counts": dict(sorted(Counter(map(len, adjoint)).items())), + "routed_variant_profiles": profiles, + "constant_sector_C_cube_terms": scalar_count, + "original_centre_reader_source_support": 112, + "actual_selected_output_coordinates": 32, + "scope": ( + "Three constant scalar current-chart codes with the actual D25 " + "routes. One common width-three basis input separates the literal " + "affine paths. Exact Fourier-character witnesses show Q noncommutation. " + "There is no small-width independence assumption, general native " + "decoder lower bound, or claim for an operator-valued code." + ), + } + (args.out / "CHECKS.json").write_text( + json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps({ + "status": receipt["status"], "paths": len(signatures), + "routed_variants": profiles, "constant_sector_terms": scalar_count, + }, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..c6c54dc3bdef3d7bf56c36885a45b98cdeb1e74c GIT binary patch literal 583358 zcmZU&18^i@+a(&?=ESy*iEZ09Cbn(cwrxyoI}>waXOsE9fA`+qRM%VS>U1ZS_dG`r 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b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py @@ -0,0 +1,339 @@ +#!/usr/bin/env python3 +"""Bind the rank-two response and the small clique cover to actual ports.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": + "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", +} +CLIQUES = [ + [5, 34, 40, 85, 97], [3, 32, 38, 50, 95], [24, 48, 67, 80, 82], + [23, 35, 55, 65, 68], [1, 17, 66, 75, 83], [8, 12, 45, 107, 109], + [29, 49, 54, 56, 108], [26, 30, 64, 73, 96], [4, 33, 69, 74, 88], + [18, 22, 84], [19, 28, 77], [39, 58, 86], [6, 98, 100, 101, 102], + [31, 59, 60, 93, 103], +] + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(relative): + raw = (LANES / relative).read_bytes() + need(sha256(raw).hexdigest() == PINS[relative], "Source pin " + relative) + return json.loads(raw) + + +def identity(n): + return [{i: F(1)} for i in range(n)] + + +def add(target, source, coefficient=F(1)): + for key, value in source.items(): + target[key] = target.get(key, F(0)) + coefficient * value + if not target[key]: + del target[key] + + +def product(a, b): + result = [] + for row in a: + value = {} + for j, coefficient in row.items(): + add(value, b[j], coefficient) + result.append(value) + return result + + +def transpose(a, n): + result = [{} for _ in range(n)] + for i, row in enumerate(a): + for j, value in row.items(): + result[j][i] = value + return result + + +def restrict(a, ports): + index = {p: i for i, p in enumerate(ports)} + return [{index[p]: value for p, value in a[row].items() if p in index} + for row in ports] + + +def rank(rows, columns): + rows = [dict(row) for row in rows] + pivot = 0 + for column in range(columns): + found = next((i for i in range(pivot, len(rows)) if rows[i].get(column)), None) + if found is None: + continue + rows[pivot], rows[found] = rows[found], rows[pivot] + c = rows[pivot][column] + rows[pivot] = {p: v / c for p, v in rows[pivot].items()} + for i in range(pivot + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[pivot], -rows[i][column]) + pivot += 1 + return pivot + + +def determinant(rows): + rows = [dict(row) for row in rows] + result = F(1) + for column in range(len(rows)): + found = next((i for i in range(column, len(rows)) if rows[i].get(column)), None) + if found is None: + return F(0) + if found != column: + rows[column], rows[found] = rows[found], rows[column] + result = -result + c = rows[column][column] + result *= c + for i in range(column + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[column], -rows[i][column] / c) + return result + + +def inverse_word(word): + return [[op, target, origin, str(1 / F(c) if op == "scale" else -F(c))] + for op, target, origin, c in reversed(word)] + + +def transpose_word(word): + return [[op, target if op == "scale" else origin, + origin if op == "scale" else target, c] + for op, target, origin, c in reversed(word)] + + +def replay(word): + state = identity(112) + maximum = F(1) + for op, target, origin, coefficient in word: + c = F(coefficient) + if op == "scale": + state[target] = {p: c * v for p, v in state[target].items() if c * v} + else: + need(op == "add" and target != origin, "Scalar word grammar") + add(state[target], state[origin], c) + maximum = max(maximum, sum(abs(c) for c in state[target].values())) + return state, maximum + + +def price(word): + result = 0 + for op, _, _, coefficient in word: + c = F(coefficient) + a, b = abs(c.numerator), c.denominator + need(a and not b & (b - 1), "Dyadic coefficient") + if op == "scale": + need(not a & (a - 1), "Dyadic unit scale") + result += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) + else: + result += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + return result + + +def maximal_cliques(ports, q): + n = len(ports) + adjacent = [sum(1 << j for j, r in enumerate(ports) + if i != j and not (q[p] & q[r]).bit_count() % 2) + for i, p in enumerate(ports)] + result = [] + + def visit(chosen, possible, excluded): + if not possible and not excluded: + result.append(chosen) + return + options = possible | excluded + pivot = max((i for i in range(n) if options >> i & 1), + key=lambda i: (adjacent[i] & possible).bit_count(), default=0) + todo = possible & ~adjacent[pivot] + while todo: + bit = todo & -todo + i = bit.bit_length() - 1 + todo -= bit + visit(chosen | bit, possible & adjacent[i], excluded & adjacent[i]) + possible -= bit + excluded |= bit + + visit(0, (1 << n) - 1, 0) + return [[ports[i] for i in range(n) if mask >> i & 1] for mask in sorted(result)] + + +def encoded(rows): + return [{str(p): str(c) for p, c in sorted(row.items())} for row in rows] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = read(next(name for name in PINS if "CYCLIC" in name)) + matching = read(next(name for name in PINS if "MATCHED" in name)) + selected, small = matching["selected_ports"], matching["small_ports"] + selected_set = set(selected) + q = cyclic["ports"] + h = identity(112) + codes = [] + for pair in cyclic["pair_codes"]: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + h[a], h[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)} + if aa != 1: + codes.append(["scale", a, None, str(aa)]) + codes.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + hi = transpose(h, 112) + for p in cyclic["affected_ports"]: + hi[p] = {k: v / 2 for k, v in hi[p].items()} + need(product(h, hi) == identity(112), "Actual pair inverse") + mode = identity(112) + mode_inverse = identity(112) + mode_u, mode_v = [{} for _ in range(112)], [] + mode_word, assignments = [], [] + for vertex, group in enumerate(cyclic["cyclic_carriers"]): + chosen = [p for p in group if selected_set.intersection(map(int, cyclic["mode_rows"][str(p)]))] + rest = [p for p in group if p not in chosen] + need(len(chosen) == 2 and len(rest) == 4, "Two selected modes per vertex") + order = chosen + rest + signs = [1, 1 if vertex % 2 == 0 else -1, 1, 1, 1, 1] + e = [{j: F((i == j) - 1) for j in range(4) if i != j} | {4: F(1)} + for i in range(4)] + e += [{5: F(1)}, {0: F(-2), 1: F(-2), 2: F(-2), 3: F(-2), 4: F(3)}] + swap = [0, 1, 2, 3, 5, 4] + ei = [{swap[j]: c for j, c in e[swap[i]].items()} for i in range(6)] + need(product(e, ei) == product(ei, e) == identity(6), "Six-mode reciprocal pair") + for i, p in enumerate(order): + mode[p] = {order[j]: c * signs[i] * signs[j] for j, c in e[i].items()} + mode_inverse[p] = {order[j]: c * signs[i] * signs[j] for j, c in ei[i].items()} + offset = len(mode_v) + local_u = [[1, 0]] * 4 + [[0, 1], [2, -1]] + local_v = [[-1, -1, -1, -1, 1, 0], [0, 0, 0, 0, -1, 1]] + for i, p in enumerate(order): + mode_u[p].update({offset + j: F(value * signs[i]) + for j, value in enumerate(local_u[i]) if value}) + mode_v.extend([{order[j]: F(value * signs[j]) for j, value in enumerate(row) if value} + for row in local_v]) + a, b, c = order[:4], order[4], order[5] + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(-signs[i])]) + for i, p in enumerate(a): + mode_word.append(["add", p, b, str(signs[i])]) + mode_word.append(["scale", b, None, "-1"]) + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(signs[i])]) + mode_word.extend([["add", b, c, "1"], ["add", c, b, "-1"], + ["add", b, c, "1"], ["scale", c, None, "-1"]]) + assignments.append({"vertex": vertex, "ordered_carriers_a_b_c": order, "signs": signs}) + need(replay(mode_word)[0] == mode, "In-place rank-two mode code") + response, response_inverse = product(hi, product(mode, h)), product(hi, product(mode_inverse, h)) + u, v = product(hi, mode_u), product(mode_v, h) + small_word = [] + need(sorted(p for group in CLIQUES for p in group) == sorted(small), "Exact disjoint64 cover") + for group in CLIQUES: + k = len(group) + need(k in (3, 5), "Dyadic clique size") + need(all((q[p] & q[r]).bit_count() % 2 == int(p == r) + for p in group for r in group), "Actual orthonormal clique") + for p in group: + response[p] = {r: F(-1) for r in group if r != p} + response_inverse[p] = {r: F(int(p == r)) - F(1, k - 1) for r in group} + u[p] = {len(v): F(-1)} + v.append({p: F(1) for p in group}) + a, rest = group[0], group[1:] + small_word.extend([["add", a, p, "1"] for p in rest]) + small_word.extend([["add", p, a, "-1"] for p in rest]) + small_word.append(["scale", a, None, str(1 - k)]) + small_word.extend([["add", a, p, "-1"] for p in rest]) + word = codes + mode_word + inverse_word(codes) + small_word + common_words = {"E": word, "inverse_E": inverse_word(word), + "transpose_E": transpose_word(word), + "inverse_transpose_E": transpose_word(inverse_word(word))} + expected = {"E": response, "inverse_E": response_inverse, + "transpose_E": transpose(response, 112), + "inverse_transpose_E": transpose(response_inverse, 112)} + word_receipts = {} + for name, gates in common_words.items(): + actual, maximum = replay(gates) + need(actual == expected[name], "Full112 scalar code " + name) + need(replay(gates + inverse_word(gates))[0] == identity(112), "Both code orders " + name) + word_receipts[name] = {"real_scalar_primitives": price(gates), + "prefix_row_l1_bound": str(maximum), "owned_fields": 0} + need(product(response, response_inverse) == product(response_inverse, response) == identity(112), + "Full112 reciprocal products") + correction = [dict(row) for row in response] + for i in range(112): + add(correction[i], {i: F(-1)}) + need(product(u, v) == correction and rank(u, 30) == rank(v, 112) == 30, + "Exact full rank30 correction factor") + l = restrict(response, selected) + li = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_inverse"]] + old_l = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_block"]] + need(l == restrict(response_inverse, selected) == old_l, "Both selected blocks retain L") + need(product(l, li) == identity(8), "Selected inverse") + ordinary = sorted(set(range(112)) - selected_set) + p = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(selected) + if response_inverse[r].get(s)} for r in ordinary] + n = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(ordinary) + if response_inverse[r].get(s)} for r in selected] + ordinary_inverse = restrict(response_inverse, ordinary) + for row, update in zip(ordinary_inverse, product(product(p, li), n)): + add(row, update, -1) + ordinary_block = restrict(response, ordinary) + need(product(ordinary_block, ordinary_inverse) == product(ordinary_inverse, ordinary_block) + == identity(104), "Both ordinary104 inverse orders") + need(all(not c.denominator & (c.denominator - 1) + for row in ordinary_inverse for c in row.values()), "Dyadic ordinary inverse") + maxima = maximal_cliques(small, q) + histogram = Counter(map(len, maxima)) + need(histogram == {4: 896, 8: 64}, "Exhaustive maximal clique census") + # A separate exhaustive extension pass checks the absence of a ninth vertex. + need(all(not any(p not in clique and all(not (q[p] & q[r]).bit_count() % 2 for r in clique) + for p in small) for clique in maxima), "Each reported clique is maximal") + receipt = { + "status": "PASS_LOW_DISPLACEMENT_RESPONSE", + "source_pins": PINS, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "correction_rank_large48": 16, "correction_rank_small64": 14, "correction_rank_full112": 30, + "selected_determinant": str(determinant(l)), + "full_determinant": str(determinant(response)), + "ordinary104_determinant": str(determinant(ordinary_block)), + "small_clique_sizes": dict(sorted(Counter(map(len, CLIQUES)).items())), + "all_maximal_small_clique_sizes": dict(sorted(histogram.items())), + "common_frame_scalar_codes": word_receipts, + "scope": "Exact port matrices, principal units, scalar codes and geometry. Native phases and terminal access are separate.", + } + payload = { + "source_pins": PINS, "ports": q, "selected_ports": selected, "ordinary_ports": ordinary, + "large_ports": cyclic["affected_ports"], "small_ports": small, + "vertex_assignments": assignments, "mode_response": encoded(mode), + "mode_inverse": encoded(mode_inverse), "small_cliques": CLIQUES, + "response": encoded(response), "response_inverse": encoded(response_inverse), + "correction_U": encoded(u), "correction_V": encoded(v), + "selected_block": encoded(l), "selected_inverse": encoded(li), + "ordinary_inverse": encoded(ordinary_inverse), "common_frame_words": common_words, + "maximal_small_cliques": maxima, + } + raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode() + (args.out / "RESPONSE-PROGRAM.json").write_bytes(raw) + receipt["payload_sha256"] = sha256(raw).hexdigest() + (args.out / "RESPONSE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md new file mode 100644 index 0000000000..5fcb324c5b --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-DUAL.md @@ -0,0 +1,190 @@ +# A native inverse-adjoint for the clean centre exchange + +The Q-entry clean word has a literal inverse-adjoint with the same +native profile and scalar price. Its selected-bank conjugate has the +same price too. The conjugate is emitted by changing the field labels +of every instruction. It does not need extra physical swap instructions. + +Both providers pass all 640 arbitrary input columns and restore all 416 +auxiliary fields. Each word costs 8,600 real scalar primitives and has +native mass 1,792. This packet supplies a local physical operation. +The routed two-call construction and the full supplier bill are +separate. + +## The actual content blocks + +Use the selected ports P, the other ports U, and the normalized reader +L=[I,B] from `CLEAN-LATE-EXCHANGE.md`. Put D=E_UP. Exact multiplication +on the source matrices gives + +```text +D = -B^T, E_U x = u + D(a+Bu), x=(a,u). +``` + +These are identities of the actual response. They are not assumptions +about an arbitrary row code. + +Let the selected target content be z and the ordinary target content +be v. The clean word has content map + +```text +alpha = a+Bu, +M(a,u,z,v) = (-z, u, alpha, v+u+D alpha). +``` + +Its inverse is obtained directly from its output: + +```text +a = third - B second, +u = second, +z = -first, +v = fourth - second - D third. +``` + +Thus its inverse-transpose is + +```text +M^(-T)(a,u,z,v) = (-z, u+Da-v, a+Bv, v). +``` + +Let S exchange only the selected X and Y coordinates. Then + +```text +Bswapclean = S M^(-T) S, +Bswapclean(a,u,z,v) = (z+Bv, u+Dz-v, -a, v). +``` + +The checker derives M^(-T) from the complete stored inverse of M. +It compares the result with these block equations and checks both +inverse product orders. No inverse of E or odd division is used. + +## Physical operator and exact order + +Let A_in and A_out denote the block diagonal physical entry and exit +operators. For the Q-entry clean word, they are unitary: + +```text +A_in = diag(Q_X, Q_P on selected Y, I_U on ordinary Y), +A_out = diag(F9_X, F9_P on selected Y, F9 q_U on ordinary Y). +``` + +The actual operation is W=A_out M A_in^-1. Therefore + +```text +W^(-*) = A_out M^(-T) A_in^-1. +``` + +All content coefficients here are real. The notation * denotes the +Hilbert adjoint of the complete physical operator, including phases. +This statement does not replace an adjoint with a transpose for a +general complex response. + +Suppose the original chronological gates are G1,...,Gn. The physical +operator is Gn...G1. Its inverse-adjoint is + +```text +Gn^(-*) ... G1^(-*). +``` + +The chronological order is unchanged. Every native gate and endpoint +view is unitary, so its inverse-adjoint is exactly the same operator, +including its global phase. For the scalar instructions: + +```text +target += c source becomes source -= c target, +target *= c becomes target *= 1/c. +``` + +The emitter applies these rules to every scalar instruction. All scalar +reads still use two fields in the same current frame. Native frame +progress is unchanged. The full column replay checks the resulting +word, including every borrowed helper. + +## Selected-bank conjugation without added swaps + +At each selected port, both input fields have the same Q frame and +both output fields have the same FULL frame. Their exact input +monomial records are also equal. Consequently S commutes with A_in +and A_out. + +The conjugated physical operator can be written + +```text +S W^(-*) S + = (S Gn^(-*) S) ... (S G1^(-*) S). +``` + +Each adjacent pair S S cancels. To emit this circuit, replace every +selected field index p with 112+p, and vice versa, in every instruction +and boundary binding. This is a different, explicit circuit on the +same physical fields. It is not an unpriced swap of live data. + +The emitter stores this field permutation. It checks all input records +by their physical target, frame, port, and complete monomial recipe. +The ninety-six ordinary output records keep their fields. The native +recipes and frame lists are unchanged byte for byte. The entry and exit +frame arrays are invariant under the selected permutation. + +The exact physical Bswapclean result is + +```text +input: + X = Q(a,u), Y_P = Q_P z, Y_U = v; + +output: + X_P = F9(z+Bv), X_U = F9(u+Dz-v), + Y_P = -F9 a, Y_U = F9 q_U v. +``` + +The unpermuted inverse-adjoint is also stored as a separate complete +word. It has content (-z,u+Da-v,a+Bv,v) with the same physical exit +frames. + +## Invoice and checks + +For both variants and both providers, the complete local invoice is + +```text +scalar primitives 8600 +native profile 1392 H1 + 64 H2 + 48 H3 + 16 H8 +native mass 1792 +native children 1520 +input monomial views 128 +output monomial views 96 +native side-map upper bound 3040 +extra boundary swap steps 0 +extra owned or private fields 0 +odd divisions 0 +``` + +Inverting the real power-of-two scales keeps their price. Transposing +and negating the ADDs also keeps their price. The H8 wrappers remain +charged. + +The exact content prefix row one-norm is 12. The additional binary +denominator height is two. These are bounds at the emitted operation +boundaries. They do not include recursive child precision or primitive +internal roundoff. + +The normal and optimized runs produce identical payloads and receipts. +The serialized programs are replayed. A wrong code ADD sign and a wrong +exchange ADD sign are rejected in all four complete words. + +```text +python3 emit_dual.py --out +python3 -O emit_dual.py --out +``` + +Both commands refuse an existing output directory. + +This construction uses the frozen clean exchange and its reviewed +native dependencies. The independent clean-exchange review is +`new-native-recipes-20261017/clean-centre-exchange-review-20261020`, +with freeze SHA256 +`6cd34040ecd7d832f1bae3d44c5a7b97dcc11022d843e48007c5474cc4f3701d`. +The cover-algebra lane supplied the useful selected-bank formulation. +AI agents prepared this literal circuit and its checks. + +The matching input types make this local conjugation legal. They do +not by themselves establish the next routed service, its scalar code, +its output decoder, or a complete multiplication bound. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md new file mode 100644 index 0000000000..83ca026c25 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md @@ -0,0 +1,192 @@ +# Clean centre rows from a late productive exchange + +This packet forms the sixteen selected centre rows without a clean +target or an extra field. It puts the old selected target values into +the selected source fields. All 416 auxiliary fields can have arbitrary +initial values and return unchanged. + +Two distinct input contracts are supplied. Initial formation accepts +selected targets in I. Reuse accepts selected targets in their positive +line frame Q. Both words cost 8,600 real scalar primitives. Their native +masses are 1,808 and 1,792, respectively. These are complete local +invoices. A full supplier still needs its routed caller, helper host, +recursive bill, and precision bound. + +## Exact inputs and source code + +The source response is the frozen rank-sixteen response E. Select the +ordered physical ports + +```text +P = [0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23]. +``` + +Write U for the other ninety-six ports. The normalized reader L has +the form L=[I,B] in P,U order. The existing row code is + +```text +C = [ I B ], C^-1 = [ I -B ]. + [ 0 I ] [ 0 I ] +``` + +The literal C word uses no extra field and costs 1,760 real scalar +primitives. It accepts arbitrary source values. + +The exact reader and code come from +`controller-followthrough-20261017/row-capture-20261020`. +The exact retained native paths come from +`row-only-capture-20261020`. The I-entry variant uses the reviewed +direct-FULL formation paths. The Q-entry variant uses the reviewed +line-entry prefix in `fixed-reader-reuse-20261020`. Every source file +and review pin is stored in the payload. + +Let q=Q^-1. Here Q has one positive line operator on each port, and F9 +is the common full nine-coordinate operator. + +For initial formation the physical inputs are + +```text +X = Qx, Y = y. +``` + +For reuse they are + +```text +X = Qx, Y_P = Q_P z, Y_U = y_U. +``` + +The x, y, and z values in each stated contract are independent and +arbitrary. In particular, z does not have to be a centre value. The +contract does not assume any relation between z and x. + +## Literal construction + +First run the complete retained source paths and the ninety-six +ordinary target paths. None of these events reads a selected target. +Then advance the sixteen selected targets to FULL. Initial formation +uses sixteen rank-nine children. Reuse uses sixteen rank-eight +line-to-FULL children, with their actual nontrivial wrappers. + +At this cut all X fields and all selected Y fields are FULL. The +content is + +```text +X = x, +Y_P = b, +Y_U = (y+Ex)_U, +``` + +where b=y_P for formation and b=z for reuse. The ordinary Y fields +retain the physical exterior q_U. Apply C to X at the common FULL +cut. Thus X_P=Lx and X_U=x_U. For every p in P, perform the following +three unit ADDs in this order: + +```text +Y_p += X_p +X_p -= Y_p +Y_p += X_p +``` + +For arbitrary values a and b, these three steps map (a,b) to (-b,a). +They cost 24 real scalar primitives per selected pair. No extra sign +instruction or temporary field is needed. + +The exact physical result is therefore + +```text +X_P = -F9 b, X_U = F9 x_U, +Y_P = F9 Lx, Y_U = F9 q_U (y+Ex)_U. +``` + +The sixteen centre values in Y_P contain no old Y contribution. The +old selected target state is still present, with a minus sign, in +X_P. The construction changes the productive data interface; it does +not erase that state. + +## Full-domain correctness + +The content map is invertible. If its output content is (u,v), recover + +```text +x_U = u_U, +x_P = v_P - B u_U, +b = -u_P, +y_U = v_U - E_U x. +``` + +All coefficients are dyadic. The checker forms this inverse independently +from the output equations and checks both product orders on all 224 data +columns. This establishes invertibility of the content map. It does not +price an inverse physical service. + +The literal forward replay checks all 640 input columns. It checks the +frame of each scalar source and target, both frames of every native +call, and all final frames. Every native recipe, frame list, and endpoint +adapter is inherited byte for byte from an independently reviewed +source. The new suffix uses only scalar operations at the common FULL +cut. It introduces no new native phase operator. + +The selected targets are advanced before the code and the exchanges. +The source code runs only after the complete retained native sweep. +Thus the proof needs no early all-source FULL cut, old source read, or +commutation of Q with the response. + +## Complete local invoices + +Both variants have the same scalar bill: + +```text +retained native word scalar operations 6456 +FULL-X row code 1760 +sixteen signed exchanges: 16*24 384 +total 8600 +``` + +Their exact child and view invoices are: + +| Item | Initial I entry | Selected Q entry | +| --- | ---: | ---: | +| Native profile | 1392 H1 + 64 H2 + 48 H3 + 16 H9 | 1392 H1 + 64 H2 + 48 H3 + 16 H8 | +| Native mass | 1808 | 1792 | +| Native children | 1520 | 1520 | +| Input monomial views | 112 | 128 | +| Output monomial views | 96 | 96 | +| Native side-map upper bound | 3008 | 3040 | +| Extra owned or private fields | 0 | 0 | +| Odd divisions | 0 | 0 | + +The sixteen direct F9 recipes have identity side maps. The H8 recipes +retain both side maps. The invoice does not transfer the identity-map +claim from F9 to H8. + +At the scalar and native operation boundaries, the maximum content row +one-norm is 22. The additional binary denominator height is one. These +are exact local content bounds. They do not include primitive internal +roundoff, recursive child precision, or the complete caller. + +## Verification and limits + +Both providers and both entry variants pass normal and optimized Python +with byte-identical payloads and receipts. The serialized payload is +replayed in each run. A missing source-code ADD and a missing exchange +ADD are both rejected in every complete word. + +Run either command with a new output directory: + +```text +python3 emit_clean_exchange.py --out +python3 -O emit_clean_exchange.py --out +``` + +The emitter refuses an existing output directory. + +The next productive source can use (Y_P,X_U), whose content is Cx. +The other bank then contains (-b,(y+Ex)_U), with mixed physical phases. +A routed next-entry proof must bind these actual roles and phases. This +packet does not apply C^-1, identify the source with x, or assume that +the same reader survives another service. + +The construction builds on the campaign's rank-sixteen response, row +capture, direct-FULL formation, and line-entry reuse packets. AI agents +prepared and checked this extension. Independent review is recorded in +a separate packet. