From 4f2ef2e623de0aac147b43c03222f3e4a7ab6d2c Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 12:57:37 -0500 Subject: [PATCH 1/3] Prove ordered centre interfaces and price complete D25 terminals --- .../DIRECT-SOURCES.json | 70 + research/ordered-centre-interfaces/NOTICE.md | 55 + .../PACKAGE-SHA256.json | 144 + .../PORTABLE-ADAPTATION.json | 8 + .../PORTABLE-ADAPTATION.patch | 28 + research/ordered-centre-interfaces/PROOF.md | 293 + research/ordered-centre-interfaces/README.md | 123 + .../ordered-centre-interfaces/RESULT.json | 31 + .../ordered-centre-interfaces/SOURCES.json | 912 ++ .../ordered-centre-interfaces/frozen/LICENSE | 201 + .../ordered-centre-interfaces/frozen/NOTICE | 415 + .../frozen/archive-members/DATA-PHASES.json | 1 + .../upstream/build/sections/05-layers.tex | 996 ++ .../BRIDGE-PROGRAMS.json.gz | Bin 0 -> 119955 bytes .../matched-stage-access-20261018/CHECKS.json | 238 + .../DIMENSION25-CHECKS.json | 57 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endpoints for every positive pair count; exact content decoder reductions.", + "proof": [ + "controller-review-20261017/REVIEW.md", + "controller-review-20261017/DECODER-REDUCTION.md" + ], + "checks": [ + "controller-review-20261017/check_review.py", + "controller-review-20261017/check_decoder.py" + ], + "boundary": "Content identities and stated finite matrix checks. No native decoder, idle access, owner schedule, or kappa claim." + }, + { + "id": "current_and_general_unit_codes", + "claim": "Five scalar codes give the ordered one-pair endpoint and its exact physical residual.", + "proof": [ + "encoded-controller/one-pair-current-codes-20261018/ONE-PAIR.md", + "encoded-controller/one-pair-general-units-20261018/GENERAL-UNITS.md" + ], + "checks": [ + "encoded-controller/one-pair-current-codes-20261018/check_and_emit.py", + "encoded-controller/one-pair-general-units-20261018/check_general_units.py" + ], + "boundary": "The native local responses and common-frame scalar access are separate explicit premises." + }, + { + "id": "physical_monomial_compiler", + "claim": "Complete-state monomial coordinate compiler and the exact line-flag obstruction for the pinned transfer.", + "proof": [ + "encoded-controller/physical-monomial-compiler-20261018/PHYSICAL-MONOMIAL-CODES.md" + ], + "checks": [ + "encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py", + "encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py" + ], + "boundary": "The compiler requires admitted composed maps. The finite prefix screen does not cover all stabilizer choices." + }, + { + "id": "retained_helper_completion", + "claim": "Retain 408 independent helper paths with profile {1:1609,2:512,3:172,4:33} and mass 3281.", + "proof": [ + "encoded-controller/retained-helper-completion-20261018/HELPER-COMPLETION.md" + ], + "checks": [ + "encoded-controller/retained-helper-completion-20261018/check_and_emit.py" + ], + "boundary": "Exact local disjoint composition. Global owner hosting and the native phase compiler remain inherited premises." + }, + { + "id": "d25_access_and_paid_completion", + "claim": "224-role D25 admission; exact separated and mixed terminals; both complete profiles have mass 5600 and fail every positive native moment.", + "proof": [ + "history-encoding/one-pair-admission-20261018/ONE-PAIR-ADMISSION.md", + "bridge-review-20261017/matched-stage-review-20261018/ACCESS-REVIEW.md", + "bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.md" + ], + "checks": [ + "history-encoding/one-pair-admission-20261018/check_admission.py", + "bridge-review-20261017/matched-stage-review-20261018/check_access.py", + "bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py" + ], + "boundary": "The row and LIFO proof is inherited. No complete precision, map, tape, integer-recovery, or kappa invoice." + } + ] +} diff --git a/research/ordered-centre-interfaces/NOTICE.md b/research/ordered-centre-interfaces/NOTICE.md new file mode 100644 index 0000000000..f0f56d56b8 --- /dev/null +++ b/research/ordered-centre-interfaces/NOTICE.md @@ -0,0 +1,55 @@ +# 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 controller-followthrough lane supplied the raw and weighted content +controllers. The controller-review lane supplied the separate ordered +normal-form and decoder proofs. The encoded-controller lane supplied +the current/general unit codes, the physical monomial compiler and +line-flag result, and the retained helper completion. The history lane +supplied the independent skeleton and one-pair role/row admission. The +bridge-access lane supplied the actual D25 views and mixed terminal. +The independent-review lane supplied the cheaper scalar code and native +phase review. The bridge-review lane supplied the separate D25 access, +terminal, and hosting review. The oblique and controller lanes supplied +the local matched response; the history lane supplied its 64-port +permutation component. These are contribution records within the same +AI-assisted campaign, not separate human author identities. + +The retained provider lineage comes from +[PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133) +at `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. Its source README and +manifest retain dcharb78's work and the preceding contributions. The +byte-equal provider copies used by the campaign 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. The exact source README files and +manifests are retained under `frozen/` and listed in `SOURCES.json`. + +The exact Clifford implementation comes from +[PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), +commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`, at the +[pinned source path](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py). +The campaign's native-source notice also 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. That full notice is retained as +[NATIVE-LIFT.md](frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/NATIVE-LIFT.md). + +The primary stream proof is the unchanged historical +`upstream/build/sections/05-layers.tex` with SHA256 +`20cfc8d12099d4e4ed9e3e7eeb6162edd9b6e0e076f24693364cd24377252594`. +The repository's full source and attribution notices are retained as +[NOTICE](frozen/NOTICE) and [LICENSE](frozen/LICENSE). Their preceding +contributor credit remains in force. Historical claims in those source +notices do not become claims of this package. + +The original source files remain byte-exact. The sole adapted checker +changes its input location and archive-member read. The original bytes, +adapted bytes, and complete diff are retained. The package replay does +not update a historical pin to the new selected construction. diff --git a/research/ordered-centre-interfaces/PACKAGE-SHA256.json b/research/ordered-centre-interfaces/PACKAGE-SHA256.json new file mode 100644 index 0000000000..c619092c03 --- /dev/null +++ b/research/ordered-centre-interfaces/PACKAGE-SHA256.json @@ -0,0 +1,144 @@ +{ + "schema": "ordered-centre-package-hashes-v1", + "files": { + "DIRECT-SOURCES.json": "11251b6007f3b09cd09599a9e984db4d80723a317b663d66cfe8d82aba720294", + "NOTICE.md": "dd74b007f461cbafa057766011f16aba09e6218c260ce438417e4ca9e2a2af9c", + "PORTABLE-ADAPTATION.json": "362e7f2c968e4572456bfe2e15a02f0cb55ecdfdf8d95453c0489de029d2278a", + "PORTABLE-ADAPTATION.patch": "5c463f9629da7f69d1c5d315cd8826c52d34e9a28359d050db1ac5a6fc8700c7", + "PROOF.md": "127508fe1217eb2010886bbba2faaae8c8565137dba1dc3454279436cd315621", + "README.md": "71812d5396504e0e312528b42f0d66dad38193b65714e174bdbe0373dd9896a9", + "RESULT.json": 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"3e2848315417072d8ad01b2cbc6ebe22b87c832157f0054ed4bd4586b8342b63", + "portable/check_access.py": "877e5cdc08d6d9ee3b77b5927dae4d8ec979c2c5da4a7add5f306dc51c1a4630", + "replay.py": "689bf40a6f019e8a8e82b8d8d6188ee1faacc5fabe458190b0b63d1fa40d8fa4", + "validation/REPLAY.json": "225be7d22cd39cc07d81cea67bd8a8388baaa4adf2bacaedc8fde137343578fc" + } +} diff --git a/research/ordered-centre-interfaces/PORTABLE-ADAPTATION.json b/research/ordered-centre-interfaces/PORTABLE-ADAPTATION.json new file mode 100644 index 0000000000..a02a43b328 --- /dev/null +++ b/research/ordered-centre-interfaces/PORTABLE-ADAPTATION.json @@ -0,0 +1,8 @@ +{ + "schema": "portable-access-adaptation-v1", + "original": "frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_access.py", + "original_sha256": "0927b3ec17d4e277b05ed62be48bd4710297960fec5f7eb2ea0066cfb571d71f", + "portable": "portable/check_access.py", + "portable_sha256": "877e5cdc08d6d9ee3b77b5927dae4d8ec979c2c5da4a7add5f306dc51c1a4630", + "scope": "Change only the source root and the archive-member read. Keep the exact DATA member hash and every mathematical check. The source archive hash was checked at extraction and is retained in SOURCES.json." +} diff --git a/research/ordered-centre-interfaces/PORTABLE-ADAPTATION.patch b/research/ordered-centre-interfaces/PORTABLE-ADAPTATION.patch new file mode 100644 index 0000000000..f4b4ad1531 --- /dev/null +++ b/research/ordered-centre-interfaces/PORTABLE-ADAPTATION.patch @@ -0,0 +1,28 @@ +--- frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_access.py ++++ portable/check_access.py +@@ -6,10 +6,9 @@ + import gzip + import json + from pathlib import Path +-import tarfile +- +- +-HERE = Path(__file__).resolve().parent ++ ++ ++HERE = Path(__file__).resolve().parents[1] / 'frozen' / 'work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018' + CHECKER_SHA = sha256(Path(__file__).read_bytes()).hexdigest() + LANES = HERE.parents[1] + ROOT = LANES.parents[2] +@@ -135,10 +134,7 @@ + packed = pin(LANES/"bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", "views_compressed") + original_views = json.loads(gzip.decompress(packed))["views"] + views = {(v["stage"],v["port"],v["side"]):v for v in original_views} +- archive = ROOT/"worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz" +- pin(archive, "archive") +- with tarfile.open(archive) as source: +- raw = source.extractfile("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json").read() ++ raw = (ROOT / "archive-members/DATA-PHASES.json").read_bytes() + need(sha256(raw).hexdigest() == PINS["data"], "Actual DATA phase source") + data = json.loads(raw)["recipes"] + dimensions = json.loads((ACCESS/"DIMENSION25-VIEWS.json").read_text()) diff --git a/research/ordered-centre-interfaces/PROOF.md b/research/ordered-centre-interfaces/PROOF.md new file mode 100644 index 0000000000..6097907b61 --- /dev/null +++ b/research/ordered-centre-interfaces/PROOF.md @@ -0,0 +1,293 @@ +# Exact ordered interfaces and complete endpoint costs + +This proof uses left actions on column contents. A product `AB` means +that `B` acts first. An inverse is used only next to its own operator. +Different stage operators need not commute. + +The source contracts, all-size row compiler, and native recipe phases +are explicit premises where stated below. None is inferred from a +small scalar matrix or from a successful finite replay. + +## 1. Raw and weighted normal forms + +The full all-pair proofs are retained in the +[independent controller review](frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/REVIEW.md). +Its [decoder proof](frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/DECODER-REDUCTION.md) +gives the complete inverse formulas. Both proofs cover every positive +pair count. They state the selected and ordinary field types separately. + +Here is the mechanism needed to interpret those results. Write each +input pair as `(a,u;b,v)`, with `a,b` selected and `u,v` ordinary. +The physical exchange acts as `(a,b)->(Q^-1 b,Qa)`. For a weighted +local response + +```text +J_s = [[R_s,L_s],[C_s,H_s]], K_s=H_s^-1, +``` + +the backward core and ordinary `K_s` factor give + +```text +h=Q^-1 b-R_s Q a-L_s v, +w=K_s u-v-K_s C_s Q a, +d=Qa. +``` + +A selected update `h-=L_s w` gives + +```text +h=Q^-1 b-L_s K_s u-(R_s-L_s K_s C_s)Qa. +``` + +This is a substitution in the displayed order. It does not move `Q` +through a stage matrix. Preparing the ordinary forward input by `H_t` +and applying its two physical exchanges gives ordinary retirement + +```text +r_i = H_ti H_si^-1 (x_i-C_si Q a_i)+C_ti a_i. +``` + +Thus the exact ordered ordinary inverse is + +```text +x_i = H_si H_ti^-1 (r_i-C_ti a_i)+C_si Q a_i. +``` + +The suffix recurrence and the descending final triangle in the full +review prove all remaining selected and ordinary endpoints. The full +decoder proof then recovers both original banks. The inverse can read +retired ordinary Y. It is not a native implementation of that read. + +For the raw model, fix original X at zero. After the stated unit +triangular output changes, the original-Y map is a direct sum of + +```text +M_s = [[Q^-1,B_s],[-D_s Q^-1,-I]], B_s D_s=13I_d. +``` + +Eliminate its lower-left block. The Schur complement is `-I+D_s B_s`. +The rectangular determinant identity gives + +```text +det(-I+D_s B_s)=(-1)^(n+d) 12^d. +``` + +With `Q` a unit at 3, each diagonal block has determinant valuation +`d`, and the causal `m`-pair map has valuation `dm`. Over characteristic +3, `B_sD_s=I`; hence `D_sB_s` is an idempotent of rank `d`. Each block +has nullity `d`, and the stated matched-bridge normal form has nullity +`dm`. The general causal determinant claim alone does not imply that +nullity. The explicit normal form is required. + +This is an obstruction to a square dyadic inverse from the restricted +completed-X observation. It is not a characteristic-zero singularity, +a native-child lower bound, or a restriction on a decoder that also +reads retired Y. An odd-denominator grid has a separate cost question. + +## 2. Five scalar codes for arbitrary unit responses + +Assume the following three native local maps and the required in-place +scalar codes are available at their stated common-frame cuts: + +```text +F0(x,y)=(x,y+E0x), +B1(x,y)=(x-G1y,y), +F2(x,y)=(x,y+E2x), +``` + +where `E0,G1,E2` are units. Execute, in chronological order, + +```text +F0; X<-E0X; Y<-G1^-1Y; B1; +X<-G1^-1X; Y<-E2Y; F2; X<-G1X. +``` + +After the first two operations the state is `(E0x,y+E0x)`. +After the first Y code and B1 it is `(-y,G1^-1(y+E0x))`. +The next two codes give +`(-G1^-1y,E2G1^-1(y+E0x))`. The last native call cancels +the original-Y part of Y, and the last X code gives + +```text +(-y,Tx), T=E2 G1^-1 E0. +``` + +No transpose, involution, or cross-stage equality is needed. The exact +content closure condition is `T=I`. A native transpose pair is covered +by `G1=E1^T`, provided its inverse scalar code is supplied. + +At the physical boundary let `W=diag(Q,I)`, let `q=Q^-1`, and let the +preterminal frame be `F diag(I,q)`. The retained signed exchange is + +```text +A=[[0,Q^2],[-I,0]]. +``` + +Direct multiplication gives + +```text +A diag(I,q) [[0,-I],[T,0]] W^-1 = diag(Q T Q^-1,I). +``` + +Thus the first-bank decoder is `Q T^-1 Q^-1`. Its chronological +operations are `Q^-1,E2^-1,G1,E0^-1,Q`. The order is part of the +claim. Equal local coefficient matrices do not establish equal routed +operators. The proof and its scalar circuit example are retained in +[GENERAL-UNITS.md](frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/GENERAL-UNITS.md). + +The matched native instance has `G1=E1^-1`, so `T=E2E1E0`. Its five +codes use current Y entrance cuts and current or past completed X cuts. +The actual D25 route and phase check admits all five occurrences. The +original 2,668-primitive code and the separately reviewed 2,396-primitive +code implement the same local matrix. Those prices exclude view costs. + +## 3. Complete-state physical monomial compiler + +Let `G_j` be one operation of an admitted physical program. Include +every productive, arbitrary helper, and owned field in the state. +Assume a replacement `W_j=H_jG_j`, where `H_j` is an admitted physical +monomial and preserves the owned-zero subspace. Set `C_0=I`. Execute + +```text +C_j W_j C_j^-1, C_(j+1)=C_j H_j. +``` + +If the current state is `C_jz`, the new state is +`C_jH_jG_jz=C_(j+1)G_jz`. Induction proves the entire program. +Applying `C_final^-1` gives the original raw endpoint. The order +`C_jH_j` is necessary. Every later use of each field, including its +use as a helper, must use the same coordinate change. + +This statement preserves a native child rank only when the composed +field, cover, and payload maps remain in the admitted map grammar. +Scalar work, map descriptors, stock, owner hosting, and precision +still need an invoice. A general permutation of payload columns or +an exchange of live and owned roles is not admitted by this theorem. + +For reciprocal logical shears, `D(E)=diag(I,E)` gives +`F_E D(E)=D(E)F_I` and `B_(E^-1)D(E)=D(E)B_I`. A physical use requires +both `Phi_in D(E) Phi_in^-1` and `Phi_out D(E) Phi_out^-1` to be +admitted monomials. Logical monomiality of `E` is insufficient. + +The exact line-flag result explains the failure in the pinned transfer. +For odd binary vectors `a,b`, write `P_a=aa^T`, `P_b=bb^T`, and let +`G` be invertible. If `b^TGa=0`, the upper-right symplectic block of +`F_n C_b^-1 K_G C_a^-1` is + +```text +(I+P_b) G^-T (I+P_a), +``` + +of rank `n-2`. The first projection has image `a^perp`; its image under +`G^-T` contains `b`, so the last projection removes one more dimension. +After multiplication by `F_n^-1`, that block is + +```text +P_b G(I+P_a)+(I+P_b)G^-T P_a. +``` + +Under the same orthogonality condition its two summands have independent +nonzero image lines, so its rank is two. The general zero-rank condition +is `G^Tb=a`. The actual 112 transfers for each provider have ranks +seven and two, respectively. The retained proof also states the exact +scope of the finite canonical-prefix screen. It does not exclude other +stabilizer choices or a changed multicall construction. See +[PHYSICAL-MONOMIAL-CODES.md](frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/PHYSICAL-MONOMIAL-CODES.md). + +## 4. Retained helper completion + +The helper packet keeps each event on live roles 224 through 631 in +the frozen independent skeleton. It also keeps all residual wrappers, +91 private allocations and returns, 16 owned clears, and phase markers. +It removes every data event. No retained event reads a data role or +couples two helpers. + +For helper `h`, each child changes frame by `T_new T_old^-1`; each +signed warp changes it by `T_new K^epsilon T_old^-1`. The path is +therefore `T_f W_h T_i^-1`. Every ordered warp word `W_h` cancels by +adjacent inverse pairs. The exact map is `T_f T_i^-1`, with the +original phase and residual wrappers. A proper exit is not changed +to FULL. Arbitrary helper contents are allowed. + +Let a new data word act only on the 224 data roles and satisfy the +same physical data entrance and exit types. Give each private or +owned use a checked lifetime. Run the helper completion, return its +private stock, then run the data word. Their live operators act on +disjoint factors, so their product has both required contracts. + +The helper profile is `{1:1609,2:512,3:172,4:33}`: 2,326 children +and mass 3,281. Its private-zero peak remains 91. The stated scalar +and map inventory must be added to the data invoice. This composition +does not prove a global owner schedule. Full details are in +[HELPER-COMPLETION.md](frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/HELPER-COMPLETION.md). + +## 5. Actual D25 admission and paid terminal + +The matched native payload uses only roles 0 through 223 in both +providers and directions. Every other slot has no event and keeps its +frame. Thus the data word is an exact direct summand for arbitrary +values in those slots. Each data field has total native rank eight. +The local profile is `{1:160,2:48,5:48,7:112,8:64}`, with mass 1,792. +Its physical types are `X_p:C_qp->F9` and `Y_p:I->F9 C_qp^-1`. +The source endpoint adapters are part of those types. + +Use independent fields `(side,port,h)` with `h` in `G=O(25,2)`. +At a stage body `d`, the owner is `h=d rho_(s,p)`. Right multiplication +by the checked route is a bijection. Distinct side-port families are +disjoint. A complete cover sweep therefore partitions the productive +stock. The next sweep begins after the previous one ends. + +The route check covers all 336 records, 672 entry identities, 672 exit +identities, 336 future-Y views, and 672 past-X views. Its Z4 phase +polynomials keep the full scalar phase. The regular cover has order +`2^144 product_(j=1..12)(2^(2j)-1)`, and the productive row count is +`224|G|`. The row split and LIFO arguments in the pinned primary source +apply to arbitrary roles of this finite count. The complete asymptotic +theorem from that source also requires a strict native moment inequality; +the present construction fails that requirement. + +For the separated terminal, apply 112 inverse intrinsic lines, the +three stage inverse codes, then 112 positive intrinsic lines. If `q` +is nonzero, choose an invertible binary chart with first column `q`. +Conjugation of the first-coordinate line implements `C_q`, and +`C_q^-1=X_qC_q` supplies the exact inverse phase. This gives 224 +rank-one children with no new field. + +The mixed terminal uses the actual invariant sets of 48 dense ports +and 64 permutation ports. On the dense set, the separated construction +uses 96 rank-one children and three restricted scalar codes. On each +permutation path, the exact kernel is + +```text +-X_(delta+b) P_G H2 P_G^-1 P_A. +``` + +The two leading columns of the checked orthogonal chart are its distinct +orthogonal line vectors `a,b`. Expanding the two line kernels checks +all four Gaussian rational coefficients and translation vectors. +These 64 paths form a field-and-cover bijection and use 64 rank-two +children. The sign and the inverse-line translation are required. + +Both terminals add mass 224 to the three-call mass 5,376. For every +positive `b` and every paid child rank `r<25`, + +```text +r^(1-b) > r*25^(-b). +``` + +Summing either complete profile gives + +```text +sum_r n_r r^(1-b) > 5600*25^(-b) = 224*25^(1-b). +``` + +The cover factor multiplies both sides. Hence both specified completed +words fail every positive native moment. Scalar and map costs cannot +reverse that failure. This is not a lower bound for every decoder. + +The complete source proof and independent review are retained in +[ONE-PAIR-ADMISSION.md](frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/ONE-PAIR-ADMISSION.md) +and [TERMINAL-HOSTING-REVIEW.md](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.md). +Arbitrary-size grouping, remainder handling, depth bounds, finite +coefficient width, map prices, and exact integer recovery remain +inherited or open obligations. No complete kappa improvement follows. diff --git a/research/ordered-centre-interfaces/README.md b/research/ordered-centre-interfaces/README.md new file mode 100644 index 0000000000..9190973a6d --- /dev/null +++ b/research/ordered-centre-interfaces/README.md @@ -0,0 +1,123 @@ +# Ordered centre interfaces and their paid endpoints + +This package gives exact controller identities, a conditional physical +coordinate compiler, and a checked one-pair endpoint with its full native +rank cost. It retains results from the October 2026 centre campaign. It +does not improve the complete multiplication exponent or certify a new +selected result. + +The concrete endpoint uses 224 independent productive roles over the +regular cover of dimension 25. Three native calls leave the ordered code +`Q E2 E1 E0 Q^-1` on one output bank. Two explicit terminal constructions +remove that code. Both have total native rank mass `5600 = 224*25` and +fail the native moment inequality for every positive improvement exponent. +This is a limit of these two complete constructions. A cheaper decoder +is not excluded. + +[PROOF.md](PROOF.md) states the claims and their assumptions. +[DIRECT-SOURCES.json](DIRECT-SOURCES.json) maps each claim to its full +proof and decisive checker. [SOURCES.json](SOURCES.json) binds every +retained byte. The complete original proofs and source reviews are in +`frozen/`; they are unchanged. + +## Results and boundaries + +| Result | Exact scope | +| --- | --- | +| Raw and weighted controller normal forms | Ordered content endpoints for every positive pair count. The raw dyadic obstruction and mod-3 nullity have the stated restricted observation class. | +| Current-stage and general-unit scalar codes | Five scalar codes give `(-y,E2 G1^-1 E0 x)`. The physical residual is `diag(Q E2 G1^-1 E0 Q^-1,I)`. Required local native and scalar access contracts remain explicit. | +| Physical monomial compiler | A complete-state coordinate change is valid when each physical code and composed map belongs to the admitted grammar. The pinned independent-path transfer fails the required local line-flag condition. | +| Retained helper completion | 408 arbitrary helper fields retain their exact productive maps. The helper profile has 2,326 children and rank mass 3,281. This is a separate local completion contract. | +| One-pair D25 admission and terminals | Exact data-only stock, route phases, scalar access, terminal kernels, and inherited row/LIFO hosting. Both paid profiles fail every positive native moment. | + +The helper completion does not add 408 productive fields to the data-only +D25 word. These are distinct contracts. The D25 word has no helper event; +the completion is available when a different data word must retain the +old 632-role local contract. + +The cheaper scalar code costs 2,396 real primitives. The separated and +mixed terminal choices have the following component totals per cover: + +| Terminal | Additional children | Complete native profile | Scalar subtotal | +| --- | --- | --- | ---: | +| Separated line passes | 224 of rank 1 | `{1:704,2:144,5:144,7:336,8:192}` | 28,264 | +| Mixed terminal | 96 of rank 1 and 64 of rank 2 | `{1:576,2:208,5:144,7:336,8:192}` | 25,896 | + +These scalar subtotals cover the three local words and their stated code +operations. They exclude the old signed exchange, global cover work, +all finite map prices, recursive work areas, and precision. The mixed +terminal has a separate inventory of 608 map calls. A map count is not +a finite real-operation price. + +## Replay + +Python 3.11 or later and its standard library are sufficient. Run one +process. The output directory must not exist. Keep at least 3 GiB free. + +```text +python3 -I -B replay.py --out /tmp/ordered-centre-replay +``` + +The command runs ten checks, first normally and then with `python -O`. +It uses isolated temporary copies and does not change the frozen files. +It checks each source hash, compares each fresh receipt with its frozen +receipt, and compares the normal and optimized outputs. For gzip output +it compares the decompressed bytes. The final line must be: + +```text +PASS_ORDERED_CENTRE_INTERFACES +``` + +`--mode normal`, `--mode optimized`, and `--only NAME` permit a focused +replay. The receipt records the selected checks, so a partial command +does not assert a complete package replay. + +One source-read change is needed for portable replay. The D25 access +checker reads the exact `DATA-PHASES.json` member from a retained file +instead of opening the large historical archive. Its member hash and +every mathematical check are unchanged. The original archive hash was +checked at extraction. The original checker, the adapted checker, and +the exact diff are retained in [PORTABLE-ADAPTATION.json](PORTABLE-ADAPTATION.json) +and [PORTABLE-ADAPTATION.patch](PORTABLE-ADAPTATION.patch). Only that +checker's self-hash is excluded from its comparison with the old receipt. + +The replay checks ordered identities, all 224 data columns, source and +terminal phases in the stated checks, scalar code inverses, helper +paths, route records, and negative controls. It does not rerun the full +native phase compiler, prove the all-size recursive compiler, run the +selected construction, or establish finite precision and integer recovery. +The original source phase reviews remain pinned premises. + +## Source context + +The packaging base is `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`, whose +selected result comes from [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470). +That is packaging context. All consumed historical source pins stay +unchanged. This package makes no applicability claim for the construction +selected at that base. + +The reciprocal-response proof is retained only because the historical +admission source manifest pins it. Its separate reciprocal three-call +family is not a new claim of this package. Metric encoder results and +later source-frame closure results are outside this package. + +## Open next questions + +Can a cheaper terminal remove the actual routed `Q T Q^-1` code? A first +step is to give an ordered native construction on the retained D25 +routes and price every map and child. The current rank equality blocks +the two terminal choices in this package. + +Can the raw or weighted content inverse obtain its queries in the +required physical cuts? A first step is a typed reader and scatter +certificate for the exact retired-Y maps. The content identities alone +do not supply those views or their cost. + +Can a proposed physical monomial compiler preserve every later helper +use and the admitted map grammar? A first step is one complete-state +conjugation certificate. Logical monomiality of a local response is +insufficient. + +Source credit and license terms are in [NOTICE.md](NOTICE.md). The work +used substantial OpenAI Codex assistance. The independent reviews in +this package are separate agent checks; they are not human review. diff --git a/research/ordered-centre-interfaces/RESULT.json b/research/ordered-centre-interfaces/RESULT.json new file mode 100644 index 0000000000..ac53dec5af --- /dev/null +++ b/research/ordered-centre-interfaces/RESULT.json @@ -0,0 +1,31 @@ +{ + "schema": "ordered-centre-result-v1", + "status": "PASS_ORDERED_CENTRE_INTERFACES", + "kind": [ + "enabling_proofs", + "scoped_negative_result" + ], + "complete_kappa_improvement": false, + "claimed_selected_applicability": false, + "packaging_base": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51", + "direct_source_manifest": "DIRECT-SOURCES.json", + "proof": "PROOF.md", + "replay": "replay.py", + "receipt": "validation/REPLAY.json", + "decisive_checks": 10, + "normal_and_optimized_checks": 20, + "data_roles": 224, + "ambient_dimension": 25, + "positive_native_moment": false, + "remaining_obligations": [ + "all-size recursive compiler premises", + 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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/ordered-centre-interfaces/frozen/archive-members/DATA-PHASES.json b/research/ordered-centre-interfaces/frozen/archive-members/DATA-PHASES.json new file mode 100644 index 0000000000..d9a4f84211 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/archive-members/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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Internal arbitrary-subspace canonical labels are checked separately.","source_parent_sha256":"f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a","status":"PASS_EXACT_Z4_DATA_ROUTE_IDLE_AND_TERMINAL_PHASES","terminal_omission_controls_rejected":112} diff --git a/research/ordered-centre-interfaces/frozen/upstream/build/sections/05-layers.tex b/research/ordered-centre-interfaces/frozen/upstream/build/sections/05-layers.tex new file mode 100644 index 0000000000..5ce8b3c83c --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/upstream/build/sections/05-layers.tex @@ -0,0 +1,996 @@ +\section{Fast simultaneous synthetic butterfly layers} +\label{sec:fast-butterfly-layers} + +We now apply the complex network to a common butterfly layer on several +axes. The array has complete address set +\[ + [P]\times[2^K]^D\times[S],\qquad 1\le D\le d, +\] +with $P,S\ge1$, in lexicographic order. Its $D$ consecutive $K$-bit +chunks each select the bit at one common offset $0\le\rho0,\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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a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/MATCHED-STAGE-ACCESS.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/MATCHED-STAGE-ACCESS.md new file mode 100644 index 0000000000..00db71220d --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/MATCHED-STAGE-ACCESS.md @@ -0,0 +1,208 @@ +# Actual stage access for the matched involution + +The new matched response has a scalar implementation at the final FULL +cut. Its two-stage raw terminal factor still has non-monomial payload +blocks. These are separate results. The first permits late scalar +decoding. It does not remove the two intrinsic line factors in the +second. + +This packet uses the new 48-port mode matching, not the preceding signed +physical-partner exchange. The 48-port source is the frozen matrix in +`controller-followthrough-20261017/matched-involution-20261018/`. +It checks both the half-Hadamard64 complement from that source and the +new permutation64 complement from `history-encoding/`. + +## The routed response and the raw terminal factor + +Let E be either specified symmetric involution. Every physical diagonal +entry is zero. The half-Hadamard64 version has four nonzero entries in +each row. The permutation64 version has four in each of the 48 matching +rows and one in each of the other 64 rows. + +Use the literal DATA stage route rho_(s,p). On the regular orthogonal +cover, the stage response has entries + +```text +(E_s x)_p(h) = sum_r E_pr x_r(h rho_(s,p) rho_(s,r)). +``` + +This formula defines the logical response. Its physical implementation +must include the DATA translations and the field frames. In particular, +the input code Q must not be discarded when a terminal is designed. + +For the isolated balanced pair with data code C=E_t E_s, the physical +input bank is Qx. The completed fields have the form + +```text +X = F (E_s x-y), Y = F q C x. +``` + +The desired raw outputs are FQx and Fy. After F is removed from the +notation, their exact decoder is + +```text +[ 0 Q C^-1 Q ] +[ -I E_s C^-1 Q ]. +``` + +Thus its upper block is Q E_s E_t Q. This equation is an isolated-pair +identity. A complete three-call or multi-pair controller must establish +its own endpoint before it uses this decoder. In particular, a single +Y normalization followed by scalar inverses returns logical x. It does +not by itself return the original physical input Qx. + +## Exact non-monomial path blocks + +Fix distinct positive stages s and t. A path through intermediate port j +in Q E_s E_t Q has coefficient E_pj E_jr and cover word + +```text +A_j = rho_(s,p) rho_(s,j) rho_(t,j) rho_(t,r). +``` + +Its payload operator, before the final common F conjugation, is + +```text +C_(q_p) C_(A_j q_r) P_(A_j). +``` + +All these paths are distinct for fixed p and r. To prove this, cancel +the fixed outside routes. The remaining map is +rho_(s,j) rho_(t,j). Its action on the l-th axis of the s block is the +l-th root complement vector of port j. Equality of all eight such +vectors would give the same root complement and the same intrinsic q. +The actual 112 q values are distinct. Therefore two intermediate ports +cannot give the same cover word. Arbitrary cover inputs can isolate +each path, so coefficients from different paths cannot cancel. + +Every nonzero E_jr has j different from r. The first new-stage route +rho_(t,j) sends a nonzero part of q_r into the t block. The two later +s-stage routes preserve that part. Hence A_j q_r has a nonzero t-block +component, while q_p lies in the root nine coordinates. The two line +directions are distinct. + +For each orthogonal cover map A, F P_A F^-1 is P_A with a translation. +The checker derives this translation from the full Z4 phase polynomial. +It verifies the constant, odd, even, and quadratic coefficients. Thus +the final physical path has the form + +```text +translation(delta_A) C_(q_p) C_(A_j q_r) P_A. +``` + +The two-line product has four nonzero entries in each one-copy row. +Their phase numerators, in translation order 0,a,b,a+b, are i,1,1,-i, +with common denominator two. At tensor width f, the exact support is +4^f. A translation or invertible address map preserves this count. + +The checker covers the actual consecutive pairs (1,2), (3,4), (5,6), +and (7,8). For each pair it checks all 1,792 paths of the half-Hadamard64 +version and all 832 paths of the permutation64 version. Every path has +two-line Fourier rank two. This path count is not a lower bound on the +number of native children in a coupled implementation. + +A concrete path lies entirely in the first 25 coordinates: + +```text +s=1, t=2, p=0, j=15, r=0, +coefficient = 1/4, +line directions = 11 and 2^24, +FULL translation = 17695243. +``` + +It is a path in the new 48-port matching, so both choices of the 64-port +complement retain it. + +A fixed number of scalar and monomial array passes has a row support +bound independent of f. The displayed 4^f support therefore excludes +such a zero-child implementation of this specified terminal factor. +The statement permits a paid native decoder, a new controller, changed +owner routes, or changed local output frames. It is not a circuit lower +bound for arbitrary algorithms. + +## A literal scalar E gauge at the final FULL cut + +The matching48 plus permutation64 version has an emitted scalar word. +For each physical pair, apply its exact signed two-field mode code. +Apply the specified signed mode transpositions. Reverse the pair code. +On the other 64 fields, apply the 32 specified negative exchanges. +The full word acts as E on arbitrary values in all 112 fields. + +For each stage s, take the literal past-X view M_(s,p) from +`BRIDGE-PROGRAMS.json.gz`. Its route and translation satisfy + +```text +M_(s,p) F = F P_(rho_(s,p)). +``` + +Apply all 112 views, execute the scalar word at each common body address, +then undo all views. The result is exactly F E_s F^-1. This uses 224 +monomial view calls. It also applies to a Y bank after that bank has +been converted to the same physical FULL frame. It does not convert a +hole frame to FULL for free. + +The emitted word has 264 complex ADDs and 230 complex SCALEs. Its exact +inherited scalar invoice is 2,668 real primitives. The checker also runs +the pinned source price function on the emitted word. The largest +intermediate row one-norm is four. There is no native child, owned field, +private buffer, or assumed zero data. The forward word and its reverse +inverse both pass all 112 independent input columns. Monomial map costs +are separate from this scalar invoice. + +## Restriction to one pair and 25 coordinates + +The root nine coordinates and the first two fresh eight-coordinate +blocks form a 25-dimensional space. Every literal route at stages 0, +1, and 2 preserves this space and fixes the other 48 coordinates. +Every corresponding DATA entry and exit translation lies in it. + +The separate dimension checker verifies all 336 orthogonal route +records, all 672 entry phase equations, and all 672 exit phase equations. +The current local types remain X:C_q to F9 and Y:I to F9 C_q^-1, with +the common exterior Fourier factors included. No additional phase or +endpoint adapter is inferred. + +These routes belong to O(25,2). Right multiplication therefore permutes +the regular O(25,2) cover. With a data-only local word, the owner views +partition each data field into its body invocations. Complete each local +cover sweep before the next stage. No helper-owner sharing is needed +for this chart statement. The local native word and recursive hosting +are separate obligations. + +The same restriction gives the exact scalar-access cones: + +- At the initial all-I cut, every routed scalar port matrix is available + through monomial views. +- On X at completed level l, every stage s at most l is available through + the literal past-X views. +- On Y at hole level l, every stage t greater than l is available through + the literal future-Y views. + +These statements do not depend on a dedicated centre bank. They apply +to the new sparse E matrix itself. At the B1 Y cut, the global hole level +is zero. E2 is available by the future-Y view. E0 is an old-chart operator; +its off-diagonal blocks have the mixed intrinsic lines and are not made +free by the local label I. + +## Validation and scope + +Run both checkers from this directory: + +```text +python3 -I -B check_matched_access.py +PASS_MATCHED_RESPONSE_STAGE_ACCESS +python3 -I -B check_dimension25.py +PASS_LITERAL_DIMENSION25_STAGE_RESTRICTION +``` + +Repeat with `-O`. The generated payloads and receipts must be identical. +All checks use exact arithmetic and the pinned source maps. This packet +does not emit the new local forward or backward native word, prove a +complete three-call endpoint, admit recursive children, or establish a +kappa improvement. + +The work uses the controller lane's matched mode specification, the +history lane's permutation64 native response, and the earlier exact +DATA phase and access calculations. OpenAI Codex assisted the work. +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/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-CHECKS.json new file mode 100644 index 0000000000..1b4af08616 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-CHECKS.json @@ -0,0 +1,324 @@ +{ + "checker_sha256": "847d0dd8cfaf869b2a425fbd3b05c309d4d5859e8eab7dd1f0cb77dd761d4b57", + "controller_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", + "dense48_scalar_gauge_replay": { + "census": { + "add": 168, + "scale": 88 + }, + "events": 256, + "native_children": 0, + "owned_fields": 0, + "peak_row_one_norm": "4", + "real_scalar_primitives": 1564 + }, + "dense_H2_fusion_claimed": false, + "five_cut_phase_checks": 560, + "independent_scalar_gauge_replay": { + "census": { + "add": 264, + "scale": 120 + }, + "events": 384, + "native_children": 0, + "owned_fields": 0, + "peak_row_one_norm": "4", + "real_scalar_primitives": 2396 + }, + "mixed_child_phase_coefficient_checks": 52160, + "mixed_map_inventory": { + "dense48_child_wrappers": 192, + "dense48_code_views": 288, + "small64_child_wrappers": 128 + }, + "mixed_native_rank_mass": 224, + "mixed_profile": { + "1": 96, + "2": 64 + }, + "mixed_scalar_real_primitives": 4820, + "program_decompressed_sha256": "b65a2b14a1e61c566063195d0ef363c7dae0d06bb2232e4c872275479f327419", + "safe_profile": { + "1": 224 + }, + "scalar_gauge_pin": "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89", + "scope": "Exact current cuts and triple raw operator. 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0 HcmV?d00001 diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25.md new file mode 100644 index 0000000000..fa69256389 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/TRIPLE25.md @@ -0,0 +1,203 @@ +# The actual three-stage terminal in dimension 25 + +This supplement binds the five scalar code cuts of the one-pair +controller. It also gives a complete terminal recipe with profile +`{1:96, 2:64}`. Its rank mass is 224. The recipe does not save rank. +It does not combine the 48 mixed rows into 48 rank-two calls. + +The controller source is +[ONE-PAIR.md](../../encoded-controller/one-pair-current-codes-20261018/ONE-PAIR.md). +Its program SHA-256 is +`f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7`. +The source proves the endpoint `(-y,T x)`, where `T=E2 E1 E0`. +After the retained raw terminal, the first output bank has code +`Q T Q^-1`. The second bank has no code. This supplement uses that +ordered endpoint. It does not replace it with the isolated two-call +endpoint in [MATCHED-STAGE-ACCESS.md](MATCHED-STAGE-ACCESS.md). + +## The five scalar cuts + +The emitted views act on the root nine coordinates and two fresh +eight-coordinate blocks. Each route and translation is the restriction +of the pinned DATA view. The exact cuts are: + +| Operation | Bank | Global completed or hole level | +| --- | --- | --- | +| E0 after F0 | X | 0 | +| E1 before B1 | Y | 0 | +| E1 after B1 | X | 1 | +| E2 before F2 | Y | 1 | +| E1 inverse after F2 | X | 2 | + +The checker verifies the full Z4 phase equation at all 560 port cuts. +It includes the route, translation, intrinsic line, and common exterior. +All ports in one code have the same frame in their specified view. +Thus each occurrence can use a scalar port circuit. The result does +not depend on a zero input or a zero borrowed field. + +The scalar circuit is the independently produced +[FULL-GAUGE.json](../../independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json), +SHA-256 +`ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89`. +This supplement replays its forward and inverse words on all 112 input +columns. It verifies that the matrix is the actual matched48 plus +permutation64 response. The price is 2,396 real scalar primitives per +code. The largest row one-norm is four. Each routed application has a +conservative allowance of 224 monomial view calls. Those map calls are +not included in the scalar price. + +## The complete raw triple + +Let rho_(s,p) be the literal stage route, with rho_(0,p)=I. A path +`p <- j <- k <- r` in `E_a E_b E_c` has cover map + +```text +A = rho_(a,p) rho_(a,j) rho_(b,j) rho_(b,k) + rho_(c,k) rho_(c,r). +``` + +The two required stage orders are `(2,1,0)` for T and `(0,1,2)` for +T inverse. The inverse order is valid because each actual E_s is an +involution. The checker uses the full routed maps, not the local +identity E cubed = E. + +In the common completed frame, the path in `Q T^(+/-1) Q^-1` is + +```text +c X_delta C_a C_b^-1 P_A, +a = q_p, b = A q_r, +c = E_pj E_jk E_kr. +``` + +Here X_delta is a uniform payload translation on every tensor copy. +The checker obtains delta from the difference of the full Fourier +phase polynomials before and after A. The serialized route and phase +are part of the program. + +For each direction, the preferred response has 3,136 paths: 3,072 on +the 48 mixed ports and 64 on the permutation ports. All paths have +distinct, orthogonal line directions a,b. For fixed p,r, distinct +intermediate pairs give distinct complete cover maps. These facts are +checked on every path. The half-Hadamard64 alternative has 7,168 paths +per direction and is checked separately; it is not used in the emitted +mixed decoder. + +The cover-map test does not collapse different owner paths into one +local matrix entry. For T, cancel the fixed left factor rho_(2,p). +The action on the second fresh block then recovers the root complement +chart of j. After that chart is removed, the remaining first-stage map +recovers k. The inverse word has the corresponding reversed recovery. +The literal checker compares all complete map columns. + +Each distinct two-line path has four nonzero address entries per copy. +Thus a path has support 4^f at tensor width f. This rules out a fixed +number of scalar and monomial passes for the specified raw operator. +It is not a lower bound on the number of children in a joint decoder. +In particular, it does not rule out shared native work between paths +or fields. + +## Literal rank-two calls on the 64 permutation ports + +Each permutation output has exactly one path. Its coefficient is -1, +and the 64 source ports form a permutation. The cover maps are +orthogonal and invertible. This gives a field and cover bijection; +it does not need a copy of an input bank. + +For each path, the program constructs an orthogonal 25 by 25 matrix G +whose first two columns are a and b. It constructs G by orthogonal +transvections, records every transvection, and checks both inverse +orders. In the stated coordinate convention, + +```text +C_b^-1 = X_b C_b, +C_a C_b = P_G H2 P_G^-1. +``` + +Consequently the exact inverse path is + +```text +-X_(delta+b) P_G H2 P_G^-1 P_A. +``` + +This is one positive rank-two child between two monomial views. The +right view includes the source field and cover map. The left view +includes the translation delta+b. The complex sign can be applied +separately. The program records both full basis matrices and the full +translation. It verifies all constant, linear, and quadratic phase +coefficients. The construction applies on each tensor copy, so it +holds at arbitrary tensor width. + +The 64 records are a literal native factorization of these 64 rows. +They do not rely on a claim that all rank-two path sums use one child. + +## The exact two-pass contract on the other 48 ports + +The 48-port set is invariant under every E_s. It has no read from the +64-port set. Apply this sequence to the 48 fields: + +1. Apply C_q^-1 on each field. +2. Apply the restricted E2 inverse, E1 inverse, and E0 inverse codes, + in that chronological order, through the final FULL views. +3. Apply C_q on each field. + +This is precisely `Q T^-1 Q^-1` on that invariant set. The program +emits all 96 rank-one recipes. An inverse line uses one positive child +and the translation q. Every recipe includes an orthogonal basis, +its inverse, and its phase check. + +The restricted scalar circuit has 256 events: 168 complex ADDs and +88 complex SCALEs. Its price is 1,564 real scalar primitives per stage. +The checker replays both orders on all 112 columns, with the other +64 fields fixed. Its largest row one-norm is four. + +The complete terminal invoice in this packet is: + +| Item | Count or price | +| --- | --- | +| Rank-one children | 96 | +| Rank-two children | 64 | +| Total native rank | 224 | +| Three restricted scalar codes | 4,692 real primitives | +| 64 complex signs | 128 real primitives | +| Total scalar primitives outside children | 4,820 | +| Restricted scalar code views | 288 | +| Rank-one child wrappers | 192 | +| Rank-two child wrappers | 128 | +| Top-level owned or private fields | 0 | + +The 608 map calls have not been converted to a finite real-operation +or precision invoice here. The inherited signed terminal remains a +separate part of the controller. The basis wrappers and cover maps +can use the existing monomial map interface. Recursive child hosting +must still be bound to these particular recipes. + +The fallback is 224 rank-one children with three full scalar codes. +The mixed profile has the same rank mass, but a different positive +moment. It must not be replaced by `{2:112}` in an invoice. + +## Verification and limits + +Run: + +```text +python3 -I -B check_triple25.py +PASS_MATCHED_TRIPLE25_AND_FIVE_CUTS +``` + +Repeat with `-O`. The program and receipt must be byte-identical. +The checker verifies 560 cut equations, both complete raw triple +directions, the full and restricted scalar codes, and 52,160 native +phase coefficient equations. The source pins are in the payload and +receipt. `TRIPLE25-FREEZE.json` preserves this supplement independently +of the earlier stage-access freeze. + +This result is an exact decoder implementation at the stated cuts. +It does not prove a lower native cost, a complete recursive supplier +invoice, or a kappa improvement. A joint decoder for the 48 mixed +fields, or a changed code placement, remains an open opportunity. + +The work uses the controller lane's ordered endpoint, the independent +review lane's scalar gauge, the history lane's permutation64 word, +and the pinned DATA phase calculations. OpenAI Codex assisted the work. +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/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_dimension25.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_dimension25.py new file mode 100644 index 0000000000..26badc448b --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_dimension25.py @@ -0,0 +1,106 @@ +"""Restrict the literal DATA charts to two fresh stage blocks.""" + +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def main(): + path = HERE / "check_matched_access.py" + spec = importlib.util.spec_from_file_location("matched_stage_source", path) + source = importlib.util.module_from_spec(spec) + spec.loader.exec_module(source) + base, ports, data = source.load() + unit = [1 << j for j in range(25)] + mask = (1 << 25) - 1 + entries = [] + counts = {"entry": 0, "exit": 0, "future_Y": 0, "past_X": 0, + "orthogonal_routes": 0, "omitted_entry_translation": 0, + "omitted_exit_translation": 0} + views = {(v["stage"], v["port"], v["side"]): v for v in data["views"]["views"]} + for p, recipe in enumerate(ports): + q = recipe["q"] + for s in range(3): + full_rho = list(base.UNIT) if s == 0 else views[s, p, "X"]["route_columns"] + need(all(v <= mask for v in full_rho[:25]) and full_rho[25:] == base.UNIT[25:], + "The literal route acts only on the 25-axis space") + rho = full_rho[:25] + need(all((a & b).bit_count() % 2 == int(i == j) + for i, a in enumerate(rho) for j, b in enumerate(rho)), "O(25,2) membership") + need([base.act(rho, v) for v in rho] == unit and base.act(rho, q) == q, + "Route involution and intrinsic line") + counts["orthogonal_routes"] += 1 + align = recipe["stage_alignment"][s] + need(all(v <= mask for v in align.values()), "All literal translations restrict") + record = {"port": p, "stage": s, "q": q, "route_columns": rho, + "literal_stage_alignment": align} + for side in ("X", "Y"): + before = ([(q, 1)] if side == "X" else []) if s == 0 else [(v, 1) for v in unit[:9 + 8 * (s - 1)]] + if s and side == "Y": + before.append((q, -1)) + body = base.product([(base.act(rho, v), power) for v, power in before]) + delta = base.act(rho, align["entry_" + side]) + actual = base.add_phase(body, base.line(delta, 2)) + expected_terms = [(v, 1) for v in unit[9:9 + 8 * s]] + if side == "X": + expected_terms.append((q, 1)) + expected = base.product(expected_terms) + need(actual == expected, "Exact current native entry including exterior") + counts["entry"] += 1 + counts["omitted_entry_translation"] += body != expected + after = [(v, 1) for v in unit[:9 + 8 * s]] + if side == "Y": + after.append((q, -1)) + body = base.product([(base.act(rho, v), power) for v, power in after]) + actual = base.add_phase(body, base.line(align["exit_" + side], 2)) + expected = base.product(after) + need(actual == expected, "Exact declared output endpoint") + counts["exit"] += 1 + counts["omitted_exit_translation"] += body != expected + if s: + for level in range(s): + terms = [(base.act(rho, v), 1) for v in unit[:9 + 8 * level]] + [(q, -1)] + actual = base.add_phase(base.product(terms), base.line(views[s, p, "Y"]["translation_after_route"], 2)) + axes = unit[9:9 + 8 * level] + unit[9 + 8 * (s - 1):9 + 8 * s] + need(actual == base.product([(v, 1) for v in axes]), "Future-Y common exterior") + counts["future_Y"] += 1 + for level in range(s, 3): + actual = base.product([(base.act(rho, v), 1) for v in unit[:9 + 8 * level]]) + delta = 0 if s == 0 else views[s, p, "X"]["translation_after_route"] + actual = base.add_phase(actual, base.line(delta, 2)) + need(actual == base.product([(v, 1) for v in unit[:9 + 8 * level]]), "Past-X common exterior") + counts["past_X"] += 1 + entries.append(record) + need(counts["entry"] == counts["exit"] == 672, "All local boundary types") + need(counts["future_Y"] == 336 and counts["past_X"] == 672, "All three-stage access cones") + witness = json.loads((HERE / "CHECKS.json").read_bytes())["witness"] + need(all(v <= mask for v in witness["route_columns"][:25]) + and witness["route_columns"][25:] == base.UNIT[25:], "Terminal witness restricts") + need(max(witness["lines"]) <= mask and witness["FULL_translation"] <= mask, + "The two-line phase witness has no discarded spectator") + program = {"schema": "matched-dimension25-views-v1", "dimension": 25, "data_fields": 224, + "stages": [0, 1, 2], "source_pins": source.PINS, "entries": entries, + "owner_contract": "Use the regular O(25,2) cover. Complete each data-only local cover sweep before the next stage.", + "native_word_claimed": False, "recursive_hosting_claimed": False} + (HERE / "DIMENSION25-VIEWS.json").write_text(json.dumps(program, sort_keys=True, indent=2) + "\n") + receipt = {"status": "PASS_LITERAL_DIMENSION25_STAGE_RESTRICTION", "source_pins": source.PINS, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), "checks": counts, + "current_Y_at_B1": {"E2": "future scalar view admitted", "E0": "old mixed-line view; not admitted as a free scalar gauge"}, + "initial_all_I": "Every routed scalar matrix is a monomial-view scalar gauge", + "terminal_upper_witness": {k: witness[k] for k in ("target", "middle", "source", "coefficient", "lines", "FULL_translation")}, + "scope": "Literal chart, endpoint, cover, and access restriction. Local native words and complete supplier admission are separate."} + (HERE / "DIMENSION25-CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py new file mode 100644 index 0000000000..8ff43e525f --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_matched_access.py @@ -0,0 +1,237 @@ +"""Check the actual matching response in complete supplier stage views.""" + +from collections import Counter, defaultdict +import ast +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] +PINS = { + "matching": ("controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json", "plain", "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902"), + "permutation64": ("history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz", "gzip", "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9"), + "views": ("bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", "compressed", "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f"), + "phase": ("bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py", "python", "cf39b15752fcb96cc22b9013dce38e13a4399d99b30dc9f53eef788d5ded2bf4"), + "scalar_price": ("new-core-transfer-20261017/emit_raw_selected.py", "source", "a07cf4894a2599993006c7b99e6cb62146ece82f2ae6df72a28100ccb3a689bc"), +} + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def load(): + data = {} + for name, (rel, kind, pin) in PINS.items(): + raw = (LANES / rel).read_bytes() + if kind == "gzip": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, name + " source pin") + if kind == "python": + spec = importlib.util.spec_from_file_location("matched_access_phase", LANES / rel) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + base, ports = module.load() + elif kind != "source": + data[name] = json.loads(gzip.decompress(raw) if kind == "compressed" else raw) + return base, ports, data + + +def rows(matrix): + return [{int(j): F(c) for j, c in row.items() if F(c)} for row in matrix] + + +def product(a, b): + result = [] + for row in a: + out = defaultdict(F) + for j, c in row.items(): + for k, d in b[j].items(): + out[k] += c * d + result.append({j: c for j, c in out.items() if c}) + return result + + +def inverse_word(word): + return [[op, p, q, str(-F(c))] if op == "add" else [op, p, q, str(1 / F(c))] + for op, p, q, c in reversed(word)] + + +def scale(word, p, c): + if c != 1: + word.append(["scale", p, p, str(c)]) + + +def swap(word, p, r, sign=1): + word += [["add", p, r, "1"], ["add", r, p, "-1"], ["add", p, r, "1"]] + scale(word, r, F(-1)) + scale(word, p, F(sign)) + scale(word, r, F(sign)) + + +def pair_word(source): + word = [] + for pair in source["pair_codes"]: + p, r = pair["ports"] + a, b = map(F, pair["matrix"][0]) + c, d = map(F, pair["matrix"][1]) + need(d == -c * b / a and abs(a) == abs(b) == abs(c) == 1, "Signed pair code") + scale(word, p, a) + scale(word, r, b) + word += [["add", p, r, "1"], ["scale", r, r, "-2"], ["add", r, p, "1"]] + scale(word, r, c / a) + need([source["modes"][j]["carrier"] for j in pair["mode_ids"]] == [p, r], "Mode carrier order") + return word + + +def scalar_word(source, permutation): + pre = pair_word(source) + word = list(pre) + for vertex in source["vertex_matchings"]: + for pair in vertex["matching_pairs"]: + p, r = [source["modes"][j]["carrier"] for j in pair["modes"]] + swap(word, p, r, pair["weight"]) + word += inverse_word(pre) + for p, r in sorted((int(p), int(r)) for p, r in permutation["partner"].items() if int(p) < int(r)): + swap(word, p, r, -1) + return word + + +def replay(word, target): + state = [{p: F(1)} for p in range(112)] + peak = F(1) + price = 0 + census = Counter() + for op, p, r, raw in word: + c = F(raw) + a, b = abs(c.numerator), c.denominator + need(b & (b - 1) == 0, "Dyadic scalar") + if op == "add": + need(p != r, "Distinct scalar rows") + out = defaultdict(F, state[p]) + for j, d in state[r].items(): + out[j] += c * d + state[p] = {j: d for j, d in out.items() if d} + price += 2 * (3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1) + else: + need(op == "scale" and a & (a - 1) == 0, "Dyadic unit scale") + state[p] = {j: c * d for j, d in state[p].items()} + price += 2 * (abs(a.bit_length() - b.bit_length()) + int(c < 0)) + census[op] += 1 + peak = max(peak, sum(abs(c) for c in state[p].values())) + need(state == target, "All 112 scalar input columns") + return {"events": len(word), "census": dict(census), "real_scalar_primitives": price, + "peak_row_one_norm": str(peak), "native_children": 0, "owned_fields": 0} + + +def compose(base, *maps): + out = list(base.UNIT) + for item in reversed(maps): + out = [base.act(item, v) for v in out] + return out + + +def main(): + base, ports, data = load() + q = [p["q"] for p in ports] + source = data["matching"] + identity = [{p: F(1)} for p in range(112)] + matched = rows(source["response"]) + permuted = [dict(row) for row in matched] + for p in data["permutation64"]["active_ports"]: + permuted[p] = rows([data["permutation64"]["response"][p]])[0] + for response in (matched, permuted): + need(product(response, response) == identity, "Both full response involutions") + need(all(p not in row for p, row in enumerate(response)), "Every physical diagonal is zero") + word = scalar_word(source, data["permutation64"]) + invoice = replay(word, permuted) + need(replay(inverse_word(word), permuted)["native_children"] == 0, "Exact inverse word") + syntax = ast.parse((LANES / PINS["scalar_price"][0]).read_text()) + price_node = next(node for node in syntax.body if isinstance(node, ast.FunctionDef) and node.name == "core_price") + price_scope = {"Q": F, "need": need} + exec(compile(ast.Module(body=[price_node], type_ignores=[]), "pinned_core_price", "exec"), price_scope) + billed = [] + for op, p, r, raw in word: + c = F(raw) + gate = [op, ["D", p]] + ([["D", r]] if op == "add" else []) + [c.numerator, c.denominator] + billed.append(["scalar", gate, 0]) + need(price_scope["core_price"](billed) == invoice["real_scalar_primitives"], "Pinned source scalar invoice") + views = {(v["stage"], v["port"], v["side"]): v for v in data["views"]["views"]} + route = {(s, p): views[s, p, "X"]["route_columns"] for s in range(1, 9) for p in range(112)} + full = base.product([(e, 1) for e in base.UNIT]) + past_checks = 0 + for s in range(1, 9): + for p in range(112): + view = views[s, p, "X"] + rho, delta = route[s, p], view["translation_after_route"] + phase = base.product([(v, 1) for v in rho]) + need(base.add_phase(phase, base.line(delta, 2)) == full, "Literal final-FULL stage view") + need(base.act(rho, q[p]) == q[p], "Own intrinsic line is fixed") + past_checks += 1 + reports = {} + witness = None + for name, response in (("half_hadamard64", matched), ("permutation64", permuted)): + stage_rows = [] + for s, t in ((1, 2), (3, 4), (5, 6), (7, 8)): + grouped = defaultdict(dict) + count = 0 + for p, row in enumerate(response): + for j, c in row.items(): + for r, d in response[j].items(): + mapping = compose(base, route[s, p], route[s, j], route[t, j], route[t, r]) + key = tuple(mapping) + need(key not in grouped[p, r], "Distinct intermediate ports have distinct owner maps") + grouped[p, r][key] = c * d + second = base.act(mapping, q[r]) + fresh = ((1 << 8) - 1) << (9 + 8 * (t - 1)) + need(second & fresh, "The second intrinsic line has a nonzero future component") + need(q[p] != second, "Two distinct positive intrinsic lines") + correction = base.add_phase(full, base.negative(base.product([(v, 1) for v in mapping]))) + need(correction[0] == correction[2] == 0, "FULL cover conjugation is a translation") + phase = base.add_phase(base.product([(q[p], 1), (second, 1)]), correction) + need(phase[0] == q[p] ^ second, "Full Z4 phase has the required odd mask") + count += 1 + if witness is None: + witness = {"stages": [s, t], "target": p, "middle": j, "source": r, + "coefficient": str(c * d), "route_columns": mapping, + "lines": [q[p], second], "FULL_translation": correction[1], + "phase": list(phase)} + stage_rows.append({"stages": [s, t], "nonzero_path_blocks": count, + "output_port_rows": len({p for p, r in grouped}), + "port_blocks": len(grouped), "rank_two_path_blocks": count}) + reports[name] = {"local_nonzero_entries": sum(map(len, response)), "stage_pairs": stage_rows} + a, b = witness["lines"] + kernel = {0: 1, a: 0, b: 0, a ^ b: 3} + need(len(kernel) == 4, "Four nonzero one-copy entries") + expanded = {0: 0} + support = [] + for width in range(1, 6): + expanded = {old ^ (v << (73 * (width - 1))): (phase + power) % 4 + for old, phase in expanded.items() for v, power in kernel.items()} + need(len(expanded) == 4**width, "Exact tensor support") + support.append(len(expanded)) + program = {"schema": "matched-final-full-gauge-v1", "source_pins": PINS, + "response": [{str(j): str(c) for j, c in row.items()} for row in permuted], + "scalar_word": word, "inverse_scalar_word": inverse_word(word), + "stage_contract": {"stages": list(range(1, 9)), "completed_level": 8, + "view_source": PINS["views"][0], "view_side": "X", + "order": ["apply_all_literal_stage_views", "scalar_word", "invert_all_literal_stage_views"], + "monomial_view_calls": 224}, "invoice": invoice} + (HERE / "FULL-GAUGE-PROGRAM.json").write_text(json.dumps(program, sort_keys=True, indent=2) + "\n") + result = {"status": "PASS_MATCHED_RESPONSE_STAGE_ACCESS", "source_pins": PINS, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "literal_FULL_view_checks": past_checks, "terminal_upper_blocks": reports, + "witness": witness, "tensor_support": support, "FULL_gauge_invoice": invoice, + "scope": "Exact specified responses and raw phase operator. No full supplier or general native lower bound."} + (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/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_triple25.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_triple25.py new file mode 100644 index 0000000000..1c7a73be54 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_triple25.py @@ -0,0 +1,273 @@ +"""Check the five current cuts and the complete three-stage raw code.""" + +from collections import defaultdict +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 +GAUGE = "independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.json" +GAUGE_PIN = "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89" +SOURCE_PIN = "d2954018666ea2c1b6557615fdf0e6eba7b651fc89e4fdac899b0ccc0f16b839" +CONTROLLER = "encoded-controller/one-pair-current-codes-20261018/PROGRAM.json" +CONTROLLER_PIN = "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7" + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def dot(a, b): + return (a & b).bit_count() & 1 + + +def binary_solution(equations): + pivots = {} + for row, rhs in equations: + while row: + lead = row.bit_length() - 1 + if lead not in pivots: + pivots[lead] = (row, rhs) + break + old, value = pivots[lead] + row ^= old + rhs ^= value + need(row or not rhs, "Consistent basis extension") + value = 0 + for lead, (row, rhs) in sorted(pivots.items()): + if dot(row, value) != rhs: + value ^= 1 << lead + need(all(dot(row, value) == rhs for row, rhs in equations), "Exact binary solution") + return value + + +def child_basis(base, wanted): + unit = [1 << j for j in range(25)] + columns = list(unit) + transvections = [] + for j, target in enumerate(wanted): + current = columns[j] + if current == target: + continue + if not dot(current, target): + changes = [current ^ target] + else: + middle = binary_solution([((1 << 25) - 1, 1), (current, 0), (target, 0)] + + [(v, 0) for v in wanted[:j]]) + changes = [current ^ middle, middle ^ target] + for vector in changes: + need(vector and not dot(vector, vector), "An orthogonal transvection") + need(all(not dot(vector, v) for v in wanted[:j]), "The earlier child axes stay fixed") + columns = [v ^ (vector if dot(vector, v) else 0) for v in columns] + transvections.append(vector) + need(columns[j] == target, "The next child axis") + inverse = [sum(((columns[j] >> i) & 1) << j for j in range(25)) for i in range(25)] + need(columns[:len(wanted)] == wanted, "The stated native axes") + need([base.act(columns, v) for v in inverse] == unit, "The left basis inverse") + need([base.act(inverse, v) for v in columns] == unit, "The right basis inverse") + return columns, inverse, transvections + + +def native_record(base, target, source, lines, translation, route, sign=1): + columns, inverse, steps = child_basis(base, lines) + need(all(dot(a, b) == int(i == j) + for i, a in enumerate(lines) for j, b in enumerate(lines)), + "The native line directions are orthonormal") + wanted = base.add_phase(base.product([(v, 1) for v in lines]), base.line(translation, 2)) + characters = [0] + [1 << j for j in range(25)] + characters += [(1 << i) ^ (1 << j) for i in range(25) for j in range(i)] + for eta in characters: + transformed = base.act(inverse, eta) + expected = sum(dot(v, eta) for v in lines) + 2 * dot(translation, eta) + actual = (transformed & ((1 << len(lines)) - 1)).bit_count() + 2 * dot(translation, eta) + need((actual - expected) % 4 == 0, "The complete child phase polynomial") + return { + "target": target, "source": source, "rank": len(lines), "sign": sign, + "cover_route_columns": route, + "child_basis_columns": columns, "child_basis_inverse_columns": inverse, + "basis_transvections_in_time_order": steps, + "output_translation": translation, + "factor_in_output_coordinates": "sign * X_translation * P_G * H_rank * P_G^-1 * P_route", + "phase": list(wanted), "phase_coefficient_checks": len(characters), + } + + +def main(): + path = HERE / "check_matched_access.py" + need(sha256(path.read_bytes()).hexdigest() == SOURCE_PIN, "Frozen stage checker") + spec = importlib.util.spec_from_file_location("triple25_source", path) + source = importlib.util.module_from_spec(spec) + spec.loader.exec_module(source) + base, ports, data = source.load() + need(sha256((source.LANES / CONTROLLER).read_bytes()).hexdigest() == CONTROLLER_PIN, + "The actual three-call controller pin") + q = [p["q"] for p in ports] + unit = [1 << j for j in range(25)] + mask = (1 << 25) - 1 + views = {(v["stage"], v["port"], v["side"]): v for v in data["views"]["views"]} + rho = {(s, p): unit if s == 0 else views[s, p, "X"]["route_columns"][:25] + for s in range(3) for p in range(112)} + full = base.product([(v, 1) for v in unit]) + matched = source.rows(data["matching"]["response"]) + preferred = [dict(row) for row in matched] + for p in data["permutation64"]["active_ports"]: + preferred[p] = source.rows([data["permutation64"]["response"][p]])[0] + raw = (source.LANES / GAUGE).read_bytes() + need(sha256(raw).hexdigest() == GAUGE_PIN, "Improved scalar gauge pin") + gauge = json.loads(raw) + need(source.rows(gauge["response"]) == preferred, "Improved gauge uses this actual response") + word = [] + for event in gauge["events"]: + if event[0] == "add": + op, p, r, a, b = event + else: + op, p, a, b = event + r = p + word.append([op, p, r, str(F(a, b))]) + invoice = source.replay(word, preferred) + need(invoice["real_scalar_primitives"] == 2396 and invoice["peak_row_one_norm"] == "4", + "Improved scalar invoice and guard") + source.replay(source.inverse_word(word), preferred) + small = set(data["permutation64"]["active_ports"]) + dense = set(range(112)) - small + dense_word = [event for event in word if event[1] in dense] + need(all(event[2] in dense for event in dense_word), "The dense code has no small-port read") + dense_target = [preferred[p] if p in dense else {p: F(1)} for p in range(112)] + dense_invoice = source.replay(dense_word, dense_target) + source.replay(source.inverse_word(dense_word), dense_target) + need(dense_invoice["real_scalar_primitives"] == 1564, "The restricted dense scalar invoice") + cuts = [] + for label, stage, side, level in (("after_F0", 0, "X", 0), ("before_B1", 1, "Y", 0), + ("after_B1", 1, "X", 1), ("before_F2", 2, "Y", 1), + ("after_F2", 1, "X", 2)): + records = [] + for p in range(112): + route = rho[stage, p] + delta = 0 if stage == 0 else views[stage, p, side]["translation_after_route"] + need(delta <= mask, "The cut translation is in D25") + terms = [(base.act(route, v), 1) for v in unit[:9 + 8 * level]] + if side == "Y": + terms.append((q[p], -1)) + actual = base.add_phase(base.product(terms), base.line(delta, 2)) + axes = unit[:9 + 8 * level] if side == "X" else unit[9:9 + 8 * level] + unit[9 + 8 * (stage - 1):9 + 8 * stage] + expected = base.product([(v, 1) for v in axes]) + need(actual == expected, "Exact five-cut common frame") + records.append({"port": p, "route_columns": route, "translation_after_route": delta, + "inverse_translation_after_route": base.act(route, delta)}) + cuts.append({"cut": label, "stage_code": stage, "side": side, "global_level": level, + "views": records, "scalar_gauge": GAUGE, "scalar_gauge_sha256": GAUGE_PIN, + "monomial_view_calls_bound": 224, "real_scalar_primitives": 2396}) + path_records = {} + reports = {} + for name, matrix in (("half_hadamard64", matched), ("permutation64", preferred)): + reports[name] = {} + for direction, stages in (("T", (2, 1, 0)), ("T_inverse", (0, 1, 2))): + grouped = defaultdict(set) + records = [] + orthogonal = 0 + for p, row in enumerate(matrix): + for j, a in row.items(): + for k, b in matrix[j].items(): + for r, c in matrix[k].items(): + factors = [rho[stages[0], p], rho[stages[0], j], rho[stages[1], j], + rho[stages[1], k], rho[stages[2], k], rho[stages[2], r]] + route = list(unit) + for factor in reversed(factors): + route = [base.act(factor, v) for v in route] + key = tuple(route) + need(key not in grouped[p, r], "Distinct complete triple owner paths") + grouped[p, r].add(key) + second = base.act(route, q[r]) + need(q[p] != second, "The two raw terminal line factors do not cancel") + correction = base.add_phase(full, base.negative(base.product([(v, 1) for v in route]))) + need(correction[0] == correction[2] == 0, "Triple FULL conjugation is a translation") + phase = base.add_phase(base.product([(q[p], 1), (second, -1)]), correction) + need(phase[0] == q[p] ^ second, "Complete raw triple odd phase") + coefficient = a * b * c + record = {"target": p, "middle": [j, k], "source": r, + "coefficient": str(coefficient), "route_columns": route, + "lines": [q[p], second], "line_powers": [1, -1], + "FULL_translation": correction[1], "phase": list(phase)} + records.append(record) + orthogonal += (q[p] & second).bit_count() % 2 == 0 + reports[name][direction] = {"stages": stages, "path_blocks": len(records), + "rank_two_path_blocks": len(records), "orthogonal_line_pairs": orthogonal, + "port_blocks": len(grouped), "first_witness": records[0]} + if name == "permutation64": + path_records[direction] = records + need(reports["permutation64"]["T"]["path_blocks"] == 3136, "Preferred complete triple count") + need(reports["half_hadamard64"]["T"]["path_blocks"] == 7168, "Alternative complete triple count") + fused = [] + source_ports = set() + for record in path_records["T_inverse"]: + if record["target"] not in small: + continue + need(record["coefficient"] == "-1", "The exact small-path scalar sign") + a, b = record["lines"] + translation = record["FULL_translation"] ^ b + child = native_record(base, record["target"], record["source"], [a, b], + translation, record["route_columns"], -1) + need(child["phase"] == record["phase"], "Absorb the inverse line as a translation") + need(base.add_phase(base.product([(a, 1), (b, 1)]), base.line(translation, 2)) + == tuple(record["phase"]), "The full signed-line identity") + fused.append(child) + source_ports.add(record["source"]) + need(len(fused) == 64 and source_ports == small, "The complete small-port bijection") + dense_lines = [] + for power in (-1, 1): + for p in sorted(dense): + dense_lines.append(native_record(base, p, p, [q[p]], q[p] if power == -1 else 0, + unit)) + need(len(dense_lines) == 96, "The two complete dense line passes") + mixed = { + "chronology": ["dense48 inverse lines", "dense48 E2 inverse code", + "dense48 E1 inverse code", "dense48 E0 inverse code", + "dense48 positive lines", "small64 direct rank-two paths"], + "dense48_line_children": dense_lines, "small64_children": fused, + "dense48_scalar_inverse_events": source.inverse_word(dense_word), + "dense48_scalar_code_stages_in_time_order": [2, 1, 0], + "dense48_code_real_scalar_primitives": 3 * dense_invoice["real_scalar_primitives"], + "small64_complex_signs": 64, "small64_sign_real_scalar_primitives": 128, + "profile": {"1": 96, "2": 64}, "native_rank_mass": 224, + "owned_fields": 0, "private_fields": 0, + "map_inventory": {"dense48_code_views": 288, "dense48_child_wrappers": 192, + "small64_child_wrappers": 128}, + "scope": "Exact operators and native recipes. Recursive hosting and finite map cost are separate.", + } + program = {"schema": "matched-triple25-v1", "source_pins": source.PINS, + "controller_path": CONTROLLER, "controller_sha256": CONTROLLER_PIN, + "stage_checker_sha256": SOURCE_PIN, "dimension": 25, "five_scalar_codes": cuts, + "preferred_response": [{str(j): str(c) for j, c in row.items()} for row in preferred], + "raw_code": "Q (E2 E1 E0) Q^-1", "raw_inverse": "Q (E0 E1 E2) Q^-1", + "path_records": path_records, + "safe_native_line_word": ["Q^-1 on112 fields", "three admitted final-FULL scalar E gauges", "Q on112 fields"], + "safe_native_profile": {"1": 224}, "mixed_native_decoder": mixed, + "dense_H2_fusion_claimed": False} + encoded = (json.dumps(program, sort_keys=True, separators=(",", ":")) + "\n").encode() + (HERE / "TRIPLE25-PROGRAMS.json.gz").write_bytes(gzip.compress(encoded, mtime=0)) + receipt = {"status": "PASS_MATCHED_TRIPLE25_AND_FIVE_CUTS", "source_pins": source.PINS, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "program_decompressed_sha256": sha256(encoded).hexdigest(), + "five_cut_phase_checks": 560, "scalar_gauge_pin": GAUGE_PIN, + "controller_sha256": CONTROLLER_PIN, + "independent_scalar_gauge_replay": invoice, "terminal_path_checks": reports, + "dense48_scalar_gauge_replay": dense_invoice, + "safe_profile": {"1": 224}, "mixed_profile": mixed["profile"], + "mixed_native_rank_mass": mixed["native_rank_mass"], + "mixed_child_phase_coefficient_checks": sum(c["phase_coefficient_checks"] + for c in fused + dense_lines), + "mixed_scalar_real_primitives": 3 * dense_invoice["real_scalar_primitives"] + 128, + "mixed_map_inventory": mixed["map_inventory"], + "dense_H2_fusion_claimed": False, + "scope": "Exact current cuts and triple raw operator. No coupled native lower bound or supplier improvement."} + (HERE / "TRIPLE25-CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-FREEZE.json new file mode 100644 index 0000000000..276c25354c --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "ACCESS-REVIEW.json": "a720cb81f03864b74be29e8e8179e5caf0add702f8601bc94017f0d17a04777c", + "ACCESS-REVIEW.md": "8a9dd0ab1a751f6d2bfce9dbd5dcca3ca5a46daa53469c4914f82241d973a86f", + "check_access.py": "0927b3ec17d4e277b05ed62be48bd4710297960fec5f7eb2ea0066cfb571d71f" + }, + "normal_optimized_receipts_equal": true, + "schema": "independent-matched-access-review-v1", + "status": "PASS_INDEPENDENT_MATCHED_D25_ACCESS_AND_FULL_GAUGE" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-REVIEW.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-REVIEW.json new file mode 100644 index 0000000000..18ae6b4a53 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-REVIEW.json @@ -0,0 +1,68 @@ +{ + "actual_one_pair_cuts": [ + { + "bank": "X", + "completed_level": 0, + "stage": 0 + }, + { + "bank": "Y", + "completed_level": 0, + "stage": 1 + }, + { + "bank": "X", + "completed_level": 1, + "stage": 1 + }, + { + "bank": "Y", + "completed_level": 1, + "stage": 2 + }, + { + "bank": "X", + "completed_level": 2, + "stage": 1 + } + ], + "checker_sha256": "0927b3ec17d4e277b05ed62be48bd4710297960fec5f7eb2ea0066cfb571d71f", + "common_frame_scalar_primitives": 2396, + "component_scalar_primitives": [ + 470, + 624, + 470, + 832 + ], + "counts": { + "entry": 672, + "entry_omission_controls": 448, + "exit": 672, + "exit_omission_controls": 448, + "future_Y": 336, + "one_pair_code_port_cuts": 560, + "orthogonal_routes": 336, + "past_X": 672 + }, + "exact_prefix_row_one_norm": "4", + "five_gauge_scalar_primitives": 11980, + "maximum_monomial_view_calls_per_gauge": 224, + "native_children_in_gauge": 0, + "owned_fields_in_gauge": 0, + "scalar_events": { + "add": 264, + "scale": 120 + }, + "scope": "Actual D25 stage views, five one-pair scalar access cuts, and complete2396-scalar common-frame gauge. No three-factor terminal, recursive host or supplier claim in this receipt.", + "source_pins": { + "access_freeze": "0b3e4f09ea0eff1f6106a2611ac80cf0976638da96e7c0e5b289224b159ba96c", + "archive": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "controller": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", + "data": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "gauge_freeze": "a83fad6b1fe12e1cad34989ad4226ab9d1d2fb268362b010845deaea2f42034d", + "matching": "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", + "native_decompressed": "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025", + "views_compressed": "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f" + }, + "status": "PASS_INDEPENDENT_MATCHED_D25_ACCESS_AND_FULL_GAUGE" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-REVIEW.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-REVIEW.md new file mode 100644 index 0000000000..69436a5613 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/ACCESS-REVIEW.md @@ -0,0 +1,117 @@ +# Independent review of the D25 views and FULL scalar code + +The actual dimension-25 entry and exit views pass. The five scalar +code cuts in the pinned one-pair program pass. The complete common-frame +code for the new response E costs 2,396 real scalar primitives. It uses +no owned field, private field, or native child. + +This review does not certify the three-factor terminal, recursive +hosting, finite precision, or a complete supplier invoice. Those are +separate obligations. + +## Exact access check + +The source is the DATA member of the pinned selected-replay archive. +The checker imports no producer. It reads the 73-axis route records +and checks each of the 336 stage-port records for stages 0, 1, and 2. +The first 25 columns preserve their span. The other 48 columns are +unchanged coordinate columns. Every restricted route is an orthogonal +involution and fixes its intrinsic line q. + +For a list of line factors, write its character phase as a polynomial +with values in Z/4Z. The values on basis vectors fix the diagonal +coefficients. Binary polar rows fix the off-diagonal coefficients. +All phases here have zero constant coefficient. Thus equality of these +data proves equality on every character; it includes the global phase. +The checker uses this representation to verify each literal route and +translation. It does not discard the even phase. + +The independent counts are 672 entry identities, 672 exit identities, +336 future-Y identities, and 672 past-X identities. Deleting the entry +translation fails in 448 cases. Deleting the exit translation fails in +448 cases. These controls reject a phase-free use of the frame labels. + +The pinned controller has these five occurrences: + +| Bank | Code stage | Completed or hole level | +| --- | --- | --- | +| X | 0 | 0 | +| Y | 1 | 0 | +| X | 1 | 1 | +| Y | 2 | 1 | +| X | 1 inverse | 2 | + +All 560 port-cut instances belong to the checked access cones. In each +specified view, every field in the code has the same frame. Scalar +mixing is therefore valid for arbitrary field values at these cuts. +This result does not permit the same code at an arbitrary Y hole. + +The all-FULL X endpoint is also checked against the actual native +payload, for both providers and both directions. No frame change is +inferred from the scalar response alone. + +## Independent scalar calculation + +The code matrix equals the actual native response. Its square is the +identity. It has 48 rows with four nonzero entries and 64 rows with one +nonzero entry. There are no diagonal entries. + +For each two-field code, let its matrix be [[a,b],[c,d]], where all +four entries have absolute value one and d=-abc. The four operations + +```text +x <- a*x +x <- x+b*y +y <- 2*d*y +y <- y+c*a*x +``` + +give the stated matrix on arbitrary x and y. The last row is +c*x+(2*d+c*a*b)*y=c*x+d*y. No zero input is used. + +The complete 112-field word consists of the pair codes, a signed +permutation in those coordinates, the inverse pair codes, and the +64-port negative permutation. The four prices are 470, 624, 470, +and 832. Their sum is 2,396. The literal census is 264 complex ADDs +and 120 complex SCALEs. Forward row replay and a separate reverse +column replay both give the full response. Applying the complete +literal word twice gives the identity. Omitting the inverse pair +code gives a different matrix. + +The exact largest prefix row one-norm is four. This is a local +coefficient growth bound, not a finite precision proof. + +Each routed application has a conservative allowance of 224 monomial +view calls. Those calls are separate from its scalar price. The five +controller codes cost 11,980 scalar primitives, which is 1,360 less +than five copies of the prior 2,668-primitive word. This subtraction +does not establish a complete supplier improvement. + +## Reproduction and provenance + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_access.py +python3 -I -B -O work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_access.py +``` + +Both runs must report: + +```text +PASS_INDEPENDENT_MATCHED_D25_ACCESS_AND_FULL_GAUGE +``` + +The receipts must have equal bytes. ACCESS-REVIEW.json contains the +source pins and exact counts. ACCESS-FREEZE.json preserves this review +separately from later terminal work. + +The bridge-access lane supplied the physical views. The independent +review lane supplied the cheaper scalar word. The oblique and controller +lanes supplied the native matched response, and the history lane supplied +its permutation64 part. The encoded-controller lane supplied the five +code cuts. This review used OpenAI Codex assistance. It made no PR, +commit, or push. + +Before a future PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-FREEZE.json new file mode 100644 index 0000000000..906766724b --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-FREEZE.json @@ -0,0 +1,11 @@ +{ + "access_review_freeze_sha256": "13df3e89b983936bd2126c67204d229fc25d1f9f011fc77505c3376476fbd499", + "files": { + "TERMINAL-HOSTING-REVIEW.json": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6", + "TERMINAL-HOSTING-REVIEW.md": "4f062b945c9871b703c7f6b5cae01de8c163bda0b0c93283b66fb171f5bf094b", + "check_terminal_and_hosting.py": "13d69f63a147e69d4b28be48a298f8f12bb025d8b2a93e0a5e6d30a371913c64" + }, + "normal_optimized_receipts_equal": true, + "schema": "independent-triple-and-one-pair-review-v1", + "status": "PASS_INDEPENDENT_TRIPLE_TERMINAL_AND_ONE_PAIR_HOSTING" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.json new file mode 100644 index 0000000000..373650a9b3 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.json @@ -0,0 +1,150 @@ +{ + "admission_freeze_sha256": "0c27631267119efca1a416f0f299a2ce398a87fea313611341133b7c3736d8ed", + "checker_sha256": "13d69f63a147e69d4b28be48a298f8f12bb025d8b2a93e0a5e6d30a371913c64", + "cover_order": "1402575762037550245974927108561766348252867730943485007822736244380743658751530106880000000", + "dense_inverse_scalar_primitives_per_stage": 1564, + "exact_native_kernel_branches": 448, + "full_rank_mass_per_cover": 5600, + "hosting_scope": "Data stock, exact owner bijections, and row/LIFO layout under the admitted all-size child contract. No all-size grouping, finite precision, or complete finite supplier invoice is established here.", + "improved_mixed_local_and_code_subtotal": 25896, + "improved_safe_local_and_eight_code_subtotal": 28264, + "local_words": { + "base": { + "backward": { + "columns": 224, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "omitted_helper_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "rank_mass": 1792, + "scalar_primitives": 3032 + }, + "forward": { + "columns": 224, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "omitted_helper_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "rank_mass": 1792, + "scalar_primitives": 3032 + } + }, + "extra": { + "backward": { + "columns": 224, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "omitted_helper_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "rank_mass": 1792, + "scalar_primitives": 3032 + }, + "forward": { + "columns": 224, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "omitted_helper_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "rank_mass": 1792, + "scalar_primitives": 3032 + } + } + }, + "mixed_full_native_profile": { + "1": 576, + "2": 208, + "5": 144, + "7": 336, + "8": 192 + }, + "mixed_terminal_map_calls": 608, + "mixed_terminal_profile": { + "1": 96, + "2": 64 + }, + "mixed_terminal_scalar_primitives": 4820, + "old_admission_local_and_eight_code_subtotal": 30440, + "ordered_controller": { + "decoder": "Q E0^-1 E1^-1 E2^-1 Q^-1", + "free_noncommuting_identity": true, + "preterminal": [ + "-y", + "E2 E1 E0 x" + ], + "raw_first_bank": "Q E2 E1 E0 Q^-1" + }, + "phase_dependency": "The previously independent native review supplies full local phase verification; this review rechecks the terminal kernels directly.", + "productive_dimension_product": 5600, + "productive_roles": "314176970696411255098383672317835662008642371731340641752292918741286579560342743941120000000", + "safe_full_native_profile": { + "1": 704, + "2": 144, + "5": 144, + "7": 336, + "8": 192 + }, + "safe_terminal_charts": 112, + "source_pins": { + "access": "13df3e89b983936bd2126c67204d229fc25d1f9f011fc77505c3376476fbd499", + "admission": "0c27631267119efca1a416f0f299a2ce398a87fea313611341133b7c3736d8ed", + "admission_proof": "799eab4224c40ec980712593cb1bcd8e62522f1fb1b5ebe79d0f3569d10111de", + "admission_sources": "49cce325ea25508f7ff22f3ec48e8ef01297104bc76a9080d482a4f9ba929f46", + "native_review": "952019e4611494972f67bf76b3636886260e425ecca2a67ceb512b144808587b", + "native_review_freeze": "8d0ac5e7890b55d871c4133a1027d2ee97690bfcf2d80206cbb7784a3bde3845", + "native_review_receipt": "5411f46eb4050b85fa53b5a285ae96933fbb764c8e65cdb35f68d002b49f3788", + "triple": "0a20fdae1f2497088e0e62e72960d81c44c48805b5685b08710ceed898bc22ce" + }, + "status": "PASS_INDEPENDENT_TRIPLE_TERMINAL_AND_ONE_PAIR_HOSTING", + "strict_positive_native_moment_failure": true, + "triple_paths": { + "T": { + "dense_paths": 3072, + "paths": 3136, + "phase_coefficients": 1022336, + "small_paths": 64 + }, + "T_inverse": { + "dense_paths": 3072, + "paths": 3136, + "phase_coefficients": 1022336, + "small_paths": 64 + } + }, + "triple_payload_decompressed_sha256": "b65a2b14a1e61c566063195d0ef363c7dae0d06bb2232e4c872275479f327419" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.md new file mode 100644 index 0000000000..e0ca1c6028 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/TERMINAL-HOSTING-REVIEW.md @@ -0,0 +1,297 @@ +# Independent review of the actual triple and one-pair stock + +The frozen triple terminal and the frozen one-pair admission packet +pass this review within their stated scopes. The terminal has an exact +implementation with 96 rank-one children and 64 rank-two children. The +new local word can use 224 independent productive data roles per cover +element. Its 408 unused helper slots do not impose a hidden input promise. + +The completed word has native rank mass 5,600 per cover element. This +equals 224 times the ambient dimension 25. Every paid child has rank +less than 25. Thus this word fails the native moment test for every +positive improvement exponent. The mixed terminal does not change that +conclusion. + +## Reviewed sources and method + +The main source packets are: + +- `bridge-access-20261017/matched-stage-access-20261018/TRIPLE25-FREEZE.json`, + SHA-256 `0a20fdae1f2497088e0e62e72960d81c44c48805b5685b08710ceed898bc22ce`. +- `history-encoding/one-pair-admission-20261018/FREEZE.json`, + SHA-256 `0c27631267119efca1a416f0f299a2ce398a87fea313611341133b7c3736d8ed`. +- This lane's `ACCESS-FREEZE.json`, + SHA-256 `13df3e89b983936bd2126c67204d229fc25d1f9f011fc77505c3376476fbd499`. + +The checker imports only the frozen independent access checker in this +review directory. It imports no producer. It checks the source hashes, +reconstructs the ordered stage products, expands the native kernels with +exact Gaussian rational coefficients, and propagates scalar output +columns backwards through the local words. + +The earlier independent matched-native review supplies the full local +native phase proof. Its receipt hash is +`5411f46eb4050b85fa53b5a285ae96933fbb764c8e65cdb35f68d002b49f3788`. +This review checks that dependency and the same local payload. It does +not count the inherited phase proof as a new native phase replay. + +## Ordered physical endpoint + +Let E_s be the full routed stage operator and put T=E_2 E_1 E_0. +Treat the three E_s and Q as free invertible operators. The five-code +controller gives + +```text +(x,y) -> (-y,T x). +``` + +This identity uses the inverse in the actual backward call. It uses +neither commutation nor E_s squared equals the identity. + +The raw input is (Qx,y). The completed physical fields before the old +terminal are (-F y,F Q^-1 T x). The old translated signed exchange +therefore leaves (F Q T x,F y). Relative to the original raw input, +the remaining code is diag(Q T Q^-1,I). + +The required first-bank inverse is Q T^-1 Q^-1. Its chronological +sequence is Q^-1, E_2^-1, E_1^-1, E_0^-1, Q. The independent check +multiplies the complete two-by-two operator matrices. It rejects both +the reversed order of the three inverse codes and deletion of the +last Q. It also checks that the actual routed T differs from the +actual routed T inverse. + +The separated construction therefore has 224 rank-one children. The +three scalar codes between its two line passes cannot be removed by +the identity E squared equals the identity at one local stage. + +## Actual path calculation + +The actual response preserves two sets of ports. Each of its 48 dense +rows has four entries. Each of its other 64 rows has one entry. For +each ordered triple, the checker composes the actual stage edge maps. +It checks every path, rather than replacing a routed stage by a local +matrix. + +There are 3,136 paths in each direction: 3,072 on the dense set and 64 +on the permutation set. For fixed output and input ports, all complete +cover maps are distinct. Right multiplication by such a map sends a +fixed regular-cover owner to a distinct owner. Thus arbitrary cover +inputs can separate the paths; cancellation between different owners +is not available. + +For a path with map A and scalar coefficient c, the complete operator +in the output chart is + +```text +c X_delta C_a C_b^-1 P_A, +a=q_p, b=A q_r. +``` + +Here X_delta is the payload translation on every tensor copy. Both +line vectors are nonzero and distinct. In the actual packet they are +orthogonal as well. The checker derives the FULL conjugation phase +from the values of its Z4 polynomial on zero, each basis vector, and +each sum of two basis vectors. These values determine all constant, +linear, and quadratic coefficients. There are 1,022,336 such checks +for each triple direction. + +The cover map and the payload map have distinct roles. The cover map +sends output owner h to input owner hA. The factor P_A writes the +source chart in the output chart. If local chart coordinates are +converted to physical coordinates, the complete path is conjugated +on its two sides by the corresponding output and input charts. +This is one field-and-address map; it does not require a duplicate +input field. The inherited final full-cover correction remains part +of the common-FULL convention. + +Each path has four nonzero one-copy address branches, so it has +support 4^f at width f. Other paths at the same output cannot cancel +these branches, because they have different source owners. This +excludes a fixed number of scalar and monomial passes for the stated +raw operator. It is not a lower bound on native children in a coupled +decoder. + +## The 64 rank-two calls + +Each permutation output has one path, with coefficient -1. The input +ports form a permutation. Each cover map is invertible. These facts +give a bijection on all 64 field-and-cover families. + +Write alpha=(1+i)/2 and beta=(1-i)/2. The exact line kernels are + +```text +C_v = alpha I + beta X_v, +C_v^-1 = beta I + alpha X_v = X_v C_v. +``` + +The supplied orthogonal basis G has first two columns a and b. The +checker verifies G, both inverse orders, and every serialized +transvection from the identity basis. The path is therefore + +```text +-X_(delta+b) P_G H2 P_G^-1 P_A. +``` + +The inverse line contributes the translation b. The sign -1 is a +scalar sign on the whole field; it is not an unrecorded phase per +tensor copy. + +As an independent check, expand both sides into four translations +with Gaussian rational coefficients. The checker compares all four +coefficients and all four translation vectors for each of the 64 +paths. It does not infer the global phase from a symplectic tableau. +Omitting the scalar sign fails. The exact one-copy identity tensors +to every positive width. + +## The remaining 48 ports + +On the invariant dense set, apply all 48 inverse intrinsic lines, +then the restricted stage inverses in chronological order 2, 1, 0, +then all 48 positive intrinsic lines. This is precisely the +restriction of Q T^-1 Q^-1. + +The 96 serialized line recipes each pass a direct two-coefficient +Gaussian check. Their charts, inverse charts, and translations pass +as well. The restricted scalar inverse fixes the other 64 ports. +Forward row and reverse column replay give the full specified map. +Its price is 1,564 real primitives per stage, and its largest prefix +row one-norm is four. + +The complete terminal component therefore has this invoice: + +| Item | Exact count or stated bound | +| --- | --- | +| Rank-one children | 96 | +| Rank-two children | 64 | +| Native rank mass | 224 | +| Three restricted scalar codes | 4,692 real primitives | +| 64 complex scalar signs | 128 real primitives | +| Total scalar primitives | 4,820 | +| Restricted code views | 288 map calls | +| Rank-one wrappers | 192 map calls | +| Rank-two wrappers | 128 map calls | +| New owned or private fields | 0 | + +The 608 map calls are an inventory, not a finite real-operation +price. Child work areas are governed by the inherited recursive +contract. This invoice does not include the old signed exchange, +all global cover work, or finite precision. There is no 112-H2 +implementation in this packet. + +## The 224-role direct summand + +For both providers and both directions, every event in the actual +local payload names a data role from 0 through 223. The 408 remaining +slots have no event and keep their initial frame. Their frame-rank +census is {0:274,1:108,2:24,4:2}. + +The independent reverse scalar replay covers all 224 data columns in +each of the four words. Scalar ADDs use distinct fields in the same +exact frame. Every native target is a data field. Every data field +gets total native rank eight. The complete local profile is +{1:160,2:48,5:48,7:112,8:64}: 432 children and rank mass 1,792. +The scalar cost is 3,032 per call. All 224 endpoint maps name data +fields. This proves an exact direct summand for arbitrary helper +values, rather than a restriction to zero helpers. + +The old admission packet's scalar words and their inverse also pass +independent replay at 2,668 primitives each. Its local-plus-eight-code +subtotal 30,440 is correct. Replacing those codes by the already +reviewed 2,396-primitive word gives 28,264 for the separated terminal. +Using the mixed terminal gives 25,896 for three local words, five +full codes, three restricted codes, and the 64 signs. These are +component subtotals and exclude the other operations stated above. + +## Owner and row hosting + +Use the regular cover G=O(25,2). For each side and port, the rule +h=d rho_(s,p) is a bijection between body labels and owner labels. +The 224 side-port families are disjoint. A complete cover sweep +therefore partitions all productive data fields. A later code or +local stage starts after that sweep has finished. No helper reuse +or input replication is needed for this argument. + +The all-ones vector in dimension 25 has norm one and is fixed by +every isometry. Its orthogonal complement is a 24-dimensional +nondegenerate alternating space. Restriction identifies O(25,2) +with Sp(24,2). A first symplectic pair has +(2^24-1)2^23 choices, and the count then continues on its +22-dimensional complement. Hence + +```text +|G| = 2^144 product_(j=1..12)(2^(2j)-1). +``` + +The checker calculates the same order by this recurrence. Its bit +length is 300. The productive role count N=224|G| has bit length +308. This large finite factor cancels from a normalized native +moment. It remains in physical stock and row reserve. + +The row split and LIFO argument in the pinned primary stream proof +applies to N arbitrary roles. If row counts are divisible by N^k, +the decomposition u=N g+w gives each role one complete suffix and +exactly 1/N of the parent volume. A child removes no address from +that suffix. The other streams are parked and restored. These are +layout facts and do not require four data pairs or the old helpers. + +The primary proof's complete asymptotic theorem assumes a strict +native moment inequality. That theorem cannot be invoked for this +word: the completed word fails the inequality. Only its row split, +complete-range, and LIFO arguments are used here. + +The parent has 25 address slots, so a binary row addition can use a +third distinct payload slot and restore its arbitrary bits. This +slot is an address part of the active stream, not an additional +productive field. The grouped children have rank at most eight; +the stated size guard is 25^2-2*8^2=497. Termination and a logarithmic +row reserve follow under the admitted size-reduction rule. Actual +arbitrary-size grouping, remainder handling, child depth bounds, +finite coefficient width, and exact integer recovery are inherited +obligations. This review does not prove them afresh. + +## Complete native consequence and limit + +The separated completion has profile +{1:704,2:144,5:144,7:336,8:192}, with 1,520 children. +The mixed completion has profile +{1:576,2:208,5:144,7:336,8:192}, with 1,456 children. +Both have mass 5,600. + +For every b>0 and every paid rank r<25, +r^(1-b)>r*25^(-b). Summation gives + +```text +sum_r n_r r^(1-b) > 5600*25^(-b) + = 224*25^(1-b). +``` + +This proves failure of the positive native moment test for both +specified completions. It does not exclude a cheaper coupled +terminal, a changed code placement, or a different local response. + +## Reproduction + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py +python3 -I -B -O work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py +``` + +Both runs must report: + +```text +PASS_INDEPENDENT_TRIPLE_TERMINAL_AND_ONE_PAIR_HOSTING +``` + +The receipts must have equal bytes. TERMINAL-HOSTING-FREEZE.json +preserves this review independently of ACCESS-FREEZE.json. + +This review credits the bridge-access lane for the literal terminal, +the history lane for the data-stock and row argument, the independent +review lane for the native phase proof and cheaper scalar code, and +the controller and oblique lanes for the local response. It used +OpenAI Codex assistance. 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/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_access.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_access.py new file mode 100644 index 0000000000..44d2b6c45a --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_access.py @@ -0,0 +1,253 @@ +"""Check the actual 25-axis views and the cheaper common-frame gauge.""" + +from collections import Counter, defaultdict +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from pathlib import Path +import tarfile + + +HERE = Path(__file__).resolve().parent +CHECKER_SHA = sha256(Path(__file__).read_bytes()).hexdigest() +LANES = HERE.parents[1] +ROOT = LANES.parents[2] +ACCESS = LANES / "bridge-access-20261017/matched-stage-access-20261018" +GAUGE = LANES / "independent-review-20261017/matched-full-gauge-20261018" +PINS = { + "access_freeze":"0b3e4f09ea0eff1f6106a2611ac80cf0976638da96e7c0e5b289224b159ba96c", + "gauge_freeze":"a83fad6b1fe12e1cad34989ad4226ab9d1d2fb268362b010845deaea2f42034d", + "views_compressed":"1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f", + "matching":"e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", + "native_decompressed":"95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025", + "archive":"f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "data":"c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "controller":"f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", +} +E = [1 << j for j in range(25)] +MASK = (1 << 25)-1 + + +def need(test, message): + if not test: + raise ValueError(message) + + +def pin(path, key, compressed=False): + raw = path.read_bytes() + if compressed: + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == PINS[key], "Pinned source: " + key) + return raw + + +def frozen(folder, key): + manifest = json.loads(pin(folder/"FREEZE.json", key)) + for name, digest in manifest["files"].items(): + need(sha256((folder/name).read_bytes()).hexdigest() == digest, "Frozen artifact: " + name) + + +def act(columns, x): + out = 0 + for j, value in enumerate(columns): + if x >> j & 1: + out ^= value + return out + + +def phase(terms): + """Use Z4 basis values and binary off-diagonal polar rows.""" + diagonal, polar = [0]*25, [0]*25 + for vector, exponent in terms: + need(vector <= MASK, "The phase direction lies in dimension25") + for j in range(25): + if vector >> j & 1: + diagonal[j] += exponent + if exponent % 2: + polar[j] ^= vector ^ (1 << j) + return tuple(x % 4 for x in diagonal), tuple(polar) + + +def translated(terms, rho, delta): + return phase([(act(rho, v), a) for v, a in terms] + [(delta, 2)]) + + +def matrix(rows): + return [{int(j):F(a) for j, a in row.items()} for row in rows] + + +def product(a, b): + out = [] + for row in a: + values = defaultdict(F) + for j, x in row.items(): + for k, y in b[j].items(): + values[k] += x*y + out.append({k:v for k, v in values.items() if v}) + return out + + +def scalar_replay(events): + rows = [{p:F(1)} for p in range(112)] + price, peak = 0, F(1) + counts = Counter() + for event in events: + op, target = event[:2] + c = F(*event[-2:]) + numerator, denominator = abs(c.numerator), c.denominator + need(numerator > 0 and denominator & (denominator-1) == 0, "Nonzero dyadic coefficient") + if op == "scale": + need(len(event) == 4 and numerator & (numerator-1) == 0, "Unit dyadic SCALE") + rows[target] = {p:c*a for p, a in rows[target].items()} + price += 2*(abs(numerator.bit_length()-denominator.bit_length()) + (c < 0)) + else: + need(op == "add" and len(event) == 5 and target != event[2], "Plain in-place ADD") + values = defaultdict(F, rows[target]) + for p, a in rows[event[2]].items(): + values[p] += c*a + rows[target] = {p:a for p, a in values.items() if a} + price += 2*(1+numerator.bit_length()+numerator.bit_count()+denominator.bit_length()) + counts[op] += 1 + peak = max(peak, sum(abs(a) for a in rows[target].values())) + return rows, price, peak, counts + + +def reverse_columns(events): + columns = [{p:F(1)} for p in range(112)] + for event in reversed(events): + c = F(*event[-2:]) + target = event[1] + if event[0] == "scale": + columns[target] = {p:c*a for p, a in columns[target].items()} + else: + source = event[2] + values = defaultdict(F, columns[source]) + for p, a in columns[target].items(): + values[p] += c*a + columns[source] = {p:a for p, a in values.items() if a} + return columns + + +def main(): + frozen(ACCESS, "access_freeze") + frozen(GAUGE, "gauge_freeze") + packed = pin(LANES/"bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", "views_compressed") + original_views = json.loads(gzip.decompress(packed))["views"] + views = {(v["stage"],v["port"],v["side"]):v for v in original_views} + archive = ROOT/"worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz" + pin(archive, "archive") + with tarfile.open(archive) as source: + raw = source.extractfile("candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json").read() + need(sha256(raw).hexdigest() == PINS["data"], "Actual DATA phase source") + data = json.loads(raw)["recipes"] + dimensions = json.loads((ACCESS/"DIMENSION25-VIEWS.json").read_text()) + entries = {(r["stage"],r["port"]):r for r in dimensions["entries"]} + counts = Counter() + cone = {} + for p, row in enumerate(data): + q = row["q"] + for s in range(3): + full_rho = [1 << j for j in range(73)] if s == 0 else views[s,p,"X"]["route_columns"] + need(all(x <= MASK for x in full_rho[:25]) and full_rho[25:] == [1 << j for j in range(25,73)], + "No route uses a discarded coordinate") + rho = full_rho[:25] + need(all(((a&b).bit_count() % 2) == (i == j) for i,a in enumerate(rho) for j,b in enumerate(rho)), + "Exact O25 membership") + need([act(rho, x) for x in rho] == E and act(rho,q) == q, "Route inverse and fixed intrinsic line") + record = entries[s,p] + align = row["stage_alignment"][s] + need(record == {"port":p,"stage":s,"q":q,"route_columns":rho,"literal_stage_alignment":align}, + "Every emitted dimension25 record equals actual source data") + need(all(x <= MASK for x in align.values()), "Every entry and exit translation restricts") + counts["orthogonal_routes"] += 1 + for side in ("X","Y"): + before = ([(q,1)] if side == "X" else []) if s == 0 else [(x,1) for x in E[:9+8*(s-1)]] + if s and side == "Y": + before += [(q,-1)] + want = [(x,1) for x in E[9:9+8*s]] + ([(q,1)] if side == "X" else []) + delta = act(rho,align["entry_"+side]) + need(translated(before,rho,delta) == phase(want), "Exact current entry with common exterior") + counts["entry"] += 1 + counts["entry_omission_controls"] += translated(before,rho,0) != phase(want) + after = [(x,1) for x in E[:9+8*s]] + ([(q,-1)] if side == "Y" else []) + need(translated(after,rho,align["exit_"+side]) == phase(after), "Exact current exit") + counts["exit"] += 1 + counts["exit_omission_controls"] += translated(after,rho,0) != phase(after) + for level in range(s,3): + full = [(x,1) for x in E[:9+8*level]] + delta = 0 if s == 0 else views[s,p,"X"]["translation_after_route"] + need(translated(full,rho,delta) == phase(full), "Every past-X view") + counts["past_X"] += 1 + cone[s,level,"X",p] = True + for level in range(s): + hole = [(x,1) for x in E[:9+8*level]] + [(q,-1)] + common = [(x,1) for x in E[9:9+8*level]+E[9+8*(s-1):9+8*s]] + delta = views[s,p,"Y"]["translation_after_route"] + need(translated(hole,rho,delta) == phase(common), "Every future-Y view") + counts["future_Y"] += 1 + cone[s,level,"Y",p] = True + cuts = [(0,0,"X"),(1,0,"Y"),(1,1,"X"),(2,1,"Y"),(1,2,"X")] + controller = json.loads(pin(LANES/"encoded-controller/one-pair-current-codes-20261018/PROGRAM.json", + "controller")) + need(controller["program"] == [ + ["forward",0],["code_X",0,1],["code_Y",1,1], + ["backward",1],["code_X",1,1],["code_Y",2,1], + ["forward",2],["code_X",1,-1]], "The pinned controller gives these five code cuts") + need(all(cone[s,level,side,p] for s,level,side in cuts for p in range(112)), "All five actual one-pair code cuts") + counts["one_pair_code_port_cuts"] = len(cuts)*112 + + matching = json.loads(pin(LANES/"controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json", "matching")) + native = json.loads(pin(LANES/"oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz", "native_decompressed", True)) + response = matrix(native["response"]) + gauge = json.loads((GAUGE/"FULL-GAUGE.json").read_text()) + need(response == matrix(gauge["response"]) == matrix(json.loads((ACCESS/"FULL-GAUGE-PROGRAM.json").read_text())["response"]), + "The cheaper gauge and stage packet use the actual same full response") + need(product(response,response) == [{p:F(1)} for p in range(112)], "The actual response is an involution") + need(all(p not in row for p,row in enumerate(response)), "No physical fixed point") + need(Counter(map(len,response)) == {4:48,1:64}, "The actual dense48 and permutation64 supports") + for provider in native["providers"].values(): + for word in provider.values(): + need(all(word["frames"][word["final"][p]] == word["frames"][1] for p in range(112)), + "All native X outputs have one common FULL frame") + need(sorted(word["frames"][1]) == [1 << j for j in range(9)], "Actual local FULL frame") + events = gauge["events"] + result, price, peak, census = scalar_replay(events) + need(result == response and reverse_columns(events) == response, "All rows and independent columns of the scalar word") + need(scalar_replay(events+events)[0] == [{p:F(1)} for p in range(112)], "The literal word squared is identity") + c = gauge["cuts"] + parts = [events[:c["code_end"]],events[c["code_end"]:c["swap_end"]], + events[c["swap_end"]:c["undo_end"]],events[c["undo_end"]:]] + bills = [scalar_replay(part)[1] for part in parts] + need(bills == [470,624,470,832] and price == 2396 and peak == 4, "Exact complete scalar price and prefix norm") + need(scalar_replay(parts[0]+parts[1]+parts[3])[0] != response, "Omitting the pair undo must fail") + need(all(gauge[name] == 0 for name in ("owned_fields","private_fields","native_children")), "No hidden scratch or native work") + # Pair-code algebra uses arbitrary values, and never a zero target. + for pair in matching["pair_codes"]: + a,b = map(F,pair["matrix"][0]) + c0,d = map(F,pair["matrix"][1]) + need(all(abs(x) == 1 for x in (a,b,c0,d)) and d == -a*b*c0, + "Every four-operation pair code has the stated exact matrix") + need(sha256(Path(__file__).read_bytes()).hexdigest() == CHECKER_SHA, "Checker bytes stayed fixed") + receipt = { + "status":"PASS_INDEPENDENT_MATCHED_D25_ACCESS_AND_FULL_GAUGE", + "source_pins":PINS, + "checker_sha256":CHECKER_SHA, + "counts":dict(sorted(counts.items())), + "actual_one_pair_cuts":[{"stage":s,"completed_level":level,"bank":side} for s,level,side in cuts], + "common_frame_scalar_primitives":price, + "component_scalar_primitives":bills, + "scalar_events":dict(census), + "exact_prefix_row_one_norm":str(peak), + "native_children_in_gauge":0, + "owned_fields_in_gauge":0, + "maximum_monomial_view_calls_per_gauge":224, + "five_gauge_scalar_primitives":5*price, + "scope":"Actual D25 stage views, five one-pair scalar access cuts, and complete2396-scalar common-frame gauge. No three-factor terminal, recursive host or supplier claim in this receipt.", + } + (HERE/"ACCESS-REVIEW.json").write_text(json.dumps(receipt,indent=2,sort_keys=True)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py new file mode 100644 index 0000000000..cb234ecede --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py @@ -0,0 +1,427 @@ +"""Check the terminal kernels, ordered endpoint, and data-only role stock.""" + +from collections import Counter, defaultdict +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.parents[2] +SELF_PIN = sha256(Path(__file__).read_bytes()).hexdigest() +UNIT = [1 << j for j in range(25)] +PINS = { + "access": "13df3e89b983936bd2126c67204d229fc25d1f9f011fc77505c3376476fbd499", + "triple": "0a20fdae1f2497088e0e62e72960d81c44c48805b5685b08710ceed898bc22ce", + "admission": "0c27631267119efca1a416f0f299a2ce398a87fea313611341133b7c3736d8ed", + "admission_proof": "799eab4224c40ec980712593cb1bcd8e62522f1fb1b5ebe79d0f3569d10111de", + "admission_sources": "49cce325ea25508f7ff22f3ec48e8ef01297104bc76a9080d482a4f9ba929f46", + "native_review": "952019e4611494972f67bf76b3636886260e425ecca2a67ceb512b144808587b", + "native_review_receipt": "5411f46eb4050b85fa53b5a285ae96933fbb764c8e65cdb35f68d002b49f3788", + "native_review_freeze": "8d0ac5e7890b55d871c4133a1027d2ee97690bfcf2d80206cbb7784a3bde3845", +} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def pinned(path, key): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == PINS[key], "Source pin: " + key) + return raw + + +def freeze(path, key=None): + raw = pinned(path, key) if key else path.read_bytes() + manifest = json.loads(raw) + for name, digest in manifest["files"].items(): + need(sha256((path.parent/name).read_bytes()).hexdigest() == digest, "Frozen bytes: " + name) + return sha256(raw).hexdigest() + + +def act(columns, value): + result = 0 + while value: + low = value & -value + result ^= columns[low.bit_length()-1] + value ^= low + return result + + +def compose(left, right): + return tuple(act(left, v) for v in right) + + +def rank(vectors): + pivots = {} + for value in vectors: + while value: + top = value.bit_length()-1 + if top in pivots: + value ^= pivots[top] + else: + pivots[top] = value + break + return len(pivots) + + +def add_to(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 scalar_price(event): + value = F(*event[-2:]) + n, d = abs(value.numerator), value.denominator + need(n > 0 and d & (d-1) == 0, "Dyadic event") + if event[0] == "scale": + need(n & (n-1) == 0, "Dyadic unit scale") + return 2*(abs(n.bit_length()-d.bit_length())+(value < 0)) + return 2*(1+n.bit_length()+n.bit_count()+d.bit_length()) + + +def local_stock(word, response, direction): + current = list(word["start"]) + need(len(current) == 632 and current[224:] == word["final"][224:], "Unused helper frames") + widths, profile, price = [0]*224, Counter(), 0 + frames = word["frames"] + for event in word["events"]: + if event[0] == "native": + _, target, old, new, width, key = event + need(0 <= target < 224 and current[target] == old, "Native data role") + need(rank(frames[old]+frames[new]) == len(frames[new]), "Nested frames") + need(width == len(frames[new])-len(frames[old]) == word["native_recipes"][key]["rank"], + "Native rank") + current[target] = new + widths[target] += width + profile[width] += 1 + else: + need(event[0] == "scalar", "No hidden event type") + op, frame = event[1:] + target = op[1] + need(0 <= target < 224 and current[target] == frame, "Scalar data role") + if op[0] == "add": + need(0 <= op[2] < 224 and op[2] != target and current[op[2]] == frame, + "Distinct equal-frame data operands") + else: + need(op[0] == "scale", "Scalar grammar") + price += scalar_price(op) + need(current == word["final"] and widths == [8]*224, "Complete data progress and untouched helper frames") + # Propagate output columns backwards. This does not use the producer's row replay. + columns = [{p:F(1)} for p in range(224)] + for event in reversed(word["events"]): + if event[0] != "scalar": + continue + op = event[1] + coefficient = F(*op[-2:]) + if op[0] == "scale": + columns[op[1]] = {p:coefficient*v for p,v in columns[op[1]].items()} + else: + add_to(columns[op[2]], columns[op[1]], coefficient) + expected = [{p:F(1)} for p in range(224)] + for p, row in enumerate(response): + for r, value in row.items(): + if direction == "forward": + expected[r][112+p] = value + else: + expected[112+p][r] = -value + need(columns == expected, "Independent reverse replay of all224 columns") + need(profile == {1:160,2:48,5:48,7:112,8:64} and price == 3032, "Local profile and scalar price") + need(len(word["endpoint_adapters"]) == 224 and + {(r["role"],r["port"]) for r in word["endpoint_adapters"]} == + {(role,p) for role in ("source","target") for p in range(112)}, "Complete data endpoint inventory") + return {"columns":224,"native_profile":dict(profile),"rank_mass":sum(widths), + "scalar_primitives":price,"omitted_helper_ranks":dict(Counter(len(frames[f]) for f in current[224:]))} + + +def reduce_letters(word): + out = [] + for letter in word: + if out and out[-1] == -letter: + out.pop() + else: + out.append(letter) + return tuple(out) + + +def ring_product(a, b): + result = defaultdict(F) + for x, u in a.items(): + for y, v in b.items(): + result[reduce_letters(x+y)] += u*v + return {w:v for w,v in result.items() if v} + + +def block_product(a, b): + result = [[{} for _ in range(2)] for _ in range(2)] + for i in range(2): + for j in range(2): + for k in range(2): + add_to(result[i][j], ring_product(a[i][k],b[k][j])) + return result + + +def diagonal(a, b): + return [[a,{}],[{},b]] + + +def ordered_controller(program): + one, minus = {():F(1)}, {():F(-1)} + identity = diagonal(one,one) + result = identity + for kind, stage, *power in program: + symbol = stage+1 + value = {(symbol if not power else symbol*power[0],):F(1)} + if kind == "forward": + event = [[one,{}],[value,one]] + elif kind == "backward": + event = [[one,{(-symbol,):F(-1)}],[{},one]] + elif kind == "code_X": + event = diagonal(value,one) + else: + need(kind == "code_Y", "Controller event") + event = diagonal(one,value) + result = block_product(event,result) + need(result == [[{},minus],[{(3,2,1):F(1)},{}]], "Ordered controller endpoint") + q, qi = {(4,):F(1)}, {(-4,):F(1)} + old = [[{},{(4,4):F(1)}],[minus,{}]] + physical = block_product(old,block_product(diagonal(one,qi),block_product(result,diagonal(qi,one)))) + need(physical == diagonal({(4,3,2,1,-4):F(1)},one), "Raw input and raw terminal endpoint") + decoder = diagonal({(4,-1,-2,-3,-4):F(1)},one) + need(block_product(decoder,physical) == identity, "Complete ordered endpoint") + wrong = diagonal({(4,-3,-2,-1,-4):F(1)},one) + need(block_product(wrong,physical) != identity, "Wrong chronological inverse order fails") + missing_line = diagonal({(-1,-2,-3,-4):F(1)},one) + need(block_product(missing_line,physical) != identity, "Missing final original-input line fails") + return {"preterminal":["-y","E2 E1 E0 x"],"raw_first_bank":"Q E2 E1 E0 Q^-1", + "decoder":"Q E0^-1 E1^-1 E2^-1 Q^-1","free_noncommuting_identity":True} + + +def gaussian_mul(a, b): + return (a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0]) + + +ALPHA, BETA = (F(1,2),F(1,2)), (F(1,2),F(-1,2)) + + +def line_kernel(vector, power): + need(power in (-1,1), "Line sign") + return {0:ALPHA if power == 1 else BETA, vector:BETA if power == 1 else ALPHA} + + +def kernel_product(a, b): + result = {} + for u, c in a.items(): + for v, d in b.items(): + value = gaussian_mul(c,d) + old = result.get(u^v,(F(0),F(0))) + result[u^v] = (old[0]+value[0],old[1]+value[1]) + return {v:c for v,c in result.items() if c != (0,0)} + + +def shifted(kernel, delta, sign=1): + return {v^delta:(sign*c[0],sign*c[1]) for v,c in kernel.items()} + + +def native_kernel(record): + g, gi = record["child_basis_columns"], record["child_basis_inverse_columns"] + need(compose(g,gi) == compose(gi,g) == tuple(UNIT), "Both native basis inverse orders") + need(all((u&v).bit_count()%2 == (i==j) for i,u in enumerate(g) for j,v in enumerate(g)), + "Native basis is orthogonal") + columns = list(UNIT) + for v in record["basis_transvections_in_time_order"]: + need(v and v.bit_count()%2 == 0, "Orthogonal transvection") + columns = [x^(v if (x&v).bit_count()%2 else 0) for x in columns] + need(columns == g, "Literal basis transvection program") + result = {0:(F(1),F(0))} + for j in range(record["rank"]): + result = kernel_product(result,line_kernel(g[j],1)) + return shifted(result,record["output_translation"],record["sign"]) + + +def phase_value(packed, eta): + odd, even, cross = packed + result = (odd&eta).bit_count()+2*(even&eta).bit_count() + for j in range(25): + if eta >> j & 1: + result += 2*((cross >> (j*(j-1)//2)) & eta & ((1<A` and `D_j:A->U` satisfy `B_j D_j=13I`. +Products keep their displayed order. In particular, this proof does not +move Q through B or D. + +At pair i use stages `s_i=2i+1` and `t_i=2i+2`. The backward local is + +```text +B_i(a,u;b,v) = (B_s v+q b, u-v-D_s q b+D_s Q a; Q a,v). +``` + +The corrected forward local is + +```text +F_i(h,k;d,v) = (h-q B_t k,k;d,v+k-D_t B_t k). +``` + +The raw forward local subtracts the additional term `D_t q d` from its +ordinary Y output. Both formulas are exact under the local conventions in +the native-escape source packet. Actual inter-call views are a separate +obligation. + +## Event order and endpoint + +Write the original pair as `(a_i,x_i;b_i^0,y_i)`. The selected variables +have dimension eight. The ordinary variables have dimension 104. Form +the ordinary suffix `z_i=x_i-z_(i+1)`, with `z_m=0`. Do not change the +selected X fields. The first full forward shear gives + +```text +b_0=b_0^0+a_0, v_0=y_0+z_0. +b_i=b_i^0 for i>0. +``` + +At each pair, run B. Add the next idle ordinary X to active ordinary X. +Subtract active ordinary Y from next idle ordinary Y. Run F. Subtract +the same idle X. Add retired ordinary Y to next idle Y. The two operations +with the next pair are absent at the last pair. At the end, in descending +pair order, add completed ordinary X from pair `i-1` to pair i. + +Define + +```text +c_i = Q a_i-q b_i, +w_i = z_i-v_i+D_s c_i, +k_i = w_i+z_(i+1), +f_i = B_s v_i+q b_i-q B_t k_i, +e_i = B_t k_i for corrected F, +e_i = B_t k_i+a_i for raw F, +r_i = v_i+k_i-D_t e_i, +v_(i+1) = y_(i+1)-v_i+r_i. +``` + +The final selected X, selected Y, and ordinary Y fields are respectively +`f_i`, `Q a_i`, and `r_i`. The final ordinary X fields are + +```text +K_0 = -y_0+D_s0 c_0, +K_i = -y_i+D_si c_i+D_t(i-1) e_(i-1), i>0. +``` + +To prove the formula for `K_i`, use +`z_(i-1)=x_(i-1)-z_i` and `k_(i-1)=w_(i-1)+z_i`. The Y bridge gives +`v_i=y_i+k_(i-1)-D_t(i-1)e_(i-1)`. Thus +`w_i+w_(i-1)=-y_i+D_si c_i+D_t(i-1)e_(i-1)`. +The descending final triangle adds the unmodified `w_(i-1)`, as required. +The first formula follows from `v_0=y_0+z_0`. + +These formulas apply to all positive pair counts. The checker tests each +formal operator block for one through six pairs. It checks both F words. +It uses only adjacent Q inverse cancellation and `B_jD_j=13I`. + +## What the completed selected query supplies + +If a decoder has both `v_i` and `k_i` in a full frame, then + +```text +b_i = Q(f_i-B_s v_i)+B_t k_i. +``` + +This is an exact selected-source recovery formula with one positive Q +operation. It is not yet a paid decoder. The completed ordinary fields +give each `w_i` by inversion of the final triangle, but they do not give +`k_i=w_i+z_(i+1)` without the original ordinary suffix. They also do not +give the incoming ordinary baseline `v_i`. A decoder must establish these +sources or eliminate them by another identity. + +## A dyadic obstruction for a restricted decoder + +Consider a causal controller in which each backward input receives its +own original Y with identity coefficient. Earlier pairs may contribute +to this input. Suppose that the extra X source at the forward call has no +dependence on the current or future original Y. Suppose also that the +final X operations are dyadic units and that productive selected Y depends +only on original X. + +For fixed original X, the diagonal block from original Y to the completed +local X before F is + +```text +R_s = [[q,B_s],[-D_s q,-I]]. +``` + +Its Schur complement after the selected block q is `-I+D_s B_s`. +Since `B_sD_s=13I`, its determinant has a factor `12^8`, apart from units +and a sign. The selected X update in F is a unit upper shear. The global +X-on-Y matrix is block triangular before its final unit operations. +Its determinant therefore has 3-adic valuation `8m`, when each selected +Q is a unit at 3. + +It follows that no dyadic linear decoder can recover all original Y from +completed X and the productive selected Y fields alone. Fix original X +and set it to zero. The selected Y fields then add no Y information. A +left inverse over the dyadic ring would force the square X-on-Y matrix +to have a unit determinant, which it does not have. + +This determinant argument does not imply that `8m` independent queries +are missing modulo 3. Off-diagonal blocks can change the rank loss. It +also does not exclude a decoder that reads ordinary retired Y, a different +selected set, a noncausal bridge, or a changed local map. For a scalar +postlower parameter lambda, the same argument holds: the local Y block +has lower row `[-lambda D_s q,-I+(1-lambda)D_sB_s]`, and its Schur +complement is still `-I+D_sB_s`. + +For the specific matched ordinary bridges in this note, there is a +stronger statement. Restrict to original X equal to zero. Undo the final +X triangle to obtain `w_i`. Undo the selected X shear to obtain +`h_i=f_i+q B_ti w_i`. Then + +```text +v_0=y_0, +v_i=y_i+L_(i-1) w_(i-1), L_(i-1)=I-D_t(i-1) B_t(i-1). +``` + +For each i greater than zero, use the old w values to replace + +```text +w_i by w_i+L_(i-1)w_(i-1), +h_i by h_i-B_si L_(i-1)w_(i-1). +``` + +These replacements are a unit lower block triangular map. They put the +X-on-Y map into the block diagonal form with diagonal blocks `R_si`. +The formal checker verifies these identities for both F variants. + +Over a field of characteristic 3, `B_sD_s=I`. Thus `D_sB_s` is a +projection of rank equal to the selected dimension. The Schur complement +`D_sB_s-I` has kernel equal to the image of D_s. Each `R_s` has nullity +eight, for selected dimension eight. The complete matched controller has +nullity `8m`. For array-valued ports, multiply this dimension by the common +scalar dimension of one array. The statement applies after reduction to +any field of characteristic 3 in which the displayed operator relations +remain valid and Q is a unit. + +Consequently, a linear decoder for this controller needs independent +information from ordinary retired Y on this `8m`-dimensional kernel. +This is an information requirement. It is not a lower bound of `8m` +native children: one physical operation may carry more than one scalar +dimension, and a changed circuit may use a different representation. + +## Verification and scope + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_raw_controller.py +``` + +Expected output: + +```text +PASS_RAW_ORDINARY_CONTROLLER +``` + +The receipt pins this note and the local source notes. The checker tests +the local inverses, the full event order, the active ordinary cuts, and +the endpoint formula in a formal ordered operator algebra. It includes +controls for a missing selected-X query and an incorrect final tail order. +It does not replay the local physical words, price inter-call native +views, or prove a complete decoder. Independent review remains required. + +The local physical selected exchanges are due to the native-escape and +coordinating lanes. The determinant observation is from the native-escape +lane. This note supplies its causal-controller scope and the distinction +between determinant valuation and rank loss. This work used AI assistance. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/WEIGHTED-RAW-CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/WEIGHTED-RAW-CHECKS.json new file mode 100644 index 0000000000..4c86e50ef6 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/WEIGHTED-RAW-CHECKS.json @@ -0,0 +1,89 @@ +{ + "status": "PASS_WEIGHTED_RAW_CONTROLLER", + "checker_sha256": "c5ae95d4c9b9330ecc488efecb922489049539d22eb635199dcdb1a8197941f4", + "proof_sha256": "22a986d9cf1a31be3d58f572d6552e6e6c30dd2ee6f4393893ea5125dd196280", + "tests": [ + { + "pairs": 1, + "B_postupper": false, + "endpoint_blocks": 16, + "active_cuts": 2 + }, + { + "pairs": 2, + "B_postupper": false, + "endpoint_blocks": 64, + "active_cuts": 4 + }, + { + "pairs": 3, + "B_postupper": false, + "endpoint_blocks": 144, + "active_cuts": 6 + }, + { + "pairs": 4, + "B_postupper": false, + "endpoint_blocks": 256, + "active_cuts": 8 + }, + { + "pairs": 5, + "B_postupper": false, + "endpoint_blocks": 400, + "active_cuts": 10 + }, + { + "pairs": 6, + "B_postupper": false, + "endpoint_blocks": 576, + "active_cuts": 12 + }, + { + "pairs": 1, + "B_postupper": true, + "endpoint_blocks": 16, + "active_cuts": 2 + }, + { + "pairs": 2, + "B_postupper": true, + "endpoint_blocks": 64, + "active_cuts": 4 + }, + { + "pairs": 3, + "B_postupper": true, + "endpoint_blocks": 144, + "active_cuts": 6 + }, + { + "pairs": 4, + "B_postupper": true, + "endpoint_blocks": 256, + "active_cuts": 8 + }, + { + "pairs": 5, + "B_postupper": true, + "endpoint_blocks": 400, + "active_cuts": 10 + }, + { + "pairs": 6, + "B_postupper": true, + "endpoint_blocks": 576, + "active_cuts": 12 + } + ], + "relations": [ + "Q q = q Q = I", + "H_j K_j = K_j H_j = I" + ], + "method": "Formal ordered words. Direct event replay and an independent endpoint recurrence. No producer imports or scalar specialization.", + "controls": [ + "Omitted selected self-block term in F", + "Early idle-X reset" + ], + "scope": "Ordered algebra. Native local replay, idle-X access, inter-call views, and a full paid decoder are separate obligations." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/WEIGHTED-RAW-CONTROLLER.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/WEIGHTED-RAW-CONTROLLER.md new file mode 100644 index 0000000000..208f2f7de2 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/WEIGHTED-RAW-CONTROLLER.md @@ -0,0 +1,166 @@ +# A weighted raw controller with an invertible ordinary block + +This theorem gives the exact ordered content map for raw selected +exchanges when the ordinary block of the local core is a unit. It covers +the five-minor selected set, and any other split with the stated unit +condition. It includes the selected self-block term in the forward call. +The theorem does not require Q to commute with a matrix block. + +## Local blocks + +Split the core matrix at stage j as + +```text +J_j = [[R_j,L_j],[C_j,H_j]], K_j=H_j^-1. +``` + +Let Q be the selected diagonal native operator and let `q=Q^-1`. +The selected physical exchange, followed by the clean backward core and +then K_s on completed ordinary X, gives + +```text +h = q b-R_s Q a-L_s v, +w = K_s u-v-K_s C_s Q a, +d = Q a, +r = v. +``` + +Here `(a,u;b,v)` are the local input contents. A further upper operation +`h-=L_s w` gives + +```text +h = q b-L_s K_s u-T_s Q a, T_s=R_s-L_s K_s C_s. +``` + +The dependence on borrowed input Y is then diagonal: selected X has +coefficient q on b, and ordinary X has coefficient -I on v. All other +terms depend only on original X. This upper operation is useful because +it removes the ordinary borrowed baseline from selected X. + +At stage t, first apply H_t to ordinary Y. Use the physical selected +exchange, the clean forward core, and the second physical selected +exchange. For input `(h,k;d,v)` the resulting map is + +```text +X_A = h+q R_t q d+q L_t k, +X_U = k, +Y_A = d, +Y_U = H_t v+C_t q d+H_t k. +``` + +The term `q R_t q d` must be retained. It vanishes for the old single +minor split, but it is present for a selected set with multiple minors. + +## Complete content controller + +Use m pairs. Let `s_i=2i+1` and `t_i=2i+2`. Write the original data as +`(a_i,x_i;b_i^0,y_i)`. Form only the ordinary X suffix +`z_i=x_i-z_(i+1)`, with `z_m=0`. Use the original full first forward +shear, so `b_0=b_0^0+a_0`, `eta_0=y_0+z_0`, and `b_i=b_i^0` for i>0. + +For each pair, run the balanced backward word. The optional postupper is +either present at every pair or absent. If a next pair exists, apply K_s +to its idle ordinary X, add that value to active ordinary X, and subtract +active ordinary Y from next idle ordinary Y. Run the balanced forward +word. Subtract the same idle ordinary X, add retired ordinary Y to next +idle ordinary Y, and then reset idle ordinary X by H_s. At the end use +the descending ordinary X triangle. + +The preparation and reset of idle X are actual operations. This note +does not infer their native legality from their content matrices. + +Define + +```text +c_i = -K_si C_si Q a_i, +w_i = K_si z_i-eta_i+c_i, +k_i = w_i+K_si z_(i+1), +E_i = H_ti K_si, +r_i = E_i x_i+H_ti c_i+C_ti a_i, +eta_(i+1) = y_(i+1)-eta_i+r_i. +``` + +Retired selected Y is `Q a_i`. Retired ordinary Y is `r_i`. Before the +last ordinary triangle, completed ordinary X is `w_i`. After that +triangle its value is + +```text +Z_0 = -y_0+(K_s0-I)z_0+c_0, +Z_i = -y_i+K_si z_i+K_s(i-1)z_(i-1)-r_(i-1)+c_i+c_(i-1), i>0. +``` + +The selected X endpoint without the optional postupper is + +```text +f_i = q b_i-R_si Q a_i-L_si eta_i+q R_ti a_i+q L_ti k_i. +``` + +With the postupper it is + +```text +f_i = q b_i-L_si K_si z_i-T_si Q a_i+q R_ti a_i+q L_ti k_i. +``` + +These identities follow by substitution into the local maps. In the +ordinary retirement, `eta_i+k_i=K_si x_i+c_i`; this cancels the borrowed +baseline. In the final ordinary X formula, substitute the Y bridge into +`w_i+w_(i-1)`. The descending tail is required so that it uses the old +`w_(i-1)`. No relation between different stage matrices is needed. + +## A selected decoder reduction + +Suppose the postupper is present. Completed ordinary X gives every w_i +by inversion of its final triangle. One positive selected Q operation, +followed by a full-frame scalar subtraction, gives + +```text +g_i = Q f_i-L_ti w_i + = b_i-Q L_si K_si z_i-Q T_si Q a_i + +R_ti a_i+L_ti K_si z_(i+1). +``` + +Thus g_i differs from the original selected borrowed input only by a +function of original X. There is no remaining eta_i term. The first +pair also has the stated `+a_0` from the first full forward call. This +reduction is exact, but it is not a complete decoder: the original +ordinary suffixes in the response are not yet supplied in a usable +physical frame. + +The ordinary retired code has invertible block `E_i=H_ti H_si^-1` and +an explicit selected-input response. Original selected X is present in +productive selected outputs. These properties remove two algebraic +obstacles from the single-minor raw code. They do not by themselves +prove that E_i can be removed within the native budget. In particular, +normalizing all ordinary retired Y to full fields and then restoring +their required hole frames generally incurs two native operations per +ordinary field. Such a decoder must be priced in full. + +## Verification and scope + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_weighted_raw_controller.py +``` + +Expected output: + +```text +PASS_WEIGHTED_RAW_CONTROLLER +``` + +The checker uses formal ordered words with only Q inverse cancellation +and `H_jK_j=K_jH_j=I`. It checks all endpoint blocks and active ordinary +cuts for one through six pairs, with and without the postupper. It also +checks the selected normalization formula. The negative controls omit +the selected self-block term and reset idle X too early. This is a +content proof. It is not a native phase, owner, finite precision, or +complete recursive cost proof. Independent review remains required. + +The weighted recurrence was derived by the upstream-refresh lane. The +balanced local words and their scalar implementation are from the +native-escape and new-core-transfer lanes. The coordinating lane proposed +the five-minor split. This note adds the ordered selected endpoint and +checks the full event order. This work used AI assistance. No publication +is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_raw_controller.