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json new file mode 100644 index 0000000000..61b6a46fe6 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/DUAL-FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "CLEAN-DUAL.md": "1515a8b82ecfcb32d7dc19a4a8bc0fcf0af870ac444bb1628443dfb378360cb9", + "dual-normal/CHECKS.json": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b", + "dual-normal/CLEAN-DUAL.json.gz": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660", + "dual-optimized/CHECKS.json": "ae71aade4909408b376ccf42c99fad56e51297f28c6f293b96639a4e880e163b", + "dual-optimized/CLEAN-DUAL.json.gz": "94f17a8561c63efa26ac79b6bdd7481dbb3c2687967ed4b198a4d14ef7ca1660", + "emit_dual.py": "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8" + }, + "normal_optimized_byte_identical": true, + "payload_decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c", + "scope": "Four exact640-column local inverse-adjoint/conjugate words with unchanged physical phase records,8600 scalar,1792 native mass. The routed caller and complete supplier remain separate.", + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json new file mode 100644 index 0000000000..8b54249651 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/FREEZE.json @@ -0,0 +1,26 @@ +{ + "files": { + "CLEAN-LATE-EXCHANGE.md": "eb8e579b11d3d4ce8e77a2d6003b1a95135d84f79ce60d48ee2370194797569c", + "emit_clean_exchange.py": "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc", + "run-normal/CHECKS.json": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b", + "run-normal/CLEAN-LATE-EXCHANGE.json.gz": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d", + "run-optimized/CHECKS.json": "c47f36dbf492b445f84ce6aa97c632a0c5ddcc3eab5d9fa9b836f28133465d2b", + "run-optimized/CLEAN-LATE-EXCHANGE.json.gz": "f71ea2ff84186e03fc076ae0355cc0db06351cb6abee64828ce86bc8a01cca7d" + }, + "normal_optimized_byte_identical": true, + "payload_decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083", + "scope": "Four complete local words, all640 input columns, arbitrary borrowed target state, and416 restored helpers. Routed next-entry and complete supplier costs remain separate.", + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING", + "variants": { + "I": { + "native_mass": 1808, + "role": "Initial clean centre formation", + "scalar": 8600 + }, + "Q": { + "native_mass": 1792, + "role": "Clean centre exchange with arbitrary selected line-frame input", + "scalar": 8600 + } + } +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json new file mode 100644 index 0000000000..bb9da0263e --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/dual-normal/CHECKS.json @@ -0,0 +1,140 @@ +{ + "actual_D_equals_negative_B_transpose": true, + "all_content_inverse_orders": true, + "native_phase_scope": "All native and endpoint spatial operators are unchanged unitary records from the reviewed Q-entry word. Each inverse-adjoint native operator equals itself.", + "negative_controls": "A wrong code or exchange ADD sign fails in all four words.", + "payload_decompressed_sha256": "6c8869b1c1b45632635805e389899b83fa8348c9fe5b84e3c9c7821bcfd0568c", + "producer_sha256": "b78a5e653e8436592fd6a8d0e183aa34dcd2f3f1d81a775a0f0d5b5c5007a1a8", + "reports": { + "base": { + "inverse_adjoint": { + "additional_content_binary_height": 2, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "extra_boundary_swap_instructions": 0, + "maximum_content_prefix_row_one_norm": "12", + "native_children": 1520, + "native_mass": 1792, + "native_phase_records_unchanged": true, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "selected_input_and_output_adapter_symmetry": true, + "unchanged_arbitrary_helpers": 416 + }, + "selected_swap_conjugate": { + "additional_content_binary_height": 2, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "extra_boundary_swap_instructions": 0, + "maximum_content_prefix_row_one_norm": "12", + "native_children": 1520, + "native_mass": 1792, + "native_phase_records_unchanged": true, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "selected_input_and_output_adapter_symmetry": true, + "unchanged_arbitrary_helpers": 416 + } + }, + "extra": { + "inverse_adjoint": { + "additional_content_binary_height": 2, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "extra_boundary_swap_instructions": 0, + "maximum_content_prefix_row_one_norm": "12", + "native_children": 1520, + "native_mass": 1792, + "native_phase_records_unchanged": true, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "selected_input_and_output_adapter_symmetry": true, + "unchanged_arbitrary_helpers": 416 + }, + "selected_swap_conjugate": { + "additional_content_binary_height": 2, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "extra_boundary_swap_instructions": 0, + "maximum_content_prefix_row_one_norm": "12", + "native_children": 1520, + "native_mass": 1792, + "native_phase_records_unchanged": true, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "selected_input_and_output_adapter_symmetry": true, + "unchanged_arbitrary_helpers": 416 + } + } + }, + "scope": "Complete local physical inverse-adjoint and selected-role conjugate. 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HmfZ7y8dF9w literal 0 HcmV?d00001 diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_clean_exchange.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_clean_exchange.py new file mode 100644 index 0000000000..f9a65bb73d --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_clean_exchange.py @@ -0,0 +1,242 @@ +#!/usr/bin/env python3 +"""Form clean centre rows by a late exchange with productive fields.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parent / "row-only-capture-20261020" +LANES = HERE.parents[2] +PINS = { + "helper": (SOURCE / "emit_capture.py", + "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f"), + "formation": (SOURCE / "direct-normal/DIRECT-FULL-CAPTURE.json.gz", + "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c"), + "capture": (LANES / "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"), + "phase_review": (LANES / "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json", + "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"), + "line_prefix": (HERE.parent / "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz", + "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e"), + "line_phase_review": (LANES / "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source " + name) + return raw + + +read("helper") +spec = importlib.util.spec_from_file_location("clean_exchange_base", PINS["helper"][0]) +base = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = base +spec.loader.exec_module(base) +n = base.n + + +def expected_map(code, response, selected): + result = n.r.identity(640) + for p in range(112): + if p in selected: + result[p] = {112 + p: F(-1)} + result[112 + p] = dict(code[p]) + else: + n.r.add(result[112 + p], response[p]) + return result + + +def inverse_content(code, response, selected): + x = n.r.identity(224)[:112] + for p in selected: + x[p] = {112 + p: F(1)} + for j, value in code[p].items(): + if j != p: + n.r.add(x[p], {j: -value}) + result = [dict(row) for row in x] + [{} for _ in range(112)] + for p in range(112): + if p in selected: + result[112 + p] = {p: F(-1)} + else: + result[112 + p] = {112 + p: F(1)} + for j, value in response[p].items(): + n.r.add(result[112 + p], x[j], -value) + return result + + +def verify(word, expected): + current = list(word["start"]) + state = n.r.identity(640) + maximum, height = F(1), 0 + for event in word["events"]: + if event[0] == "native": + _, field, old, new, rank, key = event + need(current[field] == old, "The exact native input frame") + need(len(n.basis(word["frames"][old] + word["frames"][new])) + == len(word["frames"][new]), "The native frame is nested") + need(rank == len(word["frames"][new]) - len(word["frames"][old]) + == word["native_recipes"][key]["rank"], "The exact native rank") + current[field] = new + else: + need(event[0] == "scalar", "The complete event grammar") + gate, frame = event[1:] + op, target, source, raw = gate + coefficient = F(raw) + need(current[target] == frame, "The exact scalar target frame") + if op == "add": + need(source != target and current[source] == frame, "The exact source frame") + n.r.add(state[target], state[source], coefficient) + else: + need(op == "scale", "Only ADD and SCALE instructions") + state[target] = {j: coefficient * value for j, value in state[target].items() + if coefficient * value} + maximum = max(maximum, sum(abs(value) for value in state[target].values())) + for value in state[target].values(): + d = value.denominator + need(d & (d - 1) == 0, "All content is dyadic") + height = max(height, d.bit_length() - 1) + need(state == expected, "All640 independent arbitrary input fields") + need(current == word["final"], "All640 complete final frames") + need(state[224:] == n.r.identity(640)[224:], "All416 arbitrary helpers are restored") + profile = Counter(event[4] for event in word["events"] if event[0] == "native") + direct_full = sum(event[0] == "native" and event[5] == "capture-full" + for event in word["events"]) + return { + "all_independent_input_fields": 640, "unchanged_arbitrary_helpers": 416, + "native_profile": dict(sorted(profile.items())), "native_children": sum(profile.values()), + "native_mass": sum(k * v for k, v in profile.items()), + "native_side_map_upper_bound": 2 * (sum(profile.values()) - direct_full), + "direct_full_identity_wrapper_children": direct_full, + "explicit_input_monomial_views": len(word["input_views"]), + "explicit_output_monomial_views": len(word["output_views"]), + "scalar_stage_prices": {stage: base.price(word["events"][start:end]) + for stage, (start, end) in word["stage_ranges"].items()}, + "real_scalar_primitives": base.price(word["events"]), + "maximum_content_prefix_row_one_norm": str(maximum), + "additional_content_binary_height": height, + "owned_fields": 0, "private_fields": 0, "odd_divisions": 0, + } + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + source = json.loads(read("formation")) + line_prefix = json.loads(read("line_prefix")) + capture = json.loads(read("capture")) + read("phase_review") + read("line_phase_review") + pivots = capture["pivots"] + selected = set(pivots) + code, response = n.rows(capture["code"]), n.rows(capture["response"]) + need(pivots == source["selected_ports"] and code == n.rows(source["code"]) + and response == n.rows(source["response"]), "The exact formation and row code") + for p in selected: + need(code[p].get(p) == 1 and set(code[p]) & selected == {p}, + "Each normalized reader has its own pivot") + expected = expected_map(code, response, selected) + inverse = inverse_content(code, response, selected) + need(n.r.product(expected[:224], inverse) == n.r.product(inverse, expected[:224]) + == n.r.identity(224), "Both exact content inverse orders") + providers, reports = {}, {} + for provider in source["providers"]: + providers[provider], reports[provider] = {}, {} + for entry, original in ( + ("I", source["providers"][provider]), ("Q", line_prefix["providers"][provider])): + word = deepcopy(original) + core_start, core_end = original["stage_ranges"]["retained_core"] + progress = "selected_full_progress" if entry == "I" else "selected_line_progress" + full_start, full_end = original["stage_ranges"][progress] + word["events"] = deepcopy(original["events"][core_start:core_end] + + original["events"][full_start:full_end]) + ranges = {"retained_core": [0, core_end - core_start], + "selected_progress": [core_end - core_start, len(word["events"])]} + start = len(word["events"]) + for op, target, source_index, coefficient in capture["scalar_word"]: + word["events"].append(["scalar", [op, target, source_index, coefficient], 1]) + ranges["source_row_code"] = [start, len(word["events"])] + start = len(word["events"]) + for p in pivots: + word["events"].extend([ + ["scalar", ["add", 112 + p, p, "1"], 1], + ["scalar", ["add", p, 112 + p, "-1"], 1], + ["scalar", ["add", 112 + p, p, "1"], 1], + ]) + ranges["signed_selected_exchanges"] = [start, len(word["events"])] + word["stage_ranges"] = ranges + report = verify(word, expected) + rank = 9 if entry == "I" else 8 + need(report["native_profile"] == {1: 1392, 2: 64, 3: 48, rank: 16} + and report["native_mass"] == 1664 + 16 * rank, "The exact complete native profile") + need(report["scalar_stage_prices"] == { + "retained_core": 6456, "selected_progress": 0, + "source_row_code": 1760, "signed_selected_exchanges": 384}, + "All code and exchange costs are explicit") + need(report["real_scalar_primitives"] == 8600, "The exact complete scalar invoice") + for stage in ("source_row_code", "signed_selected_exchanges"): + bad = deepcopy(word) + index = next(i for i in range(*ranges[stage]) if bad["events"][i][1][0] == "add") + del bad["events"][index] + try: + verify(bad, expected) + except ValueError: + pass + else: + raise ValueError("An omitted " + stage + " ADD was accepted") + providers[provider][entry], reports[provider][entry] = word, report + payload = { + "schema": "clean-late-sixteen-centre-exchange-v1", + "source_pins": {name: {"path": str(path), "sha256": pin} + for name, (path, pin) in PINS.items()}, + "ports": source["ports"], "selected_ports": pivots, "code": capture["code"], + "response": capture["response"], "content_map": n.r.encoded(expected[:224]), + "inverse_content_map": n.r.encoded(inverse), "providers": providers, + "physical_contract": { + "input_I": "X=Qx; Y=y, with all640 fields independent and arbitrary.", + "input_Q": "X=Qx; Y_P=Q_P z; Y_U=y_U, with independent arbitrary z.", + "source_output_I": "X_P=-F9 y_P; X_U=F9 x_U.", + "source_output_Q": "X_P=-F9 z; X_U=F9 x_U.", + "target_output": "Y_P=F9 Lx; Y_U=F9 q_U (y+Ex)_U.", + "centre_baseline": "The selected centre rows contain no borrowed-Y contribution. The old selectedY baseline is retained with a minus sign on selectedX.", + "scope": "Complete local native formation by productive exchange. The actual routed next-entry and a complete caller are separate.", + }, + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + for provider, entries in json.loads(raw)["providers"].items(): + for entry, word in entries.items(): + need(verify(word, expected) == reports[provider][entry], "The full serialized clean exchange") + (args.out / "CLEAN-LATE-EXCHANGE.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = {"status": "PASS_EXACT_CLEAN_LATE_CENTRE_EXCHANGE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "reports": reports, "content_inverse_both_orders": True, + "negative_controls": "Omitted source-code or signed-exchange ADD fails in all four complete words.", + "native_phase_scope": "Every native recipe, frame, and endpoint adapter is byte-exact inherited from the reviewed direct-FULL formation or line-entry prefix.", + "scope": payload["physical_contract"]["scope"]} + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py new file mode 100644 index 0000000000..f0fa247738 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/emit_dual.py @@ -0,0 +1,229 @@ +#!/usr/bin/env python3 +"""Emit the inverse-adjoint clean word and its selected-role conjugate.""" + +import argparse +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +PINS = { + "producer": (HERE / "emit_clean_exchange.py", + "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc"), + "source": (HERE / "run-normal/CLEAN-LATE-EXCHANGE.json.gz", + "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083"), + "freeze": (HERE / "FREEZE.json", + "96048355033e5f5bdd26dadddb869708faae6f8b0d9a61a1ae696e5a5c20c0bc"), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned clean source " + name) + return raw + + +read("producer") +spec = importlib.util.spec_from_file_location("clean_dual_base", PINS["producer"][0]) +base = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = base +spec.loader.exec_module(base) +n = base.n + + +def conjugate(rows, permutation): + result = [{} for _ in rows] + for target, row in enumerate(rows): + result[permutation[target]] = {permutation[source]: value + for source, value in row.items()} + return result + + +def expected_swap(code, response, selected): + result = n.r.identity(640) + for p in range(112): + if p in selected: + result[p] = {112 + j: value for j, value in code[p].items()} + result[112 + p] = {p: F(-1)} + else: + n.r.add(result[p], {112 + p: F(-1)}) + for j in selected: + value = response[p].get(j, F(0)) + if value: + n.r.add(result[p], {112 + j: value}) + return result + + +def lower(original, permutation): + word = deepcopy(original) + events = [] + for event in original["events"]: + new = deepcopy(event) + if event[0] == "native": + new[1] = permutation[event[1]] + else: + need(event[0] == "scalar", "The complete source event grammar") + op, target, source, raw = event[1] + coefficient = F(raw) + if op == "add": + new[1] = [op, permutation[source], permutation[target], str(-coefficient)] + else: + need(op == "scale" and coefficient, "An invertible real scale") + new[1] = [op, permutation[target], None, str(1 / coefficient)] + events.append(new) + word["events"] = events + for key in ("start", "final"): + word[key] = [original[key][permutation[p]] for p in range(640)] + need(word[key] == original[key], "Selected endpoint frame symmetry") + for record in word["input_views"]: + record["field"] = permutation[record["field"]] + record["role"] = "source" if record["field"] < 112 else "selected_target" + word["input_views"].sort(key=lambda record: record["field"]) + input_by_field = {record["field"]: record for record in original["input_views"]} + physical_keys = ("frame", "left", "right", "rank", "port") + for record in word["input_views"]: + old = input_by_field[record["field"]] + need(all(record[key] == old[key] for key in physical_keys), + "The complete same-port input adapter is invariant") + for record in word["output_views"]: + need(permutation[112 + record["port"]] == 112 + record["port"], + "Every ordinary output adapter keeps its physical field") + need(word["native_recipes"] == original["native_recipes"] + and word["frames"] == original["frames"], "All native physical records are unchanged") + word["wire_permutation"] = {str(p): q for p, q in enumerate(permutation) if p != q} + word["scalar_rule"] = "Keep event order. Transpose each ADD and negate its coefficient. Invert each real SCALE." + return word + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + read("freeze") + source = json.loads(read("source")) + for name in ("phase_review", "line_phase_review"): + base.read(name) + selected = set(source["selected_ports"]) + code, response = n.rows(source["code"]), n.rows(source["response"]) + direct = n.rows(source["content_map"]) + inverse = n.rows(source["inverse_content_map"]) + need(n.r.product(direct, inverse) == n.r.product(inverse, direct) == n.r.identity(224), + "Both source content inverse orders") + for p in range(112): + if p in selected: + need(code[p].get(p) == 1 and set(code[p]) & selected == {p}, + "The exact normalized centre minor") + continue + row = {p: F(1)} + for j in selected: + d = response[p].get(j, F(0)) + need(d == -code[j].get(p, F(0)), "The actual D=-B transpose identity") + n.r.add(row, code[j], d) + need(row == response[p], "The actual ordinary response is u+D(a+Bu)") + dual = n.r.transpose(inverse, 224) + dual_inverse = n.r.transpose(direct, 224) + need(n.r.product(dual, dual_inverse) == n.r.product(dual_inverse, dual) == n.r.identity(224), + "Both inverse-adjoint content inverse orders") + full_dual = dual + n.r.identity(640)[224:] + identity_permutation = list(range(640)) + swap_permutation = list(identity_permutation) + for p in selected: + swap_permutation[p], swap_permutation[112 + p] = 112 + p, p + swap = conjugate(full_dual, swap_permutation) + need(swap == expected_swap(code, response, selected), + "The direct Bswapclean block formula") + swap_inverse = conjugate(dual_inverse, swap_permutation[:224]) + need(n.r.product(swap[:224], swap_inverse) == n.r.product(swap_inverse, swap[:224]) + == n.r.identity(224), "Both Bswapclean content inverse orders") + providers, reports = {}, {} + for provider, entries in source["providers"].items(): + original = entries["Q"] + providers[provider], reports[provider] = {}, {} + for name, permutation, expected in ( + ("inverse_adjoint", identity_permutation, full_dual), + ("selected_swap_conjugate", swap_permutation, swap)): + word = lower(original, permutation) + report = base.verify(word, expected) + need(report["real_scalar_primitives"] == 8600 + and report["native_mass"] == 1792 + and report["native_profile"] == {1: 1392, 2: 64, 3: 48, 8: 16}, + "The full dual invoice") + need(report["native_side_map_upper_bound"] == 3040 + and report["explicit_input_monomial_views"] == 128 + and report["explicit_output_monomial_views"] == 96, + "All actual adapter and wrapper counts") + report["extra_boundary_swap_instructions"] = 0 + report["native_phase_records_unchanged"] = True + report["selected_input_and_output_adapter_symmetry"] = True + for stage in ("source_row_code", "signed_selected_exchanges"): + bad = deepcopy(word) + index = next(i for i in range(*word["stage_ranges"][stage]) + if bad["events"][i][1][0] == "add") + bad["events"][index][1][3] = str(-F(bad["events"][index][1][3])) + try: + base.verify(bad, expected) + except ValueError: + pass + else: + raise ValueError("A wrong dual ADD sign was accepted") + providers[provider][name], reports[provider][name] = word, report + payload = { + "schema": "clean-inverse-adjoint-selected-conjugate-v1", + "source_pins": {name: {"path": str(path), "sha256": pin} + for name, (path, pin) in PINS.items()}, + "ports": source["ports"], "selected_ports": source["selected_ports"], + "code": source["code"], "response": source["response"], + "content_maps": {"inverse_adjoint": n.r.encoded(dual), + "selected_swap_conjugate": n.r.encoded(swap[:224])}, + "inverse_content_maps": {"inverse_adjoint": n.r.encoded(dual_inverse), + "selected_swap_conjugate": n.r.encoded(swap_inverse)}, + "providers": providers, + "physical_contract": { + "input": "X=Q(a,u); Y_P=Q_P z; Y_U=v.", + "inverse_adjoint_output_content": "X=(-z,u+D a-v); Y=(a+Bv,v).", + "selected_swap_conjugate_output_content": "X=(z+Bv,u+D z-v); Y=(-a,v).", + "output_frames": "All X and selected Y have F9; ordinary Y has F9 q_U.", + "operators": "B is the normalized reader off-pivot block; D=-B^T, with actual real dyadic coefficients.", + "scope": "Complete local physical inverse-adjoint and selected-role conjugate. A routed caller and its full supplier bill remain separate.", + }, + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for provider, words in saved["providers"].items(): + for name, word in words.items(): + expected = n.rows(saved["content_maps"][name]) + n.r.identity(640)[224:] + report = base.verify(word, expected) + need(all(value == reports[provider][name][key] for key, value in report.items()), + "The complete serialized dual replay") + (args.out / "CLEAN-DUAL.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_EXACT_CLEAN_INVERSE_ADJOINT_AND_SELECTED_CONJUGATE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "reports": reports, "all_content_inverse_orders": True, + "actual_D_equals_negative_B_transpose": True, + "negative_controls": "A wrong code or exchange ADD sign fails in all four words.", + "native_phase_scope": "All native and endpoint spatial operators are unchanged unitary records from the reviewed Q-entry word. Each inverse-adjoint native operator equals itself.", + "scope": payload["physical_contract"]["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..31337b060e --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/clean-late-exchange-20261020/run-normal/CHECKS.json @@ -0,0 +1,127 @@ +{ + "content_inverse_both_orders": true, + "native_phase_scope": "Every native recipe, frame, and endpoint adapter is byte-exact inherited from the reviewed direct-FULL formation or line-entry prefix.", + "negative_controls": "Omitted source-code or signed-exchange ADD fails in all four complete words.", + "payload_decompressed_sha256": "b0432322c28ad3a03af8da550a0b7c7df048c7ff5a0664acc7f78efffcffd083", + "producer_sha256": "91ee4ce54a5774dfdec7ac0a83f78c5076ef14d0ee30f2dcc7ecf448b869ecbc", + "reports": { + "base": { + "I": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 16, + "explicit_input_monomial_views": 112, + "explicit_output_monomial_views": 96, + "maximum_content_prefix_row_one_norm": "22", + "native_children": 1520, + "native_mass": 1808, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "9": 16 + }, + "native_side_map_upper_bound": 3008, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + }, + "Q": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "maximum_content_prefix_row_one_norm": "22", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + } + }, + "extra": { + "I": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 16, + "explicit_input_monomial_views": 112, + "explicit_output_monomial_views": 96, + "maximum_content_prefix_row_one_norm": "22", + "native_children": 1520, + "native_mass": 1808, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "9": 16 + }, + "native_side_map_upper_bound": 3008, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + }, + "Q": { + "additional_content_binary_height": 1, + "all_independent_input_fields": 640, + "direct_full_identity_wrapper_children": 0, + "explicit_input_monomial_views": 128, + "explicit_output_monomial_views": 96, + "maximum_content_prefix_row_one_norm": "22", + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "owned_fields": 0, + "private_fields": 0, + "real_scalar_primitives": 8600, + "scalar_stage_prices": { + "retained_core": 6456, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_row_code": 1760 + }, + "unchanged_arbitrary_helpers": 416 + } + } + }, + "scope": "Complete local native formation by productive exchange. 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zu;Ov?+fMK8M(1f_k+}NdV(Cn8)#u^yq=MM@^&<9d@9pN)?rllndCc#5i}-aH+~W((^^H8~amd4iRPH&H-p;sES*V~hxWIX`{e!fq@$(Gm*zn7goG`TUq#0FaZ zZ)@H!mscHnkhd3C91q?^rf)B2Z}*`cFBxaAr^Ii+-*64?IQ(AUB=7lsDrYYWuH&EX zFE9$uC0=`np9d5i>4Wzu1A+a<=_|kY&buD&FBbR({8%Rl?3OXspN6i+I(YqBtd7&) z9v>P6>I7a=^Y3ORJ)zi*7Nk-@_c%y z=K#yU{%&OL7(%-M4hSbrgi8xykX5PZdxm3wYONq)$L^6`;KeM|ANH>D`}0yoeHt`95xY zd+wrbEby2e!(9=!`oVgx74RiGdH9V|L^@LYcq1+yZ;uM>P(J;?04)I0 x|4C-3oIhpvLB^i(>BF> bit & 1), None) + if found is None: + continue + rows[count], rows[found] = rows[found], rows[count] + for i in range(len(rows)): + if i != count and rows[i] >> bit & 1: + rows[i] ^= rows[count] + count += 1 + return tuple(rows[:count]) + + +def rows(value): + return [{int(p): F(c) for p, c in row.items()} for row in value] + + +def verify_word(word, response, direction): + current = list(word["start"]) + state = [{i: F(1)} for i in range(len(current))] + maximum = F(1) + scalar_word = [] + for event in word["events"]: + if event[0] == "native": + _, field, old, new, rank, key = event + need(current[field] == old, "Literal native entry frame") + need(len(basis(word["frames"][old] + word["frames"][new])) == len(word["frames"][new]), + "Literal nested native edge") + need(rank == len(word["frames"][new]) - len(word["frames"][old]) + == word["native_recipes"][key]["rank"], "Literal native rank") + current[field] = new + else: + need(event[0] == "scalar", "Literal event grammar") + gate, frame = event[1:] + op, target, origin, coefficient = gate + c = F(coefficient) + need(current[target] == frame, "Literal scalar target frame") + if op == "scale": + state[target] = {p: c * v for p, v in state[target].items() if c * v} + else: + need(op == "add" and target != origin and current[origin] == frame, + "Literal scalar source frame") + r.add(state[target], state[origin], c) + maximum = max(maximum, sum(abs(v) for v in state[target].values())) + scalar_word.append(gate) + expected = [{i: F(1)} for i in range(len(current))] + for target, row in enumerate(response): + if direction == "forward": + r.add(expected[112 + target], row) + else: + for origin, coefficient in row.items(): + r.add(expected[origin], {112 + target: -coefficient}) + need(state == expected and current == word["final"], "All640 columns and final frames") + profile = Counter(event[4] for event in word["events"] if event[0] == "native") + return {"all_input_columns": len(current), "untouched_arbitrary_fields": len(current) - 224, + "owned_fields": 0, "private_fields": 0, "native_profile": dict(sorted(profile.items())), + "native_mass": sum(k * v for k, v in profile.items()), "native_children": sum(profile.values()), + "real_scalar_primitives": r.price(scalar_word), "prefix_row_l1_bound": str(maximum), + "native_side_map_bound": 2 * sum(profile.values()), "endpoint_maps": 224} + + +def make_word(cyclic, model, direction): + frames = deepcopy(cyclic["frames"]) + indices = {tuple(frame): i for i, frame in enumerate(frames)} + small = set(model["small_ports"]) + current = list(cyclic["start"]) + events = [] + mode = rows(model["mode_response"]) + by_parameter = {record["id"]: record for record in cyclic["parameters"]} + transfer_records = [] + for event in cyclic["programs"][direction]: + kind = event[0] + if kind == "native": + _, field, old, new, rank = event + if field % 112 in small: + need(field < 224, "Only data fields receive native progress") + continue + need(current[field] == old, "Pinned cyclic native frame") + current[field] = new + events.append(["native", field, old, new, rank, str(old) + ":" + str(new)]) + elif kind == "parameter_add": + _, target, origin, parameter, sign, frame = event + record = by_parameter[parameter] + carriers = cyclic["cyclic_carriers"][record["vertex"]] + c = sign * mode[carriers[record["row"]]].get(carriers[record["column"]], F(0)) + if c: + transfer_records.append({"part": "large48", "event": len(events), + "coefficient": str(c), "parameter": parameter}) + events.append(["scalar", ["add", target, origin, str(c)], frame]) + else: + need(kind in ("add", "scale"), "Pinned cyclic scalar grammar") + _, target, origin, coefficient, frame = event + events.append(["scalar", [kind, target, origin, coefficient], frame]) + + def frame(vectors): + vectors = basis(vectors) + if vectors not in indices: + indices[vectors] = len(frames) + frames.append(list(vectors)) + return indices[vectors] + + def native(field, new): + old = current[field] + if old == new: + return + need(len(basis(frames[old] + frames[new])) == len(frames[new]), "Clique nested edge") + events.append(["native", field, old, new, len(frames[new]) - len(frames[old]), + str(old) + ":" + str(new)]) + current[field] = new + + q = cyclic["ports"] + for group in model["small_cliques"]: + k = len(group) + for depth in range(1, k): + for i, p in enumerate(group): + native(p, frame(q[group[(i + j) % k]] for