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_raw_controller.py new file mode 100644 index 0000000000..fe5035cfaf --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_raw_controller.py @@ -0,0 +1,227 @@ +"""Check the raw selected controller in an ordered operator algebra.""" + +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent + + +def need(value, label): + if not value: + raise ValueError(label) + + +def word_product(left, right): + word, factor = list(left + right), F(1) + changed = True + while changed: + changed = False + for i in range(len(word) - 1): + a, b = word[i:i+2] + if (a, b) in (("Q", "q"), ("q", "Q")): + del word[i:i+2] + changed = True + break + if a.startswith("B") and b == "D" + a[1:]: + del word[i:i+2] + factor *= 13 + changed = True + break + return tuple(word), factor + + +def plus(a, b, scale=1): + out = dict(a) + for word, coefficient in b.items(): + out[word] = out.get(word, F(0)) + scale * coefficient + if not out[word]: + del out[word] + return out + + +def product(a, b): + out = {} + for left, x in a.items(): + for right, y in b.items(): + word, factor = word_product(left, right) + out = plus(out, {word: factor * x * y}) + return out + + +ONE = {(): F(1)} + + +def op(name): + return {(name,): F(1)} + + +def row_add(a, b, scale=1): + return [plus(x, y, scale) for x, y in zip(a, b)] + + +def row_map(operator, row): + return [product(operator, x) for x in row] + + +def basis(n, j): + return [ONE if i == j else {} for i in range(n)] + + +def zero(n): + return [{} for _ in range(n)] + + +def local_b(a, u, b, v, s, lower=1): + r, c = row_map(op("q"), b), row_map(op("Q"), a) + h = row_add(r, row_map(op(f"B{s}"), v)) + k = row_add(u, v, -1) + k = row_add(k, row_map(product(op(f"D{s}"), op(f"B{s}")), v), 1-lower) + k = row_add(k, row_map(op(f"D{s}"), r), -lower) + k = row_add(k, row_map(op(f"D{s}"), c)) + return h, k, c, v + + +def local_f(a, u, b, v, t, corrected): + query = row_map(op(f"B{t}"), u) + h = row_add(a, row_map(op("q"), query), -1) + r = row_add(row_add(v, u), row_map(op(f"D{t}"), query), -1) + if not corrected: + r = row_add(r, row_map(product(op(f"D{t}"), op("q")), b), -1) + return h, u, b, r + + +def replay(m, corrected, mutation=None): + n = 4*m + state = [basis(n, j) for j in range(n)] + for i in range(m-2, -1, -1): + state[4*i+1] = row_add(state[4*i+1], state[4*i+5], -1) + state[2] = row_add(state[2], state[0]) + state[3] = row_add(state[3], state[1]) + cuts = [] + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + state[j:j+4] = local_b(*state[j:j+4], s) + if i+1 < m: + state[j+1] = row_add(state[j+1], state[j+5]) + state[j+7] = row_add(state[j+7], state[j+3], -1) + cuts.append({"active_X_U": state[j+1], "input_Y_U": state[j+3]}) + state[j:j+4] = local_f(*state[j:j+4], t, corrected) + if mutation == "omit_selected_X_query": + state[j] = row_add(state[j], row_map(product(op("q"), op(f"B{t}")), state[j+1])) + if i+1 < m: + state[j+1] = row_add(state[j+1], state[j+5], -1) + state[j+7] = row_add(state[j+7], state[j+3]) + tail = range(1, m) if mutation == "ascending_tail" else range(m-1, 0, -1) + for i in tail: + state[4*i+1] = row_add(state[4*i+1], state[4*i-3]) + return state, cuts + + +def formulas(m, corrected): + n = 4*m + original = [basis(n, j) for j in range(n)] + z = [zero(n) for _ in range(m+1)] + for i in range(m-1, -1, -1): + z[i] = row_add(original[4*i+1], z[i+1], -1) + v = row_add(original[3], z[0]) + previous_response, previous_k, previous_a = zero(n), zero(n), zero(n) + out, cuts = [], [] + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + a = original[j] + b = row_add(original[j+2], a) if not i else original[j+2] + c = row_add(row_map(op("Q"), a), row_map(op("q"), b), -1) + w = row_add(row_add(z[i], v, -1), row_map(op(f"D{s}"), c)) + k = row_add(w, z[i+1]) + query = row_map(op(f"B{t}"), k) + selected = row_add(row_add(row_map(op(f"B{s}"), v), row_map(op("q"), b)), row_map(op("q"), query), -1) + response = query if corrected else row_add(query, a) + retired = row_add(row_add(v, k), row_map(op(f"D{t}"), response), -1) + completed = row_add(row_map(op(f"D{s}"), c), original[j+3], -1) + if i: + completed = row_add(completed, row_map(op(f"D{s-1}"), previous_response)) + out += [selected, completed, row_map(op("Q"), a), retired] + cuts.append({"active_X_U": k, "input_Y_U": v}) + if i+1 < m: + v = row_add(row_add(original[j+7], v, -1), retired) + previous_response, previous_k, previous_a = response, k, a + return out, cuts + + +def local_inverse_checks(): + rows = [basis(4, j) for j in range(4)] + for lower in (0, 1, F(1, 2), -1): + h, k, c, v = local_b(*rows, 1, lower) + r = row_add(h, row_map(op("B1"), v), -1) + u = row_add(k, v) + u = row_add(u, row_map(product(op("D1"), op("B1")), v), lower-1) + u = row_add(u, row_map(op("D1"), r), lower) + u = row_add(u, row_map(op("D1"), c), -1) + need([row_map(op("q"), c), u, row_map(op("Q"), r), v] == rows, "Backward inverse") + for corrected in (False, True): + h, u, b, r = local_f(*rows, 2, corrected) + a = row_add(h, row_map(product(op("q"), op("B2")), u)) + v = row_add(row_add(r, u, -1), row_map(product(op("D2"), op("B2")), u)) + if not corrected: + v = row_add(v, row_map(product(op("D2"), op("q")), b)) + need([a, u, b, v] == rows, "Forward inverse") + + +def borrowed_normal_form(m, corrected): + n = 4*m + endpoint = replay(m, corrected)[0] + restricted = [[block if j % 4 >= 2 else {} for j, block in enumerate(row)] for row in endpoint] + w = [restricted[4*i+1] for i in range(m)] + for i in range(1, m): + w[i] = row_add(w[i], w[i-1], -1) + h = [row_add(restricted[4*i], row_map(product(op("q"), op(f"B{2*i+2}")), w[i])) for i in range(m)] + for i in range(m): + s = 2*i+1 + ordinary, selected = w[i], h[i] + if i: + previous = row_add(w[i-1], row_map(product(op(f"D{s-1}"), op(f"B{s-1}")), w[i-1]), -1) + ordinary = row_add(ordinary, previous) + selected = row_add(selected, row_map(op(f"B{s}"), previous), -1) + b, y = basis(n, 4*i+2), basis(n, 4*i+3) + expected_selected = row_add(row_map(op("q"), b), row_map(op(f"B{s}"), y)) + expected_ordinary = row_add(row_map(product(op(f"D{s}"), op("q")), b), y) + expected_ordinary = row_map({(): F(-1)}, expected_ordinary) + need(selected == expected_selected and ordinary == expected_ordinary, "Borrowed-state block diagonal form") + + +def main(): + local_inverse_checks() + tests = [] + for corrected in (False, True): + for m in range(1, 7): + actual, cuts = replay(m, corrected) + expected, expected_cuts = formulas(m, corrected) + need(actual == expected, "Every endpoint operator block") + need(cuts == expected_cuts, "Every active ordinary cut") + borrowed_normal_form(m, corrected) + need(replay(m, corrected, "omit_selected_X_query")[0] != actual, "Missing selected query control") + if m > 2: + need(replay(m, corrected, "ascending_tail")[0] != actual, "Wrong tail order control") + tests.append({"pairs": m, "forward": "corrected" if corrected else "raw", "endpoint_blocks": (4*m)**2, "active_cuts": 2*m}) + sources = [HERE / "RAW-ORDINARY-CONTROLLER.md", HERE.parent / "native-escape-20261017/ZERO-LINE-BACKWARD.md", HERE.parent / "native-escape-20261017/RAW-SELECTED-FORWARD.md"] + result = { + "status": "PASS_RAW_ORDINARY_CONTROLLER", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins": {str(p.relative_to(HERE.parent)): sha256(p.read_bytes()).hexdigest() for p in sources}, + "tests": tests, + "local_inverse_cases": 6, + "borrowed_normal_form_cases": 12, + "relations": ["Q q = q Q = I", "B_s D_s = 13 I"], + "method": "Formal ordered operator words. Direct event replay and a separate endpoint recurrence. No scalar specialization and no producer imports.", + "controls": ["Omitted selected X query", "Ascending final X tail"], + "scope": "Content algebra only. This does not prove native inter-call views or a paid physical decoder." + } + (HERE / "RAW-CONTROLLER-CHECKS.json").write_text(json.dumps(result, indent=2) + "\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_weighted_raw_controller.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_weighted_raw_controller.py new file mode 100644 index 0000000000..699d39a2ee --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_weighted_raw_controller.py @@ -0,0 +1,201 @@ +"""Check the weighted raw controller with formal ordered operators.""" + +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +ONE = {(): F(1)} + + +def need(value, label): + if not value: + raise ValueError(label) + + +def word_product(left, right): + word = list(left + right) + changed = True + while changed: + changed = False + for i in range(len(word)-1): + a, b = word[i:i+2] + inverse = (a, b) in (("Q", "q"), ("q", "Q")) + inverse |= a[0] in "HK" and b == ("K" if a[0] == "H" else "H") + a[1:] + if inverse: + del word[i:i+2] + changed = True + break + return tuple(word) + + +def plus(a, b, scale=1): + out = dict(a) + for word, value in b.items(): + out[word] = out.get(word, F(0)) + scale*value + if not out[word]: + del out[word] + return out + + +def product(a, b): + out = {} + for left, x in a.items(): + for right, y in b.items(): + out = plus(out, {word_product(left, right): x*y}) + return out + + +def operator(*names): + out = ONE + for name in names: + out = product(out, {(name,): F(1)}) + return out + + +def row_add(a, b, scale=1): + return [plus(x, y, scale) for x, y in zip(a, b)] + + +def row_map(op, row): + return [product(op, value) for value in row] + + +def basis(n, j): + return [ONE if i == j else {} for i in range(n)] + + +def zero(n): + return [{} for _ in range(n)] + + +def replay(m, upper, mutation=None): + n = 4*m + state = [basis(n, j) for j in range(n)] + for i in range(m-2, -1, -1): + state[4*i+1] = row_add(state[4*i+1], state[4*i+5], -1) + state[2], state[3] = row_add(state[2], state[0]), row_add(state[3], state[1]) + cuts = [] + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + a, u, b, v = state[j:j+4] + d = row_map(operator("Q"), a) + h = row_add(row_add(row_map(operator("q"), b), row_map(operator(f"R{s}"), d), -1), row_map(operator(f"L{s}"), v), -1) + w = row_map(operator(f"K{s}"), row_add(row_add(u, row_map(operator(f"C{s}"), d), -1), row_map(operator(f"H{s}"), v), -1)) + if upper: + h = row_add(h, row_map(operator(f"L{s}"), w), -1) + state[j:j+4] = [h, w, d, v] + if i+1 < m: + state[j+5] = row_map(operator(f"K{s}"), state[j+5]) + state[j+1] = row_add(state[j+1], state[j+5]) + state[j+7] = row_add(state[j+7], state[j+3], -1) + cuts.append({"active_X_U": state[j+1], "input_Y_U": state[j+3]}) + state[j+3] = row_map(operator(f"H{t}"), state[j+3]) + h, k, d, v = state[j:j+4] + h = row_add(h, row_map(operator("q", f"R{t}", "q"), d)) + h = row_add(h, row_map(operator("q", f"L{t}"), k)) + v = row_add(row_add(v, row_map(operator(f"C{t}", "q"), d)), row_map(operator(f"H{t}"), k)) + if mutation == "omit_selected_self_term": + h = row_add(h, row_map(operator("q", f"R{t}", "q"), d), -1) + state[j:j+4] = [h, k, d, v] + if i+1 < m: + if mutation == "early_idle_reset": + state[j+5] = row_map(operator(f"H{s}"), state[j+5]) + state[j+1] = row_add(state[j+1], state[j+5], -1) + state[j+7] = row_add(state[j+7], state[j+3]) + if mutation != "early_idle_reset": + state[j+5] = row_map(operator(f"H{s}"), state[j+5]) + for i in range(m-1, 0, -1): + state[4*i+1] = row_add(state[4*i+1], state[4*i-3]) + return state, cuts + + +def formulas(m, upper): + n = 4*m + original = [basis(n, j) for j in range(n)] + z = [zero(n) for _ in range(m+1)] + for i in range(m-1, -1, -1): + z[i] = row_add(original[4*i+1], z[i+1], -1) + eta = row_add(original[3], z[0]) + out, cuts, ws = [], [], [] + rprev, cprev = zero(n), zero(n) + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + a, x = original[j:j+2] + b = row_add(original[j+2], a) if not i else original[j+2] + ca = row_map(operator(f"K{s}", f"C{s}", "Q"), a) + w = row_add(row_add(row_map(operator(f"K{s}"), z[i]), eta, -1), ca, -1) + k = row_add(w, row_map(operator(f"K{s}"), z[i+1])) + retired = row_add(row_map(operator(f"H{t}", f"K{s}"), x), row_map(operator(f"C{t}"), a)) + retired = row_add(retired, row_map(operator(f"H{t}"), ca), -1) + if upper: + h = row_add(row_map(operator("q"), b), row_map(operator(f"L{s}", f"K{s}"), z[i]), -1) + h = row_add(h, row_map(operator(f"R{s}", "Q"), a), -1) + h = row_add(h, row_map(operator(f"L{s}"), ca)) + else: + h = row_add(row_map(operator("q"), b), row_map(operator(f"R{s}", "Q"), a), -1) + h = row_add(h, row_map(operator(f"L{s}"), eta), -1) + h = row_add(row_add(h, row_map(operator("q", f"R{t}"), a)), row_map(operator("q", f"L{t}"), k)) + completed = row_add(row_map(operator(f"K{s}"), z[i]), original[j+3], -1) + completed = row_add(completed, ca, -1) + if i: + completed = row_add(completed, row_map(operator(f"K{s-2}"), z[i-1])) + completed = row_add(row_add(completed, cprev, -1), rprev, -1) + else: + completed = row_add(completed, z[0], -1) + out += [h, completed, row_map(operator("Q"), a), retired] + cuts.append({"active_X_U": k, "input_Y_U": eta}) + ws.append(w) + if i+1 < m: + eta = row_add(row_add(original[j+7], eta, -1), retired) + rprev, cprev = retired, ca + return out, cuts, ws, z + + +def selected_normalization(m, endpoint, ws, z): + n = 4*m + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + actual = row_add(row_map(operator("Q"), endpoint[j]), row_map(operator(f"L{t}"), ws[i]), -1) + a = basis(n, j) + b = row_add(basis(n, j+2), a) if not i else basis(n, j+2) + expected = row_add(b, row_map(operator("Q", f"L{s}", f"K{s}"), z[i]), -1) + expected = row_add(expected, row_map(operator("Q", f"R{s}", "Q"), a), -1) + expected = row_add(expected, row_map(operator("Q", f"L{s}", f"K{s}", f"C{s}", "Q"), a)) + expected = row_add(expected, row_map(operator(f"R{t}"), a)) + expected = row_add(expected, row_map(operator(f"L{t}", f"K{s}"), z[i+1])) + need(actual == expected, "Selected normalization and pure input response") + + +def main(): + tests = [] + for upper in (False, True): + for m in range(1, 7): + actual, cuts = replay(m, upper) + expected, expected_cuts, ws, z = formulas(m, upper) + need(actual == expected, "Every weighted endpoint operator block") + need(cuts == expected_cuts, "Every weighted active cut") + if upper: + selected_normalization(m, actual, ws, z) + need(replay(m, upper, "omit_selected_self_term")[0] != actual, "Selected self-block control") + if m > 1: + need(replay(m, upper, "early_idle_reset")[0] != actual, "Early idle reset control") + tests.append({"pairs": m, "B_postupper": upper, "endpoint_blocks": (4*m)**2, "active_cuts": 2*m}) + result = { + "status": "PASS_WEIGHTED_RAW_CONTROLLER", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "proof_sha256": sha256((HERE / "WEIGHTED-RAW-CONTROLLER.md").read_bytes()).hexdigest(), + "tests": tests, + "relations": ["Q q = q Q = I", "H_j K_j = K_j H_j = I"], + "method": "Formal ordered words. Direct event replay and an independent endpoint recurrence. No producer imports or scalar specialization.", + "controls": ["Omitted selected self-block term in F", "Early idle-X reset"], + "scope": "Ordered algebra. 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No native access, storage schedule, or cost is supplied." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/DECODER-REDUCTION.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/DECODER-REDUCTION.md new file mode 100644 index 0000000000..4732872850 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/DECODER-REDUCTION.md @@ -0,0 +1,169 @@ +# Separate decoder reductions + +These identities are follow-through from the controller review. They +give exact content inverses and identify specific query inputs. They +do not give a native decoder or a recursive invoice. In particular, +they do not convert a retired hole-frame array to a full-frame array +at no cost. + +## Raw controller: one fresh retired query in each reverse step + +Use the notation of the raw review. Undo the final ordinary X triangle +to obtain w_i. The other final outputs are f_i, d_i=Q a_i, and r_i. +Recover a_i=q d_i in content coordinates. Set z_m=0 and process the +pairs in reverse order. Let delta be zero for corrected F and one for +raw F. Define + +```text +k_i = w_i+z_(i+1), +t_i = B_ti k_i, +e_i = t_i+delta a_i, +p_i = B_si r_i-B_si k_i+B_si D_ti e_i, +beta_i = f_i+q t_i-p_i, +v_i = r_i-k_i+D_ti e_i, +z_i = w_i+v_i+D_si beta_i-D_si Q a_i, +b_i = Q beta_i. +``` + +The forward local implies `v_i=r_i-k_i+D_ti e_i`, so p_i=B_si v_i. +The selected output then gives beta_i=q b_i. The backward ordinary +output gives the stated z_i. These are direct substitutions; no odd +division or stage commutation is used. They prove the reverse induction. + +At the end, recover the original inputs by + +```text +x_i = z_i+z_(i+1), +y_0 = v_0-z_0, +y_i = v_i+v_(i-1)-r_(i-1), i>0, +b_0^0 = b_0-a_0, +b_i^0 = b_i, i>0. +``` + +At each reverse step, the only query in these formulas that directly +reads the current retired ordinary bank is B_si r_i. The query t_i +reads w_i plus the already recovered next suffix. The remaining terms +use the two selected query values and small cross-stage products. +This is an exact reduction to one fresh rank-eight retired-Y query per +pair, provided the next suffix and the resulting ordinary updates are +available in the needed views. + +Those conditions are not proved here. The retired r_i is in the target +hole frames. Its query is in the old s_i chart, whereas the retirement +was at t_i. Also, the updated z_i must be used by the previous reverse +step. The identity does not provide this frame transfer. Calling every +term a rank-eight correction does not price its ordinary scatter. + +For the restricted original-X-zero map, this query has a precise +information role. Completed X determines w_i and +`h_i=f_i+q B_ti w_i`. One additional echo B_si r_i gives +`B_si v_i=B_si r_i-B_si(I-D_ti B_ti)w_i`. It then gives b_i and v_i, +and hence all original Y. This is a sufficient selected-dimension +observation per pair for that restricted problem. The mod-3 nullity +bound in the review is not a native price for this observation. + +## Weighted controller: two small query factors for the ordinary inverse + +The weighted retirement satisfies + +```text +r_i-C_ti a_i = H_ti H_si^-1 (x_i-C_si Q a_i). +``` + +It follows that + +```text +x_i = H_si H_ti^-1 (r_i-C_ti a_i)+C_si Q a_i. (1) +``` + +This is an ordered two-factor inverse. It is not a high-degree +polynomial inverse. After (1), form the original suffixes z_i and set + +```text +eta_i = K_si z_i-K_si C_si Q a_i-w_i. +``` + +The original y values follow from the same Y-bridge inverse: +`y_0=eta_0-z_0` and +`y_i=eta_i+eta_(i-1)-r_(i-1)` for i>0. For the postupper variant, +write `g_i=Q f_i-L_ti w_i`. Then + +```text +b_i = g_i+Q L_si K_si z_i+Q T_si Q a_i + -R_ti a_i-L_ti K_si z_(i+1). +``` + +Subtract a_0 from b_0 to undo the first full F0. This gives a complete +content inverse. The checker also verifies the version without the +postupper. + +For the actual five-minor split, write +`H_j=I-M_j N_j`, with M_j the ordinary restriction of the injection and +N_j the ordinary query. The actual matrix has N_j M_j=9I. Hence +`H_j^-1=I-M_j N_j/8`. Let `r'=r_i-C_ti a_i`. Equation (1) can be evaluated +as + +```text +q_t = N_ti r', +v = r'-M_ti q_t/8, +q_s = N_si v, +x_i = v-M_si q_s+C_si Q a_i. +``` + +The two queries each have eight output fields, even though the selected +bank has forty fields. The difference `H_si H_ti^-1-I` has image in +the sum of the two eight-field injection images. Its rank is therefore +at most sixteen fields. This bound does not identify a cheap physical +scatter into the 72 ordinary target fields. + +`check_decoder.py` reads the actual R from the new-core interface. It +checks the five selected minors, the ordinary Gram matrix, and both +orders of the 72-dimensional H inverse with integer numerator matrices. +Thus the five-minor specialization is tied to the actual source matrix, +not only to a formal rank-eight model. + +## Why completed X alone supplies no clean weighted query + +The weighted postupper output does not supply an additional clean query +of original ordinary X from its completed X bank alone. To see this, +fix original X. Undo the final ordinary triangle. The original-Y part +of w_i is `-eta_i`, and the eta recurrence is unit lower triangular in +the original y inputs because r_i is independent of original Y. +Normalize selected X to g_i. Its original-Y part is exactly b_i. +Thus the map from all original Y to all completed X is a unit. + +For a fixed original X, completed X can therefore take every value as +original Y varies. A linear observation of completed X that removes +all arbitrary original-Y dependence must be zero. In fact, the same +surjectivity statement prevents any function of completed X alone +from giving a nonconstant, baseline-independent query of original X. +The productive selected outputs add the known a_i, but do not add a +query of the ordinary original X. + +This is a restricted observation statement. A decoder can read ordinary +retired Y, change the controller, use related rather than independent +input roles, or retain an additional record. The two query factors in +(1) are the specific remaining access task for this unchanged endpoint. +The statement is not a general lower bound on native work. + +## Verification and scope + +Run from the workspace root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py +``` + +Expected output: + +```text +PASS_CONTENT_DECODER_REDUCTIONS_ONLY +``` + +The checker uses the separate reverse controller engine in this review +directory, not a producer engine. It verifies all original input blocks +after the displayed inverse for m=1 through 8, both raw F choices, and +both weighted postupper choices. It uses exact ordered words. The +actual Gram and inverse check uses exact integers. No physical native +word, global owner path, storage schedule, or complete cost was emitted. +No kappa improvement follows from this packet. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/INPUTS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/INPUTS.json new file mode 100644 index 0000000000..6a54d882aa --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/INPUTS.json @@ -0,0 +1,18 @@ +{ + "controller-followthrough-20261017/RAW-ORDINARY-CONTROLLER.md": "1b6a6a86cda137b013cf4999c83ecb1f5131330ae642ce6ea61c96b2edc79382", + "controller-followthrough-20261017/WEIGHTED-RAW-CONTROLLER.md": "22a986d9cf1a31be3d58f572d6552e6e6c30dd2ee6f4393893ea5125dd196280", + "controller-followthrough-20261017/check_raw_controller.py": 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"67c5970de8e16a9834759f1fba3f4766608e80b16e57ae35858bee3e8aeb2800", + "new-core-transfer-20261017/BALANCED-FIVE-MINOR-RECEIPT.json": "c04c7154e34b2ec79a985ab9696615a26b57ed08a1d3b191456825a8ce2e2484", + "independent-review-20261017/NEW-RAW-REVIEW.md": "982f892bd9fc0fd28501ecedb04ead55dfcc283e52e1925ba512d311e87d62f9", + "independent-review-20261017/NEW-RAW-REVIEW-FINAL.json": "67d9a15273e32dcc7a3c91f6afe83a1466b4b3225ff3e9642bd9ae64d1e9d66b", + "independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json": "924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d", + "new-core-transfer-20261017/INTERFACE.json": "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/REVIEW.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/REVIEW.json new file mode 100644 index 0000000000..07a9adf99d --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/REVIEW.json @@ -0,0 +1,530 @@ +{ + "status": "PASS_INDEPENDENT_RAW_AND_WEIGHTED_CONTROLLERS", + "checker_sha256": "75d017f9adbf9a870f43f26e87a0b759e4735b7aa51bda9d7482f9671e436393", + "source_sha256": { + "controller-followthrough-20261017/RAW-ORDINARY-CONTROLLER.md": "1b6a6a86cda137b013cf4999c83ecb1f5131330ae642ce6ea61c96b2edc79382", + "controller-followthrough-20261017/WEIGHTED-RAW-CONTROLLER.md": "22a986d9cf1a31be3d58f572d6552e6e6c30dd2ee6f4393893ea5125dd196280", + "controller-followthrough-20261017/check_raw_controller.py": "bc78a0bc901f73e6a73069d9257064fdf1b18de87c2d331d1f218c5d141a431e", + "controller-followthrough-20261017/check_weighted_raw_controller.py": "c5ae95d4c9b9330ecc488efecb922489049539d22eb635199dcdb1a8197941f4", + "controller-followthrough-20261017/RAW-CONTROLLER-CHECKS.json": 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No producer imports or execution.", + "formal_relations": [ + "Q q = q Q = I", + "H_j K_j = K_j H_j = I" + ], + "cases": [ + { + "family": "raw", + "option": false, + "pairs": 1, + "operator_blocks": 16, + "cut_blocks": 8, + "events": 20 + }, + { + "family": "raw", + "option": false, + "pairs": 2, + "operator_blocks": 64, + "cut_blocks": 32, + "events": 44 + }, + { + "family": "raw", + "option": false, + "pairs": 3, + "operator_blocks": 144, + "cut_blocks": 72, + "events": 68 + }, + { + "family": "raw", + "option": false, + "pairs": 4, + "operator_blocks": 256, + "cut_blocks": 128, + "events": 92 + }, + { + "family": "raw", + "option": false, + "pairs": 5, + "operator_blocks": 400, + "cut_blocks": 200, + "events": 116 + }, + { + "family": "raw", + "option": false, + "pairs": 6, + "operator_blocks": 576, + "cut_blocks": 288, + "events": 140 + }, + { + "family": "raw", + "option": false, + "pairs": 7, + "operator_blocks": 784, + "cut_blocks": 392, + "events": 164 + }, + { + "family": 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false, + "early_idle_reset" + ], + [ + "weighted", + true, + "omit_initial_selected" + ], + [ + "weighted", + true, + "omit_initial_ordinary" + ], + [ + "weighted", + true, + "ascending_tail" + ], + [ + "weighted", + true, + "wrong_plus_y" + ], + [ + "weighted", + true, + "omit_selected_self" + ], + [ + "weighted", + true, + "early_idle_reset" + ] + ], + "exact_integer_specializations": [ + { + "seed": 1, + "pairs": 1, + "corrected": false, + "determinant": "-144", + "nullity_mod_3": 2 + }, + { + "seed": 1, + "pairs": 2, + "corrected": false, + "determinant": "20736", + "nullity_mod_3": 4 + }, + { + "seed": 1, + "pairs": 4, + "corrected": false, + "determinant": "429981696", + "nullity_mod_3": 8 + }, + { + "seed": 1, + "pairs": 1, + "corrected": true, + "determinant": "-144", + "nullity_mod_3": 2 + }, + { + "seed": 1, + "pairs": 2, + "corrected": true, + "determinant": "20736", + "nullity_mod_3": 4 + }, + { + "seed": 1, + "pairs": 4, + "corrected": true, + "determinant": "429981696", + 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"pairs": 1, + "corrected": true, + "determinant": "-144", + "nullity_mod_3": 2 + }, + { + "seed": 3, + "pairs": 2, + "corrected": true, + "determinant": "20736", + "nullity_mod_3": 4 + }, + { + "seed": 3, + "pairs": 4, + "corrected": true, + "determinant": "429981696", + "nullity_mod_3": 8 + } + ], + "all_m_proof": "REVIEW.md gives the induction and the block-diagonal reduction for every positive m.", + "scope": "Ordered content algebra. Local native reviews are dependencies. No new local native replay, inter-call access, idle owner schedule, finite-grid implementation, or complete kappa claim." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/REVIEW.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/REVIEW.md new file mode 100644 index 0000000000..5e065127d7 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/REVIEW.md @@ -0,0 +1,302 @@ +# Independent review of the raw and weighted controllers + +Both controller proofs pass this review. Their formulas give the complete +ordered content endpoint for every positive pair count. No material +algebra error was found. The proof does not move Q through a stage matrix. + +This review accepts content identities. It does not accept a physical +inter-call implementation, an idle-owner schedule, a decoder invoice, or +a new complete kappa value. The separate decoder note in this directory +does not enlarge this accepted scope. + +## Inputs and independent method + +`INPUTS.json` pins the two controller proofs, their checkers and receipts, +the local raw proofs, and the relevant local reviews. The six controller +files are also retained under `reviewed-inputs/`. No source file was +changed. The two main proof pins are: + +```text +RAW-ORDINARY-CONTROLLER.md +1b6a6a86cda137b013cf4999c83ecb1f5131330ae642ce6ea61c96b2edc79382 +WEIGHTED-RAW-CONTROLLER.md +22a986d9cf1a31be3d58f572d6552e6e6c30dd2ee6f4393893ea5125dd196280 +``` + +The independent checker imports and runs no producer code. It constructs +each local from the physical selected exchange, the clean-core block +shears, and the stated scalar factors. It then constructs the controller +from its individual events. Starting from each output covector, it +propagates coefficients backward through that event tape. Coefficients +are finite sums of ordered words. It cancels only adjacent Q inverses +and adjacent H_j/K_j inverses. It does not use B_j D_j=13I in the +endpoint calculation. This makes the endpoint identity stronger than a +test on commuting scalar stages. + +This reverse calculation is compared with a separately entered endpoint +recurrence. It checks both raw forward choices and both weighted +postupper choices, for m=1 through 8. It checks 13,056 endpoint operator +blocks and all active ordinary cuts. Twenty-two controls reject omitted +initial selected or ordinary F0 updates, the wrong final triangle order, +a wrong plus-Y sign, missing selected terms, and an early idle reset. + +The checker also uses exact integer matrices with selected dimension two +and ordinary dimension three. Each stage has rectangular B_j,D_j with +B_j D_j=13I. The selected Q does not commute with a cross-stage product. +For three such instances, both raw forward choices, and m=1,2,4, an +integer determinant calculation and elimination over GF(3) check the +claimed determinant and nullity. These finite instances support the +implementation check; the argument below proves the dimension statements +for all m. + +## Local derivation + +Write the two input banks as `(a,u;b,v)`. The physical selected exchange +has content action `(a,b)->(q b,Q a)`, with q=Q^-1. It is not a logical +swap. The independent raw local reviews verify this distinction with the +actual input and output phase conventions. + +For the raw split, the clean core is + +```text +J_s = [[0,-B_s],[-D_s,I-D_s B_s]]. +``` + +After the input exchange, clean backward operation, and completed-X +lower shear, the output is + +```text +(q b+B_s v, u-v-D_s q b+D_s Q a; Q a,v). +``` + +Two selected exchanges around the clean forward core give + +```text +(h-q B_t k,k; d,v+k-D_t B_t k-D_t q d). +``` + +The corrected forward input step adds D_t q d to v. It removes only the +last term. These derivations use no Q commutation and no division by 12. + +For the weighted split write + +```text +J_j = [[R_j,L_j],[C_j,H_j]], K_j=H_j^-1. +``` + +The input exchange, backward core, and K_s on ordinary X give + +```text +h=q b-R_s Q a-L_s v, +w=K_s u-v-K_s C_s Q a, +d=Q a. +``` + +Subtracting L_s w from h gives +`h=q b-L_s K_s u-T_s Q a`, where +`T_s=R_s-L_s K_s C_s`. For the forward local, apply H_t to v before +the two exchanges and the core. Its selected X is +`h+q R_t q d+q L_t k`; its ordinary Y is +`H_t v+C_t q d+H_t k`. In particular, the selected self-block term +`q R_t q d` is required. It is absent only when R_t=0. + +The raw native maps have separate independent reviews for the old and +new providers. The weighted local factors are stated in the pinned +five-minor packet. This review checks their algebra but does not repeat +their full native word or accept an unreviewed native extension by +inference. The global weighted theorem is conditional on its stated +local maps and on actual access to its idle operations. + +## Complete raw endpoint for every m + +Use original inputs `(a_i,x_i;b_i^0,y_i)`. Define the ordinary suffix +`z_i=x_i-z_(i+1)`, with z_m=0. The initial full F0 gives +`b_0=b_0^0+a_0` and `v_0=y_0+z_0`; for i>0, b_i=b_i^0. +At pair i let s=2i+1 and t=2i+2, and set + +```text +c_i=Q a_i-q b_i, +w_i=z_i-v_i+D_s c_i, +k_i=w_i+z_(i+1), +f_i=B_s v_i+q b_i-q B_t k_i, +e_i=B_t k_i (corrected forward), +e_i=B_t k_i+a_i (raw forward), +r_i=v_i+k_i-D_t e_i. +``` + +Inductively, the active pair enters B with ordinary X=z_i and Y=v_i. +B gives w_i. The plus-X write gives k_i and the minus-Y write changes +the next Y to y_(i+1)-v_i. F gives f_i and r_i. Subtracting the same +idle X returns the active ordinary X to w_i. The plus-Y write therefore +sets the next incoming value to +`v_(i+1)=y_(i+1)-v_i+r_i`. No operation changes the next idle X. +This proves the induction, including the last pair where z_m=0 and the +next-bank operations are absent. + +Before the final triangle, the pair output is +`(f_i,w_i;Q a_i,r_i)`. The descending triangle changes ordinary X to +w_0 for i=0 and w_i+w_(i-1) for i>0. It uses old w_(i-1), not a value +that has already received its own predecessor. Substitution gives + +```text +X_U,0=-y_0+D_s0 c_0, +X_U,i=-y_i+D_si c_i+D_t(i-1) e_(i-1), i>0. +``` + +All other displayed raw endpoints follow. This proof covers every +positive m and both forward choices. The initial full F0 is essential +to the first line and to the b_0 selected response. + +## Complete weighted endpoint for every m + +Keep the same suffix and selected initial F0 update. Put +`eta_0=y_0+z_0`. Define + +```text +c_i=-K_si C_si Q a_i, +w_i=K_si z_i-eta_i+c_i, +k_i=w_i+K_si z_(i+1), +E_i=H_ti K_si, +r_i=E_i x_i+H_ti c_i+C_ti a_i. +``` + +The idle preparation changes the next X from z_(i+1) to +K_si z_(i+1). Both the plus-X and minus-X operations use this same +value. Only after the minus-X operation does H_si return the idle bank +to z_(i+1). Thus the next pair has the input required for induction. +Resetting the idle bank before its subtraction gives a different map. + +At the forward call, +`eta_i+k_i=K_si x_i+c_i`. Its ordinary output is therefore r_i and +has no original-Y dependence. The next Y is +`eta_(i+1)=y_(i+1)-eta_i+r_i`. Before the final triangle, completed +ordinary X is w_i. After the descending triangle it is + +```text +Z_0=-y_0+(K_s0-I)z_0+c_0, +Z_i=-y_i+K_si z_i+K_s(i-1)z_(i-1) + -r_(i-1)+c_i+c_(i-1), i>0. +``` + +Selected Y is Q a_i. Without the postupper, selected X is + +```text +f_i=q b_i-R_si Q a_i-L_si eta_i+q R_ti a_i+q L_ti k_i. +``` + +With the postupper, replace the two terms +`-R_si Q a_i-L_si eta_i` by +`-L_si K_si z_i-T_si Q a_i`. This proves both full endpoints. +The only inverse identities used are Qq=qQ=I and H_jK_j=K_jH_j=I. +Different stage matrices need not commute. + +Undo the final ordinary triangle. In the postupper case, the selected +normalization is + +```text +Q f_i-L_ti w_i + = b_i-Q L_si K_si z_i-Q T_si Q a_i + +R_ti a_i+L_ti K_si z_(i+1). +``` + +This removes eta_i, as claimed. A positive Q operation on the selected +bank means an operation on each selected field. In the five-minor case +that bank has forty fields. This algebra does not price those operations +or supply the original suffixes in the required views. + +## Factor 12, the coefficient ring, and exact nullity + +Let d be the selected scalar dimension and n the ordinary scalar +dimension in a finite representation. With original X fixed at zero, +the causal raw controller has diagonal original-Y to completed-X block + +```text +M_s = [[q,B_s],[-D_s q,-I]]. +``` + +Eliminate its lower-left block using q. The Schur complement is +`-I+D_s B_s`. The determinant identity for rectangular products gives + +```text +det(-I+D_s B_s)=(-1)^n det(I-B_s D_s) + =(-1)^(n+d) 12^d. +``` + +If Q is a unit at 3, the 3-adic valuation of det M_s is d. Causal +earlier-pair contributions do not change the diagonal determinants. +Final unit operations do not change the valuation. Thus it is dm for +the restricted global map. For eight array-valued ports with array +dimension N, d=8N, not eight scalar coordinates. + +This is a dyadic-ring obstruction. A square dyadic left inverse would +force the determinant to be a unit. It is not a characteristic-zero +singularity: `-I+D_s B_s` has the rational inverse +`-I+D_s B_s/12`. A legal implementation on an odd-denominator grid is +outside the dyadic-linear restriction. Its precision, access, and cost +must be checked separately. This review does not treat an odd denominator +as a general prohibition in the research model. + +For the source note's scalar postlower parameter lambda, the lower row +is `[-lambda D_s q,-I+(1-lambda)D_s B_s]`. Its Schur complement is again +`-I+D_s B_s`, because the eliminated term is `-lambda D_s B_s`. +Thus the determinant statement has the stated parameter scope. This +does not extend the following matched-bridge normal form to a changed +controller without a new calculation. + +For the matched bridges there is an exact stronger result. Undo the +final X triangle and set +`h_i=f_i+q B_ti w_i`. With original X zero, put +`L_i=I-D_ti B_ti`. Then + +```text +v_0=y_0, +v_i=y_i+L_(i-1)w_(i-1). +``` + +Use the old w values to replace +`(h_i,w_i)` by +`(h_i-B_si L_(i-1)w_(i-1), w_i+L_(i-1)w_(i-1))`. +This is a unit lower triangular output change. It gives a direct sum +of the M_si blocks. Over a field of characteristic 3, B_sD_s=I, so +D_sB_s is an idempotent of rank d. Its 1-eigenspace is exactly im D_s. +Each M_s therefore has nullity d, and the matched controller has +nullity dm. The statement requires the displayed relations and an +invertible Q after reduction. It holds for both raw forward choices. + +The determinant alone would not prove this nullity. The matrices +`diag(3,3)` and `[[3,1],[0,3]]` both have determinant 9, but have nullities +two and one over GF(3). The checker includes this control. For the more +general causal class, only the determinant claim is accepted without +an additional normal-form argument. + +The resulting dm-dimensional information requirement is not a native +child lower bound. It does not apply to a decoder that also uses ordinary +retired Y, to a changed noncausal controller, or to a changed local map. + +## Reproduction and limits + +Run from the workspace root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py +``` + +Expected output: + +```text +PASS_INDEPENDENT_RAW_AND_WEIGHTED_CONTROLLERS +formal cases=32 blocks=13056 controls=22 +``` + +All checks remain active under optimization. The receipt records the +exact source and checker hashes. The run uses one Python process and +no numerical library or floating arithmetic. It does not rerun the +producer checkers or any large native recipe sweep. + +The review leaves actual inter-call Q views, idle K/H access, owner +hosting, finite-grid precision, the complete decoder, and the full +recursive invoice open. It adds no complete kappa claim. Research and +review used OpenAI Codex under the user's direction. No human review is +claimed. No PR, commit, push, or publication was made. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py new file mode 100644 index 0000000000..552daf9125 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py @@ -0,0 +1,106 @@ +"""Check the separate content decoder reductions.""" + +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location("independent_controller_review", HERE/"check_review.py") +review = importlib.util.module_from_spec(spec) +spec.loader.exec_module(review) +add, neg, apply = review.add, review.neg, review.apply + + +def decode(m, family, option): + endpoint = review.make_tape(m, family, option).rows() + w = [endpoint[4*i+1] for i in range(m)] + for i in range(1, m): + w[i] = add(w[i], neg(w[i-1])) + a = [apply("q", endpoint[4*i+2]) for i in range(m)] + retired = [endpoint[4*i+3] for i in range(m)] + suffix = [{} for _ in range(m+1)] + incoming, selected = [{} for _ in range(m)], [{} for _ in range(m)] + if family == "weighted": + original = [] + for i in range(m): + s, t = 2*i+1, 2*i+2 + value = add(retired[i], neg(apply(f"C{t}", a[i]))) + original.append(add(apply(f"H{s} K{t}", value), apply(f"C{s} Q", a[i]))) + for i in range(m-1, -1, -1): + suffix[i] = add(original[i], neg(suffix[i+1])) + for i in range(m-1, -1, -1): + s, t = 2*i+1, 2*i+2 + f = endpoint[4*i] + if family == "raw": + k = add(w[i], suffix[i+1]) + echo_t = apply(f"B{t}", k) + response = echo_t if option else add(echo_t, a[i]) + fresh_query = apply(f"B{s}", retired[i]) + echo_s = add(fresh_query, neg(apply(f"B{s}", k)), apply(f"B{s} D{t}", response)) + beta = add(f, apply("q", echo_t), neg(echo_s)) + selected[i] = apply("Q", beta) + incoming[i] = add(retired[i], neg(k), apply(f"D{t}", response)) + suffix[i] = add(w[i], incoming[i], apply(f"D{s}", beta), neg(apply(f"D{s} Q", a[i]))) + else: + incoming[i] = add(apply(f"K{s}", suffix[i]), neg(apply(f"K{s} C{s} Q", a[i])), neg(w[i])) + k = add(w[i], apply(f"K{s}", suffix[i+1])) + if option: + g = add(apply("Q", f), neg(apply(f"L{t}", w[i]))) + selected[i] = add(g, apply(f"Q L{s} K{s}", suffix[i]), apply(f"Q R{s} Q", a[i]), neg(apply(f"Q L{s} K{s} C{s} Q", a[i])), neg(apply(f"R{t}", a[i])), neg(apply(f"L{t} K{s}", suffix[i+1]))) + else: + selected[i] = add(apply("Q", f), apply(f"Q R{s} Q", a[i]), apply(f"Q L{s}", incoming[i]), neg(apply(f"R{t}", a[i])), neg(apply(f"L{t}", k))) + recovered = [] + for i in range(m): + y = add(incoming[i], incoming[i-1], neg(retired[i-1])) if i else add(incoming[0], neg(suffix[0])) + b = selected[i] if i else add(selected[i], neg(a[0])) + recovered.extend((a[i], add(suffix[i], suffix[i+1]), b, y)) + review.require(recovered == [review.input_value(j) for j in range(4*m)], "Complete content inverse") + + +def actual_five_minor(): + path = HERE.parent/"new-core-transfer-20261017/INTERFACE.json" + pins = json.loads((HERE/"INPUTS.json").read_text()) + review.require(sha256(path.read_bytes()).hexdigest() == pins[str(path.relative_to(HERE.parent))], "Frozen actual source matrix") + source = json.loads(path.read_text()) + r = [[int(row.get(str(j), "0")) for j in range(112)] for row in source["R"]] + selected = [0,7,20,27,36,46,57,111,21,37,47,76,81,87,92,110,1,6,22,28,33,49,58,109,2,9,14,19,88,95,101,106,3,8,15,18,89,94,102,105] + review.require(len(set(selected)) == 40, "Disjoint selected minors") + for start in range(0, 40, 8): + minor = selected[start:start+8] + gram = [[sum(r[i][p]*r[j][p] for p in minor) for j in range(8)] for i in range(8)] + review.require(gram == [[4*int(i==j) for j in range(8)] for i in range(8)], "Each selected minor Gram equals 4 I") + ordinary = [j for j in range(112) if j not in selected] + gram = [[sum(r[i][p]*r[j][p] for p in ordinary) for j in range(8)] for i in range(8)] + review.require(gram == [[36*int(i==j) for j in range(8)] for i in range(8)], "Actual ordinary Gram equals 36 I") + matrix = [[sum(r[k][i]*r[k][j] for k in range(8)) for j in ordinary] for i in ordinary] + h = [[4*int(i==j)-matrix[i][j] for j in range(72)] for i in range(72)] + inverse = [[32*int(i==j)-matrix[i][j] for j in range(72)] for i in range(72)] + identity = [[128*int(i==j) for j in range(72)] for i in range(72)] + review.require(review.matrix_multiply(h, inverse) == identity, "Actual H times inverse") + review.require(review.matrix_multiply(inverse, h) == identity, "Actual inverse times H") + return {"source": str(path.relative_to(HERE.parent)), "sha256": sha256(path.read_bytes()).hexdigest(), "selected_count": 40, "ordinary_count": 72, "gram": "36 I", "both_inverse_orders": True} + + +def main(): + cases = [] + for family in ("raw", "weighted"): + for option in (False, True): + for m in range(1, 9): + decode(m, family, option) + cases.append([family, option, m]) + result = { + "status": "PASS_CONTENT_DECODER_REDUCTIONS_ONLY", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "review_engine_sha256": sha256((HERE/"check_review.py").read_bytes()).hexdigest(), + "cases": cases, + "actual_five_minor": actual_five_minor(), + "scope": "Exact content inverse and query decomposition. No native access, storage schedule, or cost is supplied.", + } + (HERE/"DECODER-CHECKS.json").write_text(json.dumps(result, indent=2)+"\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py new file mode 100644 index 0000000000..0a053dac7e --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py @@ -0,0 +1,413 @@ +"""Check the ordered controller maps by reverse output propagation.""" + +from collections import Counter +from fractions import Fraction +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +ONE = {(): 1} + + +def require(test, label): + if not test: + raise ValueError(label) + + +def add(*terms): + result = Counter() + for term in terms: + result.update(term) + return {word: value for word, value in result.items() if value} + + +def neg(value): + return {word: -coefficient for word, coefficient in value.items()} + + +def symbol(name): + return {(name,): 1} + + +def reduce_word(word): + stack = [] + for letter in word: + previous = stack[-1] if stack else "" + cancel = (previous, letter) in (("Q", "q"), ("q", "Q")) + if previous[:1] in ("H", "K") and letter[:1] in ("H", "K"): + cancel |= previous[0] != letter[0] and previous[1:] == letter[1:] + if cancel: + stack.pop() + else: + stack.append(letter) + return tuple(stack) + + +def multiply(left, right): + result = Counter() + for a, x in left.items(): + for b, y in right.items(): + result[reduce_word(a + b)] += x * y + return {word: value for word, value in result.items() if value} + + +def apply(names, value): + return multiply({tuple(names.split()): 1}, value) + + +def input_value(index): + return symbol(f"@{index}") + + +class Tape: + def __init__(self, size): + self.size = size + self.events = [] + self.cuts = [] + + def plus(self, target, source, names="", sign=1): + self.events.append(("add", target, source, {tuple(names.split()): sign})) + + def scale(self, target, name): + self.events.append(("scale", target, symbol(name))) + + def swap(self, left, right): + self.events.append(("swap", left, right)) + + def exchange(self, selected_x, selected_y): + self.swap(selected_x, selected_y) + self.scale(selected_x, "q") + self.scale(selected_y, "Q") + + def rows(self, outputs=None, stop=None): + outputs = range(self.size) if outputs is None else outputs + result = [] + for output in outputs: + covector = [{} for _ in range(self.size)] + covector[output] = ONE + for event in reversed(self.events[:stop]): + kind, target = event[:2] + if kind == "add": + _, _, source, operator = event + covector[source] = add(covector[source], multiply(covector[target], operator)) + elif kind == "scale": + covector[target] = multiply(covector[target], event[2]) + else: + source = event[2] + covector[target], covector[source] = covector[source], covector[target] + expression = {} + for source, coefficient in enumerate(covector): + expression = add(expression, multiply(coefficient, input_value(source))) + result.append(expression) + return result + + +def make_tape(m, family, option, mutation=None): + tape = Tape(4 * m) + for i in range(m - 2, -1, -1): + tape.plus(4*i + 1, 4*i + 5, sign=-1) + if mutation != "omit_initial_selected": + tape.plus(2, 0) + if mutation != "omit_initial_ordinary": + tape.plus(3, 1) + for i in range(m): + a, u, b, v = range(4*i, 4*i + 4) + s, t = 2*i + 1, 2*i + 2 + tape.exchange(a, b) + if family == "raw": + tape.plus(a, v, f"B{s}") + tape.plus(u, b, f"D{s}") + tape.plus(u, v, sign=-1) + tape.plus(u, v, f"D{s} B{s}") + tape.plus(u, a, f"D{s}", -1) + else: + tape.plus(a, b, f"R{s}", -1) + tape.plus(a, v, f"L{s}", -1) + tape.plus(u, b, f"C{s}", -1) + tape.plus(u, v, f"H{s}", -1) + tape.scale(u, f"K{s}") + if option: + tape.plus(a, u, f"L{s}", -1) + if i + 1 < m: + if family == "weighted": + tape.scale(u + 4, f"K{s}") + tape.plus(u, u + 4) + tape.plus(v + 4, v, sign=-1) + tape.cuts.append((len(tape.events), (u, v))) + if family == "raw" and option: + tape.plus(v, b, f"D{t} q") + if family == "weighted": + tape.scale(v, f"H{t}") + tape.exchange(a, b) + if family == "raw": + if mutation != "omit_selected_query": + tape.plus(b, u, f"B{t}", -1) + tape.plus(v, a, f"D{t}", -1) + tape.plus(v, u) + tape.plus(v, u, f"D{t} B{t}", -1) + else: + if mutation != "omit_selected_self": + tape.plus(b, a, f"R{t}") + tape.plus(b, u, f"L{t}") + tape.plus(v, a, f"C{t}") + tape.plus(v, u, f"H{t}") + tape.exchange(a, b) + if i + 1 < m: + if family == "weighted" and mutation == "early_idle_reset": + tape.scale(u + 4, f"H{s}") + tape.plus(u, u + 4, sign=-1) + tape.plus(v + 4, v, sign=-1 if mutation == "wrong_plus_y" else 1) + if family == "weighted" and mutation != "early_idle_reset": + tape.scale(u + 4, f"H{s}") + order = range(1, m) if mutation == "ascending_tail" else range(m - 1, 0, -1) + for i in order: + tape.plus(4*i + 1, 4*i - 3) + return tape + + +def endpoint_formula(m, family, option): + initial = [input_value(j) for j in range(4*m)] + suffix = [{} for _ in range(m + 1)] + for i in range(m - 1, -1, -1): + suffix[i] = add(initial[4*i + 1], neg(suffix[i + 1])) + incoming = add(initial[3], suffix[0]) + endpoint, cuts, before_tail = [], [], [] + previous_response, previous_correction, previous_retirement = {}, {}, {} + for i in range(m): + a, x, b, y = initial[4*i:4*i + 4] + if i == 0: + b = add(b, a) + s, t = 2*i + 1, 2*i + 2 + if family == "raw": + correction = add(apply("Q", a), neg(apply("q", b))) + w = add(suffix[i], neg(incoming), apply(f"D{s}", correction)) + k = add(w, suffix[i + 1]) + selected = add(apply(f"B{s}", incoming), apply("q", b), neg(apply(f"q B{t}", k))) + response = apply(f"B{t}", k) + if not option: + response = add(response, a) + retired = add(incoming, k, neg(apply(f"D{t}", response))) + ordinary = add(neg(y), apply(f"D{s}", correction)) + if i: + ordinary = add(ordinary, apply(f"D{s-1}", previous_response)) + previous_response = response + else: + correction = neg(apply(f"K{s} C{s} Q", a)) + w = add(apply(f"K{s}", suffix[i]), neg(incoming), correction) + k = add(w, apply(f"K{s}", suffix[i + 1])) + retired = add(apply(f"H{t} K{s}", x), apply(f"H{t}", correction), apply(f"C{t}", a)) + selected = add(apply("q", b), neg(apply(f"R{s} Q", a)), apply(f"q R{t}", a), apply(f"q L{t}", k)) + if option: + selected = add(selected, neg(apply(f"L{s} K{s}", suffix[i])), neg(apply(f"L{s}", correction))) + else: + selected = add(selected, neg(apply(f"L{s}", incoming))) + ordinary = add(neg(y), apply(f"K{s}", suffix[i]), correction) + if i: + ordinary = add(ordinary, apply(f"K{s-2}", suffix[i - 1]), neg(previous_retirement), previous_correction) + else: + ordinary = add(ordinary, neg(suffix[0])) + previous_correction = correction + endpoint.extend((selected, ordinary, apply("Q", a), retired)) + cuts.extend((k, incoming)) + before_tail.append(w) + previous_retirement = retired + if i + 1 < m: + incoming = add(initial[4*i + 7], neg(incoming), retired) + return endpoint, cuts, before_tail, suffix + + +def restrict_to_y(value): + return {word: c for word, c in value.items() if int(word[-1][1:]) % 4 >= 2} + + +def normal_forms(m, family, option, endpoint, suffix): + w = [endpoint[4*i + 1] for i in range(m)] + for i in range(1, m): + w[i] = add(w[i], neg(w[i - 1])) + if family == "raw": + w = list(map(restrict_to_y, w)) + h = [add(restrict_to_y(endpoint[4*i]), apply(f"q B{2*i+2}", w[i])) for i in range(m)] + for i in range(m): + s = 2*i + 1 + correction = add(w[i-1], neg(apply(f"D{s-1} B{s-1}", w[i-1]))) if i else {} + left = add(h[i], neg(apply(f"B{s}", correction))) + lower = add(w[i], correction) + require(left == add(apply("q", input_value(4*i+2)), apply(f"B{s}", input_value(4*i+3))), "Raw selected diagonal block") + require(lower == add(neg(apply(f"D{s} q", input_value(4*i+2))), neg(input_value(4*i+3))), "Raw ordinary diagonal block") + elif option: + for i in range(m): + s, t = 2*i + 1, 2*i + 2 + a, b = input_value(4*i), input_value(4*i + 2) + if not i: + b = add(b, a) + actual = add(apply("Q", endpoint[4*i]), neg(apply(f"L{t}", w[i]))) + expected = add(b, neg(apply(f"Q L{s} K{s}", suffix[i])), neg(apply(f"Q R{s} Q", a)), apply(f"Q L{s} K{s} C{s} Q", a), apply(f"R{t}", a), apply(f"L{t} K{s}", suffix[i + 1])) + require(actual == expected, "Weighted selected normalization") + require(restrict_to_y(actual) == input_value(4*i + 2), "Weighted selected borrowed unit") + restricted = list(map(restrict_to_y, w)) + for i, value in enumerate(restricted): + lower = add(value, restricted[i-1]) if i else value + require(lower == neg(input_value(4*i + 3)), "Weighted ordinary borrowed unit") + + +def matrix_multiply(a, b): + return [[sum(x*y for x, y in zip(row, col)) for col in zip(*b)] for row in a] + + +def eye(n): + return [[int(i == j) for j in range(n)] for i in range(n)] + + +def inverse(a): + n = len(a) + rows = [[Fraction(x) for x in row] + [Fraction(i == j) for j in range(n)] for i, row in enumerate(a)] + for c in range(n): + p = next(i for i in range(c, n) if rows[i][c]) + rows[c], rows[p] = rows[p], rows[c] + divisor = rows[c][c] + rows[c] = [x/divisor for x in rows[c]] + for i in range(n): + if i != c: + coefficient = rows[i][c] + rows[i] = [x-coefficient*y for x, y in zip(rows[i], rows[c])] + return [row[n:] for row in rows] + + +def bareiss(a): + a = [row[:] for row in a] + previous, sign = 1, 1 + for c in range(len(a)-1): + if not a[c][c]: + p = next((i for i in range(c+1, len(a)) if a[i][c]), None) + if p is None: + return 0 + a[c], a[p] = a[p], a[c] + sign *= -1 + pivot = a[c][c] + for i in range(c+1, len(a)): + for j in range(c+1, len(a)): + numerator = a[i][j]*pivot-a[i][c]*a[c][j] + require(numerator % previous == 0, "Exact determinant division") + a[i][j] = numerator//previous + a[i][c] = 0 + previous = pivot + return sign*a[-1][-1] + + +def rank_mod(a, prime): + rows = [[x % prime for x in row] for row in a] + pivot = 0 + for c in range(len(rows[0])): + p = next((i for i in range(pivot, len(rows)) if rows[i][c]), None) + if p is None: + continue + rows[pivot], rows[p] = rows[p], rows[pivot] + scale = pow(rows[pivot][c], -1, prime) + rows[pivot] = [x*scale % prime for x in rows[pivot]] + for i in range(pivot+1, len(rows)): + scale = rows[i][c] + rows[i] = [(x-scale*y) % prime for x, y in zip(rows[i], rows[pivot])] + pivot += 1 + return pivot + + +def numeric_raw_checks(): + results = [] + for seed in (1, 2, 3): + qmat = [[1, seed], [1, seed+1]] + operators = {"Q": qmat, "q": inverse(qmat)} + for stage in range(1, 9): + p = eye(3) + for step in range(5): + target, source = (stage+step) % 3, (stage+step+1) % 3 + p[target] = [x+(seed+step+1)*y for x, y in zip(p[target], p[source])] + operators[f"D{stage}"] = [row[:2] for row in p] + operators[f"B{stage}"] = [[13*x for x in row] for row in inverse(p)[:2]] + require(matrix_multiply(operators[f"B{stage}"], operators[f"D{stage}"]) == [[13, 0], [0, 13]], "Rectangular BD relation") + cross = matrix_multiply(operators["B1"], operators["D2"]) + require(matrix_multiply(qmat, cross) != matrix_multiply(cross, qmat), "Noncommuting selected operators") + for corrected in (False, True): + for m in (1, 2, 4): + expressions = make_tape(m, "raw", corrected).rows() + dimensions = [2, 3, 2, 3]*m + outputs = [j for j in range(4*m) if j % 4 < 2] + inputs = [j for j in range(4*m) if j % 4 >= 2] + offsets, offset = {}, 0 + for j in inputs: + offsets[j], offset = offset, offset + dimensions[j] + matrix = [] + for output in outputs: + block = [[0]*offset for _ in range(dimensions[output])] + for word, coefficient in expressions[output].items(): + source = int(word[-1][1:]) + if source not in offsets: + continue + value = eye(dimensions[source]) + for name in reversed(word[:-1]): + value = matrix_multiply(operators[name], value) + for i, row in enumerate(value): + for j, x in enumerate(row): + block[i][offsets[source]+j] += coefficient*x + require(all(Fraction(x).denominator == 1 for row in block for x in row), "Integer specialization") + matrix.extend([[int(x) for x in row] for row in block]) + determinant = bareiss(matrix) + nullity = len(matrix)-rank_mod(matrix, 3) + require(abs(determinant) == 12**(2*m), "Exact determinant factor") + require(nullity == 2*m, "Exact characteristic-three nullity") + results.append({"seed": seed, "pairs": m, "corrected": corrected, "determinant": str(determinant), "nullity_mod_3": nullity}) + require(bareiss([[3, 0], [0, 3]]) == bareiss([[3, 1], [0, 3]]) == 9, "Equal determinant witness") + require(rank_mod([[3, 0], [0, 3]], 3) == 0 and rank_mod([[3, 1], [0, 3]], 3) == 1, "Different nullity witness") + return results + + +def main(): + inputs = json.loads((HERE/"INPUTS.json").read_text()) + for name, digest in inputs.items(): + require(sha256((LANES/name).read_bytes()).hexdigest() == digest, f"Frozen source: {name}") + for name in list(inputs)[:6]: + require((HERE/"reviewed-inputs"/Path(name).name).read_bytes() == (LANES/name).read_bytes(), "Retained source snapshot") + cases, controls = [], [] + for family in ("raw", "weighted"): + for option in (False, True): + for m in range(1, 9): + tape = make_tape(m, family, option) + actual = tape.rows() + expected, cut_expected, _, suffix = endpoint_formula(m, family, option) + require(actual == expected, "Complete ordered endpoint") + cuts = [] + for stop, outputs in tape.cuts: + cuts.extend(tape.rows(outputs, stop)) + require(cuts == cut_expected, "Active cut rows") + normal_forms(m, family, option, actual, suffix) + cases.append({"family": family, "option": option, "pairs": m, "operator_blocks": (4*m)**2, "cut_blocks": 8*m*m, "events": len(tape.events)}) + for mutation in ("omit_initial_selected", "omit_initial_ordinary", "ascending_tail", "wrong_plus_y", "omit_selected_query" if family == "raw" else "omit_selected_self"): + require(make_tape(4, family, option, mutation).rows() != endpoint_formula(4, family, option)[0], mutation) + controls.append([family, option, mutation]) + if family == "weighted": + require(make_tape(4, family, option, "early_idle_reset").rows() != endpoint_formula(4, family, option)[0], "early_idle_reset") + controls.append([family, option, "early_idle_reset"]) + result = { + "status": "PASS_INDEPENDENT_RAW_AND_WEIGHTED_CONTROLLERS", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_sha256": inputs, + "input_manifest_sha256": sha256((HERE/"INPUTS.json").read_bytes()).hexdigest(), + "method": "Reverse output propagation through independently assembled swaps, clean-core block shears, local factors, and controller events. No producer imports or execution.", + "formal_relations": ["Q q = q Q = I", "H_j K_j = K_j H_j = I"], + "cases": cases, + "operator_blocks_checked": sum(case["operator_blocks"] for case in cases), + "cut_blocks_checked": sum(case["cut_blocks"] for case in cases), + "controls": controls, + "exact_integer_specializations": numeric_raw_checks(), + "all_m_proof": "REVIEW.md gives the induction and the block-diagonal reduction for every positive m.", + "scope": "Ordered content algebra. Local native reviews are dependencies. No new local native replay, inter-call access, idle owner schedule, finite-grid implementation, or complete kappa claim.", + } + (HERE/"REVIEW.json").write_text(json.dumps(result, indent=2) + "\n") + print(result["status"]) + print(f"formal cases={len(cases)} blocks={result['operator_blocks_checked']} controls={len(controls)}") + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/RAW-CONTROLLER-CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/RAW-CONTROLLER-CHECKS.json new file mode 100644 index 0000000000..3b13bb5ea5 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/RAW-CONTROLLER-CHECKS.json @@ -0,0 +1,95 @@ +{ + "status": "PASS_RAW_ORDINARY_CONTROLLER", + "checker_sha256": "bc78a0bc901f73e6a73069d9257064fdf1b18de87c2d331d1f218c5d141a431e", + "source_pins": { + "controller-followthrough-20261017/RAW-ORDINARY-CONTROLLER.md": "1b6a6a86cda137b013cf4999c83ecb1f5131330ae642ce6ea61c96b2edc79382", + "native-escape-20261017/ZERO-LINE-BACKWARD.md": "20ba259395352733e9bf4a5f2b47a10bc62ba134dc543f71da8fba0c2083242c", + "native-escape-20261017/RAW-SELECTED-FORWARD.md": "5680d8674cc9829b87881a38568787b8a423877091e0c6ab7dcd4982457c418e" + }, + "tests": [ + { + "pairs": 1, + "forward": "raw", + "endpoint_blocks": 16, + "active_cuts": 2 + }, + { + "pairs": 2, + "forward": "raw", + "endpoint_blocks": 64, + "active_cuts": 4 + }, + { + "pairs": 3, + "forward": "raw", + "endpoint_blocks": 144, + "active_cuts": 6 + }, + { + "pairs": 4, + "forward": "raw", + "endpoint_blocks": 256, + "active_cuts": 8 + }, + { + "pairs": 5, + "forward": "raw", + "endpoint_blocks": 400, + "active_cuts": 10 + }, + { + "pairs": 6, + "forward": "raw", + "endpoint_blocks": 576, + "active_cuts": 12 + }, + { + "pairs": 1, + "forward": "corrected", + "endpoint_blocks": 16, + "active_cuts": 2 + }, + { + "pairs": 2, + "forward": "corrected", + "endpoint_blocks": 64, + "active_cuts": 4 + }, + { + "pairs": 3, + "forward": "corrected", + "endpoint_blocks": 144, + "active_cuts": 6 + }, + { + "pairs": 4, + "forward": "corrected", + "endpoint_blocks": 256, + "active_cuts": 8 + }, + { + "pairs": 5, + "forward": "corrected", + "endpoint_blocks": 400, + "active_cuts": 10 + }, + { + "pairs": 6, + "forward": "corrected", + "endpoint_blocks": 576, + "active_cuts": 12 + } + ], + "local_inverse_cases": 6, + "borrowed_normal_form_cases": 12, + "relations": [ + "Q q = q Q = I", + "B_s D_s = 13 I" + ], + "method": "Formal ordered operator words. Direct event replay and a separate endpoint recurrence. No scalar specialization and no producer imports.", + "controls": [ + "Omitted selected X query", + "Ascending final X tail" + ], + "scope": "Content algebra only. This does not prove native inter-call views or a paid physical decoder." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/RAW-ORDINARY-CONTROLLER.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/RAW-ORDINARY-CONTROLLER.md new file mode 100644 index 0000000000..529bee6a84 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/RAW-ORDINARY-CONTROLLER.md @@ -0,0 +1,196 @@ +# An ordered raw controller with ordinary bridges + +This note gives the exact content map for a controller that uses the raw +selected backward and forward words. It includes the original first +forward shear, all ordinary bridges, and the final ordinary X triangle. +It identifies the information that a decoder must obtain. It does not +claim a physical decoder or a complete supplier. + +## Local conventions + +Let A be the eight selected ports and let U be the other 104 ports. Put +`Q=Q_A` and `q=Q_A^-1`. These operators act on selected coordinates. +For each stage j, let `B_j:U->A` and `D_j:A->U` satisfy `B_j D_j=13I`. +Products keep their displayed order. In particular, this proof does not +move Q through B or D. + +At pair i use stages `s_i=2i+1` and `t_i=2i+2`. The backward local is + +```text +B_i(a,u;b,v) = (B_s v+q b, u-v-D_s q b+D_s Q a; Q a,v). +``` + +The corrected forward local is + +```text +F_i(h,k;d,v) = (h-q B_t k,k;d,v+k-D_t B_t k). +``` + +The raw forward local subtracts the additional term `D_t q d` from its +ordinary Y output. Both formulas are exact under the local conventions in +the native-escape source packet. Actual inter-call views are a separate +obligation. + +## Event order and endpoint + +Write the original pair as `(a_i,x_i;b_i^0,y_i)`. The selected variables +have dimension eight. The ordinary variables have dimension 104. Form +the ordinary suffix `z_i=x_i-z_(i+1)`, with `z_m=0`. Do not change the +selected X fields. The first full forward shear gives + +```text +b_0=b_0^0+a_0, v_0=y_0+z_0. +b_i=b_i^0 for i>0. +``` + +At each pair, run B. Add the next idle ordinary X to active ordinary X. +Subtract active ordinary Y from next idle ordinary Y. Run F. Subtract +the same idle X. Add retired ordinary Y to next idle Y. The two operations +with the next pair are absent at the last pair. At the end, in descending +pair order, add completed ordinary X from pair `i-1` to pair i. + +Define + +```text +c_i = Q a_i-q b_i, +w_i = z_i-v_i+D_s c_i, +k_i = w_i+z_(i+1), +f_i = B_s v_i+q b_i-q B_t k_i, +e_i = B_t k_i for corrected F, +e_i = B_t k_i+a_i for raw F, +r_i = v_i+k_i-D_t e_i, +v_(i+1) = y_(i+1)-v_i+r_i. +``` + +The final selected X, selected Y, and ordinary Y fields are respectively +`f_i`, `Q a_i`, and `r_i`. The final ordinary X fields are + +```text +K_0 = -y_0+D_s0 c_0, +K_i = -y_i+D_si c_i+D_t(i-1) e_(i-1), i>0. +``` + +To prove the formula for `K_i`, use +`z_(i-1)=x_(i-1)-z_i` and `k_(i-1)=w_(i-1)+z_i`. The Y bridge gives +`v_i=y_i+k_(i-1)-D_t(i-1)e_(i-1)`. Thus +`w_i+w_(i-1)=-y_i+D_si c_i+D_t(i-1)e_(i-1)`. +The descending final triangle adds the unmodified `w_(i-1)`, as required. +The first formula follows from `v_0=y_0+z_0`. + +These formulas apply to all positive pair counts. The checker tests each +formal operator block for one through six pairs. It checks both F words. +It uses only adjacent Q inverse cancellation and `B_jD_j=13I`. + +## What the completed selected query supplies + +If a decoder has both `v_i` and `k_i` in a full frame, then + +```text +b_i = Q(f_i-B_s v_i)+B_t k_i. +``` + +This is an exact selected-source recovery formula with one positive Q +operation. It is not yet a paid decoder. The completed ordinary fields +give each `w_i` by inversion of the final triangle, but they do not give +`k_i=w_i+z_(i+1)` without the original ordinary suffix. They also do not +give the incoming ordinary baseline `v_i`. A decoder must establish these +sources or eliminate them by another identity. + +## A dyadic obstruction for a restricted decoder + +Consider a causal controller in which each backward input receives its +own original Y with identity coefficient. Earlier pairs may contribute +to this input. Suppose that the extra X source at the forward call has no +dependence on the current or future original Y. Suppose also that the +final X operations are dyadic units and that productive selected Y depends +only on original X. + +For fixed original X, the diagonal block from original Y to the completed +local X before F is + +```text +R_s = [[q,B_s],[-D_s q,-I]]. +``` + +Its Schur complement after the selected block q is `-I+D_s B_s`. +Since `B_sD_s=13I`, its determinant has a factor `12^8`, apart from units +and a sign. The selected X update in F is a unit upper shear. The global +X-on-Y matrix is block triangular before its final unit operations. +Its determinant therefore has 3-adic valuation `8m`, when each selected +Q is a unit at 3. + +It follows that no dyadic linear decoder can recover all original Y from +completed X and the productive selected Y fields alone. Fix original X +and set it to zero. The selected Y fields then add no Y information. A +left inverse over the dyadic ring would force the square X-on-Y matrix +to have a unit determinant, which it does not have. + +This determinant argument does not imply that `8m` independent queries +are missing modulo 3. Off-diagonal blocks can change the rank loss. It +also does not exclude a decoder that reads ordinary retired Y, a different +selected set, a noncausal bridge, or a changed local map. For a scalar +postlower parameter lambda, the same argument holds: the local Y block +has lower row `[-lambda D_s q,-I+(1-lambda)D_sB_s]`, and its Schur +complement is still `-I+D_sB_s`. + +For the specific matched ordinary bridges in this note, there is a +stronger statement. Restrict to original X equal to zero. Undo the final +X triangle to obtain `w_i`. Undo the selected X shear to obtain +`h_i=f_i+q B_ti w_i`. Then + +```text +v_0=y_0, +v_i=y_i+L_(i-1) w_(i-1), L_(i-1)=I-D_t(i-1) B_t(i-1). +``` + +For each i greater than zero, use the old w values to replace + +```text +w_i by w_i+L_(i-1)w_(i-1), +h_i by h_i-B_si L_(i-1)w_(i-1). +``` + +These replacements are a unit lower block triangular map. They put the +X-on-Y map into the block diagonal form with diagonal blocks `R_si`. +The formal checker verifies these identities for both F variants. + +Over a field of characteristic 3, `B_sD_s=I`. Thus `D_sB_s` is a +projection of rank equal to the selected dimension. The Schur complement +`D_sB_s-I` has kernel equal to the image of D_s. Each `R_s` has nullity +eight, for selected dimension eight. The complete matched controller has +nullity `8m`. For array-valued ports, multiply this dimension by the common +scalar dimension of one array. The statement applies after reduction to +any field of characteristic 3 in which the displayed operator relations +remain valid and Q is a unit. + +Consequently, a linear decoder for this controller needs independent +information from ordinary retired Y on this `8m`-dimensional kernel. +This is an information requirement. It is not a lower bound of `8m` +native children: one physical operation may carry more than one scalar +dimension, and a changed circuit may use a different representation. + +## Verification and scope + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_raw_controller.py +``` + +Expected output: + +```text +PASS_RAW_ORDINARY_CONTROLLER +``` + +The receipt pins this note and the local source notes. The checker tests +the local inverses, the full event order, the active ordinary cuts, and +the endpoint formula in a formal ordered operator algebra. It includes +controls for a missing selected-X query and an incorrect final tail order. +It does not replay the local physical words, price inter-call native +views, or prove a complete decoder. Independent review remains required. + +The local physical selected exchanges are due to the native-escape and +coordinating lanes. The determinant observation is from the native-escape +lane. This note supplies its causal-controller scope and the distinction +between determinant valuation and rank loss. This work used AI assistance. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/WEIGHTED-RAW-CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/WEIGHTED-RAW-CHECKS.json new file mode 100644 index 0000000000..4c86e50ef6 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/WEIGHTED-RAW-CHECKS.json @@ -0,0 +1,89 @@ +{ + "status": "PASS_WEIGHTED_RAW_CONTROLLER", + "checker_sha256": "c5ae95d4c9b9330ecc488efecb922489049539d22eb635199dcdb1a8197941f4", + "proof_sha256": "22a986d9cf1a31be3d58f572d6552e6e6c30dd2ee6f4393893ea5125dd196280", + "tests": [ + { + "pairs": 1, + "B_postupper": false, + "endpoint_blocks": 16, + "active_cuts": 2 + }, + { + "pairs": 2, + "B_postupper": false, + "endpoint_blocks": 64, + "active_cuts": 4 + }, + { + "pairs": 3, + "B_postupper": false, + "endpoint_blocks": 144, + "active_cuts": 6 + }, + { + "pairs": 4, + "B_postupper": false, + "endpoint_blocks": 256, + "active_cuts": 8 + }, + { + "pairs": 5, + "B_postupper": false, + "endpoint_blocks": 400, + "active_cuts": 10 + }, + { + "pairs": 6, + "B_postupper": false, + "endpoint_blocks": 576, + "active_cuts": 12 + }, + { + "pairs": 1, + "B_postupper": true, + "endpoint_blocks": 16, + "active_cuts": 2 + }, + { + "pairs": 2, + "B_postupper": true, + "endpoint_blocks": 64, + "active_cuts": 4 + }, + { + "pairs": 3, + "B_postupper": true, + "endpoint_blocks": 144, + "active_cuts": 6 + }, + { + "pairs": 4, + "B_postupper": true, + "endpoint_blocks": 256, + "active_cuts": 8 + }, + { + "pairs": 5, + "B_postupper": true, + "endpoint_blocks": 400, + "active_cuts": 10 + }, + { + "pairs": 6, + "B_postupper": true, + "endpoint_blocks": 576, + "active_cuts": 12 + } + ], + "relations": [ + "Q q = q Q = I", + "H_j K_j = K_j H_j = I" + ], + "method": "Formal ordered words. Direct event replay and an independent endpoint recurrence. No producer imports or scalar specialization.", + "controls": [ + "Omitted selected self-block term in F", + "Early idle-X reset" + ], + "scope": "Ordered algebra. Native local replay, idle-X access, inter-call views, and a full paid decoder are separate obligations." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/WEIGHTED-RAW-CONTROLLER.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/WEIGHTED-RAW-CONTROLLER.md new file mode 100644 index 0000000000..208f2f7de2 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/WEIGHTED-RAW-CONTROLLER.md @@ -0,0 +1,166 @@ +# A weighted raw controller with an invertible ordinary block + +This theorem gives the exact ordered content map for raw selected +exchanges when the ordinary block of the local core is a unit. It covers +the five-minor selected set, and any other split with the stated unit +condition. It includes the selected self-block term in the forward call. +The theorem does not require Q to commute with a matrix block. + +## Local blocks + +Split the core matrix at stage j as + +```text +J_j = [[R_j,L_j],[C_j,H_j]], K_j=H_j^-1. +``` + +Let Q be the selected diagonal native operator and let `q=Q^-1`. +The selected physical exchange, followed by the clean backward core and +then K_s on completed ordinary X, gives + +```text +h = q b-R_s Q a-L_s v, +w = K_s u-v-K_s C_s Q a, +d = Q a, +r = v. +``` + +Here `(a,u;b,v)` are the local input contents. A further upper operation +`h-=L_s w` gives + +```text +h = q b-L_s K_s u-T_s Q a, T_s=R_s-L_s K_s C_s. +``` + +The dependence on borrowed input Y is then diagonal: selected X has +coefficient q on b, and ordinary X has coefficient -I on v. All other +terms depend only on original X. This upper operation is useful because +it removes the ordinary borrowed baseline from selected X. + +At stage t, first apply H_t to ordinary Y. Use the physical selected +exchange, the clean forward core, and the second physical selected +exchange. For input `(h,k;d,v)` the resulting map is + +```text +X_A = h+q R_t q d+q L_t k, +X_U = k, +Y_A = d, +Y_U = H_t v+C_t q d+H_t k. +``` + +The term `q R_t q d` must be retained. It vanishes for the old single +minor split, but it is present for a selected set with multiple minors. + +## Complete content controller + +Use m pairs. Let `s_i=2i+1` and `t_i=2i+2`. Write the original data as +`(a_i,x_i;b_i^0,y_i)`. Form only the ordinary X suffix +`z_i=x_i-z_(i+1)`, with `z_m=0`. Use the original full first forward +shear, so `b_0=b_0^0+a_0`, `eta_0=y_0+z_0`, and `b_i=b_i^0` for i>0. + +For each pair, run the balanced backward word. The optional postupper is +either present at every pair or absent. If a next pair exists, apply K_s +to its idle ordinary X, add that value to active ordinary X, and subtract +active ordinary Y from next idle ordinary Y. Run the balanced forward +word. Subtract the same idle ordinary X, add retired ordinary Y to next +idle ordinary Y, and then reset idle ordinary X by H_s. At the end use +the descending ordinary X triangle. + +The preparation and reset of idle X are actual operations. This note +does not infer their native legality from their content matrices. + +Define + +```text +c_i = -K_si C_si Q a_i, +w_i = K_si z_i-eta_i+c_i, +k_i = w_i+K_si z_(i+1), +E_i = H_ti K_si, +r_i = E_i x_i+H_ti c_i+C_ti a_i, +eta_(i+1) = y_(i+1)-eta_i+r_i. +``` + +Retired selected Y is `Q a_i`. Retired ordinary Y is `r_i`. Before the +last ordinary triangle, completed ordinary X is `w_i`. After that +triangle its value is + +```text +Z_0 = -y_0+(K_s0-I)z_0+c_0, +Z_i = -y_i+K_si z_i+K_s(i-1)z_(i-1)-r_(i-1)+c_i+c_(i-1), i>0. +``` + +The selected X endpoint without the optional postupper is + +```text +f_i = q b_i-R_si Q a_i-L_si eta_i+q R_ti a_i+q L_ti k_i. +``` + +With the postupper it is + +```text +f_i = q b_i-L_si K_si z_i-T_si Q a_i+q R_ti a_i+q L_ti k_i. +``` + +These identities follow by substitution into the local maps. In the +ordinary retirement, `eta_i+k_i=K_si x_i+c_i`; this cancels the borrowed +baseline. In the final ordinary X formula, substitute the Y bridge into +`w_i+w_(i-1)`. The descending tail is required so that it uses the old +`w_(i-1)`. No relation between different stage matrices is needed. + +## A selected decoder reduction + +Suppose the postupper is present. Completed ordinary X gives every w_i +by inversion of its final triangle. One positive selected Q operation, +followed by a full-frame scalar subtraction, gives + +```text +g_i = Q f_i-L_ti w_i + = b_i-Q L_si K_si z_i-Q T_si Q a_i + +R_ti a_i+L_ti K_si z_(i+1). +``` + +Thus g_i differs from the original selected borrowed input only by a +function of original X. There is no remaining eta_i term. The first +pair also has the stated `+a_0` from the first full forward call. This +reduction is exact, but it is not a complete decoder: the original +ordinary suffixes in the response are not yet supplied in a usable +physical frame. + +The ordinary retired code has invertible block `E_i=H_ti H_si^-1` and +an explicit selected-input response. Original selected X is present in +productive selected outputs. These properties remove two algebraic +obstacles from the single-minor raw code. They do not by themselves +prove that E_i can be removed within the native budget. In particular, +normalizing all ordinary retired Y to full fields and then restoring +their required hole frames generally incurs two native operations per +ordinary field. Such a decoder must be priced in full. + +## Verification and scope + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_weighted_raw_controller.py +``` + +Expected output: + +```text +PASS_WEIGHTED_RAW_CONTROLLER +``` + +The checker uses formal ordered words with only Q inverse cancellation +and `H_jK_j=K_jH_j=I`. It checks all endpoint blocks and active ordinary +cuts for one through six pairs, with and without the postupper. It also +checks the selected normalization formula. The negative controls omit +the selected self-block term and reset idle X too early. This is a +content proof. It is not a native phase, owner, finite precision, or +complete recursive cost proof. Independent review remains required. + +The weighted recurrence was derived by the upstream-refresh lane. The +balanced local words and their scalar implementation are from the +native-escape and new-core-transfer lanes. The coordinating lane proposed +the five-minor split. This note adds the ordered selected endpoint and +checks the full event order. This work used AI assistance. No publication +is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/check_raw_controller.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/check_raw_controller.py new file mode 100644 index 0000000000..fe5035cfaf --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/check_raw_controller.py @@ -0,0 +1,227 @@ +"""Check the raw selected controller in an ordered operator algebra.""" + +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent + + +def need(value, label): + if not value: + raise ValueError(label) + + +def word_product(left, right): + word, factor = list(left + right), F(1) + changed = True + while changed: + changed = False + for i in range(len(word) - 1): + a, b = word[i:i+2] + if (a, b) in (("Q", "q"), ("q", "Q")): + del word[i:i+2] + changed = True + break + if a.startswith("B") and b == "D" + a[1:]: + del word[i:i+2] + factor *= 13 + changed = True + break + return tuple(word), factor + + +def plus(a, b, scale=1): + out = dict(a) + for word, coefficient in b.items(): + out[word] = out.get(word, F(0)) + scale * coefficient + if not out[word]: + del out[word] + return out + + +def product(a, b): + out = {} + for left, x in a.items(): + for right, y in b.items(): + word, factor = word_product(left, right) + out = plus(out, {word: factor * x * y}) + return out + + +ONE = {(): F(1)} + + +def op(name): + return {(name,): F(1)} + + +def row_add(a, b, scale=1): + return [plus(x, y, scale) for x, y in zip(a, b)] + + +def row_map(operator, row): + return [product(operator, x) for x in row] + + +def basis(n, j): + return [ONE if i == j else {} for i in range(n)] + + +def zero(n): + return [{} for _ in range(n)] + + +def local_b(a, u, b, v, s, lower=1): + r, c = row_map(op("q"), b), row_map(op("Q"), a) + h = row_add(r, row_map(op(f"B{s}"), v)) + k = row_add(u, v, -1) + k = row_add(k, row_map(product(op(f"D{s}"), op(f"B{s}")), v), 1-lower) + k = row_add(k, row_map(op(f"D{s}"), r), -lower) + k = row_add(k, row_map(op(f"D{s}"), c)) + return h, k, c, v + + +def local_f(a, u, b, v, t, corrected): + query = row_map(op(f"B{t}"), u) + h = row_add(a, row_map(op("q"), query), -1) + r = row_add(row_add(v, u), row_map(op(f"D{t}"), query), -1) + if not corrected: + r = row_add(r, row_map(product(op(f"D{t}"), op("q")), b), -1) + return h, u, b, r + + +def replay(m, corrected, mutation=None): + n = 4*m + state = [basis(n, j) for j in range(n)] + for i in range(m-2, -1, -1): + state[4*i+1] = row_add(state[4*i+1], state[4*i+5], -1) + state[2] = row_add(state[2], state[0]) + state[3] = row_add(state[3], state[1]) + cuts = [] + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + state[j:j+4] = local_b(*state[j:j+4], s) + if i+1 < m: + state[j+1] = row_add(state[j+1], state[j+5]) + state[j+7] = row_add(state[j+7], state[j+3], -1) + cuts.append({"active_X_U": state[j+1], "input_Y_U": state[j+3]}) + state[j:j+4] = local_f(*state[j:j+4], t, corrected) + if mutation == "omit_selected_X_query": + state[j] = row_add(state[j], row_map(product(op("q"), op(f"B{t}")), state[j+1])) + if i+1 < m: + state[j+1] = row_add(state[j+1], state[j+5], -1) + state[j+7] = row_add(state[j+7], state[j+3]) + tail = range(1, m) if mutation == "ascending_tail" else range(m-1, 0, -1) + for i in tail: + state[4*i+1] = row_add(state[4*i+1], state[4*i-3]) + return state, cuts + + +def formulas(m, corrected): + n = 4*m + original = [basis(n, j) for j in range(n)] + z = [zero(n) for _ in range(m+1)] + for i in range(m-1, -1, -1): + z[i] = row_add(original[4*i+1], z[i+1], -1) + v = row_add(original[3], z[0]) + previous_response, previous_k, previous_a = zero(n), zero(n), zero(n) + out, cuts = [], [] + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + a = original[j] + b = row_add(original[j+2], a) if not i else original[j+2] + c = row_add(row_map(op("Q"), a), row_map(op("q"), b), -1) + w = row_add(row_add(z[i], v, -1), row_map(op(f"D{s}"), c)) + k = row_add(w, z[i+1]) + query = row_map(op(f"B{t}"), k) + selected = row_add(row_add(row_map(op(f"B{s}"), v), row_map(op("q"), b)), row_map(op("q"), query), -1) + response = query if corrected else row_add(query, a) + retired = row_add(row_add(v, k), row_map(op(f"D{t}"), response), -1) + completed = row_add(row_map(op(f"D{s}"), c), original[j+3], -1) + if i: + completed = row_add(completed, row_map(op(f"D{s-1}"), previous_response)) + out += [selected, completed, row_map(op("Q"), a), retired] + cuts.append({"active_X_U": k, "input_Y_U": v}) + if i+1 < m: + v = row_add(row_add(original[j+7], v, -1), retired) + previous_response, previous_k, previous_a = response, k, a + return out, cuts + + +def local_inverse_checks(): + rows = [basis(4, j) for j in range(4)] + for lower in (0, 1, F(1, 2), -1): + h, k, c, v = local_b(*rows, 1, lower) + r = row_add(h, row_map(op("B1"), v), -1) + u = row_add(k, v) + u = row_add(u, row_map(product(op("D1"), op("B1")), v), lower-1) + u = row_add(u, row_map(op("D1"), r), lower) + u = row_add(u, row_map(op("D1"), c), -1) + need([row_map(op("q"), c), u, row_map(op("Q"), r), v] == rows, "Backward inverse") + for corrected in (False, True): + h, u, b, r = local_f(*rows, 2, corrected) + a = row_add(h, row_map(product(op("q"), op("B2")), u)) + v = row_add(row_add(r, u, -1), row_map(product(op("D2"), op("B2")), u)) + if not corrected: + v = row_add(v, row_map(product(op("D2"), op("q")), b)) + need([a, u, b, v] == rows, "Forward inverse") + + +def borrowed_normal_form(m, corrected): + n = 4*m + endpoint = replay(m, corrected)[0] + restricted = [[block if j % 4 >= 2 else {} for j, block in enumerate(row)] for row in endpoint] + w = [restricted[4*i+1] for i in range(m)] + for i in range(1, m): + w[i] = row_add(w[i], w[i-1], -1) + h = [row_add(restricted[4*i], row_map(product(op("q"), op(f"B{2*i+2}")), w[i])) for i in range(m)] + for i in range(m): + s = 2*i+1 + ordinary, selected = w[i], h[i] + if i: + previous = row_add(w[i-1], row_map(product(op(f"D{s-1}"), op(f"B{s-1}")), w[i-1]), -1) + ordinary = row_add(ordinary, previous) + selected = row_add(selected, row_map(op(f"B{s}"), previous), -1) + b, y = basis(n, 4*i+2), basis(n, 4*i+3) + expected_selected = row_add(row_map(op("q"), b), row_map(op(f"B{s}"), y)) + expected_ordinary = row_add(row_map(product(op(f"D{s}"), op("q")), b), y) + expected_ordinary = row_map({(): F(-1)}, expected_ordinary) + need(selected == expected_selected and ordinary == expected_ordinary, "Borrowed-state block diagonal form") + + +def main(): + local_inverse_checks() + tests = [] + for corrected in (False, True): + for m in range(1, 7): + actual, cuts = replay(m, corrected) + expected, expected_cuts = formulas(m, corrected) + need(actual == expected, "Every endpoint operator block") + need(cuts == expected_cuts, "Every active ordinary cut") + borrowed_normal_form(m, corrected) + need(replay(m, corrected, "omit_selected_X_query")[0] != actual, "Missing selected query control") + if m > 2: + need(replay(m, corrected, "ascending_tail")[0] != actual, "Wrong tail order control") + tests.append({"pairs": m, "forward": "corrected" if corrected else "raw", "endpoint_blocks": (4*m)**2, "active_cuts": 2*m}) + sources = [HERE / "RAW-ORDINARY-CONTROLLER.md", HERE.parent / "native-escape-20261017/ZERO-LINE-BACKWARD.md", HERE.parent / "native-escape-20261017/RAW-SELECTED-FORWARD.md"] + result = { + "status": "PASS_RAW_ORDINARY_CONTROLLER", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins": {str(p.relative_to(HERE.parent)): sha256(p.read_bytes()).hexdigest() for p in sources}, + "tests": tests, + "local_inverse_cases": 6, + "borrowed_normal_form_cases": 12, + "relations": ["Q q = q Q = I", "B_s D_s = 13 I"], + "method": "Formal ordered operator words. Direct event replay and a separate endpoint recurrence. No scalar specialization and no producer imports.", + "controls": ["Omitted selected X query", "Ascending final X tail"], + "scope": "Content algebra only. This does not prove native inter-call views or a paid physical decoder." + } + (HERE / "RAW-CONTROLLER-CHECKS.json").write_text(json.dumps(result, indent=2) + "\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/check_weighted_raw_controller.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/check_weighted_raw_controller.py new file mode 100644 index 0000000000..699d39a2ee --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/reviewed-inputs/check_weighted_raw_controller.py @@ -0,0 +1,201 @@ +"""Check the weighted raw controller with formal ordered operators.""" + +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +ONE = {(): F(1)} + + +def need(value, label): + if not value: + raise ValueError(label) + + +def word_product(left, right): + word = list(left + right) + changed = True + while changed: + changed = False + for i in range(len(word)-1): + a, b = word[i:i+2] + inverse = (a, b) in (("Q", "q"), ("q", "Q")) + inverse |= a[0] in "HK" and b == ("K" if a[0] == "H" else "H") + a[1:] + if inverse: + del word[i:i+2] + changed = True + break + return tuple(word) + + +def plus(a, b, scale=1): + out = dict(a) + for word, value in b.items(): + out[word] = out.get(word, F(0)) + scale*value + if not out[word]: + del out[word] + return out + + +def product(a, b): + out = {} + for left, x in a.items(): + for right, y in b.items(): + out = plus(out, {word_product(left, right): x*y}) + return out + + +def operator(*names): + out = ONE + for name in names: + out = product(out, {(name,): F(1)}) + return out + + +def row_add(a, b, scale=1): + return [plus(x, y, scale) for x, y in zip(a, b)] + + +def row_map(op, row): + return [product(op, value) for value in row] + + +def basis(n, j): + return [ONE if i == j else {} for i in range(n)] + + +def zero(n): + return [{} for _ in range(n)] + + +def replay(m, upper, mutation=None): + n = 4*m + state = [basis(n, j) for j in range(n)] + for i in range(m-2, -1, -1): + state[4*i+1] = row_add(state[4*i+1], state[4*i+5], -1) + state[2], state[3] = row_add(state[2], state[0]), row_add(state[3], state[1]) + cuts = [] + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + a, u, b, v = state[j:j+4] + d = row_map(operator("Q"), a) + h = row_add(row_add(row_map(operator("q"), b), row_map(operator(f"R{s}"), d), -1), row_map(operator(f"L{s}"), v), -1) + w = row_map(operator(f"K{s}"), row_add(row_add(u, row_map(operator(f"C{s}"), d), -1), row_map(operator(f"H{s}"), v), -1)) + if upper: + h = row_add(h, row_map(operator(f"L{s}"), w), -1) + state[j:j+4] = [h, w, d, v] + if i+1 < m: + state[j+5] = row_map(operator(f"K{s}"), state[j+5]) + state[j+1] = row_add(state[j+1], state[j+5]) + state[j+7] = row_add(state[j+7], state[j+3], -1) + cuts.append({"active_X_U": state[j+1], "input_Y_U": state[j+3]}) + state[j+3] = row_map(operator(f"H{t}"), state[j+3]) + h, k, d, v = state[j:j+4] + h = row_add(h, row_map(operator("q", f"R{t}", "q"), d)) + h = row_add(h, row_map(operator("q", f"L{t}"), k)) + v = row_add(row_add(v, row_map(operator(f"C{t}", "q"), d)), row_map(operator(f"H{t}"), k)) + if mutation == "omit_selected_self_term": + h = row_add(h, row_map(operator("q", f"R{t}", "q"), d), -1) + state[j:j+4] = [h, k, d, v] + if i+1 < m: + if mutation == "early_idle_reset": + state[j+5] = row_map(operator(f"H{s}"), state[j+5]) + state[j+1] = row_add(state[j+1], state[j+5], -1) + state[j+7] = row_add(state[j+7], state[j+3]) + if mutation != "early_idle_reset": + state[j+5] = row_map(operator(f"H{s}"), state[j+5]) + for i in range(m-1, 0, -1): + state[4*i+1] = row_add(state[4*i+1], state[4*i-3]) + return state, cuts + + +def formulas(m, upper): + n = 4*m + original = [basis(n, j) for j in range(n)] + z = [zero(n) for _ in range(m+1)] + for i in range(m-1, -1, -1): + z[i] = row_add(original[4*i+1], z[i+1], -1) + eta = row_add(original[3], z[0]) + out, cuts, ws = [], [], [] + rprev, cprev = zero(n), zero(n) + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + a, x = original[j:j+2] + b = row_add(original[j+2], a) if not i else original[j+2] + ca = row_map(operator(f"K{s}", f"C{s}", "Q"), a) + w = row_add(row_add(row_map(operator(f"K{s}"), z[i]), eta, -1), ca, -1) + k = row_add(w, row_map(operator(f"K{s}"), z[i+1])) + retired = row_add(row_map(operator(f"H{t}", f"K{s}"), x), row_map(operator(f"C{t}"), a)) + retired = row_add(retired, row_map(operator(f"H{t}"), ca), -1) + if upper: + h = row_add(row_map(operator("q"), b), row_map(operator(f"L{s}", f"K{s}"), z[i]), -1) + h = row_add(h, row_map(operator(f"R{s}", "Q"), a), -1) + h = row_add(h, row_map(operator(f"L{s}"), ca)) + else: + h = row_add(row_map(operator("q"), b), row_map(operator(f"R{s}", "Q"), a), -1) + h = row_add(h, row_map(operator(f"L{s}"), eta), -1) + h = row_add(row_add(h, row_map(operator("q", f"R{t}"), a)), row_map(operator("q", f"L{t}"), k)) + completed = row_add(row_map(operator(f"K{s}"), z[i]), original[j+3], -1) + completed = row_add(completed, ca, -1) + if i: + completed = row_add(completed, row_map(operator(f"K{s-2}"), z[i-1])) + completed = row_add(row_add(completed, cprev, -1), rprev, -1) + else: + completed = row_add(completed, z[0], -1) + out += [h, completed, row_map(operator("Q"), a), retired] + cuts.append({"active_X_U": k, "input_Y_U": eta}) + ws.append(w) + if i+1 < m: + eta = row_add(row_add(original[j+7], eta, -1), retired) + rprev, cprev = retired, ca + return out, cuts, ws, z + + +def selected_normalization(m, endpoint, ws, z): + n = 4*m + for i in range(m): + j, s, t = 4*i, 2*i+1, 2*i+2 + actual = row_add(row_map(operator("Q"), endpoint[j]), row_map(operator(f"L{t}"), ws[i]), -1) + a = basis(n, j) + b = row_add(basis(n, j+2), a) if not i else basis(n, j+2) + expected = row_add(b, row_map(operator("Q", f"L{s}", f"K{s}"), z[i]), -1) + expected = row_add(expected, row_map(operator("Q", f"R{s}", "Q"), a), -1) + expected = row_add(expected, row_map(operator("Q", f"L{s}", f"K{s}", f"C{s}", "Q"), a)) + expected = row_add(expected, row_map(operator(f"R{t}"), a)) + expected = row_add(expected, row_map(operator(f"L{t}", f"K{s}"), z[i+1])) + need(actual == expected, "Selected normalization and pure input response") + + +def main(): + tests = [] + for upper in (False, True): + for m in range(1, 7): + actual, cuts = replay(m, upper) + expected, expected_cuts, ws, z = formulas(m, upper) + need(actual == expected, "Every weighted endpoint operator block") + need(cuts == expected_cuts, "Every weighted active cut") + if upper: + selected_normalization(m, actual, ws, z) + need(replay(m, upper, "omit_selected_self_term")[0] != actual, "Selected self-block control") + if m > 1: + need(replay(m, upper, "early_idle_reset")[0] != actual, "Early idle reset control") + tests.append({"pairs": m, "B_postupper": upper, "endpoint_blocks": (4*m)**2, "active_cuts": 2*m}) + result = { + "status": "PASS_WEIGHTED_RAW_CONTROLLER", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "proof_sha256": sha256((HERE / "WEIGHTED-RAW-CONTROLLER.md").read_bytes()).hexdigest(), + "tests": tests, + "relations": ["Q q = q Q = I", "H_j K_j = K_j H_j = I"], + "method": "Formal ordered words. Direct event replay and an independent endpoint recurrence. No producer imports or scalar specialization.", + "controls": ["Omitted selected self-block term in F", "Early idle-X reset"], + "scope": "Ordered algebra. Native local replay, idle-X access, inter-call views, and a full paid decoder are separate obligations." + } + (HERE / "WEIGHTED-RAW-CHECKS.json").write_text(json.dumps(result, indent=2) + "\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/NORMALIZATION-PROGRAMS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/NORMALIZATION-PROGRAMS.json new file mode 100644 index 0000000000..b84f99a667 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/NORMALIZATION-PROGRAMS.json @@ -0,0 +1 @@ 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Full terminal access, global hosting, and complete kappa cost are separate.", + "status": "PASS_ONE_PAIR_CURRENT_CODES" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/FREEZE.json new file mode 100644 index 0000000000..e4c59642f3 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "CHECKS.json": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd", + "ONE-PAIR.md": "86c87e8080c305c605541d70afc523b8ff65a94cbf2bc9e134289984d86f1f6e", + "PROGRAM.json": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", + "REPRODUCTION.json": "75e700814bd171f85e8c28319bd06b3671a86c4dcaa2a9c85c48063dee79fe0c", + "check_and_emit.py": "36477532246e37c6ae8c2321dda6e02a5540a298535c022a837dcb68860adc19" + }, + "status": "FROZEN_ONE_PAIR_CURRENT_CODES" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/ONE-PAIR.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/ONE-PAIR.md new file mode 100644 index 0000000000..45b2125d2e --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/ONE-PAIR.md @@ -0,0 +1,199 @@ +# Three calls with current-stage port codes + +This packet gives a complete three-call content word for the fresh +matched response. It uses one X bank and one Y bank. Each bank has 112 +productive fields. The five added port codes use current Y cuts or +current/past completed X cuts. There is no borrowed helper, bridge, +idle data job, or retained record in this controller. + +The exact preterminal output is + +```text +(-y, T x), T = E2 E1 E0. +``` + +The remaining physical code is `diag(Q T Q^-1,I)`. This packet keeps +that code explicit. It does not claim that the three-call supplier is +closed without a terminal decoder. + +## Actual local source + +The data source is the frozen +[matched native involution](../../oblique-native-20261017/matched-native-involution/MATCHED-NATIVE.md). +Its payload is +[MATCHED-NATIVE-PROGRAM.json.gz](../../oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz), +with decompressed SHA-256 +`95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025`. +The source supplies + +```text +F_s(x,y) = (x, y + E_s x), +B_s(x,y) = (x - E_s^-1 y, y). +``` + +The local coefficient matrix E is symmetric and satisfies E^2=I. Its +48-port part uses the paired-mode matching. Its other 64 rows form a +negative port permutation with 32 swaps and no fixed point. Those 64 +rows are not a diagonal minus identity. + +Each E_s is the response after the actual stage cover views. The three +operators need not be equal. The proof below uses only their inverses; +it does not use E_s^2=I. The source word supplies the inverse because its +actual coefficient matrix is a symmetric involution. + +The native entrance and exit types remain the original types: + +```text +X_p: C_qp -> F9, +Y_p: I -> F9 C_qp^-1. +``` + +The source has no helper reads, owned C fields, or private fields. Its +three successive local jobs advance the productive data through the +25-axis construction. The complete owner and recursive host checks +belong to the separate one-pair admission packet. + +## Ordered word + +Execute these operations in the stated order: + +| Step | Operation | Code cut | +| --- | --- | --- | +| 1 | F0 | Native word | +| 2 | X <- E0 X | Completed X at level 0 | +| 3 | Y <- E1 Y | Current Y entrance at stage 1 | +| 4 | B1 | Native word | +| 5 | X <- E1 X | Completed X at level 1 | +| 6 | Y <- E2 Y | Current Y entrance at stage 2 | +| 7 | F2 | Native word | +| 8 | X <- E1^-1 X | Completed X at level 2 | + +Both providers have the same scalar code decomposition. The route views +for each occurrence still depend on its stage and cut. The code in step +8 is a past-stage code at a completed X cut. No code uses a past-stage +Y query or a future-stage completed-X query. + +For arbitrary input x,y, the successive states are + +```text +after step 2: (E0 x, y + E0 x), +after step 5: (-E1 y, E1 y + E1 E0 x), +after step 7: (-E1 y, E2 E1 E0 x), +after step 8: (-y, E2 E1 E0 x). +``` + +Every product has its displayed order. The cancellation at B1 uses its +actual reciprocal response E1^-1. The cancellation at F2 uses the E1 +code on X and the E2 code on Y. No commutation is used. + +For the literal endpoint `(-y,x)`, the exact condition is T=I. Equality +of the three local coefficient matrices does not establish this +condition after stage routing. Even if the routed response were one +common involution E, the product would be E, not I. + +## Literal scalar codes + +The emitted port circuit factors the actual local response as + +```text +E = A^-1 M A, +``` + +where A is the 24-pair Hadamard code on the 48 coupled ports and the +identity elsewhere. M is a signed permutation on all 112 ports. The +checker obtains M from the exact response and verifies every entry. +It lowers every swap into three unit ADDs and a sign. It then applies +the inverse pair code. + +The resulting circuit has 494 scalar gates and costs 2,668 real scalar +primitives. It needs no helper, owned field, private field, or native +child. The inverse circuit is also emitted and checked on all 112 input +columns. The code needs a common physical frame in its stage view. +The separate cut check supplies that view. A conservative allowance is +224 view calls per code, for gather and scatter on all 112 ports. + +This circuit is an implementation of the local port matrix in a proved +common-frame chart. It is not an implementation of Q E Q^-1 at a hole +cut. Those two operations are not identified. + +## Physical endpoint and direct decoder + +Let Q be the diagonal intrinsic line operator, q=Q^-1, and let F be the +common completed 25-axis frame. The raw input is W(x,y), where +W=diag(Q,I). The preterminal physical frame is F diag(I,q). The old +signed terminal is + +```text +A = [[0,Q^2],[-I,0]]. +``` + +The ordered endpoint equation is + +```text +A diag(I,q) [[0,-I],[T,0]] W^-1 + = diag(Q T Q^-1,I). +``` + +Thus a direct decoder on the first output bank has three steps, all in +the common-F coordinate convention: + +1. Apply Q^-1 to all 112 fields. +2. Apply T^-1=E0^-1 E1^-1 E2^-1. The chronological order of these three + scalar codes is E2^-1, then E1^-1, then E0^-1. +3. Apply Q to all 112 fields. + +The second step uses only current or past stage charts at final FULL. +The two line passes use 224 rank-one children. This is an explicit +costed construction hypothesis for the line calls; this packet does +not emit their 25-axis native recipes or their global hosting. + +A cheaper decoder, or a changed native response that makes the routed +product T simpler, is still useful. One cannot instead leave T in the +output and use the unchanged outer twiddle or pointwise product. +Such a change needs a separate encoded outer-operation contract. + +## Local invoice and native-rank limit + +Three data calls have profile + +```text +{1:480, 2:144, 5:144, 7:336, 8:192}, +``` + +with 1,296 children and rank mass 5,376. The three local scalar bills +and the five port codes sum to 22,436 real scalar primitives. The old +signed terminal costs 2,688 more. The five codes have a conservative +1,120-view allowance. These counts exclude precision and recursive +hosting costs. + +The direct two-pass decoder adds 224 rank-one children and three scalar +port codes. Its resulting rank mass is exactly + +```text +5376 + 224 = 5600 = 224 * 25. +``` + +It therefore leaves no rank deficit. In the unit-width native-only +moment test, it also fails every positive b: each native child has rank +less than 25, so r^(1-b) > r*25^(-b). Summing this strict inequality and +using total rank 5,600 gives a native moment greater than the productive +weight 224*25^(1-b). This conclusion applies to this direct decoder, +not to every implementation of the remaining code. + +## Verification + +The checker imports no producer. It reads the pinned native data word, +builds and checks both scalar code orders on all 112 columns, and checks +the generic three-call word in a free ordered group. It checks the raw +Q boundary and the complete direct inverse in the same group. It +rejects deletion of each of the five required port codes. + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -I -B work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py +``` + +Both runs must report `PASS_ONE_PAIR_CURRENT_CODES` and produce the same +payload and receipt. `FREEZE.json` records their hashes. The native +phase checks are pinned predecessor results, not a new full native +replay in this packet. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/PROGRAM.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/PROGRAM.json new file mode 100644 index 0000000000..c54e751a73 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/PROGRAM.json @@ -0,0 +1 @@ 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diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/REPRODUCTION.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/REPRODUCTION.json new file mode 100644 index 0000000000..fb143aa52d --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/REPRODUCTION.json @@ -0,0 +1,7 @@ +{ + "output_sha256": { + "CHECKS.json": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd", + "PROGRAM.json": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7" + }, + "status": "PASS_BYTE_IDENTICAL_NORMAL_AND_OPTIMIZED" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py new file mode 100644 index 0000000000..07a026b9a6 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py @@ -0,0 +1,231 @@ +#!/usr/bin/env python3 +"""Check the three-call current-cut controller and its scalar port codes.""" + +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +DATA = LANES / 'oblique-native-20261017/matched-native-involution' +DATA_PIN = '95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025' +RECEIPT_PIN = '7bc873d627e022d4677b740633c9cd5f86c5e675d84460d538b4b6314c79536c' + + +def need(test, message): + if not test: + raise ValueError(message) + + +def add(target, source, scalar=F(1)): + for key, coefficient in source.items(): + value = target.get(key, 0) + scalar * coefficient + if value: + target[key] = value + else: + target.pop(key, None) + + +def product(left, right): + result = [] + for row in left: + out = {} + for j, c in row.items(): + add(out, right[j], c) + result.append(out) + return result + + +def apply_gates(gates, size=112): + rows = [{i: F(1)} for i in range(size)] + for gate in gates: + op, target = gate[:2] + need(0 <= target < size, 'Scalar target range') + if op == 'scale': + c = F(*gate[2:]) + rows[target] = {j: c * v for j, v in rows[target].items() if c * v} + else: + source = gate[2] + need(op == 'add' and 0 <= source < size and source != target, 'Scalar source range') + add(rows[target], rows[source], F(*gate[3:])) + return rows + + +def inverse_gates(gates): + out = [] + for gate in reversed(gates): + if gate[0] == 'scale': + c = 1 / F(*gate[2:]) + out.append(['scale', gate[1], c.numerator, c.denominator]) + else: + c = -F(*gate[3:]) + out.append(['add', gate[1], gate[2], c.numerator, c.denominator]) + return out + + +def scalar_cost(gates): + total = 0 + for gate in gates: + c = F(*gate[-2:]) + a, b = abs(c.numerator), c.denominator + need(a > 0 and b & (b - 1) == 0, 'Dyadic scalar') + if gate[0] == 'scale': + need(a & (a - 1) == 0, 'Dyadic unit scale') + total += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) + else: + total += 2 * (3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1) + return total + + +def scalar_code(word, response): + entrance = [] + for pair in word['pair_codes']: + for op, target, source, value in pair['code']: + if target >= 112: + continue + c = F(value) + entrance.append([op, target, c.numerator, c.denominator] if op == 'scale' + else [op, target, source, c.numerator, c.denominator]) + exit_code = inverse_gates(entrance) + a, ai = apply_gates(entrance), apply_gates(exit_code) + identity = [{i: F(1)} for i in range(112)] + need(product(a, ai) == product(ai, a) == identity, 'Both pair-code inverse orders') + middle = product(product(a, response), ai) + need(all(len(row) == 1 and abs(next(iter(row.values()))) == 1 for row in middle), + 'The middle code is a signed permutation') + permutation = [next(iter(row)) for row in middle] + signs = [next(iter(row.values())) for row in middle] + need(sorted(permutation) == list(range(112)), 'Bijective middle code') + middle_code, cycles, visited = [], [], set() + for first in range(112): + if first in visited: + continue + cycle, p = [], first + while p not in visited: + visited.add(p) + cycle.append(p) + p = permutation[p] + need(p == first, 'Permutation cycle closes') + cycles.append(cycle) + for x, y in zip(cycle, cycle[1:]): + middle_code += [['add', x, y, 1, 1], ['add', y, x, -1, 1], + ['add', x, y, 1, 1], ['scale', y, -1, 1]] + middle_code += [['scale', i, -1, 1] for i, c in enumerate(signs) if c == -1] + need(apply_gates(middle_code) == middle, 'Every signed permutation input') + gates = entrance + middle_code + exit_code + need(apply_gates(gates) == response, 'All112 scalar response columns') + need(apply_gates(inverse_gates(gates)) == response, 'The actual scalar response is its inverse') + return gates, {'scalar_gates': len(gates), 'real_scalar_primitives': scalar_cost(gates), + 'middle_cycles': cycles, 'owned_fields': 0, 'private_fields': 0, + 'native_children': 0, 'conservative_stage_views': 224} + + +def reduce_word(word): + out = [] + for symbol in word: + if out and out[-1] == -symbol: + out.pop() + else: + out.append(symbol) + return tuple(out) + + +def left(symbol, row): + out = {} + for (source, word), value in row.items(): + add(out, {(source, reduce_word((symbol,) + word)): value}) + return out + + +PROGRAM = [ + ['forward', 0], ['code_X', 0, 1], + ['code_Y', 1, 1], ['backward', 1], ['code_X', 1, 1], + ['code_Y', 2, 1], ['forward', 2], ['code_X', 1, -1], +] + + +def replay(program, raw=False): + x = {(0, (-4,) if raw else ()): F(1)} + y = {(1, ()): F(1)} + for event in program: + kind, stage = event[:2] + symbol = stage + 1 + if kind == 'forward': + add(y, left(symbol, x)) + elif kind == 'backward': + add(x, left(-symbol, y), -1) + elif kind == 'code_X': + x = left(event[2] * symbol, x) + else: + need(kind == 'code_Y', 'Known controller event') + y = left(event[2] * symbol, y) + return x, y + + +def main(): + raw = gzip.decompress((DATA / 'MATCHED-NATIVE-PROGRAM.json.gz').read_bytes()) + need(sha256(raw).hexdigest() == DATA_PIN, 'Frozen data word') + need(sha256((DATA / 'MATCHED-NATIVE-RECEIPT.json').read_bytes()).hexdigest() == RECEIPT_PIN, + 'Frozen native receipt') + source = json.loads(raw) + response = [{int(j): F(v) for j, v in row.items()} for row in source['response']] + identity = [{i: F(1)} for i in range(112)] + need(product(response, response) == identity, 'Actual full response involution') + need(all(response[i].get(j, 0) == response[j].get(i, 0) for i in range(112) for j in range(112)), + 'Actual response symmetry') + payload = {'schema': 'one-pair-current-code-controller-v1', 'data_payload_pin': DATA_PIN, + 'program': PROGRAM, 'providers': {}} + receipt = {'status': 'PASS_ONE_PAIR_CURRENT_CODES', 'providers': {}} + for provider, item in source['providers'].items(): + gates, bill = scalar_code(item['forward'], response) + profile = Counter(e[4] for e in item['forward']['events'] if e[0] == 'native') + need(sum(k * v for k, v in profile.items()) == 1792, 'Data call mass') + payload['providers'][provider] = {'scalar_E_code': gates, 'scalar_E_inverse_code': inverse_gates(gates)} + receipt['providers'][provider] = {'one_code': bill, 'three_call_native_profile': + dict(sorted((k, 3 * v) for k, v in profile.items())), + 'three_call_native_mass': 5376, + 'local_and_five_code_real_scalar': 3 * 3032 + 5 * bill['real_scalar_primitives'], + 'old_terminal_real_scalar': 2688, + 'five_code_view_bound': 1120, + 'naive_terminal_extra_rank_one_children': 224, + 'naive_terminal_scalar_inverse_codes': 3, + 'new_borrowed_or_owned_fields': 0} + x, y = replay(PROGRAM) + need(x == {(1, ()): -1} and y == {(0, (3, 2, 1)): 1}, 'Ordered generic three-call endpoint') + xr, yr = replay(PROGRAM, raw=True) + # q acts on Y before the retained Q^2 terminal. No E is moved through Q. + preterminal_y = left(-4, yr) + final_x = left(4, left(4, preterminal_y)) + final_y = {k: -v for k, v in xr.items()} + need(final_x == {(0, (4, 3, 2, 1, -4)): 1} and final_y == {(1, ()): 1}, + 'Physical Q T Q^-1 endpoint') + decoded = final_x + for symbol in (-4, -3, -2, -1, 4): + decoded = left(symbol, decoded) + need(decoded == {(0, ()): 1}, 'Ordered two-pass terminal inverse') + rejected = [] + for i, event in enumerate(PROGRAM): + if event[0].startswith('code_'): + xx, yy = replay(PROGRAM[:i] + PROGRAM[i+1:]) + need((xx, yy) != (x, y), 'Omitted current code changes the endpoint') + rejected.append(i) + receipt.update({'generic_ordered_endpoint': ['-y', 'E2 E1 E0 x'], + 'physical_raw_output_code': ['Q E2 E1 E0 Q^-1', 'I'], + 'omitted_code_controls': rejected, + 'future_X_codes': 0, 'past_Y_codes': 0, + 'scope': 'Current-cut code circuit and exact residual. Full terminal access, global hosting, and complete kappa cost are separate.'}) + data = json.dumps(payload, sort_keys=True, separators=(',', ':')).encode() + (HERE / 'PROGRAM.json').write_bytes(data + b'\n') + receipt['payload_sha256'] = sha256(data + b'\n').hexdigest() + receipt['checker_sha256'] = sha256(Path(__file__).read_bytes()).hexdigest() + (HERE / 'CHECKS.json').write_text(json.dumps(receipt, sort_keys=True, indent=2) + '\n') + print(json.dumps(receipt, sort_keys=True, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/CHECKS.json new file mode 100644 index 0000000000..7d0c86856c --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/CHECKS.json @@ -0,0 +1,64 @@ +{ + "checker_sha256": "92e0de17508acefc75dcb372bfc7719c5d870035dce1d20da667cd3459094d99", + "content_endpoint": [ + "-y", + "E2 G1^-1 E0 x" + ], + "native_or_host_claimed": false, + "omitted_code_controls": [ + 1, + 2, + 4, + 5, + 7 + ], + "physical_raw_output": [ + "Q E2 G1^-1 E0 Q^-1", + "I" + ], + "predecessor_proof_sha256": "86c87e8080c305c605541d70afc523b8ff65a94cbf2bc9e134289984d86f1f6e", + "program": [ + [ + "F", + 1 + ], + [ + "X", + 1 + ], + [ + "Y", + -2 + ], + [ + "B", + 2 + ], + [ + "X", + -2 + ], + [ + "Y", + 3 + ], + [ + "F", + 3 + ], + [ + "X", + 2 + ] + ], + "proof_sha256": "9fc6ffeee34e87cf8bcefa4f5a8acbcf99c0f82db686081a0ec9695e87dfedf4", + "status": "PASS_ONE_PAIR_GENERAL_UNITS", + "three_field_code": { + "input_columns_checked": 3, + "inverse_orders_checked": 2, + "owned_or_borrowed_fields": 0, + "real_scalar_primitives_each_direction": 52, + "signed_factor_two_scales": 1, + "unit_adds": 6 + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/FREEZE.json new file mode 100644 index 0000000000..634510e77e --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/FREEZE.json @@ -0,0 +1,9 @@ +{ + "files": { + "CHECKS.json": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6", + "GENERAL-UNITS.md": "9fc6ffeee34e87cf8bcefa4f5a8acbcf99c0f82db686081a0ec9695e87dfedf4", + "REPRODUCTION.json": "4a6e8652b4a164dfb607a9472752b1b35e5c4d42784d3f9f3d4a6de181f4c31d", + "check_general_units.py": "92e0de17508acefc75dcb372bfc7719c5d870035dce1d20da667cd3459094d99" + }, + "status": "FROZEN_ONE_PAIR_GENERAL_UNITS" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/GENERAL-UNITS.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/GENERAL-UNITS.md new file mode 100644 index 0000000000..b077abea46 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/GENERAL-UNITS.md @@ -0,0 +1,136 @@ +# Three calls with two unit response types + +This packet extends the five-code one-pair controller. The backward +native response need not be the inverse of a forward response. It is +sufficient that each local response is a unit and that its required +scalar code is available in its own common-frame chart. + +The native local maps are + +```text +F0(x,y) = (x,y+E0 x), +B1(x,y) = (x-G1 y,y), +F2(x,y) = (x,y+E2 x). +``` + +E0, G1, and E2 are arbitrary units. They can be noncommuting routed +operators. No transpose or involution relation is needed for the +ordered content identity. + +## The five code operations + +Execute this word: + +| Step | Operation | Required cut | +| --- | --- | --- | +| 1 | F0 | Native word | +| 2 | X <- E0 X | Completed X at stage 0 | +| 3 | Y <- G1^-1 Y | Current Y entrance at stage 1 | +| 4 | B1 | Native word | +| 5 | X <- G1^-1 X | Completed X at stage 1 | +| 6 | Y <- E2 Y | Current Y entrance at stage 2 | +| 7 | F2 | Native word | +| 8 | X <- G1 X | Completed X at stage 2 | + +The successive states are + +```text +after step 2: (E0 x, y+E0 x), +after step 4: (-y, G1^-1(y+E0 x)), +after step 5: (-G1^-1 y, G1^-1(y+E0 x)), +after step 7: (-G1^-1 y, E2 G1^-1 E0 x), +after step 8: (-y, E2 G1^-1 E0 x). +``` + +Each cancellation uses adjacent inverse factors. There is no old-stage +Y code or future-stage completed-X code. The last operation uses a +past-stage code on completed X. + +The exact closure condition for this word is + +```text +E2 G1^-1 E0 = I. +``` + +Thus a native transpose pair, with G1=E1^T in its routed chart, gives +T=E2 E1^-T E0. There is no need to first synthesize a native shear by +E1^-1. This conclusion does require an in-place scalar circuit for +G1^-1 at its own chart. A determinant statement alone is not such a +circuit or a cost certificate. + +The five scalar cuts are the same cuts as those in +[the matched one-pair packet](../one-pair-current-codes-20261018/ONE-PAIR.md). +That packet pins the current matched native word. The present theorem +does not replace its source with an unproved native word. + +## Physical boundary + +Keep Q as the port-diagonal positive intrinsic line, and let q=Q^-1. +The physical entrance is W=diag(Q,I). The preterminal frame is +F diag(I,q). The retained signed terminal is + +```text +A = [[0,Q^2],[-I,0]]. +``` + +In the common-F coordinate chart, the complete map is + +```text +A diag(I,q) [[0,-I],[T,0]] W^-1 = diag(Q T Q^-1,I), +T = E2 G1^-1 E0. +``` + +No response is moved through Q. An exact terminal decoder must remove +Q T Q^-1, or a new outer-operation contract must consume that code. +The direct decoder applies Q^-1, then E2^-1, then G1, then E0^-1, +then Q. Its two line passes remain 224 rank-one children on 112 fields. +This theorem does not reduce that bill. + +## A small unit code for the new response search + +Let J3 be the three-by-three all-ones matrix. The matrix C=I-J3 has +zero diagonal and determinant -2. Its inverse is I-J3/2. Both matrices +are dyadic units. The following in-place circuit implements C on three +arbitrary input fields a,b,c: + +```text +a += b +a += c +b -= a +c -= a +a *= -2 +a -= b +a -= c +``` + +The output is (-b0-c0,-a0-c0,-a0-b0). Reverse these operations to apply +C^-1. Each direction has six unit ADDs and one signed factor-two scale. +The existing scalar tariff charges 52 real primitives per direction. +No accumulator, private field, or initial zero is used. + +Six-mode blocks diag(C,C), one for each of eight vertices, therefore +need 16 such code circuits. Their total is 832 real primitives before +the physical pair-code conjugacy and cover views. This is only the +scalar code cost. The native zero-diagonal response, its other 64 +ports, phase recipes, and complete one-pair bill are separate work. + +In a single common chart with E0=G1=E2=C, the residual is C, not C^3. +With different routed charts it remains E2 G1^-1 E0. The common-chart +identity does not remove the routed or intrinsic-line code. + +## Verification + +The checker uses an ordered free group for the native response and Q +symbols. It checks the complete content map, the physical boundary, +the direct inverse, and deletion of each of the five code operations. +It separately checks both orders of the three-field scalar inverse on +all three input columns. It imports no producer. + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -I -B work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py +``` + +Both runs must report PASS_ONE_PAIR_GENERAL_UNITS and emit the same +receipt. No new native word, owner schedule, terminal implementation, +precision bound, or kappa improvement is claimed. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/REPRODUCTION.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/REPRODUCTION.json new file mode 100644 index 0000000000..57c8b30cdd --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/REPRODUCTION.json @@ -0,0 +1,22 @@ +{ + "runs": [ + { + "flags": [ + "-I", + "-B" + ], + "receipt_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6", + "stdout": "PASS_ONE_PAIR_GENERAL_UNITS" + }, + { + "flags": [ + "-I", + "-O", + "-B" + ], + "receipt_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6", + "stdout": "PASS_ONE_PAIR_GENERAL_UNITS" + } + ], + "status": "PASS_BYTE_IDENTICAL" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py new file mode 100644 index 0000000000..785aea7fe9 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py @@ -0,0 +1,122 @@ +#!/usr/bin/env python3 +"""Check the three-call unit interface and a three-field dyadic code.""" + +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +PIN = '86c87e8080c305c605541d70afc523b8ff65a94cbf2bc9e134289984d86f1f6e' +PROGRAM = [('F', 1), ('X', 1), ('Y', -2), ('B', 2), + ('X', -2), ('Y', 3), ('F', 3), ('X', 2)] + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def word(items): + out = [] + for item in items: + if out and out[-1] == -item: + out.pop() + else: + out.append(item) + return tuple(out) + + +def left(symbol, row): + return {(source, word((symbol,) + path)): value + for (source, path), value in row.items()} + + +def add(a, b, scale=1): + out = dict(a) + for key, value in b.items(): + value = out.get(key, 0) + scale * value + if value: + out[key] = value + else: + out.pop(key, None) + return out + + +def replay(program, raw=False): + x, y = {(0, (-4,) if raw else ()): F(1)}, {(1, ()): F(1)} + for kind, symbol in program: + if kind == 'F': + y = add(y, left(symbol, x)) + elif kind == 'B': + x = add(x, left(symbol, y), -1) + elif kind == 'X': + x = left(symbol, x) + else: + need(kind == 'Y', 'Known code kind') + y = left(symbol, y) + return x, y + + +GATES = [('add', 0, 1, F(1)), ('add', 0, 2, F(1)), + ('add', 1, 0, F(-1)), ('add', 2, 0, F(-1)), + ('scale', 0, 0, F(-2)), ('add', 0, 1, F(-1)), + ('add', 0, 2, F(-1))] + + +def apply(gates, rows=None): + rows = [{i: F(1)} for i in range(3)] if rows is None else list(rows) + for kind, target, source, coefficient in gates: + if kind == 'scale': + rows[target] = {j: coefficient * c for j, c in rows[target].items()} + else: + rows[target] = add(rows[target], rows[source], coefficient) + return rows + + +def main(): + prior = HERE.parent / 'one-pair-current-codes-20261018/ONE-PAIR.md' + need(sha256(prior.read_bytes()).hexdigest() == PIN, 'Frozen predecessor scope') + expected = ({(1, ()): -1}, {(0, (3, -2, 1)): 1}) + need(replay(PROGRAM) == expected, 'Generic ordered endpoint') + rejected = [] + for i, (kind, _) in enumerate(PROGRAM): + if kind in ('X', 'Y'): + need(replay(PROGRAM[:i] + PROGRAM[i+1:]) != expected, 'Omitted code control') + rejected.append(i) + x, y = replay(PROGRAM, raw=True) + final_x = left(4, left(4, left(-4, y))) + final_y = {key: -value for key, value in x.items()} + need(final_x == {(0, (4, 3, -2, 1, -4)): 1} + and final_y == {(1, ()): 1}, 'Exact physical Q boundary') + for symbol in (-4, -3, 2, -1, 4): + final_x = left(symbol, final_x) + need(final_x == {(0, ()): 1}, 'Direct physical inverse order') + inverse = [(kind, target, source, 1/c if kind == 'scale' else -c) + for kind, target, source, c in reversed(GATES)] + identity = [{i: F(1)} for i in range(3)] + c = [{j: F(-1) for j in range(3) if j != i} for i in range(3)] + ci = [{j: F(int(i == j)) - F(1, 2) for j in range(3)} for i in range(3)] + need(apply(GATES) == c and apply(inverse) == ci, 'All scalar code columns') + need(apply(inverse, c) == apply(GATES, ci) == identity, 'Both scalar inverse orders') + receipt = { + 'status': 'PASS_ONE_PAIR_GENERAL_UNITS', + 'predecessor_proof_sha256': PIN, + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'proof_sha256': sha256((HERE / 'GENERAL-UNITS.md').read_bytes()).hexdigest(), + 'program': PROGRAM, + 'content_endpoint': ['-y', 'E2 G1^-1 E0 x'], + 'physical_raw_output': ['Q E2 G1^-1 E0 Q^-1', 'I'], + 'omitted_code_controls': rejected, + 'three_field_code': {'input_columns_checked': 3, 'inverse_orders_checked': 2, + 'unit_adds': 6, 'signed_factor_two_scales': 1, + 'real_scalar_primitives_each_direction': 52, + 'owned_or_borrowed_fields': 0}, + 'native_or_host_claimed': False, + } + (HERE / 'CHECKS.json').write_text(json.dumps(receipt, indent=2, sort_keys=True) + '\n') + print(receipt['status']) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/FREEZE.json new file mode 100644 index 0000000000..249ed79ab4 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/FREEZE.json @@ -0,0 +1,17 @@ +{ + "commands_run": [ + "python3 -I -B check_line_flags.py", + "python3 -I -B screen_warped_matching.py" + ], + "files": { + "LINE-FLAGS.json": "87df66f2d161abf6930844daa07c440ef6d40ff34043c92769615ca89079666d", + "PHYSICAL-MONOMIAL-CODES.md": "b3ff398562b87a83d9ab99adb788af259834f491157a137175be030f47ff447c", + "WARPED-MATCHING.json": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2", + "check_line_flags.py": "87cb3b2474b0108ce63c4751230b5a3e784959c8c6e0dd9154ba85d40ec33184", + "screen_warped_matching.py": "48c82b0ee39bd568d37a8eb17fa6d4b5ceccbe9ac7346e88fcda47c53dfe7555" + }, + "future_PR_standard": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "publication": "Local only. No PR, commit, push, or publication.", + "scope": "The exact local rank proof and finite canonical-prefix screen pass. The screen does not cover all stabilizer choices at nonempty warp cuts. The whole-program compiler is a conditional theorem with explicit map and owner premises.", + "status": "PASS_PHYSICAL_LINE_FLAGS" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/LINE-FLAGS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/LINE-FLAGS.json new file mode 100644 index 0000000000..a2adc16814 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/LINE-FLAGS.json @@ -0,0 +1,1600 @@ +{ + "binary_formula": { + "all_cases": 2688, + "invertible_matrices": 168, + "orthogonal_line_cases": 1152 + }, + "checker_sha256": "87cb3b2474b0108ce63c4751230b5a3e784959c8c6e0dd9154ba85d40ec33184", + "pins": { + "compiler": 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a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/PHYSICAL-MONOMIAL-CODES.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/PHYSICAL-MONOMIAL-CODES.md new file mode 100644 index 0000000000..e7c4c3c925 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/PHYSICAL-MONOMIAL-CODES.md @@ -0,0 +1,158 @@ +# Physical monomial codes and the retained line flags + +This note separates two statements. A physical monomial output code can +be carried through a complete native program by a change of coordinates. +The current independent-path transfer does not meet the required local +boundary condition. Its FULL code is monomial, but its hole code is not. + +No owner schedule or complete supplier price is claimed here. The paid +terminal for a common response is in the separate +`../common-monomial-terminal-20261018/` packet. + +## A whole-program coordinate change + +Let G_j be one operation of an admitted physical program. Include all +productive fields, arbitrary helper fields, and owned fields in its +state. Suppose a replacement word W_j has the exact physical map + + W_j = H_j G_j, + +where H_j is a known monomial operator on this complete state. It must +preserve the owned-zero subspace. Put C_0=I. Execute + + C_j W_j C_j^-1, + C_(j+1)=C_j H_j. (1) + +If the state before this operation is C_j z, its state afterward is +C_j H_j G_j z. This proves (1) by induction. For an unchanged operation, +use H_j=I. At the end apply C_final^-1. The result is the original raw +physical endpoint. No residual code reaches an unchanged outer twiddle +or product. + +The order C_j H_j is required. Replacing it by H_j C_j is incorrect in +general. Also, every later use of a renamed live field must be changed. +This includes a productive data field that later serves as a helper. +Changing only the local data names is not sufficient. + +For a structured monomial that permutes fields and cover rows and applies +one affine quadratic-phase map to each payload column, the following +conjugation rules are finite: + +- An ADD uses the renamed fields and the composed monomial read map. +- A COPY or CLEAR uses the renamed field. A monomial sends zero to zero. +- A one-field Clifford child has the same Fourier rank under left and + right monomial maps. Its address wrappers change. +- Every arbitrary helper boundary equation is conjugated with the same + complete-state code. + +These rules preserve a child profile only when the admitted array-map +grammar contains all the composed maps and when the field, cover, and +payload factorization is retained. They do not authorize an arbitrary +permutation that mixes payload columns or owned fields with live fields. +The scalar work, view descriptors, temporary stock, precision, and owner +schedule still need a finite invoice and a source certificate. + +## A sufficient reciprocal-response condition + +For logical reciprocal shears, put D(E)=diag(I,E). Then + + F_E D(E)=D(E) F_I, + B_(E^-1) D(E)=D(E) B_I. (2) + +Thus a pre-Y E code converts either call to an ideal call followed by a +Y code. In physical frames Phi_in and Phi_out, the precode and output +code are + + P=Phi_in D(E) Phi_in^-1, + H=Phi_out D(E) Phi_out^-1. (3) + +If both (3) are admitted physical monomials, equations (1) and (2) give +a complete program compiler. Logical monomiality of E alone does not +imply either condition in (3). + +In the original local frames, X enters as Qx and Y enters as y. They +exit as F x and F q y, where q=Q^-1. The Y output code has blocks + + F q_t E_ts Q_s F^-1. (4) + +The current transfer packet proves that E and F E F^-1 are monomial. +It does not prove that (4) is monomial. + +## An exact line-flag test + +Use the binary symplectic matrix of a Clifford operator. A monomial has +zero upper-right block. Its left or right multiplication preserves the +rank of that block. Let a and b be odd binary vectors, so a^T a=b^T b=1. +Set P_a=a a^T and P_b=b b^T. Let G be invertible. + +Use the common phase change that converts K_G to the address permutation +P_G, F_n to the full Walsh operator H_n, and C_a to H_a at the binary +symplectic level. If b^T G a=0, the upper-right block of + + F_n C_b^-1 K_G C_a^-1 + +is + + (I+P_b) G^-T (I+P_a). (5) + +Its rank is n-2. Indeed, I+P_a has an (n-1)-dimensional image a^perp. +G^-T a^perp contains b exactly because b^T G a=0. The last projection +therefore removes one further dimension. + +After right multiplication by F_n^-1, the upper-right block becomes +the former upper-left block: + + P_b G(I+P_a)+(I+P_b)G^-T P_a. (6) + +It has rank two. Its two nonzero summands have independent image lines, +one in span(b) and one in b^perp. Their source rows are also independent. +The general zero-rank condition for (6) is G^T b=a. + +For an empty-warp transfer, the source cut space U contains a, the target +cut space V is a subspace of b^perp, and G maps U to V. Hence b^T G a=0. +This proves the rank test for every K_G transfer with these three flag +conditions. It is not limited to one basis extension or one matching. + +## Actual packet checks + +The pinned independent-path packet has 112 matched transfers, for each +of two providers. The port permutation has 106 fixed points and three +two-cycles. Every matched source frame contains its intrinsic q_s. Every +matched target frame is orthogonal to its intrinsic q_t. + +For all 112 blocks of each provider, the exact signed Clifford table gives + + rank(F9 q_t E_ts q_s)=7, + rank(F9 q_t E_ts Q_s F9^-1)=2. + +The original identity-response forward call has diagonal block rank +eight and cross-block rank nine. The changed forward call has diagonal +block rank eight and cross-block rank seven. The source input with two +nonzero output blocks and the target output with two nonzero input blocks +identify this cross block. Therefore independent physical monomial field +permutations and address maps at the two boundaries cannot turn this +single call into the original forward call. + +The separate `screen_warped_matching.py` also permits all actual signed +prefix warp histories, using the fixed canonical intertwiner +K_V K_U^-1 at each cut. It checks 21,906 distinct cut/frame/prefix cases +per provider. The resulting 12,311 port edges contain no edge that meets +G_E^T q_t=q_s. This finite screen does not exclude other stabilizer choices +at nonempty-warp cuts. + +These statements do not rule out a changed multi-transfer response, a +multi-call compiler, a paid terminal, or a common response built on the +whole 73-axis flag. They reject a free call-by-call use of (2) for the +present local matching. + +## Verification + +Run both scripts in this folder with one process at a time. The rank +checker reads the pinned recipes, checks their signed Clifford products, +and checks the binary formula on every invertible three-bit matrix and +all odd input/output vectors. The matching screen reads the full native +event order. It does not import the producer. + +No PR, commit, push, or publication is part of this packet. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/WARPED-MATCHING.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/WARPED-MATCHING.json new file mode 100644 index 0000000000..acf94d7619 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/WARPED-MATCHING.json @@ -0,0 +1,38 @@ +{ + "checker_sha256": "48c82b0ee39bd568d37a8eb17fa6d4b5ceccbe9ac7346e88fcda47c53dfe7555", + "pins": { + "compiler": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "payload_decompressed": "8fe1147e5cb80d9f1d9ef309b0ee6f42b1a64cc5ebabd19b818623c246c9fd64" + }, + "providers": { + "base": { + "all_equal_rank_edges": 12311, + "empty_history_flag_checks": { + "source_tests": 346806, + "target_tests": 7717366 + }, + "hole_compatible_edge_records": [], + "hole_compatible_edges": 0, + "hole_compatible_matching_size": 0, + "matching": [], + "stats": { + "cut_frame_prefix_cases": 21906 + } + }, + "extra": { + "all_equal_rank_edges": 12311, + "empty_history_flag_checks": { + "source_tests": 346806, + "target_tests": 7717366 + }, + "hole_compatible_edge_records": [], + "hole_compatible_edges": 0, + "hole_compatible_matching_size": 0, + "matching": [], + "stats": { + "cut_frame_prefix_cases": 21906 + } + } + }, + "scope": "Canonical equal-rank K_v K_u^-1 transfers with all actual signed prefix warp histories. A binary boundary screen, not a new native word." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py new file mode 100644 index 0000000000..e441e0a2b4 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py @@ -0,0 +1,118 @@ +#!/usr/bin/env python3 +"""Check the physical line-flag ranks from the exact source recipes.""" + +from collections import Counter +from hashlib import sha256 +import gzip +import importlib.util +import itertools +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PAYLOAD = LANES / 'history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON-PROGRAMS.json.gz' +COMPILER = LANES / 'new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py' +PINS = { + 'payload_decompressed': '8fe1147e5cb80d9f1d9ef309b0ee6f42b1a64cc5ebabd19b818623c246c9fd64', + 'compiler': '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', +} + + +def need(value, message): + if not value: + raise AssertionError(message) + + +def mm(a, b, n, ce): + bt = ce.transpose(b, n) + return tuple(sum(ce.parity(x & y) << j for j, y in enumerate(bt)) for x in a) + + +def add(a, b): + return tuple(x ^ y for x, y in zip(a, b)) + + +def projection(q, n): + return tuple(q if q >> i & 1 else 0 for i in range(n)) + + +def recipe_op(record, ce): + return (ce.diag(9, record['quadratic_rows'], record['linear_Z4']) + .then(ce.perm(9, record['matrix_rows'])) + .then(ce.xgate(9, record['offset'])) + .then(ce.Op(9, ce.identity(9), [('phase', record['phase'])]))) + + +def check_binary_formula(ce): + n, count, orthogonal_count = 3, 0, 0 + identity = tuple(1 << i for i in range(n)) + odd = [q for q in range(1 << n) if ce.parity(q)] + for g in itertools.product(range(1, 1 << n), repeat=n): + if ce.rank(g) != n: + continue + git = ce.transpose(ce.inv(g, n), n) + for a, b in itertools.product(odd, repeat=2): + pa, pb = projection(a, n), projection(b, n) + ua, ub = add(identity, pa), add(identity, pb) + aa = add(mm(mm(pb, g, n, ce), ua, n, ce), mm(mm(ub, git, n, ce), pa, n, ce)) + bb = add(mm(mm(pb, g, n, ce), pa, n, ce), mm(mm(ub, git, n, ce), ua, n, ce)) + need((ce.rank(aa) == 0) == (ce.mv(ce.transpose(g, n), b) == a), 'Exact zero-rank condition') + if ce.parity(b & ce.mv(g, a)) == 0: + need(ce.rank(bb) == n - 2 and ce.rank(aa) == 2, 'Line-flag rank formula') + orthogonal_count += 1 + count += 1 + return {'invertible_matrices': 168, 'all_cases': count, 'orthogonal_line_cases': orthogonal_count} + + +def check_provider(provider, ce): + f = ce.fourier(9) + ports = provider['canonical']['ports'] + ranks = Counter() + witnesses = [] + for edge in provider['transfers']: + s, t = edge['source'], edge['target'] + a, b = ports[s], ports[t] + e = recipe_op(edge['response']['recipe'], ce) + ei = recipe_op(edge['inverse_response']['recipe'], ce) + need(e.then(ei).tab == ce.identity(9), 'Inverse signed table') + need(e.then(ei).zero_state() == ce.ident(9).zero_state(), 'Inverse global phase') + g = tuple(edge['response']['recipe']['matrix_rows']) + need(ce.parity(b & ce.mv(g, a)) == 0, 'Actual source-to-hole line condition') + u, v = edge['source_frame_basis'], edge['target_frame_basis'] + need(ce.rank(u + [a]) == len(u), 'Source line in source frame') + need(all(ce.parity(x & b) == 0 for x in v), 'Target frame in target hole') + cross = ce.cgate(9, a, -1).then(e).then(ce.cgate(9, b, -1)).then(f) + hole = f.adjoint().then(ce.cgate(9, a)).then(e).then(ce.cgate(9, b, -1)).then(f) + full = f.adjoint().then(e).then(f) + rank = lambda op: ce.rank([x for x, z, phase in op.tab[9:]]) + observed = (rank(cross), rank(hole), rank(full)) + need(observed == (7, 2, 0), 'Actual three physical ranks') + need(ce.mv(ce.transpose(g, 9), b) != a, 'Hole condition is rejected') + ranks[str(observed)] += 1 + witnesses.append({'source': s, 'target': t, 'q_source': a, 'q_target': b, + 'G_transpose_q_target': ce.mv(ce.transpose(g, 9), b)}) + return {'checked_edges': len(witnesses), 'rank_histogram': dict(ranks), 'witnesses': witnesses} + + +def main(): + raw = gzip.decompress(PAYLOAD.read_bytes()) + need(sha256(raw).hexdigest() == PINS['payload_decompressed'], 'Payload pin') + need(sha256(COMPILER.read_bytes()).hexdigest() == PINS['compiler'], 'Compiler pin') + spec = importlib.util.spec_from_file_location('line_flag_clifford', COMPILER) + ce = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = ce + spec.loader.exec_module(ce) + data = json.loads(raw) + result = {'status': 'PASS_PHYSICAL_LINE_FLAGS', 'pins': PINS, + 'binary_formula': check_binary_formula(ce), + 'providers': {name: check_provider(p, ce) for name, p in data['providers'].items()}, + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'proof_sha256': sha256((HERE / 'PHYSICAL-MONOMIAL-CODES.md').read_bytes()).hexdigest()} + (HERE / 'LINE-FLAGS.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py new file mode 100644 index 0000000000..fd22561b08 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py @@ -0,0 +1,176 @@ +#!/usr/bin/env python3 +"""Test the physical hole condition at the retained transfer cuts.""" + +from collections import Counter, defaultdict, deque +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PAYLOAD = LANES / 'history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON-PROGRAMS.json.gz' +COMPILER = LANES / 'new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py' +PINS = { + 'payload_decompressed': '8fe1147e5cb80d9f1d9ef309b0ee6f42b1a64cc5ebabd19b818623c246c9fd64', + 'compiler': '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', +} + + +def need(value, message): + if not value: + raise AssertionError(message) + + +def matmul(a, b, ce): + bt = ce.transpose(b, 9) + return tuple(sum(ce.parity(row & col) << j for j, col in enumerate(bt)) for row in a) + + +def maximum_matching(edges): + adjacency = defaultdict(list) + for s, t in sorted(edges): + adjacency[s].append(t) + left, right = {}, {} + for start in range(112): + queue, seen, pred, end = deque([start]), {start}, {}, None + while queue and end is None: + s = queue.popleft() + for t in adjacency[s]: + if t in pred: + continue + pred[t] = s + if t not in right: + end = t + break + if right[t] not in seen: + seen.add(right[t]) + queue.append(right[t]) + if end is None: + continue + while True: + s, t = pred[end], end + old = left.get(s) + left[s], right[t] = t, s + if old is None: + break + end = old + return left + + +def check_provider(provider, ce): + canonical = provider['canonical'] + ports = canonical['ports'] + need(len(ports) == 112, 'Port count') + frames = list(canonical['start']) + history = [[] for _ in frames] + identity = tuple(1 << j for j in range(9)) + warp_rows = {row['op']: ce.transpose(tuple(row['G_columns']), 9) for row in canonical['warps']} + warp_rows.update({-symbol: ce.inv(g, 9) for symbol, g in list(warp_rows.items())}) + prefixes = [identity for _ in frames] + factors = [ce.transpose(ce.basis_extend(basis, 9), 9) for basis in canonical['frames']] + factor_inverse = [ce.inv(g, 9) for g in factors] + active = False + graph, boundary_graph, pairs_seen = {}, {}, set() + flag_checks = Counter() + stats = Counter() + cache = {} + events = provider['programs']['forward'] + for index, event in enumerate(events): + tag = event[0] + # Remove only the emitted transfer. The retained native path stays fixed. + if tag == 'monomial_view' or (tag == 'scalar' and event[1][0] == 'add'): + continue + if event[:2] == ['phase', 'A']: + active = True + elif event[:2] == ['phase', 'exit_adapters']: + active = False + if tag == 'climb': + target, old, new = event[2:5] + need(frames[target] == old, 'Climb frame') + frames[target] = new + elif tag == 'warp': + token, symbol, old, new = event[1:5] + need(token[0] == 'L', 'Live warp') + target = token[1] + need(frames[target] == old, 'Warp frame') + frames[target] = new + prefixes[target] = matmul(warp_rows[symbol], prefixes[target], ce) + if history[target] and history[target][-1] == -symbol: + history[target].pop() + else: + history[target].append(symbol) + if not active or tag not in ('phase', 'climb', 'warp'): + continue + targets = defaultdict(list) + for t in range(112): + target = 112 + t + rank = len(canonical['frames'][frames[target]]) + if 1 <= rank <= 8: + targets[rank].append(t) + for s in range(112): + u = frames[s] + rank = len(canonical['frames'][u]) + if not 1 <= rank <= 8: + continue + if not history[s]: + flag_checks['source_tests'] += 1 + need(ce.rank(canonical['frames'][u] + [ports[s]]) == rank, 'Source line in frame') + for t in targets[rank]: + target, v = 112 + t, frames[112 + t] + if not history[target]: + flag_checks['target_tests'] += 1 + need(all(ce.parity(w & ports[t]) == 0 for w in canonical['frames'][v]), 'Target frame in hole') + key = (s, t, u, v, prefixes[s], prefixes[target]) + if key in pairs_seen: + continue + pairs_seen.add(key) + stats['cut_frame_prefix_cases'] += 1 + record = {'source': s, 'target': t, 'cut': index, 'rank': rank, + 'source_frame': u, 'target_frame': v, + 'source_warps': list(history[s]), 'target_warps': list(history[target])} + graph.setdefault((s, t), record) + # G_E = W_t^-1 G_v G_u^-1 W_s, in mathematical order. + pkey = (u, v, prefixes[s], prefixes[target]) + if pkey not in cache: + g = matmul(factor_inverse[u], prefixes[s], ce) + g = matmul(factors[v], g, ce) + g = matmul(ce.inv(prefixes[target], 9), g, ce) + cache[pkey] = ce.transpose(g, 9) + need(ce.parity(ports[s] & ports[s]) == 1 and ce.parity(ports[t] & ports[t]) == 1, 'Odd lines') + if ce.mv(cache[pkey], ports[t]) == ports[s]: + boundary_graph.setdefault((s, t), record) + need(frames == canonical['final'], 'Final frames') + need(all(not w for w in history), 'All logical warp histories close') + need(all(g == identity for g in prefixes), 'All binary prefix maps close') + matching = maximum_matching(boundary_graph) + return { + 'all_equal_rank_edges': len(graph), 'hole_compatible_edges': len(boundary_graph), + 'hole_compatible_matching_size': len(matching), 'stats': dict(stats), + 'empty_history_flag_checks': dict(flag_checks), + 'matching': [boundary_graph[s, t] for s, t in sorted(matching.items())], + 'hole_compatible_edge_records': list(boundary_graph.values()), + } + + +def main(): + raw = gzip.decompress(PAYLOAD.read_bytes()) + need(sha256(raw).hexdigest() == PINS['payload_decompressed'], 'Payload pin') + need(sha256(COMPILER.read_bytes()).hexdigest() == PINS['compiler'], 'Compiler pin') + spec = importlib.util.spec_from_file_location('monomial_compiler_exact', COMPILER) + ce = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = ce + spec.loader.exec_module(ce) + data = json.loads(raw) + result = {'pins': PINS, 'providers': {name: check_provider(p, ce) for name, p in data['providers'].items()}} + result['checker_sha256'] = sha256(Path(__file__).read_bytes()).hexdigest() + result['scope'] = 'Canonical equal-rank K_v K_u^-1 transfers with all actual signed prefix warp histories. A binary boundary screen, not a new native word.' + (HERE / 'WARPED-MATCHING.