j in range(depth))) + native(112 + p, frame(q[group[(i - j) % k]] for j in range(1, depth + 1))) + for i, p in enumerate(group): + target_port = group[(i + depth) % k] + need(current[p] == current[112 + target_port], "Every clique transfer has equal frames") + target, origin, coefficient = ((112 + target_port, p, "-1") if direction == "forward" + else (p, 112 + target_port, "1")) + transfer_records.append({"part": "small64", "event": len(events), + "source_port": p, "target_port": target_port, + "coefficient": coefficient}) + events.append(["scalar", ["add", target, origin, coefficient], current[p]]) + for p in group: + native(p, cyclic["final"][p]) + native(112 + p, cyclic["final"][112 + p]) + need(current == cyclic["final"], "Full native frame completion") + return {"frames": frames, "start": cyclic["start"], "final": cyclic["final"], + "events": events, "transfer_records": transfer_records} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = json.loads(read("independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json")) + model = json.loads(read("new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json")) + core = json.loads(read("new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz")) + for provider, data in core["providers"].items(): + need(data["canonical"]["ports"] == cyclic["ports"], "Pinned provider directions " + provider) + need(len(data["canonical"]["start"]) == 632, "Pinned live-field count " + provider) + words = {direction: make_word(cyclic, model, direction) for direction in ("forward", "backward")} + need(words["forward"]["frames"] == words["backward"]["frames"], "Both directions use the same actual frames") + frames = words["forward"]["frames"] + edge_pairs = sorted({(event[2], event[3]) for word in words.values() + for event in word["events"] if event[0] == "native"}) + recipes = {} + for i, (old, new) in enumerate(edge_pairs): + operation = compiler.canonical_frame(9, tuple(frames[old])).adjoint().then( + compiler.canonical_frame(9, tuple(frames[new]))) + record, _ = compiler.lower_child(operation) + need(record["rank"] == len(frames[new]) - len(frames[old]), "Fresh native rank") + phase.equal(phase.recipe(record), phase.adjoint(phase.frame(frames[old], 9)) + + phase.frame(frames[new], 9), "Fresh native phase " + str((old, new))) + recipes[str(old) + ":" + str(new)] = record + if (i + 1) % 100 == 0: + print("Native phases", i + 1, "/", len(edge_pairs), flush=True) + endpoints = [] + for p, q in enumerate(cyclic["ports"]): + for role in ("source", "target"): + conventional = (compiler.cgate(9, q) if role == "source" + else compiler.cgate(9, q, -1).then(compiler.fourier(9))) + circuit = (("C", q, 1),) if role == "source" else (("C", q, -1),) + phase.fourier(9) + frame = cyclic["start"][p] if role == "source" else cyclic["final"][112 + p] + operation = conventional.adjoint().then(compiler.canonical_frame(9, tuple(frames[frame]))) + record, _ = compiler.lower_child(operation) + need(record["rank"] == 0, "Endpoint adapter is monomial") + phase.equal(phase.recipe(record), phase.adjoint(circuit) + phase.frame(frames[frame], 9), + "Fresh conventional endpoint " + str((role, p))) + endpoints.append({"port": p, "role": role, "frame": frame, **record}) + reports = {} + for direction, word in words.items(): + word["native_recipes"] = recipes + word["endpoint_adapters"] = endpoints + reports[direction] = verify_word(word, rows(model["response"]), direction) + need(reports["forward"]["native_profile"] == {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}, + "Complete profile") + need(reports["forward"]["native_mass"] == 1792 and reports["forward"]["real_scalar_primitives"] == 5288, + "Complete local invoice") + # Deletion of one nonzero transfer must change the complete content map. + bad = deepcopy(words["forward"]) + del bad["events"][bad["transfer_records"][0]["event"]] + try: + verify_word(bad, rows(model["response"]), "forward") + except ValueError: + pass + else: + raise ValueError("The missing transfer control was accepted") + payload = {"schema": "low-displacement-native-v1", "source_pins": PINS, + "response": model["response"], "common_frame_words": model["common_frame_words"], + "selected_ports": model["selected_ports"], "small_cliques": model["small_cliques"], + "providers": {provider: words for provider in core["providers"]}} + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for provider, directions in saved["providers"].items(): + for direction, word in directions.items(): + need(verify_word(word, rows(saved["response"]), direction) == reports[direction], + "Serialized provider replay " + provider + " " + direction) + (args.out / "NATIVE-PROGRAM.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = {"status": "PASS_LOW_DISPLACEMENT_NATIVE", "source_pins": PINS, + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "fresh_native_phase_checks": len(recipes), "fresh_endpoint_phase_checks": len(endpoints), + "reports": reports, "same_geometry_both_providers_checked": True, + "negative_control": "one nonzero transfer omitted and rejected", + "scope": "Complete local data shears and exact phases. Helpers are unchanged; their progress, recursive hosting, routed codes and terminal remain open."} + (args.out / "NATIVE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/CARRIER-PREFIX.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/CARRIER-PREFIX.md new file mode 100644 index 0000000000..88709fb3e0 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/CARRIER-PREFIX.md @@ -0,0 +1,40 @@ +# The complete carrier prefix + +This packet stops the independently reviewed local reuse word before its +selected query. It supplies a concrete native prefix for a separate +routed reader query. + +The input is \(X=Qx\), \(Y_U=y_U\), and \(Y_P=Q_Pz\), with arbitrary +independent records \(z\). The output is + +\[ +X'=F_9x,\qquad +Y'_U=F_9q_U(y+Ex)_U,\qquad +Y'_P=F_9z. +\] + +All 416 auxiliary fields are unchanged. The word has 2406 events: +2390 retained-core events followed by sixteen line-to-FULL native +calls. It has no selected query. Both providers pass all 640 independent +columns and every exact read, write, and native frame check. + +The profile is \(1392H_1+64H_2+48H_3+16H_8\), with native mass 1792, +1520 children, and 6456 scalar primitives. There are 128 input views, +96 ordinary output views, and a native side-map upper bound of 3040. +The content prefix row one-norm is 22; its additional binary denominator +height is one. There is no extra owned or private field. + +Every physical recipe and adapter is copied from the pinned line-entry +reuse packet, whose independent review is also pinned. The two output +directories have byte-identical payloads and receipts under normal and +optimized Python. + +This packet supplies only the native prefix. The global dispatcher, +past-reader query, and their full invoices are separate. It does not +replace a past reader with the current reader. + +Run `emit_prefix.py --out ` with normal Python or +optimized Python. The emitter rejects an existing output directory. + +AI agents prepared this extension of the reviewed productive row-capture +and line-entry reuse constructions. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json new file mode 100644 index 0000000000..bc2670414d --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/PREFIX-FREEZE.json @@ -0,0 +1,12 @@ +{ + "files": { + "CARRIER-PREFIX.md": "2ef1ff2371a01289310137570b0ce03b2739c85e74c1e7ba94ea434eedcff1b4", + "emit_prefix.py": "657afc180b397e851fbefa16f56ace98129072a6bd2faf5d84dbc2391720698e", + "prefix-normal/CARRIER-PREFIX.json.gz": "42b7d01235d86252c52d979bbc8dd8978cd08f57ef0f968124cbf18c7cb1a70c", + "prefix-normal/CHECKS.json": "82c8bb1dd1bc0c05d37cffe30697f7762627526ea012855f35d4b72ae537583d", + "prefix-optimized/CARRIER-PREFIX.json.gz": "42b7d01235d86252c52d979bbc8dd8978cd08f57ef0f968124cbf18c7cb1a70c", + "prefix-optimized/CHECKS.json": "82c8bb1dd1bc0c05d37cffe30697f7762627526ea012855f35d4b72ae537583d" + }, + "normal_optimized_byte_identical": true, + "scope": "Exact carrier-only prefix. Global dispatcher and routed query are separate." +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json new file mode 100644 index 0000000000..006f55295f --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/QUERY-FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "ROUTED-QUERY.md": "2ee46160065120ca90477ebabebd833c8e0dc4678544fb33c267193cada5e7cd", + "emit_routed_query.py": "78d505f55b4646fff0d1c40b53ad11327874bee6ebd074013c4288197f3fe900", + "query-normal/CHECKS.json": "55cb6d50b4a219ba3cea2ee59a3b15b03afa3c3c749dd13a72ee6148414845a2", + "query-normal/ROUTED-QUERY.json.gz": "b6a1031861db0b2293880af7c01919c5c628a8c23e7a293f73976a82e25011ac", + "query-optimized/CHECKS.json": "55cb6d50b4a219ba3cea2ee59a3b15b03afa3c3c749dd13a72ee6148414845a2", + "query-optimized/ROUTED-QUERY.json.gz": "b6a1031861db0b2293880af7c01919c5c628a8c23e7a293f73976a82e25011ac" + }, + "normal_optimized_byte_identical": true, + "payload_decompressed_sha256": "b94f7b8467bdcaf9150045fc5f7a1999640daab742faaaba55993c102be49d4a", + "scope": "Literal global FULL reader query and exact native carrier prefix. Actual D25 dispatcher, recursive hosting and complete supplier are separate.", + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/ROUTED-QUERY.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/ROUTED-QUERY.md new file mode 100644 index 0000000000..72d7769e03 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/ROUTED-QUERY.md @@ -0,0 +1,152 @@ +# A literal query for a centre reader retained from an earlier stage + +This packet expands the bridge worker's fixed-reader construction into +literal scalar and field-map instructions. It checks their composition +with the complete native carrier prefix. It covers the actual D25 stage +pairs \((s,t)=(0,1),(0,2),(1,2)\). + +The local carrier prefix and the query use different charts. The prefix +has the exact local native charts. The query starts after the dispatcher +has placed all X fields and the sixteen selected Y fields in the global +FULL chart at level \(t\). The dispatcher is a separate binding. This +packet does not assume that those charts are identical. + +## Required update + +Let \(P\) be the sixteen selected ports. Let \(J\) insert values at \(P\). +The normalized reader and its unit row code at stage \(s\) are + +\[ +L_s=J^T+B_s,\qquad B_sJ=0,\qquad C_s=I+JB_s. +\] + +All symbols include their actual ordered owner routes. The native +response at stage \(t\) is \(E_t\). The query must add +\(L_sE_tx\) to the selected record. It must restore every X field. + +The native prefix accepts arbitrary independent selected records \(z\). +Before the query its contents are + +\[ +X=x,\qquad Y_P=z,\qquad Y_U=y_U+(E_tx)_U, +\] + +with the prefix's stated physical output frames. After the query the +selected content is \(z+L_sE_tx\). If \(z=L_sy\), it is exactly +\(L_s(y+E_tx)\). The ordinary output content is already correct and is +not accessed by the query. + +## Literal query order + +The source theorem gives + +\[ +L_sE_tC_t^{-1} +=B_s-B_t+(L_sE_tJ)J^T. +\] + +The emitted word executes: + +1. Add \(B_sX_U\) to \(Y_P\), through the actual past-stage FULL views. +2. Add \(X_P\) to \(Y_P\). +3. Apply \(C_t\) to X, through the current-stage FULL views. +4. Subtract the current \(X_P\) from \(Y_P\). +5. Add \((L_sE_tJ)X_P\) to \(Y_P\). +6. Apply \(C_t^{-1}\) to X through the same current-stage views. + +Steps 2 and 4 account for \(-B_tX_U\). The X fields in step 5 contain +the current reader \(L_tX\). Step 6 restores the original source bank. +No inverse of \(E_t\) and no odd division is used. + +Every view is an explicit `map` event. Both the entry map and its inverse +are present. For each term in step 5, the word maps the selected X +source, adds its scalar multiple to the selected Y target, and restores +the X source with the exact inverse map. A scale of a target is also +explicit. No target baseline is assumed to be zero. + +## Exact owner paths and phases + +The verifier represents a coefficient by a pair consisting of its input +field and a 25-dimensional orthogonal owner matrix. It multiplies the +matrices in chronological operator order. Terms can cancel only when +their complete ordered matrices agree. It does not identify the +responses at stages \(s\) and \(t\). + +For each map with matrix \(R\), the packet records a translation +\(\delta_R\), the inverse matrix, and the inverse translation. It +checks orthogonality, both matrix inverse orders, and that every +uncompleted axis is fixed. It verifies the complete Z4 phase identity + +\[ +F_{9+8t}P_RF_{9+8t}^{-1}=X_{\delta_R}P_R. +\] + +This is a polynomial identity, including its quadratic and linear +parts. It holds on the complete spatial domain; it is not a sample of +spatial points. The phase checker is the pinned source implementation. +An independent review of this integration must still check that +dependency and the actual dispatcher. + +The actual payload contains 545 distinct FULL maps for each pair with +reader stage zero, and 1616 for pair \((1,2)\). These counts include +distinct inverse and view maps where required. The instruction count +remains 2064 map calls in every pair. + +## Verification and price + +Both native providers are replayed on all 640 independent local input +columns before the query. The global query is then replayed on all +640 independent formal fields. The result matches the direct expression +\(L_sE_t\), with all 3808 owner-path terms. All 112 X fields are restored. +The 96 ordinary Y fields and all 416 helpers are unchanged by the query. + +The serialized payload is read and checked again. Controls that omit +one middle source view or the final source-code restoration fail. +Normal and optimized Python give byte-identical outputs. + +| Part | Scalar primitives | Explicit map calls | +| --- | ---: | ---: | +| Past-reader complement query | 1760 | 224 | +| Two selected-field copies | 256 | 0 | +| Current source code and its inverse | 3520 | 448 | +| Middle selected-source query | 5632 | 1392 | +| Query total | 11168 | 2064 | + +Adding the native prefix gives 17624 scalar primitives and native +profile + +\[ +1392H_1+64H_2+48H_3+16H_8, +\] + +with mass 1792. The query maps are additional to the prefix's 128 input +views, 96 output views, and native side-map upper bound 3040. The actual +global dispatcher must also be charged. There are no extra owned or +private fields and no new native child in the query. + +The exact formal coefficient sweep gives prefix row one-norm 448 and +binary denominator height two for every pair. This is an upper bound +for the actual register norm. Distinct formal owner paths may have +further dependencies in their action on arrays, so it is not a claim +that the induced spatial operator norm is exactly 448. These bounds +apply to the stated independent inputs at the query entrance. A +recursive precision certificate must also account for how those inputs +were formed and for each child implementation. + +Reproduce into new directories: + +```sh +python3 emit_routed_query.py --out replay-normal +python3 -O emit_routed_query.py --out replay-optimized +``` + +The result is a concrete query implementation and a checked native +prefix, with the exact intended splice stated. A complete D25 service +requires the separately pinned dispatcher that proves that splice. +Recursive hosting and the complete supplier remain open. The local +same-reader price 9880 is not the price of this past-reader service. + +This packet implements the fixed-reader theorem and source-view records +from the bridge-access lane. It uses the reviewed productive row-capture +and line-entry native family. AI agents prepared the code, proof, and +checks. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_prefix.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_prefix.py new file mode 100644 index 0000000000..0a3f7ddbc0 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_prefix.py @@ -0,0 +1,97 @@ +#!/usr/bin/env python3 +"""Emit the checked native prefix before a routed reader query.""" + +import argparse +from copy import deepcopy +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parent / "row-only-capture-20261020" +LANES = HERE.parents[2] +PINS = { + "reuse": (SOURCE / "reuse-normal/LINE-ENTRY-REUSE.json.gz", + "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110"), + "checker": (SOURCE / "emit_capture.py", + "1557c9f38b1d89f6d38e920d8db604607519a99cf37366b4c15414aed489cf1f"), + "review": (LANES / "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source " + name) + return raw + + +read("checker") +spec = importlib.util.spec_from_file_location("reuse_prefix_base", PINS["checker"][0]) +base = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = base +spec.loader.exec_module(base) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + source = json.loads(read("reuse")) + read("review") + response = base.n.rows(source["response"]) + selected = set(source["selected_ports"]) + providers, reports = {}, {} + for provider, original in source["providers"].items(): + word = deepcopy(original) + end = original["stage_ranges"]["late_query"][0] + word["events"] = word["events"][:end] + del word["stage_ranges"]["late_query"] + report = base.verify(word, base.n.r.identity(112), response, + [{} for _ in range(112)], selected) + need(report["real_scalar_primitives"] == 6456 and report["native_mass"] == 1792, + "The complete carrier-only invoice") + need(end == 2406 and len(word["events"]) == end, "The exact complete prefix cut") + providers[provider], reports[provider] = word, report + payload = { + "schema": "sixteen-record-carrier-prefix-v1", + "source_pins": {key: {"path": str(path), "sha256": pin} + for key, (path, pin) in PINS.items()}, + "ports": source["ports"], "selected_ports": source["selected_ports"], + "ordinary_ports": source["ordinary_ports"], "response": source["response"], + "providers": providers, + "physical_contract": { + "input": "X=Qx; Y_U=y_U; Y_P=Q_P z, with arbitrary independent z.", + "output": "Xout=F9x; Yout_U=F9q_U(y+Ex)_U; Yout_P=F9z.", + "scope": "The complete native prefix ends before any selected reader query.", + }, + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + for provider, word in json.loads(raw)["providers"].items(): + need(base.verify(word, base.n.r.identity(112), response, + [{} for _ in range(112)], selected) == reports[provider], + "The serialized prefix passes") + (args.out / "CARRIER-PREFIX.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = {"status": "PASS_EXACT_CARRIER_ONLY_PREFIX", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "reports": reports} + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_routed_query.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_routed_query.py new file mode 100644 index 0000000000..ca0e863c35 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/emit_routed_query.py @@ -0,0 +1,330 @@ +#!/usr/bin/env python3 +"""Emit and replay the complete old-reader query after the native prefix.""" + +import argparse +from collections import defaultdict +from fractions import Fraction as F +from functools import cache +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[2] +UNIT = tuple(1 << j for j in range(25)) +PINS = { + "prefix": (HERE / "prefix-normal/CARRIER-PREFIX.json.gz", + "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e"), + "prefix_checker": (HERE / "emit_prefix.py", + "657afc180b397e851fbefa16f56ace98129072a6bd2faf5d84dbc2391720698e"), + "query": (LANES / "bridge-access-20261017/row-capture-access-20261020/reuse-normal/REUSE-PROGRAM.json", + "eead344f9a3f642056fd29b05a7e24d1a5d3504eec005eedc83e26b7fed8b82b"), + "capture": (LANES / "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"), + "phase": (LANES / "bridge-access-20261017/check_bridge_access.py", + "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111"), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source " + name) + return raw + + +def module(name): + read(name) + spec = importlib.util.spec_from_file_location("routed_query_" + name, PINS[name][0]) + result = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = result + spec.loader.exec_module(result) + return result + + +prefix_checker = module("prefix_checker") +base = prefix_checker.base +phase = module("phase") + + +def act(columns, value): + result = 0 + while value: + bit = value & -value + result ^= columns[bit.bit_length() - 1] + value ^= bit + return result + + +@cache +def compose(left, right): + return tuple(act(left, value) for value in right) + + +def transpose(columns): + return tuple(sum(((columns[j] >> i) & 1) << j for j in range(25)) + for i in range(25)) + + +def add(target, source, coefficient=F(1)): + for key, value in source.items(): + target[key] = target.get(key, F(0)) + coefficient * value + if not target[key]: + del target[key] + + +def product(left, right): + result = [] + for row in left: + out = {} + for (j, a), coefficient in row.items(): + for (k, b), value in right[j].items(): + add(out, {(k, compose(a, b)): coefficient * value}) + result.append(out) + return result + + +def routed(rows, ports, views): + rho = {view["port"]: tuple(view["route_columns"]) for view in views} + return [{(j, compose(rho[p], rho[j])): value for j, value in row.items()} + for p, row in zip(ports, rows)] + + +def initial_prefix(response, selected): + state = [{(i, UNIT): F(1)} for i in range(640)] + for p in range(112): + if p not in selected: + add(state[112 + p], response[p]) + return state + + +def replay(events, maps, initial, selected): + state = [dict(row) for row in initial] + scalar_cost = 0 + map_cost = 0 + maximum = max(sum(abs(value) for value in row.values()) for row in state) + height = 0 + for event in events: + if event[0] == "map": + _, field, index = event + need(field < 112 or field - 112 in selected, "A query map uses only FULL fields") + route = tuple(maps[index]["columns"]) + state[field] = {(i, compose(route, a)): value + for (i, a), value in state[field].items()} + map_cost += 1 + else: + need(event[0] == "scalar", "The literal query event grammar") + _, op, target, source, raw = event + value = F(raw) + need(target < 112 or target - 112 in selected, "A scalar target is FULL") + if op == "add": + need(source < 112 or source - 112 in selected, "A scalar source is FULL") + need(target != source, "Distinct source and target arrays") + add(state[target], state[source], value) + else: + need(op == "scale", "Only ADD and SCALE instructions") + state[target] = {key: value * other for key, other in state[target].items()} + scalar_cost += base.n.r.price([[op, target, source, raw]]) + maximum = max(maximum, sum(abs(other) for other in state[target].values())) + for other in state[target].values(): + d = other.denominator + need(d & (d - 1) == 0, "Every query coefficient is dyadic") + height = max(height, d.bit_length() - 1) + return state, {"scalar_primitives": scalar_cost, "monomial_maps": map_cost, + "exact_prefix_content_one_norm": str(maximum), + "additional_binary_height": height} + + +def make_query(pair, capture, pivots): + maps, indices, events, stages = [], {}, [], {} + full = phase.product([(v, 1) for v in UNIT[:9 + 8 * pair["service_stage"]]]) + + def register(columns, translation): + columns = tuple(columns) + key = columns, translation + if key in indices: + return indices[key] + inverse = transpose(columns) + need(compose(columns, inverse) == compose(inverse, columns) == UNIT, + "Each actual query route is orthogonal") + need(columns[9 + 8 * pair["service_stage"]:] == UNIT[9 + 8 * pair["service_stage"]:], + "Each query route fixes the uncompleted axes") + transformed = phase.product([(act(columns, v), 1) + for v in UNIT[:9 + 8 * pair["service_stage"]]]) + need(phase.add_phase(transformed, phase.line(translation, 2)) == full, + "The complete Z4 phase of each FULL view") + indices[key] = len(maps) + maps.append({"columns": columns, "translation": translation, + "inverse_columns": inverse, "inverse_translation": act(inverse, translation)}) + return indices[key] + + def view(field, record, inverse=False): + route = tuple(record["route_columns"]) + delta = record["translation"] + if inverse: + route = transpose(route) + delta = act(route, delta) + events.append(["map", field, register(route, delta)]) + + def begin(): + return len(events) + + def end(name, start): + stages[name] = [start, len(events)] + + old = {view["port"]: view for view in pair["old_reader_views"]} + current = {view["port"]: view for view in pair["current_code_views"]} + ordinary = sorted(set(range(112)) - set(pivots)) + old_fields = [(p, p) for p in ordinary] + [(112 + p, p) for p in pivots] + start = begin() + for field, p in old_fields: + view(field, old[p]) + for op, p, r, coefficient in capture["scalar_word"]: + events.append(["scalar", op, 112 + p, r, coefficient]) + for field, p in reversed(old_fields): + view(field, old[p], True) + end("old_reader_complement", start) + start = begin() + for p in pivots: + events.append(["scalar", "add", 112 + p, p, "1"]) + end("first_selected_copy", start) + + def code_stage(name, word): + start = begin() + for p in range(112): + view(p, current[p]) + for op, p, r, coefficient in word: + events.append(["scalar", op, p, r, coefficient]) + for p in reversed(range(112)): + view(p, current[p], True) + end(name, start) + + code_stage("current_code", capture["scalar_word"]) + start = begin() + for p in pivots: + events.append(["scalar", "add", 112 + p, p, "-1"]) + end("second_selected_copy", start) + start = begin() + for op, p, r, coefficient, route_index in pair["middle_query"]: + if op == "scale": + events.append(["scalar", "scale", 112 + p, None, coefficient]) + else: + need(op == "mapped_add_restore", "The pinned middle-query grammar") + record = pair["middle_routes"][route_index] + forward = register(record["columns"], record["FULL_translation"]) + backward = register(record["inverse_columns"], record["inverse_FULL_translation"]) + need(tuple(maps[forward]["inverse_columns"]) == tuple(maps[backward]["columns"]) + and maps[forward]["inverse_translation"] == maps[backward]["translation"], + "The literal source restoration map") + events.append(["map", r, forward]) + events.append(["scalar", "add", 112 + p, r, coefficient]) + events.append(["map", r, backward]) + end("middle_query", start) + code_stage("current_inverse_code", capture["inverse_scalar_word"]) + return events, maps, stages + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + prefix = json.loads(read("prefix")) + query = json.loads(read("query")) + capture = json.loads(read("capture")) + pivots = query["pivots"] + selected = set(pivots) + need(pivots == prefix["selected_ports"] == capture["pivots"], "One actual pivot set") + response = base.n.rows(prefix["response"]) + reader = base.n.rows(capture["centre_reader"]) + prefix_reports = {} + for provider, word in prefix["providers"].items(): + prefix_reports[provider] = base.verify( + word, base.n.r.identity(112), response, [{} for _ in range(112)], selected) + reports, words = {}, {} + for pair in query["pairs"]: + key = str(pair["reader_stage"]) + ":" + str(pair["service_stage"]) + et = routed(response, range(112), pair["current_code_views"]) + ls = routed(reader, pivots, pair["old_reader_views"]) + direct = product(ls, et) + need(sum(map(len, direct)) == 3808, "Every direct old-reader owner path") + initial = initial_prefix(et, selected) + expected = [dict(row) for row in initial] + for p, row in zip(pivots, direct): + add(expected[112 + p], row) + events, maps, stages = make_query(pair, capture, pivots) + actual, report = replay(events, maps, initial, selected) + need(actual == expected, "All640 complete arbitrary fields with exact ordered owner paths") + need(actual[:112] == initial[:112] and actual[224:] == initial[224:], + "Every source and arbitrary helper is restored") + need(report["scalar_primitives"] == 11168 and report["monomial_maps"] == 2064, + "The complete literal routed-query invoice") + query_initial = [{(i, UNIT): F(1)} for i in range(640)] + query_expected = [dict(row) for row in query_initial] + for p, row in zip(pivots, direct): + add(query_expected[112 + p], row) + query_actual, query_bound = replay(events, maps, query_initial, selected) + need(query_actual == query_expected, "The query is valid on every independent FULL input") + negative_index = next(i for i in range(*stages["middle_query"]) if events[i][0] == "map") + bad = events[:negative_index] + events[negative_index + 1:] + bad_state, _ = replay(bad, maps, initial, selected) + need(bad_state != expected, "An omitted middle source view is rejected") + bad = events[:stages["current_inverse_code"][0]] + bad_state, _ = replay(bad, maps, initial, selected) + need(bad_state != expected, "An omitted source-code restoration is rejected") + words[key] = {"reader_stage": pair["reader_stage"], "service_stage": pair["service_stage"], + "events": events, "maps": maps, "stage_ranges": stages} + reports[key] = {**report, "exact_query_entry_unit_bound": query_bound, + "complete_local_scalar": 6456 + report["scalar_primitives"], + "native_mass": 1792, "native_profile": {"1": 1392, "2": 64, "3": 48, "8": 16}, + "restored_source_fields": 112, "unchanged_arbitrary_helpers": 416, + "direct_owner_path_terms": 3808, "distinct_checked_full_maps": len(maps)} + payload = { + "schema": "fixed-reader-literal-global-query-v1", + "source_pins": {key: {"path": str(path), "sha256": pin} + for key, (path, pin) in PINS.items()}, + "pivots": pivots, "native_prefixes": prefix["providers"], "queries": words, + "physical_contract": { + "query_entrance": "All X and selected Y fields are in the actual completed global FULL frame.", + "query": "X is restored; selected Y gains L_s E_t X; ordinary Y and all helpers are unchanged.", + "complete_content": "The selected record z gains L_s E_t x after the checked native carrier prefix. If z=L_s y, it is L_s(y+E_t x).", + "scope": "The complete D25 entry/exit dispatcher that puts the local prefix into these global charts is a separate pinned binding.", + }, + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for key, word in saved["queries"].items(): + pair = next(p for p in query["pairs"] if + key == str(p["reader_stage"]) + ":" + str(p["service_stage"])) + et = routed(response, range(112), pair["current_code_views"]) + actual, report = replay(word["events"], word["maps"], initial_prefix(et, selected), selected) + need(report["scalar_primitives"] == reports[key]["scalar_primitives"] + and report["monomial_maps"] == reports[key]["monomial_maps"], + "The serialized query invoice") + expected = initial_prefix(et, selected) + for p, row in zip(pivots, product(routed(reader, pivots, pair["old_reader_views"]), et)): + add(expected[112 + p], row) + need(actual == expected, "The serialized complete operator map") + (args.out / "ROUTED-QUERY.