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + for name, r in result['providers'].items(): + print(name, r['all_equal_rank_edges'], r['hole_compatible_edges'], r['hole_compatible_matching_size'], r['stats']) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md new file mode 100644 index 0000000000..19b10c0cd1 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md @@ -0,0 +1,265 @@ +# A controller for reciprocal native responses + +This note gives a complete ordered content controller for reciprocal +responses. It includes the original phase terminal. It also lists each +additional code operation and its required cut. Thus a native construction +can test a finite set of access conditions. + +The current interior packet proves a forward response E and a backward +response E^T. It does not prove a backward response E^-1. This note does +not identify these two matrices. Its new construction has an explicit +reciprocal-response premise. + +## 1. Required local contract + +Let X and Y be arbitrary productive banks. Each bank has 112 fields with +the complete cover and payload coordinates. At stage s, let E_s be an +invertible operator on this whole bank space. In the original logical +frames, assume that the following native words are available: + + F_s(x,y) = (x, y + E_s x), + B_s(x,y) = (x - E_s^-1 y, y). + +Only F at even stages and B at odd stages is needed. Each native word must +restore every arbitrary helper and every private field according to its +own contract. Both words must have the original X-line/Y-hole input and +output frames. An inverse as an abstract matrix does not meet this premise. + +The E_s in this note is the routed operator on the complete bank. Equality +of two local 112-by-112 coefficient matrices is not sufficient to give +E_s=E_t. The cover routes are part of this equality. + +Code operations such as X<-E_t^-1 E_s X also need an implementation. +Sections 3 and 5 state their locations. No new child count is assigned to +an operation merely because the matrix is invertible. + +## 2. The retained scalar controller + +Use m pairs and 2m+1 local calls. First apply F0 to pair zero. For each +i=0,...,m-1, apply B_(2i+1) and then F_(2i+2) to pair i. If a next pair +exists, put a plus bridge before this F and a minus bridge after it: + + plus: X_i += X_(i+1), Y_(i+1) -= Y_i, + minus: X_i -= X_(i+1), Y_(i+1) += Y_i. + +The next X bank reaches FULL at the preceding odd stage before the plus +bridge. It reaches the next even level before the minus bridge. Keep the +old idle native jobs at those sites. + +After the local calls, keep the old idle tails. In descending i order, +apply the final full bridges + + X_i += X_(i-1), Y_(i-1) -= Y_i. + +For unit local responses, this word gives (-y_i,x_i) on every pair. +One proof uses the values before the final bridges. Put w_-1=0. The +completed X values obey w_i=-y_i-w_(i-1). The retired Y values are +x_i+x_(i+1), with x_m=0. The descending bridges give -y_i and x_i. + +For m=4, the checker reads the pinned source recipe directly. It verifies +all 19 content events and all ten idle sites. It does not replace the +source recipe with an unrelated network. + +## 3. A complete code placement for arbitrary E_s + +Use the local responses from section 1. Insert the following operations +in the listed order. Every multiplication below acts on the left. + +1. Before F0, apply Y0<-E0 Y0. After F0, apply X0<-E1^-1 X0. +2. Immediately before B1, apply Y0<-E0^-1 Y0. +3. After each B_s, where s=2i+1, apply + X_i<-E_(s+1)^-1 E_s X_i. +4. At the first FULL cut of the next idle X bank, before the plus bridge, + apply X_(i+1)<-E_(s+1)^-1 X_(i+1). +5. After the minus bridge at stage t=2i+2, apply + X_(i+1)<-E_(t+1)^-1 E_t X_(i+1). +6. After the old idle tails and before the final descending bridges, + apply X_i<-E_(2i+2) X_i for every pair. + +Steps 4 and 5 are absent for the last pair. There are 4m+1 code factors. +The exact four-pair table is in CHECKS.json. The table separates a Y entry +stage from a completed X level. + +### Ordered proof + +Compare the changed state with the unit-response network in section 2. +After step 1, X0 carries code E1^-1 and Y0 carries code E0. Step 2 removes +the Y code. Thus B1 subtracts the correct ideal Y from the coded X. + +Before B_s, the active X carries E_s^-1 and the active Y is plain. The +backward call gives E_s^-1(x-y), with Y unchanged. Step 3 changes this X +code to E_(s+1)^-1. Step 4 gives the same code to the next X bank. Both +parts of the plus bridge therefore act on the correct ideal contents. + +At F_(s+1), its response cancels the X code. Its Y output is the ideal +sum, with no residual code. The X code remains E_(s+1)^-1. Both parts of +the minus bridge are valid. Step 5 changes the next X code to the inverse +required by its next backward call. This proves the invariant by induction. + +Each retired X bank has code E_(2i+2)^-1. Step 6 removes all these codes +before the final bridges. Those bridges now act on plain ideal contents. +The complete preterminal endpoint is exactly + + X_i=-y_i, Y_i=x_i. (1) + +This proof treats all X and Y inputs as independent. No input, query, or +helper baseline is set to zero. The native helper contracts remain a +separate premise; the code factors act only on productive banks. + +## 4. Common routed response: ten code factors for four pairs + +If every global E_s is one common operator E, the two transition factors +in steps 3 and 5 are identities. The construction needs only 2m+2 code +factors. For four pairs these are: + +| Code | Cut | Number | +| --- | --- | ---: | +| E on Y0 | Original I input before F0 | 1 | +| E^-1 on X0 | FULL after F0 | 1 | +| E^-1 on Y0 | Current I entrance before B1 | 1 | +| E^-1 on each next X | First FULL cuts, levels 1,3,5 | 3 | +| E on every X | Final FULL, before the three tail bridges | 4 | + +After B1, all X banks that take part in a bridge carry E^-1 and all Y +banks are plain. This is why every original bridge can remain unchanged. +The final X decoding is at FULL. There is no Y-hole terminal decoding. + +If E and E^-1 have admitted scalar/cover graph circuits at these cuts, +these factors need no additional native child. Their scalar work, views, +temporary fields, and precision are still part of the supplier bill. +The note does not supply such a circuit or bill for the actual E_s. + +There is also a shorter one-pair identity. In chronological order, use + + F_E; + B_(E^-1), then X<-E^-1 X; + Y<-E^-1 Y, F_E, then X<-E^2 X. + +Its output is (-y,x). The three code factors are at a completed X cut, +a current Y input, and a completed X cut. This is an ordered identity +for one common routed response. It does not authorize repeated native +calls on one stage, nor does it prove that repeated calls advance new axes. + +## 5. The exact stage-access obligation + +The general construction places most unresolved work on completed X. +Its first tests in the actual four-pair word are: + +| Code | Required cut | Issue not removed by invertibility | +| --- | --- | --- | +| E1^-1 | X0 FULL at level0 | A future-stage code | +| E0^-1 | Y0 current entrance at stage1 | A past-stage Y code | +| E2^-1 E1 | X0 FULL after B1, level1 | A future-stage transition | +| E2^-1 | X1 first FULL, level1 | A future-stage preparation | +| E3^-1 E2 | X1 FULL after the minus bridge, level2 | A future-stage transition | +| E4^-1 E3; E4^-1 | Active and idle X at level3 | The next transition and preparation | +| E5^-1 E4 | Next X at level4 | A future-stage transition | +| E6^-1 E5; E6^-1 | Active and idle X at level5 | The next transition and preparation | +| E7^-1 E6 | Next X at level6 | A future-stage transition | +| E8^-1 E7 | Active X at level7 | The last transition | +| E2,E4,E6,E8 | Final FULL at level8 | Past/current code circuits | + +This is a finite construction hypothesis. An implementation can use a +different circuit for a product; it need not execute its factors +separately. The table does not claim that these products are free. + +The three-call calculation also gives an exact test for other wrappers. +Write the forward wrappers as pre-Y b0/post-X a0 and pre-Y b2/post-X a2. +Write the backward wrappers as pre-Y b1/post-X a1. For arbitrary +invertible a0,b0, closure to (-y,x) is equivalent to + + b1 = E1 a0 E0^-1, + a1 = E2^-1 a0^-1, + b2 = a0^-1 E1^-1, + a2 = b0^-1 E0 E2. (2) + +These equations follow by setting all four ordered endpoint blocks to +the target blocks. They show where a different boundary choice moves a +code. A future E2 in a1 cannot be dropped because the desired endpoint +has a dyadic inverse. + +## 6. The physical terminal + +Let Q be the diagonal intrinsic port-line operator and q=Q^-1. The raw +original input is W(x,y), with W=diag(Q,I). Before the old terminal, the +physical frames are F V, with V=diag(I,q). Suppress the common F in the +following equation. The retained terminal is + + A = [[0,Q^2],[-I,0]]. + +Let J0=[[0,-I],[I,0]]. Then the exact physical equation is + + A V J0 = W. (3) + +Consequently (1), together with the stated native phase contract, gives +the original FULL transform on the raw original inputs. No E crosses Q +in this proof. No encoded representation passes into an unchanged outer +twiddle or pointwise product. + +In contrast, substitute a common E into the raw controller and omit the +codes in section 4. The logical endpoint is + + [[0,-E^-1],[E,0]]. + +After the old terminal, its code relative to the raw original inputs is + + diag(Q E Q^-1, E^-1). (4) + +The first code is not E. It cannot be decoded by an untyped FULL scalar +E^-1 operation. The actual interior E has 564 nonzero entries, all off +the diagonal. All 112 port directions are distinct. For each nonzero +entry e_pr, a one-column Fourier character separates Q_p from Q_r. +Thus every nonzero entry supplies a nonzero commutator term with Q. +The checker verifies these 564 actual-source witnesses. It does not use +the older H-response obstruction as a substitute. + +Leaving (4) as an outer representation needs a new contract. With an +unchanged twiddle T, the input and output codes must satisfy the exact +intertwining equation C_out T=T C_in. A common code must commute with T. +The pointwise product also needs its own encoded multiplication identity. +A matrix inverse alone proves neither condition. A changed terminal or +encoded outer operation can be useful, but its execution and price must +be supplied separately. + +## 7. Complementary centre responses + +The root's separate construction uses RK=14I and a centre projection P: + + E = I-K[I-(12/13)P]R, + E^-1 = I-K[I-(12/13)(I-P)]R. + +This is a reciprocal pair over a ring that contains 1/13. Its native +emission and centre-child bill belong to the root's separate packet. +The controller proof above applies if its stated global and cut +conditions hold. It does not require a dyadic-only coefficient ring. + +For every such P, both centre eigenvalues differ from one. Hence + + im(I-E_s) = im(K_s). + +A change of P cannot make two global E_s equal when their routed K_s +images differ. It changes the centre splitting, not the response image. +This observation does not rule out a paid transition or a changed native +response. It only prevents a false use of the common-E corollary. + +## 8. Verification and remaining work + +Run one process from the campaign directory: + + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -I -B lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py + +Expected output: + + PASS_RECIPROCAL_RESPONSE_CONTROLLER + +The checker uses free ordered invertible symbols. It checks every input +block for one through eight pairs, the common and distinct-stage cases, +the general three-call identity, the exact retained recipe, equation (3), +and equation (4). Mutation controls remove required codes and reverse a +transition order. It reads the actual interior matrix for the Q tests. +It does not import or run another lane's proof engine. + +The induction proves the all-m statement. The finite checks do not replace +that proof. The complete supplier still needs reciprocal native words, +the stated cut circuits, owner admission, all scalar/native/precision +costs, and recursive hosting. No complete kappa improvement is claimed. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/CHECKS.json new file mode 100644 index 0000000000..4e7b5445b2 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/CHECKS.json @@ -0,0 +1,95 @@ +{ + "checker_sha256": "3360e647d62bfaa2392a32e8f10b5f7c008584b382bf89c00c5195bfa314bbdf", + "payload_decompressed_sha256": "2ebc31760a95b1dd15576928d60cbdfbf6a4b5e6c1146c31a805b718feb5b69d", + "providers": { + "base": { + "all_net_helper_warp_words_empty": true, + "arbitrary_helper_columns": 408, + "events": { + "adapter": 530, + "climb": 2326, + "phase": 11, + "residual_adapter": 390, + "scalar": 16, + "warp": 184, + "zero_buffer": 182 + }, + "helper_data_scalar_couplings": 0, + "monomial_map_bound_including_child_sides": 5756, + "native_children": 2326, + "native_profile": { + "1": 1609, + "2": 512, + "3": 172, + "4": 33 + }, + "native_rank_mass": 3281, + "negative_controls": [ + "missing helper warp", + "data read", + "missing residual wrapper" + ], + "new_native_phase_recipes": 0, + "owned_C_roles_reserved": 8, + "private_zero_allocations": 91, + "private_zero_peak": 91, + "productive_helper_widths": { + "4": 26, + "5": 2, + "6": 18, + "7": 50, + "8": 99, + "9": 213 + }, + "same_signed_native_subsequence_as_both_source_words": true, + "top_level_real_scalar_bound": 32, + "untouched_data_columns": 224 + }, + "extra": { + "all_net_helper_warp_words_empty": true, + "arbitrary_helper_columns": 408, + "events": { + "adapter": 530, + "climb": 2326, + "phase": 11, + "residual_adapter": 390, + "scalar": 16, + "warp": 184, + "zero_buffer": 182 + }, + "helper_data_scalar_couplings": 0, + "monomial_map_bound_including_child_sides": 5756, + "native_children": 2326, + "native_profile": { + "1": 1609, + "2": 512, + "3": 172, + "4": 33 + }, + "native_rank_mass": 3281, + "negative_controls": [ + "missing helper warp", + "data read", + "missing residual wrapper" + ], + "new_native_phase_recipes": 0, + "owned_C_roles_reserved": 8, + "private_zero_allocations": 91, + "private_zero_peak": 91, + "productive_helper_widths": { + "4": 26, + "5": 2, + "6": 18, + "7": 50, + "8": 99, + "9": 213 + }, + "same_signed_native_subsequence_as_both_source_words": true, + "top_level_real_scalar_bound": 32, + "untouched_data_columns": 224 + } + }, + "scope": "Exact local helper completion. The supplied native recipes are pinned predecessor recipes. No new data response, global owner schedule, or complete kappa calculation is claimed.", + "source_payload_decompressed_sha256": "8fe1147e5cb80d9f1d9ef309b0ee6f42b1a64cc5ebabd19b818623c246c9fd64", + "status": "PASS_RETAINED_HELPER_COMPLETION" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/FREEZE.json new file mode 100644 index 0000000000..eaff364c21 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "CHECKS.json": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1", + "HELPER-COMPLETION-PROGRAMS.json.gz": "b9d025f393b0ec34a3872fe822f57bba4bdd4600b7359ea46422a7028618f7bc", + "HELPER-COMPLETION.md": "b02bf331d6ebbcf970681f2955b27dd83004008dcd18aaf378a05cb12d3f34cb", + "REPRODUCTION.json": "b109437430277921717e8d7a47f8ab72429053a63eb8e8e2aec6afe47a718990", + "check_and_emit.py": "3360e647d62bfaa2392a32e8f10b5f7c008584b382bf89c00c5195bfa314bbdf" + }, + "payload_decompressed_sha256": "2ebc31760a95b1dd15576928d60cbdfbf6a4b5e6c1146c31a805b718feb5b69d", + "status": "FROZEN_RETAINED_HELPER_COMPLETION" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/HELPER-COMPLETION-PROGRAMS.json.gz b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/HELPER-COMPLETION-PROGRAMS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..72a57ec0a3e745e3c5740a91b7afac8887193dd2 GIT binary patch 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O*Z&U(FJjW_IwJtXbFIJt literal 0 HcmV?d00001 diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON.json new file mode 100644 index 0000000000..44ec024d09 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON.json @@ -0,0 +1,115 @@ +{ + "payload_decompressed_sha256": "8fe1147e5cb80d9f1d9ef309b0ee6f42b1a64cc5ebabd19b818623c246c9fd64", + "producer_sha256": "47b7e8e9e286acb2e21718b5266c7d33fcb611026877a899a2649f247f6fa22a", + "providers": { + "base": { + "additional_native_children": 0, + "additional_private_arrays": 0, + "all_net_warp_words_empty": true, + "all_selected_prefix_warp_words_empty": true, + "arbitrary_helper_roles": 408, + "arbitrary_symbolic_columns_per_word": 640, + "chosen_diagonal_ports": 106, + "chosen_matching_size": 112, + "complete_words": 2, + "controls": [ + "Wrong global phase", + "Wrong view frame", + "Wrong backward ADD sign" + ], + "direct_equal_frame_edges": 312, + "direct_maximum_matching": 68, + "equal_rank_empty_warp_edges": 12311, + "exact_intertwining_checks": 112, + "explicit_monomial_column_checks": 114688, + "full_conjugated_response_rank_zero": true, + "live_roles": 632, + "native_child_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_children": 3507, + "native_rank_mass": 5073, + "new_complex_monomial_array_maps": 224, + "new_unit_complex_ADDs": 112, + "owned_C_roles": 8, + "private_zero_roles": 91, + "retained_complex_CLEARs": 16, + "retained_endpoint_adapters": 978, + "retained_private_allocations": 91, + "retained_residual_adapters": 390, + "retained_warp_events": 240, + "selected_ranks": { + "1": 12, + "2": 48, + "4": 3, + "5": 2, + "6": 1, + "7": 11, + "8": 35 + }, + "top_level_real_scalar_bound": 928 + }, + "extra": { + "additional_native_children": 0, + "additional_private_arrays": 0, + "all_net_warp_words_empty": true, + "all_selected_prefix_warp_words_empty": true, + "arbitrary_helper_roles": 408, + "arbitrary_symbolic_columns_per_word": 640, + "chosen_diagonal_ports": 106, + "chosen_matching_size": 112, + "complete_words": 2, + "controls": [ + "Wrong global phase", + "Wrong view frame", + "Wrong backward ADD sign" + ], + "direct_equal_frame_edges": 312, + "direct_maximum_matching": 68, + "equal_rank_empty_warp_edges": 12311, + "exact_intertwining_checks": 112, + "explicit_monomial_column_checks": 114688, + "full_conjugated_response_rank_zero": true, + "live_roles": 632, + "native_child_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_children": 3507, + "native_rank_mass": 5073, + "new_complex_monomial_array_maps": 224, + "new_unit_complex_ADDs": 112, + "owned_C_roles": 8, + "private_zero_roles": 91, + "retained_complex_CLEARs": 16, + "retained_endpoint_adapters": 978, + "retained_private_allocations": 91, + "retained_residual_adapters": 390, + "retained_warp_events": 240, + "selected_ranks": { + "1": 12, + "2": 48, + "4": 3, + "5": 2, + "6": 1, + "7": 11, + "8": 35 + }, + "top_level_real_scalar_bound": 928 + } + }, + "scope": "Two local shear words with a unitary monomial block response. No global controller, owner reassignment, precision invoice, or complete kappa claim.", + "source_pins": { + "compiler": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "core_decompressed": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "native_freeze": "928c29f5949cddafa3510fe0f95c8b400022ee37410d512c2dcef207bfda2f27" + }, + "status": "PASS_INDEPENDENT_NATIVE_MONOMIAL_SHEARS" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON.md new file mode 100644 index 0000000000..bb8d54730f --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/INDEPENDENT-SKELETON.md @@ -0,0 +1,195 @@ +# Two monomial shears on the independent native paths + +The construction removes all scalar mixing from the two current native +provider words. It retains every native child, physical warp, endpoint +adapter, residual adapter, private allocation, and owned CLEAR. It then +adds 112 transfers. The transfers give the local maps + + F_E: (x, y) -> (x, y + E x), + B_E: (x, y) -> (x - E* y, y). + +Here E is a permutation of the 112 port fields with one unitary monomial +address operator in each nonzero block. Thus E* = E^-1. The 408 arbitrary +helper roles retain their original native endpoint operators. The words +use the original 632 live roles, eight owned C roles, and 91 private zero +roles. They add no native child and no private role. + +The local result does not establish a global controller, a change of +productive owners, a finite precision invoice, or a complete kappa +improvement. In particular, a monomial logical response does not by itself +give a free code change at every physical endpoint. + +## Pinned inputs and physical convention + +`INDEPENDENT-SKELETON.json` pins the current centre-deleted core and the +exact Clifford compiler. The full programs and recipes are in +`INDEPENDENT-SKELETON-PROGRAMS.json.gz`. The two providers are checked +separately. + +Both new words use the **forward signed K_G physical warp recipes**. +The new backward word does not use the old literal conjugate-K backward +lowering. This is a deliberate choice of a new physical word. All its +retained native operators have accepted forward recipes. + +The accepted native recipe packet is +`../../new-native-recipes-20261017/FREEZE.json`. Its generation receipts +bind the actual frames, child edges, endpoint adapters, physical warps, +and helper residual wrappers. This construction compares those fields +with the current core and checks every recipe-file pin. It does not +regenerate the old child recipes. + +All original `scalar` events are removed except the 16 owned C0 CLEARs. +Every other event is retained in its original order. After this deletion, +the forward and backward event streams are byte-equal. Each of the 632 +live fields has an empty reduced signed warp word at the end. The 91 +private zero fields receive no scalar input and remain zero. + +The transfer cuts lie after phase A and before the first exit adapter. +The fields at these cuts have their literal canonical frames. No +intrinsic endpoint frame is treated as a canonical frame without its +adapter. + +## Actual equal-rank frame maps + +Let U and V be two proper canonical frame subspaces of the same rank r, +where 1 <= r <= 8. The pinned compiler defines + + T_U = K_U F_r K_U^-1, + T_V = K_V F_r K_V^-1. + +The basis extension, address permutation, and quadratic phase of K_U and +K_V are the ones in the actual `canonical_frame` function. They are not +chosen from the ranks alone. Set + + P = K_V K_U^-1. + +Then + + P T_U = T_V P. + +P and P^-1 are monomial address operators. The producer checks both +factorizations and this ordered identity from the full signed Pauli +table and the exact Gaussian image of the zero basis vector. The two +checks determine the global phase. It also checks all 512 columns of +each emitted monomial recipe against the literal permutation and phase +circuit. A changed global phase is rejected. + +For each selected P, the producer also checks that F_9 P F_9^-1 is +monomial. That is a separate endpoint fact. It does not establish a free +conjugate through the 112 individual output holes. + +## Matching and chronology + +The direct equal-frame graph has 312 edges and maximum matching size 68. +The producer saves a matching and a vertex cover of the same size. This +is only a statement about direct single transfers in the retained frame +history. + +The equal-rank graph with empty source and target logical warp histories +has 12,311 edges. It contains a complete matching. The saved matching +uses 106 diagonal port pairs and six other pairs. It is not claimed to +maximize the number of diagonal pairs. + +Each matched edge records the source port, target port, original event +cut, two actual frame bases, both empty warp histories, and both exact +monomial recipes. These records make the event placement checkable. + +At a forward edge from X_s in T_U to Y_t in T_V, execute + + X_s <- P X_s, + Y_t <- Y_t + X_s, + X_s <- P^-1 X_s. + +The first operation changes the physical source frame from T_U to T_V +and changes its logical value by P. The ADD therefore has equal physical +frames. The last operation restores the source exactly. The matching +uses each source and each target once. Since both logical prefix warp +words at the cut are empty, this edge gives E_ts = P. + +At the same cut in the new backward word, execute + + Y_t <- P^-1 Y_t, + X_s <- X_s - Y_t, + Y_t <- P Y_t. + +The ADD now has frame T_U. It gives the block -P^-1 in the reciprocal +position. The full matching therefore gives -E^-1. The entire native +chronology is unchanged; the backward construction does not reverse +the child schedule. + +## Arbitrary helper states and complete endpoints + +No new scalar event reads or writes a helper. With all original scalar +mixing removed, each helper follows its own native path. In canonical +coordinates its total logical warp is the identity. If its entrance and +exit frames are T_i and T_f, its physical path is therefore + + T_f T_i^-1. + +The retained residual wrappers give the same productive child operator +as in the accepted input. A proper helper exit is not replaced by FULL, +and the proof does not call this physical path the identity when the two +frames differ. + +The logical replay starts with 640 independent input symbols: all 632 +live fields and all eight owned C fields. In each of the four complete +words it checks every output coefficient and every frame. All 408 +arbitrary helper inputs retain their required logical values. C0 is +cleared, C1 through C7 are unchanged, and every private zero field is +zero when released. Thus the word is valid on the usual owned-zero +input domain, and the replay also checks the effect of arbitrary owned +input values. + +With the retained intrinsic endpoint adapters, the physical data +contract is + + input: X_p = C_p x_p, Y_p = y_p; + F_E: X_p = F_9 x_p, Y_p = F_9 C_p^-1 (y + E x)_p; + B_E: X_p = F_9 (x - E^-1 y)_p, Y_p = F_9 C_p^-1 y_p. + +The intrinsic C_p operators and their ordering are unchanged. The +construction does not identify these equations with a conventional +identity shear without a separately checked code or controller. + +## Exact local invoice + +Each provider and each direction has the following retained child +profile: + +| Child rank | Count | +| --- | ---: | +| 1 | 2433 | +| 2 | 724 | +| 3 | 228 | +| 4 | 102 | +| 5 | 20 | + +There are 3,507 children and rank mass 5,073. All 240 physical warp events, +978 endpoint adapter events, 390 residual adapter events, and 91 private +allocations remain. No new native child is added. + +The new transfer operations use 224 complex monomial array maps and 112 +unit complex ADDs. The retained 16 complex CLEARs remain. With the +inherited scalar compiler, these top-level scalar events cost + + 112 * 8 + 16 * 2 = 928 real scalar primitives. + +This number excludes the separately counted monomial maps and the +unchanged native lowering cost. It is not a complete finite invoice. + +## Verification and scope + +Run one process: + + python3 -I -B work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/emit_independent_skeleton.py + +The producer checks both complete words for both providers, all selected +native phases, all endpoint maps, all helper and private states, the +native profile, and the scalar count. It rejects a wrong global phase, +a wrong view frame, and a wrong backward ADD sign. The separate +independent review is recorded outside this producer packet. + +The exact local identities extend to each positive tensor depth, since +the address identities hold as operators and scalar ADD commutes with +tensor application. The tensor statement does not grant a common global +port code after the stage routes. That obligation remains separate. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/emit_independent_skeleton.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/emit_independent_skeleton.py new file mode 100644 index 0000000000..bbe6297bed --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/independent-skeleton-20261018/emit_independent_skeleton.py @@ -0,0 +1,483 @@ +#!/usr/bin/env python3 +"""Build two shear words on the retained independent native paths.""" + +from collections import Counter, defaultdict, deque +from copy import deepcopy +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +CORE = LANES / 'new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz' +NATIVE = LANES / 'new-native-recipes-20261017' +COMPILER = NATIVE / 'sources/vendor/clifford/clifford_exact.py' +PINS = { + 'core_decompressed': 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa', + 'compiler': '2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962', + 'native_freeze': '928c29f5949cddafa3510fe0f95c8b400022ee37410d512c2dcef207bfda2f27', +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def digest(path): + return sha256(path.read_bytes()).hexdigest() + + +def encoded(value): + return json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + + +def pin_sources(): + raw = gzip.decompress(CORE.read_bytes()) + need(sha256(raw).hexdigest() == PINS['core_decompressed'], 'Core input pin') + need(digest(COMPILER) == PINS['compiler'], 'Exact compiler pin') + need(digest(NATIVE / 'FREEZE.json') == PINS['native_freeze'], 'Native freeze pin') + spec = importlib.util.spec_from_file_location('skeleton_clifford', COMPILER) + module = importlib.util.module_from_spec(spec) + # dataclass reads the module registry when it resolves a field type. + import sys + sys.modules[spec.name] = module + spec.loader.exec_module(module) + return json.loads(raw), module + + +def keep(event): + return event[0] != 'scalar' or event[1][0] == 'clear' + + +def push_word(word, symbol): + if word and word[-1] == -symbol: + word.pop() + else: + word.append(symbol) + + +def scan(word, events): + frames = list(word['start']) + histories = [[] for _ in frames] + direct, equal_rank = {}, {} + active = False + first, last = None, None + for index, event in enumerate(events): + tag = event[0] + if event[:2] == ['phase', 'A']: + active, first = True, index + 1 + elif event[:2] == ['phase', 'exit_adapters']: + active, last = False, index + if tag == 'climb': + target, old, new, rank = event[2:6] + need(frames[target] == old, 'Original climb frame') + need(len(word['frames'][new]) - len(word['frames'][old]) == rank, 'Original climb rank') + frames[target] = new + elif tag == 'warp': + token, symbol, old, new = event[1:5] + need(token[0] == 'L', 'All retained warps act on live roles') + target = token[1] + need(frames[target] == old, 'Original warp frame') + frames[target] = new + push_word(histories[target], symbol) + if not active or tag not in ('phase', 'climb', 'warp'): + continue + target_ranks = defaultdict(list) + for t in range(112): + target_ranks[len(word['frames'][frames[112 + t]])].append(t) + for s in range(112): + u = frames[s] + rank = len(word['frames'][u]) + if not 1 <= rank <= 8: + continue + for t in target_ranks[rank]: + v = frames[112 + t] + record = { + 'source': s, 'target': t, 'original_cut': index + 1, + 'source_frame': u, 'target_frame': v, 'rank': rank, + 'source_prefix_warps': list(histories[s]), + 'target_prefix_warps': list(histories[112 + t]), + } + if u == v: + direct.setdefault((s, t), record) + if not histories[s] and not histories[112 + t]: + equal_rank.setdefault((s, t), record) + need(frames == word['final'], 'Original final frames') + need(all(not h for h in histories), 'Every signed warp word cancels') + need(first is not None and last is not None, 'Canonical interval') + return direct, equal_rank, first, last + + +def matching(graph, prefer_diagonal=False): + adjacency = {s: sorted(t for a, t in graph if a == s) for s in range(112)} + left = {s: s for s in range(112) if prefer_diagonal and (s, s) in graph} + right = {t: s for s, t in left.items()} + for start in range(112): + if start in left: + continue + queue = deque([start]) + seen_left, predecessor = {start}, {} + end = None + while queue and end is None: + s = queue.popleft() + for t in adjacency[s]: + if t in predecessor: + continue + predecessor[t] = s + if t not in right: + end = t + break + next_s = right[t] + if next_s not in seen_left: + seen_left.add(next_s) + queue.append(next_s) + if end is None: + continue + t = end + while True: + s = predecessor[t] + old_t = left.get(s) + left[s], right[t] = t, s + if old_t is None: + break + t = old_t + # An alternating reachability set gives a vertex cover of the same size. + seen_left = set(range(112)) - set(left) + seen_right = set() + queue = deque(seen_left) + while queue: + s = queue.popleft() + for t in adjacency[s]: + if left.get(s) == t or t in seen_right: + continue + seen_right.add(t) + if t in right and right[t] not in seen_left: + seen_left.add(right[t]) + queue.append(right[t]) + cover_left = set(range(112)) - seen_left + need(all(s in cover_left or t in seen_right for s, t in graph), 'Matching vertex cover') + need(len(cover_left) + len(seen_right) == len(left), 'Matching and cover sizes') + return left, {'source_vertices': sorted(cover_left), 'target_vertices': sorted(seen_right)} + + +def kop(ce, columns): + rows = ce.transpose(tuple(columns), 9) + inverse_transpose = ce.transpose(ce.inv(rows, 9), 9) + quadratic = tuple((1 << i) ^ sum(ce.parity(x & y) << j + for j, y in enumerate(inverse_transpose)) + for i, x in enumerate(inverse_transpose)) + return ce.perm(9, rows).then(ce.diag(9, quadratic)) + + +def equal(a, b): + return a.tab == b.tab and a.zero_state() == b.zero_state() + + +def circuit_columns(circuit): + out = [] + for source in range(512): + address, phase = source, 0 + for event in circuit: + tag = event[0] + if tag == 'P': + address = sum(((row & address).bit_count() & 1) << i + for i, row in enumerate(event[1])) + elif tag == 'X': + address ^= event[1] + elif tag == 'D': + quadratic, linear = event[1:] + phase += sum(linear[i] for i in range(9) if address >> i & 1) + phase += 2 * sum(((quadratic[i] >> (i + 1)) & (address >> (i + 1))).bit_count() + for i in range(9) if address >> i & 1) + else: + need(tag == 'phase', 'A monomial circuit has no Fourier gate') + phase += event[1] + out.append((address, phase % 4)) + return out + + +def recipe_columns(recipe): + out = [] + for source in range(512): + phase = recipe['phase'] + sum(recipe['linear_Z4'][i] for i in range(9) if source >> i & 1) + phase += 2 * sum(((recipe['quadratic_rows'][i] >> (i + 1)) & (source >> (i + 1))).bit_count() + for i in range(9) if source >> i & 1) + address = recipe['offset'] ^ sum(((row & source).bit_count() & 1) << i + for i, row in enumerate(recipe['matrix_rows'])) + out.append((address, phase % 4)) + return out + + +def monomial_record(ce, op): + compiled, recipe = ce.monomial(op) + need(equal(compiled, op), 'Exact monomial table and phase') + need(circuit_columns(op.circuit) == recipe_columns(recipe), 'All 512 monomial columns') + return {'recipe': recipe, 'circuit': op.circuit} + + +def make_edges(ce, word, graph, chosen): + records = [] + full = ce.fourier(9) + for s, t in sorted(chosen.items()): + record = deepcopy(graph[s, t]) + u, v, rank = record['source_frame'], record['target_frame'], record['rank'] + ub, vb = word['frames'][u], word['frames'][v] + ku = kop(ce, ce.basis_extend(ub, 9)) + kv = kop(ce, ce.basis_extend(vb, 9)) + tu, tv = ce.canonical_frame(9, ub), ce.canonical_frame(9, vb) + hr = ce.fourier(9, range(rank)) + need(equal(ku.adjoint().then(hr).then(ku), tu), 'Actual source frame factorization') + need(equal(kv.adjoint().then(hr).then(kv), tv), 'Actual target frame factorization') + p = ku.adjoint().then(kv) + need(equal(tu.then(p), p.then(tv)), 'Exact physical and logical intertwining') + positive, negative = monomial_record(ce, p), monomial_record(ce, p.adjoint()) + table, inverse = recipe_columns(positive['recipe']), recipe_columns(negative['recipe']) + need(all(inverse[j] == (i, (-phase) % 4) for i, (j, phase) in enumerate(table)), 'All reciprocal columns') + full_product = full.adjoint().then(p).then(full) + full_compiled, full_recipe = ce.monomial(full_product) + need(equal(full_compiled, full_product), 'FULL response view is monomial') + wrong = dict(positive['recipe'], phase=(positive['recipe']['phase'] + 1) % 4) + need(recipe_columns(wrong) != table, 'Wrong global phase is rejected') + record.update({ + 'view_id': s, 'source_frame_basis': ub, 'target_frame_basis': vb, + 'source_factor_columns': ce.basis_extend(ub, 9), + 'target_factor_columns': ce.basis_extend(vb, 9), + 'positive': positive, 'negative': negative, + 'response': positive, 'inverse_response': negative, + 'full_conjugate_response': {'recipe': full_recipe, 'circuit': full_compiled.circuit}, + }) + records.append(record) + return records + + +def emit(events, edges, direction): + by_cut = defaultdict(list) + for edge in edges: + by_cut[edge['original_cut']].append(edge) + out = [] + for index, event in enumerate(events): + if keep(event): + out.append(deepcopy(event)) + for edge in by_cut[index + 1]: + s, t, u, v = (edge[k] for k in ('source', 'target', 'source_frame', 'target_frame')) + identifier = edge['view_id'] + if direction == 'forward': + out.extend([ + ['monomial_view', ['L', s], identifier, 1, u, v], + ['scalar', ['add', ['L', 112 + t], ['L', s], 1, 1], v], + ['monomial_view', ['L', s], identifier, -1, v, u], + ]) + else: + out.extend([ + ['monomial_view', ['L', 112 + t], identifier, -1, v, u], + ['scalar', ['add', ['L', s], ['L', 112 + t], -1, 1], u], + ['monomial_view', ['L', 112 + t], identifier, 1, u, v], + ]) + need(set(by_cut) <= set(range(1, len(events) + 1)), 'All transfer cuts are emitted') + return out + + +def left_operator(row, kind, identifier, power): + out = {} + token = (kind, identifier, power) + inverse = (kind, identifier, -power) + for (source, operators), coefficient in row.items(): + changed = operators[1:] if operators and operators[0] == inverse else (token,) + operators + out[source, changed] = coefficient + return out + + +def replay(events, word, edges): + n = len(word['start']) + state = {p: {(p, ()): 1} for p in range(n + 8)} + frames = dict(enumerate(word['start'])) + frames.update({n + p: 0 for p in range(8)}) + active_zeros = set() + edge_map = {e['view_id']: e for e in edges} + def slot(token): + kind, index = token + if kind == 'L': + need(0 <= index < n, 'Live role range') + return index + if kind == 'C': + need(0 <= index < 8, 'Owned role range') + return n + index + need(kind == 'Z', 'Private role namespace') + return ('Z', index) + for event in events: + tag = event[0] + if tag == 'scalar': + gate, frame = event[1:] + target = slot(gate[1]) + if gate[0] == 'clear': + need(target == n, 'Only original owned C0 is cleared') + state[target], frames[target] = {}, frame + else: + need(gate[0] == 'add' and gate[3] in (-1, 1) and gate[4] == 1, 'Only unit transfers remain') + source = slot(gate[2]) + need(source != target and frames[source] == frames[target] == frame, 'Equal-frame transfer') + for key, coefficient in state[source].items(): + state[target][key] = state[target].get(key, 0) + gate[3] * coefficient + if not state[target][key]: + del state[target][key] + elif tag == 'climb': + target, old, new, rank = event[2:6] + need(frames[target] == old, 'Retained native source frame') + need(len(word['frames'][new]) - len(word['frames'][old]) == rank, 'Retained child rank') + frames[target] = new + elif tag == 'warp': + target, symbol, old, new = slot(event[1]), event[2], event[3], event[4] + need(frames[target] == old, 'Retained warp source frame') + frames[target] = new + state[target] = left_operator(state[target], 'K', abs(symbol), 1 if symbol > 0 else -1) + elif tag == 'monomial_view': + target, identifier, power, old, new = slot(event[1]), *event[2:] + edge = edge_map[identifier] + pair = (edge['source_frame'], edge['target_frame']) + need((old, new) == (pair if power == 1 else pair[::-1]), 'View has the checked frames') + need(frames[target] == old, 'View source frame') + frames[target] = new + state[target] = left_operator(state[target], 'P', identifier, power) + elif tag == 'zero_buffer': + target = ('Z', event[2]) + if event[1] == 'alloc': + need(target not in active_zeros, 'Private zero allocation') + state[target], frames[target] = {}, 1 + active_zeros.add(target) + else: + need(target in active_zeros and not state[target], 'Private zero restoration') + active_zeros.remove(target) + else: + need(tag in ('phase', 'adapter', 'residual_adapter'), 'Known complete event') + need(not active_zeros, 'No private zero role remains live') + need([frames[p] for p in range(n)] == word['final'], 'Every live endpoint frame') + need(all(frames[n + p] == 0 for p in range(8)), 'Owned endpoint frames') + return state + + +def check_endpoint(state, n, edges, direction): + wanted = {p: {(p, ()): 1} for p in range(n + 8)} + wanted[n] = {} + for e in edges: + s, t, identifier = e['source'], e['target'], e['view_id'] + if direction == 'forward': + wanted[112 + t][s, (('P', identifier, 1),)] = 1 + else: + wanted[s][112 + t, (('P', identifier, -1),)] = -1 + need(all(state[p] == wanted[p] for p in range(n + 8)), 'All arbitrary input columns') + need(all(not row for p, row in state.items() if isinstance(p, tuple)), 'All private zero columns') + + +def verify_native_dependencies(provider, word): + directory = NATIVE / provider + receipt_path = directory / 'GENERATION-RECEIPT.json' + receipt = json.loads(receipt_path.read_text()) + need(receipt['status'] == 'PASS_FRESH_SOURCE_NATIVE_RECIPES', 'Native generation status') + for name, pin in receipt['output_sha256'].items(): + need(digest(directory / name) == pin, 'Native recipe pin: ' + name) + canonical = json.loads(gzip.decompress((directory / 'CANONICAL-WORD.json.gz').read_bytes())) + for key in ('frames', 'start', 'final', 'warps', 'warp_edges'): + need(canonical[key] == word[key], 'Native canonical field: ' + key) + residuals = json.loads((directory / 'RESIDUAL-ADAPTERS.json').read_text()) + classes = {(word['start'][p], word['final'][p]) for p in range(224, len(word['start']))} + for start, final in classes: + if final != 1: + need(f'{start}:{final}' in residuals['recipes'], 'Proper helper residual recipe') + return {'generation_receipt_sha256': digest(receipt_path), + 'recipe_sha256': receipt['output_sha256'], + 'helper_endpoint_classes': [list(x) for x in sorted(classes)]} + + +def main(): + core, ce = pin_sources() + payload = {'schema': 'independent-native-monomial-shears-v1', 'source_pins': PINS, + 'warp_convention': 'Use the retained forward signed K implementation in both directions.', + 'providers': {}} + receipt = {'status': 'PASS_INDEPENDENT_NATIVE_MONOMIAL_SHEARS', 'providers': {}} + for provider, item in core['providers'].items(): + word, original = item['canonical'], item['programs'] + need(len(word['start']) == 632 and len(word['zero_buffers']) == 91, 'Original live and private stock') + skeleton = [e for e in original['forward'] if keep(e)] + need(skeleton == [e for e in original['backward'] if keep(e)], 'Both stripped skeletons are byte-equal') + native = verify_native_dependencies(provider, word) + direct, candidates, first, last = scan(word, original['forward']) + direct_match, direct_cover = matching(direct) + chosen, cover = matching(candidates, prefer_diagonal=True) + need(len(chosen) == 112, 'Complete equal-rank matching') + edges = make_edges(ce, word, candidates, chosen) + programs = {direction: emit(original[direction], edges, direction) + for direction in ('forward', 'backward')} + for direction, events in programs.items(): + state = replay(events, word, edges) + check_endpoint(state, 632, edges, direction) + retained = [e for e in events if e[0] != 'monomial_view' and not (e[0] == 'scalar' and e[1][0] == 'add')] + need(retained == skeleton, 'Every retained native event and wrapper is unchanged') + profile = Counter(e[5] for e in skeleton if e[0] == 'climb') + need(dict(profile) == {1: 2433, 2: 724, 3: 228, 4: 102, 5: 20}, 'Native child profile') + need(sum(k * v for k, v in profile.items()) == 5073, 'Native rank mass') + scalar_count = Counter(e[1][0] for e in programs['forward'] if e[0] == 'scalar') + need(dict(scalar_count) == {'clear': 16, 'add': 112}, 'Complete scalar event count') + # The first malformed view must fail before a transfer can use it. + bad = deepcopy(programs['forward']) + position = next(i for i, e in enumerate(bad) if e[0] == 'monomial_view') + bad[position][4] = -1 + rejected = False + try: + replay(bad, word, edges) + except ValueError: + rejected = True + need(rejected, 'Wrong view frame is rejected') + bad = deepcopy(programs['backward']) + position = next(i for i, e in enumerate(bad) if e[0] == 'scalar' and e[1][0] == 'add') + bad[position][1][3] = 1 + rejected = False + try: + check_endpoint(replay(bad, word, edges), 632, edges, 'backward') + except ValueError: + rejected = True + need(rejected, 'Wrong backward sign is rejected') + payload['providers'][provider] = { + 'canonical': word, 'native_dependencies': native, 'canonical_cut_range': [first, last], + 'direct_equal_frame_graph': {'edges': [list(x) for x in sorted(direct)], + 'matching': sorted(map(list, direct_match.items())), 'vertex_cover': direct_cover}, + 'equal_rank_zero_warp_graph': {'edges': [list(x) for x in sorted(candidates)], + 'matching': sorted(map(list, chosen.items())), 'vertex_cover': cover}, + 'transfers': edges, 'programs': programs, + } + receipt['providers'][provider] = { + 'live_roles': 632, 'arbitrary_helper_roles': 408, 'owned_C_roles': 8, 'private_zero_roles': 91, + 'arbitrary_symbolic_columns_per_word': 640, 'complete_words': 2, + 'direct_equal_frame_edges': len(direct), 'direct_maximum_matching': len(direct_match), + 'equal_rank_empty_warp_edges': len(candidates), 'chosen_matching_size': len(edges), + 'chosen_diagonal_ports': sum(e['source'] == e['target'] for e in edges), + 'selected_ranks': dict(sorted(Counter(e['rank'] for e in edges).items())), + 'all_net_warp_words_empty': True, 'all_selected_prefix_warp_words_empty': True, + 'exact_intertwining_checks': 112, 'explicit_monomial_column_checks': 112 * 512 * 2, + 'full_conjugated_response_rank_zero': True, + 'native_child_profile': dict(sorted(profile.items())), 'native_children': sum(profile.values()), + 'native_rank_mass': 5073, 'retained_warp_events': 240, + 'retained_endpoint_adapters': sum(e[0] == 'adapter' for e in skeleton), + 'retained_residual_adapters': sum(e[0] == 'residual_adapter' for e in skeleton), + 'retained_private_allocations': sum(e[:2] == ['zero_buffer', 'alloc'] for e in skeleton), + 'new_complex_monomial_array_maps': 224, 'new_unit_complex_ADDs': 112, + 'retained_complex_CLEARs': 16, 'top_level_real_scalar_bound': 928, + 'additional_native_children': 0, 'additional_private_arrays': 0, + 'controls': ['Wrong global phase', 'Wrong view frame', 'Wrong backward ADD sign'], + } + print(provider, 'PASS', receipt['providers'][provider], flush=True) + raw = encoded(payload) + (HERE / 'INDEPENDENT-SKELETON-PROGRAMS.json.gz').write_bytes(gzip.compress(raw, mtime=0)) + receipt['payload_decompressed_sha256'] = sha256(raw).hexdigest() + receipt['producer_sha256'] = digest(Path(__file__)) + receipt['source_pins'] = PINS + receipt['scope'] = ('Two local shear words with a unitary monomial block response. ' + 'No global controller, owner reassignment, precision invoice, or complete kappa claim.') + (HERE / 'INDEPENDENT-SKELETON.json').write_text(json.dumps(receipt, sort_keys=True, indent=2) + '\n') + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/CHECKS.json new file mode 100644 index 0000000000..26bdcec6e0 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/CHECKS.json @@ -0,0 +1,3950 @@ +{ + "bridge_jobs": 0, + "checker_sha256": "d83f86ad6eb4a013d1102463f2dbdc79abb9cdf2586d375f2bd5d76eb58fba34", + "complete_native_children": 1520, + "complete_native_profile_per_cover": { + "1": 704, + "2": 144, + "5": 144, + "7": 336, + "8": 192 + }, + "complete_native_rank": 5600, + "controller": { + "H2_fusion_claimed": false, + "extra_H1": 224, + "missing_final_Q_rejected": true, + "paid_terminal_order": [ + "Q^-1", + "E2^-1", + "E1^-1", + "E0^-1", + "Q" + ], + "post_old_terminal": [ + "Q E2 E1 E0 x", + "y" + ], + "preterminal": [ + "-y", + "E2 E1 E0 x" + ], + "wrong_inverse_order_rejected": true + }, + "cover_order": "1402575762037550245974927108561766348252867730943485007822736244380743658751530106880000000", + "cover_order_bits": 300, + "dimension": 25, + "gauge_words": [ + { + "peak": "4", + "scalar": 2668, + "word": "scalar_word" + }, + { + "peak": "4", + "scalar": 2668, + "word": "inverse_scalar_word" + } + ], + "identity_tail_idle": { + "from": 2, + "to": 2 + }, + "independent_productive_role_count": "314176970696411255098383672317835662008642371731340641752292918741286579560342743941120000000", + "local_words": { + "base": { + "backward": { + "checked_input_columns": 224, + "children": 432, + "helper_operands": 0, + "maximum_array_norm_bound": "6", + "omitted_helper_start_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "owned_fields": 0, + "profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "rank_mass": 1792, + "scalar": 3032 + }, + "forward": { + "checked_input_columns": 224, + "children": 432, + "helper_operands": 0, + "maximum_array_norm_bound": "6", + "omitted_helper_start_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "owned_fields": 0, + "profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "rank_mass": 1792, + "scalar": 3032 + } + }, + "extra": { + "backward": { + "checked_input_columns": 224, + "children": 432, + "helper_operands": 0, + "maximum_array_norm_bound": "6", + "omitted_helper_start_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "owned_fields": 0, + "profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "rank_mass": 1792, + "scalar": 3032 + }, + "forward": { + "checked_input_columns": 224, + "children": 432, + "helper_operands": 0, + "maximum_array_norm_bound": "6", + "omitted_helper_start_ranks": { + "0": 274, + "1": 108, + "2": 24, + "4": 2 + }, + "owned_fields": 0, + "profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "rank_mass": 1792, + "scalar": 3032 + } + } + }, + "native_halving_margin": 497, + "nonzero_idle_jobs": 0, + "omitted_unused_helper_slots": 408, + "phase_scope": "The source packets supply complete native and D25 phase checks. This checker binds their pins and checks scalar, frame, stock and route data; it does not rerun their phase compilers.", + "prefix_bound_local_and_codes": "14155776", + "preterminal_native_rank": 5376, + "productive_role_count_bits": 308, + "projected_role_count": 224, + "scalar_subtotal_local_and_eight_codes": 30440, + "scope": "Structural one-pair hosting and a paid exact terminal. Complete finite supplier pricing and a cheaper terminal are not proved. 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a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/FREEZE.json new file mode 100644 index 0000000000..1eaa94ea18 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/FREEZE.json @@ -0,0 +1,12 @@ +{ + "files": { + "CHECKS.json": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944", + "ONE-PAIR-ADMISSION.md": "799eab4224c40ec980712593cb1bcd8e62522f1fb1b5ebe79d0f3569d10111de", + "SOURCE-PINS.json": "49cce325ea25508f7ff22f3ec48e8ef01297104bc76a9080d482a4f9ba929f46", + "check_admission.py": "d83f86ad6eb4a013d1102463f2dbdc79abb9cdf2586d375f2bd5d76eb58fba34" + }, + "normal_optimized_receipts_equal": true, + "schema": "one-pair-admission-freeze-v1", + "scope": "Structural data and row hosting with a separated224-H1 terminal. No new finite supplier or kappa claim.", + "status": "PASS_ONE_PAIR_STOCK_AND_PAID_TERMINAL" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/ONE-PAIR-ADMISSION.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/ONE-PAIR-ADMISSION.md new file mode 100644 index 0000000000..c14d0d7bcb --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/ONE-PAIR-ADMISSION.md @@ -0,0 +1,316 @@ +# One pair: data stock, native hosting, and the paid terminal + +## Result + +The fresh matched word can use one pair of 112-field data banks. Its +three local calls are F0, B1, and F2. The ambient label space has +dimension 25. No local helper, query buffer, inter-pair bridge, or +nonzero idle job is required by this word. + +This is a new 224-role local contract. It does not remove helper +progress from an old 632-role contract and then count that progress +as free. The checker verifies that every event in the new word uses +only roles 0 through 223. The other 408 slots in its source payload +have no event and have identical start and final frames. Their frame +rank counts are {0:274, 1:108, 2:24, 4:2}. Thus the direct summand on +the 224 data roles is exact for arbitrary input data. + +The current-stage controller has a literal paid completion. It uses +224 additional rank-one children. This completion has total rank +5600 = 224*25 and fails the native moment test for every positive +improvement exponent. The obstruction in this construction is its +terminal cost, not a requirement for four data pairs. A cheaper +terminal is not ruled out. + +This packet proves the changed row and owner contract under the +inherited all-size native-child and stream compiler contracts. It +does not prove those general compiler contracts again. It does not +supply a complete finite precision, map, tape, or kappa invoice. + +## Sources and checks + +`SOURCE-PINS.json` gives exact paths and hashes for all inputs. The +main inputs are the matched native word, the literal dimension-25 +stage views, the current-code controller, and the primary stream +proof in `upstream/build/sections/05-layers.tex`. + +The new checker imports no producer. For each provider and each +direction, it reads the serialized native word and checks all 224 +independent data columns, every scalar frame, every native rank, +every data endpoint, and every field's total native progress. It +also checks the actual scalar E code and its inverse. Native kernel +phases and the complete DATA phase identities are pinned source +premises; this checker does not rerun their phase compilers. + +## The local stock is 224, not 632 + +The word has only two event types: scalar and native. Its scalar +events are reversible ADD and signed dyadic-unit SCALE operations. +Each native event acts on one data role. Its two side maps act on +that role's payload address. Neither type names another physical +field as hidden scratch. + +The local profile is + +```text +{1:160, 2:48, 5:48, 7:112, 8:64}. +``` + +It has 432 children and rank mass 1792. Every one of the 224 fields +gets total rank eight. There are 508 scalar events and 3032 real +scalar primitives per call. There are 224 local endpoint maps and +at most 864 native side maps per call. All these counts come from +the serialized events. The local maximum-array norm bound is six. + +The two providers have the same coefficient response E. The exact +relations E^T=E and E^2=I make the backward response reciprocal. +The physical local types are + +```text +X_p: C_qp -> F9, +Y_p: I -> F9 C_qp^-1. +``` + +The endpoint adapters in the source are part of this contract. +Canonical frame labels alone do not replace them. + +## Complete owner layout at dimension 25 + +Let G=O(25,2). Allocate the independent productive fields + +```text +(side, port, h), side in {X,Y}, 0 <= port < 112, h in G. +``` + +Thus 224 is the local field count. The recursive row split uses +N=224*|G| independent roles. Distinct cover owners do not contain +copies of the same input, and no such promise is used. + +At stage s and body d, port p uses owner h=d rho_(s,p), with the +literal DATA entry and exit translations. Each rho_(s,p) belongs +to G and is an involution. For a fixed side and port, right +multiplication by rho_(s,p) is a bijection of G. Different ports +and sides are separate families. Therefore the 224-role body +invocations partition the productive fields. Complete a whole +cover sweep before the next stage or port-code sweep. + +The dimension-25 packet checks all 336 route records, 672 entry +phase identities, 672 exit phase identities, 336 future-Y views, +and 672 past-X views. All translations use the first 25 axes; +the discarded 48 route columns are identity columns. This is an +exact restriction of the supplied charts, not a dimension-only +argument. The inherited final full-cover correction remains part +of the output convention. + +There is no helper assignment or collision condition left in +these data-only sweeps. In particular, no old helper is silently +reassigned to a data owner. The number of replicas can be one. + +For reference, + +```text +|O(25,2)| = 2^144 * product_(i=1..12) (2^(2i)-1). +``` + +The cover order has 300 bits and N has 308 bits. The formula follows +by fixing the all-ones vector and counting symplectic bases in its +24-dimensional orthogonal complement. The finite cover cancels +from a normalized native moment. It does not cancel from row +reserve, map work, or physical stock. + +## The controller and its legal cuts + +Use E_s for the complete routed operator at stage s. It is a +conjugate of the local port matrix by the stage owner views. Its +inverse is supplied by the actual backward word. The E_s need not +be equal or commute. + +The current-code controller executes + +```text +F0; +X <- E0 X; +Y <- E1 Y; +B1; +X <- E1 X; +Y <- E2 Y; +F2; +X <- E1^-1 X. +``` + +The two Y codes are at the current entrance cuts. The three X +codes use current or past charts at completed X cuts. The checked +access cones contain all five occurrences. Each scalar port code +has a literal 494-gate word, costs 2668 real primitives, and uses +no additional child or array. A conservative view allowance is +224 maps per occurrence. These are priced scalar operations, not +free matrix inverses at an arbitrary frame. + +The exact ordered endpoint is + +```text +(x,y) -> (-y, Kx), K=E2 E1 E0. +``` + +The checker derives this identity with free ordered invertible +symbols. It does not use a commutation or the involution relation. +The retained general recipe has an identity tail idle from level +2 to level 2 in the one-pair case. This has no native job. There is +no next pair, so there is no plus bridge, minus bridge, next-X +preparation, or descending final bridge. + +## A literal two-line terminal + +Let Q be the diagonal intrinsic line operator. Let F be the +completed common 25-axis frame, with the standard full-cover +correction included. The raw input is (Qx,y). Before the old +terminal the fields are + +```text +(-Fy, F Q^-1 Kx). +``` + +The old translated signed exchange gives (F Q Kx,Fy). Execute +the following operations on the first output bank: + +1. Apply Q^-1 to each of its 112 fields. +2. Apply E2^-1, then E1^-1, then E0^-1 at FULL. +3. Apply Q to each of its 112 fields. + +The states are F Kx, F x, and F Qx. The second output remains Fy. +This proves the original raw output contract. The order in step +2 is required. The checker rejects its reverse and also rejects +omission of the final Q. + +These line calls have explicit native address charts. For a +nonzero intrinsic vector q, choose a bit j with q_j=1. Let A_q +have first column q and all standard basis columns except e_j +as its other columns. This is an invertible 25 by 25 binary +matrix. The checker emits it for every port. Put + +```text +alpha=(1+i)/2, beta=(1-i)/2, +C_q=alpha I+beta X_q. +``` + +Then + +```text +P_Aq C_first P_Aq^-1 = C_q, +C_q^-1 = X_q C_q. +``` + +Both equations include the complete scalar phase. They follow +by conjugating the literal translation X_first and using C_q^2=X_q. +For owner h, use h A_q and direction hq. These payload maps leave +the owner index fixed and use full payload ranges. The payload +chart can be in GL(25,2); it need not be in O(25,2). The binary +row-addition compiler admits such a chart. At width f the +same identity acts in each of the f columns. Each Q or Q^-1 +pass therefore has exactly 112 rank-one children per cover. +The inverse pass has a translation wrapper as well. No owned +query field or arbitrary helper baseline is used. + +This is a separated 224-H1 construction. The three port codes +between the line passes do not generally commute with Q. +There is no emitted 112-H2 fusion claim. + +## Recursive row and work-area contract + +The primary stream proof at lines 540 through 614 splits complete +rows among the finite network roles. It then parks the other role +streams on a LIFO tape and passes only the active stream to the +child. Its proof uses arbitrary values in every role. It does not +require a particular number of data pairs or the old local helpers. + +Use that split with N=224*|G|, not with 224 alone. A native event +then gets one active stream of volume V/N. That stream retains +every spectator range and all f columns of its active axes. The +serialized monomial side maps change only that stream. The +remaining role streams are parked and are restored after the +child returns. Coefficient registers and the fixed work tapes +belong to the stream machine; they are not additional independent +productive input owners. + +The row reserve must cover the depth of the admitted child tree. +For a grouped child of rank r, the active dimension is r/25 of +the parent at an exact split. Here r<=8. Thus a reserve for any +upper bound on that tree depth is finite and logarithmic in the +input dimension. This statement does not replace the inherited +arbitrary-size grouping and remainder rules. If those rules are +used, their actual depth bound must be used in the row reserve. +The native size guard has margin + +```text +25^2 - 2*8^2 = 497 > 0. +``` + +The binary payload compiler uses a third address slot for a row +addition and restores its arbitrary bits. That slot is part of +the active payload, not a new field. The ambient 25-slot parent +has such a slot. The primary proof at lines 130 through 188 and +450 through 470 supplies this distinction. A recursive child +uses the same admitted machine contract on its own active +stream; it does not borrow an old parent helper field. + +This proves that the new local stock causes no new recursive +helper-hosting or parent-row obstruction under the stated child +contract. It is not a new proof of the arbitrary-size compiler, +the finite precision transfer, or exact integer recovery. + +## Complete rank consequence and remaining cost + +The three data calls have profile + +```text +{1:480, 2:144, 5:144, 7:336, 8:192}. +``` + +Their mass is 5376. The paid terminal gives + +```text +{1:704, 2:144, 5:144, 7:336, 8:192}, +``` + +with 1520 children and mass 5600. Multiply every count and the +productive role count by |G| for the whole cover. All paid ranks +are less than 25. Hence, for every b>0, + +```text +sum_r n_r r^(1-b) > 25^(-b) sum_r n_r r + = 224 * 25^(1-b). +``` + +The specified full word cannot give a positive native improvement +exponent. Finite scalar and map costs cannot reverse this failure. +This is a statement about this full word, not a lower bound on +every decoder for Q K Q^-1. + +The exact subtotal for the three local scalar words and all eight +E-code occurrences is 30440 real primitives per cover. The old +signed exchange, global views, line wrappers, final cover maps, +recursive work areas, and precision must also be charged. A norm +bound for the three local words and eight E-code words is +6^3*4^8=14155776. This bound does not replace a full finite invoice. + +## Reproduction + +Run one process from the repository root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -I -B work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py --out /tmp/one-pair-admission-optimized.json +``` + +Both commands report `PASS_ONE_PAIR_STOCK_AND_PAID_TERMINAL`. +The two receipts must be byte-equal. `FREEZE.json` records the +local proof, checker, source pins, and receipt hashes. + +The native matching comes from the oblique and controller lanes; +the 64-port component comes from the history lane. The literal +stage phases and scalar access come from the bridge-access lane. +The five-code controller comes from the encoded-controller lane. +The primary stream proof supplies the inherited row and work-tape +method. This new audit used OpenAI Codex assistance. 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/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/SOURCE-PINS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/SOURCE-PINS.json new file mode 100644 index 0000000000..e113fb074c --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/SOURCE-PINS.json @@ -0,0 +1,72 @@ +{ + "controller_proof": { + "kind": "text", + "path": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md", + "sha256": "5facaac62ec417bae33690fa645150774d3820eb17be9e5033e779840f9821d5" + }, + "current_controller": { + "kind": "plain", + "path": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/PROGRAM.json", + "sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7" + }, + "current_controller_proof": { + "kind": "text", + "path": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/ONE-PAIR.md", + "sha256": "86c87e8080c305c605541d70afc523b8ff65a94cbf2bc9e134289984d86f1f6e" + }, + "current_controller_receipt": { + "kind": "plain", + "path": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/CHECKS.json", + "sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd" + }, + "dimension_checker": { + "kind": "text", + "path": "work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/check_dimension25.py", + "sha256": "cd0dbdb4f8ca86c423f198f2d7b7fb8653ef942a310b03b33b017d728b31d8be" + }, + "dimension_proof": { + "kind": "text", + "path": "work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/MATCHED-STAGE-ACCESS.md", + "sha256": "0887be18fc5e0b1f62c4dd3209df4f61e60ccd9d46f2ba23c2b59d303f1b31f2" + }, + "dimension_receipt": { + "kind": "plain", + "path": "work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-CHECKS.json", + "sha256": "194773d0db5ecd4f044068483213e5d834063cb61585eb0bf7bc75a58d1bcb1f" + }, + "dimension_views": { + "kind": "plain", + "path": "work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + }, + "gauge": { + "kind": "plain", + "path": "work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/FULL-GAUGE-PROGRAM.json", + "sha256": "94055f5cbb57e67a7f70b896a39d77449be332291f3f0b2afbd563a2a5141c49" + }, + "local_payload": { + "kind": "gzip", + "path": "work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz", + "sha256": "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025" + }, + "local_proof": { + "kind": "text", + "path": "work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE.md", + "sha256": "60f11b2f3f7a342f080e5715702a7cc8030e625211bac1787d728ffb72918664" + }, + "local_receipt": { + "kind": "plain", + "path": "work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-RECEIPT.json", + "sha256": "7bc873d627e022d4677b740633c9cd5f86c5e675d84460d538b4b6314c79536c" + }, + "retained_schedule": { + "kind": "plain", + "path": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/NORMALIZATION-PROGRAMS.json", + "sha256": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9" + }, + "stream_source": { + "kind": "text", + "path": "upstream/build/sections/05-layers.tex", + "sha256": "20cfc8d12099d4e4ed9e3e7eeb6162edd9b6e0e076f24693364cd24377252594" + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py new file mode 100644 index 0000000000..5500c591e0 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py @@ -0,0 +1,264 @@ +"""Check the one-pair data stock and a paid terminal construction.""" + +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json + + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[4] + + +def need(condition, label): + if not condition: + raise ValueError(label) + + +def add(row, other, coefficient=Q(1)): + for key, value in other.items(): + row[key] = row.get(key, 0) + coefficient * value + if not row[key]: + del row[key] + + +def rank(rows): + pivots = {} + for value in rows: + while value: + p = value.bit_length() - 1 + if p in pivots: + value ^= pivots[p] + else: + pivots[p] = value + break + return len(pivots) + + +def price(kind, value): + a, b = abs(value.numerator), value.denominator + need(a > 0 and b & (b - 1) == 0, "Nonzero dyadic coefficient") + if kind == "scale": + need(a & (a - 1) == 0, "Unit scale") + return 2 * (abs(a.bit_length() - b.bit_length()) + (value < 0)) + return 2 * (3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1) + + +def local_audit(word, response, direction): + need(len(word["start"]) == len(word["final"]) == 632, "Frozen role count") + need(word["start"][224:] == word["final"][224:], + "Omitted helper slots have unchanged physical frame") + frames = word["frames"] + current = word["start"][:224] + rows = [{i: Q(1)} for i in range(224)] + widths, profile = [0] * 224, Counter() + scalar = 0 + peak = Q(1) + for event in word["events"]: + if event[0] == "native": + _, target, old, new, width, key = event + need(0 <= target < 224 and current[target] == old, "Data-only native target") + need(rank(frames[old] + frames[new]) == len(frames[new]), "Nested productive path") + need(width == len(frames[new]) - len(frames[old]) > 0, "Exact positive rank") + need(word["native_recipes"][key]["rank"] == width, "Literal native recipe") + current[target] = new + widths[target] += width + profile[width] += 1 + else: + need(event[0] == "scalar", "No private or allocation event") + op, frame = event[1:] + kind, target = op[:2] + need(0 <= target < 224 and current[target] == frame, "Data-only scalar target") + if kind == "scale": + value = Q(*op[2:]) + rows[target] = {i: value * c for i, c in rows[target].items()} + else: + need(kind == "add", "Only reversible ADD and SCALE") + origin = op[2] + need(0 <= origin < 224 and origin != target and current[origin] == frame, + "Data-only scalar source in the same exact frame") + value = Q(*op[3:]) + add(rows[target], rows[origin], value) + scalar += price(kind, value) + peak = max(peak, sum(map(abs, rows[target].values()))) + expected = [{i: Q(1)} for i in range(224)] + for t, row in enumerate(response): + if direction == "forward": + add(expected[112 + t], row) + else: + for s, value in row.items(): + add(expected[s], {112 + t: -value}) + need(rows == expected and current == word["final"][:224], "All 224 independent input columns") + need(widths == [8] * 224, "Every retained data path has rank eight") + need(len(word["endpoint_adapters"]) == 224, "Only the 224 data endpoint maps") + need(all(r["role"] in ("source", "target") and 0 <= r["port"] < 112 + for r in word["endpoint_adapters"]), "No endpoint helper operand") + need(profile == {1: 160, 2: 48, 5: 48, 7: 112, 8: 64}, "Complete native profile") + need(scalar == 3032 and peak == 6, "Literal scalar invoice and prefix bound") + return {"profile": dict(sorted(profile.items())), "scalar": scalar, + "children": sum(profile.values()), "rank_mass": sum(widths), + "maximum_array_norm_bound": str(peak), "checked_input_columns": 224, + "helper_operands": 0, "owned_fields": 0, + "omitted_helper_start_ranks": dict(sorted(Counter( + len(frames[f]) for f in word["start"][224:]).items()))} + + +def reduce_word(word): + out = [] + for letter in word: + if out and out[-1] == -letter: + out.pop() + else: + out.append(letter) + return tuple(out) + + +def code(row, word): + result = {} + for (origin, old), value in row.items(): + add(result, {(origin, reduce_word(tuple(word) + old)): value}) + return result + + +def controller_audit(): + # The symbols 1,2,3 denote E0,E1,E2; 4 denotes Q. + x, y = {(0, ()): 1}, {(1, ()): 1} + add(y, code(x, [1])) + x = code(x, [1]) + y = code(y, [2]) + add(x, code(y, [-2]), -1) + x = code(x, [2]) + y = code(y, [3]) + add(y, code(x, [3])) + x = code(x, [-2]) + need(x == {(1, ()): -1} and y == {(0, (3, 2, 1)): 1}, "Ordered current-cut triple") + raw_x, raw_y = code(y, [4]), {key: -value for key, value in x.items()} + need(raw_y == {(1, ()): 1}, "Raw Y endpoint") + first = code(raw_x, [-4]) + decoded = code(first, [-1, -2, -3]) + final = code(decoded, [4]) + need(final == {(0, (4,)): 1}, "Literal two-line terminal returns the raw X input") + need(code(first, [-3, -2, -1]) != decoded, "Reject reversed inverse order") + need(decoded != final, "Reject omission of the final original-input line") + return {"preterminal": ["-y", "E2 E1 E0 x"], + "post_old_terminal": ["Q E2 E1 E0 x", "y"], + "paid_terminal_order": ["Q^-1", "E2^-1", "E1^-1", "E0^-1", "Q"], + "extra_H1": 224, "H2_fusion_claimed": False, + "wrong_inverse_order_rejected": True, "missing_final_Q_rejected": True} + + +def gauge_audit(gauge, response): + out = [] + for key in ("scalar_word", "inverse_scalar_word"): + rows = [{i: Q(1)} for i in range(112)] + cost, peak = 0, Q(1) + for kind, target, source, coefficient in gauge[key]: + value = Q(coefficient) + need(0 <= target < 112 and 0 <= source < 112, "Gauge data stock") + if kind == "add": + need(target != source, "Gauge ADD has distinct operands") + add(rows[target], rows[source], value) + else: + need(kind == "scale", "Gauge scalar grammar") + rows[target] = {i: value * c for i, c in rows[target].items()} + cost += price(kind, value) + peak = max(peak, sum(map(abs, rows[target].values()))) + need(rows == response and cost == 2668 and peak <= 4, "Actual E and E inverse scalar words") + out.append({"word": key, "scalar": cost, "peak": str(peak)}) + return out + + +def main(out_path): + pins_path = HERE / "SOURCE-PINS.json" + pins = json.loads(pins_path.read_bytes()) + sources = {} + for key, item in pins.items(): + raw = (ROOT / item["path"]).read_bytes() + if item["kind"] == "gzip": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == item["sha256"], "Source pin: " + key) + sources[key] = raw.decode() if item["kind"] == "text" else json.loads(raw) + payload = sources["local_payload"] + response = [{int(i): Q(v) for i, v in row.items()} for row in payload["response"]] + for i, row in enumerate(response): + square = {} + for j, value in row.items(): + need(value == response[j].get(i, 0), "Symmetric local response") + add(square, response[j], value) + need(square == {i: Q(1)}, "Exact reciprocal involution") + local = {provider: {direction: local_audit(word, response, direction) + for direction, word in words.items()} + for provider, words in payload["providers"].items()} + gauge = gauge_audit(sources["gauge"], response) + schedule = [e for e in sources["retained_schedule"]["schedule"] + if e["kind"] == "local" and e["pair"] == 0] + need(schedule == [{"kind": "local", "stage": s, "pair": 0, "reverse": s == 1} + for s in range(3)], "Retained first-pair local order") + need(sources["current_controller"]["program"] == [ + ["forward", 0], ["code_X", 0, 1], ["code_Y", 1, 1], + ["backward", 1], ["code_X", 1, 1], ["code_Y", 2, 1], + ["forward", 2], ["code_X", 1, -1]], "Literal five-code placement") + views = sources["dimension_views"]["entries"] + need(len(views) == 336 and {(v["stage"], v["port"]) for v in views} + == {(s, p) for s in range(3) for p in range(112)}, "Complete D25 records") + lines = {} + for v in views: + route = v["route_columns"] + need(len(route) == 25 and all(0 < a < 1 << 25 for a in route), "D25 route bounds") + need(all((a & b).bit_count() % 2 == (i == j) + for i, a in enumerate(route) for j, b in enumerate(route)), "Regular cover route") + need(all(0 <= a < 1 << 25 for a in v["literal_stage_alignment"].values()), "D25 translation bounds") + if v["stage"] == 0: + lines[v["port"]] = v["q"] + need(len(lines) == 112 and all(q and q.bit_count() % 2 for q in lines.values()), "All intrinsic lines") + for words in payload["providers"].values(): + for word in words.values(): + need(all(word["frames"][word["start"][p]] == [q] for p, q in lines.items()), + "The terminal lines are the physical input lines in both providers") + terminal_lines = [] + for p, q in sorted(lines.items()): + pivot = (q & -q).bit_length() - 1 + basis = [q] + [1 << i for i in range(25) if i != pivot] + need(rank(basis) == 25, "Explicit rank-one child address chart") + terminal_lines.append({"port": p, "q": q, "chart_columns": basis, + "positive": "P_chart C_first P_chart^-1", + "inverse": "X_q P_chart C_first P_chart^-1"}) + group = 1 << 144 + for i in range(1, 13): + group *= (1 << (2 * i)) - 1 + local_profile = Counter({1: 160, 2: 48, 5: 48, 7: 112, 8: 64}) + full_profile = Counter({r: 3 * n for r, n in local_profile.items()}) + full_profile[1] += 224 + need(sum(r * n for r, n in full_profile.items()) == 224 * 25, "Safe terminal exhausts rank deficit") + receipt = { + "status": "PASS_ONE_PAIR_STOCK_AND_PAID_TERMINAL", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins_sha256": sha256(pins_path.read_bytes()).hexdigest(), "sources": pins, + "local_words": local, "gauge_words": gauge, "controller": controller_audit(), + "projected_role_count": 224, "omitted_unused_helper_slots": 408, + "dimension": 25, "stage_calls": schedule, "nonzero_idle_jobs": 0, + "bridge_jobs": 0, "identity_tail_idle": {"from": 2, "to": 2}, + "cover_order": str(group), "cover_order_bits": group.bit_length(), + "independent_productive_role_count": str(224 * group), + "productive_role_count_bits": (224 * group).bit_length(), + "complete_native_profile_per_cover": dict(sorted(full_profile.items())), + "preterminal_native_rank": 5376, "complete_native_rank": 5600, + "complete_native_children": sum(full_profile.values()), + "scalar_subtotal_local_and_eight_codes": 3 * 3032 + 8 * 2668, + "native_halving_margin": 25 * 25 - 2 * 8 * 8, + "prefix_bound_local_and_codes": str(6 ** 3 * 4 ** 8), + "terminal_line_charts": terminal_lines, + "phase_scope": "The source packets supply complete native and D25 phase checks. This checker binds their pins and checks scalar, frame, stock and route data; it does not rerun their phase compilers.", + "scope": "Structural one-pair hosting and a paid exact terminal. Complete finite supplier pricing and a cheaper terminal are not proved. The specified complete profile fails every positive native improvement exponent." + } + out_path.write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, default=HERE / "CHECKS.json") + main(parser.parse_args().out) diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json new file mode 100644 index 0000000000..3cfc26d8f9 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json @@ -0,0 +1,105 @@ +{ + "backward_binding": "Both a consistent K choice and the literal inverse-transpose choice conjugate(K) have exact rank-zero recipes. The literal dual differs in 172 of 180 physical classes per provider.", + "clean_payload_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "interpreter_sha256": "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b", + "max_rss_bytes": 150323200, + "method": "Independent Pauli conjugation and exact 512-entry Gaussian zero-state vectors; no generator or Clifford compiler import", + "providers": { + "base": { + "child_classes": 3036, + "endpoint_classes": 224, + "frames": 1130, + "helper_width_profile": { + "4": 26, + "5": 2, + "6": 18, + "7": 50, + "8": 99, + "9": 213 + }, + "literal_dual_classes": 180, + "literal_dual_recipes_different_from_forward": 172, + "native_occurrences": { + "backward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + }, + "forward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + } + }, + "negative_controls": [ + "wrong global phase with equal Pauli action", + "wrong FULL terminal", + "literal conjugate K can differ from K" + ], + "physical_warp_classes": 180, + "pins": { + "CANONICAL-WORD.json.gz": "bd6f84f6e7be075064f04e6141568d295631a3feab1efa75ff0326e6efa4f472", + "CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "LITERAL-DUAL-WARP-RECIPES.json": "e880f4e6ff6308675b766bfa63d472c1050b01f17fac78f8810b04eedc6e0a6e", + "LOCAL-PROGRAMS.json.gz": "4048b4494793f31c6c9ce85a7de584c53cafae0cd5c119eb1084b221cfe04ad9", + "RESIDUAL-ADAPTERS.json": "8a6130051284adf76ec932bc2a190058cc99efbed5d862bee819e3bc8c29a31b" + }, + "raw_warps": 72, + "residual_classes": 56, + "seconds": 63.83301916599157, + "status": "PASS_INDEPENDENT_NATIVE_CORE_LIFT", + "wrapped_helpers": 195 + }, + "extra": { + "child_classes": 3036, + "endpoint_classes": 224, + "frames": 1130, + "helper_width_profile": { + "4": 26, + "5": 2, + "6": 18, + "7": 50, + "8": 99, + "9": 213 + }, + "literal_dual_classes": 180, + "literal_dual_recipes_different_from_forward": 172, + "native_occurrences": { + "backward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + }, + "forward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + } + }, + "negative_controls": [ + "wrong global phase with equal Pauli action", + "wrong FULL terminal", + "literal conjugate K can differ from K" + ], + "physical_warp_classes": 180, + "pins": { + "CANONICAL-WORD.json.gz": "1cf1714fc2a26c18b2b380827054246550c1402fde379745f626ff61f4ee6224", + "CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "LITERAL-DUAL-WARP-RECIPES.json": "0bafa16eea7a49af963346117cf61ca638859748752d5f0ed47a18fe6c4594ff", + "LOCAL-PROGRAMS.json.gz": "4048b4494793f31c6c9ce85a7de584c53cafae0cd5c119eb1084b221cfe04ad9", + "RESIDUAL-ADAPTERS.json": "dd8d70e07ae6ecc028d7691611966fcaee946279964736997af0aa78c61c2282" + }, + "raw_warps": 72, + "residual_classes": 56, + "seconds": 37.52593279199209, + "status": "PASS_INDEPENDENT_NATIVE_CORE_LIFT", + "wrapped_helpers": 195 + } + }, + "scope": "Local phase-aware native lift. The whole scalar map is in the separate logical review. Global hosting, owner, controller, and recursive supplier admission remain separate.", + "status": "PASS_INDEPENDENT_NEW_CORE_NATIVE_RECIPES" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-RAW-REVIEW-FINAL.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-RAW-REVIEW-FINAL.json new file mode 100644 index 0000000000..b2e2777657 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-RAW-REVIEW-FINAL.json @@ -0,0 +1,204 @@ +{ + "independent_engine_pins": { + "check_new_core.py": "6106c9808185747b221c149a668c8d087abbc34d79b9a7aca95e8a813e18186a", + "check_oblique_backward.py": "7d9e52f9f120be04adeb9cdc3e26658373b221c35920e89160fdc0f16e7bdacd" + }, + "method": "Reverse propagation through every literal event, with disjoint signed Q, K, and dual-K symbols; only adjacent inverse symbols cancel. Physical boundaries are conjugated by explicit endpoint Q operators.", + "providers": { + "base": { + "negative_controls": { + "B0:input_exchange:omit": true, + "B0:suffix:omit": true, + "B8:prefix:line": true, + "F8:prefix:omit": true, + "F8:suffix:omit": true + }, + "programs": { + "B0": { + "arbitrary_helpers_restored": 408, + "arbitrary_input_columns": 640, + "boundary_scalar_cost": 4382, + "core_frame_checks": 18080, + "core_warp_events": 240, + "exact_signed_line_columns": 8192, + "native_children": 3507, + "native_rank_mass": 5073, + "new_monomial_wrappers": 0, + "new_rank_one_children": 0, + "owned_cleanup_scalar_cost": 14, + "private_outputs_zero": 8, + "scalar": 168896, + "zero_buffer_outputs_zero": 91 + }, + "B16": { + "arbitrary_helpers_restored": 408, + "arbitrary_input_columns": 640, + "boundary_scalar_cost": 12798, + "core_frame_checks": 18080, + "core_warp_events": 240, + "exact_signed_line_columns": 8192, + "native_children": 3523, + "native_rank_mass": 5089, + 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"Local operator-coded maps and complete local costs, with exact core native and signed-line dependencies. Inter-call code conversion, exterior caller phases, controller, legal owner/hosting, precision, and full supplier remain separate.", + "source_pins": { + "CLEAN-J-PROGRAMS.json.gz": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "RAW-SELECTED-TRANSFER.json": "da1831b17a79a4fd9ebe689d4f76e357bc912eda1e6b252818a7ef5685b1a739", + "RAW-SELECTED-TRANSFER.json.gz": "bc9fab3bc7c849da7eb055a9d7340bf110c11cdd54da049a8297a1324bfa54b1", + "RAW-SELECTED-TRANSFER.md": "53d8663fab6c1a6999fbc29ac310675fbea2b45f607f2f702af9787305c4ab03", + "emit_raw_selected.py": "a07cf4894a2599993006c7b99e6cb62146ece82f2ae6df72a28100ccb3a689bc" + }, + "status": "PASS_INDEPENDENT_NEW_RAW_SELECTED_TRANSFER", + "two_sided_inverse_checks": { + "B0": "both orders in the free Q algebra", + "F8": "both orders in the free Q algebra" + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-RAW-REVIEW.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-RAW-REVIEW.md new file mode 100644 index 0000000000..32115c4955 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-RAW-REVIEW.md @@ -0,0 +1,143 @@ +# Independent review of the new raw selected exchanges + +The five raw selected exchange maps pass on both new providers. The +zero-line backward map B0 puts the original selected X input into +productive selected Y output. It adds no native child to the clean-J +core. The coded forward map F8 puts the dense ordinary query into +completed selected X and adds eight rank-one children. These are exact +local operator-coded maps. Their inter-call conversion and complete +supplier cost remain open obligations. + +## Direct derivation + +Let A select ports `[0,7,20,27,36,46,57,111]`, and let U be the other +ports. The literal R of the new core gives + + J = [[0,-B],[-D,I-DB]], BD=13I. + +Write the content input as `x=(a,u)` and `y=(b,v)`. Physical X input is +Qx; physical Y input is y. At output the physical data are `F x'` and +`F Q^-1 y'`. Each Q_p is the positive port-line operator. F commutes with +each Q_p because both are products or linear combinations of commuting +translations. The proof does not move Q through B or D. + +Put `r=Q_A^-1 b`. A physical exchange of selected X and Y gives the core +content inputs `(r,u)` and `(Q_A a,v)`. The clean-J backward core gives + + X_A = r+Bv, + X_U = u+D Q_A a-v+DBv, + Y_A = Q_A a, + Y_U = v. + +The completed-X shear `X_U -= D X_A` gives B0: + + X_A' = Bv+r, + X_U' = u-v-Dr+D Q_A a, + Y_A' = Q_A a, + Y_U' = v. + +In physical selected Y the code cancels exactly: +`F Q_A^-1 Y_A'=F a`. Thus original selected input information is carried +by a productive output. The operation does not claim a free recovery of +all other information. Its content inverse is + + v = Y_U', + r = X_A'-Bv, + b = Q_A r, + a = Q_A^-1 Y_A', + u = X_U'+v+Dr-D Y_A'. + +The eight-line input code `v -= Dr` gives B8. It has selected X +`Bv-12r`, ordinary X `u-v+D Q_A a`, selected Y `Q_A a`, and ordinary Y +`v-Dr`. The second eight-line block removes `D Q_A a` from ordinary X +and gives B16. The factor 12 follows from `BD=13I`. + +For the forward map, first add `Dr` to ordinary Y, exchange the selected +physical inputs, use the clean-J forward core, and exchange the selected +physical outputs. This gives F8: + + X_A' = a-Q_A^-1 B u, + X_U' = u, + Y_A' = b, + Y_U' = v+(I-DB)u. + +Its content inverse is + + u = X_U', + a = X_A'+Q_A^-1 B X_U', + b = Y_A', + v = Y_U'-X_U'+DB X_U'. + +F0 omits the input code. Its ordinary Y row has the additional term +`-D Q_A^-1 b`; its other rows agree with F8. The checker verifies both +orders of the B0 and F8 inverse formulas in the free Q algebra. These +inverses prove information preservation. They are not priced native +decoder constructions. + +## Literal verification and cost + +`check_new_raw.py` does not import the producer. It uses the pinned +independent scalar and line-check engines. It propagates output +coefficients backward through every event in each of the ten complete +words. Explicit Q operations convert physical input to core content and +core content to physical output. The operator alphabet has disjoint Q, +forward-K, and dual-K symbols. It cancels only adjacent inverse symbols. +It does not sort symbols or assume that Q commutes through the native +warps or the query matrices. + +All 640 arbitrary live and private input columns have the stated +response. All 408 borrowed helpers have the identity logical response. +Every private zero-buffer output row is zero at release, for all 91 +buffers. All eight C outputs are zero. The final seven explicit clears +of C1 through C7 cost 14 real primitives and are included below. + +| Word | Real scalar primitives | Native rank mass | Child count | New rank-one children | +| --- | ---: | ---: | ---: | ---: | +| B0 | 168896 | 5073 | 3507 | 0 | +| B8 | 173104 | 5081 | 3515 | 8 | +| B16 | 177312 | 5089 | 3523 | 16 | +| F0 | 164944 | 5073 | 3507 | 0 | +| F8 | 169152 | 5081 | 3515 | 8 | + +Every retained core is the exact reviewed clean-J word. Its scalar +frames, native frames, 240 warp occurrences, and 91 buffer lifetimes are +checked again. The complete local scalar bill is recomputed. Physical +boundary operations are checked as operations on data or owned private +fields; they do not require equality of the two logical frames that the +exchange changes. No borrowed helper is a boundary source or target. +Each private copy starts from a cleared C0. Every new line has two +explicit monomial wrappers. All sixteen signed recipes pass independent +checks on all 512 spatial basis columns, for 8192 checks per provider. + +The fresh native review in `NEW-CORE-NATIVE-REVIEW.md` supplies every +retained core phase recipe, including the literal dual warp table for +the backward word and the proper-terminal helper wrappers. It also +checks wrapper placement. No earlier provider geometry is substituted. + +## Reproduction and controls + +The final run used: + + python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/check_new_raw.py --out work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-RAW-REVIEW-FINAL.json + +It returned `PASS_INDEPENDENT_NEW_RAW_SELECTED_TRANSFER`. All checks +remain active under `-O`. For each provider, five complete-word negative +controls reject a wrong inverse-line sign, an omitted backward input +exchange, an omitted backward lower shear, an omitted forward output +exchange, and an omitted forward input code. The latter is the verified +F0 map, which differs from F8. Both orders of both displayed content +inverses also pass. + +The result resolves a local source-information return problem by changing +the interface: selected original input can be carried into productive +output at no added native rank cost. A controller must now use the exact +operator-coded rows. A raw physical exchange does not supply a free +cross-call code conversion, decoder, or owner assignment. The caller's +exterior phases, legal inter-call views, private hosting, recursive +children, precision, and complete invoice remain separate obligations. + +The producer's proof and predecessor credit are in +`../new-core-transfer-20261017/RAW-SELECTED-TRANSFER.md`. Input pins, +independent-engine pins, exact results, and review hashes are in the +receipt and freeze file. OpenAI Codex assisted this independent review. +No PR, push, or publication commit was made. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/CHECKS.json new file mode 100644 index 0000000000..71440934bd --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/CHECKS.json @@ -0,0 +1,23 @@ +{ + "all_rows_and_columns": 112, + "checker_sha256": "fa22b64bf6c15e970d8c74b3de2139fef599cf27430a730c7e344db8a4926bd2", + "literal_square_identity": true, + "native_children": 0, + "owned_fields": 0, + "payload_sha256": "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89", + "private_fields": 0, + "real_scalar_invoice": { + "mode_swaps": 624, + "pair_code": 470, + "pair_undo": 470, + "small_swaps": 832 + }, + "scope": "Common-FULL scalar implementation of actual E=E^-1. 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b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.md new file mode 100644 index 0000000000..0c3a907fe6 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/FULL-GAUGE.md @@ -0,0 +1,78 @@ +# The actual matched response as a common-FULL scalar map + +The frozen full native response E is a symmetric dyadic involution. +This packet implements E=E^-1 on 112 arbitrary data fields in a common +FULL frame. The cost is 2396 real scalar primitives. It uses no native +child, owned field, or private field. The actual matched native X exits +all have this frame, so the map can be appended there. + +On the 48-port component, write E=A^-1 M A. The matrix A is the direct +sum of the 24 actual signed two-field codes. The matrix M consists of +24 signed transpositions of their mode carriers. On the other 64 ports, +E is the actual 32 negative transpositions. The packet pins the full +native response, including this negative-permutation component. + +For one pair code [[a,b],[c,d]], each entry is a signed unit and its rows +are orthogonal. Thus d=-abc. The following four operations apply it: + +```text +x <- a x +x <- x + b y +y <- 2d y +y <- y + ca x. +``` + +The second output is ca(ax+by)+2dy=cx+dy. A scale by one is omitted. +Reverse these operations and invert their coefficients for the inverse +code. Across all pairs the code costs 470 real primitives, and the +inverse code costs 470. + +A signed transposition (x,y)->(w y,w x), with w=+1 or -1, has the word + +```text +x <- x+y +y <- y-x +x <- x+y. +``` + +These three additions give (y_old,-x_old). If w=+1, negate the second +field. If w=-1, negate the first. Each transposition costs 26 real +primitives. Thus the 24 mode transpositions cost 624 and the 32 physical +negative transpositions cost 832. The complete total is + +```text +470 + 624 + 470 + 832 = 2396. +``` + +The payload gives every scalar event. A forward row replay and a reverse +column replay each equal the actual full E on all 112 inputs. Repeating +the same literal word gives identity in both replays. The check rejects +omission of the pair undo. Exact prefix row sums bound the array norm; +the resulting bound is in `CHECKS.json`. This is a top-level bound, not +a recursive precision certificate. + +Every operation requires the same physical frame on its source and +target. In a common FULL frame, scalar port maps commute with the common +F_9 operation, so these operations have the stated logical response. +The proof does not permit the map on the unequal Y-hole frames. It also +does not identify E at different supplier stages. Such stage changes +must use their actual physical port view and pay its access cost. + +This is a fixed scalar word, not a minimality claim. It supplies a +concrete endpoint gauge for the new response. A complete controller, +source-retirement proof, terminal phase map, host, and total recurrence +remain separate. No kappa result or publication is claimed. + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/emit_full_gauge.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/emit_full_gauge.py +``` + +The expected output is `PASS_MATCHED_COMMON_FULL_GAUGE`. The normal and +optimized payload and receipt bytes agree. This work uses the controller +lane's matched modes and the oblique-native and history lanes' full +native response. The scalar pair factor was derived in this lane's +cyclic-flag construction. The work was produced with AI assistance. +Independent review is separate. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/REPRODUCTION.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/REPRODUCTION.json new file mode 100644 index 0000000000..112cd467bc --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/REPRODUCTION.json @@ -0,0 +1,11 @@ +{ + "byte_identical": true, + "normal": { + "CHECKS.json": "e644a88ee397e37191f40a8cd8e06859824c9433d773100357cf4a0f7fd779be", + "FULL-GAUGE.json": "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89" + }, + "optimized": { + "CHECKS.json": "e644a88ee397e37191f40a8cd8e06859824c9433d773100357cf4a0f7fd779be", + "FULL-GAUGE.json": "ea8717a63861b7bc9acc2d8e8b0501503a928859042e453234a2fc0c65797f89" + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/emit_full_gauge.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/emit_full_gauge.py new file mode 100644 index 0000000000..68db189919 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-full-gauge-20261018/emit_full_gauge.py @@ -0,0 +1,164 @@ +#!/usr/bin/env python3 +"""Emit the actual involution as a common-FULL scalar word.""" +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + 'matching': ('controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json', + 'e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902'), + 'native': ('oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz', + '95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025'), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def add(target, source, scale): + for p, value in source.items(): + result = target.get(p, 0)+scale*value + if result: + target[p] = result + else: + target.pop(p, None) + + +def cost(event): + kind = event[0] + value = F(*event[-2:]) + a, b = abs(value.numerator), value.denominator + need(a and b & (b-1) == 0, 'Dyadic coefficient') + if kind == 'scale': + need(a & (a-1) == 0, 'Unit scale') + return 2*(abs(a.bit_length()-b.bit_length())+int(value < 0)) + return 2*(1+a.bit_length()+a.bit_count()+b.bit_length()) + + +def replay(events): + rows = [{i: F(1)} for i in range(112)] + maximum = F(1) + for event in events: + target = event[1] + value = F(*event[-2:]) + if event[0] == 'scale': + rows[target] = {p: value*c for p, c in rows[target].items()} + else: + need(event[0] == 'add' and target != event[2], 'Scalar grammar') + add(rows[target], rows[event[2]], value) + maximum = max(maximum, sum(abs(c) for c in rows[target].values())) + return rows, maximum + + +def reverse_columns(events): + columns = [{i: F(1)} for i in range(112)] + for event in reversed(events): + target = event[1] + value = F(*event[-2:]) + if event[0] == 'scale': + columns[target] = {p: value*c for p, c in columns[target].items()} + else: + add(columns[event[2]], columns[target], value) + return columns + + +def main(): + data = {} + for name, (relative, pin) in PINS.items(): + raw = (LANES/relative).read_bytes() + if relative.endswith('.gz'): + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, 'Actual source pin '+name) + data[name] = json.loads(raw) + matching, native = data['matching'], data['native'] + response = [{int(p): F(c) for p, c in row.items()} for row in native['response']] + events, code = [], [] + + def append(kind, target, origin, value, buffer=events): + value = F(value) + if kind == 'scale': + if value != 1: + buffer.append([kind, target, value.numerator, value.denominator]) + else: + buffer.append([kind, target, origin, value.numerator, value.denominator]) + + for pair in matching['pair_codes']: + x, y = pair['ports'] + a, b, c, d = [F(value) for row in pair['matrix'] for value in row] + need(all(abs(v) == 1 for v in (a, b, c, d)) and a*c+b*d == 0, 'Actual pair code') + append('scale', x, None, a, code) + append('add', x, y, b, code) + append('scale', y, None, 2*d, code) + append('add', y, x, c*a, code) + events.extend(code) + code_end = len(events) + + def signed_swap(x, y, weight): + need(weight in (-1, 1), 'Signed swap weight') + append('add', x, y, 1) + append('add', y, x, -1) + append('add', x, y, 1) + append('scale', y if weight == 1 else x, None, -1) + + modes = matching['modes'] + mode_swaps = [] + for i, row in enumerate(matching['mode_response']): + need(len(row) == 1, 'One matched mode') + j, weight = next(iter(row.items())) + j, weight = int(j), F(weight) + if i < j: + x, y = modes[i]['carrier'], modes[j]['carrier'] + signed_swap(x, y, weight) + mode_swaps.append([x, y, str(weight)]) + need(len(mode_swaps) == 24, 'All24 mode swaps') + swap_end = len(events) + for event in reversed(code): + value = F(*event[-2:]) + append(event[0], event[1], None if event[0] == 'scale' else event[2], + 1/value if event[0] == 'scale' else -value) + undo_end = len(events) + small_swaps = [] + for x in matching['small_ports']: + need(len(response[x]) == 1, 'Actual small permutation') + y, weight = next(iter(response[x].items())) + need(weight == -1 and response[y] == {x: F(-1)}, 'Actual negative involution') + if x < y: + signed_swap(x, y, weight) + small_swaps.append([x, y, str(weight)]) + need(len(small_swaps) == 32, 'All32 small swaps') + result, bound = replay(events) + need(result == response and reverse_columns(events) == response, 'Exact rows and independent columns of the symmetric response') + identity = [{i: F(1)} for i in range(112)] + need(replay(events+events)[0] == identity and reverse_columns(events+events) == identity, 'The literal gauge is its own inverse') + invoice = {'pair_code': sum(map(cost, events[:code_end])), + 'mode_swaps': sum(map(cost, events[code_end:swap_end])), + 'pair_undo': sum(map(cost, events[swap_end:undo_end])), + 'small_swaps': sum(map(cost, events[undo_end:]))} + need(invoice['pair_code']+invoice['pair_undo'] == 940 and invoice['mode_swaps'] == 624 + and invoice['small_swaps'] == 832 and sum(invoice.values()) == 2396, 'Complete common-FULL scalar invoice') + need(replay(events[:swap_end]+events[undo_end:])[0] != response, 'Omitted pair undo is rejected') + payload = {'schema': 'matched-common-full-gauge-v1', 'frame': 'FULL', 'live_fields': 112, + 'owned_fields': 0, 'private_fields': 0, 'native_children': 0, + 'events': events, 'mode_swaps': mode_swaps, 'small_swaps': small_swaps, + 'cuts': {'code_end': code_end, 'swap_end': swap_end, 'undo_end': undo_end}, + 'response': native['response'], 'source_pins': {k: v[1] for k, v in PINS.items()}} + (HERE/'FULL-GAUGE.json').write_text(json.dumps(payload, indent=2, sort_keys=True)+'\n') + receipt = {'status': 'PASS_MATCHED_COMMON_FULL_GAUGE', 'source_pins': {k: v[1] for k, v in PINS.items()}, + 'all_rows_and_columns': 112, 'literal_square_identity': True, 'real_scalar_invoice': invoice, + 'total_real_scalar_primitives': sum(invoice.values()), 'top_level_array_norm_bound': str(bound), + 'owned_fields': 0, 'private_fields': 0, 'native_children': 0, + 'payload_sha256': sha256((HERE/'FULL-GAUGE.json').read_bytes()).hexdigest(), + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope': 'Common-FULL scalar implementation of actual E=E^-1. Access at other frames and full controller are separate.'} + (HERE/'CHECKS.json').write_text(json.dumps(receipt, indent=2, sort_keys=True)+'\n') + print(receipt['status']) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/CHECKS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/CHECKS.json new file mode 100644 index 0000000000..edc9aca061 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/CHECKS.json @@ -0,0 +1,130 @@ +{ + "both_dyadic_principal_inverse_orders": true, + "checker_sha256": "862d5ac822b2772bf6ef3cd4b619f935ea008e1a9e9a600b0d4b36833eec8926", + "distinct_native_and_endpoint_phase_checks": 608, + "full_response_symmetric_involution": true, + "input_pins": { + "clean": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "directions": "b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5", + "matching": "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", + "native": "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025", + "small": "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9" + }, + "matching_matrix_peer_freeze_sha256": "799f6849de59330a179f17f393c56f75d30df8844204cbfc6e9f3a6c867d74f6", + "method": "Independent reverse columns; separate prefix frame and norm ledger; explicit mode routing; new direct Pauli and Gaussian-state interpreter, with no producer imports.", + "phase_interpreter_sha256": "e1671c7c8129445aa0d9c324e377f9310d6e1c5dcdf566bd11ab90d17c47a305", + "producer_pins": { + "FREEZE.json": "b35eae3fb4b53f51cfbed6bec8968b950c70e65bfe777cbe0d15e86c36dd4ab5", + "MATCHED-NATIVE-RECEIPT.json": "7bc873d627e022d4677b740633c9cd5f86c5e675d84460d538b4b6314c79536c", + "MATCHED-NATIVE.md": "60f11b2f3f7a342f080e5715702a7cc8030e625211bac1787d728ffb72918664", + "emit_matched_involution.py": "5f0e174607359ade1b25d01e9efb7816a2a2d7a4225a074d867652920bf3f460" + }, + "providers": { + "base": { + "backward": { + "arbitrary_untouched_helpers": 408, + "endpoint_maps": 224, + "input_columns": 632, + "matching_scalar_real_primitives": 384, + "native_children": 432, + "native_mass": 1792, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "native_recipe_records": 384, + "native_side_map_bound": 864, + "owned_fields_used": 0, + "pair_codes_and_inverse_scalar_real_primitives": 2136, + "private_fields_used": 0, + "productive_rank_each": 8, + "query_rank": 0, + "scalar_real_primitives": 3032, + "small64_scalar_real_primitives": 512, + "top_level_array_l2_norm_bound": "6" + }, + "forward": { + "arbitrary_untouched_helpers": 408, + "endpoint_maps": 224, + "input_columns": 632, + "matching_scalar_real_primitives": 384, + "native_children": 432, + "native_mass": 1792, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "native_recipe_records": 384, + "native_side_map_bound": 864, + "owned_fields_used": 0, + "pair_codes_and_inverse_scalar_real_primitives": 2136, + "private_fields_used": 0, + "productive_rank_each": 8, + "query_rank": 0, + "scalar_real_primitives": 3032, + "small64_scalar_real_primitives": 512, + "top_level_array_l2_norm_bound": "6" + } + }, + "extra": { + "backward": { + "arbitrary_untouched_helpers": 408, + "endpoint_maps": 224, + "input_columns": 632, + "matching_scalar_real_primitives": 384, + "native_children": 432, + "native_mass": 1792, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "native_recipe_records": 384, + "native_side_map_bound": 864, + "owned_fields_used": 0, + "pair_codes_and_inverse_scalar_real_primitives": 2136, + "private_fields_used": 0, + "productive_rank_each": 8, + "query_rank": 0, + "scalar_real_primitives": 3032, + "small64_scalar_real_primitives": 512, + "top_level_array_l2_norm_bound": "6" + }, + "forward": { + "arbitrary_untouched_helpers": 408, + "endpoint_maps": 224, + "input_columns": 632, + "matching_scalar_real_primitives": 384, + "native_children": 432, + "native_mass": 1792, + "native_profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "native_recipe_records": 384, + "native_side_map_bound": 864, + "owned_fields_used": 0, + "pair_codes_and_inverse_scalar_real_primitives": 2136, + "private_fields_used": 0, + "productive_rank_each": 8, + "query_rank": 0, + "scalar_real_primitives": 3032, + "small64_scalar_real_primitives": 512, + "top_level_array_l2_norm_bound": "6" + } + } + }, + "scope": "Complete full112 native data shears and exact exterior. Helper native progress, recursive hosting, routed controller, terminal, full precision, and supplier cost remain separate.", + "status": "PASS_INDEPENDENT_FULL_MATCHED_NATIVE" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/FREEZE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/FREEZE.json new file mode 100644 index 0000000000..486e59910b --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/FREEZE.json @@ -0,0 +1,13 @@ +{ + "files": { + "CHECKS.json": "5411f46eb4050b85fa53b5a285ae96933fbb764c8e65cdb35f68d002b49f3788", + "REPRODUCTION.json": "8d72eb69aa7faec33b5bbe0cd61dbd428e4757afa50e0efc70f8b8c94910218a", + "REVIEW.md": "952019e4611494972f67bf76b3636886260e425ecca2a67ceb512b144808587b", + "check_native.py": "862d5ac822b2772bf6ef3cd4b619f935ea008e1a9e9a600b0d4b36833eec8926" + }, + "phase_interpreter": { + "path": "../paired-centre-review-20261018/exact_phases.py", + "sha256": "e1671c7c8129445aa0d9c324e377f9310d6e1c5dcdf566bd11ab90d17c47a305" + }, + "status": "PASS_INDEPENDENT_FULL_MATCHED_NATIVE" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/REPRODUCTION.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/REPRODUCTION.json new file mode 100644 index 0000000000..508e5fb63a --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/REPRODUCTION.json @@ -0,0 +1,5 @@ +{ + "byte_identical": true, + "normal": "5411f46eb4050b85fa53b5a285ae96933fbb764c8e65cdb35f68d002b49f3788", + "optimized": "5411f46eb4050b85fa53b5a285ae96933fbb764c8e65cdb35f68d002b49f3788" +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/REVIEW.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/REVIEW.md new file mode 100644 index 0000000000..30a815b914 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/REVIEW.md @@ -0,0 +1,123 @@ +# Independent review of the full matched native data word + +The frozen full 112-port native data word passes this independent review. +Both directions and both providers implement the stated response. No +material error was found. This accepts the data word, its physical +boundary, and its local invoice. It does not accept a complete supplier. + +The producer freeze is +`b35eae3fb4b53f51cfbed6bec8968b950c70e65bfe777cbe0d15e86c36dd4ab5`. +All consumed hashes are in `CHECKS.json`. This checker imports no +producer module or Clifford compiler. It uses the separate exact phase +interpreter written for the preceding independent pair-code review. +The producer uses a different interpreter from an older lane. + +## Complete map and arbitrary state + +The review reconstructs the actual response by routing each original +port basis input through the pinned pair rows, signed mode matching, +and inverse code. On the other 64 ports it uses the pinned negative +permutation. That permutation has 32 disjoint negative transpositions; +each source direction is orthogonal to its assigned target direction. +The new 64-port response differs from the normalized Hadamard block in +the earlier matrix packet. The checker rejects substitution of that old +full matrix. + +The actual full response E is symmetric and satisfies E^2=I. Its +selected block L equals the earlier eight-port block. The checker +verifies both orders of the selected and ordinary inverses and checks +that their entries are dyadic. Equivalently, writing E=[[L,B],[D,H]], +the ordinary inverse is H-D L^-1 B. The identities E^2=I and L^-1 L=I +prove both inverse orders without a commutation assumption. + +A reverse event replay checks every one of the 632 input columns of +each serialized word. It gives exactly + +```text +F_E(x,y,h) = (x,y+E x,h), +B_E(x,y,h) = (x-E^T y,y,h). +``` + +The two productive banks are arbitrary. All 408 helper fields are also +arbitrary and are physically unchanged. Every event acts on one of the +224 data fields. There are no copy, clear, reset, owned-field, or +private-field events. No hidden zero-state premise is used. + +The pair code and its inverse preserve each arbitrary initial target +value. A separate forward ledger checks every scalar source and target +frame and every strictly nested native transition. It also checks each +literal matching transfer, its sign, its physical carriers, and the +inclusion of the source plane in the target pair hole. Every mode occurs +once as a source and once as a target. The entire inherited 64-port +suffix agrees with its pinned source, including ordered frame bases and +full native recipe records. + +## Physical phases and endpoint order + +The independent phase interpreter constructs the monomial permutation +and phase on all 512 binary points. It compares all 18 Pauli images and +one exact Gaussian rational reference state for each Clifford. The +Pauli images determine the operator up to scalar; the nonzero reference +state fixes that scalar. No floating-point comparison is used. + +There are 608 distinct native and endpoint comparisons after exact +deduplication. They cover all 384 native recipes in each word and all +224 endpoint records in each word. The checker also compares the +actual I and FULL frames with I and F_9. It retains the literal ordered +bases; it does not replace equal subspaces by equal phase operators. + +For an intended exterior map L_p and canonical frame T_p, each stored +endpoint adapter is checked as T_p L_p^-1. This adapter converts an +input exterior to the canonical frame. Its inverse converts a canonical +output to the stated exterior. The source exterior is C_q; the target +exterior is F_9 C_q^-1. Thus the physical forward exit is + +```text +(F_9 x, F_9 C_q^-1(y+E x), h) +``` + +from physical entry (C_q x,y,h). The backward exit has first component +F_9(x-E^T y) and second component F_9 C_q^-1 y. Each port keeps its own +q. No response matrix is moved through C_q. This packet uses the fixed +original exterior, not a new common-W exterior. + +The check rejects a wrong matching sign and omission of the complete +pair undo. It also rejects a global phase change that preserves every +Pauli image but changes the exact reference state. + +## Full local invoice and scope + +Every data field receives exactly eight productive native rank. The +profile is 160 H1, 48 H2, 48 H5, 112 H7, and 64 H8 children. There are +432 children and native mass 1792. There is no separate query rank. + +The scalar total is 3032 real primitives in every direction and provider: +2136 for both banks' pair codes and inverse codes, 384 for the 48 signed +matching transfers, and 512 for the 64 negative-permutation transfers. +There are 224 endpoint maps and at most 864 native side maps. No +top-level owned or private fields are used. + +Exact absolute row sums after every scalar event give a top-level array +norm bound of six times the largest input-array norm. Native and +endpoint maps are unitary. This does not bound a recursive child's +internal state or establish the full precision contract. + +The word does not advance the borrowed helpers to their former native +endpoints. A helper completion must be composed and priced separately. +The complete controller still needs source access, stage transport, +physical terminal maps, restoration, hosting, internal child costs, and +the full precision and recurrence proof. Neither native mass nor the +local scalar reduction alone proves a supplier or kappa improvement. + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/check_native.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/check_native.py +``` + +The final output is `PASS_INDEPENDENT_FULL_MATCHED_NATIVE`. The normal +and optimized runs produce the same receipt bytes. The frozen H6 and +bundled mode-query services were not independently replayed in this +review; they remain separate producer results. This review was produced +with AI assistance. No publication is authorized. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/check_native.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/check_native.py new file mode 100644 index 0000000000..e226842b8b --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/matched-native-review-20261018/check_native.py @@ -0,0 +1,344 @@ +#!/usr/bin/env python3 +"""Review the full matched native word with a separate exact interpreter.""" +from collections import Counter, defaultdict +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES/'oblique-native-20261017/matched-native-involution' +PINS = { + 'FREEZE.json': 'b35eae3fb4b53f51cfbed6bec8968b950c70e65bfe777cbe0d15e86c36dd4ab5', + 'MATCHED-NATIVE.md': '60f11b2f3f7a342f080e5715702a7cc8030e625211bac1787d728ffb72918664', + 'emit_matched_involution.py': '5f0e174607359ade1b25d01e9efb7816a2a2d7a4225a074d867652920bf3f460', + 'MATCHED-NATIVE-RECEIPT.json': '7bc873d627e022d4677b740633c9cd5f86c5e675d84460d538b4b6314c79536c', +} +INPUTS = { + 'native': ('oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz', + '95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025'), + 'matching': ('controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json', + 'e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902'), + 'small': ('history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz', + '87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9'), + 'clean': ('new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz', + 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa'), + 'directions': ('history-encoding/independent-skeleton-20261018/fresh-three-child/FRESH-THREE-CHILD-PROGRAMS.json.gz', + 'b08cb4146f1aec241e027cd62c942f6eca4ddab3e97f000a9c0017575d36deb5'), +} +# The phase module was written for the preceding independent pair review. +# The native producer uses a different interpreter from an older lane. +PHASE_PATH = HERE.parent/'paired-centre-review-20261018/exact_phases.py' +PHASE_PIN = 'e1671c7c8129445aa0d9c324e377f9310d6e1c5dcdf566bd11ab90d17c47a305' +PEER_PATH = HERE.parent/'matched-involution-review-20261018/FREEZE.json' +PEER_PIN = '799f6849de59330a179f17f393c56f75d30df8844204cbfc6e9f3a6c867d74f6' + + +def need(test, message): + if not test: + raise ValueError(message) + + +def rows(value): + return [{int(p): F(c) for p, c in row.items()} for row in value] + + +def add(target, source, scale=F(1)): + for p, value in source.items(): + new = target.get(p, 0)+scale*value + if new: + target[p] = new + else: + target.pop(p, None) + + +def span(vectors): + out = {0} + for v in vectors: + out |= {x ^ v for x in out} + return out + + +def apply(matrix, vector): + answer = {i: sum(c*vector.get(p, 0) for p, c in row.items()) for i, row in enumerate(matrix)} + return {i: c for i, c in answer.items() if c} + + +def restrict(matrix, ports): + index = {p: i for i, p in enumerate(ports)} + return [{index[p]: c for p, c in matrix[r].items() if p in index} for r in ports] + + +def parse(event): + gate, frame = event[1:] + kind, target = gate[:2] + need(kind in ('add', 'scale'), 'Only reversible scalar operations') + origin = gate[2] if kind == 'add' else None + return kind, target, origin, F(*gate[-2:]), frame + + +def price(kind, value): + a, b = abs(value.numerator), value.denominator + need(a and b & (b-1) == 0, 'Dyadic scalar coefficient') + if kind == 'scale': + need(a & (a-1) == 0, 'Unit dyadic scale') + return 2*(abs(a.bit_length()-b.bit_length())+int(value < 0)) + return 2*(1+a.bit_length()+a.bit_count()+b.bit_length()) + + +def reverse(events): + columns = [{i: F(1)} for i in range(632)] + for event in reversed(events): + if event[0] == 'native': + continue + need(event[0] == 'scalar', 'No unlisted event') + kind, target, origin, value, _ = parse(event) + if kind == 'scale': + columns[target] = {i: value*c for i, c in columns[target].items()} + else: + add(columns[origin], columns[target], value) + return columns + + +def expected(response, backward): + columns = [{i: F(1)} for i in range(632)] + for target, row in enumerate(response): + for origin, value in row.items(): + if backward: + add(columns[112+target], {origin: -value}) + else: + add(columns[origin], {112+target: value}) + return columns + + +def full_response(matching, small, q): + mode_rows = [{int(p): F(c) for p, c in mode['coefficients'].items()} for mode in matching['modes']] + matching_rows = rows(matching['mode_response']) + little = rows(small['response']) + large = set(matching['large_ports']) + active = set(small['active_ports']) + need(large.isdisjoint(active) and large | active == set(range(112)), 'Disjoint complete response support') + for p in active: + need(len(little[p]) == 1, 'One negative-permutation entry per small row') + r, value = next(iter(little[p].items())) + need(r != p and r in active and value == -1 and little[r] == {p: F(-1)}, '32 negative transpositions') + need((q[p] & q[r]).bit_count() % 2 == 0, 'Actual small permutation source access') + need(all(not little[p] for p in large), 'Small response vanishes on the large block') + result = [{} for _ in range(112)] + for column in range(112): + code = {i: row[column] for i, row in enumerate(mode_rows) if column in row} + routed = apply(matching_rows, code) + decoded = defaultdict(F) + for mode, value in routed.items(): + for p, coefficient in mode_rows[mode].items(): + decoded[p] += coefficient*value/2 + for p in active: + decoded[p] += little[p].get(column, 0) + for p, value in decoded.items(): + if value: + result[p][column] = value + need(all(result[p].get(r, 0) == result[r].get(p, 0) for p in range(112) for r in range(112)), 'Actual full symmetry') + for column in range(112): + unit = {column: F(1)} + need(apply(result, apply(result, unit)) == unit, 'Actual full112 involution') + return result + + +def ledger(word, source, matching, small_word, response, backward): + frames = word['frames'] + current = list(word['start']) + need(current == source['start'] and len(current) == 632, 'All actual entry frames') + wanted = source['start'][:] + wanted[:112] = [1]*112 + wanted[112:224] = source['final'][112:224] + need(word['final'] == wanted, 'All actual final frames and unchanged helpers') + state = [{i: F(1)} for i in range(632)] + profile, progress, scalar_cost, maximum = Counter(), Counter(), 0, F(1) + for event in word['events']: + if event[0] == 'scalar': + kind, target, origin, value, frame = parse(event) + need(0 <= target < 224 and current[target] == frame, 'Scalar target is a productive field in its actual frame') + if kind == 'add': + need(0 <= origin < 224 and origin != target and current[origin] == frame, 'Equal-frame productive scalar source') + add(state[target], state[origin], value) + else: + state[target] = {i: value*c for i, c in state[target].items()} + scalar_cost += price(kind, value) + maximum = max(maximum, sum(abs(c) for c in state[target].values())) + else: + need(event[0] == 'native', 'Only scalar and native events') + _, target, old, new, rank, key = event + need(0 <= target < 224 and current[target] == old, 'No helper or owned native access') + need(key == str(old)+':'+str(new) and word['native_recipes'][key]['rank'] == rank, 'Literal native binding') + need(span(frames[old]) < span(frames[new]), 'Strict monotone native progress') + need(rank == len(frames[new])-len(frames[old]) and 1 <= rank <= 8, 'Exact proper-child rank') + current[target] = new + progress[target] += rank + profile[rank] += 1 + need(current == word['final'], 'Complete final frame vector') + need(all(progress[p] == 8 for p in range(224)), 'Exactly eight productive rank on every data field') + need(profile == Counter({1: 160, 2: 48, 5: 48, 7: 112, 8: 64}), 'Complete native profile') + need(scalar_cost == 3032 and maximum == 6, 'Complete scalar and top-level norm invoice') + need(all(state[p] == {p: F(1)} for p in range(224, 632)), 'Every arbitrary helper is untouched') + need(reverse(word['events']) == expected(response, backward), 'Independent all632 reverse columns') + + modes = matching['modes'] + seen = set() + for pair in word['pair_codes']: + a, b = pair['ports'] + need(not ({a, b} & seen), 'Disjoint pair code fields') + seen |= {a, b} + P = span([source['ports'][a], source['ports'][b]]) + need(span(frames[pair['plane']]) == P and len(P) == 4, 'Exact source pair plane') + need(span(frames[pair['pair_hole']]) == {v for v in range(512) if all((v & p).bit_count() % 2 == 0 for p in P)}, 'Exact target pair perpendicular') + need(seen == set(matching['large_ports']), 'All48 pair-coded ports') + need(len(word['transfer_cuts']) == 48, 'All48 matching transfers') + need(all({cut[key] for cut in word['transfer_cuts']} == set(range(48)) for key in ('source_mode', 'target_mode')) + and len({cut['add_event'] for cut in word['transfer_cuts']}) == 48, 'Every mode is used once in the matching metadata') + for cut in word['transfer_cuts']: + i, j = cut['source_mode'], cut['target_mode'] + source_mode, target_mode = modes[i], modes[j] + need(i != j and source_mode['vertex'] == target_mode['vertex'], 'Same-vertex off-diagonal matching') + need(rows(matching['mode_response'])[j] == {i: F(cut['weight'])}, 'Actual matching coefficient') + s, t = source_mode['carrier'], 112+target_mode['carrier'] + need(cut['source'] == s and cut['target'] == t, 'Literal carrier addresses') + kind, target, origin, value, frame = parse(word['events'][cut['add_event']]) + need(kind == 'add' and frame == cut['frame'], 'Exact transfer event and frame') + need((target, origin, value) == ((s, t, -F(cut['weight'])) if backward else (t, s, F(cut['weight']))), 'Ordered transpose shear transfer') + P = span(source['ports'][p] for p in source_mode['ports']) + Q = span(source['ports'][p] for p in target_mode['ports']) + need(span(frames[frame]) == P and all((p & r).bit_count() % 2 == 0 for p in P for r in Q), 'Actual matched source access') + + inherited = word['events'][word['inherited_64_first_event']:] + need(len(inherited) == len(small_word['events']), 'Complete inherited64 event suffix') + for actual, prior in zip(inherited, small_word['events']): + need(actual[0] == prior[0], 'Inherited event kind') + if actual[0] == 'scalar': + need(actual[1] == prior[1] and frames[actual[2]] == small_word['frames'][prior[2]], 'Inherited scalar event and literal basis') + else: + need(actual[1] == prior[1] and actual[4] == prior[4] + and frames[actual[2]] == small_word['frames'][prior[2]] + and frames[actual[3]] == small_word['frames'][prior[3]] + and word['native_recipes'][actual[5]] == small_word['native_recipes'][prior[5]], 'Inherited native event and full phase recipe') + small_cost = sum(price(parse(e)[0], parse(e)[3]) for e in inherited if e[0] == 'scalar') + need(small_cost == 512, 'All64 inherited signed ADDs are priced') + matching_cost = sum(price('add', parse(word['events'][cut['add_event']])[3]) for cut in word['transfer_cuts']) + pair_cost = scalar_cost-small_cost-matching_cost + need(matching_cost == 384 and pair_cost == 2136, 'Independent scalar cost partition') + return {'input_columns': 632, 'arbitrary_untouched_helpers': 408, 'native_profile': dict(sorted(profile.items())), + 'native_children': sum(profile.values()), 'native_mass': sum(k*v for k, v in profile.items()), + 'productive_rank_each': 8, 'query_rank': 0, 'owned_fields_used': 0, 'private_fields_used': 0, + 'scalar_real_primitives': scalar_cost, 'small64_scalar_real_primitives': small_cost, + 'pair_codes_and_inverse_scalar_real_primitives': pair_cost, 'matching_scalar_real_primitives': matching_cost, + 'top_level_array_l2_norm_bound': str(maximum), 'endpoint_maps': 224, 'native_side_map_bound': 864} + + +def main(): + for name, pin in PINS.items(): + need(sha256((SOURCE/name).read_bytes()).hexdigest() == pin, 'Producer source pin '+name) + need(sha256(PEER_PATH.read_bytes()).hexdigest() == PEER_PIN, 'Independent matching matrix review') + for name, pin in json.loads(PEER_PATH.read_bytes())['files'].items(): + need(sha256((PEER_PATH.parent/name).read_bytes()).hexdigest() == pin, 'Matching peer artifact '+name) + need(sha256(PHASE_PATH.read_bytes()).hexdigest() == PHASE_PIN, 'Distinct exact phase interpreter pin') + spec = importlib.util.spec_from_file_location('distinct_matched_phase', PHASE_PATH) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + data = {} + for name, (relative, pin) in INPUTS.items(): + raw = (LANES/relative).read_bytes() + if relative.endswith('.gz'): + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, 'Pinned input '+name) + data[name] = json.loads(raw) + payload, matching, small = [data[k] for k in ('native', 'matching', 'small')] + q = [r['q'] for r in data['directions']['transfers']] + response = full_response(matching, small, q) + need(response == rows(payload['response']), 'Actual merged full112 matrix') + selected = payload['selected_ports'] + ordinary = payload['ordinary_ports'] + need(selected == matching['selected_ports'] and ordinary == sorted(set(range(112))-set(selected)), 'Exact selected partition') + L, H = restrict(response, selected), restrict(response, ordinary) + Linv, Hinv = rows(payload['selected_inverse']), rows(payload['ordinary_inverse']) + need(L == rows(payload['selected_block']) == rows(matching['selected_block']), 'Unchanged selected block') + for matrix, inverse in ((L, Linv), (H, Hinv)): + for p in range(len(matrix)): + unit = {p: F(1)} + need(apply(matrix, apply(inverse, unit)) == apply(inverse, apply(matrix, unit)) == unit, 'Both principal inverse orders') + need(all(c.denominator & (c.denominator-1) == 0 for matrix in (Linv, Hinv) for row in matrix for c in row.values()), 'Exact dyadic principal inverses') + frame_cache, verified, reports = {}, set(), {} + + def frame(vectors): + key = tuple(vectors) + if key not in frame_cache: + frame_cache[key] = phase.frame(key) + return frame_cache[key] + + for provider, words in payload['providers'].items(): + source = data['clean']['providers'][provider]['canonical'] + need(source['ports'] == q, 'Provider and independent actual port directions agree') + reports[provider] = {} + for direction, word in words.items(): + backward = direction == 'backward' + report = ledger(word, source, matching, small['providers'][provider][direction], response, backward) + phase.equal(frame(word['frames'][0]), [], 'Actual I frame') + phase.equal(frame(word['frames'][1]), phase.fourier(9), 'Actual FULL frame') + for key, record in word['native_recipes'].items(): + old, new = map(int, key.split(':')) + identity = (tuple(word['frames'][old]), tuple(word['frames'][new]), json.dumps(record, sort_keys=True)) + if identity not in verified: + phase.equal(phase.recipe(record), phase.adjoint(frame(word['frames'][old]))+frame(word['frames'][new]), 'Complete native edge '+key) + verified.add(identity) + endpoints = word['endpoint_adapters'] + need(len(endpoints) == 224 and {(r['role'], r['port']) for r in endpoints} + == {(role, p) for role in ('source', 'target') for p in range(112)}, 'All224 endpoint records') + for record in endpoints: + p, role = record['port'], record['role'] + f = word['start'][p] if role == 'source' else word['final'][112+p] + need(record['rank'] == 0 and record['frame'] == f, 'Exact endpoint rank and frame') + conventional = [('C', q[p], 1)] if role == 'source' else [('C', q[p], -1)]+phase.fourier(9) + identity = ('endpoint', role, q[p], tuple(word['frames'][f]), json.dumps(record, sort_keys=True)) + if identity not in verified: + phase.equal(phase.recipe(record), phase.adjoint(conventional)+frame(word['frames'][f]), 'Ordered endpoint '+role+' '+str(p)) + verified.add(identity) + report['native_recipe_records'] = len(word['native_recipes']) + reports[provider][direction] = report + print(provider, direction, 'all632 columns and full phases PASS', flush=True) + if provider == 'base' and not backward: + need(response != rows(matching['response']) + and reverse(word['events']) != expected(rows(matching['response']), False), 'The old64 Hadamard response is not substituted for the new permutation') + mutation = json.loads(json.dumps(word['events'])) + cut = word['transfer_cuts'][0]['add_event'] + mutation[cut][1][-2] *= -1 + need(reverse(mutation) != expected(response, False), 'Wrong matching sign is rejected') + large = set(matching['large_ports']) + undo_first = max(i for i, e in enumerate(word['events'][:word['inherited_64_first_event']]) + if e[0] == 'native' and e[1] in large and e[3] == 1)+1 + undo_last = next(i for i in range(undo_first, len(word['events'])) if word['events'][i][0] == 'native') + need(all(e[0] == 'scalar' for e in word['events'][undo_first:undo_last]) and undo_last > undo_first, 'Complete pair undo segment') + need(reverse(word['events'][:undo_first]+word['events'][undo_last:]) != expected(response, False), 'Omitted source and target pair undo is rejected') + first = next(iter(word['native_recipes'].values())) + wrong = json.loads(json.dumps(first)) + wrong['left']['phase'] = (wrong['left']['phase']+1) % 4 + try: + phase.equal(phase.recipe(wrong), phase.recipe(first), 'Wrong global phase') + except ValueError as error: + need('reference state' in str(error), 'Global phase mutation passes Pauli action but fails exact state') + else: + raise ValueError('A wrong global phase was accepted') + result = {'status': 'PASS_INDEPENDENT_FULL_MATCHED_NATIVE', 'producer_pins': PINS, + 'input_pins': {name: pin for name, (_, pin) in INPUTS.items()}, + 'phase_interpreter_sha256': PHASE_PIN, 'matching_matrix_peer_freeze_sha256': PEER_PIN, + 'full_response_symmetric_involution': True, 'both_dyadic_principal_inverse_orders': True, + 'distinct_native_and_endpoint_phase_checks': len(verified), 'providers': reports, + 'method': 'Independent reverse columns; separate prefix frame and norm ledger; explicit mode routing; new direct Pauli and Gaussian-state interpreter, with no producer imports.', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope': 'Complete full112 native data shears and exact exterior. Helper native progress, recursive hosting, routed controller, terminal, full precision, and supplier cost remain separate.'} + (HERE/'CHECKS.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/RAW-SELECTED-FORWARD.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/RAW-SELECTED-FORWARD.md new file mode 100644 index 0000000000..0e1487bde8 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/RAW-SELECTED-FORWARD.md @@ -0,0 +1,120 @@ +# Forward queries through a physical selected exchange + +Two physical selected exchanges expose a dense ordinary query in the +selected completed X fields. They preserve the selected Y contents. The +retained clean-J forward core supplies all native work in the basic +variant. A second variant uses eight inverse line copies to remove one +selected-Y term from the ordinary output. + +This is a local mechanism with an explicit operator code. It is not the +record-free lower-unit F_L map. The selected X code and ordinary Y code +must be handled by a complete controller. No complete supplier or kappa +claim is made. + +## Exact maps + +Use the same selected set A, ordinary set U, matrices B and D, and native +Q_A operators as in `RAW-SELECTED-BACKWARD.md`. In particular, + +```text +J = [[0,-B],[-D,I-DB]], BD=13I. +``` + +First exchange physical selected X and Y. Execute the unchanged clean-J +forward core. Then exchange physical selected X and Y again, at its full +output boundary. At input the exchange has logical action +`(x_A,y_A)->(Q_A^-1 y_A,Q_A x_A)`. At output it has the same logical +cross operators because X has operator F and Y has operator `F Q_A^-1`. +The exact resulting map is + +```text +X_A' = x_A-Q_A^-1 B x_U, +X_U' = x_U, +Y_A' = y_A, +Y_U' = y_U+(I-DB)x_U-D Q_A^-1 y_A. +``` + +Both physical exchanges use three unit ADDs and one negative SCALE per +selected port. They do not claim that unequal logical frames are equal. +Their physical common-address operations retain the displayed Q operators. + +For the second variant, before the input exchange add +`D Q_A^-1 y_A` to ordinary Y. Form each inverse selected line in the one +owned C0 array, scatter its D column, then clear C0. The result is + +```text +X_A' = x_A-Q_A^-1 B x_U, +X_U' = x_U, +Y_A' = y_A, +Y_U' = y_U+(I-DB)x_U. +``` + +No Q operator is commuted through B or D in either derivation. + +The second map is a unit on all inputs. It has the content inverse + +```text +x_U = X_U', +x_A = X_A'+Q_A^-1 B X_U', +y_A = Y_A', +y_U = Y_U'-X_U'+D B X_U'. +``` + +Here `B X_U'` can be formed from completed FULL X. The displayed inverse +still needs native placement for its inverse line and for the ordinary +Y scatter. The content formula alone is not a paid decoder. + +## What becomes possible + +The fixed monotone forward paths cannot send original x_p to its matching +ordinary Y_p. This construction crosses the logical frame classes with +physical selected exchanges. The same retained forward core now puts +`Q_A^-1 B x_U` into selected X, relative to its previous selected X value. +There is no separate native read of all 104 ordinary source fields. + +This is a reusable local interface: a controller can carry the selected X +code and the ordinary rank-eight response together. The raw backward word +in this directory carries original selected X into productive Y. Their +coded variants use 16 new rank-one children per pair. A controller must +prove that their final codes can be removed within the full budget. No +such complete controller is proved in this packet. + +## Local invoice and verification + +The raw variant has 202,554 real scalar primitives and native mass 5,522. +It adds no native child. The coded variant has 206,762 real scalar +primitives and native mass 5,530. It adds eight rank-one children and +sixteen monomial wrappers. Both restore all 480 arbitrary helper inputs +and clear the eight owned private outputs. C0 is the only new copy target. + +Run + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/emit_raw_selected_forward.py +``` + +The first line is + +```text +PASS_RAW_SELECTED_FORWARD_LOCAL_OPERATOR +``` + +The checker pins and uses the ordered-operator interpreter from the raw +backward packet. It replays both variants on all 712 formal input columns +through every retained scalar event and checks the inherited frame ledger. +It checks the explicit inverse and four mutation controls. It also checks +all 8,192 signed line basis columns with exact Gaussian coefficients. +The complete unchanged core native proof is inherited. A new full physical +Gaussian replay of the old core is not claimed. + +`RAW-SELECTED-FORWARD.json` pins the interpreter, source matrices, original +core, recipe packet, emitter, and complete local payload. Actual inter-call +views, new child hosting, the global controller, and the full recursive +scalar, storage, and precision invoice remain open. An independent review +is required before this local packet is used as an accepted dependency. + +This construction follows the raw selected backward exchange proposed by +the coordinating and native-escape lanes. It uses the prior clean-J and +exact native recipe packets. Research and verification used OpenAI Codex +under the user's direction. No independent human review is claimed. No +publication is authorized. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/ZERO-LINE-BACKWARD.