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = {"status": "PASS_EXACT_LITERAL_ROUTED_QUERY_AND_NATIVE_PREFIX", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "prefix_reports": prefix_reports, "query_reports": reports, + "scope": "Exact local prefix and global FULL query. The actual D25 dispatcher is a separate binding; recursive hosting and the supplier remain open."} + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..10606e5e975b74a86921422158d1967b7ba22069 GIT binary patch literal 142430 zcmYIu18`-{^LCt#ZF_HQ+qP}nwr$(l*tRz|H@34IWAoj8fAz2L)~QoC^r6 z(>+5J^9|(R5A5rz*RI}_!Hat|w*VBH5Lcq)4aR-6VRz5IBXo)w{3eie4CF?;&WIyEF5Nk<@R?v 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"4": "1", + "6": "-1" + }, + { + "1": "1", + "5": "-1" + }, + { + "0": "-1", + "3": "-1" + } + ], + "selected_ports": [ + 0, + 7, + 15, + 36, + 42, + 46, + 79, + 89 + ], + "small_cliques": [ + [ + 5, + 34, + 40, + 85, + 97 + ], + [ + 3, + 32, + 38, + 50, + 95 + ], + [ + 24, + 48, + 67, + 80, + 82 + ], + [ + 23, + 35, + 55, + 65, + 68 + ], + [ + 1, + 17, + 66, + 75, + 83 + ], + [ + 8, + 12, + 45, + 107, + 109 + ], + [ + 29, + 49, + 54, + 56, + 108 + ], + [ + 26, + 30, + 64, + 73, + 96 + ], + [ + 4, + 33, + 69, + 74, + 88 + ], + [ + 18, + 22, + 84 + ], + [ + 19, + 28, + 77 + ], + [ + 39, + 58, + 86 + ], + [ + 6, + 98, + 100, + 101, + 102 + ], + [ + 31, + 59, + 60, + 93, + 103 + ] + ], + "small_ports": [ + 1, + 3, + 4, + 5, + 6, + 8, + 12, + 17, + 18, + 19, + 22, + 23, + 24, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 38, + 39, + 40, + 45, + 48, + 49, + 50, + 54, + 55, + 56, + 58, + 59, + 60, + 64, + 65, + 66, + 67, + 68, + 69, + 73, + 74, + 75, + 77, + 80, + 82, + 83, + 84, + 85, + 86, + 88, + 93, + 95, + 96, + 97, + 98, + 100, + 101, + 102, + 103, + 107, + 108, + 109 + ], + "source_pins": { + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + }, + "vertex_assignments": [ + { + "ordered_carriers_a_b_c": [ + 0, + 72, + 2, + 70, + 71, + 76 + ], + "signs": [ + 1, + 1, + 1, + 1, + 1, + 1 + ], + "vertex": 0 + }, + { + "ordered_carriers_a_b_c": [ + 27, + 15, + 13, + 14, + 78, + 81 + ], + "signs": [ + 1, + -1, + 1, + 1, + 1, + 1 + ], + "vertex": 1 + }, + { + "ordered_carriers_a_b_c": [ + 53, + 36, + 11, + 21, + 41, + 91 + ], + "signs": [ + 1, + 1, + 1, + 1, + 1, + 1 + ], + "vertex": 2 + }, + { + "ordered_carriers_a_b_c": [ + 111, + 89, + 9, + 51, + 37, + 43 + ], + "signs": [ + 1, + -1, + 1, + 1, + 1, + 1 + ], + "vertex": 3 + }, + { + "ordered_carriers_a_b_c": [ + 20, + 79, + 25, + 16, + 47, + 99 + ], + "signs": [ + 1, + 1, + 1, + 1, + 1, + 1 + ], + "vertex": 4 + }, + { + "ordered_carriers_a_b_c": [ + 7, + 94, + 61, + 10, + 63, + 92 + ], + "signs": [ + 1, + -1, + 1, + 1, + 1, + 1 + ], + "vertex": 5 + }, + { + "ordered_carriers_a_b_c": [ + 57, + 42, + 44, + 106, + 104, + 87 + ], + "signs": [ + 1, + 1, + 1, + 1, + 1, + 1 + ], + "vertex": 6 + }, + { + "ordered_carriers_a_b_c": [ + 46, + 105, + 62, + 52, + 110, + 90 + ], + "signs": [ + 1, + -1, + 1, + 1, + 1, + 1 + ], + "vertex": 7 + } + ] +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/NATIVE-LIFT.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/NATIVE-LIFT.md new file mode 100644 index 0000000000..a1fc7101cb --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/NATIVE-LIFT.md @@ -0,0 +1,140 @@ +# Native recipes for the new centre-deleted core + +This lane checks the native operators for both PR3133 provider words. +The words are the byte-equal copies in PR3148. It uses the new frame and +warp data. It does not use the earlier T74 frame data. + +Fresh generation passed for both providers. Each run checked 1130 frames, +3036 directed child edges, 224 endpoint adapters, 180 signed physical warp +classes, 72 logical warp operators, and 56 residual wrapper classes. The +residual classes include 32 proper terminal pairs, of which 24 are cold. +Each source run rejected 25 wrapper mutations and 13 warp mutations. + +The fresh child and residual recipe files have the same hashes as the +authenticated PR3133 native receipt. Both literal dual runs also passed: +each checked all 180 signed classes on all 512 columns. In each provider, +172 literal dual recipes differ from the forward recipes. All literal +dual recipes have rank zero. Thus the choice of logical warp orientation +does affect the phase tables, but it does not add native children. + +The independent interpreter review is a separate calculation. The scalar +map, stock, controller, precision, and complete kappa calculation are also +separate checks. `RESULT.json` gives the generation result; `FREEZE.json` +pins its inputs, scripts, proofs, and outputs. + +## Exact operator test + +For a binary subspace U, let T_U be the canonical Clifford frame in the +pinned source. A child from U to V must implement T_V T_U^{-1}. The +generator derives its recipe from this product. It checks the full Pauli +table and the exact Gaussian dyadic image of the zero basis vector. These +two checks include the global phase. + +To see this, let A and B be unitary operators with the same action on all +Pauli generators. Then B^{-1} A commutes with every X and Z generator. An +operator that commutes with every Z generator is diagonal in the standard +basis. If it also commutes with every X generator, all diagonal entries +are equal. Thus A is a scalar multiple of B. Equality on the zero basis +vector fixes that scalar as one. The argument applies to each generated +Clifford product. It also proves equality of all positive tensor powers. + +Each child recipe has the form L C_[r] R, with R applied first. The +serialized L and R are monomial Clifford operators. For a nested frame +change, the checked r is the difference of the frame dimensions. The +physical warp product is T_V K_G^{sign} T_U^{-1}. Its checked r is zero. +The separate Gaussian matrix implementation checks every one of its 512 +columns. + +A helper that enters at E and leaves at V has residual T_V T_E^{-1}. +The recipes include the proper terminal subspaces of the new words. They +also include the cold pairs with E equal to zero. The exact wrapper test +checks R^{-1}, then the residual, then L^{-1}; the result is C_[r]. It does +not replace a proper terminal frame by FULL. + +## Literal dual warps + +The backward scalar proof uses the inverse transpose of each logical +warp. For a unitary warp K this is the entrywise conjugate of K. The +source emitter stores the same signed warp labels for both orientations. +The orientation must therefore select a physical implementation. + +There are two valid routes. The free-operator proof can establish the +endpoint identity for an arbitrary consistent choice of invertible warp +generators. The physical implementation can then use the forward K in +both orientations. Alternatively, the literal dual implementation can +use conjugate(K) in the backward orientation. This lane supplies exact +recipes for the second route as well. + +The literal dual route has a general rank-zero closure property. Let K +be a monomial Clifford operator whose nonzero entries are fourth roots of +unity. Every source K_G has this property. In a standard basis, K is an affine +permutation with a phase of the form + + i^(c + alpha.x + 2 q(x)), + +where q is a binary quadratic form. Conjugation changes this phase by +2(c + alpha.x) modulo 4. The quadratic term vanishes. After the affine +permutation, this phase is a signed Z Pauli. Thus + + conjugate(K) K^{-1} = P + +for a Pauli P. Suppose the accepted physical warp is + + W = T_V K T_U^{-1} + +and W is monomial. Then its literal dual counterpart is + + T_V conjugate(K) T_U^{-1} = (T_V P T_V^{-1}) W. + +A Clifford frame maps a Pauli to a Pauli. A Pauli is monomial. Hence the +literal dual counterpart is monomial and needs no native child. Apply the +same argument to K^{-1} for a negative signed occurrence. This proof does +not require U and V to be FULL, or require the Pauli to be diagonal after +frame conjugation. + +`generate_dual_warps.py` also checks this conclusion directly for each +signed class of each new provider. It uses the physical product +T_V conjugate(K_G)^{sign} T_U^{-1}. A separate Gaussian matrix calculation +compares all 512 columns. A wrong global phase must fail. + +## Source and credit + +The core comes from +[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), at +commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. The byte-equal provider +words are in +[PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), at +commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`: + +- [Base word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz). +- [Extra word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz). + +The unchanged recipe sources come from +[PR2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), at +commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`: + +- [Phase compiler](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_phases.py). +- [Residual wrappers](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_adapters.py). +- [Gaussian matrix implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_gauss.py). +- [Serialized warp checker](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_check_recipes.py). +- [Exact Clifford implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py). + +The source files retain their original author and AI-assistance notices. +The wrapper source credits the PR458 construction. The warp source credits +Cinna Davis and PR2226. OpenAI Codex assisted this lane's driver, literal +dual calculation, proof, and local checks. The independent review is a +separate agent calculation. It is not a maintainer review. + +## Reproduction + +Use one process and the workspace Python that has NumPy: + + work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_recipes.py + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_dual_warps.py + python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/freeze_results.py + +The first command checks every source and input pin before generation. +It runs the wrapper, phase, and serialized warp checks for each provider. +The second command checks the source and first-stage output pins before +it generates the literal dual recipes. The scripts write results only +inside this lane. No PR, push, or publication commit is part of this work. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json new file mode 100644 index 0000000000..786ab73ff4 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "REPRODUCTION.json": "5fe7900ca1791738790a663c882ea411d8e3f41cdb9f9b7f5d23f06deffbf939", + "REVIEW.md": "f6ddd5a2581319ac5b07d402384c4847bce88f10505cca926c9287e838e1760f", + "check.py": "c2a8f93e2c1cf23f8fc279e6dc87d6bd923e60c438531fe1770b0992d1dfdb7d", + "normal/INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5", + "normal/REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f", + "optimized/INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5", + "optimized/REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f" + }, + "publication": "No PR, push, commit, or publication.", + "scope": "Both local arbitrary-record provider words, exact phases, same-reader restriction, and complete local invoice. No routed past-reader query or complete supplier claim.", + "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..e94c51f785 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json @@ -0,0 +1,8 @@ +{ + "normal_optimized_byte_identical": { + "INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5", + "REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f" + }, + "source_files_rechecked": 35, + "status": "PASS" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md new file mode 100644 index 0000000000..5a1315e905 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md @@ -0,0 +1,199 @@ +# Independent review of the local line-entry reuse interface + +The frozen word accepts sixteen arbitrary independent records in +positive line frames and preserves them as additive baselines. +Both providers pass the complete local map, frame, phase, and +invoice checks. No material defect was found. + +This is local reuse with the same reader. It is separate from the +query for a reader kept from an earlier routed stage. + +## Frozen inputs and method + +The producer +[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json) +has SHA256 +`a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60`. +The decompressed payload SHA256 is +`efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110`. + +The accepted formation +[review](../row-capture-native-review-20261020/FREEZE.json) +has SHA256 +`488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532`. +Its exact source payload has decompressed SHA256 +`7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2`. + +The checker imports only the pinned independent review helper and +its integer Gaussian phase interpreter. It imports no producer +code. It checks the new word by reverse output-column propagation +and a separate forward prefix-row pass. It compares exact spatial +columns for every new native recipe. + +## Exact arbitrary-record contract + +Keep the fixed selected set P and the actual response E from the +formation packet. Put \(W=V_P^{-1}V\), and let C have rows W on P +and identity rows elsewhere. For independent inputs x, ordinary +target values \(y_R\), and selected records \(z_P\), the physical +input is + +\[ +X_p=Q_px_p,\qquad +Y_p=y_p\quad(p\in R),\qquad +Y_p=Q_pz_p\quad(p\in P). +\] + +The physical output is + +\[ +X'_p=F_9x_p,\qquad +Y'_p=F_9q_p(y+Ex)_p\quad(p\in R),\qquad +Y'_p=F_9[z_p+(CEx)_p]\quad(p\in P). +\] + +The ordinary formula uses only \(y_R\); no selected baseline y is +needed there. All sixteen z records are independent of each other, +of x, and of every other field. The word does not form or decode z. + +## Literal order and field checks + +The word contains no row precode. Its event list is exactly: + +1. The 2390 retained core events from the accepted formation word. +2. Sixteen selected line-to-FULL native calls. +3. The 248 events in the accepted late-query word. + +Every retained event has its original bytes and order. No retained +event reads or writes a selected target. The selected records +therefore remain unchanged until their line-to-FULL calls. + +The new input frame on each selected target is exactly the source +line frame for that port. Its input adapter is the accepted source +adapter for that same port, with an explicit binding to the target +field. All 128 input view fields are distinct. + +Every source and selected target is FULL before the late query. +Every scalar addition has the same actual source and target frame. +The final declarations are identical to those of the formation +word. A selected input declared as I is rejected. + +Both providers pass all 640 arbitrary input columns. The column +for each selected record is exactly the unit column for that +record's output. All 416 fields outside the two data banks retain +their arbitrary values. No event accesses those fields, and no +new or owned field is introduced. + +The forward row pass agrees with the reverse-column result. An +omitted late query is rejected. + +## Exact phases + +All 1447 retained native recipes are byte equal to the accepted +formation records. The 112 source input adapters and the 96 +outgoing ordinary adapters are also exact inherited records. +The sixteen additional input adapters use the accepted source +records with their explicit new field bindings. + +For each selected port p, the new recipe must satisfy + +\[ +N_p\Gamma_{\mathrm{line}(p)}=F_9. +\] + +The independent interpreter checks this exact identity on all +512 spatial input columns. There are sixteen new recipes, hence +8192 complete spatial columns and 4194304 nonzero coefficients. +The checks include global phase. A wrong global phase is rejected. + +Combining this identity with the accepted input-adapter identity +gives the physical operation \(Q_pz_p\mapsto F_9z_p\). +No Q operator is moved through the reader or the response. +The exact spatial identities tensor to all widths admitted by +the retained native primitive contract. + +These H8 recipes retain their two generic monomial maps. The +identity-map refinement for a complete F9 call does not apply here. + +## Local invoice and precision scope + +Each provider has the exact profile + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H8. +``` + +The complete local counts are: + +| Item | Count | +| --- | ---: | +| Native children | 1520 | +| Native mass | 1792 | +| Old real scalar units | 9880 | +| Retained-core scalar units | 6456 | +| Late-query scalar units | 3424 | +| Input monomial views | 128 | +| Output monomial views | 96 | +| Native side-map upper bound | 3040 | +| New or private fields | 0 | +| Odd-arithmetic scans | 0 | + +The exact content row one-norm at emitted operation boundaries +is at most 112. The additional content binary denominator height +is one. These bounds include the full retained word and query. +They do not bound primitive internals, recursive-child numerical +guards, or accumulated roundoff. + +The sixteen calls remain rank-eight calls. Their exact recursive +sizes, the owner-view work, and the complete caller must be priced +before any complete supplier cost can be claimed. + +## The reader condition is necessary + +If z stores \(Wy\), the selected output stores \(W(y+Ex)\). +Thus the local update preserves that same reader. + +For a different stored reader L, the required update is \(LEx\). +The emitted update \(WEx\) is equal to it on all source inputs if +and only if + +\[ +(L-W)E=0. +\] + +The checker verifies both exact inverse orders for this actual E. +Therefore that condition is equivalent to \(L=W\). More generally, +the same implication holds for ordered operators when E has an +inverse. It does not require any commutation of L, W, or E. + +Consequently, a reader from an earlier routed stage needs its +actual ordered query \(L_sE_t\), unless equality of the transported +reader with the current local reader has been proved. The separate +bridge-access construction supplies such queries under its own +premises and invoice. The 9880 local figure is not that invoice. + +This review proves the local line-entry interface. It does not +prove a complete routed reuse, a final decoder, a recursive host, +a complete supplier, or a kappa improvement. + +## Reproduction and credit + +Run from the workspace root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized +``` + +The required final line is +`PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE`. +The reproduction receipt records the final byte comparison and +source hash checks. +Both runs completed with the required result. Their result and +input receipts are byte identical. All 35 consumed source files +were rechecked and are unchanged. + +The producer proof retains the controller, cyclic-family, and +formation-work credit. AI assistance was used. No PR, push, commit, +or publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py new file mode 100644 index 0000000000..0419f9c41f --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py @@ -0,0 +1,200 @@ +#!/usr/bin/env python3 +"""Check the exact local interface for arbitrary line-encoded records.""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PREVIOUS = HERE.parent/'row-capture-native-review-20261020' +HELPER = PREVIOUS/'check.py' +HELPER_PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84' +if sha256(HELPER.read_bytes()).hexdigest() != HELPER_PIN: + raise ValueError('Independent review helper pin') +spec = importlib.util.spec_from_file_location('independent_row_review', HELPER) +review = importlib.util.module_from_spec(spec) +spec.loader.exec_module(review) +review.read(HELPER, HELPER_PIN) +need, read, frozen = review.need, review.read, review.frozen +P = review.P +SOURCE = review.NATIVE + + +def trace(word): + current = list(word['start']) + profile, used = Counter(), set() + for i, event in enumerate(word['events']): + if i == word['stage_ranges']['late_query'][0]: + need(all(current[p] == 1 for p in range(112)) and + all(current[112+p] == 1 for p in P), 'Complete common-FULL query cut') + if event[0] == 'native': + _, field, before, after, rank, key = event + need(0 <= field < 224 and current[field] == before, 'Native field and input frame') + need(word['native_recipes'][key]['rank'] == rank, 'Native occurrence rank') + current[field] = after + profile[rank] += 1 + used.add(key) + else: + need(event[0] == 'scalar', 'Event opcode') + _, scalar, frame = event + op, target, origin, _ = scalar + need(0 <= target < 224 and current[target] == frame, 'Scalar target frame') + if op == 'add': + need(0 <= origin < 224 and current[origin] == frame and target != origin, + 'Scalar source frame') + else: + need(op == 'scale' and origin is None, 'Scale grammar') + need(current == word['final'], 'Exact complete final frames') + need(used == set(word['native_recipes']), 'Every stored native recipe is used') + return profile + + +def check_word(word, old, e, ce): + need(word['frames'] == old['frames'] and word['final'] == old['final'], + 'Exact inherited frame geometry and output declarations') + expected_start = list(old['start']) + for p in P: + expected_start[112+p] = old['start'][p] + need(len(word['frames'][expected_start[112+p]]) == 1, + 'Selected canonical line frame') + need(word['start'] == expected_start, 'Only selected input frames change') + start, end = old['stage_ranges']['retained_core'] + kept = old['events'][start:end] + start, end = old['stage_ranges']['late_query'] + query = old['events'][start:end] + progress = [['native', 112+p, old['start'][p], 1, 8, 'capture-line:'+str(p)] for p in P] + need(word['events'] == kept+progress+query, 'Exact complete local reuse order') + need(word['retained_original_event_indices'] == old['retained_original_event_indices'], + 'Same retained raw events') + need(word['stage_ranges'] == { + 'precode': [0, 0], 'retained_core': [0, 2390], + 'selected_line_progress': [2390, 2406], 'late_query': [2406, 2654]}, + 'Exact reuse stage boundaries') + selected = {112+p for p in P} + for event in kept: + if event[0] == 'scalar': + need(event[1][1] not in selected and + (event[1][0] != 'add' or event[1][2] not in selected), + 'Retained core does not access selected records') + else: + need(event[1] not in selected, 'Retained native core does not access selected records') + inherited = set(old['native_recipes'])-{'capture-full'} + fresh = {'capture-line:'+str(p) for p in P} + need(set(word['native_recipes']) == inherited|fresh, 'Exact native recipe set') + for key in inherited: + need(word['native_recipes'][key] == old['native_recipes'][key], + 'Byte-equal inherited native recipe') + need(word['output_views'] == old['output_views'], 'All96 exact outgoing views') + source_views = {r['port']: r for r in old['input_views']} + inputs = [{**r, 'field': r['port']} for r in old['input_views']] + inputs += [{**source_views[p], 'role': 'selected_target', 'field': 112+p, + 'source_entry_port': p} for p in P] + need(word['input_views'] == inputs, 'Copied source adapters bound to actual target fields') + need(len({r['field'] for r in inputs}) == 128, 'Distinct charged input view fields') + count = trace(word) + need(count == {1: 1392, 2: 64, 3: 48, 8: 16}, 'Complete reuse native profile') + scalars = [event[1] for event in word['events'] if event[0] == 'scalar'] + expected = review.unit(640) + for p in range(112): + review.add(expected[112+p], ce[p] if p in P else e[p]) + columns = review.reverse(scalars, 640) + need(columns == review.transpose(expected, 640), 'All640 arbitrary input columns') + for p in P: + need(columns[112+p] == {112+p: F(1)}, 'Independent selected record preserved exactly') + actual, bound = review.prefix(scalars, 640) + need(actual == expected and actual[224:] == review.unit(640)[224:], + 'Separate forward map and arbitrary outside fields') + need(bound == {'row_one_norm': '112', 'binary_height': 1}, 'Complete local content bounds') + need(review.price(scalars) == 9880, 'Complete reuse scalar invoice') + need(review.price([e[1] for e in kept if e[0] == 'scalar']) == 6456 and + review.price([e[1] for e in query if e[0] == 'scalar']) == 3424, 'Both scalar stages') + bad = dict(word) + bad['start'] = list(word['start']) + bad['start'][112+P[0]] = 0 + try: + trace(bad) + except ValueError: + pass + else: + raise ValueError('Wrong selected I-frame control') + need(review.reverse([e[1] for e in kept if e[0] == 'scalar'], 640) != columns, + 'Omitted late-query control') + return { + 'input_columns': 640, 'arbitrary_selected_records': 16, 'unchanged_arbitrary_roles': 416, + 'events': len(word['events']), 'native_profile': dict(sorted(count.items())), + 'native_children': sum(count.values()), 'native_mass': sum(k*v for k, v in count.items()), + 'real_scalar_primitives': 9880, 'retained_scalar_primitives': 6456, + 'late_query_scalar_primitives': 3424, 'input_views': 128, 'output_views': 96, + 'native_side_maps_upper_bound': 3040, 'new_fields': 0, 'private_fields': 0, + 'odd_scans': 0, 'growth': bound, 'inherited_distinct_recipes': len(inherited), + 'fresh_distinct_recipes': len(fresh), + } + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', required=True, type=Path) + args = parser.parse_args() + frozen(PREVIOUS, 'FREEZE.json', + '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532') + frozen(SOURCE, 'LINE-ENTRY-REUSE-FREEZE.json', + 'a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60') + original = json.loads(read(SOURCE/'run-normal/PRODUCTIVE-CAPTURE.json.gz', + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', True)) + payload = json.loads(read(SOURCE/'reuse-normal/LINE-ENTRY-REUSE.json.gz', + 'efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110', True)) + need(payload['source_decompressed_sha256'] == + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', + 'Exact formation source') + need(payload['schema'] == 'productive-sixteen-line-entry-reuse-v1', 'Reuse schema') + need(payload['selected_ports'] == P and payload['ports'] == original['ports'] and + payload['ordinary_ports'] == original['ordinary_ports'], 'Actual ordered ports') + need(payload['response'] == original['response'] and + payload['selected_query_response'] == original['captured_response'], + 'Same local reader response') + need(set(payload['providers']) == {'base', 'extra'} and + payload['providers']['base'] == payload['providers']['extra'], 'Both exact providers') + e, ce = review.rows(payload['response']), review.rows(payload['selected_query_response']) + reports = {name: check_word(word, original['providers'][name], e, ce) + for name, word in payload['providers'].items()} + phase = review.inherit() + word = payload['providers']['base'] + full = [('C', 1 << j, 1) for j in range(9)] + checks = [] + for p in P: + frame = word['start'][112+p] + native = phase.recipe(word['native_recipes']['capture-line:'+str(p)]) + result = phase.compare(phase.canonical(word['frames'][frame])+native, + full, 'Exact selected line progress '+str(p), 512) + checks.append({'port': p, 'frame': frame, **result}) + first = P[0] + frame = word['start'][112+first] + bad = phase.canonical(word['frames'][frame])+phase.recipe( + word['native_recipes']['capture-line:'+str(first)])+phase.compile_circuit([['phase', 1]]) + need(phase.run(bad, 0) != phase.run(full, 0), 'Wrong global phase control') + raw = json.loads(read(review.RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz', + 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True)) + inverse = review.rows(raw['model']['response_inverse']) + need(review.mul(e, inverse) == review.unit(112) and + review.mul(inverse, e) == review.unit(112), 'Actual invertible response') + report = { + 'status': 'PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE', + 'literal_words': reports, 'fresh_phase_checks': checks, + 'exact_response_inverse_orders': True, + 'negative_controls': ['wrong selected I input frame', 'omitted late query', 'wrong global phase'], + 'reader_scope': 'The required update for a stored reader L is L E. Since E is invertible, equality with W E on all inputs requires L=W. No routed reader change is priced here.', + 'scope': 'Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.', + } + args.out.mkdir(parents=True, exist_ok=True) + for name, value in [('REVIEW.json', report), ('INPUTS.json', review.INPUTS)]: + (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n') + print(report['status'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json new file mode 100644 index 0000000000..668725b9d5 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json @@ -0,0 +1,110 @@ +{ + "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": { + "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json": { + "sha256": "a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE.md": { + "sha256": "f2ceaf4ba246a20226aec105145d29c2442bd58681256487439b04064815aa2c" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_line_entry_reuse.py": { + "sha256": "c8a799f29b6244190e2880b44206a240b8cd16427661c3cc7aff9f1905bdec62" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/CHECKS.json": { + "sha256": "cfb3da51fb929a1ffa35b6a1cb973426431d98acba355cf2d6b606bf32450048" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz": { + "decompressed_sha256": "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110", + "sha256": "b3cc486c4ecf0574a8a9a6a94ba62a068340ed30525a3dcf889dd19cf7d84047" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-optimized/CHECKS.json": { + "sha256": "cfb3da51fb929a1ffa35b6a1cb973426431d98acba355cf2d6b606bf32450048" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-optimized/LINE-ENTRY-REUSE.json.gz": { + "sha256": "b3cc486c4ecf0574a8a9a6a94ba62a068340ed30525a3dcf889dd19cf7d84047" + }, + "new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/run-normal/PRODUCTIVE-CAPTURE.json.gz": { + "decompressed_sha256": "7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2", + 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"inherited_distinct_recipes": 1447, + "input_columns": 640, + "input_views": 128, + "late_query_scalar_primitives": 3424, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_maps_upper_bound": 3040, + "new_fields": 0, + "odd_scans": 0, + "output_views": 96, + "private_fields": 0, + "real_scalar_primitives": 9880, + "retained_scalar_primitives": 6456, + "unchanged_arbitrary_roles": 416 + } + }, + "negative_controls": [ + "wrong selected I input frame", + "omitted late query", + "wrong global phase" + ], + "reader_scope": "The required update for a stored reader L is L E. Since E is invertible, equality with W E on all inputs requires L=W. No routed reader change is priced here.", + "scope": "Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.", + "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md new file mode 100644 index 0000000000..64df4c61d3 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md @@ -0,0 +1,98 @@ +# Independent derivation of the selected-row service + +This derivation precedes the review of the emitted word. It gives the +map that the word must implement. It does not certify that word. + +Let V have r independent rows. Let P be an ordered set of r ports, +and let V_P be the square submatrix on those columns. Assume V_P is +invertible. Put W=V_P^{-1}V. Then W_P=I. + +Define C to have rows W on P and identity rows on the other ports. +If B=W-pi_P, where pi_P selects P, then + +\[ +C=I+\iota_P B,\qquad B\iota_P=0,\qquad +C^{-1}=I-\iota_P B. +\] + +Here iota_P inserts r coordinates at P. Thus C is a shear. Its +determinant is one. If W is dyadic, both C and its inverse are dyadic. +Every addition uses an unchanged coordinate outside P. No extra field +or zero-input assumption is needed. Reversing the literal additions +gives the inverse. + +The row code is independent of the basis used for the row space of V. +Replacing V by A V, for any invertible A, leaves W unchanged. + +For the present response E, direct normalization of the pinned V gives +eight rows of support 21 and eight rows of support 8. The first rows +have pivot coefficient 1 and twenty coefficients of magnitude 1/2. +The other rows have pivot coefficient 1 and seven coefficients 1. +The precode therefore has 216 complex additions, at 2048 old real +scalar units under the retained scalar invoice. + +These rows are left eigenvectors: + +\[ +WE=\Lambda W,\qquad +\Lambda=\operatorname{diag}(-5I_8,-7I_8). +\] + +Therefore the selected rows of CE are exactly Lambda W. Their direct +late additions cost 3696 old real scalar units. These are separate +costs; they do not include the retained core or the new native children. + +## Physical operation + +Use Q for the diagonal family of positive input line operators, +q=Q^{-1}, and F for the common full operator. The raw forward word has +physical contract + +\[ +(Qx,y)\longmapsto(Fx,Fq(y+Ex)). +\] + +Suppose the exact event list permits all operations on the selected +target fields to be removed. Every retained operation must have no +read from those fields. The source subsystem and the other targets +must retain their original event lists. + +Apply C to current input Y while all target fields have the I frame. +Apply F to each selected target. Run the retained source and ordinary +target operations. After all source fields have reached F, add +the selected rows of CE from those source fields to the selected +targets. The physical result is + +\[ +X'=Fx,\qquad +Y'_P=F[C(y+Ex)]_P,\qquad +Y'_R=F[q(y+Ex)]_R. +\] + +Scalar coefficients commute with the common F in the final query. +No step commutes C or E through Q. In particular, the precode acts +on the physical current-I target values. It does not act on a +changed logical frame. + +Write T for the output operator that is F on P and Fq on R. +Then the full target contract is T C(y+Ex), since C is identity +on the rows in R. This is an invertible output representation. +Its entry into a later word, inverse, final decode, and recursive +hosting require their own implementation and cost. + +## Required literal checks + +The review must check the selected set and every removed event. +It must reject a retained read of a removed target. It must check +the exact full-frame recipe, including its global phase, and all +inherited native records. It must check that every source has +reached the same F frame before the final query. + +The complete word must pass every arbitrary input column. The +unchanged helper fields must retain their arbitrary values. +The native and scalar invoice must include the precode, all retained +events, the sixteen full children, and the late query. + +No PR, push, commit, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json new file mode 100644 index 0000000000..60530966a8 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json @@ -0,0 +1,15 @@ +{ + "files": { + "DERIVATION.md": "74bfa14362b8a704d409cb3995fe645173e99205653528bcf6b47f62de7455a1", + "REPRODUCTION.json": "9525e5e1871d60a01c8acd222944abe6edab71f9d5448410265859dcece6901f", + "REVIEW.md": "39cb0df65e81f92854d0238d9023eaa092205bdce8e3b81724c2e4d19a3ef4f1", + "check.py": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84", + "normal/INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1", + "normal/REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56", + "optimized/INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1", + "optimized/REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56" + }, + "publication": "No PR, push, commit, or publication.", + "scope": "Both complete local providers, direct-FULL refinement, exact physical phases, arbitrary inputs, and local invoice. No recursive hosting, later-stage conversion, full decoder, supplier, or kappa claim.", + "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..b8d020d7f9 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json @@ -0,0 +1,8 @@ +{ + "normal_optimized_byte_identical": { + "INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1", + "REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56" + }, + "source_files_rechecked": 44, + "status": "PASS" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md new file mode 100644 index 0000000000..8bdaaa327e --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md @@ -0,0 +1,255 @@ +# Independent review of the selected-row native service + +The frozen word forms the sixteen centre rows of the actual rank16 +response in sixteen existing target fields. It preserves arbitrary +target baselines and all 416 fields outside the two data banks. +It uses no new field, private field, or odd-arithmetic scan. + +The local service and its direct-FULL refinement pass the independent +checks below. No material defect was found. The output representation +has changed. Its use by a complete recursive caller remains open. + +## Inputs and independent method + +The main producer +[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/FREEZE.json) +has SHA256 +`5321a8ff856042c5ca30ce6b29b90a51ccd4dcf02317820243bfffbb433c84d8`. +Its decompressed payload SHA256 is +`7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2`. + +The separate direct-FULL +[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL-FREEZE.json) +has SHA256 +`f0d3b0d7c8d93e391089a2d28066dd02b4a9b28e306dea5f4e7cb5fc895b054e`. +Its decompressed payload SHA256 is +`fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c`. + +The actual source word is the rank16 extension at decompressed SHA256 +`d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4`. +The controller's scalar +[freeze](../../controller-followthrough-20261017/row-capture-20261020/FREEZE.json) +has SHA256 +`0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf`. + +The checker imports no producer code. It constructs the pivot inverse +from the exact signed Hadamard Gram matrix. It then constructs C, +its inverse, CE, and the encoded response independently. It checks +the scalar words by reverse output-column propagation. A separate +forward row pass checks the complete map and every scalar prefix. + +The physical phase interpreter is the pinned independent integer +Gaussian interpreter from the isotropic-pair review. It uses literal +address maps and exact Gaussian coefficients. It does not import +the producer's Clifford compiler or phase checker. + +## Exact code and physical contract + +The independent derivation is in [DERIVATION.md](DERIVATION.md). +Let \(E=I+UV\), and let P be the ordered set + +```text +0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23. +``` + +Put \(W=V_P^{-1}V\). The actual pivot Gram matrix is +\(\operatorname{diag}(2I_8,I_8)\). This gives a direct exact inverse +for \(V_P\), with both inverse orders checked. + +Define C to have rows W on P and identity rows elsewhere. The +correction \(C-I\) has square zero and rank sixteen. Thus + +\[ +C=I+\iota_P(W-\pi_P),\qquad +C^{-1}=I-\iota_P(W-\pi_P). +\] + +The checker verifies both matrix inverse orders and both literal +scalar inverse orders. The code and inverse are dyadic and each +cost 1760 old real scalar units. They need no extra field. + +The actual rows satisfy + +\[ +WE=\operatorname{diag}(-5I_8,-7I_8)W. +\] + +The selected rows of CE are therefore those same sixteen queries +with multipliers -5 or -7. The scalar late-query word adds these +rows to an arbitrary existing target value. It costs 3424 units. +It does not divide by five or seven. + +Write \(q=Q^{-1}\). For physical input \((Qx,y)\), the exact output is + +\[ +X'=F_9x,\qquad +Y'_P=F_9[C(y+Ex)]_P,\qquad +Y'_R=F_9[q(y+Ex)]_R. +\] + +The selected values include the arbitrary baseline \(Wy\). No +baseline is set to zero or removed from the output contract. +Equivalently, \(Y'=TC(y+Ex)\), where T is \(F_9\) on P and +\(F_9q\) on R. This is an invertible output representation. +No step commutes C or E through Q. + +## Complete operation order + +The checker derives the deletion from the original literal word. +It removes all events whose target is selected Y. For each provider, +this is exactly 128 H1 calls and 122 scalar events. Those scalar +events cost 928 units. + +Every retained event is inspected. No retained scalar event reads a +selected target. All retained events appear in their original order +and with their exact original bytes. Removing only one member of a +selected large pair fails the retained-read check. + +The new complete word has four stages: + +| Stage | Event interval, end excluded | Real scalar units | +| --- | --- | ---: | +| Current-I precode C | 0 to 232 | 1760 | +| Retained original word | 232 to 2622 | 6456 | +| Sixteen I-to-FULL children | 2622 to 2638 | 0 | +| Late common-FULL query | 2638 to 2886 | 3424 | + +Every source and selected target has frame FULL before the late +query. Every scalar addition has the same actual source and target +frame. All final frame declarations are checked. The 96 ordinary +target declarations are unchanged. The selected targets end in FULL. + +Both providers pass all 640 independent input columns. A separate +forward pass gives the same complete map. Every field numbered +224 through 639 retains its arbitrary input. No operation addresses +these fields. There is no CLEAR, hidden zero field, or new owned state. +Deleting the precode or late query is rejected by the full-column test. + +## Physical phases + +There are 1447 distinct retained native recipes. Each is byte equal +to the exact ordered frame pair in the already accepted rank16 word. +The inherited phase proof is pinned by +[the independent extension freeze](../low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json), +at SHA256 +`c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c`, +and its base native review. This review does not repeat that full +phase sweep. + +The new rank-nine recipe occurs sixteen times. The independent +interpreter checks all 512 spatial input columns against the exact +nine positive coordinate kernels. Every column has 512 exact +nonzero coefficients. The comparison includes the global phase. +A wrong global phase is rejected. + +All 112 source entry adapters are exact inherited records. The +96 ordinary outgoing adapters are new explicit inverse monomials. +For each, the checker composes it with the accepted incoming +target adapter in both orders. Every one of the 512 input columns +is exactly the identity in both orders. This proves the outgoing +map to \(F_9q_p\), including phase. + +No outgoing hole adapter is present on a selected target. Its +canonical FULL frame is exactly \(F_9\). These exact spatial +identities tensor to every width admitted by the retained primitive +contract. They are exact equalities, not equalities up to phase. + +The checker verifies the executed recipes. The producer's +descriptive compiler circuits are not executed by this review. +Their intended endpoint functions are checked through the exact +inverse-adapter identities above. + +## Direct-FULL refinement + +The accepted native recipe convention uses +\(C_{e_0}\cdots C_{e_{r-1}}\) between its two monomial maps. +At rank nine, this is already the required \(F_9\). Identity +left and right maps therefore suffice. + +The checker verifies that direct recipe on every spatial column. +It then compares both complete refined provider words with the +main packet. All events, frames, endpoint views, and matrices are +byte equal. Only the shared rank-nine recipe changes. Thus the +complete-word correctness proof transfers by exact substitution. +There is no need for a new logical-column replay of an unchanged +event list. + +The refinement removes the two nontrivial side maps from each of +the sixteen new calls. It does not change their sizes or number. +The native side-map upper bound drops from 3040 to 3008. + +## Complete local invoice and precision scope + +Each provider has the profile + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H9. +``` + +This is 1520 recursive calls and native mass 1808. The complete +old scalar invoice is 11640. The direct refinement has 112 input +monomial views, 96 output monomial views, and at most 3008 native +side maps. It uses no odd-arithmetic scan or new field. + +The high-rank calls remain sixteen rank-nine calls. A complete +recurrence must use their exact sizes. Replacing their costs by +native mass alone is not a complete cost calculation. + +The exact content row one-norm over the entire emitted word is at +most 132. The additional content binary denominator height is one. +Both bounds include the precode and the late scaled queries. +Under the unitary native charts, the first bound also applies to +the per-field Hilbert norm at operation boundaries. + +These are local content bounds. They do not price primitive +internals, recursive-child guards, rounding error, outer owner +views, or the full numerical precision requirement. + +## Reuse and remaining scope + +The row-replacement argument is structural. If a forward word has +independent source progress, an isolated selected target set, and +an invertible row code that can be formed at the common input +frame, replace those target paths by frame advances and a late +coded response query. The output retains every arbitrary target +baseline. The present word verifies all these premises. + +The separate +[access packet](../../bridge-access-20261017/row-capture-access-20261020/FREEZE.json), +at SHA256 +`9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11`, +binds the construction to its literal D25 owner views. This review +pins that packet but does not rerun its phase census. + +That packet gives the next current-entry type as Q on selected +carriers and I elsewhere. This is not the old all-I target type. +A later caller must consume that type or implement its conversion. +No such conversion, final decoder, full controller, or recursive +host is included in the local invoice. + +This review establishes local centre formation in existing output +fields. It does not establish a complete supplier or a kappa +improvement. + +## Reproduction and credit + +Run from the workspace root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized +``` + +The required final line is `PASS_INDEPENDENT_ROW_CAPTURE_NATIVE`. +`REPRODUCTION.json` records the byte comparison and final source +hash checks. +Both runs completed with that result. Their result and input +receipts are byte identical. All 44 consumed source files were +rechecked and are unchanged. + +The producer proof records the source, cyclic, controller, and +bridge-access contributions. The independent review supplied the +direct-FULL identity-map deduction. AI assistance was used. +No PR, push, commit, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py new file mode 100644 index 0000000000..6fa689d442 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py @@ -0,0 +1,450 @@ +#!/usr/bin/env python3 +"""Check the selected-row code and its complete native service.""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +INPUTS = {} +P = [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23] +RAW = LANES/'new-core-transfer-20261017/low-displacement-20261020' +ALG = LANES/'controller-followthrough-20261017/row-capture-20261020' +NATIVE = RAW/'row-only-capture-20261020' +ACCEPTED = LANES/'new-native-recipes-20261017/low-displacement-review-20261020' + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(path, pin=None, compressed=False): + data = path.read_bytes() + content = gzip.decompress(data) if compressed else data + need(pin is None or sha256(content).hexdigest() == pin, + 'Input pin: '+str(path)) + INPUTS[str(path.relative_to(LANES))] = {'sha256': sha256(data).hexdigest()} + if compressed: + INPUTS[str(path.relative_to(LANES))]['decompressed_sha256'] = sha256(content).hexdigest() + return content + + +def frozen(path, name, pin): + obj = json.loads(read(path/name, pin)) + for name, digest in obj['files'].items(): + read(path/name, digest) + return obj + + +def rows(value): + return [{int(k): F(v) for k, v in row.items() if F(v)} for row in value] + + +def unit(n): + return [{i: F(1)} for i in range(n)] + + +def add(target, source, coefficient=F(1)): + for key, value in source.items(): + x = target.get(key, F(0))+coefficient*value + if x: + target[key] = x + else: + target.pop(key, None) + + +def mul(a, b): + out = [] + for row in a: + result = {} + for k, v in row.items(): + add(result, b[k], v) + out.append(result) + return out + + +def rank(a): + pivots = {} + for original in a: + row = dict(original) + while row: + j = min(row) + if j not in pivots: + value = row[j] + pivots[j] = {k: v/value for k, v in row.items()} + break + add(row, pivots[j], -row[j]) + return len(pivots) + + +def transpose(a, n): + out = [{} for _ in range(n)] + for i, row in enumerate(a): + for j, v in row.items(): + out[j][i] = v + return out + + +def price(events): + total = 0 + for op, _, _, value in events: + c = F(value) + n, d = abs(c.numerator), c.denominator + need(n > 0 and d & (d-1) == 0, 'Nonzero dyadic coefficient') + if op == 'scale': + need(n & (n-1) == 0, 'Dyadic unit scale') + total += 2*(abs(n.bit_length()-d.bit_length())+(c < 0)) + else: + need(op == 'add', 'Scalar opcode') + total += 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) + return total + + +def reverse(events, n): + """Propagate output columns through the scalar word in reverse order.""" + columns = unit(n) + for op, target, origin, value in reversed(events): + c = F(value) + if op == 'scale': + columns[target] = {k: c*v for k, v in columns[target].items()} + else: + need(op == 'add' and target != origin, 'Distinct ADD fields') + add(columns[origin], columns[target], c) + return columns + + +def prefix(events, n): + """Compute exact prefix rows, separately from the reverse pass.""" + state = unit(n) + norm, height = F(1), 0 + for op, target, origin, value in events: + c = F(value) + if op == 'scale': + state[target] = {k: c*v for k, v in state[target].items()} + else: + add(state[target], state[origin], c) + norm = max(norm, sum(map(abs, state[target].values()), F(0))) + for x in state[target].values(): + d = x.denominator + need(d & (d-1) == 0, 'Dyadic prefix coefficient') + height = max(height, d.bit_length()-1) + return state, {'row_one_norm': str(norm), 'binary_height': height} + + +def algebra(raw, code): + model = raw['model'] + e, u, v = (rows(model[name]) for name in ('response', 'correction_U', 'correction_V')) + uv = mul(u, v) + expected_e = unit(112) + for row, correction in zip(expected_e, uv): + add(row, correction) + need(e == expected_e, 'Actual response factorization') + vp = [{j: row[p] for j, p in enumerate(P) if p in row} for row in v] + # The actual pivot blocks are signed two-coordinate Hadamards and units. + vp_t = transpose(vp, 16) + gram = [{i: F(2 if i < 8 else 1)} for i in range(16)] + need(mul(vp, vp_t) == gram, 'Actual pivot Gram matrix') + vi = [{j: x/(2 if j < 8 else 1) for j, x in row.items()} for row in vp_t] + need(mul(vi, vp) == unit(16) and mul(vp, vi) == unit(16), 'Pivot inverse orders') + w = mul(vi, v) + c, ci, b = unit(112), unit(112), [] + for i, p in enumerate(P): + need({j: w[i].get(q, F(0)) for j, q in enumerate(P)} == + {j: F(i == j) for j in range(16)}, 'Normalized pivot columns') + c[p] = dict(w[i]) + correction = dict(w[i]) + add(correction, {p: F(1)}, F(-1)) + b.append(correction) + add(ci[p], correction, F(-1)) + need(mul(c, ci) == unit(112) and mul(ci, c) == unit(112), 'Shear inverse orders') + need(rank(b) == 16, 'Exact shear displacement rank') + lamb = [{i: F(-5 if i < 8 else -7)} for i in range(16)] + need(mul(w, e) == mul(lamb, w), 'Selected left eigenvectors') + ce = mul(c, e) + encoded = mul(ce, ci) + need(all(set(row)-{i} <= set(P) for i, row in enumerate(encoded)), + 'Encoded response changes only pivot columns') + for name, value in [('pivot_minor', vp), ('pivot_minor_inverse', vi), + ('centre_reader', w), ('code', c), ('code_inverse', ci), + ('response', e), ('selected_capture_response', ce), + ('encoded_response', encoded)]: + need(rows(code[name]) == value, 'Independent algebra: '+name) + need(code['pivots'] == P, 'Exact selected ports') + for name, matrix in [('scalar_word', c), ('inverse_scalar_word', ci)]: + events = code[name] + need(reverse(events, 112) == transpose(matrix, 112), 'Reverse code: '+name) + need(price(events) == 1760, 'Code scalar price') + for op, target, origin, _ in events: + need(target in P and (op == 'scale' or origin not in P), 'Unchanged shear source') + word = code['scalar_word']+code['inverse_scalar_word'] + need(reverse(word, 112) == unit(112), 'Literal inverse order') + need(reverse(code['inverse_scalar_word']+code['scalar_word'], 112) == unit(112), + 'Other literal inverse order') + query = unit(224) + for p in P: + add(query[p], {112+j: x for j, x in ce[p].items()}) + need(reverse(code['final_query_word'], 224) == transpose(query, 224), + 'Arbitrary-baseline late query') + need(price(code['final_query_word']) == 3424, 'Late query scalar price') + a, pre_bound = prefix(code['scalar_word'], 112) + need(a == c, 'Separate forward code') + a, query_bound = prefix(code['final_query_word'], 224) + need(a == query, 'Separate forward late query') + return e, c, ce, { + 'code_price': 1760, 'query_price': 3424, + 'code_prefix': pre_bound, 'query_prefix_on_independent_inputs': query_bound, + 'displacement_rank': 16, 'extra_fields': 0, 'odd_scans': 0, + } + + +def inherit(): + frozen(ACCEPTED, 'NATIVE-REVIEW-FREEZE.json', + 'cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976') + frozen(ACCEPTED, 'EXTENSIONS-REVIEW-FREEZE.json', + 'c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c') + phase_path = LANES/'new-native-recipes-20261017/isotropic-pair-review-20261018/check.py' + read(phase_path, 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18') + spec = importlib.util.spec_from_file_location('independent_spatial_phase', phase_path) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + return phase + + +def select_raw(raw_word, selected): + indices, removed = [], [] + for i, event in enumerate(raw_word['events']): + need(event[0] in ('native', 'scalar'), 'Raw event grammar') + target = event[1] if event[0] == 'native' else event[1][1] + (removed if target in selected else indices).append(i) + for i in indices: + event = raw_word['events'][i] + if event[0] == 'scalar' and event[1][0] == 'add': + need(event[1][2] not in selected, 'Retained read of removed target') + return indices, removed + + +def check_word(word, old, code, e, c, ce): + need(word['frames'] == old['frames'] and word['start'] == old['start'], + 'Unchanged exact input geometry') + selected = {112+p for p in P} + indices, removed = select_raw(old, selected) + need(word['retained_original_event_indices'] == indices, 'Exact removal indices') + kept = [old['events'][i] for i in indices] + cut = [old['events'][i] for i in removed] + need(Counter(x[0] for x in cut) == {'native': 128, 'scalar': 122}, + 'Complete removed inventory') + need(Counter(x[4] for x in cut if x[0] == 'native') == {1: 128}, + 'Only the selected rank-one children are removed') + need(price([x[1] for x in cut if x[0] == 'scalar']) == 928, 'Removed scalar price') + pre = [['scalar', [op, 112+t, None if s is None else 112+s, v], 0] + for op, t, s, v in code['scalar_word']] + progress = [['native', 