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/ZERO-LINE-BACKWARD.md new file mode 100644 index 0000000000..493fae13a6 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/ZERO-LINE-BACKWARD.md @@ -0,0 +1,107 @@ +# A raw selected backward local with no new native lines + +## Result + +This local uses the raw selected swap and the clean backward core from +`RAW-SELECTED-BACKWARD.md`. It omits the eight-line input correction. It has +native mass 5522 and scalar cost 206506 under the inherited core invoice. +It is a changed encoding of the two data banks. It is not the lower-unit +local from the selected-source retirement theorem. + +The endpoint conventions are unchanged. At input the physical data are +`X_p = Q_p x_p` and `Y_p = y_p`. At output they are `X_p = F x'_p` and +`Y_p = F Q_p^-1 y'_p`. The common full operator F commutes with each Q_p. +No proof step moves Q through B or D. + +Let A be the eight selected ports, and let U be the 104 other ports. Write +`x = (a,u)`, `y = (b,v)`, and `r = Q_A^-1 b`. The exact logical map is + +```text +X_A = r + B_s v +X_U = u - v - D_s r + D_s Q_A a +Y_A = Q_A a +Y_U = v. +``` + +The physical selected Y bank is therefore `F a`. It holds the original +selected X in the full frame. The coefficient of r in selected X is +1. +There is no factor 12 to invert. + +## Circuit + +At each selected port, swap the physical X and Y arrays. Use three ADDs +and one negative SCALE. Execute the unchanged clean backward core. Then +apply the scalar lower shear `L(-D_s)` to completed full X. No new native +line is used. + +A physical swap between the input arrays is not a scalar swap in their +logical coordinates. It sends `(x_A,y_A)` to +`(Q_A^-1 y_A,Q_A x_A)`. This distinction is required for the formula above. + +The scalar cost is 202138 for the core, 208 for the swaps, and 4160 for +the lower shear. The native cost is the inherited 5522. All 480 arbitrary +helper arrays return to their inputs. The eight owned private arrays +return to zero. + +## Inverse and use by a controller + +The map has the following exact inverse: + +```text +v = Y_U +r = X_A - B_s Y_U +b = Q_A r +c = Y_A +a = Q_A^-1 c +u = X_U + Y_U + D_s r - D_s c. +``` + +This is a unit encoding. It requires no division by 12 or 13. The formula +does not give a free physical inverse: the displayed `B_s Y_U` query is +still over different hole frames. + +A later controller may know v in a completed full bank. In that case the +selected source b can be recovered from completed X as `Q_A(X_A-B_s v)`. +This needs eight positive native lines, with their copy and scatter costs. +If a subsequent corrected raw forward local changes selected X by +`-Q_A^-1 B_t k`, the formula becomes + +```text +b = Q_A (X_A - B_s v) + B_t k. +``` + +This identity preserves operator order. A controller must prove where it +obtains v and k in the full frame, and must restore all other data and +borrowed state. The local result does not prove that controller. + +## Check and scope + +Run: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/check_zero_line_backward.py +``` + +Expected status: + +```text +PASS_ZERO_LINE_BACKWARD_LOCAL_OPERATOR +``` + +The checker pins and replays the literal core and boundary events. It +checks all 712 formal input columns with ordered Q operator words. It +cancels only adjacent inverse pairs on the same port. It checks the +arbitrary-helper and private-zero contracts, the selected physical output, +the selected-source inverse, the exact local invoice, and three negative +controls. The full physical core proof is inherited from the pinned core. +No native line is added by this variant. + +Independent review, actual inter-call views, the global controller, and +the complete recursive and owner invoice remain open. This note gives no +new complete kappa value. + +This result uses the centre-free core, the raw selected exchange, and the +selected-source retirement work. The zero-line variant and its use in +selected-source recovery were identified in the coordinated controller +follow-through. The source packet and checker pins are in +`ZERO-LINE-BACKWARD.json`. This work was produced with AI assistance. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/BALANCED-FIVE-MINOR-RECEIPT.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/BALANCED-FIVE-MINOR-RECEIPT.json new file mode 100644 index 0000000000..630b6b5fdd --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/BALANCED-FIVE-MINOR-RECEIPT.json @@ -0,0 +1,155 @@ +{ + "status": "PASS_PR3133_BALANCED_FIVE_MINOR_WORDS", + "selected_ports": 40, + "ordinary_ports": 72, + "factorization_events": 776, + "factorization_scalar_real_primitives": 7744, + "factorization_private_fields": 0, + "factorization_native_children": 0, + "fused_upper_extra_scalars": 1600, + "providers": { + "base": { + "programs": { + "balanced_backward": { + "all_formal_input_columns": 640, + "arbitrary_helpers_restored": 408, + "owned_private_zero": 8, + "private_zero_buffers_restored": 91, + "core_scalar_frame_checks": 18080, + "core_warp_events": 240, + "scalar_real_primitives": 173312, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_rank_mass": 5073, + "native_children": 3507, + "new_native_children": 0, + "new_private_fields": 0 + }, + "diagonal_backward": { + "all_formal_input_columns": 640, + "arbitrary_helpers_restored": 408, + "owned_private_zero": 8, + "private_zero_buffers_restored": 91, + "core_scalar_frame_checks": 18080, + "core_warp_events": 240, + "scalar_real_primitives": 174912, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_rank_mass": 5073, + "native_children": 3507, + "new_native_children": 0, + "new_private_fields": 0 + }, + "balanced_forward": { + "all_formal_input_columns": 640, + "arbitrary_helpers_restored": 408, + "owned_private_zero": 8, + "private_zero_buffers_restored": 91, + "core_scalar_frame_checks": 18080, + "core_warp_events": 240, + "scalar_real_primitives": 174352, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_rank_mass": 5073, + "native_children": 3507, + "new_native_children": 0, + "new_private_fields": 0 + } + }, + "controls": { + "missing_backward_unit_factor": true, + "missing_forward_unit_factor": true + } + }, + "extra": { + "programs": { + "balanced_backward": { + "all_formal_input_columns": 640, + "arbitrary_helpers_restored": 408, + "owned_private_zero": 8, + "private_zero_buffers_restored": 91, + "core_scalar_frame_checks": 18080, + "core_warp_events": 240, + "scalar_real_primitives": 173312, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_rank_mass": 5073, + "native_children": 3507, + "new_native_children": 0, + "new_private_fields": 0 + }, + "diagonal_backward": { + "all_formal_input_columns": 640, + "arbitrary_helpers_restored": 408, + "owned_private_zero": 8, + "private_zero_buffers_restored": 91, + "core_scalar_frame_checks": 18080, + "core_warp_events": 240, + "scalar_real_primitives": 174912, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_rank_mass": 5073, + "native_children": 3507, + "new_native_children": 0, + "new_private_fields": 0 + }, + "balanced_forward": { + "all_formal_input_columns": 640, + "arbitrary_helpers_restored": 408, + "owned_private_zero": 8, + "private_zero_buffers_restored": 91, + "core_scalar_frame_checks": 18080, + "core_warp_events": 240, + "scalar_real_primitives": 174352, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20 + }, + "native_rank_mass": 5073, + "native_children": 3507, + "new_native_children": 0, + "new_private_fields": 0 + } + }, + "controls": { + "missing_backward_unit_factor": true, + "missing_forward_unit_factor": true + } + } + }, + "payload_sha256": "a16521b290c39468fa491e1da10e5d5ffe6869226563a02ac8146a4feaca0afe", + "checker_sha256": "3a0674bff49f6e333f8123460ef9caaffb126dacfd34b21255241a4c882d24c3", + "source_pins": { + "core": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "native_replay": "a07cf4894a2599993006c7b99e6cb62146ece82f2ae6df72a28100ccb3a689bc" + }, + "scope": "Six complete local native words. No new native children or private fields. All 640 formal columns and all 91 zero buffers are checked. Inter-call H_t H_s^-1 decoding, global owner hosting, complete precision, and complete kappa cost remain open." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/BALANCED-FIVE-MINORS.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/BALANCED-FIVE-MINORS.md new file mode 100644 index 0000000000..7f0e5bef29 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/BALANCED-FIVE-MINORS.md @@ -0,0 +1,200 @@ +# Five-minor encoding on the new native core + +The actual PR3133 core has a forty-field selected set for which the +ordinary borrowed-state block is a dyadic unit. That block and its inverse +can be applied in place. They need no new private field or recursive +child. The resulting backward word carries all forty selected X inputs +into productive selected Y. An optional upper shear makes the borrowed-Y +response diagonal. The corresponding original-X response is also a +dyadic unit. + +These are complete local words. A controller must still bind their +operator codes and views. No complete supplier or kappa gain is claimed. + +## The actual matrices + +Use the source matrix R, K=R^T/4, and J=I-KR. The pinned core has +RK=14I. Select the union S of these five eight-port minors: + + [0,7,20,27,36,46,57,111] + [21,37,47,76,81,87,92,110] + [1,6,22,28,33,49,58,109] + [2,9,14,19,88,95,101,106] + [3,8,15,18,89,94,102,105] + +Let U be the remaining 72 ports. Each listed minor has R_A K_A=I. +The exact ordinary Gram matrix is R_U K_U=9I. Thus + + H = J_UU = I-K_U R_U, + H^-1 = I-K_U R_U/8. + +This H is the ordinary data block. It is not the helper-debt matrix +called H in the earlier clean-J proof. + +## An in-place unit factorization + +Use the retained minor A=`[4,11,12,17,90,97,99,104]` inside U. Write +U=A union W. Set L=K_A R_W and M=K_W R_A. Both matrices have 256 nonzero +entries, each equal to 1/2 or -1/2. Define + + T(a,w)=(a+Lw,w). + +Then + + H = T^-1 [[-8I,0],[-M,I]] T. + +To apply H, perform these steps in order: + + a += Lw; w -= Ma; a *= -8; a -= Lw. + +To apply H^-1, reverse the steps and invert each step: + + a += Lw; a *= -1/8; w += Ma; a -= Lw. + +Every shear has disjoint source and target sets. Each SCALE is a dyadic +unit. These operations preserve all information and use no scratch. +Each complete factor has 768 ADDs and eight SCALEs. Its cost is 7744 real +scalar primitives under the source price rule. + +For the optional upper shear, insert + + x_S += K_S R_A a + +after the -1/8 SCALE in H^-1, before either restore shear. At this point +the pivot a equals K_A R_U times the final ordinary output. The inserted +step therefore implements x_S += K_S R_U x_U after H^-1. It has 160 +nonzero half-unit ADDs and costs 1600 scalar primitives. The pivot is a +live temporary query, not a saved query from a previous invocation. The +checker rejects the same short scatter after the pivot has been restored. + +## Local endpoint maps + +Write input x=(a,u), y=(b,v), in S,U order. Let Q be the diagonal positive +line operator on S and q=Q^-1. Physical input X is Q_p x_p on each port; +input Y is y. At output, physical X is F x' and physical Y is +F Q_p^-1 y', with common full operator F. No Q is commuted through a +dense matrix. + +The balanced backward word first exchanges selected physical X and Y, +runs the complete clean-J backward core, and applies H^-1 to full-frame +ordinary X. Its map is + + X_S' = q b - J_SS Q a - J_SU v, + X_U' = H^-1 u - v - H^-1 J_US Q a, + Y_S' = Q a, + Y_U' = v. + +Add the fused upper shear to obtain the diagonal-borrowed variant. With +c=R_S Q a+R_U u, its map is + + X_S' = q b - Q a - K_S c/8, + X_U' = u - v - K_U c/8, + Y_S' = Q a, + Y_U' = v. + +The borrowed-Y block in X is diag(q,-I). Physical selected Y is exactly +F a in both backward variants. It contains the original selected X input. + +The balanced forward word first applies H to ordinary input Y. It then +exchanges selected X and Y, runs the complete clean-J forward core, and +exchanges selected physical X and Y again. Its map is + + X_S' = a + q J_SS q b + q J_SU u, + X_U' = u, + Y_S' = b, + Y_U' = H(u+v) + J_US q b. + +The H input step acts on fields at I. The inverse and fused upper steps +act on full-frame X. They do not need line transforms, wrappers, helper +access, or private storage. Each physical exchange uses three unit ADDs +and one negative SCALE. It operates on the same physical addresses and +does not identify different logical frames. + +## The stronger content unit + +For the diagonal-borrowed backward word, put E=diag(-I_S,I_U). Apart +from the explicit input Q on S, its original-X response is + + A = E - KR/8, + A^-1 = E + E K R E/4. + +Both matrices are dyadic. The determinant is 1/256. The checker verifies +both inverse orders on all 112 columns of the actual source matrix using +integer numerator matrices. This is a content inverse; its placement in +a native controller is a separate obligation. + +More generally, select k complete orthogonal minors. Then the ordinary +block is H_k=I-K_U R_U, with R_U K_U=(14-k)I. For k different from 13, + + H_k^-1 = I + K_U R_U/(k-13). + +The same pivot factor uses the SCALE 1/(k-13). For k=5,9,11,12 this is a +dyadic unit. Five is the first positive number of complete selected +minors with this property. This statement concerns that minor family; +it does not rule out other selections or exact rational arithmetic. + +The diagonal-borrowed original-X response is + + A_k = E + KR/(k-13), + det(A_k) = det(E) ((1-k)/(k-13))^8. + +For k=5 the inverse above is a dyadic unit. For k=1, the X response has +an eight-dimensional kernel even over the rationals: the columns of EK +span it. The complete two-register backward map is still a unit because +selected Y retains selected X. Thus rational division removes the +ordinary-block restriction at k=1, but it does not give an invertible +X response there. This distinction may affect the controller design. + +For k different from 1 and 13, the general content inverse is +`A_k^-1=E+E K R E/(k-1)`. Within this complete-minor family, k=5 and k=9 +give both a dyadic ordinary-block unit and a dyadic X-response unit. +The cases k=11 and k=12 give an ordinary-block unit, but their X-response +determinants are 5^8 and 11^8. They are not dyadic units. + +## Complete local invoice and checks + +| Word | Scalar primitives | Native rank mass | Native children | +| --- | ---: | ---: | ---: | +| Balanced backward | 173312 | 5073 | 3507 | +| Diagonal-borrowed backward | 174912 | 5073 | 3507 | +| Balanced forward | 174352 | 5073 | 3507 | + +Each row includes the full 164514-scalar clean-J core, all physical +exchanges, all unit factors, and the 14-scalar final cleanup of C1 through +C7. The native profile is `{1:2433,2:724,3:228,4:102,5:20}` in every row. +No new native child, wrapper, or private field is added. + +The emitter checks all six words, on both source providers. It replays +all 632 arbitrary live inputs, eight arbitrary owned inputs, and 91 +private zero buffers. All 408 helpers restore; all owned fields and +zero buffers return to zero. The literal native core, scalar frames, +warp order, and zero-buffer lifetimes are checked. Q, K, and dual-K +remain separate ordered symbols. Only adjacent exact inverses cancel. +The source phase dependency uses the independently reviewed fresh native +recipes and the separate literal dual-warp tables. + +Run with one process: + + python3 -I -B emit_balanced_five_minors.py + python3 -I -B check_five_minor_unit.py + +The two receipts record exact input and output hashes. Independent review +of this extension is still required. The decoder H_t H_s^-1 between +successive views, exterior phase, owner hosting, full recursive precision, +and the complete supplier bill remain open. + +## Sources and credit + +The source words, contributor credit, and commit-pinned links are in +`CLEAN-J-TRANSFER.md`. The selected minor partition and balanced endpoint +mechanism were developed in `lanes/native-escape-20261017` with the +coordinating and controller lanes. This lane independently derived the +pivot factor, fused the upper shear, and transferred the mechanism onto +the changed source geometry. The native-escape source packet is +`RAW-MINOR-SUBSETS.md`, with proof SHA256 +`65c63ed233fd34dbc163b1c98f7c0c80533760656fac7d21acc1d47c995e3e08`. +Its program payload has decompressed SHA256 +`10ec46ba44ed7bf7deeec98333c03e358b777898cb6642091e758afabd6e8a3d`. +OpenAI Codex assisted this work. No human +review or maintainer selection is claimed. No PR, push, or publication +commit was made. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/INTERFACE.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/INTERFACE.json new file mode 100644 index 0000000000..75c32b9d97 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/INTERFACE.json @@ -0,0 +1,858 @@ +{ + "R": [ + { + "0": "1", + "92": "1", + "87": "1", + "7": "1", + "76": "1", + "57": "1", + "81": "1", + "27": "1", + "70": "1", + "63": "1", + "90": "1", + "10": "1", + "71": "1", + "62": "1", + "11": "1", + "91": "1", + "72": "1", + "61": "1", + "25": "1", + "79": "1", + "2": "1", + "94": "1", + "9": "1", + "89": "1", + "12": "1", + "103": "1", + "56": "1", + "38": "1", + "100": "1", + "17": "1", + "77": "1", + "31": "1", + "101": "1", + "18": "1", + 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"303": "-2" + } + ], + "ports_equal_previous": true, + "source_cut_sha256": { + "base": "49bdc172f1f53253c15fa4bf5be2d5741701d2fe9d18943f8b79c3ded0b96a3e", + "extra": "34af6f955bf8d95f68868cc282fa739532a5a6117df50d753fd996d44cea6731" + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/NATIVE-LIFT.md b/research/ordered-centre-interfaces/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/ordered-centre-interfaces/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/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/RAW-REVIEW.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/RAW-REVIEW.json new file mode 100644 index 0000000000..a8f16c0678 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/RAW-REVIEW.json @@ -0,0 +1,120 @@ +{ + "actual_Q_B_noncommutation_witness": { + "B_entry": "1/2", + "Gaussian_denominator": 2, + "basis_input": 0, + "ordinary_direction": 19, + "ordinary_port": 1, + "selected_direction": 11, + "selected_port": 0 + }, + "boundary_access": "Boundary ADDs are actual common-address operations on physical data arrays. They do not identify unequal logical frames. The coded endpoint formulas keep those operators explicitly.", + "checker_sha256": "c6ba81bd2e382e021b2c2ea853f75576dc101400a7cce3408003fe365c7e7bef", + "core": { + "backward": { + "exact_input_columns": 712, + "native_mass": 5522, + "profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82 + }, + "scalar_cost": 202138, + "scalar_events": 20089 + }, + "forward": { + "exact_input_columns": 712, + "native_mass": 5522, + "profile": { + "1": 2412, + "2": 418, + "3": 432, + "4": 142, + "5": 82 + }, + "scalar_cost": 202138, + "scalar_events": 20089 + } + }, + "data_endpoint_frame_checks": 448, + "inherited_native_review_sha256": "61b3990c983b96b8bff01feab8c83a612ea41612b948b1059186ce9ffa9692ea", + "input_manifest_sha256": "b487cfd991808af629abbd1132dfa9de8d09ff82bccc102c30139540d508258e", + "method": "Reverse transpose accumulation of the retained scalar core, followed by matrix composition over a free group algebra of the Q operators. No producer code is imported.", + "negative_controls": { + "actual_native_Q_through_B_counterexample": true, + "move_Q_through_dense_B": true, + "omit_B8_input_code": true, + "omit_B_input_swap": true, + "omit_B_output_lower_shear": true, + "omit_F_output_swap": true, + "replace_physical_swap_by_logical_swap": true, + "wrong_inverse_line_sign": true + }, + "not_claimed": [ + "Actual inter-call controller or decoder", + "New child hosting", + "Complete recursive scalar, storage, and precision invoice", + "New kappa" + ], + "not_repeated": [ + "Full old-core Clifford recipe sweep", + "Full 712-array physical Gaussian operator replay" + ], + "seconds": 3.9096893329988234, + "signed_line_checks": { + "F_commutation_checks": 16, + "all_basis_columns": 8192, + "independent_Pauli_and_zero_state_checks": 16, + "signed_recipes": 16 + }, + "status": "PASS_INDEPENDENT_RAW_SELECTED_LOCAL_REVIEW", + "variants": { + "B0": { + "all_input_columns": 712, + "data_inverse_columns": 224, + "helpers_restored": 480, + "native_mass": 5522, + "new_rank_one_children": 0, + "owned_private_zero": 8, + "scalar_cost": 206506 + }, + "B16": { + "all_input_columns": 712, + "data_inverse_columns": 224, + "helpers_restored": 480, + "native_mass": 5538, + "new_rank_one_children": 16, + "owned_private_zero": 8, + "scalar_cost": 214922 + }, + "B8": { + "all_input_columns": 712, + "data_inverse_columns": 224, + "helpers_restored": 480, + "native_mass": 5530, + "new_rank_one_children": 8, + "owned_private_zero": 8, + "scalar_cost": 210714 + }, + "F0": { + "all_input_columns": 712, + "data_inverse_columns": 224, + "helpers_restored": 480, + "native_mass": 5522, + "new_rank_one_children": 0, + "owned_private_zero": 8, + "scalar_cost": 202554 + }, + "F8": { + "all_input_columns": 712, + "data_inverse_columns": 224, + "helpers_restored": 480, + "native_mass": 5530, + "new_rank_one_children": 8, + "owned_private_zero": 8, + "scalar_cost": 206762 + } + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/RAW-REVIEW.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/RAW-REVIEW.md new file mode 100644 index 0000000000..cba3b07126 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/RAW-REVIEW.md @@ -0,0 +1,166 @@ +# Independent review of the raw selected local maps + +The five local maps pass this review. No material error was found in their +formulas, physical exchanges, new line recipes, or stated local invoices. +The accepted scope is a local map on the declared input and output arrays. +There is no accepted global controller, decoder, owner allocation, or new +complete kappa value in this result. + +| Variant | Added rank-one children | Native mass | Real scalar bound | +| --- | ---: | ---: | ---: | +| B0: no input line correction | 0 | 5522 | 206506 | +| B8: input line correction | 8 | 5530 | 210714 | +| B16: input and ordinary-output corrections | 16 | 5538 | 214922 | +| F0: raw forward exchange | 0 | 5522 | 202554 | +| F8: coded forward exchange | 8 | 5530 | 206762 | + +These bounds count the literal non-child scalar operations and the native +rank profile. They are not a complete recursive cost calculation. Child +hosting, actual inter-call views, final code removal, storage, and precision +remain separate obligations. + +## Independent method + +`check_raw_selected.py` does not import a producer checker or emitter. It +reads the frozen event packets and checks that each retained core is the +byte-exact old centre-free core. It reconstructs that core by a reverse +transpose calculation. Starting with every output covector, it passes +through the scalar events in reverse order. An event `t += c s` changes +the source covector by `w_s += c w_t`. An owned clear deletes the target +covector. This method computes every input column of the local linear map. + +The result on all 712 input columns is exactly + + F_core: (x,y,h) -> (x,y+Jx,h), + B_core: (x,y,h) -> (x-Jy,y,h), + +with all eight owned private outputs zero. The checker derives +`J=I-R^T R/4` directly from the pinned source matrix. It verifies the block +identities `J_AA=0`, `J_AU=-B`, `J_UA=-D`, `J_UU=I-DB`, and `BD=13I`. + +The checker then composes the physical boundary tapes with the reconstructed +matrix over a free group algebra. Each Q_p and Q_p inverse is a distinct +formal operator. Reduction cancels only adjacent inverse letters. It does +not commute two Q operators or move a Q operator through B or D. Equality +in this algebra proves the displayed local formulas for every substitution +of invertible operators. In particular, it applies to the actual native Q +operators once their physical recipes are checked. + +Every variant is checked on all 712 input columns. Its data inverse is +also checked on all 224 data columns. All 480 logical helper values are +unchanged under the inherited native endpoint and wrapper contract. The +new boundaries never touch a helper. The retained physical residual child +progress on helpers is not an identity on unframed arrays; the review does +not make that different claim. + +## Actual physical coordinates + +The input convention is `X_p=Q_p x_p`, `Y_p=y_p`. The output convention is +`X_p=F x'_p`, `Y_p=F Q_p^-1 y'_p`. The review checks all 448 data endpoint +frame declarations in the canonical word. It also checks every retained +scalar frame, every native nested-subspace transition, and every ordinary +and residual adapter endpoint. + +A physical selected exchange therefore sends + + (x_A,y_A) -> (Q_A^-1 y_A,Q_A x_A). + +The literal three ADDs and one negative SCALE implement the exchange on +arbitrary arrays. They do not equate the two logical frame labels. The +checker rejects a replacement by a logical swap. At the final boundary, +the same physical exchange has the same two cross operators after the +common F factor is removed. + +Each Q_p is a linear combination of the identity and the translation X_qp. +The full F is a product of such coordinate translation operators. Thus F +commutes with every Q_p and its inverse. The separate native interpreter +also verifies this equality, including global phase, for all 16 signed +selected line classes. This is the only commutation needed to remove the +common F factor. No proof step moves Q through a port mixing matrix. + +The boundary ADDs act at common physical addresses of the local arrays. +Their resulting operator code is retained in the formulas. This establishes +a physical local array operation with an encoded interface. It does not +establish that a proposed outer controller supplies or consumes these +views at its actual call sites. + +## Accepted formulas + +Write `x=(a,u)`, `y=(b,v)`, and `r=Q_A^-1 b`. The B0 map is + + X_A = r+Bv, + X_U = u-v-Dr+DQ_A a, + Y_A = Q_A a, + Y_U = v. + +For B8 the map is + + X_A = Bv-12r, + X_U = u-v+DQ_A a, + Y_A = Q_A a, + Y_U = v-Dr. + +B16 has the same selected and Y outputs as B8, with `X_U=u-v`. In all +three backward variants, physical selected Y is exactly `F a`. + +Both forward variants have + + X_A = a-Q_A^-1 Bu, + X_U = u, + Y_A = b. + +F0 has `Y_U=v+(I-DB)u-DQ_A^-1 b`. F8 has `Y_U=v+(I-DB)u`. + +The inverse checks do not divide by 12 or 13. For B8 and B16, +`r=X_A-BY_U` and `v=Y_U+Dr`. For B0, `r=X_A-BY_U` and `v=Y_U`. +The other data follow by the stated signed Q and scalar operations. +These are content inverses. In particular, the `B Y_U` query may span +different physical hole frames. The algebraic inverse is not a free +native decoder. + +## New line kernels and verification boundary + +The review pins the 16 signed line recipes from the earlier uniform-signed +packet. A separate Pauli and exact Gaussian state interpreter checks each +recipe against the intrinsic signed C_q operator. A second decoder applies +both serialized monomial wrappers, their affine addresses, translations, +quadratic terms, linear phases, and global phases to every basis input. +It compares all 8192 signed basis columns exactly. A wrong global phase +is rejected. + +The retained core's full native phase proof is inherited from the pinned +`NATIVE-LIFT-REVIEW.json`, with SHA256 +`61b3990c983b96b8bff01feab8c83a612ea41612b948b1059186ce9ffa9692ea`. +That receipt binds the exact core payload used here. This review repeats +the full scalar map and frame ledger. It does not repeat the old Clifford +recipe sweep or construct a dense physical operator on 712 arrays. + +The controls also reject an omitted input code, an omitted lower shear, +an omitted physical swap, a wrong inverse-line sign, an omitted output +swap, and movement of Q through B. The last control has an actual native +counterexample: the selected and ordinary line directions give different +translated support on spatial basis input zero. The receipt records the +ports and the nonzero B entry. + +## Inputs and reproduction + +The reviewed producer files are the frozen raw-selected backward, forward, +and zero-line backward packets in `../native-escape-20261017`. Their source +proofs and checkers are pinned in `RAW-REVIEW-INPUTS.json`. The retained +core, canonical word, source matrix, prior native review, signed-line +packet, and independent spatial decoder are also pinned there. + +Run from the workspace root: + + python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/check_raw_selected.py + +Expected final status: + + PASS_INDEPENDENT_RAW_SELECTED_LOCAL_REVIEW + +The result is in `RAW-REVIEW.json`. `RAW-REVIEW-FREEZE.json` pins this proof, +the checker, the input manifest, and the result. The native-escape lane, +the coordinating lane, and the prior centre-free and uniform-signed lanes +supplied the constructions. This lane supplied the separate review. +Research and review used OpenAI Codex under the user's direction. No human +or maintainer review is claimed. No PR, push, or publication commit was made. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/SOURCE-PINS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/SOURCE-PINS.json new file mode 100644 index 0000000000..c3df9a69e7 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/SOURCE-PINS.json @@ -0,0 +1,10 @@ +{ + "source_commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "source_sha256": { + "bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce", + "bw_check_recipes.py": "d600b959a0ac462dc28deb8c0d5d8f9e0c76d7f7d7b6f92a296c5ef9e0a1de19", + "bw_gauss.py": "0884b14d6d77cde419a3c773ad9b21d0d18de1e6e20e6b6d5add458ed32ba4cb", + "bw_phases.py": "9d1a620e26715f4c42fd0347ecc14ef5a4a9031867869b64e8bae4d8526a821e", + "vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/base/CLIFFORD-RECIPES.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/base/CLIFFORD-RECIPES.json new file mode 100644 index 0000000000..fed4d40157 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/base/CLIFFORD-RECIPES.json @@ -0,0 +1 @@ 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b/research/ordered-centre-interfaces/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 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"7": 112, + "8": 64 + }, + "real_scalar_primitives": 3032, + "top_level_max_array_l2_amplification_bound": "6" + }, + "forward": { + "all_input_columns": 632, + "arbitrary_untouched_helpers": 408, + "endpoint_map_count": 224, + "extra_query_children": 0, + "native_children": 432, + "native_mass": 1792, + "native_recipe_count": 384, + "native_side_map_bound": 864, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "real_scalar_primitives": 3032, + "top_level_max_array_l2_amplification_bound": "6" + } + }, + "extra": { + "backward": { + "all_input_columns": 632, + "arbitrary_untouched_helpers": 408, + "endpoint_map_count": 224, + "extra_query_children": 0, + "native_children": 432, + "native_mass": 1792, + "native_recipe_count": 384, + "native_side_map_bound": 864, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 160, + "2": 48, + "5": 48, + "7": 112, + "8": 64 + }, + "real_scalar_primitives": 3032, + 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"f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e" + ], + "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py": [ + "plain", + "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + ], + "oblique-native-20261017/paired-centre-formation/emit_paired_centres.py": [ + "plain", + "8582219e08c11dd26f121bcd1940f1f590f7abde0203b2a0e3b0bfa035942b93" + ] + } +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE.md b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE.md new file mode 100644 index 0000000000..4e88dd46f2 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE.md @@ -0,0 +1,112 @@ +# A full native involution with no extra query child + +## Result and exact boundary + +This packet gives a full 112 by 112 response E with + + E^T = E, + E^2 = I. + +It emits both native shears for both current providers: + + F_E(x,y,h) = (x, y+Ex, h), + B_E(x,y,h) = (x-E^T y, y, h). + +The 48-port component is the controller lane's signed matching of pair modes. The 64-port component is the history lane's negative physical permutation. The latter replaces the half-Hadamard component in the controller's original matrix packet. This distinction is recorded in the payload and checked by an exact full-matrix square. + +The word uses only the native progress of the two productive data banks. It uses no owned field, no private field, and no extra query child. All 408 arbitrary borrowed fields are unchanged. Their previous native progress is not supplied by this data word. A separate helper completion, recursive host, complete controller, precision bound, and final assembly remain obligations. This packet does not claim a kappa improvement. + +The physical entry is (C_q x,y,h). The forward exit is (F_9 x,F_9 C_q^-1(y+Ex),h). The backward exit is (F_9(x-E^T y),F_9 C_q^-1 y,h). Each port uses its own q. All native and endpoint phase records use the original fixed exterior. No common-W exterior is used in this packet. + +## The 48-port matching + +Each of 24 physical pairs has a signed Hadamard code H_e, with H_e H_e^T=2I and H_e^-1=H_e^T/2. Let H be their direct sum. The code has two modes per physical pair. The two modes belong to the two incident centre vertices. At each of the eight vertices, the six incident modes are paired in a signed matching. Its matrix A_v is symmetric, has zero diagonal, and satisfies A_v^2=I. Let A be their direct sum. The physical response is + + E48 = H^-1 A H. + +It follows that E48 is symmetric and squares to I. The chosen matching also preserves the intended selected principal block. These facts are proved in the pinned controller packet and are checked again for the full response in this producer. + +For mode i, let P_i be the rank-two span of the two q labels in its physical pair. Distinct incident pair planes at one vertex are orthogonal. If source mode i is matched to target mode j, then + + P_i subset P_j-perp. + +The target pair hole P_j-perp has rank seven and lies in each of the two final target holes for that pair. The producer checks all these inclusions from the literal binary labels in each provider. It lowers each literal canonical frame pair, so equality of subspaces is not used as equality of phase operators. + +## Native schedule + +The X fields of each physical pair move from their rank-one entry lines to P_i through rank one. They receive the pair code H_e at P_i. The Y pair receives the same code at its common I entry. + +For each target mode j with matched source i, execute the following steps: + +1. Move the coded Y_j field from I to the exact source frame P_i through rank two. +2. Add A_ji X_i to Y_j. Both fields have the same canonical frame. +3. Move Y_j from P_i to its pair hole P_j-perp through rank five. + +All X fields then move from their pair planes to FULL through rank seven. The inverse pair code restores the physical X coordinates at FULL. Each Y physical pair now has both coded fields at its common pair hole. The inverse pair code is applied there. Each field then moves from the pair hole to its own final hole through rank one. + +The resulting logical Y update is H^-1 A H x. Every arbitrary initial Y input has coefficient one after its code and inverse code. No initial Y value is assumed to be zero. + +For the backward word, replace step 2 by X_i <- X_i-A_ji Y_j. Keep the native progress directions unchanged. Since H H^T=2I, the decoded update is -E48^T y. Each X source mode and each Y target mode occurs in one matching edge, so a transfer cannot change another transfer's input. The producer checks the full map without relying on that argument alone. + +## The 64-port component + +The other 64 ports use the history lane's frozen negative-permutation word. Each source line is orthogonal to its assigned target label. The target moves from I to that source line through rank one, receives one signed ADD, and completes its hole progress through rank seven. The X source completes FULL through rank eight. + +This component consists of 32 disjoint negative transpositions, so its response is symmetric and squares to I. It is disjoint from the 48-port word in both data banks. The merged emitter remaps frame identifiers by their literal ordered bases, checks the inherited native records in canonical JSON form, and replays the full union. It does not replace a native record merely because two frames span the same subspace. + +## A general sufficient condition + +Let a pair code H have H H^T=cI for a scalar unit c. Suppose a one-to-one mode assignment i -> j has an admitted common source frame P_i, and P_i lies in a common pair hole for target j. Suppose the source and target native paths through these frames have the same total rank as their required productive progress. Then any admitted scalar weight on that assignment can be transferred at P_i with no extra query child. + +The resulting forward response is H^-1 A H, where A is the weighted mode permutation. Reversing the scalar transfer gives its transpose in the backward shear. A weighted permutation is a unit when all weights are units. A symmetric signed matching gives an involution. This construction changes the source and target native paths; it is outside the old fixed-word transfer span and its orthogonality obstructions. + +The frozen payload proves the stated matching and actual phase recipes. It does not claim every abstract matching has the required frame inclusions. Those inclusions and phase recipes remain explicit hypotheses of the general statement. + +## Selected and ordinary principal units + +The selected set is S={0,7,15,36,42,46,79,89}. The selected block L=E_SS is the same as the controller's pinned block. Its exact dyadic inverse is part of this payload and is checked in both the inherited proof and this producer. + +Write the full response in selected and ordinary blocks as + + E = [[L,B],[D,H0]]. + +Since E^2=I and L is a unit, the ordinary principal block is also a unit, with + + H0^-1 = H0-D L^-1 B. + +Indeed H0^2+DB=I and H0D=-DL, so both products with the stated inverse are I. The producer constructs this inverse and checks both orders exactly. This establishes the scalar principal-unit premise required by the proposed interface. It does not by itself admit a new native use of that inverse at an arbitrary frame. + +## Invoice + +The complete data word has native profile + +| Rank | Child count | +| --- | ---: | +| 1 | 160 | +| 2 | 48 | +| 5 | 48 | +| 7 | 112 | +| 8 | 64 | + +The total is 432 children and rank mass 1792. Each of the 224 productive fields receives total rank eight. The 48-port part has mass 768; the 64-port part has mass 1024. There is no query capture to add to this invoice. + +The exact scalar cost is 3032 real primitives in each direction and provider. All source and target pair codes, inverse codes, matching transfers, and inherited 64-port ADDs are included. There are no top-level owned or private fields. There are 224 endpoint maps and at most 864 native side maps, before internal recursive costs. The top-level maximum-array norm bound is 6. It is computed from exact absolute coefficient row sums after every scalar operation. + +The native rank total alone is not a full recurrence. A helper completion must supply its actual physical endpoints and all of its native, map, owned, private, and restoration costs. The complete controller must also account for stage changes, exterior phases, terminal decoding, and all recursive children. + +## Verification and credit + +The producer verifies all 632 input columns, including 408 arbitrary borrowed columns. It checks every scalar frame, every native frame and rank, each endpoint, and the complete response. It reads the serialized payload and repeats the full coefficient and frame replay. It checks symmetry, the full involution identity, and both principal inverses with exact rational arithmetic. + +Every distinct new physical native edge is checked by an exact interpreter separate from the Clifford compiler. The check includes all Pauli images and an exact reference state, so it fixes global phase. The original endpoint adapter order is checked for both providers. The proof and receipt state the scope of these producer checks; independent review is separate. + +The controller lane supplied the signed matching and selected principal-unit construction. The history lane supplied the 64-port negative-permutation word. The root agent supplied the sparse matched routing schedule. The paired-centre work supplied the pair-code source representation and its actual frame geometry. The exact tools and all dependencies are pinned. This work used AI assistance. No PR or publication is authorized. + +Run the producer from the workspace root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/emit_matched_involution.py +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/emit_matched_involution.py +``` + +Each run must complete all four words with native mass 1792 and scalar cost 3032. The frozen normal and optimized payload and receipt bytes agree. diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/REPRODUCTION.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/REPRODUCTION.json new file mode 100644 index 0000000000..b12d287835 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/REPRODUCTION.json @@ -0,0 +1,7 @@ +{ + "files": { + "MATCHED-NATIVE-PROGRAM.json.gz": "61fd6d0283de4af6ad53c013cd8220d8ea55d971c6980ce5259053ce31d366bd", + "MATCHED-NATIVE-RECEIPT.json": "7bc873d627e022d4677b740633c9cd5f86c5e675d84460d538b4b6314c79536c" + }, + "normal_and_optimized_byte_equal": true +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/emit_matched_involution.py b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/emit_matched_involution.py new file mode 100644 index 0000000000..795f2b5f20 --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/emit_matched_involution.py @@ -0,0 +1,315 @@ +#!/usr/bin/env python3 +"""Emit the full data response through two disjoint native matchings.""" +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] +UTILITY=HERE.parent/'radical-centre-carry/emit_radical_centres.py' +UTILITY_SHA='fc7d93bf1efc963fa5db880aaaf9d53578083e32b4e75ef43cb739042713a2f6' +if sha256(UTILITY.read_bytes()).hexdigest()!=UTILITY_SHA: + raise ValueError('Pinned native utility changed') +spec=importlib.util.spec_from_file_location('matching_native_utility',UTILITY) +u=importlib.util.module_from_spec(spec) +sys.modules[spec.name]=u +spec.loader.exec_module(u) +need,basis,add=u.need,u.basis,u.add +PINS={ + 'controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json': + ('plain','e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902'), + 'history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz': + ('decompressed','87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9'), +} +PHASE_CACHE={} +ENDPOINT_CACHE=set() + + +def read(relative): + mode,want=PINS[relative] + raw=(LANES/relative).read_bytes() + if mode=='decompressed': + raw=gzip.decompress(raw) + need(sha256(raw).hexdigest()==want,'Pinned input '+relative) + return json.loads(raw) + + +def rational_rows(rows): + return [{int(k):F(v) for k,v in row.items()} for row in rows] + + +def multiply(left,right): + product=[] + for row in left: + value={} + for j,c in row.items(): + add(value,right[j],c) + product.append(value) + return product + + +def build(provider,canonical,matching,component64,response,direction): + frames=deepcopy(canonical['frames']) + index={tuple(row):i for i,row in enumerate(frames)} + + def frame_id(vectors): + vectors=tuple(vectors) + if vectors not in index: + index[vectors]=len(frames) + frames.append(list(vectors)) + return index[vectors] + + start=list(canonical['start']) + finish=list(start) + finish[:112]=[1]*112 + finish[112:224]=canonical['final'][112:224] + current=list(start) + state=[{i:F(1)} for i in range(len(start))] + events,recipes=[],{} + prefix_bound=F(1) + + def scalar(op,target,origin=None,coefficient=F(1)): + nonlocal prefix_bound + frame=current[target] + coefficient=F(coefficient) + if op=='scale': + gate=[op,target,coefficient.numerator,coefficient.denominator] + state[target]={k:coefficient*v for k,v in state[target].items() if coefficient*v} + else: + need(op=='add' and target!=origin and current[origin]==frame,'Equal-frame scalar addition') + gate=[op,target,origin,coefficient.numerator,coefficient.denominator] + add(state[target],state[origin],coefficient) + events.append(['scalar',gate,frame]) + prefix_bound=max(prefix_bound,sum(abs(v) for v in state[target].values())) + + def native(target,new): + old=current[target] + need(old!=new,'Nontrivial native edge') + key=str(old)+':'+str(new) + physical=(tuple(frames[old]),tuple(frames[new])) + if physical not in PHASE_CACHE: + operation=u.compiler.canonical_frame(9,physical[0]).adjoint().then( + u.compiler.canonical_frame(9,physical[1])) + record,_=u.compiler.lower_child(operation) + need(record['rank']==abs(len(frames[new])-len(frames[old])),'Exact nested native rank') + u.phase.equal(u.phase.recipe(record),u.phase.adjoint(u.phase.frame(frames[old],9))+ + u.phase.frame(frames[new],9),'Matching native edge '+key) + PHASE_CACHE[physical]=record + recipes[key]=PHASE_CACHE[physical] + events.append(['native',target,old,new,recipes[key]['rank'],key]) + current[target]=new + + modes=matching['modes'] + mode_by_id={mode['id']:mode for mode in modes} + planes,holes={},{} + codes=[] + for pair in matching['pair_codes']: + a,b=pair['ports'] + plane_basis=basis((canonical['ports'][a],canonical['ports'][b])) + need(len(plane_basis)==2,'Pair plane rank') + plane=frame_id(plane_basis) + hole_basis=basis(v for v in range(1,512) if all((v&q).bit_count()%2==0 for q in plane_basis)) + need(len(hole_basis)==7,'Pair-hole rank') + hole=frame_id(hole_basis) + for mid in pair['mode_ids']: + planes[mid],holes[mid]=plane,hole + native(a,plane) + native(b,plane) + av,bv,aw,bw=[F(c) for row in pair['matrix'] for c in row] + need(av*aw+bv*bw==0 and all(abs(c)==1 for c in (av,bv,aw,bw)),'Hadamard pair rows') + local=[] + + def code(op,target,origin=None,coefficient=F(1)): + if op=='scale' and coefficient==1: + return + scalar(op,target,origin,coefficient) + local.append((op,target,origin,F(coefficient))) + + for offset in (0,112): + code('scale',offset+a,coefficient=av) + code('scale',offset+b,coefficient=bv) + code('add',offset+a,offset+b) + code('scale',offset+b,coefficient=-2) + code('add',offset+b,offset+a) + code('scale',offset+b,coefficient=aw/av) + need(state[a]=={a:av,b:bv} and state[b]=={a:aw,b:bw},'Coded X pair') + need(state[112+a]=={112+a:av,112+b:bv} and state[112+b]=={112+a:aw,112+b:bw},'Coded Y pair') + codes.append({'ports':[a,b],'plane':plane,'pair_hole':hole,'code':local}) + transfer_cuts=[] + A=rational_rows(matching['mode_response']) + for target_mode,row in enumerate(A): + need(len(row)==1,'One mode source per target') + source_mode,weight=next(iter(row.items())) + need(source_mode!=target_mode and abs(weight)==1,'Signed off-diagonal matching') + source=mode_by_id[source_mode]['carrier'] + target=112+mode_by_id[target_mode]['carrier'] + need(mode_by_id[source_mode]['vertex']==mode_by_id[target_mode]['vertex'],'One vertex per matching edge') + source_plane=planes[source_mode] + target_hole=holes[target_mode] + need(len(basis((*frames[source_plane],*frames[target_hole])))==7,'Source plane lies in the target pair hole') + native(target,source_plane) + transfer_cuts.append({'source_mode':source_mode,'target_mode':target_mode,'weight':str(weight), + 'source':source,'target':target,'frame':source_plane,'add_event':len(events)}) + if direction=='forward': + scalar('add',target,source,weight) + else: + scalar('add',source,target,-weight) + native(target,target_hole) + for p in matching['large_ports']: + native(p,1) + for pair in reversed(codes): + for op,target,origin,c in reversed(pair['code']): + scalar(op,target,origin,1/c if op=='scale' else -c) + for p in matching['large_ports']: + native(112+p,finish[112+p]) + + inherited=component64['providers'][provider][direction] + old_to_new={i:frame_id(row) for i,row in enumerate(inherited['frames'])} + inherited_first=len(events) + for event in inherited['events']: + if event[0]=='native': + _,target,old,new,rank,key=event + need(current[target]==old_to_new[old],'Inherited native entry frame') + native(target,old_to_new[new]) + need(events[-1][4]==rank and json.dumps(recipes[events[-1][5]],sort_keys=True)==json.dumps(inherited['native_recipes'][key],sort_keys=True), + 'Inherited native recipe is unchanged') + else: + need(event[0]=='scalar','Inherited event grammar') + gate,frame=event[1:] + op,target,origin,num,den=gate + need(current[target]==old_to_new[frame] and op=='add','Inherited scalar frame') + scalar(op,target,origin,F(num,den)) + expected=[{i:F(1)} for i in range(len(start))] + for t,row in enumerate(response): + if direction=='forward': + add(expected[112+t],row) + else: + for s,c in row.items(): + add(expected[s],{112+t:-c}) + need(state==expected and current==finish,'All native data and borrowed input columns') + endpoints=json.loads(u.read('new-native-recipes-20261017/'+provider+'/CLIFFORD-RECIPES.json'))['endpoint_adapters'] + for record in endpoints: + port,role=record['port'],record['role'] + key=provider,role,port + if key not in ENDPOINT_CACHE: + conventional=(('C',canonical['ports'][port],1),) if role=='source' else ( + ('C',canonical['ports'][port],-1),)+u.phase.fourier(9) + f=start[port] if role=='source' else finish[112+port] + u.phase.equal(u.phase.recipe(record),u.phase.adjoint(conventional)+u.phase.frame(frames[f],9), + 'Matched endpoint '+str(key)) + ENDPOINT_CACHE.add(key) + profile=Counter(event[4] for event in events if event[0]=='native') + word={'frames':frames,'start':start,'final':finish,'events':events,'native_recipes':recipes, + 'endpoint_adapters':endpoints,'pair_codes':codes,'transfer_cuts':transfer_cuts, + 'inherited_64_first_event':inherited_first} + receipt={'all_input_columns':len(start),'arbitrary_untouched_helpers':len(start)-224, + 'owned_fields':0,'private_fields':0,'extra_query_children':0, + 'profile':dict(sorted(profile.items())),'native_mass':sum(k*v for k,v in profile.items()), + 'native_children':sum(profile.values()),'real_scalar_primitives':u.scalar_price(events), + 'native_recipe_count':len(recipes),'endpoint_map_count':len(endpoints), + 'native_side_map_bound':2*sum(profile.values()), + 'top_level_max_array_l2_amplification_bound':str(prefix_bound)} + print(provider,direction,receipt,flush=True) + return word,receipt + + +def replay(word,response,direction): + current=list(word['start']) + state=[{i:F(1)} for i in range(len(current))] + for event in word['events']: + if event[0]=='native': + _,target,old,new,rank,key=event + need(current[target]==old and word['native_recipes'][key]['rank']==rank,'Serialized native edge') + current[target]=new + else: + need(event[0]=='scalar','Serialized grammar') + gate,frame=event[1:] + op,target=gate[:2] + need(current[target]==frame,'Serialized scalar target') + if op=='scale': + c=F(*gate[2:]) + state[target]={k:c*v for k,v in state[target].items() if c*v} + else: + need(op=='add','Serialized scalar kind') + origin=gate[2] + need(target!=origin and current[origin]==frame,'Serialized scalar source') + add(state[target],state[origin],F(*gate[3:])) + expected=[{i:F(1)} for i in range(len(current))] + for t,row in enumerate(response): + if direction=='forward': + add(expected[112+t],row) + else: + for s,c in row.items(): + add(expected[s],{112+t:-c}) + need(state==expected and current==word['final'],'Serialized all-column map') + + +def encode(value): + if isinstance(value,F): + return str(value) + raise TypeError(type(value).__name__) + + +def main(): + core=json.loads(u.read('new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz')) + matching=read('controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json') + component64=read('history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz') + large=set(matching['large_ports']) + need(large.isdisjoint(component64['active_ports']) and large|set(component64['active_ports'])==set(range(112)), + 'Disjoint complete response support') + old=rational_rows(matching['response']) + small=rational_rows(component64['response']) + response=[old[i] if i in large else small[i] for i in range(112)] + need(all(response[i].get(j,0)==response[j].get(i,0) for i in range(112) for j in range(112)), + 'Symmetric full response') + need(multiply(response,response)==[{i:F(1)} for i in range(112)],'Full response is an involution') + selected=matching['selected_ports'] + L=[{j:response[p].get(q,0) for j,q in enumerate(selected) if response[p].get(q,0)} for p in selected] + need(L==rational_rows(matching['selected_block']),'Selected principal block is unchanged') + need(multiply(L,rational_rows(matching['selected_inverse']))==[{i:F(1)} for i in range(8)], + 'Selected dyadic inverse') + ordinary=[p for p in range(112) if p not in selected] + Linv=rational_rows(matching['selected_inverse']) + B=[{j:response[p].get(q,0) for j,q in enumerate(ordinary) if response[p].get(q,0)} for p in selected] + D=[{j:response[p].get(q,0) for j,q in enumerate(selected) if response[p].get(q,0)} for p in ordinary] + H=[{j:response[p].get(q,0) for j,q in enumerate(ordinary) if response[p].get(q,0)} for p in ordinary] + Hinv=deepcopy(H) + for row,correction in zip(Hinv,multiply(multiply(D,Linv),B)): + add(row,correction,-1) + identity=[{i:F(1)} for i in range(len(ordinary))] + need(multiply(H,Hinv)==identity and multiply(Hinv,H)==identity,'Ordinary principal inverse in both orders') + programs,receipts={},{} + for provider,item in core['providers'].items(): + programs[provider],receipts[provider]={},{} + for direction in ('forward','backward'): + word,receipt=build(provider,item['canonical'],matching,component64,response,direction) + programs[provider][direction]=word + receipts[provider][direction]=receipt + payload={'schema':'full-matched-native-involution-v1','response':response,'selected_ports':selected, + 'selected_block':L,'selected_inverse':matching['selected_inverse'], + 'ordinary_ports':ordinary,'ordinary_inverse':Hinv,'providers':programs} + encoded=(json.dumps(payload,default=encode,sort_keys=True,separators=(',',':'))+'\n').encode() + decoded=json.loads(encoded) + for provider,words in decoded['providers'].items(): + for direction,word in words.items(): + replay(word,rational_rows(decoded['response']),direction) + (HERE/'MATCHED-NATIVE-PROGRAM.json.gz').write_bytes(gzip.compress(encoded,mtime=0)) + receipt={'schema':'full-matched-native-involution-receipt-v1','source_pins':PINS, + 'utility_sha256':UTILITY_SHA,'utility_source_pins':u.PINS, + 'producer_sha256':sha256(Path(__file__).read_bytes()).hexdigest(), + 'payload_decompressed_sha256':sha256(encoded).hexdigest(),'providers':receipts, + 'distinct_native_phases_checked':len(PHASE_CACHE),'endpoint_phases_checked':len(ENDPOINT_CACHE), + 'full_response_symmetric':True,'full_response_square_identity':True,'selected_inverse_checked':True, + 'ordinary_inverse_both_orders_checked':True, + 'scope':'Full112 data response and both native shears; borrowed helper progress and global supplier remain separate.'} + (HERE/'MATCHED-NATIVE-RECEIPT.json').write_text(json.dumps(receipt,sort_keys=True,indent=2)+'\n') + + +if __name__=='__main__': + main() diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3133/research/rank7-coupled-586-588-carrier-fold/README.md b/research/ordered-centre-interfaces/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/ordered-centre-interfaces/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. 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adapters; PR2969 comparator" + }, + { + "pr": 2942, + "head": "a027b0f6fdb0ab2b42ba10fc31b53960166bf2bf", + "upstream_path": "research/paired-extension-normal45/run_registered.py", + "package_path": "run_registered.py", + "change": "new statuses, control counts, comparator and receipt bindings" + } + ], + "new_sources": [ + "data/WORD-base.json.gz", + "data/WORD-extra.json.gz", + "data/STAGE1-FRAME-EDITS.json", + "data/TRANSFORM-226.json", + "data/TRANSFORM-228.json", + "data/TRANSFORM-230.json", + "data/TRANSFORM-363.json", + "data/TRANSFORM-395.json", + "data/REWRITES-2957.json (Jeremy Kothe's PR2957 rewrites, re-addressed to the stage-2 word with exact preimages)", + "allocation/FILL.json.gz", + "allocation/PROFILE.json", + "allocation/PROVIDERS.json", + "allocation/SEARCH.json", + "certificates/RELAX-CAP.json", + "certificates/RELAX-STAGES.json", + "construction/" + ], + "upstream_exports": [ + { + "pr": 2969, + "head": "e2ca469b08385d3d5e29a918d66dbefaf889e9f3", + "package": 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"manifest_sha256": "751b46364742cbb947f7db07c130ff09085b38b52c520d3b47f2dadc1e21ba80", + "files": 637, + "builder": "tools/build_overlay.py (stage rank7-joint-endframes) on PR2917 tools/build_extension.py output" + }, + "source_boundary": "Only this new package is submitted. The parent words are PR2942s, byte-identical; exact frozen ancestor exports remain unchanged. Full replay performs no network fetch." +} diff --git a/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3148/research/coupled-carrier-cap740/README.md b/research/ordered-centre-interfaces/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/ordered-centre-interfaces/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/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3148/research/coupled-carrier-cap740/SOURCE-PINS.json b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3148/research/coupled-carrier-cap740/SOURCE-PINS.json new file mode 100644 index 0000000000..e59a0271bb --- /dev/null +++ b/research/ordered-centre-interfaces/frozen/work/centre-encoding-campaign-20261014/upstream-refresh-20261017/pr3148/research/coupled-carrier-cap740/SOURCE-PINS.json @@ -0,0 +1,10 @@ +{ + "research/rank7-joint-endframes/allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c", + "research/rank7-joint-endframes/allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1", + "research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz": 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b/research/ordered-centre-interfaces/portable/check_access.py @@ -0,0 +1,249 @@ +"""Check the actual 25-axis views and the cheaper common-frame gauge.""" + +from collections import Counter, defaultdict +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parents[1] / 'frozen' / 'work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018' +CHECKER_SHA = sha256(Path(__file__).read_bytes()).hexdigest() +LANES = HERE.parents[1] +ROOT = LANES.parents[2] +ACCESS = LANES / "bridge-access-20261017/matched-stage-access-20261018" +GAUGE = LANES / "independent-review-20261017/matched-full-gauge-20261018" +PINS = { + "access_freeze":"0b3e4f09ea0eff1f6106a2611ac80cf0976638da96e7c0e5b289224b159ba96c", + "gauge_freeze":"a83fad6b1fe12e1cad34989ad4226ab9d1d2fb268362b010845deaea2f42034d", + "views_compressed":"1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f", + "matching":"e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", + "native_decompressed":"95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025", + "archive":"f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "data":"c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "controller":"f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", +} +E = [1 << j for j in range(25)] +MASK = (1 << 25)-1 + + +def need(test, message): + if not test: + raise ValueError(message) + + +def pin(path, key, compressed=False): + raw = path.read_bytes() + if compressed: + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == PINS[key], "Pinned source: " + key) + return raw + + +def frozen(folder, key): + manifest = json.loads(pin(folder/"FREEZE.json", key)) + for name, digest in manifest["files"].items(): + need(sha256((folder/name).read_bytes()).hexdigest() == digest, "Frozen artifact: " + name) + + +def act(columns, x): + out = 0 + for j, value in enumerate(columns): + if x >> j & 1: + out ^= value + return out + + +def phase(terms): + """Use Z4 basis values and binary off-diagonal polar rows.""" + diagonal, polar = [0]*25, [0]*25 + for vector, exponent in terms: + need(vector <= MASK, "The phase direction lies in dimension25") + for j in range(25): + if vector >> j & 1: + diagonal[j] += exponent + if exponent % 2: + polar[j] ^= vector ^ (1 << j) + return tuple(x % 4 for x in diagonal), tuple(polar) + + +def translated(terms, rho, delta): + return phase([(act(rho, v), a) for v, a in terms] + [(delta, 2)]) + + +def matrix(rows): + return [{int(j):F(a) for j, a in row.items()} for row in rows] + + +def product(a, b): + out = [] + for row in a: + values = defaultdict(F) + for j, x in row.items(): + for k, y in b[j].items(): + values[k] += x*y + out.append({k:v for k, v in values.items() if v}) + return out + + +def scalar_replay(events): + rows = [{p:F(1)} for p in range(112)] + price, peak = 0, F(1) + counts = Counter() + for event in events: + op, target = event[:2] + c = F(*event[-2:]) + numerator, denominator = abs(c.numerator), c.denominator + need(numerator > 0 and denominator & (denominator-1) == 0, "Nonzero dyadic coefficient") + if op == "scale": + need(len(event) == 4 and numerator & (numerator-1) == 0, "Unit dyadic SCALE") + rows[target] = {p:c*a for p, a in rows[target].items()} + price += 2*(abs(numerator.bit_length()-denominator.bit_length()) + (c < 0)) + else: + need(op == "add" and len(event) == 5 and target != event[2], "Plain in-place ADD") + values = defaultdict(F, rows[target]) + for p, a in rows[event[2]].items(): + values[p] += c*a + rows[target] = {p:a for p, a in values.items() if a} + price += 2*(1+numerator.bit_length()+numerator.bit_count()+denominator.bit_length()) + counts[op] += 1 + peak = max(peak, sum(abs(a) for a in rows[target].values())) + return rows, price, peak, counts + + +def reverse_columns(events): + columns = [{p:F(1)} for p in range(112)] + for event in reversed(events): + c = F(*event[-2:]) + target = event[1] + if event[0] == "scale": + columns[target] = {p:c*a for p, a in columns[target].items()} + else: + source = event[2] + values = defaultdict(F, columns[source]) + for p, a in columns[target].items(): + values[p] += c*a + columns[source] = {p:a for p, a in values.items() if a} + return columns + + +def main(): + frozen(ACCESS, "access_freeze") + frozen(GAUGE, "gauge_freeze") + packed = pin(LANES/"bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", "views_compressed") + original_views = json.loads(gzip.decompress(packed))["views"] + views = {(v["stage"],v["port"],v["side"]):v for v in original_views} + raw = (ROOT / "archive-members/DATA-PHASES.json").read_bytes() + need(sha256(raw).hexdigest() == PINS["data"], "Actual DATA phase source") + data = json.loads(raw)["recipes"] + dimensions = json.loads((ACCESS/"DIMENSION25-VIEWS.json").read_text()) + entries = {(r["stage"],r["port"]):r for r in dimensions["entries"]} + counts = Counter() + cone = {} + for p, row in enumerate(data): + q = row["q"] + for s in range(3): + full_rho = [1 << j for j in range(73)] if s == 0 else views[s,p,"X"]["route_columns"] + need(all(x <= MASK for x in full_rho[:25]) and full_rho[25:] == [1 << j for j in range(25,73)], + "No route uses a discarded coordinate") + rho = full_rho[:25] + need(all(((a&b).bit_count() % 2) == (i == j) for i,a in enumerate(rho) for j,b in enumerate(rho)), + "Exact O25 membership") + need([act(rho, x) for x in rho] == E and act(rho,q) == q, "Route inverse and fixed intrinsic line") + record = entries[s,p] + align = row["stage_alignment"][s] + need(record == {"port":p,"stage":s,"q":q,"route_columns":rho,"literal_stage_alignment":align}, + "Every emitted dimension25 record equals actual source data") + need(all(x <= MASK for x in align.values()), "Every entry and exit translation restricts") + counts["orthogonal_routes"] += 1 + for side in ("X","Y"): + before = ([(q,1)] if side == "X" else []) if s == 0 else [(x,1) for x in E[:9+8*(s-1)]] + if s and side == "Y": + before += [(q,-1)] + want = [(x,1) for x in E[9:9+8*s]] + ([(q,1)] if side == "X" else []) + delta = act(rho,align["entry_"+side]) + need(translated(before,rho,delta) == phase(want), "Exact current entry with common exterior") + counts["entry"] += 1 + counts["entry_omission_controls"] += translated(before,rho,0) != phase(want) + after = [(x,1) for x in E[:9+8*s]] + ([(q,-1)] if side == "Y" else []) + need(translated(after,rho,align["exit_"+side]) == phase(after), "Exact current exit") + counts["exit"] += 1 + counts["exit_omission_controls"] += translated(after,rho,0) != phase(after) + for level in range(s,3): + full = [(x,1) for x in E[:9+8*level]] + delta = 0 if s == 0 else views[s,p,"X"]["translation_after_route"] + need(translated(full,rho,delta) == phase(full), "Every past-X view") + counts["past_X"] += 1 + cone[s,level,"X",p] = True + for level in range(s): + hole = [(x,1) for x in E[:9+8*level]] + [(q,-1)] + common = [(x,1) for x in E[9:9+8*level]+E[9+8*(s-1):9+8*s]] + delta = views[s,p,"Y"]["translation_after_route"] + need(translated(hole,rho,delta) == phase(common), "Every future-Y view") + counts["future_Y"] += 1 + cone[s,level,"Y",p] = True + cuts = [(0,0,"X"),(1,0,"Y"),(1,1,"X"),(2,1,"Y"),(1,2,"X")] + controller = json.loads(pin(LANES/"encoded-controller/one-pair-current-codes-20261018/PROGRAM.json", + "controller")) + need(controller["program"] == [ + ["forward",0],["code_X",0,1],["code_Y",1,1], + ["backward",1],["code_X",1,1],["code_Y",2,1], + ["forward",2],["code_X",1,-1]], "The pinned controller gives these five code cuts") + need(all(cone[s,level,side,p] for s,level,side in cuts for p in range(112)), "All five actual one-pair code cuts") + counts["one_pair_code_port_cuts"] = len(cuts)*112 + + matching = json.loads(pin(LANES/"controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json", "matching")) + native = json.loads(pin(LANES/"oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz", "native_decompressed", True)) + response = matrix(native["response"]) + gauge = json.loads((GAUGE/"FULL-GAUGE.json").read_text()) + need(response == matrix(gauge["response"]) == matrix(json.loads((ACCESS/"FULL-GAUGE-PROGRAM.json").read_text())["response"]), + "The cheaper gauge and stage packet use the actual same full response") + need(product(response,response) == [{p:F(1)} for p in range(112)], "The actual response is an involution") + need(all(p not in row for p,row in enumerate(response)), "No physical fixed point") + need(Counter(map(len,response)) == {4:48,1:64}, "The actual dense48 and permutation64 supports") + for provider in native["providers"].values(): + for word in provider.values(): + need(all(word["frames"][word["final"][p]] == word["frames"][1] for p in range(112)), + "All native X outputs have one common FULL frame") + need(sorted(word["frames"][1]) == [1 << j for j in range(9)], "Actual local FULL frame") + events = gauge["events"] + result, price, peak, census = scalar_replay(events) + need(result == response and reverse_columns(events) == response, "All rows and independent columns of the scalar word") + need(scalar_replay(events+events)[0] == [{p:F(1)} for p in range(112)], "The literal word squared is identity") + c = gauge["cuts"] + parts = [events[:c["code_end"]],events[c["code_end"]:c["swap_end"]], + events[c["swap_end"]:c["undo_end"]],events[c["undo_end"]:]] + bills = [scalar_replay(part)[1] for part in parts] + need(bills == [470,624,470,832] and price == 2396 and peak == 4, "Exact complete scalar price and prefix norm") + need(scalar_replay(parts[0]+parts[1]+parts[3])[0] != response, "Omitting the pair undo must fail") + need(all(gauge[name] == 0 for name in ("owned_fields","private_fields","native_children")), "No hidden scratch or native work") + # Pair-code algebra uses arbitrary values, and never a zero target. + for pair in matching["pair_codes"]: + a,b = map(F,pair["matrix"][0]) + c0,d = map(F,pair["matrix"][1]) + need(all(abs(x) == 1 for x in (a,b,c0,d)) and d == -a*b*c0, + "Every four-operation pair code has the stated exact matrix") + need(sha256(Path(__file__).read_bytes()).hexdigest() == CHECKER_SHA, "Checker bytes stayed fixed") + receipt = { + "status":"PASS_INDEPENDENT_MATCHED_D25_ACCESS_AND_FULL_GAUGE", + "source_pins":PINS, + "checker_sha256":CHECKER_SHA, + "counts":dict(sorted(counts.items())), + "actual_one_pair_cuts":[{"stage":s,"completed_level":level,"bank":side} for s,level,side in cuts], + "common_frame_scalar_primitives":price, + "component_scalar_primitives":bills, + "scalar_events":dict(census), + "exact_prefix_row_one_norm":str(peak), + "native_children_in_gauge":0, + "owned_fields_in_gauge":0, + "maximum_monomial_view_calls_per_gauge":224, + "five_gauge_scalar_primitives":5*price, + "scope":"Actual D25 stage views, five one-pair scalar access cuts, and complete2396-scalar common-frame gauge. No three-factor terminal, recursive host or supplier claim in this receipt.", + } + (HERE/"ACCESS-REVIEW.json").write_text(json.dumps(receipt,indent=2,sort_keys=True)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/replay.py b/research/ordered-centre-interfaces/replay.py new file mode 100644 index 0000000000..ebf42e1cbc --- /dev/null +++ b/research/ordered-centre-interfaces/replay.py @@ -0,0 +1,141 @@ +#!