112+p, 0, 1, 9, 'capture-full'] for p in P] + late = [['scalar', [op, 112+t, None if s is None else s-112, v], 1] + for op, t, s, v in code['final_query_word']] + need(word['events'] == pre+kept+progress+late, 'Exact complete operation order') + stages = [('precode', pre), ('retained_core', kept), + ('selected_full_progress', progress), ('late_query', late)] + cursor, expected_ranges = 0, {} + for name, events in stages: + expected_ranges[name] = [cursor, cursor+len(events)] + cursor += len(events) + need(word['stage_ranges'] == expected_ranges, 'Exact stage boundaries') + need(cursor == 2886, 'Complete event count') + final = list(old['final']) + for field in selected: + final[field] = 1 + need(word['final'] == final, 'Exact changed output frames') + need(old['frames'][0] == [] and len(old['frames'][1]) == 9, 'I and FULL declarations') + current = list(word['start']) + count, used = Counter(), set() + for i, event in enumerate(word['events']): + if i == expected_ranges['late_query'][0]: + need(all(current[p] == 1 for p in range(112)) and + all(current[p] == 1 for p in selected), 'Late common-FULL cut') + if event[0] == 'native': + _, field, before, after, r, key = event + need(0 <= field < 224 and current[field] == before, 'Native field and old frame') + need(word['native_recipes'][key]['rank'] == r, 'Native rank binding') + if key == 'capture-full': + need(field in selected and (before, after, r) == (0, 1, 9), + 'Only selected complete FULL replacements') + else: + need(word['native_recipes'][key] == old['native_recipes'][key], + 'Exact inherited phase record') + need(key == str(before)+':'+str(after), 'Ordered inherited frame pair') + current[field] = after + count[r] += 1 + used.add(key) + else: + _, scalar, frame = event + op, target, origin, _ = scalar + need(0 <= target < 224 and current[target] == frame, 'Scalar target frame') + if op == 'add': + need(0 <= origin < 224 and current[origin] == frame, 'Scalar source frame') + else: + need(op == 'scale' and origin is None, 'Scale grammar') + need(current == final, 'Complete final frame ledger') + need(used == set(word['native_recipes']), 'Every stored recipe is used') + need(count == {1: 1392, 2: 64, 3: 48, 9: 16}, 'Complete native profile') + scalars = [event[1] for event in word['events'] if event[0] == 'scalar'] + expected = unit(640) + for p in range(112): + target = 112+p + expected[target] = {112+j: v for j, v in c[p].items()} + add(expected[target], ce[p] if p in P else e[p]) + need(reverse(scalars, 640) == transpose(expected, 640), 'All640 reverse input columns') + actual, growth = prefix(scalars, 640) + need(actual == expected and actual[224:] == unit(640)[224:], 'Separate forward row check') + need(growth == {'row_one_norm': '132', 'binary_height': 1}, + 'Complete operation-boundary content bounds') + need(price(scalars) == 11640, 'Complete scalar invoice') + stage_prices = {name: price([e[1] for e in events if e[0] == 'scalar']) + for name, events in stages} + need(stage_prices == {'precode': 1760, 'retained_core': 6456, + 'selected_full_progress': 0, 'late_query': 3424}, + 'All four scalar stage bills') + input_views = [r for r in old['endpoint_adapters'] if r['role'] == 'source'] + need(word['input_views'] == input_views, 'All112 exact input phase adapters') + outputs = word['output_views'] + need(len(outputs) == 96 and {r['port'] for r in outputs} == set(range(112))-set(P), + 'Exactly the96 ordinary output adapters') + for r in outputs: + need(r['frame'] == final[112+r['port']] and r['recipe']['rank'] == 0 and + r['recipe']['right'] is None, 'One output monomial in the actual ordinary frame') + full = [['C', 1 << j, 1] for j in range(9)] + need(word['new_full_recipe_circuit'] == full, 'Declared complete positive FULL kernel') + need(reverse([x[1] for x in kept+progress+late if x[0] == 'scalar'], 640) != + transpose(expected, 640), 'Missing precode control') + need(reverse([x[1] for x in pre+kept+progress if x[0] == 'scalar'], 640) != + transpose(expected, 640), 'Missing late query control') + try: + select_raw(old, selected-{112+27}) + except ValueError: + pass + else: + raise ValueError('Incomplete selected-pair control') + return { + 'input_columns': 640, 'unchanged_arbitrary_roles': 416, 'events': cursor, + 'removed_events': len(removed), 'removed_scalar_price': 928, + 'native_profile': dict(sorted(count.items())), + 'native_children': sum(count.values()), 'native_mass': sum(r*n for r, n in count.items()), + 'real_scalar_primitives': price(scalars), 'scalar_stage_prices': stage_prices, + 'input_views': 112, 'output_views': 96, + 'native_side_maps_upper_bound': 2*sum(count.values()), + 'inherited_distinct_native_recipes': len(used)-1, + 'new_distinct_native_recipes': 1, 'growth': growth, + 'private_fields': 0, 'new_fields': 0, 'odd_scans': 0, + } + + +def phases(word, old, phase): + full = [('C', 1 << j, 1) for j in range(9)] + record = word['native_recipes']['capture-full'] + result = {'full': phase.compare(phase.recipe(record), full, 'New complete F9', 512)} + old_target = {r['port']: r for r in old['endpoint_adapters'] if r['role'] == 'target'} + inverse_checks = [] + for view in word['output_views']: + p = view['port'] + inherited = phase.recipe(old_target[p]) + new = phase.recipe(view['recipe']) + left = phase.compare(inherited+new, [], 'Output inverse '+str(p), 1) + right = phase.compare(new+inherited, [], 'Output inverse other order '+str(p), 1) + inverse_checks.append({'port': p, 'orders': [left, right]}) + result['output_inverse_monomials'] = inverse_checks + identity = {'matrix_rows': [1 << j for j in range(9)], + 'quadratic_rows': [0]*9, 'linear_Z4': [0]*9, 'offset': 0, 'phase': 0} + direct = {'rank': 9, 'left': identity, 'right': identity} + result['identity_wrapper_corollary'] = phase.compare( + phase.recipe(direct), full, 'Direct identity-wrapper F9', 512) + bad = phase.recipe(record)+phase.compile_circuit([['phase', 1]]) + need(phase.run(bad, 0) != phase.run(full, 0), 'Wrong global phase control') + result['scope'] = 'Exact executed recipes; descriptive compiler circuits are not executed.' + return result + + +def direct_refinement(payload): + frozen(NATIVE, 'DIRECT-FULL-FREEZE.json', + 'f0d3b0d7c8d93e391089a2d28066dd02b4a9b28e306dea5f4e7cb5fc895b054e') + direct = json.loads(read(NATIVE/'direct-normal/DIRECT-FULL-CAPTURE.json.gz', + 'fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c', True)) + need(direct['refinement_source_decompressed_sha256'] == + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', + 'Exact refinement source') + need(set(direct) == set(payload)|{'refinement_source_decompressed_sha256'}, + 'No additional refinement state') + for key in set(payload)-{'providers', 'schema'}: + need(direct[key] == payload[key], 'Unchanged refinement metadata: '+key) + identity = {'matrix_rows': [1 << j for j in range(9)], + 'quadratic_rows': [0]*9, 'linear_Z4': [0]*9, 'offset': 0, 'phase': 0} + expected = {'rank': 9, 'left': identity, 'right': identity} + for name, word in payload['providers'].items(): + changed = direct['providers'][name] + need(set(changed) == set(word), 'Unchanged word schema') + for key in set(word)-{'native_recipes'}: + need(changed[key] == word[key], 'Exact unchanged complete word: '+key) + need(set(changed['native_recipes']) == set(word['native_recipes']), + 'No additional native recipe') + for key, record in word['native_recipes'].items(): + need(changed['native_recipes'][key] == (expected if key == 'capture-full' else record), + 'Only the direct FULL recipe changes') + return {'providers': ['base', 'extra'], 'changed_occurrences_per_word': 16, + 'all_events_and_boundary_views_byte_equal': True, + 'real_scalar_primitives': 11640, 'native_children': 1520, 'native_mass': 1808, + 'native_side_maps_upper_bound': 3008, + 'proof': 'Exact complete-word substitution using the independently checked identity-wrapper kernel.'} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + frozen(ALG, 'FREEZE.json', '0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf') + raw = json.loads(read(RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz', + 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True)) + code = json.loads(read(ALG/'run-normal/ROW-CAPTURE.json', + '4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7')) + e, c, ce, algebra_report = algebra(raw, code) + frozen(NATIVE, 'FREEZE.json', + '5321a8ff856042c5ca30ce6b29b90a51ccd4dcf02317820243bfffbb433c84d8') + frozen(LANES/'bridge-access-20261017/row-capture-access-20261020', 'FREEZE.json', + '9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11') + payload = json.loads(read(NATIVE/'run-normal/PRODUCTIVE-CAPTURE.json.gz', + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', True)) + need(payload['schema'] == 'productive-sixteen-full-capture-v1', 'Native schema') + need(payload['selected_ports'] == P and payload['ports'] == raw['model']['ports'], + 'Exact physical selected ports and line directions') + need(payload['ordinary_ports'] == sorted(set(range(112))-set(P)) and + payload['inverse_code'] == code['code_inverse'], 'Complete inverse and ordinary metadata') + for key, expected in [('response', e), ('code', c), ('captured_response', ce)]: + need(rows(payload[key]) == expected, 'Native matrix contract: '+key) + need(set(payload['providers']) == {'base', 'extra'}, 'Both providers') + need(payload['providers']['base'] == payload['providers']['extra'], + 'Byte-equal provider payloads') + word_reports = {} + for provider, word in payload['providers'].items(): + word_reports[provider] = check_word(word, raw['providers'][provider]['forward'], code, e, c, ce) + phase = inherit() + phase_report = phases(payload['providers']['base'], raw['providers']['base']['forward'], phase) + refinement_report = direct_refinement(payload) + report = { + 'status': 'PASS_INDEPENDENT_ROW_CAPTURE_NATIVE', + 'algebra': algebra_report, 'literal_words': word_reports, + 'phases': phase_report, 'direct_full_refinement': refinement_report, + 'negative_controls': ['missing precode', 'missing late query', + 'incomplete selected pair', 'wrong global phase'], + 'scope': 'Complete local forward native service with changed output representation. No free later-stage conversion, global decoder, recursive host, or complete supplier claim.', + } + args.out.mkdir(parents=True, exist_ok=True) + (args.out/'REVIEW.json').write_text(json.dumps(report, indent=2, sort_keys=True)+'\n') + (args.out/'INPUTS.json').write_text(json.dumps(INPUTS, indent=2, sort_keys=True)+'\n') + print(report['status']) + + +if __name__ == '__main__': + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json new file mode 100644 index 0000000000..7ef7d475fc --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json @@ -0,0 +1,137 @@ +{ + "bridge-access-20261017/row-capture-access-20261020/ACCESS.md": { + "sha256": "b28785e70fd700a4ed564f4cfc9d154c1b154939541053dc8fb802911c1448b1" + }, + "bridge-access-20261017/row-capture-access-20261020/FREEZE.json": { + "sha256": "9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11" + }, + "bridge-access-20261017/row-capture-access-20261020/check_access.py": { + "sha256": "48baba6e09b787924c496c8d4ce89c9dd3f77585946516f90ff8803d45adb5cd" + }, + "bridge-access-20261017/row-capture-access-20261020/run-normal/ACCESS-PROGRAM.json": { + "sha256": "c2d6a3300f759c4052236fec5ca8ef446f35b444f78369eaa9aed9ab9625f139" + }, + "bridge-access-20261017/row-capture-access-20261020/run-normal/CHECKS.json": { + "sha256": "fc30fa5c4923633ff2aac86881656a086416193a90511bf06754fc9f7c17174b" + }, + "bridge-access-20261017/row-capture-access-20261020/run-optimized/ACCESS-PROGRAM.json": { + "sha256": "c2d6a3300f759c4052236fec5ca8ef446f35b444f78369eaa9aed9ab9625f139" + }, + 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No free later-stage conversion, global decoder, recursive host, or complete supplier claim.", + "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<(x-Sy,y)", + "coded_backward": "(x,y)->(S^-1x-y,y)", + "coded_forward": "(x,y)->(x,S(x+y))", + "forward": "(x,y)->(x,y+Sx)" + }, + "inherited": "The 16 intrinsic line recipes and their full spatial phase checks are unchanged from the accepted selected-unit packet.", + "kernel": "S=J-pi_A", + "open": [ + "Global child hosting", + "Changing-chart controller and endpoint decoding", + "Finite precision and complete supplier invoice" + ], + "payload_sha256": "17122a343fb8a3dd804b2d7042d523aa209d0684447cdba63d84cc5561b6144f", + "self_adjoint": true, + "source_pins": { + "clean_core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877", + "owned_payload": "c5ef4e5667838d140a0edfd214cdc3558d882a7b7c3505314919b6929f6b40a2", + "owned_producer": "37049a4547de15e88d408cfbb6fea8ad3f6a12292483c47dd5be22a8296bab43", + "signed_payload": "587a9259b728e96dad5383d00b3efe49ba8bf2109548e259d041c788968adcca", + "word_compressed": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + "status": "PASS_UNIFORM_SIGNED_UNIT_SHEARS_712_COLUMNS" +} diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3133/research/rank7-coupled-586-588-carrier-fold/README.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3133/research/rank7-coupled-586-588-carrier-fold/README.md new file mode 100644 index 0000000000..8ff62ac757 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3133/research/rank7-coupled-586-588-carrier-fold/README.md @@ -0,0 +1,258 @@ +# Coupled `B + restore` dying-helper carrier folds lowering helpers `586` & `588` to rank 7 (`width 6`): conditional κ = 0.001729776089405120334238 − 10⁻⁴⁶ − 10⁻⁷⁰ + +**Selected frontier & archival base disclosure (`certificates/selected-result.json`, `docs/research/pr-intake-decisions.json`, `docs/research/current-priorities.md` Priority Revision 6):** The official selected conditional bound on `main` remains **`κ = 0.001672660197076918`** (PR #1094). This package is built directly and solely on top of our **actual parent lineage**: **PR #2979** (`mdumitrean`, Marius-Paul Dumitrean), **PR #3015** (`jeremykothe2`, Jeremy Kothe), and **PR #3042** (`dcharb78`), which are recorded in `docs/research/pr-intake-decisions.json` as **archived author claims (`merged_for_archive_only`, `partially_reviewed`)**. Concurrent downstream packages on `main`—**PR #3050** (`petalas`, Nick Petalas), **PR #3051** (`jeremydiviney`, Jeremy Diviney), **PR #3054** (`petalas`), **PR #3056** (`petalas`), **PR #3057** (`petalas`), **PR #3060** (`petalas`), **PR #3064** (`dataisfire`), **PR #3065** (`petalas`), and **PR #3103** (`Arham-Tahir64`) (**archived author claims (`merged_for_archive_only`, `partially_reviewed`)**), alongside open PRs **#3112**, **#3119**, **#3126** (`jwr404`, `V45` invoice/chronology audits), **#3114** (`mdumitrean`), **#3115** (`dataisfire`), and **#3125** (`navinor`, negative ceiling screen of `R489`/`R480` on card `complex-new-helper-inventory`)—were **not** used as inputs to construct this package and are cited solely as **external comparators / scoped optimality baselines**. Per `docs/research/current-priorities.md` (**Priority Revision 6**, `incumbent-optimization` / `complex-new-helper-inventory`), reopening a domain bounded by scoped negative/optimality results requires explicitly naming the **changed hypothesis**: +- **PR #3057** and **PR #3065** (`petalas`, **archived author claims (`merged_for_archive_only`, `partially_reviewed`)**) report (author-checked) that on PR #3042's six-skip words, with scalar operations/order and helper endpoints fixed, **all 6,141 `A`/`B`/`restore` frames are already at their global optimum**. +- **Open PR #3114** (`mdumitrean`) reports (author-checked) that with `A`, `B`, warps, and helper endpoints (`{6:16, 7:52}`) fixed, replacing `restore` by any legal scalar gate sequence and re-solving all frames satisfies `cert(W') >= 10,868,103,087 = cert(PR3042)`—so PR #3042's `-29,976` restore saving (`-12 H1 + 6 H2`) exhausts restore-only improvements under fixed `A`, `B`, and fixed helper endpoints. +- **PR #3051**, **PR #3054**, and **PR #3103** (**archived author claims (`merged_for_archive_only`, `partially_reviewed`)**, plus 30-digit refinement open **PR #3115**) report (author-checked) that at $T=740$ ($20 \mid T$), the fixed helper width inventory `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` attains its continuous relaxation cap (`κ = 0.0017297379500642785512428...`). + +**Changed hypothesis in this package (`research/rank7-coupled-586-588-carrier-fold`):** We relax the joint invariance of **`B`-phase carrier routing and `helper_final` terminal subspaces** by coupling a **`B`-phase dying-helper carrier fold** on `(586, 438)` and `(588, 440)` (`B_586_438` and `B_588_440`) with **Stage-1 `helper_final` lowering** of entering helpers `586` ($E_{30} \to V_{30,76,82}$) and `588` ($E_{30} \to V_{30,97,127}$) from rank 8 (`width 7`) to rank 7 (`width 6`), shifting the per-call helper width inventory from **`{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` to `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}`** (`24` lowered rank-7 helpers instead of `22`, at unchanged `91` private zero buffers and `66,813` physical families). Neither move works alone (Stage-1 lowering of `586` or `588` alone has a negative surrogate margin of **`-3,345`** each; Stage-2 folding at `dim 8` alone has a negative surrogate margin of **`-973`** each), but together they exhibit a **`+4,983` per-helper (`+9,966` joint) positive cross-term synergy**, saving `-2,091,965` local climb units per helper against the rounded guide value `BE = 2,091,300` for a **surrogate margin of `+665` each = `+1,330` together** on top of `R1_E42 + R2_E7`'s `-29,976` (while the $\kappa$ result and `RELAX-CAP` certificate carry the actual claim). Paired with a repacked literal $T=74$ allocation (`allocation/FILL.json.gz`, `T74_optimal_idle39`), the certified literal $T=74$ root is **`κ in [0.0017297760894051203342384, 0.0017297760894051203342385]`** (`+3.99230172e-8` over PR #3042's $T=74$ root and **`+3.81393408e-8` strictly above PR #3054/#3115's $T=740$ cap-attaining root**), and the new continuous relaxation cap rises to **`RELAX-CAP in [0.0017297774946785970118869, 0.0017297774946785970118870]`** (**`+3.95446143e-8` above PR #3054's $T=740$ cap**). +- **Extended Declared-Edit Checker vs. Unchanged Exact Auditor:** The Stage-4 declared-edit applier and independent edit reviewer (`edits/declared_edits.py`, `edits/edits_review.py`, `verify.py`) were extended from single-hunk `restore` replacements to support multi-hunk `B + restore` edits with automatic `warps` index shifting and declared `helper_final` lowerings to codimension-2 subspaces (`V_{30,76,82}`, `V_{30,97,127}`). The exact forward/dual linear auditor (`vendor/audit_local.py`), monotone frame/cleanup engine (`vendor/preload_move.py`), and two-sided structure certificate checker (`structure.py`) are **unchanged and byte-identical to PR #3042's** (and PR #2979 / PR #2917's). + +```text +Status / UTC update / priority revision: DONE (conditional candidate) · 2026-10-17 · priority revision 6 · base main 997e6a9c +Selected conditional result on main: κ = 0.001672660197076918 (PR #1094, certificates/selected-result.json) +Archival parent lineage & external comparators: Built solely on PR #2979, PR #3015, and PR #3042 (archived author claims: + merged_for_archive_only, partially_reviewed in docs/research/pr-intake-decisions.json). Concurrent PRs #3050, #3051, #3054, + #3056, #3057, #3060, #3064, #3065, #3103 (archived) and #3112, #3114, #3115, #3119, #3125, #3126 (open) are cited solely as external comparators. +Concrete question and changed premise (docs/research/current-priorities.md, Priority Revision 6): PR #3065 reports (author-checked) + all 6,141 frames in PR #3042's words are globally optimal under fixed gates and fixed helper endpoints, and open PR #3114 reports + (author-checked) PR #3042's -29,976 restore saving is globally optimal over all restore gate sequences under fixed A, B, and fixed + helper endpoints {6:16, 7:52}. In PR #2979, entering helpers 586 and 588 were the only two restored helpers whose causal lower bounds + L_586, L_588 already had dimension 7 (k=0 blocking causal gates), yet Stage-1 lowering alone had a -3,345 surrogate margin each. + Can coupling a B-phase dying-helper carrier fold on (586, 438) and (588, 440) with Stage-1 helper_final lowering give 586 and 588 + a positive surrogate margin, shift the width inventory to {6:18, 7:50}, and beat both PR #3042 (T=74) and PR #3054/#3115 (T=740)? +Established result and evidence status: yes. Four declared edits in edits/EDITS.json—R1_E42 (26 -> 33 gates skipping {22, 40, 54, 63}), + R2_E7 (13 -> 15 gates skipping {5, 73}), B_586_438 (6 hunks, 6 -> 5 gates + helper_final[586] -> V_{30,76,82}), and B_588_440 + (6 hunks, 6 -> 5 gates + helper_final[588] -> V_{30,97,127})—move the local profile to {1:2433, 2:724, 3:228, 4:102, 5:20, 8:8} + and the width inventory to {4:26, 5:2, 6:18, 7:50, 8:99, 9:213} (91 buffers). With the repacked literal T74 allocation + (T74_optimal_idle39), complete fresh-native admission and modern outer release pass at + κ = 0.001729776089405120334238 - 10^-46 - 10^-70 (literal root κ in [0.0017297760894051203342384, 0.0017297760894051203342385]; + RELAX-CAP in [0.0017297774946785970118869, 0.0017297774946785970118870]). Author-checked (AI-assisted); not maintainer-reviewed. +Public artifact URL + exact commit: research/rank7-coupled-586-588-carrier-fold (see the PR). +Next useful task: compose the {4:26, 5:2, 6:18, 7:50, 8:99, 9:213} words with a T=740 (20 | T) cap-attaining allocation to close the + 1.4053e-9 T=74 integer-rounding gap, or compose with PR #3060/#3076 native primitive contractions. +Active claim / expiry: released. +``` + +--- + +## 1. Headline Comparison Table + +| Package / Record | Intake / Review Status (`pr-intake-decisions.json`) | κ (headline; candidate rows carry `− 10⁻⁴⁶ − 10⁻⁷⁰`) | Exact Root / Cap Bracket | Local Profile per Call | Helper Width Inventory | Complete Paid Profile ($T=74$ unless noted) | +|---|---|---|---|---|---|---| +| **Selected Result (PR #1094)** | **Official selected conditional bound (`certificates/selected-result.json`)** | **`0.001672660197076918`** | `20908252463461475 / 12500000000000000000` | Selected `k8` baseline | Selected `k8` baseline | Selected `k8` baseline | +| **PR #2969** (`Dugongue`) | Archived comparator (`allocation/baseline/CLAIM.json`) | `0.00172403522474810487855` | Cap-level at $T=370$ | `{1:2430, 2:628, 3:282, 4:110, 5:26, 8:8}` | `{4:26, 5:2, 7:62, 8:100, 9:218}` (86 buf) | $T=370$ baseline | +| **PR #2979** (`mdumitrean`) | **Archived author claim (`merged_for_archive_only`, `partially_reviewed`)** | `0.001729033982646513517717` | Root `0.0017290339826465...`
    Cap `0.0017290357648755...` | `{1:2445, 2:706, 3:232, 4:108, 5:18, 8:8}` | `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` (91 buf) | `{1:1645680, 2:470196, 3:159468, 4:71928, 5:13716, 8:5328, 48:28190}` | +| **PR #3015** (`jeremykothe2`) | **Archived author claim (`merged_for_archive_only`, `partially_reviewed`)** | `0.001729150973534224428695` | 1 skip (`63` via `61`) | `{1:2443, 2:707, 3:232, 4:108, 5:18, 8:8}` | `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` (91 buf) | `{1:1644348, 2:470862, 3:159468, 4:71928, 5:13716, 8:5328, 48:28190}` | +| **PR #3042** (`dcharb78`, audited in **#3050**, **#3065**, **#3114**) | **Archived author claim (`merged_for_archive_only`, `partially_reviewed`)** | `0.001729736166387915986812` | Root `[0.0017297361663879159868125, ...6]`
    Cap `[0.0017297379500642785512428, ...9]` | `{1:2433, 2:712, 3:232, 4:108, 5:18, 8:8}` | `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` (91 buf) | `{1:1637688, 2:474192, 3:159468, 4:71928, 5:13716, 8:5328, 48:28190}` | +| **PR #3051 / #3054 / #3103** (`jeremydiviney` / `petalas` / `Arham-Tahir64`) & open **PR #3115** (`dataisfire`) | **Archived author claims (`merged_for_archive_only`, `partially_reviewed`)** / open (#3115) | `0.001729737950064278551242` (`#3054`)
    `0.001729737950064278551242895823` (`#3115`, `− 10⁻⁵² − 10⁻⁷⁶`) | Attains `{6:16, 7:52}` cap at $T=740$ ($20 \mid T$) | `{1:2433, 2:712, 3:232, 4:108, 5:18, 8:8}` | `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` (91 buf) | $T=740$ cap-attaining profile (`6,660` calls) | +| **This Package (`rank7-coupled-586-588-carrier-fold`)** | **New conditional candidate (author-checked, AI-assisted)** | **`0.001729776089405120334238`** | **Root `[0.0017297760894051203342384, 0.0017297760894051203342385]`**
    **`RELAX-CAP` `[0.0017297774946785970118869, 0.0017297774946785970118870]`** | **`{1:2433, 2:724, 3:228, 4:102, 5:20, 8:8}`** | **`{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}` (91 buf)** | **`{1:1637692, 2:482184, 3:156741, 4:67932, 5:14710, 8:5328, 39:1, 48:28256}`** | + +### Exact Certified Gains (`check_cap.py`, `CLAIM.json`) +- **Over PR #3042 ($T=74$ literal root):** **`+3.99230172e-8`** (`0.0017297760894051203342384 - 0.0017297361663879159868125`). +- **Over PR #3051 / PR #3054 / PR #3115 ($T=740$ cap-attaining root):** **`+3.81393408e-8`** (`0.0017297760894051203342384 - 0.0017297379500642785512428`, beating the $T=740$ ceiling of the old `{6:16, 7:52}` inventory already at $T=74$). +- **Continuous Relaxation Cap Gain (`RELAX-CAP` over PR #3054 / PR #3042 cap):** **`+3.95446143e-8`** (`0.0017297774946785970118869 - 0.0017297379500642785512428`). +- **Remaining $T=74$ Integer-Rounding Gap to `RELAX-CAP`:** **`1.4053e-9`** (`0.0017297774946785970118869 - 0.0017297760894051203342385`), which is strictly smaller than PR #3042 / PR #2979's `1.7837e-9` gap at $T=74$ and arises from the $20 \mid T$ fractional-basis period effect (`idle_per_replica = {1: 234, 3: 1323/20, 5: 75/4, 48: 7637/20}` in `certificates/RELAX-CAP.json`) closed at $T=740$ in PR #3024, #3030, #3051, #3054, and #3103 (and partially at $T=148$ in PR #3022, #3028, #3064). +- **Over pinned comparators (`comparators/` & `allocation/baseline/`):** + - Over PR #2979: `742106758606816521 / 10^24` $\approx$ **`+7.4210675861e-7`** + - Over PR #2969: `717608082126931961 / (1.25 × 10^23)` $\approx$ **`+5.7408646570e-6`** + - Over PR #2966: `2870908440834078413 / (5 × 10^23)` $\approx$ **`+5.7418168817e-6`** + - Over PR #2957: `6058674334382163267 / 10^24` $\approx$ **`+6.0586743344e-6`** + - Over PR #2942: `3479884770953003121 / (5 × 10^23)` $\approx$ **`+6.9597695419e-6`** + +--- + +## 2. Literal `edits/EDITS.json` Specification (All 4 Edits & `helper_final` Lowerings) + +Every gate count (`len(old) -> len(new)`), register ID, rational coefficient, subspace frame basis, and per-edit profile delta below is derived programmatically and literally from `edits/EDITS.json` (which applies identically to `base` and `extra`). Across all 4 edits (`14` hunks total per word) and `2` `helper_final` lowerings, the only registers touched in `edits/EDITS.json` are: +- **`R1_E42` (`14` registers):** `[18, 22, 34, 40, 45, 54, 61, 63, 92, 103, 108, 226, 228, 230]` +- **`R2_E7` (`6` registers):** `[5, 59, 73, 96, 363, 395]` +- **`B_586_438` (`7` registers):** `[75, 136, 140, 144, 187, 438, 586]` +- **`B_588_440` (`7` registers):** `[84, 162, 172, 196, 221, 440, 588]` + +### Summary Table of the 4 Declared Edits in `edits/EDITS.json` + +| Edit ID | Section & Source Addresses | Hunks & Literal Gate Counts (`len(old) -> len(new)`) | Touched Registers | `helper_final` Lowering (`old -> new`) | Per-Call Profile $\Delta$ | Surrogate Guide $\Delta$ (`c1=2,116,671`, rounded guide `BE=2,091,300`; $\kappa$ carries the claim) | +|---|---|---|---|---|---|---| +| **`R1_E42`** | `restore[162:188]` | 1 hunk: **`26 -> 33`** | `18, 22, 34, 40, 45, 54, 61, 63, 92, 103, 108, 226, 228, 230` (skips `E_42` for `{22, 40, 54, 63}`) | None | **`-8 H1 + 4 H2`** | **`-19,984`** (`+19,984` surrogate margin) | +| **`R2_E7`** | `restore[190:203]` | 1 hunk: **`13 -> 15`** | `5, 59, 73, 96, 363, 395` (skips `E_7` for `{5, 73}`) | None | **`-4 H1 + 2 H2`** | **`-9,992`** (`+9,992` surrogate margin) | +| **`B_586_438`** | `B[52:53]`, `B[784:785]`, `B[794:795]`, `B[1214:1215]`, `B[1230:1231]`, `restore[85:86]` | 6 hunks: **`6 -> 5`** (`1 -> 0` at `B[52:53]`, five `1 -> 1`) | `75, 136, 140, 144, 187, 438, 586` | `586`: `E_30` (`8`) $\to$ `V_{30,76,82}` (`7`) (`[256,128,70,32,18,12,1]`, width `7 -> 6`) | **`+6 H2 - 2 H3 - 3 H4 + 1 H5`** | **`-2,091,965`** vs `BE = -2,091,300` $\implies$ **`+665` surrogate margin** | +| **`B_588_440`** | `B[57:58]`, `B[789:790]`, `B[799:800]`, `B[1222:1223]`, `B[1238:1239]`, `restore[88:89]` | 6 hunks: **`6 -> 5`** (`1 -> 0` at `B[57:58]`, five `1 -> 1`) | `84, 162, 172, 196, 221, 440, 588` | `588`: `E_30` (`8`) $\to$ `V_{30,97,127}` (`7`) (`[256,128,65,33,18,10,6]`, width `7 -> 6`) | **`+6 H2 - 2 H3 - 3 H4 + 1 H5`** | **`-2,091,965`** vs `BE = -2,091,300` $\implies$ **`+665` surrogate margin** | +| **Total** | `B` (`-2` gates, `cleanup` `+2` at `FULL`, warps shifted) + `restore` (`+9` gates) | **14 hunks (`51 -> 58` gates)** | `34` distinct registers | `586, 588` lowered (`{6:16, 7:52} -> {6:18, 7:50}`) | **`-12 H1 + 18 H2 - 4 H3 - 6 H4 + 2 H5`** | **`-4,213,906`** vs `2*BE = -4,182,600` $\implies$ **`+31,306` surrogate margin** | + +### 2.1 Edit 1: `R1_E42` (`restore[162:188]`, `26 -> 33` Gates, Skipping `{22, 40, 54, 63}`, `-8 H1 + 4 H2 = -19,984`) +*(From PR #3042 by dcharb78, superseding PR #3015's single-register edit `R1` on `restore[178:180]`; subsequently audited in external PRs #3050 and #3114.)* +- **Exact $\mathbb{Q}$-Linear Map (`old` and `new` are 100% identical across all 14 touched registers):** + $$X_{18}' = -X_{226}, \quad X_{22}' = -X_{230}, \quad X_{108}' = -X_{22} + 2 X_{34},$$ + $$X_{226}' = -\frac{1}{4} X_{18} - \frac{1}{4} X_{40} + \frac{1}{2} X_{54}, \quad X_{228}' = \frac{1}{4} X_{22} - \frac{1}{2} X_{34} + \frac{1}{4} X_{108},$$ + $$X_{230}' = -\frac{1}{4} X_{22} + \frac{1}{2} X_{34} - \frac{1}{4} X_{40} + \frac{1}{4} X_{45} + \frac{1}{2} X_{54} + \frac{1}{4} X_{61} + \frac{1}{4} X_{63} - \frac{1}{4} X_{92} + \frac{1}{4} X_{103} + \frac{1}{4} X_{228} + \frac{1}{4} X_{230},$$ + and $X_r' = X_r$ for $r \in \{34, 40, 45, 54, 61, 63, 92, 103\}$. +- **Literal Gate Sequence (`33` gates in `new` vs `26` in `old`):** + 1. **Registers `40` and `54` via swap with `226` at Group B's rank-7 subspace $W_B = V_{25,42,51} = [256, 128, 64, 34, 17, 11, 4]$ and `18` at $\text{FULL} = [256, 128, 64, 32, 16, 8, 4, 2, 1]$ (`NEW[0..8]` and `NEW[20..25]`):** + - `NEW[0..3]` at $W_B$ ($\dim 7$): `['add', 40, 54, -2, 1]`, `['add', 40, 226, -1, 1]`, `['add', 226, 40, 1, 1]`, `['add', 40, 226, -1, 1]` (swapping $X_{40} - 2 X_{54}$ into `226` and $-X_{226}$ into `40` at $\dim 7$). + - `NEW[4..8]` at $E_{42} = [256, 128, 64, 34, 16, 10, 4, 1]$ ($\dim 8$): `['add', 18, 226, 1, 1]`, `['scale', 18, 1, -4]`, `['add', 18, 226, -1, 1]`, `['add', 226, 18, 1, 1]`, `['add', 18, 226, -1, 1]` (setting $X_{226}' = -\frac{1}{4} X_{18} - \frac{1}{4} X_{40} + \frac{1}{2} X_{54}$ and leaving `18` with $-(X_{40} - 2 X_{54})$). + - `NEW[20..21]` at $E_{42}$ ($\dim 8$): `['add', 230, 18, -1, 1]` and `['add', 230, 45, -1, 1]` (accumulating $X_{40} - 2 X_{54} - X_{45}$ into `230`). + - `NEW[22..25]` at $\text{FULL}$ ($\dim 9$): `['add', 40, 18, -1, 1]`, `['add', 18, 40, 1, 1]`, `['add', 40, 18, -1, 1]`, `['add', 40, 54, 2, 1]` (swapping `18` and `40` at rank 9 so $X_{18}' = -X_{226}$, and uncomputing `-2*54` on `40` at rank 9). Both `40` and `54` skip $E_{42}$ and climb `7 -> 9` directly (`-4 H1 + 2 H2 = -9,992`). + 2. **Register `22` via swaps with `228` and `230` at Group A's rank-7 subspace $W_A = V_{30,42,52} = [256, 128, 64, 38, 20, 10, 1]$ (`NEW[9..19]`):** + - `NEW[9..16]` at $W_A$ ($\dim 7$): `['add', 22, 34, -2, 1]`, 3-add swap `['add', 22, 228, -1, 1]`, `['add', 228, 22, 1, 1]`, `['add', 22, 228, -1, 1]`, and 4-add swap/transfer `['add', 22, 230, -1, 1]`, `['add', 230, 22, 1, 1]`, `['add', 22, 230, -1, 1]`, `['add', 230, 22, 1, 1]`. This places $X_{22}' = -X_{230}$ onto `22` already at $\dim 7$ ($W_A$), so `22` never touches $E_{42}$ and climbs `7 -> 9` directly at `'end'` (`-2 H1 + 1 H2 = -4,996`), while `228` and `230` carry $X_{22} - 2 X_{34}$ into `NEW[17..19]` (`['add', 228, 108, 1, 1]`, `['scale', 228, 1, 4]`, `['add', 108, 228, -4, 1]` at $E_{42}$). + 3. **Register `63` via carrier `61` at $V_{45} = V_{7,42,45} = [256, 128, 64, 35, 16, 11, 5]$ (`NEW[26..32]`, PR #3015's `R1`):** + - `NEW[26]` at $V_{45}$ ($\dim 7$): `['add', 61, 63, 1, 1]`; `NEW[27]` at $E_{42}$ ($\dim 8$): `['add', 230, 61, -1, 1]`; `NEW[28]` at $\text{FULL}$ ($\dim 9$): `['add', 61, 63, -1, 1]` (so `63` skips $E_{42}$ and climbs `7 -> 9` directly, `-2 H1 + 1 H2 = -4,996`), followed by `NEW[29..32]` at $E_{42}$ ($\dim 8$): `['add', 230, 92, 1, 1]`, `['add', 230, 103, -1, 1]`, `['add', 230, 108, -1, 1]`, `['scale', 230, 1, -4]`. + +### 2.2 Edit 2: `R2_E7` (`restore[190:203]`, `13 -> 15` Gates, Skipping `{5, 73}`, `-4 H1 + 2 H2 = -9,992`) +*(From PR #3042 by dcharb78; subsequently audited in external PRs #3050 and #3114.)* +- **Exact $\mathbb{Q}$-Linear Map (`old` and `new` are 100% identical across all 6 touched registers):** + $$X_5' = -X_{395}, \quad X_{59}' = -X_{363}, \quad X_{96}' = X_5 + X_{395}, \quad X_{73}' = X_{73},$$ + $$X_{363}' = -\frac{1}{4} X_{59} + \frac{1}{4} X_{73} + \frac{1}{4} X_{363}, \quad X_{395}' = -\frac{1}{4} X_5 + \frac{1}{4} X_{96} - \frac{1}{4} X_{395}.$$ +- **Literal Gate Sequence (`15` gates in `new` vs `13` in `old`):** + 1. **Register `73` via pivot `363` at Group C's rank-7 subspace $W_C = V_{7,25,30} = [256, 128, 64, 32, 19, 11, 6]$ and carrier `59` at $\text{FULL}$ (`NEW[0..6]`):** + - `NEW[0]` at $W_C$ ($\dim 7$): `['add', 363, 73, 1, 1]` (folding $X_{73}$ into `363` at $\dim 7$). + - `NEW[1..5]` at $E_7 = [256, 128, 64, 32, 16, 8, 5, 3]$ ($\dim 8$): `['add', 59, 363, -1, 1]`, `['scale', 59, 1, -4]`, `['add', 59, 363, -1, 1]`, `['add', 363, 59, 1, 1]`, `['add', 59, 363, -1, 1]` (producing $X_{363}'$ on `363` and $-X_{363} - X_{73}$ on `59`). + - `NEW[6]` at $\text{FULL}$ ($\dim 9$): `['add', 59, 73, 1, 1]` (cleaning $-X_{73}$ from `59` at rank 9 so `73` skips $E_7$ and climbs `7 -> 9` directly, `-2 H1 + 1 H2 = -4,996`). + 2. **Register `5` via pivot `395` at Group D's rank-7 subspace $W_D = V_{7,51,52} = [256, 128, 64, 37, 21, 8, 3]$ and carrier `96` at $\text{FULL}$ (`NEW[7..14]`):** + - `NEW[7]` at $W_D$ ($\dim 7$): `['add', 395, 5, 1, 1]` (folding $X_5$ into `395` at $\dim 7$). + - `NEW[8..13]` at $E_7$ ($\dim 8$): `['add', 96, 395, -1, 1]`, `['scale', 96, 1, 4]`, `['add', 96, 395, -1, 1]`, `['add', 395, 96, 1, 1]`, `['add', 96, 395, -1, 1]`, `['scale', 96, -1, 1]` (producing $X_{395}'$ on `395` and $X_5 + X_{395}$ on `96`). + - `NEW[14]` at $\text{FULL}$ ($\dim 9$): `['add', 5, 96, -1, 1]` (setting $X_5' = -X_{395}$ at rank 9 so `5` skips $E_7$ and climbs `7 -> 9` directly, `-2 H1 + 1 H2 = -4,996`). + +### 2.3 Edit 3: `B_586_438` + `helper_final["586"]` (`6` Hunks, `6 -> 5` Gates, Lowering `586` from $E_{30}$ to $V_{30,76,82}$, `+665` Surrogate Margin) +- **Algebraic, Subspace & `cleanup` Mechanism:** + In `w_base`, entering helper `586` (`start_extra = [30]`, $\dim 1$) and dying cold helper `438` ($\dim 3$ at `B[759]: 586 += 438`) feed target `136` via `B[52]: 136 += 1/2*586` ($\dim 1$) and `B[784]: 136 -= 1/2*586` ($\dim 6$). Because `B[759]: 586 += 438` occurs between `B[52]` and `B[784]`, the net contribution of `B[52]` and `B[784]` to wire `136` is simply: + $$\frac{1}{2} X_{586} - \frac{1}{2}(X_{586} + X_{438}) = -\frac{1}{2} X_{438}.$$ + Later at `B[1215]: 136 += 75`, wire `136` receives **source register `75`** (which has no other readers after `B[794]` and ends at $\text{FULL}$, $\dim 9$). By deleting `B[52]`, moving `B[794]: 140 -= 1/2*438` to `B[784]` at the 4D join frame $J_{140,438} = [257, 129, 32, 30]$, and folding `75 -= 1/2*438` into `B[794]` at the 5D join frame $J_{75,438} = [257, 129, 70, 32, 30]$, both `438` and `586` traverse a monotone 5-step nested subspace tower entirely inside $L_{586} = V_{30,76,82} = E_{30} \cap E_{76} \cap E_{82} = [256, 128, 70, 32, 18, 12, 1]$ ($\dim 7$): + $$U_{759}(3) \;\subset\; J_{140,438}(4) \;\subset\; J_{75,438}(5) \;\subset\; U_{1214,L}(6) \;\subset\; L_{586}(7).$$ + Compared with PR #3042, `B` loses 1 gate (`B[52]`), `restore` is unchanged except for the frame at `restore[85]`, and inverse-reverse `cleanup` gains 1 gate at $\text{FULL}$ (`75 += 1/2*438`), which costs no frame steps and leaves the total `B + restore + cleanup` gate count unchanged. +- **Literal 6 Hunks in `edits/EDITS.json` (`B_586_438`, `6 -> 5` gates total):** + 1. **Hunk 0 (`B[52:53]`, `1 -> 0` gates):** deletes `['add', 136, 586, 1, 2, [30]]` ($\dim 1$), shifting all `B` warps with position $> 52$ by $-1$. + 2. **Hunk 1 (`B[784:785]`, `1 -> 1` gates):** replaces `['add', 136, 586, -1, 2, [289, 161, 64, 18, 10, 6]]` ($\dim 6$) with `['add', 140, 438, -1, 2, [257, 129, 32, 30]]` ($\dim 4$, normals `[6, 10, 12, 18, 20, 24, 30, 64, 70, 74, ...]`). + 3. **Hunk 2 (`B[794:795]`, `1 -> 1` gates):** replaces `['add', 140, 438, -1, 2, [256, 128, 76, 32, 30, 1]]` ($\dim 6$) with `['add', 75, 438, -1, 2, [257, 129, 70, 32, 30]]` ($\dim 5$, normals `[6, 24, 30, 74, 76, 82, 84, ...]`). + 4. **Hunk 3 (`B[1214:1215]`, `1 -> 1` gates):** lowers the frame of `['add', 144, 438, -1, 2]` from `[256, 128, 70, 32, 20, 10, 1]` ($\dim 7$, normals `[30, 74, 84]`) to `[256, 128, 70, 32, 30, 1]` ($\dim 6$, normals `[6, 24, 30, 74, 76, 82, 84]`). + 5. **Hunk 4 (`B[1230:1231]`, `1 -> 1` gates):** lowers the frame of `['add', 187, 586, -1, 2]` from `[288, 160, 64, 18, 10, 6, 1]` ($\dim 7$, normals `[30, 416, 446]`) to `[288, 160, 70, 18, 12, 1]` ($\dim 6$, normals `[30, 76, 82, 416, 446, 492, 498]`). + 6. **Hunk 5 (`restore[85:86]`, `1 -> 1` gates):** lowers the frame of `['add', 586, 438, -1, 1]` from `[256, 128, 64, 32, 18, 10, 6, 1]` ($\dim 8$, $E_{30}$) to `[256, 128, 70, 32, 18, 12, 1]` ($\dim 7$, $V_{30,76,82}$), and lowers `helper_final["586"]` from `[256, 128, 64, 32, 18, 10, 6, 1]` (`8` basis vectors) to `[256, 128, 70, 32, 18, 12, 1]` (`7` basis vectors, reducing `width(586)` from $8 - 1 = 7$ to $7 - 1 = 6$). +- **Exact Per-Register Profile Delta (`B_586_438` + `helper_final["586"]`):** + - `586`: `[1, 3, 6, 7, 8] -> [1, 3, 6, 7]` (`-1 H1 = -2,116,671`) + - `136`: `[0, 1, 2, 6, 7, 8] -> [0, 1, 2, 7, 8]` (`-1 H1 - 1 H4 + 1 H5 = -9,006`) + - `140`: `[0, 1, 2, 6, 7, 8] -> [0, 1, 2, 4, 7, 8]` (`-1 H1 + 1 H2 + 1 H3 - 1 H4 = +3,102`) + - `75`: `[1, 2, 3, 7, 9] -> [1, 2, 3, 5, 7, 9]` (`+2 H2 - 1 H4 = +9,979`) + - `438`: `[0, 1, 2, 3, 6, 7, 8, 9] -> [0, 1, 2, 3, 4, 5, 6, 7, 9]` (`+1 H1 + 1 H2 - 1 H3 = +6,877`) + - `144`: `[0, 1, 2, 4, 7, 8] -> [0, 1, 2, 4, 6, 7, 8]` (`+1 H1 + 1 H2 - 1 H3 = +6,877`) + - `187`: `[0, 1, 2, 4, 7, 8] -> [0, 1, 2, 4, 6, 7, 8]` (`+1 H1 + 1 H2 - 1 H3 = +6,877`) + - **Total for `B_586_438`:** **`+6 H2 - 2 H3 - 3 H4 + 1 H5 = -2,091,965` units/call** vs rounded guide `BE = -2,091,300` $\implies$ **`+665` surrogate margin per call**. + +### 2.4 Edit 4: `B_588_440` + `helper_final["588"]` (`6` Hunks, `6 -> 5` Gates, Lowering `588` from $E_{30}$ to $V_{30,97,127}$, `+665` Surrogate Margin) +- **Algebraic, Subspace & `cleanup` Mechanism:** + Symmetrically, entering helper `588` (`start_extra = [30]`, $\dim 1$) and dying cold helper `440` ($\dim 3$ at `B[763]: 588 += 440`) feed target `221` via `B[57]: 221 -= 588` ($\dim 1$) and `B[789]: 221 += 588` ($\dim 6$), whose net contribution to `221` is $-X_{588} + (X_{588} + X_{440}) = +X_{440}$. Deleting `B[57]`, moving `172 += 440` to `B[789]` at the 4D join frame $J_{172,440} = [268, 161, 65, 30]$, and folding `84 += 440` into **source register `84`** at `B[799]` (before `B[1223]: 221 += 84`) at the 5D join frame $J_{84,440} = [262, 161, 65, 20, 10]$ routes `440` and `588` along the 5-step nested subspace tower inside $L_{588} = V_{30,97,127} = E_{30} \cap E_{97} \cap E_{127} = [256, 128, 65, 33, 18, 10, 6]$ ($\dim 7$): + $$U_{763}(3) \;\subset\; J_{172,440}(4) \;\subset\; J_{84,440}(5) \;\subset\; U_{1222,L}(6) \;\subset\; L_{588}(7).$$ + Compared with PR #3042, across `B_586_438` and `B_588_440` combined, `B` loses 2 gates (`B[52]` and `B[57]`), `restore` is unchanged except for the frames at `restore[85]` and `restore[88]`, and `cleanup` gains 2 gates at $\text{FULL}$ (`75 += 1/2*438` and `84 -= 440`), costing no frame steps and keeping the total gate count unchanged. +- **Literal 6 Hunks in `edits/EDITS.json` (`B_588_440`, `6 -> 5` gates total):** + 1. **Hunk 0 (`B[57:58]`, `1 -> 0` gates):** deletes `['add', 221, 588, -1, 1, [30]]` ($\dim 1$), shifting all `B` warps with position $> 57$ by an additional $-1$. + 2. **Hunk 1 (`B[789:790]`, `1 -> 1` gates):** replaces `['add', 221, 588, 1, 1, [256, 161, 97, 18, 10, 6]]` ($\dim 6$) with `['add', 172, 440, 1, 1, [268, 161, 65, 30]]` ($\dim 4$, normals `[12, 18, 30, 97, 109, 115, 127, ...]`). + 3. **Hunk 2 (`B[799:800]`, `1 -> 1` gates):** replaces `['add', 172, 440, 1, 1, [268, 128, 64, 32, 30, 1]]` ($\dim 6$) with `['add', 84, 440, 1, 1, [262, 161, 65, 20, 10]]` ($\dim 5$, normals `[30, 97, 127, 160, 190, 193, 223, 266, 276, ...]`). + 4. **Hunk 3 (`B[1222:1223]`, `1 -> 1` gates):** lowers the frame of `['add', 162, 440, 1, 1]` from `[262, 128, 64, 32, 20, 10, 1]` ($\dim 7$, normals `[30, 266, 276]`) to `[262, 128, 65, 33, 20, 10]` ($\dim 6$, normals `[30, 97, 127, 266, 276, 363, 373]`). + 5. **Hunk 4 (`B[1238:1239]`, `1 -> 1` gates):** lowers the frame of `['add', 196, 588, 1, 1]` from `[256, 160, 96, 18, 10, 6, 1]` ($\dim 7$, normals `[30, 224, 254]`) to `[256, 161, 96, 18, 10, 6]` ($\dim 6$, normals `[30, 97, 127, 129, 159, 224, 254]`). + 6. **Hunk 5 (`restore[88:89]`, `1 -> 1` gates):** lowers the frame of `['add', 588, 440, -1, 1]` from `[256, 128, 64, 32, 18, 10, 6, 1]` ($\dim 8$, $E_{30}$) to `[256, 128, 65, 33, 18, 10, 6]` ($\dim 7$, $V_{30,97,127}$), and lowers `helper_final["588"]` from `[256, 128, 64, 32, 18, 10, 6, 1]` (`8` basis vectors) to `[256, 128, 65, 33, 18, 10, 6]` (`7` basis vectors, reducing `width(588)` from $8 - 1 = 7$ to $7 - 1 = 6$). +- **Exact Per-Register Profile Delta (`B_588_440` + `helper_final["588"]`):** + - `588`: `-2,116,671`; `221`: `-9,006`; `172`: `+3,102`; `84`: `+9,979`; `440`: `+6,877`; `162`: `+6,877`; `196`: `+6,877`. + - **Total for `B_588_440`:** **`+6 H2 - 2 H3 - 3 H4 + 1 H5 = -2,091,965` units/call** vs rounded guide `BE = -2,091,300` $\implies$ **`+665` surrogate margin per call**. + +--- + +## 3. Single-Move Negative Controls & 91-Helper Exhaustion Proofs + +### 3.1 Single-Move Negative Controls: Why `586` and `588` Lose Under Stage-1 Alone (`-3,345`) and Stage-2 Alone (`-973`), But Gain `+665` Surrogate Margin Each (`+1,330` Together) When Coupled + +In PR #2979 (`construction/STAGE-PRICES.json`, lines 773–803), helpers `586` and `588` were the **only two restored helpers in the entire word** whose causal lower bounds $L_{586} = V_{30,76,82}$ and $L_{588} = V_{30,97,127}$ already had dimension 7 ($k = 0$ blocking causal gates) that remained unlowered at `end_dim = 8` ($E_{30}$). Evaluating the two single-move controls against the coupled rewrite explains why neither a frame-only solver (PR #2979 Stage 1 / PR #3065) nor a fixed-endpoint gate search (PR #2957 Stage 3 / PR #3114) could discover this improvement: + +| Configuration (per helper `586` or `588`, and joint for the pair) | `helper_final` (`586, 588`) | `B`-Phase Gate Topology | Local Profile $\Delta$ (per helper / joint) | Local Climb Cost $\Delta$ (per helper / joint) | Rounded Guide Charge (`BE = 2,091,300`) | **Surrogate Margin (per helper / joint; $\kappa$ carries the claim)** | +|---|---|---|---|---|---|---| +| **1. Stage-1 Lowering Alone (Fixed Scalar Gates)** | $\dim 7$ ($V_{30,76,82}$, $V_{30,97,127}$) | Unfolded (`B[52], B[784]` and `B[57], B[789]` kept; frames intersected with $L_h$) | `-1 H1 + 7 H2 - 2 H3 - 2 H4` each
    (`-2 H1 + 14 H2 - 4 H3 - 4 H4` joint) | `-2,087,955` each
    (`-4,175,910` joint) | `+2,091,300` each
    (`+4,182,600` joint) | **`-3,345` each (`-6,690` joint — LOSES)** | +| **2. Stage-2 Carrier Fold Alone at `dim 8` (Fixed Endpoints)** | $\dim 8$ ($E_{30}$, unchanged) | Folded (`B[52], B[57]` deleted; `140, 172` at $\dim 4$; `75, 84` at $\dim 6 = \text{meet}(B[1214], B[1215])$) | `-1 H1 + 2 H2 - 2 H4 + 1 H5` each
    (`-2 H1 + 4 H2 - 4 H4 + 2 H5` joint) | `+973` each
    (`+1,946` joint) | `0` (`width 7` unchanged) | **`-973` each (`-1,946` joint — LOSES)** | +| **3. Coupled Carrier Fold + `dim 7` Lowering (`B_586_438`, `B_588_440`)** | **$\dim 7$ ($V_{30,76,82}$, $V_{30,97,127}$)** | **Folded along 5-step subspace towers (`140, 172` at $\dim 4$; `75, 84` at $\dim 5$)** | **`+6 H2 - 2 H3 - 3 H4 + 1 H5` each**
    **(`+12 H2 - 4 H3 - 6 H4 + 2 H5` joint)** | **`-2,091,965` each**
    **(`-4,183,930` joint)** | **`+2,091,300` each**
    **(`+4,182,600` joint)** | **`+665` each (`+1,330` joint — WINS)** | + +- **Origin of the `+4,983` per-helper (`+9,966` joint) positive cross-term synergy:** + 1. Under **Stage-1 lowering alone**, keeping `B[784]: 136 -= 1/2*586` (and `B[789]: 221 += 588`) inside $L_{586}$ forces `B[784]`'s frame to drop from $\dim 6$ to $\dim 5$, which adds an extra intermediate stop to both `586` (`[1, 3, 5, 6, 7]` instead of `[1, 3, 6, 7]`, costing `+6,877`) and `136` (`[0, 1, 2, 5, 7, 8]` instead of `[0, 1, 2, 7, 8]`, costing `+3,102` vs baseline and `+12,108` vs the folded `[0, 1, 2, 7, 8]` trajectory). + 2. Under **Stage-2 folding at `dim 8` alone**, `B[1214]: 144 -= 1/2*438` remains at $\dim 7$ and `restore[85]: 586 -= 438` remains at $\dim 8$ ($E_{30}$), so folding `438` into `140` ($\dim 4$) and `75` ($\dim 6$) inserts an extra stop on `438` (`[0, 1, 2, 3, 4, 6, 7, 8, 9]`, costing `+6,877`) while `586` only saves `-8,098` (`[1, 3, 7, 8]` vs `[1, 3, 6, 7, 8]`), resulting in a surrogate margin of `-973` per helper. + 3. When **coupled**, `B[1214]` and `B[1230]` drop to $\dim 6$ inside $L_{586}$ while `586` and `136` bypass `B[784]` completely, eliminating both the `+6,877` stop on `586` and the `+12,108` stop on `136` simultaneously (`-3,345 - 973 + 4,983 = +665` surrogate margin per helper). + +### 3.2 Exhaustive 91-Helper Causal Lower-Bound Scan & Structural Obstruction Proofs for All Remaining Candidates + +Tracing the causal lower bound $L_h = \text{lo}[\text{last}[h]]$ across all **91 restored helpers** in the word (`26` at `end_dim = 4`, `30` at `end_dim = 7`, `35` at `end_dim = 8`) by the minimum number $k$ of blocking causal gates in `B + restore` whose removal drops $\dim(L_h)$ shows that beyond `586` and `588` ($k = 0$), every remaining candidate with $k \le 2$ is blocked by one of three exact structural locks: + +1. **The Double Cone Lock on Entering Quartet Sisters `584` and `590` ($\dim 8 \to 7$ at $E_{51}$, $k = 1$ blocking gate):** + - **Free-Operator Algebra Status (`PASS`):** Replacing `B[59]` with `214 += 566`, `B[1196]` with `168 -= 1/2*439`, and `B[1204]` with `214 += 444` while deleting `B[13, 48, 60, 753, 765]` and `restore[82, 91]` leaves `584` and `590` with **0 gates in the entire circuit** and passes 100% of `audit_local.py`'s forward and dual free-operator checks across all 632 inputs. + - **Causal Frame-Chain Obstruction (`FAIL`, 28–74 DAG `lo <= hi` violations across all chronological placements):** Why did `586` and `588` ($E_{30}$) lower cleanly to $\dim 7$ while their even-quartet sisters `584` and `590` ($E_{51}$) are locked at $\dim 8$? + - For `586/438` (and `588/440`), both remaining consumers `187` (`B[1230]`, receiving dying helper `506`) and `144` (`B[1214]`, receiving dying helper `530`) have causal lower bounds contained inside the **same** 7D subspace $L_{586} = V_{30,76,82}$ (and $L_{588} = V_{30,97,127}$). + - For `584/439` (and `590/444`), the two consumers sit in **transverse 7D cones** inside $E_{51}$: the right consumer `115` (`B[1244]: 115 -= 1/2*439`, or `130` at `B[1252]: 130 += 444`) receives **post-warp cold helper `273`** (`B_WARP[541]`, or `289` from `B_WARP[545]`) at $\text{lo\_dim} = 5$ (`[21, 51, 67, 86, 112]`), hard-pinning `B[1244]` to $\text{lo} = \text{hi} = W_{\text{right}} = E_{51} \cap E_{67} \cap E_{112}$ ($\dim 7$); whereas the left consumer `168` (`B[1196]`, or `214` at `B[1204]`) receives entering helper `554` (`B[771]: 168 += 554`, or `566` at `B[59]`), which is upper-bounded by `B[913]: 273 += 554` (`hi_dim = 6`) inside $U_{6,\text{left}} \subseteq W_{\text{left}} = E_{51} \cap E_{82} \cap E_{97}$ ($\dim 7$). Because $U_{6,\text{left}} \not\subseteq W_{\text{right}}$, their join is $\text{join}(U_{6,\text{left}}, W_{\text{right}}) = E_{51}$ ($\dim 8$). + +2. **The Restored-Dirt Isolation Lock on Entering Carrier Helpers `531, 543` and `554, 555, 566, 567` ($\dim 8 \to 7$, $k = 1$ `B` gate):** + - **Causal Frame-Chain Status (`PASS` when `B[916]: 305 += 531` and `B[918]: 321 += 543` are removed):** Deleting `B[916]` and `B[918]` alone drops `531` and `543` to $L_{586} = V_{30,76,82}$ and $L_{588} = V_{30,97,127}$ ($\dim 7$, `width 7 -> 6`) with 0 DAG violations, because `restore[57..59]` and `restore[64..66]` automatically lie inside $L_{586}$ and $L_{588}$. + - **Free-Operator Algebra Obstruction (`FAIL`, `bad_read = [531, 587]` / `[543, 589]`, `bad_targets = [36, 37, 46, 47]`):** At `B[275]: 351 -= 531`, `B[659]: 351 += 1`, and `B[660]: 531 += 351`, helper `531` isolates the clean sum $X_{351} + X_1$ (cancelling $X_{531}$), while `351` retains $-X_{531}$ and immediately absorbs $-\frac{1}{2}(X_{587} + X_{436})$ at `B[661, 786]`. Because consumer `305` is a **warped cold helper** (`B_WARP[385]` before `B[916]` and `B_WARP[611]` after `B[1586]`), routing `305` onto `351` pollutes `305` and output targets `36, 37, 46, 47` with restored helpers `531, 587` and breaks inverse-warp `cleanup` across `B_WARP[611]`. The exact same lock holds for `543` (`321`/`367`), `554, 555` (`273`), and `566, 567` (`289`). + +3. **The Grassmann `6 + 6 - 4 = 8` and `5 + 5 - 3 = 7` Fork-and-Uncompute Lock on the 12 Three-Gate Cold Helpers (`500, 501, 512, 513` at $\dim 8$ and `572..575, 580..583` at $\dim 7$, $k = 1$ gate):** + - Each of these 12 cold helpers $h$ has 1 gate in `A` ($p \mathrel{-}= h$) and 3 post-`A` gates: `B[idx_fold]: h += p` ($\dim 3$), `B[idx_c1]: c_1 += h` ($\dim 6$ or $5$), and `restore[idx_rest]: h -= p` ($\dim 8$ or $7$), while partner $p$ feeds a second consumer `B[idx_c2]: c_2 += p` ($\dim 6$ or $5$). + - **Why `restore: h -= p` is locked at $\dim 8$ (for `500..513`) and $\dim 7$ (for `572..583`):** At `restore: h -= p`, the gate frame must contain $\text{join}(\text{lo}[c_1], \text{lo}[c_2])$. By Grassmann's identity $\dim(U_1 + U_2) = \dim(U_1) + \dim(U_2) - \dim(U_1 \cap U_2)$: + - For `500, 501` ($p = 310, 308$ at $E_{102}$) and `512, 513` ($p = 326, 324$ at $E_{75}$), $\dim(\text{lo}[c_1]) = 6$, $\dim(\text{lo}[c_2]) = 6$, and $\dim(\text{lo}[c_1] \cap \text{lo}[c_2]) = 4$, forcing $\dim(\text{join}(\text{lo}[c_1], \text{lo}[c_2])) = 6 + 6 - 4 = 8$. + - For `572..575, 580..583` ($p = 408, 105, 412, 414, 424, 44, 428, 430$), $\dim(\text{lo}[c_1]) = 5$, $\dim(\text{lo}[c_2]) = 5$, and $\dim(\text{lo}[c_1] \cap \text{lo}[c_2]) = 3$, forcing $\dim(\text{join}(\text{lo}[c_1], \text{lo}[c_2])) = 5 + 5 - 3 = 7$. + - **Why free-algebra splitting (`c_1 += h` at $\dim 3$ + `c_1 += p` at $\dim 6/5$) fails causally (`26` DAG violations per helper):** Consumer $c_1$ is warped by `B_WARP` immediately before `B[idx_c1]` (with pre-warp `hi_dim = 2`), and consumer $c_2$ executes chronologically *before* $c_1$ (`B[825..828]` before `B[835..844]`; `B[853..864]` before `B[885..896]`), so $h$ cannot be discharged into $c_1$ before $c_1$'s `B_WARP` nor uncomputed against $p$ before $p$ climbs to $\text{lo}[c_2]$. + +--- + +## 4. Relaxation Cap (`certificates/RELAX-CAP.json`) & Literal $T=74$ Allocation (`T74_optimal_idle39`) + +- **Fixed-Capacity Relaxation Cap (`tools/relax_exact.py`, `check_cap.py`):** + The exact same 10-pattern optimal LP basis over all 2,551 count-vector patterns remains primal feasible and dual optimal for the shifted width inventory `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}` and local profile `{1:2433, 2:724, 3:228, 4:102, 5:20, 8:8}`: + - Per-replica basis counts (`certificates/RELAX-CAP.json`): `8:[8]` $\times 672$, `32:[7,8,8,9]` $\times 61/4$, `32:[4,9,9,9]` $\times 234$ (`idle=1`), `48:[9,9,9,9,9]` $\times 1323/20$ (`idle=3`), `32:[9,9,9]` $\times 75/4$ (`idle=5`), `32:[6,8,9,9]` $\times 162$, `32:[5,9,9,9]` $\times 18$, `16:[8,8]` $\times 53/4$, `16:[7,9]` $\times 1739/4$, and `48:[]` $\times 7637/20$ (`idle=48`). + - Shifting two roles per call from width $7 \to 6$ (`+18` bins of `32:[6,8,9,9]` per replica) eliminates $9/10$ of an `idle=3` bin and $9/2$ of an `idle=5` bin per replica while freeing $+9/10$ of a completely empty `48:[]` (`idle=48`) bin per replica (`+66.6` empty `cap=48` bins across $T=74$), raising the exact relaxation cap to: + $$\kappa_{\text{cap}} \in \left[\frac{17297774946785970118869}{10^{25}},\; \frac{1729777494678597011887}{10^{24}}\right] = [0.0017297774946785970118869,\; 0.0017297774946785970118870].$$ +- **Literal $T=74$ Realization (`allocation/FILL.json.gz`, `T74_optimal_idle39`):** + - Because `width(586)` and `width(588)` shrink from $7 \to 6$ (`allocation/PROVIDERS.json` indices `356` and `358`), naive in-place compaction without repacking `FILL.json.gz` would open 1-unit idle holes inside 1,332 zero-idle bins (`16:[7,9]` and `32:[7,7,9,9]`). + - Applying the LP basis shift on the $T=37$ chronological Hall-marriage window structure (converting 1 early `32:[7,7,9,9]` bin and 88 early `16:[7,9]` bins with `hi <= 44` to `32:[6,8,9,9]` and `16:[8,8]` to satisfy Hall's condition on the 45 early calls $t \in [0, 44]$, while converting 420 late `16:[8,8]` bins to `16:[7,9]` and adding $+666$ `32:[6,8,9,9]` bins per 37 replicas) and consolidating the two $T=37$ remainder bins across the two halves of $T=74$ yields `allocation/FILL.json.gz` (`271,728` role rows, `SHA256 = 68b8bae90144248774b1920cd27f9519caa3dc427704d8a9da6d4c491d912fc4`): + - **Literal $T=74$ idle histogram:** `{1: 17314, 3: 4893, 5: 1390, 39: 1, 48: 28256}` (`+66` completely empty `48:[]` bins, `-63` `idle=3` bins, and `-338` `idle=5` bins vs PR #2979 / PR #3042). + - **Complete $T=74$ paid profile (`allocation/PROFILE.json`):** `{1: 1637692, 2: 482184, 3: 156741, 4: 67932, 5: 14710, 8: 5328, 39: 1, 48: 28256}` (rank mass $74 \times 65,088 = 4,816,512$). + - **Certified literal $T=74$ root (`tools/root.py`):** **`κ in [0.0017297760894051203342384, 0.0017297760894051203342385]`** (headline `0.001729776089405120334238 - 10^-46 - 10^-70`). + +--- + +## 5. Verification & Replay + +1. **Bounded Registered Check (`run_registered.py`, Python 3.12 stdlib, ~55s):** + - `verify_manifest.py` / `MANIFEST.json`: verifies exact SHA256 pins for all 155 files in the package. + - `verify.py`: rebuilds all stage-1, stage-2, stage-3 (`data/WORD-{base,extra}.json.gz`), and stage-4 (`edits/FINAL-WORD-{base,extra}.json.gz`) words from `data/PARENT-{base,extra}.json.gz` and the declared records; runs `vendor/audit_local.py` (`PASS_INDEPENDENT_EXACT_BORROWING_WORD`, forward and dual across all 632 inputs, 91 restored endpoints and buffers) and `vendor/preload_move.py` (`frame_report`) on every stage word; and rejects **100 semantic tamper controls** (`{'stage1': 20, 'stage2': 52, 'stage3': 14, 'stage4': 14}`). + - `edits/edits_review.py`: independently applies `edits/declared_edits.py` (`R1_E42`, `R2_E7`, `B_586_438`, `B_588_440`), runs `vendor/audit_local.py` forward and dual over all 632 inputs on both parent and candidate words, and rejects **21 semantic tamper controls per word** (`PASS_INDEPENDENT_EDIT_REVIEW {'base': 21, 'extra': 21}`). + - `check_allocation.py`: runs the vendored PR #2839 owner engine (`allocation/vendor/independent_owners.py`) on `allocation/FILL.json.gz` (`271,728` roles, six width classes `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}`, 91-buffer physical stock `66,813`), rejects 5 owner controls, and verifies strict moment improvement over PR #2969 (`PASS_RANK7_LITERAL_OWNERS_AND_EXACT_MOMENT`). + - `check_cap.py`: verifies Fractions-only relaxation cap certificates (`certificates/RELAX-CAP.json` and `certificates/RELAX-STAGES.json`), the literal gap `1.4053e-9`, 5 cap controls, and exact gains over PR #2979, PR #2969, PR #2966, PR #2957, and PR #2942 (`PASS_LITERAL_ALLOCATION_BELOW_FIXED_INVENTORY_CAP_WITH_RECORDED_GAP`). + - Cryptographic binding of all stored receipts in `evidence/` (`OVERLAY-DERIVATION.json`, `EDITS-DERIVATION.json`, `EDITS-REVIEW.json`, `ADAPTER-DERIVATION.json`, `FULL-NATIVE-RECEIPT.json`, `ADMISSION-RESULT.json`, `RELEASE-RECEIPT.json`, `FULL-REPLAY-RESULT.json`) to the exact words, allocation, and `CLAIM.json`. +2. **Complete Cold/Retained Replay (`reproduce.py` & `verify_release.py`):** + ```sh + python3.12 -B scripts/research_package.py --package research/rank7-coupled-586-588-carrier-fold + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \ + python3.12 -B research/rank7-coupled-586-588-carrier-fold/reproduce.py --repo . --work /tmp/rank7-coupled-replay --jobs 2 + ``` + +--- + +## Base Package Lineage Summary (PR #2979, `mdumitrean`) + +This package retains PR #2979's three-stage producer chain (`data/PARENT-{base,extra}.json.gz` $\to$ `data/WORD-{base,extra}.json.gz`) unchanged before applying Stage 4 (`edits/EDITS.json` $\to$ `edits/FINAL-WORD-{base,extra}.json.gz`): +- **Stage 1 (`data/STAGE1-FRAME-EDITS.json`):** Joint codimension-2 end-frame lowering of 22 restored helpers in five shared rank-7 groups (`V45`: `249, 251, 265, 267`; `A`: `331, 450, 451, 508, 509`; `B`: `299, 448, 449, 484, 485`; `C`: `452, 453, 532, 533`; `D`: `454, 455, 556, 557`; 139 gate frame edits, margin `+142,394` units; single-lowering negative controls verified in `verify.py` and independently in open PR #3112). +- **Stage 2 (`data/TRANSFORM-{226,228,230,363,395}.json`):** Five rank-8 paired extractions at normal 42 (`226, 228, 230`) and normal 7 (`363, 395`), raising the buffer count from 86 to 91 (margin `+66,903` units). +- **Stage 3 (`data/REWRITES-2957.json`):** Jeremy Kothe's fourteen PR #2957 rewrites re-addressed with exact preimages (`vendor/declared_rewrites.py`, margin `+52,350` units). + +--- + +## Open next questions + +1. **Closing the `1.4053e-9` integer-rounding gap at $T=740$ ($20 \mid T$):** + The optimal LP basis in `certificates/RELAX-CAP.json` has per-replica counts with denominators $4$ and $20$ (`idle_per_replica = {1: 234, 3: 1323/20, 5: 75/4, 48: 7637/20}`), which become exact integers whenever $20 \mid T$. Composing the `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}` words with a $T=740$ chronological flow allocation (as PR #3024, #3030, #3051, #3054, #3103, #3115 did for the `{6:16, 7:52}` inventory) should close the remaining `1.4053e-9` integer gap and reach `RELAX-CAP in [0.0017297774946785970118869, 0.0017297774946785970118870]`. +2. **Unlocking the Double Cone Lock on `584` and `590` via joint `B_WARP` re-synthesis:** + In the free operator algebra, entering helpers `584` and `590` can be completely eliminated (`0` gates in `A+B+restore` across all 632 forward and dual inputs), but post-warp cold helpers `273` and `289` (`B_WARP[541, 545]`) pin right consumers `115` and `130` to $W_{\text{right}} = E_{51} \cap E_{67} \cap E_{112}$ ($\dim 7$) while entering helpers `554` and `566` pin left consumers `168` and `214` to $U_{6,\text{left}} \subseteq E_{51} \cap E_{82} \cap E_{97}$ ($\dim 6$). Jointly re-synthesizing `B_WARP[541, 545]` on `273, 289` and the `554, 566` consumer cone is required to align the two 7D cones inside $E_{51}$. +3. **Composing with native-tariff contractions (PR #3056, #3060, #3076):** + Re-addressing the commuting `A`/`restore`/`cleanup` native-tariff contractions from PR #3056, #3060, and #3076 on top of `edits/FINAL-WORD-{base,extra}.json.gz` can lower the native primitive operation count while preserving the `{1:2433, 2:724, 3:228, 4:102, 5:20, 8:8}` paid profile and `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}` width inventory. + +--- + +## Credit + +- **PR #2979 (`mdumitrean`, Marius-Paul Dumitrean)**: the base words, Stage 1–3 producer, rank-7 overlay, cap machinery, and checkers. +- **PR #3015 (`jeremykothe2`, Jeremy Kothe)**: the declared literal edit stage (`edits/`, `tools/build_edits.py`, `edits/edits_review.py`) and edit `R1` (`63` via carrier `61`). +- **PR #3042 (`dcharb78`, with AI assistance)**: the six restore carrier/pivot skips (`R1_E42`, `R2_E7`) on PR #2979's words that serve as the direct starting words for `B_586_438` and `B_588_440`. +- **Inherited lineage**: Jeremy Diviney (PR #2908), Mason Hale (PR #2917), Jeremy Kothe (PR #2966 / #2957 / #2948 / #2894 / #2833), Dugongue (PR #2969 / #2863 / #2839), Marius-Paul Dumitrean (PR #2942 / #2930 / #2843), RossRichardson (PR #2918), Yiyang Lu (PR #2857 / #2848), philippeVV (PR #2853), Gareth Davidson (PR #1995 / #2013), Tekalign (`independent_owners.py`), icekylinx (`audit_local.py`), and themilkman216. +- **New here (`dcharb78`, with substantial AI assistance)**: the coupled `B + restore` dying-helper carrier folds (`B_586_438` and `B_588_440`) and `helper_final` lowerings on `586` and `588`, the single-move negative controls and 91-helper causal exhaustion proofs, the repacked `T74_optimal_idle39` allocation (`allocation/FILL.json.gz`), the 21-control per-word edit review and 100-control four-stage replay, and the complete fresh-native admission and release receipts. Apache-2.0. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3148/research/coupled-carrier-cap740/README.md b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3148/research/coupled-carrier-cap740/README.md new file mode 100644 index 0000000000..f540563133 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3148/research/coupled-carrier-cap740/README.md @@ -0,0 +1,191 @@ +# Attaining the coupled-carrier packing cap at T740 + +Jeremy Diviney, with substantial OpenAI Codex assistance. Apache-2.0. + +**Finite checks and the complete composed release pass.** A new, literal +145-row exchange attains the fixed-inventory packing cap of dcharb78's +[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133) words: + +``` +kappa = 0.001729777494678597011886 - 10^-46 - 10^-70 +root in [0.0017297774946785970118869, + 0.0017297774946785970118870] +``` + +The gain over Gonzalo Mier's more precise, unchanged-T74 +[PR3143](https://github.com/CrocSwap/integer-mult-bounds/pull/3143) claim is +approximately **1.4052734766776475e-9**. `BASELINE-PR3143.json` retains its exact +rational claim at `dcfaf1d1a7cfebaab22b95776a36a543bc684d50`. The PR3133 source +head is `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. Neither pending claim is +described as a selected or independently admitted frontier. + +This contribution is the changed-inventory packing repair, its deterministic +generator and full source/word/allocation binding. It uses Nick Petalas's +existing ten-copy interleaving method, differential checker and cap proof +(PR3024), and the three-allocation-argument integration pattern (PR3030). +PR3133's local words, ordered widths and source validators are unchanged. +The old PR3024 exchange cannot simply be reused on this different inventory. + +The pre-submission overlap refresh found Gonzalo Mier's earlier +[handoff #3145](https://github.com/CrocSwap/integer-mult-bounds/discussions/3145) +and Hiroki Kumazaki's +[stopped transport attempt](https://github.com/CrocSwap/integer-mult-bounds/discussions/3145#discussioncomment-18992630). +That attempt found no matching preimages for the old journals and requested a +new journal generated from the changed fill. This package provides that new +journal, constructed before reading that handoff in detail; it does not dispute +the old-journal failure or claim priority for the T740 objective. No fresh +flow census is required by this particular deterministic repair. PR3143's fill, +provider bytes and both words equal the pinned PR3133 inputs. The complete run +uses PR3133's original endpoint precision and strictly exceeds PR3143's more +precise T74 result. + +## Exact exchange + +Start with ten interleaved copies of PR3133's literal T74 fill. Its three +non-tight bins per copy are two `48:[4,8,9,9,9,9]` bins and one `48:[9]` bin. +Use 25 compatible `32:[9,9,9]` donor bins: + +``` +20 * 48:[4,8,9,9,9,9] + 10 * 48:[9] + 25 * 32:[9,9,9] + -> 20 * 32:[4,9,9,9] + 5 * 32:[8,8,8,8] + + 21 * 48:[9,9,9,9,9] + 9 * 48:[] +``` + +Move the twenty width-4 roles into twenty donor bins. Move the twenty width-8 +roles into five other donor bins, releasing fifteen width-9 roles. Repack those +fifteen and the ninety width-9 roles in the old 48-bins into twenty-one groups +of five. Nine 48-bins become empty. `construct.py` chooses concrete legal bins +deterministically; `EXCHANGE.json` binds every changed row to its exact preimage. + +The exchange changes 145 roles in 55 bins and touches 123 calls. The idle-count +delta is `{1:+20, 3:+21, 5:-25, 39:-10, 48:+9}`. The capacity multiset and each +helper width are preserved. The unchanged full owner checker checks all +**2,717,280** rows, including unchanged bins and calls. Chronological source +availability, compact prefixes, non-overlap and same-call physical-family +exclusion are required; the aggregate identity alone would not suffice. + +## Complete bill and cap + +There are 740 replicas, 6,660 invocations and 408 helpers per invocation. + +| Component | Exact rank counts | +|---|---| +| Local, per invocation | `{1:2433, 2:724, 3:228, 4:102, 5:20, 8:8}` | +| Idle, all replicas | `{1:173160, 3:48951, 5:13875, 48:282569}` | +| Total | `{1:16376940, 2:4821840, 3:1567431, 4:679320, 5:147075, 8:53280, 48:282569}` | + +The total equals 6,660 local bills plus the idle bill, with rank mass +`65088 * 740`. Both literal words derive the ordered helper inventory +`{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}`. The exact forward and dual operator +audit checks 632 independent inputs for each word, frames, restoration and +literal inverse cleanup. + +`cap_check.py` adapts Petalas's exact rational dual proof to this inventory and +local bill. It enumerates all 2,551 patterns and proves strictly positive +reduced cost for 2,539 throughout the root bracket; the same twelve patterns +are tight. The feasible primal basis is PR3133's retained `RELAX-CAP.json`. +Our idle bill is exactly 740 times that basis's idle bill, so the attained +moment and fractional cap are identical, rather than merely close numerically. + +The tight-pattern residue identity now reads +`20 * N_(48:[9,9,9,9,9]) = 1323 * T`. Since `gcd(1323,20)=1`, any cap-attaining +integral packing requires `20 | T`. The first multiple of the retained T74 +chronology satisfying this is 740. This is not a proof that every possible +chronology needs 740 replicas. + +All **91** private cleanup buffers are charged. Physical stock is +`896*740 + 408 + 8 + 91 + 2 = 663549`, compared with PR3133's 66,813. +The larger fixed stock is a material cost of this small exponent improvement. +The complete strict replay rebuilt the actual prefix and outer invoice: the +prefix requirement is 1,479 bits, within the paid 2,048-bit payload. + +## Reproduction and evidence + +The bounded checks use Python 3.12 and its standard library: + +```sh +python3 -B scripts/research_package.py --package research/coupled-carrier-cap740 +``` + +`verify.py` checks the words, all owners, complete moment, exact cap, and stored +release bindings. `test_allocation.py` checks regeneration and semantic failures +(stale or duplicate edits, lost moves, unavailable windows, overlaps, physical +family collisions, unpaid prefix holes and invalid cap data). `test_bindings.py` +checks recipe substitution, stale input rejection, compression portability and +refusal of disabled assertions. Stored receipt validation is not a fresh native +or outer replay. Regenerated fills are compared by their full decoded payload; +immutable source containers retain exact byte hashes. + +For a complete replay, fetch the pinned Git objects in `FETCH.txt`, install +`requirements-full.txt` in a Python 3.12 virtual environment, then use a fresh +output directory: + +```sh +nice -n 15 ionice -c 3 env OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \ + python3 -B research/coupled-carrier-cap740/reproduce.py \ + --repo . --work /tmp/coupled-cap740-new --jobs 2 +``` + +The default bootstraps the retained parent fresh. An explicit `--retained PATH` +reuses the predecessor's authenticated parent/native cache, while rebuilding +both current providers. `--dry-run` exports exact sources, materializes every +row and checks the recipe; it does not claim a release. The full controller +changes exactly `--fill`, `--order`, and `--dispatch` in PR3133's final admission +command. All scientific source stages remain unchanged. + +The recorded full run uses an authenticated retained cache. All eleven source +stages passed in 30.1 minutes with two low-priority single-thread audit +workers. Both current native providers were rebuilt; two retained native +providers and the retained parent were reused explicitly. A full fresh retained +bootstrap was not rerun in this session. Exact logs, raw receipts and scope are +in `evidence/`; `RUN.json` records the executed command. The public exporter, +materializer and recipe dry run also passed independently of this execution. + +## Scope and expansion decision + +This is a conditional finite supplier and outer certificate. The inherited +all-size, compiler, physical/native and analytic multiplication-theorem +obligations remain. No selected record is changed. An archive merge or passing +CI would not establish independent scientific admission. + +The explicit user task was to exceed the strongest reported repository claim. +Before expanding, we reran Arham Tahir's code-disjoint PR3136 coupled-carrier +local audit successfully, pinned both providers and their complete bill, and +bounded the task to the demonstrable packing gap. The changed inventory makes +the old cap witness inapplicable. The acceptance test requires every role, +all buffers and the complete native/physical/prefix/outer release; partial +checks cannot support a released endpoint. See `TASK.json` for the evidence and +obligation ledger. Failed preliminary operator-valued probes are not claimed +as a general obstruction or a new contribution here. + +## Open next questions + +- Independently replay this exact source and allocation and inspect the larger + physical bill before any frontier adoption. Maintainer scientific review and + inherited theorem obligations remain; the first step is the explicit full + reproduction above. +- Can a different chronology realize the same cap with fewer replicas? The + residue certificate permits multiples of 20 but does not construct them. + First build a legal owner-window model at T20; reject candidates that fail + source availability or pay back the saving in physical/prefix costs. +- Further exponent improvement needs changed words, widths, capacities or a + different moment model: this fixed-word packing relaxation is attained. + Start with a concrete paid change and audit both its producer and consumer + before another downstream packing search. + +## Credit + +The coupled folds, literal T74 fill and changed-inventory cap are dcharb78's +PR3133. The underlying joint rank-7 words and relaxation tools are Marius-Paul +Dumitrean's PR2979/2942/2930, building on Jeremy Kothe's rewrites/preload chain, +Mason Hale's paired extension, Jeremy Diviney's paired-extraction certificate, +Yiyang Lu's shared-kernel/flow work, Dugongue's packing lineage, Tekalign's +owner/admission checks and icekylinx's exact operator audit. Petalas supplied +the PR3024 lift/dual argument and PR3030 integration pattern. Gonzalo Mier's +PR3143 supplies the precise comparison claim; Arham Tahir's PR3136 supplied +the separately replayed local audit. Retained source notices and full earlier +credits are in `vendor/PR3133-NOTICE` and `vendor/PR3133-CREDITS.md`. + +The new deterministic exchange, integration and verification work are by +Jeremy Diviney with substantial OpenAI Codex assistance. No independent human +or formal-kernel review is claimed. diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json new file mode 100644 index 0000000000..d9a4f84211 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3251/research/adaptive-kernel-demotion/inputs/DATA-PHASES.json @@ -0,0 +1 @@ +{"cover_correction":{"complete_small_cover_checks":[{"n":1,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":1},{"n":2,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":2},{"n":3,"nonzero_full_kernel_corrections":0,"orthogonal_matrices":6},{"n":4,"nonzero_full_kernel_corrections":24,"orthogonal_matrices":48},{"n":5,"nonzero_full_kernel_corrections":600,"orthogonal_matrices":720}],"formula":"delta(g)_i = (weight(row_i(g))-1)/2 mod 2; apply X_delta(g) to EVERY final live stream in cover class g.","mandatory":true,"reason":"P_g C_all P_g^-1 = C_all X_delta(g) exactly. Orthogonality cancels all quadratic cross terms; both sides fix the uniform vector."},"global_phase_argument":"Every C_q and every linear address permutation fixes the uniform vector. Equality of the exact Z4 Fourier multiplier therefore fixes the scalar phase as 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b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_capture.py new file mode 100644 index 0000000000..3ff37bc7c6 --- /dev/null +++ b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/emit_capture.py @@ -0,0 +1,291 @@ +#!/usr/bin/env python3 +"""Emit sixteen productive centre rows at the exact full frame.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +PARENT = HERE.parent +LANES = PARENT.parents[1] +PINS = { + "native": ( + PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + ), + "capture": ( + LANES / "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7", + ), + "helper": ( + PARENT / "emit_native.py", + "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745", + ), + "cyclic": ( + LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + ), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source " + name) + return raw + + +read("helper") +spec = importlib.util.spec_from_file_location("row_capture_native", PINS["helper"][0]) +n = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = n +spec.loader.exec_module(n) + + +def price(events): + return n.r.price([event[1] for event in events if event[0] == "scalar"]) + + +def verify(word, code, response, captured_response, selected): + current = list(word["start"]) + state = [{p: F(1)} for p in range(640)] + maximum = F(1) + height = 0 + for event in word["events"]: + if event[0] == "native": + _, field, old, new, rank, key = event + need(current[field] == old, "The exact native entry frame") + need(len(n.basis(word["frames"][old] + word["frames"][new])) + == len(word["frames"][new]), "A nested native frame") + need(rank == len(word["frames"][new]) - len(word["frames"][old]) + == word["native_recipes"][key]["rank"], "The exact native rank") + current[field] = new + else: + need(event[0] == "scalar", "The event grammar") + gate, frame = event[1:] + op, target, source, coefficient = gate + coefficient = F(coefficient) + need(current[target] == frame, "The exact scalar target frame") + if op == "add": + need(source != target and current[source] == frame, "The exact current source frame") + n.r.add(state[target], state[source], coefficient) + else: + need(op == "scale", "Only dyadic scalar instructions") + state[target] = {p: coefficient * value for p, value in state[target].items()} + maximum = max(maximum, sum(abs(value) for value in state[target].values())) + for value in state[target].values(): + denominator = value.denominator + need(denominator & (denominator - 1) == 0, "No odd denominator") + height = max(height, denominator.bit_length() - 1) + expected = [{p: F(1)} for p in range(640)] + for p in range(112): + if p in selected: + expected[112 + p] = {112 + j: value for j, value in code[p].items()} + n.r.add(expected[112 + p], captured_response[p]) + else: + n.r.add(expected[112 + p], response[p]) + need(state == expected, "All640 independent arbitrary input columns") + need(current == word["final"], "All complete output frames") + need(state[224:] == [{p: F(1)} for p in range(224, 640)], "All416 helpers are unchanged") + profile = Counter(event[4] for event in word["events"] if event[0] == "native") + return { + "arbitrary_input_columns": 640, "unchanged_source_fields": 112, + "unchanged_arbitrary_helper_fields": 416, "selected_full_targets": len(selected), + "ordinary_hole_targets": 112 - len(selected), "native_profile": dict(sorted(profile.items())), + "native_children": sum(profile.values()), "native_mass": sum(k * v for k, v in profile.items()), + "native_side_map_upper_bound": 2 * sum(profile.values()), + "explicit_input_monomial_views": len(word["input_views"]), + "explicit_output_monomial_views": len(word["output_views"]), + "real_scalar_primitives": price(word["events"]), + "scalar_stage_prices": {stage: price(word["events"][start:stop]) + for stage, (start, stop) in word["stage_ranges"].items()}, + "maximum_content_prefix_row_one_norm": str(maximum), + "additional_content_binary_height": height, + "owned_fields": 0, "private_fields": 0, "fixed_odd_scans": 0, + } + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + source = json.loads(read("native")) + capture = json.loads(read("capture")) + cyclic = json.loads(read("cyclic")) + selected_list = capture["pivots"] + selected = set(selected_list) + need(selected_list == [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23], + "The fixed physical pivot set") + code, inverse_code = n.rows(capture["code"]), n.rows(capture["code_inverse"]) + response, captured = n.rows(capture["response"]), n.rows(capture["selected_capture_response"]) + need(response == n.rows(source["model"]["response"]), "The exact native response") + need(n.r.product(code, response) == captured, "The ordered captured response C E") + need(n.r.product(code, inverse_code) == n.r.product(inverse_code, code) == n.r.identity(112), + "Both row-code inverse orders") + for p in range(112): + if p in selected: + need(code[p].get(p) == 1 and set(code[p]) & selected == {p}, "Normalized row shear") + multiplier = F(-5 if selected_list.index(p) < 8 else -7) + need(captured[p] == {j: multiplier * value for j, value in code[p].items()}, + "The actual centre left eigenvector") + else: + need(code[p] == {p: F(1)} and captured[p] == response[p], "The ordinary rows stay unchanged") + for pair in cyclic["pair_codes"]: + ports = set(pair["ports"]) + need(not ports & selected or ports <= selected, "No selected physical pair is split") + fresh_phases = 0 + words, reports, removals = {}, {}, {} + for provider, directions in source["providers"].items(): + original = directions["forward"] + frames = original["frames"] + need(frames[0] == [] and len(frames[1]) == 9, "The exact I and FULL frames") + full = n.compiler.canonical_frame(9, tuple(frames[1])) + full_recipe, _ = n.compiler.lower_child(full) + need(full_recipe["rank"] == 9, "An explicit full rank-nine child") + n.phase.equal(n.phase.recipe(full_recipe), n.phase.frame(frames[1], 9), + "Exact new full-frame child " + provider) + n.phase.equal(n.phase.frame(frames[1], 9), n.phase.fourier(9), + "The selected FULL exit has the exact F9 phase " + provider) + fresh_phases += 2 + selected_fields = {112 + p for p in selected} + kept, deleted, retained_indices = [], [], [] + for index, event in enumerate(original["events"]): + target = event[1] if event[0] == "native" else event[1][1] + if target in selected_fields: + deleted.append(event) + else: + if event[0] == "scalar" and event[1][0] == "add": + need(event[1][2] not in selected_fields, "No retained read of a selected target") + kept.append(event) + retained_indices.append(index) + pre = [] + for op, target, source_index, coefficient in capture["scalar_word"]: + need(target in selected and (op != "add" or source_index not in selected), + "The precode uses only current ordinary Y sources") + pre.append(["scalar", [op, 112 + target, None if source_index is None + else 112 + source_index, coefficient], 0]) + events = pre + deepcopy(kept) + ranges = {"precode": [0, len(pre)], "retained_core": [len(pre), len(events)]} + current = list(original["start"]) + for event in kept: + if event[0] == "native": + need(current[event[1]] == event[2], "The retained frame path is continuous") + current[event[1]] = event[3] + need(all(current[p] == 1 for p in range(112)), "All112 sources are FULL at the query cut") + need(all(current[112 + p] == 0 for p in selected), "The selected target baselines remain in I") + start_full = len(events) + for p in selected_list: + events.append(["native", 112 + p, 0, 1, 9, "capture-full"]) + ranges["selected_full_progress"] = [start_full, len(events)] + start_query = len(events) + for op, target, source_index, coefficient in capture["final_query_word"]: + need(op in ("add", "scale") and target in selected, "The fully dyadic final query") + if op == "add": + need(112 <= source_index < 224, "The final query reads a completed X source") + events.append(["scalar", [op, 112 + target, None if source_index is None + else source_index - 112, coefficient], 1]) + ranges["late_query"] = [start_query, len(events)] + used = {event[5] for event in kept if event[0] == "native"} + recipes = {key: original["native_recipes"][key] for key in sorted(used)} + recipes["capture-full"] = full_recipe + input_views, output_views = [], [] + for record in original["endpoint_adapters"]: + p = record["port"] + if record["role"] == "source": + need(record["frame"] == original["start"][p] and record["rank"] == 0, + "The pinned physical input adapter") + input_views.append(record) + elif p not in selected: + conventional = n.compiler.cgate(9, source["model"]["ports"][p], -1).then( + n.compiler.fourier(9)) + canonical = n.compiler.canonical_frame(9, tuple(frames[record["frame"]])) + operation = canonical.adjoint().then(conventional) + recipe, _ = n.compiler.lower_child(operation) + need(recipe["rank"] == 0, "An explicit ordinary physical output view") + circuit = n.phase.adjoint(n.phase.frame(frames[record["frame"]], 9)) \ + + (("C", source["model"]["ports"][p], -1),) + n.phase.fourier(9) + n.phase.equal(n.phase.recipe(recipe), circuit, "Exact ordinary output view") + fresh_phases += 1 + output_views.append({"port": p, "frame": record["frame"], "recipe": recipe, + "circuit": circuit}) + final = list(original["final"]) + for p in selected: + final[112 + p] = 1 + word = {"start": original["start"], "final": final, "frames": frames, "events": events, + "native_recipes": recipes, "input_views": input_views, "output_views": output_views, + "stage_ranges": ranges, "retained_original_event_indices": retained_indices, + "new_full_recipe_circuit": n.phase.frame(frames[1], 9)} + report = verify(word, code, response, captured, selected) + need(report["native_profile"] == {1: 1392, 2: 64, 3: 48, 9: 16}, "The full native invoice") + need(report["scalar_stage_prices"] == {"precode": 1760, "retained_core": 6456, + "selected_full_progress": 0, "late_query": 3424}, + "The full literal scalar invoice") + need(report["real_scalar_primitives"] == 11640 and report["native_mass"] == 1808, + "The complete local prices") + need(len(input_views) == 112 and len(output_views) == 96, "All actual boundary views") + words[provider], reports[provider] = word, report + removals[provider] = {"events": len(deleted), "native_profile": dict(Counter( + event[4] for event in deleted if event[0] == "native")), + "scalar_primitives": price(deleted), "no_retained_selected_target_read": True} + for stage in ("precode", "late_query"): + bad = deepcopy(word) + index = next(i for i in range(*ranges[stage]) if bad["events"][i][0] == "scalar" + and bad["events"][i][1][0] == "add") + del bad["events"][index] + try: + verify(bad, code, response, captured, selected) + except ValueError: + pass + else: + raise ValueError("An omitted " + stage + " term was accepted") + payload = { + "schema": "productive-sixteen-full-capture-v1", + "source_pins": {name: {"path": str(path), "sha256": pin} for name, (path, pin) in PINS.items()}, + "ports": source["model"]["ports"], "selected_ports": selected_list, + "ordinary_ports": sorted(set(range(112)) - selected), "code": capture["code"], + "inverse_code": capture["code_inverse"], "response": capture["response"], + "captured_response": capture["selected_capture_response"], "providers": words, + "physical_contract": { + "input": "X_p=Q_p x_p; Y_p=y_p; all416 helpers arbitrary", + "source_output": "X_p=F9 x_p for all112 ports", + "ordinary_target_output": "Y_p=F9 q_p (y+E x)_p for p outside P", + "selected_target_output": "Y_p=F9 [C(y+E x)]_p for p in P", + "helpers": "All416 unchanged; no owned or private field", + }, + } + data = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(data) + for provider, word in saved["providers"].items(): + need(verify(word, code, response, captured, selected) == reports[provider], + "The complete serialized replay") + (args.out / "PRODUCTIVE-CAPTURE.json.gz").write_bytes(gzip.compress(data, mtime=0)) + receipt = { + "status": "PASS_COMPLETE_PRODUCTIVE_FULL_CAPTURE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(data).hexdigest(), + "source_pins": payload["source_pins"], "reports": reports, "removed_events": removals, + "fresh_phase_checks": fresh_phases, "negative_controls": ["omitted precode ADD", "omitted late-query ADD"], + "scope": "Complete local arbitrary-baseline capture with exact changed output phases. No next-stage I-frame claim, recursive hosting or final supplier improvement.", + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz b/research/phase-coded-callers/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/reuse-normal/LINE-ENTRY-REUSE.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..dd14386af97237ad6ac139d078374d21549a3a9c GIT binary patch literal 144819 zcmXt<19T_PLF_(ZtWA zDyumD;m?;N(R0#RD)GZHUwa#@B}(3HG#*rG{sOAVf`3N`j0XR14`y<^KObIt{@owF z>$D*l6@avB^lyOpmI17R~ 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