/usr/bin/env python3 +"""Replay the pinned controller checks in isolated temporary copies.""" + +import argparse +import gzip +import hashlib +import json +import os +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile +import time + + +HERE = Path(__file__).resolve().parent +LANES = Path('work/centre-encoding-campaign-20261014/lanes') +JOBS = [ + ('ordered-normal-forms', 'controller-review-20261017/check_review.py', ['REVIEW.json']), + ('content-decoders', 'controller-review-20261017/check_decoder.py', ['DECODER-CHECKS.json']), + ('current-codes', 'encoded-controller/one-pair-current-codes-20261018/check_and_emit.py', ['CHECKS.json', 'PROGRAM.json']), + ('general-units', 'encoded-controller/one-pair-general-units-20261018/check_general_units.py', ['CHECKS.json']), + ('physical-line-flags', 'encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py', ['LINE-FLAGS.json']), + ('canonical-prefix-screen', 'encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py', ['WARPED-MATCHING.json']), + ('retained-helpers', 'encoded-controller/retained-helper-completion-20261018/check_and_emit.py', ['CHECKS.json', 'HELPER-COMPLETION-PROGRAMS.json.gz']), + ('one-pair-admission', 'history-encoding/one-pair-admission-20261018/check_admission.py', ['CHECKS.json']), + ('terminal-and-hosting', 'bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py', ['TERMINAL-HOSTING-REVIEW.json']), + ('d25-access', 'bridge-review-20261017/matched-stage-review-20261018/check_access.py', ['ACCESS-REVIEW.json']), +] + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def sha(data): + return hashlib.sha256(data).hexdigest() + + +def verify_sources(): + manifest = json.loads((HERE / 'SOURCES.json').read_text()) + for item in manifest['files']: + path = HERE / item['package_path'] + data = path.read_bytes() + require(sha(data) == item['sha256'], 'Source hash: ' + item['package_path']) + if 'decompressed_sha256' in item: + require(sha(gzip.decompress(data)) == item['decompressed_sha256'], + 'Payload hash: ' + item['package_path']) + adaptation = json.loads((HERE / 'PORTABLE-ADAPTATION.json').read_text()) + for kind in ('original', 'portable'): + require(sha((HERE / adaptation[kind]).read_bytes()) == adaptation[kind + '_sha256'], + 'Portable source hash: ' + kind) + return manifest + + +def payload(path, access=False): + data = path.read_bytes() + if path.suffix == '.gz': + return gzip.decompress(data) + if access: + value = json.loads(data) + value.pop('checker_sha256') + return json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + return data + + +def run_job(job, optimized, output): + label, relative, outputs = job + mode = 'optimized' if optimized else 'normal' + destination = output / mode / label + destination.mkdir(parents=True, exist_ok=False) + with tempfile.TemporaryDirectory(prefix='ordered-centre-', dir=output) as temporary: + workspace = Path(temporary) + shutil.copytree(HERE / 'frozen', workspace / 'frozen') + if label == 'd25-access': + shutil.copytree(HERE / 'portable', workspace / 'portable') + script = workspace / 'portable/check_access.py' + else: + script = workspace / 'frozen' / LANES / relative + command = [sys.executable, '-I', '-B'] + (['-O'] if optimized else []) + [str(script)] + environment = dict(os.environ) + environment.update({key: '1' for key in ('OPENBLAS_NUM_THREADS', 'OMP_NUM_THREADS', 'MKL_NUM_THREADS')}) + started = time.monotonic() + result = subprocess.run(command, cwd=workspace / 'frozen', env=environment, + text=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, check=False) + (destination / 'stdout.txt').write_text(result.stdout) + require(result.returncode == 0, label + ' failed; see ' + str(destination / 'stdout.txt')) + hashes = {} + for name in outputs: + relative_output = LANES / Path(relative).parent / name + actual = workspace / 'frozen' / relative_output + expected = HERE / 'frozen' / relative_output + actual_payload = payload(actual, label == 'd25-access') + require(actual_payload == payload(expected, label == 'd25-access'), + 'Changed proof receipt: ' + label + '/' + name) + shutil.copyfile(actual, destination / name) + hashes[name] = {'file_sha256': sha(actual.read_bytes()), 'compared_payload_sha256': sha(actual_payload)} + return {'id': label, 'mode': mode, 'seconds': round(time.monotonic() - started, 3), + 'checker': 'portable/check_access.py' if label == 'd25-access' else 'frozen/' + str(LANES / relative), + 'outputs': hashes, 'matches_frozen_receipts': True, + 'comparison': 'Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise.'} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + parser.add_argument('--mode', choices=['normal', 'optimized', 'both'], default='both') + parser.add_argument('--only', choices=[item[0] for item in JOBS], action='append') + args = parser.parse_args() + output = args.out.resolve() + output.mkdir(parents=True, exist_ok=False) + require(shutil.disk_usage(output).free >= 3 * 1024 ** 3, 'Keep at least 3 GiB free before replay') + manifest = verify_sources() + results = [] + for optimized in ([False, True] if args.mode == 'both' else [args.mode == 'optimized']): + for job in JOBS: + if args.only and job[0] not in args.only: + continue + print(('optimized' if optimized else 'normal') + ' ' + job[0], flush=True) + results.append(run_job(job, optimized, output)) + if args.mode == 'both': + normal = {r['id']: r['outputs'] for r in results if r['mode'] == 'normal'} + for result in results: + if result['mode'] == 'optimized': + require(result['outputs'] == normal[result['id']], 'Normal and optimized outputs differ: ' + result['id']) + receipt = { + 'status': 'PASS_ORDERED_CENTRE_INTERFACES', 'source_files': len(manifest['files']), + 'source_manifest_sha256': sha((HERE / 'SOURCES.json').read_bytes()), + 'replay_sha256': sha(Path(__file__).read_bytes()), + 'python': sys.version, 'jobs': results, 'mode': args.mode, + 'normal_optimized_equal': args.mode == 'both', + 'scope': 'Ordered algebra, exact finite source checks, and conditional local/host proofs. No new native phase compiler sweep, selected replay, all-size compiler proof, finite precision proof, or complete kappa calculation.', + } + (output / 'REPLAY.json').write_text(json.dumps(receipt, indent=2) + '\n') + print(receipt['status'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/validation/REPLAY.json b/research/ordered-centre-interfaces/validation/REPLAY.json new file mode 100644 index 0000000000..aaefeb76b2 --- /dev/null +++ b/research/ordered-centre-interfaces/validation/REPLAY.json @@ -0,0 +1,308 @@ +{ + "status": "PASS_ORDERED_CENTRE_INTERFACES", + "source_files": 128, + "source_manifest_sha256": "369aaa43acaa99201d5d555336b8606399fe85c91910c9852d4faae61c95e23f", + "replay_sha256": "689bf40a6f019e8a8e82b8d8d6188ee1faacc5fabe458190b0b63d1fa40d8fa4", + "python": "3.14.7 (main, Aug 5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]", + "jobs": [ + { + "id": "ordered-normal-forms", + "mode": "normal", + "seconds": 2.45, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py", + "outputs": { + "REVIEW.json": { + "file_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91", + "compared_payload_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "content-decoders", + "mode": "normal", + "seconds": 1.333, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py", + "outputs": { + "DECODER-CHECKS.json": { + "file_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9", + "compared_payload_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "current-codes", + "mode": "normal", + "seconds": 0.186, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd", + "compared_payload_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd" + }, + "PROGRAM.json": { + "file_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", + "compared_payload_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "general-units", + "mode": "normal", + "seconds": 0.06, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6", + "compared_payload_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "physical-line-flags", + "mode": "normal", + "seconds": 1.632, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py", + "outputs": { + "LINE-FLAGS.json": { + "file_sha256": "87df66f2d161abf6930844daa07c440ef6d40ff34043c92769615ca89079666d", + "compared_payload_sha256": "87df66f2d161abf6930844daa07c440ef6d40ff34043c92769615ca89079666d" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "canonical-prefix-screen", + "mode": "normal", + "seconds": 36.292, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py", + "outputs": { + "WARPED-MATCHING.json": { + "file_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2", + "compared_payload_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "retained-helpers", + "mode": "normal", + "seconds": 0.593, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1", + "compared_payload_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1" + }, + "HELPER-COMPLETION-PROGRAMS.json.gz": { + "file_sha256": "b9d025f393b0ec34a3872fe822f57bba4bdd4600b7359ea46422a7028618f7bc", + "compared_payload_sha256": "2ebc31760a95b1dd15576928d60cbdfbf6a4b5e6c1146c31a805b718feb5b69d" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "one-pair-admission", + "mode": "normal", + "seconds": 0.237, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944", + "compared_payload_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "terminal-and-hosting", + "mode": "normal", + "seconds": 12.164, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py", + "outputs": { + "TERMINAL-HOSTING-REVIEW.json": { + "file_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6", + "compared_payload_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "d25-access", + "mode": "normal", + "seconds": 0.612, + "checker": "portable/check_access.py", + "outputs": { + "ACCESS-REVIEW.json": { + "file_sha256": "e193988525a65810e353d110e58d97f8e4224cec366e59b8f98e0d8d358ab85b", + "compared_payload_sha256": "69272fc31f859202adfec91f1b68bdee3ab308983595a848a5a124da509c46e8" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "ordered-normal-forms", + "mode": "optimized", + "seconds": 2.331, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py", + "outputs": { + "REVIEW.json": { + "file_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91", + "compared_payload_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "content-decoders", + "mode": "optimized", + "seconds": 1.687, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py", + "outputs": { + "DECODER-CHECKS.json": { + "file_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9", + "compared_payload_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "current-codes", + "mode": "optimized", + "seconds": 0.209, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd", + "compared_payload_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd" + }, + "PROGRAM.json": { + "file_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", + "compared_payload_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "general-units", + "mode": "optimized", + "seconds": 0.149, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6", + "compared_payload_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "physical-line-flags", + "mode": "optimized", + "seconds": 2.42, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py", + "outputs": { + "LINE-FLAGS.json": { + "file_sha256": "87df66f2d161abf6930844daa07c440ef6d40ff34043c92769615ca89079666d", + "compared_payload_sha256": "87df66f2d161abf6930844daa07c440ef6d40ff34043c92769615ca89079666d" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "canonical-prefix-screen", + "mode": "optimized", + "seconds": 32.41, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py", + "outputs": { + "WARPED-MATCHING.json": { + "file_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2", + "compared_payload_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "retained-helpers", + "mode": "optimized", + "seconds": 0.774, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1", + "compared_payload_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1" + }, + "HELPER-COMPLETION-PROGRAMS.json.gz": { + "file_sha256": "b9d025f393b0ec34a3872fe822f57bba4bdd4600b7359ea46422a7028618f7bc", + "compared_payload_sha256": "2ebc31760a95b1dd15576928d60cbdfbf6a4b5e6c1146c31a805b718feb5b69d" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "one-pair-admission", + "mode": "optimized", + "seconds": 0.273, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944", + "compared_payload_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "terminal-and-hosting", + "mode": "optimized", + "seconds": 11.473, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py", + "outputs": { + "TERMINAL-HOSTING-REVIEW.json": { + "file_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6", + "compared_payload_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "d25-access", + "mode": "optimized", + "seconds": 0.401, + "checker": "portable/check_access.py", + "outputs": { + "ACCESS-REVIEW.json": { + "file_sha256": "e193988525a65810e353d110e58d97f8e4224cec366e59b8f98e0d8d358ab85b", + "compared_payload_sha256": "69272fc31f859202adfec91f1b68bdee3ab308983595a848a5a124da509c46e8" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + } + ], + "mode": "both", + "normal_optimized_equal": true, + "scope": "Ordered algebra, exact finite source checks, and conditional local/host proofs. No new native phase compiler sweep, selected replay, all-size compiler proof, finite precision proof, or complete kappa calculation." +} diff --git a/research/publication-reviews/ordered-centre-interfaces/COLD-PORTABILITY.json b/research/publication-reviews/ordered-centre-interfaces/COLD-PORTABILITY.json new file mode 100644 index 0000000000..7bfd6be661 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/COLD-PORTABILITY.json @@ -0,0 +1,22 @@ +{ + "PATH": "/nonexistent", + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-B", + "/tmp/ordered-centre-independent-review-20261022/package/replay.py", + "--out", + "/tmp/ordered-centre-independent-review-20261022/replay" + ], + "file_count": 140, + "jobs": 20, + "normal_optimized_equal": true, + "package_manifest_sha256": "a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9", + "package_unchanged": true, + "replay_receipt_sha256": "e2dc8d40deb0697e0c4a87dc1bc32f3e66aaf970ff8cc93a6361cb0ab721228c", + "seconds": 98.034, + "source_manifest_sha256": "369aaa43acaa99201d5d555336b8606399fe85c91910c9852d4faae61c95e23f", + "source_package_matches_export": true, + "status": "PASS_GIT_FREE_ORDERED_CENTRE_EXPORT", + "working_directory": "/tmp/ordered-centre-independent-review-20261022" +} diff --git a/research/publication-reviews/ordered-centre-interfaces/COLD-REPLAY.json b/research/publication-reviews/ordered-centre-interfaces/COLD-REPLAY.json new file mode 100644 index 0000000000..3a7cd77f64 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/COLD-REPLAY.json @@ -0,0 +1,308 @@ +{ + "status": "PASS_ORDERED_CENTRE_INTERFACES", + "source_files": 128, + "source_manifest_sha256": "369aaa43acaa99201d5d555336b8606399fe85c91910c9852d4faae61c95e23f", + "replay_sha256": "689bf40a6f019e8a8e82b8d8d6188ee1faacc5fabe458190b0b63d1fa40d8fa4", + "python": "3.14.7 (main, Aug 5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]", + "jobs": [ + { + "id": "ordered-normal-forms", + "mode": "normal", + "seconds": 2.004, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py", + "outputs": { + "REVIEW.json": { + "file_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91", + "compared_payload_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "content-decoders", + "mode": "normal", + "seconds": 0.981, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py", + "outputs": { + "DECODER-CHECKS.json": { + "file_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9", + "compared_payload_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "current-codes", + "mode": "normal", + "seconds": 0.118, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd", + "compared_payload_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd" + }, + "PROGRAM.json": { + "file_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", + "compared_payload_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; 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omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "canonical-prefix-screen", + "mode": "normal", + "seconds": 30.978, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py", + "outputs": { + "WARPED-MATCHING.json": { + "file_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2", + "compared_payload_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "retained-helpers", + "mode": "normal", + "seconds": 0.45, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1", + "compared_payload_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1" + }, + "HELPER-COMPLETION-PROGRAMS.json.gz": { + "file_sha256": "b9d025f393b0ec34a3872fe822f57bba4bdd4600b7359ea46422a7028618f7bc", + "compared_payload_sha256": "2ebc31760a95b1dd15576928d60cbdfbf6a4b5e6c1146c31a805b718feb5b69d" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "one-pair-admission", + "mode": "normal", + "seconds": 0.217, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944", + "compared_payload_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "terminal-and-hosting", + "mode": "normal", + "seconds": 11.771, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py", + "outputs": { + "TERMINAL-HOSTING-REVIEW.json": { + "file_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6", + "compared_payload_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "d25-access", + "mode": "normal", + "seconds": 0.751, + "checker": "portable/check_access.py", + "outputs": { + "ACCESS-REVIEW.json": { + "file_sha256": "e193988525a65810e353d110e58d97f8e4224cec366e59b8f98e0d8d358ab85b", + "compared_payload_sha256": "69272fc31f859202adfec91f1b68bdee3ab308983595a848a5a124da509c46e8" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "ordered-normal-forms", + "mode": "optimized", + "seconds": 2.275, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_review.py", + "outputs": { + "REVIEW.json": { + "file_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91", + "compared_payload_sha256": "dd2c2e216ac0deedeb518e120df16eac76fbc298b7c3d35e5e284b0fd003ef91" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "content-decoders", + "mode": "optimized", + "seconds": 1.374, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/controller-review-20261017/check_decoder.py", + "outputs": { + "DECODER-CHECKS.json": { + "file_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9", + "compared_payload_sha256": "6151c56c54c83281d39eb46d02141a7fa3b4419b938202a14463bac48ed80ef9" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "current-codes", + "mode": "optimized", + "seconds": 0.168, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-current-codes-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd", + "compared_payload_sha256": "415f935e6d1ef1ac1393aa84b6f07c15739af742191a81c20accefaed0c8dadd" + }, + "PROGRAM.json": { + "file_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7", + "compared_payload_sha256": "f66186f2f67ea00eb8ae6447ec9cbddbdf410f141e61149871b0915e599845d7" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "general-units", + "mode": "optimized", + "seconds": 0.085, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/one-pair-general-units-20261018/check_general_units.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6", + "compared_payload_sha256": "dffe2390cde225e8d4503256ca9cad890f68b4226dd8f9e00433b8d33817e8f6" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "physical-line-flags", + "mode": "optimized", + "seconds": 1.922, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/check_line_flags.py", + "outputs": { + "LINE-FLAGS.json": { + "file_sha256": "87df66f2d161abf6930844daa07c440ef6d40ff34043c92769615ca89079666d", + "compared_payload_sha256": "87df66f2d161abf6930844daa07c440ef6d40ff34043c92769615ca89079666d" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "canonical-prefix-screen", + "mode": "optimized", + "seconds": 28.753, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/physical-monomial-compiler-20261018/screen_warped_matching.py", + "outputs": { + "WARPED-MATCHING.json": { + "file_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2", + "compared_payload_sha256": "28df8917d48a0233354883d00f4801f51eabbcf27bdeaf1046efbc813187afb2" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "retained-helpers", + "mode": "optimized", + "seconds": 0.401, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/encoded-controller/retained-helper-completion-20261018/check_and_emit.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1", + "compared_payload_sha256": "8891b7349e6d1f9842427197e41660d95895106563de22bdbb07a32dbf4493f1" + }, + "HELPER-COMPLETION-PROGRAMS.json.gz": { + "file_sha256": "b9d025f393b0ec34a3872fe822f57bba4bdd4600b7359ea46422a7028618f7bc", + "compared_payload_sha256": "2ebc31760a95b1dd15576928d60cbdfbf6a4b5e6c1146c31a805b718feb5b69d" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "one-pair-admission", + "mode": "optimized", + "seconds": 0.17, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/history-encoding/one-pair-admission-20261018/check_admission.py", + "outputs": { + "CHECKS.json": { + "file_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944", + "compared_payload_sha256": "2e0f82f337b4d2984b590fc59bc0f8d73beec35b47f1ac9dc11086249ca2c944" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "terminal-and-hosting", + "mode": "optimized", + "seconds": 9.298, + "checker": "frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/matched-stage-review-20261018/check_terminal_and_hosting.py", + "outputs": { + "TERMINAL-HOSTING-REVIEW.json": { + "file_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6", + "compared_payload_sha256": "9ce7d63a0a04cb20015cb4c9f436c44358228cc39b1fafb6ae5c73bdba7b66f6" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + }, + { + "id": "d25-access", + "mode": "optimized", + "seconds": 0.372, + "checker": "portable/check_access.py", + "outputs": { + "ACCESS-REVIEW.json": { + "file_sha256": "e193988525a65810e353d110e58d97f8e4224cec366e59b8f98e0d8d358ab85b", + "compared_payload_sha256": "69272fc31f859202adfec91f1b68bdee3ab308983595a848a5a124da509c46e8" + } + }, + "matches_frozen_receipts": true, + "comparison": "Decompressed bytes for gzip; omit only checker_sha256 for the path-only access adaptation; exact bytes otherwise." + } + ], + "mode": "both", + "normal_optimized_equal": true, + "scope": "Ordered algebra, exact finite source checks, and conditional local/host proofs. No new native phase compiler sweep, selected replay, all-size compiler proof, finite precision proof, or complete kappa calculation." +} diff --git a/research/publication-reviews/ordered-centre-interfaces/COLD-STDERR.txt b/research/publication-reviews/ordered-centre-interfaces/COLD-STDERR.txt new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/publication-reviews/ordered-centre-interfaces/COLD-STDOUT.txt b/research/publication-reviews/ordered-centre-interfaces/COLD-STDOUT.txt new file mode 100644 index 0000000000..ab49b11867 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/COLD-STDOUT.txt @@ -0,0 +1,21 @@ +normal ordered-normal-forms +normal content-decoders +normal current-codes +normal general-units +normal physical-line-flags +normal canonical-prefix-screen +normal retained-helpers +normal one-pair-admission +normal terminal-and-hosting +normal d25-access +optimized ordered-normal-forms +optimized content-decoders +optimized current-codes +optimized general-units +optimized physical-line-flags +optimized canonical-prefix-screen +optimized retained-helpers +optimized one-pair-admission +optimized terminal-and-hosting +optimized d25-access +PASS_ORDERED_CENTRE_INTERFACES diff --git a/research/publication-reviews/ordered-centre-interfaces/INDEPENDENT-CHECK.json b/research/publication-reviews/ordered-centre-interfaces/INDEPENDENT-CHECK.json new file mode 100644 index 0000000000..40bad5fc87 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/INDEPENDENT-CHECK.json @@ -0,0 +1,71 @@ +{ + "complete_profiles": [ + { + "complete_profile": { + "1": 704, + "2": 144, + "5": 144, + "7": 336, + "8": 192 + }, + "complete_rank_mass": 5600, + "terminal": "separated", + "terminal_rank_mass": 224 + }, + { + "complete_profile": { + "1": 576, + "2": 208, + "5": 144, + "7": 336, + "8": 192 + }, + "complete_rank_mass": 5600, + "terminal": "mixed", + "terminal_rank_mass": 224 + } + ], + "complete_state_compiler_order": true, + "imports_package_code": false, + "invertible_three_bit_maps": 168, + "moment_argument": "For b>0 and each 0r*25^(-b). The verified total mass 5600 gives strict failure for both specified completions.", + "native_data_checks": [ + { + "children": 432, + "data_columns": 224, + "direction": "backward", + "provider": "base", + "rank_mass": 1792 + }, + { + "children": 432, + "data_columns": 224, + "direction": "forward", + "provider": "base", + "rank_mass": 1792 + }, + { + "children": 432, + "data_columns": 224, + "direction": "backward", + "provider": "extra", + "rank_mass": 1792 + }, + { + "children": 432, + "data_columns": 224, + "direction": "forward", + "provider": "extra", + "rank_mass": 1792 + } + ], + "native_payload_decompressed_sha256": "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025", + "native_payload_sha256": "61fd6d0283de4af6ad53c013cd8220d8ea55d971c6980ce5259053ce31d366bd", + "negative_controls": 7, + "ordered_unit_endpoint": true, + "orthogonal_line_cases": 1152, + "scope": "Exact rational counterchecks and finite binary identities support the separately read algebraic proof. Source native phases and all-size contracts remain inherited.", + "status": "PASS_INDEPENDENT_ORDERED_INTERFACE_CHECK", + "symplectic_composition_cases": 2688, + "zero_rank_flag_cases": 384 +} diff --git a/research/publication-reviews/ordered-centre-interfaces/REVIEW.json b/research/publication-reviews/ordered-centre-interfaces/REVIEW.json new file mode 100644 index 0000000000..73b7d041b4 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/REVIEW.json @@ -0,0 +1,87 @@ +{ + "accepted_scope": [ + "All-positive-pair-count ordered content identities and stated decoder reductions.", + "General-unit one-pair code with explicit common-frame access premises.", + "Complete-state monomial compiler with admitted map premises and the stated line-flag result.", + "Separate local retained-helper completion.", + "224-role D25 admission with inherited row, LIFO, and native phase premises.", + "Two specified terminal constructions with complete rank mass 5600 and strict positive-moment failure." + ], + "evidence": { + "COLD-PORTABILITY.json": "7535c1cf1701d424fabc97606775bda1db851e9838848bc5b49d01f510355b4d", + "COLD-REPLAY.json": "e2dc8d40deb0697e0c4a87dc1bc32f3e66aaf970ff8cc93a6361cb0ab721228c", + "COLD-STDERR.txt": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855", + "COLD-STDOUT.txt": "f6bcd2f572f8946ca332923f347a3bcdf0250c1cd5ab1cc36270cef5b528c3e7", + "INDEPENDENT-CHECK.json": "7709df120635cac4ae12ce62f7e06d666a783e08782b1cbcf826828acd0515c9", + "REVIEW.md": "b531b81b79822c9cd61929b42e39e4fe7e2d36290f15c769567d427ec46194c4", + "REVIEWED-PACKAGE-SHA256.json": "a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9", + "SOURCE-ORIGINS.json": "01c1fcec93b655ceb6fbdeccbe13bd8697d8711193b71be124c0626bafb2c48d", + "independent_check.py": "10ec9d03cfa43261e27e1503d740256d6e9808de6d64d7f98da8ac1ab637e978" + }, + "external_actions": { + "commit": false, + "frontier_change": false, + "merge": false, + "publish": false, + "push": false + }, + "free_disk_bytes_after": 8972042240, + "fresh_copied_replay": { + "PATH": "/nonexistent", + "files_unchanged": true, + "git_free": true, + "modes": [ + "normal", + "optimized" + ], + "normal_optimized_equal": true, + "runs": 20, + "seconds": 98.034, + "serial": true, + "status": "PASS" + }, + "independent_check": { + "binary_full_matrix_cases": 2688, + "columns_per_native_word": 224, + "imports_package_code": false, + "native_payload_decompressed_sha256": "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025", + "native_words": 4, + "negative_controls": 7, + "orthogonal_line_cases": 1152, + "status": "PASS" + }, + "not_established": [ + "Selected PR4470 applicability", + "Universal terminal or decoder lower bound", + "All stabilizer or multicall impossibility", + "A new all-size native phase compiler proof", + "Complete map or tape price", + "Finite precision and exact integer recovery", + "Complete kappa improvement" + ], + "package": "../../ordered-centre-interfaces", + "package_files": 140, + "package_manifest_sha256": "a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9", + "resolved_findings": [ + { + "file": "RESULT.json", + "issue": "The old required_terminal_native_mass field labeled the complete mass 5600 as terminal mass.", + "proof_or_checker_changed": false, + "resolution": "Replaced by complete_native_rank_mass=5600, terminal_native_rank_mass=224, and an explicit scope excluding a universal terminal lower bound.", + "severity": "P2" + } + ], + "review_date": "2026-10-22", + "reviewer_lane": "gauge_limits_package", + "schema": "ordered-centre-independent-review-v1", + "source_files": 128, + "source_manifest_sha256": "369aaa43acaa99201d5d555336b8606399fe85c91910c9852d4faae61c95e23f", + "source_origins": { + "all_128_byte_equal": true, + "archive_member_sha256": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "archives_rehashed": 1, + "historical_archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" + }, + "status": "ACCEPTED", + "unresolved_findings": [] +} diff --git a/research/publication-reviews/ordered-centre-interfaces/REVIEW.md b/research/publication-reviews/ordered-centre-interfaces/REVIEW.md new file mode 100644 index 0000000000..bf613cc88d --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/REVIEW.md @@ -0,0 +1,123 @@ +# Independent review: ordered centre interfaces + +Status: **ACCEPTED after one metadata correction**. + +The reviewed package is `../../ordered-centre-interfaces`. +Its `PACKAGE-SHA256.json` has SHA256 +`a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9`. +The manifest covers 139 files. The package has 140 files with the manifest. +All checks below use this final version. No proof or certificate issue remains. + +## Resolved issue + +The first `RESULT.json` used `required_terminal_native_mass: 5600`. +This label could state a terminal lower bound that the proofs do not give. +The two specified complete constructions each have rank mass 5600. +Their terminal rank mass is 224. + +The producer replaced that field with `complete_native_rank_mass: 5600` +and `terminal_native_rank_mass: 224`. The new `native_mass_scope` states +that these values apply to the separated and mixed constructions. It +excludes a lower bound for every terminal. No proof, checker, or source +changed. The producer then made the final manifest above. + +## Proof review + +I read the package proof and its direct proof dependencies. I also read +the independent ordered normal forms, decoder reduction, current and +general unit codes, physical monomial codes, helper completion, one-pair +admission, D25 access, terminal hosting, native review, and primary row +split and LIFO text. The source list is in +[`DIRECT-SOURCES.json`](../../ordered-centre-interfaces/DIRECT-SOURCES.json). + +The raw and weighted endpoint results have induction proofs for every +positive pair count. They do not depend only on finite test cases. The +raw decoder determinant uses the matched local Schur complement. Its +exact nullity modulo 3 also uses the explicit unit-triangular reduction. +The determinant alone does not give that nullity. These results concern +content maps. They do not prove a native decoder cost or idle access. + +The general-unit one-pair construction preserves multiplication order. +The chronological word gives `(-y, T x)`, where +`T = E2 G1^-1 E0`. The physical residual is +`diag(Q T Q^-1, I)`. Its decoder has the stated reverse order. +The result requires the stated local responses and common-frame scalar +access. It gives no general multicall or decoder lower bound. + +The monomial compiler acts on the complete state, including helpers and +owned fields. Its recurrence is `C_(j+1) = C_j H_j`. Admission of the +composed maps remains a premise. Every later use of a helper must use +the same coordinates. The line result is scoped to the stated transfer. +Under `b^T G a = 0`, the two ranks are `n-2` and 2. The zero-rank flag +condition is `G^T b = a`. The finite prefix screen only tests its stated +canonical prefix choices. It does not cover all stabilizer choices. + +The retained 408-helper result is a separate local composition result. +Its profile has 2326 children and rank mass 3281. It is not an extra +charge in the data-only D25 word. The latter uses exactly 224 roles and +has local profile `{1:160,2:48,5:48,7:112,8:64}`, with 432 children and +rank mass 1792. Endpoint adapters are part of this contract. The D25 +role and row proof uses the inherited serial cover and LIFO premises. +It does not supply an all-size native phase compiler or a full price. + +The separated terminal has 224 rank-one children. The mixed terminal +has 96 rank-one and 64 rank-two children. Each adds rank mass 224. +Their complete profiles have mass `3*1792 + 224 = 5600 = 224*25`. +Each child has rank strictly between 0 and 25. Thus, for every `b > 0`, +`r^(1-b) > r*25^(-b)` for every child. Summation proves that both +specified complete words fail the strict positive native moment test. +This is not a lower bound for every terminal. The scalar subtotals, +28264 and 25896, are exact under the stated scalar primitive prices. +The mixed map-call inventory is not a complete operation price. + +## Fresh independent evidence + +The fresh copy used an unrelated directory, an absolute Python 3.14.7 +path, `-I -B`, and `PATH=/nonexistent`. It had no Git metadata. All ten +checks ran in normal and optimized modes. All 20 runs passed in +98.034 seconds. Their outputs agree across modes. All 140 package files +remained unchanged. The source package and the copy matched before and +after replay. See [`COLD-PORTABILITY.json`](COLD-PORTABILITY.json) and +[`COLD-REPLAY.json`](COLD-REPLAY.json). Runs were serial. + +I independently compared all 128 frozen inputs with their source bytes. +They match. I also rehashed the historical source archive and its exact +`DATA-PHASES.json` member. The archive SHA256 is +`f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6`. +The member SHA256 is +`c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa`. +See [`SOURCE-ORIGINS.json`](SOURCE-ORIGINS.json). + +The separate [`independent_check.py`](independent_check.py) imports no +package code. Exact rational matrices verify the noncommuting unit +word, physical residual, decoder order, and full-state compiler order. +Seven negative controls reject omitted scalar codes and wrong orders. +An exhaustive three-bit matrix check uses all 168 invertible maps and +all odd line pairs. It verifies 2688 full symplectic compositions, +including 1152 orthogonal-line cases. It checks the zero-rank flag by +full matrix multiplication. It does not merely evaluate the displayed +block formulas. + +That checker also reads the exact native payload and independently +replays all four words on all 224 data columns. It checks role bounds, +local profiles, unchanged helper frames, and the forward and backward +endpoints. It derives both complete profiles, both terminal masses, +and both scalar subtotals. It passed under `-I -O -B`. See +[`INDEPENDENT-CHECK.json`](INDEPENDENT-CHECK.json). These finite checks +support the separately read algebraic proofs; they do not replace them. + +## Source and scope boundaries + +The historical provider pins, source credit, and license notices remain +intact. The sole checker adaptation changes where the exact archive +member is read. The patch retains the source hash and all mathematical +checks. Receipt comparison excludes only that checker's own source hash. +The original source and complete adaptation patch are in the package. + +The packaging base `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51` and +selected PR #4470 give context only. This review does not transfer the +historical results to that construction. No selected replay, new native +phase compiler sweep, all-size compiler proof, finite map/tape price, +precision proof, or exact integer-recovery proof ran in this review. +No complete kappa improvement follows. No commit, push, publication, +merge, or frontier change was made. diff --git a/research/publication-reviews/ordered-centre-interfaces/REVIEWED-PACKAGE-SHA256.json b/research/publication-reviews/ordered-centre-interfaces/REVIEWED-PACKAGE-SHA256.json new file mode 100644 index 0000000000..c619092c03 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/REVIEWED-PACKAGE-SHA256.json @@ -0,0 +1,144 @@ +{ + "schema": "ordered-centre-package-hashes-v1", + "files": { + "DIRECT-SOURCES.json": "11251b6007f3b09cd09599a9e984db4d80723a317b663d66cfe8d82aba720294", + "NOTICE.md": "dd74b007f461cbafa057766011f16aba09e6218c260ce438417e4ca9e2a2af9c", + "PORTABLE-ADAPTATION.json": "362e7f2c968e4572456bfe2e15a02f0cb55ecdfdf8d95453c0489de029d2278a", + "PORTABLE-ADAPTATION.patch": "5c463f9629da7f69d1c5d315cd8826c52d34e9a28359d050db1ac5a6fc8700c7", + "PROOF.md": "127508fe1217eb2010886bbba2faaae8c8565137dba1dc3454279436cd315621", + "README.md": 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len(a) + rows = [[F(x) for x in row] + unit for row, unit in zip(a, eye(n))] + for i in range(n): + j = next(j for j in range(i, n) if rows[j][i]) + rows[i], rows[j] = rows[j], rows[i] + scale = rows[i][i] + rows[i] = [x / scale for x in rows[i]] + for j in range(n): + if j != i: + scale = rows[j][i] + rows[j] = [x - scale * y for x, y in zip(rows[j], rows[i])] + return [r[n:] for r in rows] + + +def block(a, b, c, d): + return [x + y for x, y in zip(a, b)] + [x + y for x, y in zip(c, d)] + + +def chronological(operations): + result = eye(len(operations[0])) + for operation in operations: + result = mm(operation, result) + return result + + +def binary_rank(a): + rows = list(a) + pivots = {} + for x in rows: + while x: + bit = x.bit_length() - 1 + if bit in pivots: + x ^= pivots[bit] + else: + pivots[bit] = x + break + return len(pivots) + + +def bm(a, b): + result = [] + for row in a: + value = 0 + for j, source in enumerate(b): + if row >> j & 1: + value ^= source + result.append(value) + return result + + +def bt(a): + return [sum(((row >> i) & 1) << j for j, row in enumerate(a)) for i in range(len(a))] + + +def bi(a): + n = len(a) + rows = [row | (1 << (i + n)) for i, row in enumerate(a)] + for i in range(n): + j = next(j for j in range(i, n) if rows[j] >> i & 1) + rows[i], rows[j] = rows[j], rows[i] + for j in range(n): + if j != i and rows[j] >> i & 1: + rows[j] ^= rows[i] + need([x & ((1 << n) - 1) for x in rows] == [1 << i for i in range(n)], "Binary inverse") + return [x >> n for x in rows] + + +def bb(a, b, c, d): + n = len(a) + return [x | (y << n) for x, y in zip(a, b)] + [x | (y << n) for x, y in zip(c, d)] + + +def line_hadamard(a, n): + pa = [a if (a >> i) & 1 else 0 for i in range(n)] + complement = [row ^ (1 << i) for i, row in enumerate(pa)] + return bb(complement, pa, pa, complement) + + +def matvec(a, x): + return sum(((row & x).bit_count() % 2) << i for i, row in enumerate(a)) + + +def check(args): + i = eye(2) + z = [[F(0)] * 2 for _ in range(2)] + neg = [[-x for x in row] for row in i] + e0 = [[F(1), F(1)], [F(0), F(1)]] + g1 = [[F(1), F(0)], [F(1), F(1)]] + e2 = [[F(2), F(1)], [F(1), F(1)]] + q = [[F(1), F(2)], [F(1), F(3)]] + gi, qi = inverse(g1), inverse(q) + need(mm(e0, g1) != mm(g1, e0), "Noncommuting test source") + operations = [block(i, z, e0, i), block(e0, z, z, i), block(i, z, z, gi), + block(i, [[-x for x in r] for r in g1], z, i), + block(gi, z, z, i), block(i, z, z, e2), block(i, z, e2, i), + block(g1, z, z, i)] + t = mm(e2, mm(gi, e0)) + endpoint = block(z, neg, t, z) + need(chronological(operations) == endpoint, "General-unit ordered endpoint") + for omitted in (1, 2, 4, 5, 7): + need(chronological(operations[:omitted] + operations[omitted + 1:]) != endpoint, + "Omitted code must change the endpoint") + exchange = block(z, mm(q, q), neg, z) + physical = mm(exchange, mm(block(i, z, z, qi), mm(endpoint, block(qi, z, z, i)))) + residual = mm(q, mm(t, qi)) + need(physical == block(residual, z, z, i), "Physical Q conjugation") + decoder = chronological([qi, inverse(e2), g1, inverse(e0), q]) + need(mm(decoder, residual) == i, "Chronological terminal inverse") + wrong = chronological([qi, inverse(e0), g1, inverse(e2), q]) + need(mm(wrong, residual) != i, "Wrong terminal order must fail") + + h = [[[F(0), F(1)], [F(1), F(0)]], [[F(1), F(0)], [F(0), F(-1)]], + [[F(0), F(-1)], [F(1), F(0)]]] + c, physical_word = i, i + bad_c, bad_word = i, i + for gate, error in zip((e0, g1, e2), h): + replacement = mm(error, gate) + physical_word = mm(mm(c, mm(replacement, inverse(c))), physical_word) + c = mm(c, error) + bad_word = mm(mm(bad_c, mm(replacement, inverse(bad_c))), bad_word) + bad_c = mm(error, bad_c) + old_word = chronological([e0, g1, e2]) + need(mm(inverse(c), physical_word) == old_word, "Complete-state code order") + need(mm(inverse(bad_c), bad_word) != old_word, "Reversed code order must fail") + + n = 3 + units, zero = [1 << j for j in range(n)], [0] * n + full = bb(zero, units, units, zero) + odd = [a for a in range(1, 1 << n) if a.bit_count() % 2] + gl_count = cases = orthogonal = zero_cases = 0 + for g in product(range(1, 1 << n), repeat=n): + if binary_rank(g) != n: + continue + gl_count += 1 + address = bb(g, zero, zero, bt(bi(g))) + for a, b in product(odd, repeat=2): + composed = bm(full, bm(line_hadamard(b, n), bm(address, line_hadamard(a, n)))) + first_rank = binary_rank([row >> n for row in composed[:n]]) + terminal = bm(composed, full) + terminal_rank = binary_rank([row >> n for row in terminal[:n]]) + flag = ((b & matvec(g, a)).bit_count() % 2) == 0 + zero_flag = matvec(bt(g), b) == a + need((terminal_rank == 0) == zero_flag, "Exact zero-rank flag") + if flag: + need((first_rank, terminal_rank) == (n - 2, 2), "Orthogonal line ranks") + orthogonal += 1 + zero_cases += zero_flag + cases += 1 + need((gl_count, cases, orthogonal) == (168, 2688, 1152), "Complete three-bit family") + + path = args.package / 'frozen/work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz' + raw = path.read_bytes() + data = json.loads(gzip.decompress(raw)) + response = [{int(k): F(v) for k, v in row.items()} for row in data['response']] + inventory = [] + for provider, programs in data['providers'].items(): + for direction, word in programs.items(): + profile, progress = Counter(), Counter() + rows = [{j: F(1)} for j in range(224)] + for event in word['events']: + if event[0] == 'native': + _, target, before, after, rank, recipe = event + need(0 <= target < 224 and rank > 0, "Native data role") + profile[rank] += 1 + progress[target] += rank + else: + need(event[0] == 'scalar', "Only scalar or native events") + gate = event[1] + target = gate[1] + need(0 <= target < 224, "Scalar data target") + if gate[0] == 'scale': + rows[target] = {j: F(gate[2], gate[3]) * v for j, v in rows[target].items()} + else: + need(gate[0] == 'add' and 0 <= gate[2] < 224, "Scalar data source") + for j, v in list(rows[gate[2]].items()): + value = rows[target].get(j, F(0)) + F(gate[3], gate[4]) * v + if value: + rows[target][j] = value + else: + rows[target].pop(j, None) + need(word['start'][224:] == word['final'][224:], "Unused helper frames") + need(set(progress) == set(range(224)) and set(progress.values()) == {8}, "Every field has rank mass eight") + need(dict(profile) == {1:160, 2:48, 5:48, 7:112, 8:64}, "Local profile") + expected = [{j: F(1)} for j in range(224)] + for port, row in enumerate(response): + target = 112 + port if direction == 'forward' else port + offset = 0 if direction == 'forward' else 112 + sign = 1 if direction == 'forward' else -1 + expected[target].update({offset + j: sign * value for j, value in row.items()}) + need(rows == expected, "Full scalar endpoint on 224 columns") + inventory.append({'provider': provider, 'direction': direction, 'children': sum(profile.values()), + 'rank_mass': sum(r * v for r, v in profile.items()), 'data_columns': 224}) + base = Counter({1:480, 2:144, 5:144, 7:336, 8:192}) + complete = [] + for name, terminal in [('separated', Counter({1:224})), ('mixed', Counter({1:96, 2:64}))]: + profile = base + terminal + mass = sum(r * count for r, count in profile.items()) + need(mass == 224 * 25 and all(0 < r < 25 for r in profile), "Strict moment premises") + complete.append({'terminal': name, 'terminal_rank_mass': sum(r * count for r, count in terminal.items()), + 'complete_profile': dict(profile), 'complete_rank_mass': mass}) + need(3 * 3032 + 8 * 2396 == 28264, "Separated scalar subtotal") + need(3 * 3032 + 5 * 2396 + 3 * 1564 + 128 == 25896, "Mixed scalar subtotal") + result = {'status':'PASS_INDEPENDENT_ORDERED_INTERFACE_CHECK', 'imports_package_code': False, + 'ordered_unit_endpoint': True, 'complete_state_compiler_order': True, + 'negative_controls': 7, 'symplectic_composition_cases': cases, + 'invertible_three_bit_maps': gl_count, 'orthogonal_line_cases': orthogonal, + 'zero_rank_flag_cases': zero_cases, 'native_payload_sha256': sha256(raw).hexdigest(), + 'native_payload_decompressed_sha256': sha256(gzip.decompress(raw)).hexdigest(), + 'native_data_checks': inventory, 'complete_profiles': complete, + 'moment_argument': 'For b>0 and each 0r*25^(-b). The verified total mass 5600 gives strict failure for both specified completions.', + 'scope': 'Exact rational counterchecks and finite binary identities support the separately read algebraic proof. Source native phases and all-size contracts remain inherited.'} + args.out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(result['status']) + + +if __name__ == '__main__': + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--package',type=Path,required=True) + parser.add_argument('--out',type=Path,required=True) + check(parser.parse_args()) From 4258585b17450907d26b137c047e254cd9007bae Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 13:38:45 -0500 Subject: [PATCH 2/3] Add common-cover terminal and all-pair reciprocal controller --- .../common-cover-terminal/ANNEX-MANIFEST.json | 175 + .../annexes/common-cover-terminal/NOTICE.md | 16 + .../annexes/common-cover-terminal/README.md | 118 + .../common-cover-terminal/SOURCES.json | 130 + .../evidence/DOCUMENT-LINKS.json | 50 + .../evidence/REPLAY.json | 44 + .../evidence/replay/REPLAY.json | 44 + .../replay/rank_limit/normal/CHECKS.json | 22 + .../replay/rank_limit/normal/stdout.log | 1 + .../replay/rank_limit/optimized/CHECKS.json | 22 + .../replay/rank_limit/optimized/stdout.log | 1 + .../replay/terminal/normal/CHECKS.json | 826 + .../replay/terminal/normal/stdout.log | 1 + .../replay/terminal/optimized/CHECKS.json | 826 + .../replay/terminal/optimized/stdout.log | 1 + .../CYCLE-COVER-PROGRAMS.json | 103050 +++++++++++++++ .../CYCLE-COVER-RESPONSE.md | 220 + .../lanes/circuit-interface/INTERFACE.json | 1441 + .../NORMALIZATION-PROGRAMS.json | 1 + .../CHECKS.json | 71 + .../COMMON-TERMINAL.md | 212 + .../FREEZE.json | 16 + .../TERMINAL-PROGRAMS.json | 45500 +++++++ .../check_common_terminal.py | 274 + .../CHECKS.json | 22 + .../FREEZE.json | 12 + .../LIMIT.md | 64 + .../check_limit.py | 105 + .../CHECKS.json | 826 + .../FREEZE.json | 12 + .../REPRODUCTION.json | 4 + .../common-terminal-review-20261018/REVIEW.md | 152 + .../check_terminal.py | 238 + .../common-cover-terminal/notices/LICENSE | 201 + .../annexes/common-cover-terminal/replay.py | 89 + .../reciprocal-controller/ANNEX-MANIFEST.json | 82 + .../annexes/reciprocal-controller/PROOF.md | 47 + .../reciprocal-controller/PUBLICATION.md | 7 + .../annexes/reciprocal-controller/README.md | 24 + .../annexes/reciprocal-controller/REVIEW.json | 15 + .../annexes/reciprocal-controller/REVIEW.md | 65 + .../reciprocal-controller/SOURCES.json | 41 + .../annexes/reciprocal-controller/TASK.json | 9 + .../reciprocal-controller/VALIDATION.json | 35 + .../lanes/circuit-interface/INTERFACE.json | 1441 + .../NORMALIZATION-PROGRAMS.json | 1 + .../reciprocal-response-20261018/CHECKS.json | 368 + .../reciprocal-response-20261018/FREEZE.json | 9 + .../RECIPROCAL-CONTROLLER.md | 265 + .../check_reciprocal_controller.py | 252 + .../interior-cut/UNIT-MODE-CANDIDATE.json | 1863 + .../annexes/reciprocal-controller/replay.py | 72 + .../validation/normal.log | 1 + .../validation/optimized.log | 1 + .../BASE-PRESERVATION-CHECK.json | 7 + .../BODY-CLAIM-CHECK.json | 15 + .../CAMPAIGN-SOURCE-CHECK.json | 96 + .../FINAL-ANNEX-INTEGRITY.json | 219 + .../INITIAL-INPUT-HASHES.json | 22 + .../common-terminal-review/PROOF-REVIEW.md | 96 + .../common-terminal-review/REPLAY.json | 44 + .../common-terminal-review/REVIEW.json | 235 + .../common-terminal-review/REVIEW.md | 57 + .../SOURCE-PROOF-PINS.json | 14 + .../replay-logs/rank_limit/normal/CHECKS.json | 22 + .../replay-logs/rank_limit/normal/stdout.log | 1 + .../rank_limit/optimized/CHECKS.json | 22 + .../rank_limit/optimized/stdout.log | 1 + .../replay-logs/terminal/normal/CHECKS.json | 826 + .../replay-logs/terminal/normal/stdout.log | 1 + .../terminal/optimized/CHECKS.json | 826 + .../replay-logs/terminal/optimized/stdout.log | 1 + 72 files changed, 161890 insertions(+) create mode 100644 research/ordered-centre-interfaces/annexes/common-cover-terminal/ANNEX-MANIFEST.json create mode 100644 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"bytes": 11357, + "path": "notices/LICENSE", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + { + "bytes": 4026, + "path": "replay.py", + "sha256": "88b8afc8f12f0863dfad34bbb4933523db681223c7b6ab4be0d61244a4684b9a" + } + ], + "scope": "Additive annex. Existing accepted package files and manifests are unchanged." +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/NOTICE.md b/research/ordered-centre-interfaces/annexes/common-cover-terminal/NOTICE.md new file mode 100644 index 0000000000..5dc960ddd4 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/NOTICE.md @@ -0,0 +1,16 @@ +# Notice + +The bridge-access lane supplied the actual common ten-cycle cover response +and phase records. The encoded-controller lane supplied the common-response +controller, finite terminal, and universal cover-only line-cut limit. +The independent-review lane supplied the separate terminal proof, complete +phase and kernel check, and symbolic rank review. This annex packages those +existing results; it does not claim a new construction. + +Substantial OpenAI Codex assistance was used for the original research, +proofs, checks, and this package. These are agent reviews, not independent +human review. New wrapper material uses Apache-2.0; the +[license](notices/LICENSE) is retained. The [parent notice](../../NOTICE.md) +retains the historical source and contributor lineage. Frozen sources are +unchanged. Historical local-only status text remains evidence of the +status at that freeze. diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/README.md b/research/ordered-centre-interfaces/annexes/common-cover-terminal/README.md new file mode 100644 index 0000000000..9bc48909d0 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/README.md @@ -0,0 +1,118 @@ +# Common-cover terminal and its standalone rank limit + +This annex supplies the actual terminal for the common cover response on +D=73 binary axes. It also proves a sharp standalone rank-two bound for +every orthogonal extension of the admitted first line cut. It is distinct +from the paid one-pair D25 terminals in the parent package. + +No complete kappa improvement follows. The terminal is finite under the +stated map and child contracts. Fresh local native words, whole-cover +scheduling, recursive hosting, finite map costs, and precision remain +separate obligations. The full native-moment conclusion also requires +the complete path and idle ledger. + +Read the [construction](frozen/lanes/encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md), +[universal line-cut proof](frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md), +[independent proof review](frozen/lanes/independent-review-20261017/common-terminal-review-20261018/REVIEW.md), +and [fresh replay receipt](evidence/REPLAY.json). + +## Exact terminal + +The actual common response acts only on the cover label: +(E f)_p(h)=f_p(h L_p), where each L_p is the pinned orthogonal ten-cycle. +The raw controller gives (-E^-1 y, E x) for every positive pair count. +This follows from the common-response change of variables and does not +use E^10=I. The check separately verifies the actual four-pair schedule +with nineteen content events and ten idle sites. + +At the physical terminal, U=-F E^-1 y and V=F Q^-1 E x. Put +M_I=F E^-1 F^-1 and M_E=F E F^-1. The ordered terminal applies Q, M_I, +and Q to V; it applies M_E to U, then makes the signed exchange +(X,Y)=(V,-U). The endpoint is (F Q x,F y) on arbitrary input arrays. +No commutation of E with Q is used. No encoded result passes to an +unchanged outer twiddle or product. + +For each actual port, the X branch uses the distinct positive line +transforms C_(h q) and C_(h L_p^-1 q). Their directions are orthogonal. +One rank-two native child implements their product. The exact wrappers +bind the cover direction, affine offset, and four Gaussian kernel +coefficients, including the global phase. The Y branch uses one FULL +cover/translation map and the retained signed exchange. The complete +polynomial and address identities hold at every tensor depth. + +| Per four-pair replica | Count | +| --- | ---: | +| Positive rank-two children | 448 | +| Native rank mass | 896 | +| Child wrapper maps | 896 | +| Additional FULL cover/translation maps | 448 | +| Total monomial maps | 1344 | +| Old line-square maps removed | 448 | +| Net increase in monomial maps | 896 | +| Retained signed-exchange real primitives | 10752 | + +The signed exchange uses the same retained work as the old terminal. +No new full-cover record or helper field is needed by this terminal. +Its map count is not an execution price, and the recursive child cost +is not included in the table. + +## Sharp class and limit + +Let q and v be odd binary vectors with q^T v=0. Every admitted orthogonal +L with Lq=v gives w=L^-1 q with q^T w=0. Both q and w have norm one. +The standalone X terminal has Clifford upper-right block q q^T+w w^T, +which has rank two. Monomial views preserve this rank; the rank of a +Clifford product is at most the sum of its factors' ranks. Thus every +one-field Clifford terminal word in this class needs total native rank +at least two. The actual recipe attains the bound. + +This is a theorem for a port-diagonal orthogonal cover-only response and +the stated first line cut. It does not bound circuits that mix fields, +change that cut, use a payload response, or fuse the terminal with an +earlier operation. It is not a multiplication-algorithm lower bound. + +If the complete productive paths and idle accounting give rank +2mn(D-1), this terminal brings the total to 2mnD. For positive b and +child widths r at most D, r^(1-b) is at least r D^-b. Repartitioning that +same rank therefore cannot give positive native-moment savings. This +last application remains conditional on the full ledger. + +## Replay and source scope + +Run with Python 3.11 or later, the standard library, at least 3 GiB free, +and a new output directory. No network is required. + +```sh +python3 -I -B replay.py --out /tmp/common-cover-terminal-annex +``` + +Expected final line: + +```text +PASS_COMMON_COVER_TERMINAL_ANNEX +``` + +The runner uses unchanged source checkers in fresh copies. It runs the +independent terminal check and the separate finite rank-control check in +normal and optimized Python. All four receipts match their frozen bytes. +The terminal check verifies every actual port, full Z4 coefficients, +complete affine four-point kernels, both cover directions, and wrong-line, +missing-line, missing-translation, and wrong-cover controls. The finite +rank check enumerates all orthogonal matrices in dimensions three and +five and checks all 112 actual cycles. The universal rank claim follows +from the symbolic proof, not from these finite dimensions. + +The old independent review did not rerun that finite enumeration. This +annex does, and records it separately. No producer emitter, complete +native supplier, global owner schedule, or recursive precision check was +rerun. [SOURCES.json](SOURCES.json) pins the eighteen original inputs. +The [common-response source proof](frozen/lanes/bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-RESPONSE.md) +is retained as context; its full stage-admission producer suite was not +rerun. [NOTICE.md](NOTICE.md) gives contribution credit and the license. + +## Open next question + +A cheaper complete supplier would need a result outside the sharp class, +such as a proved fusion with productive work or a different admitted +response. Any such construction still needs the actual path, owner, +map-cost, and precision ledger. 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No recursive hosting, map-time price, complete supplier invoice, or precision certificate.", + "source_pins": { + "bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json": "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da", + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "encoded-controller/NORMALIZATION-PROGRAMS.json": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9", + "encoded-controller/common-monomial-terminal-20261018/CHECKS.json": "27f222e13cc26291fe3d0dd25b1740029c906f5cbb080db79d9599fb262795b2", + "encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md": "d57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad", + "encoded-controller/common-monomial-terminal-20261018/FREEZE.json": "e342c8d646a5c7cb5ee8cfd53d231c91a572b24894b9217a3a9533c00cce09f0", + "encoded-controller/common-monomial-terminal-20261018/TERMINAL-PROGRAMS.json": "c87e99deeffa12b30b37f633c784118623aba1a4680ad3ae925d29be4f91a4d6", + "encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py": "4d28d8b98cf6de28e6eb2195e5ca1e461ab0aea5991a3aa700f2a1330fef5cfe", + "encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json": "4103d8e89f10b8d8dcf7ba54c8e51cc6c685e36b9fff40ad86dc1d6bf532a427", + "encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md": "5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3" + }, + "status": "PASS_INDEPENDENT_COMMON_COVER_TERMINAL" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/evidence/replay/terminal/normal/stdout.log b/research/ordered-centre-interfaces/annexes/common-cover-terminal/evidence/replay/terminal/normal/stdout.log new file mode 100644 index 0000000000..144265da52 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/evidence/replay/terminal/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_COMMON_COVER_TERMINAL diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/evidence/replay/terminal/optimized/CHECKS.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/evidence/replay/terminal/optimized/CHECKS.json new file mode 100644 index 0000000000..3237944fef --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/evidence/replay/terminal/optimized/CHECKS.json @@ -0,0 +1,826 @@ +{ + "checker_sha256": "a74cb8ea2464396d44cf86e9d87ca798f66009074facc28819f0a81f062838ec", + "controller": { + "actual_content_events": 19, + "actual_idle_sites": 10, + "arbitrary_input_blocks": 8, + "arithmetic": "Free Laurent integer coefficients; no cycle relation is used." + }, + "inventory_per_replica": { + "FULL_source_maps": 448, + "child_wrapper_maps": 896, + "native_rank_mass": 896, + "net_added_monomial_maps": 896, + "new_full_cover_records": 0, + "new_top_level_scalar_primitives_beyond_retained_exchange": 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"c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-RESPONSE.md b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-RESPONSE.md new file mode 100644 index 0000000000..45fd0c8d13 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-RESPONSE.md @@ -0,0 +1,220 @@ +# One cover response at all nine pure-line cuts + +This packet gives one unitary response E on the actual 73-axis cover. +The same E has a physical monomial transfer at all nine cuts of the +fresh three-child template. The transfer needs no native child and no +temporary array. It applies to arbitrary cover contents. It does not +assume that different cover classes contain the same data. + +The result removes a stage-transport obstacle for a changed local +template. It does not improve the complete supplier exponent by itself. +The direct terminal decoder has rank mass 896 per four-pair replica. +Together with the productive advances, that decoder exhausts the rank +budget. A cheaper decoder or a fusion with productive advances is still +needed for a supplier gain. + +## Sources and conventions + +The source archive is +`worktrees/k5-persistent-cleanup/research/community-frontier1094-audit/selected-replay.tar.gz`, +SHA-256 `f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6`. +The checker reads its member +`candidate/strict/global/base/work/complex-nine-native/DATA-PHASES.json`, +SHA-256 `c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa`. +The imported phase and route code is `../check_bridge_access.py`, +SHA-256 `9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111`. + +Use the full cover G=O(73,2). This is the selected cover; no larger cover +is used. Its elements act on column vectors on the left. A cover label +h is independent of a payload address. The route rho_(s,p) exchanges +the eight root complement axes with the eight axes of stage s. It is +the identity at stage zero. All these routes are orthogonal +involutions. + +C_w is the pure directional complex transform. On a Fourier character +chi it has eigenvalue i raised to the bit w.chi. For an ordered list A, +write C_A for the product of its C_w factors. T_d is the payload +translation by d. Its Fourier eigenvalue is (-1) raised to d.chi. +All these transforms commute. The statements hold on every coordinate +copy. For width f, apply each translation on all f copies. + +The fresh local word is in +`../../history-encoding/independent-skeleton-20261018/fresh-three-child/`. +Its exact transfer frames are C_q and C_v. They are not the compiler's +`canonical_frame([q])` and `canonical_frame([v])`. The native child +recipes are a separate dependency. This packet proves their global +transfer-slot condition, including the exterior frames. + +## The common response + +Fix a port p. Let q be its actual odd port vector, and let v_0 be the +first complement vector in its actual orthogonal chart. For 1<=s<=8, +let v_s be the first coordinate axis of the stage-s block. The ten +vectors + + q, v_0, v_1, ..., v_8 + +are orthonormal. Define L_p to cycle these vectors in the displayed +order and fix their orthogonal complement. Then L_p is orthogonal, +has order ten, and has inverse L_p^T. Its literal 73 columns and inverse +columns are in `CYCLE-COVER-PROGRAMS.json` for every port. + +Define E on the complete cover family by + + (E f)_p(h) = f_p(h L_p). + (E^-1 f)_p(h) = f_p(h L_p^-1). + +E acts only on the cover label. It does not change a payload address. +It is a permutation and therefore a unitary map. It is independent of +the stage. No commutation with the intrinsic Q operator is assumed. + +In the forward direction, source class h sends its content to target +class h L_p^-1. Both classes are in the original cover. This orientation +fixes the order of every route and phase below. + +## Exact physical transfer at every cut + +At stage zero, the source and target cut frames in owner coordinates +are C_q and C_v0. At stage s>0, define A_s as the ordered coordinate +axes of the first 9+8(s-1) coordinates. The two frames are + + source: C_A_s, + target: C_A_s C_q^-1 C_v_s. + +Write U_s and V_s for these two frame products. The target is at +h L_p^-1 when the source is at h. The required physical block is + + V_(s,h L_p^-1) U_(s,h)^-1. + +The cycle maps the source polar subspace onto the target polar +subspace. More is needed for the pure-C phases. Let phi_A(chi) be the +sum modulo four of the bits w.chi for the factors C_w in A, with the +stated signs. The checker expands this as a full quadratic polynomial +over binary coordinates, with coefficients modulo four. For every +port and stage it proves + + phi_V_s(L_p chi) - phi_U_s(chi) = 2 delta_(p,s).chi. + +Equivalently, it substitutes L_p^-1 into the target factor vectors. +Thus the complete physical block is exactly + + T_(h delta_(p,s)). (1) + +There is no missing constant phase: all frame products have value one +on the zero character. The checker proves (1) by coefficient equality, +not by a finite sample of characters. Omitting delta fails in 896 of +the 1,008 cut cases. At stage zero the phase correction is zero. + +One forward transfer can therefore use the following exact word: + +1. Use the cover map h -> h L_p^-1 and the translation in (1) as a + temporary view of X. +2. Add that X view into Y with coefficient one. +3. Restore the original X view. + +The source is unchanged. The target content becomes y+E x in its +correct frame. In the reverse word, use the inverse matching and +translation, subtract Y from X, and restore the Y view. Since E is +unitary, this is the required reciprocal response E^-1. The result is +an operator identity on both arbitrary banks; no zero-input premise +is used. + +## Literal body routes and whole-cover sweeps + +For source owner h, the current source invocation body is + + d_x = h rho_(s,p). + +For its matching target owner h L_p^-1, the target body is + + d_y = h L_p^-1 rho_(s,p) + = d_x rho_(s,p) L_p^-1 rho_(s,p). (2) + +The payload stores the literal columns of (2). The checker verifies +both the body equation and its inverse. In general d_x and d_y are +different. A same-body transfer is not used. + +The old DATA entry translations are also retained. The checker proves +that the actual entry view converts U_s to the common exterior times +C_q, and converts V_s to the same exterior times C_v0. It uses the +literal DATA entry_X and entry_Y values and verifies that they agree. +The owner-coordinate transfer (1) must be composed with these entry +views. Undoing an entry view, applying (1), and restoring the view is +one valid finite monomial implementation. Adjacent maps can instead +be composed. This is scalar and address work, not a free omitted cost. + +The three-child word must run in three complete cover sweeps. First, +prepare all target C_v0 lines. Second, run all matched transfers (2). +Third, run all productive completions. This order is legal for the +following reasons. Each child is an operation on one productive data +field and returns its own recursive workspace. Each transfer has one +unchanged source and one target. The matching in (2) is a bijection, +so each target is written once for this port. Different ports use +different fields. No private or helper value has to survive between +two bodies. Consequently the order within each sweep is arbitrary, +and the sweep boundary creates no additional storage obligation. + +This argument supplies a rescheduling of the helper-free word. It +does not authorize such a rescheduling for an old word with live +private or helper state across its body boundaries. + +## Native profile and FULL code + +The fresh native children on each port are + + C_v0, rank 1; + F_9 C_q^-1, rank 8; + F_9 C_q^-1 C_v0^-1, rank 7. + +There are 112 of each. The profile is {1:112,7:112,8:112}, with 336 +children and rank mass 1,792. The transfers add 112 unit complex ADDs +and no native child. The separate native emitter gives the exact +monomial side maps and scalar price. Whole-cover routing and its finite +address price must also be included in the complete supplier invoice. + +Let F be the full 73-axis pure-C frame. The physical FULL codes +M_E=F E F^-1 and M_Einv=F E^-1 F^-1 are monomial. At output class h, +their literal forms are + + (M_E z)_p(h) = T_(h delta_E,p) z_p(h L_p), + (M_Einv z)_p(h) = T_(h delta_Einv,p) z_p(h L_p^-1). + +The two delta values are stored as `FULL_E_output_translation` and +`FULL_E_inverse_output_translation`. The checker proves both complete +phase equations and both orientation conventions for every port. + +The common-response controller algebra is a separate dependency. Its +raw endpoint after the old terminal has code + + diag(Q E Q^-1, E^-1). + +The direct correction is Q^-1, M_Einv, Q on the first bank, and M_E +on the second. Since L_p^-1 q=v_8, the two line directions at the first +bank output are h q and h v_8. They are distinct and orthogonal. This +uses two rank-one children per port, or one rank-two child. For four +pairs the rank mass is 896. This proof does not remove either line. + +The total productive rank is 64,512 before that correction. The direct +correction brings it to 65,408=896*73. Thus this direct completion has +no positive native-moment margin. A local admission result must not be +reported as a complete exponent improvement. + +## Verification and status + +Run one process: + + python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py + +Expected output: `PASS_COMMON_CYCLE_COVER_RESPONSE`. +The normal and `-O` runs produced identical program and receipt bytes. +The receipt records 1,008 complete transfer phase checks, 2,016 entry +frame checks, 1,008 body bijections, and 224 FULL code phase checks. +All arithmetic is exact. These checks do not replay the full supplier +or its recursive hosting. Independent review is recorded separately. + +This work uses the selected native geometry, the helper-free template +from the history-encoding lane, and the common-response controller +algebra from the encoded-controller lane. OpenAI Codex supplied the +research and verification under the user's direction. No PR, push, or +publication is authorized. 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"actual_content_events": 19, + "actual_idle_sites": 10, + "all_m_free_E_tests": [ + { + "arbitrary_input_blocks": 4, + "pairs": 1 + }, + { + "arbitrary_input_blocks": 16, + "pairs": 2 + }, + { + "arbitrary_input_blocks": 36, + "pairs": 3 + }, + { + "arbitrary_input_blocks": 64, + "pairs": 4 + }, + { + "arbitrary_input_blocks": 100, + "pairs": 5 + }, + { + "arbitrary_input_blocks": 144, + "pairs": 6 + }, + { + "arbitrary_input_blocks": 196, + "pairs": 7 + }, + { + "arbitrary_input_blocks": 256, + "pairs": 8 + } + ], + "checker_sha256": "4d28d8b98cf6de28e6eb2195e5ca1e461ab0aea5991a3aa700f2a1330fef5cfe", + "exact_native_kernel_checks": 112, + "inventory_per_replica": { + "FULL_source_maps": 448, + "child_wrapper_maps": 896, + "native_rank_mass": 896, + "net_added_monomial_maps": 896, + "new_full_cover_records": 0, + "new_top_level_scalar_primitives_beyond_retained_exchange": 0, + "old_line_square_maps_removed": 448, + "pairs": 4, + "ports_per_bank": 112, + "rank_two_children": 448, + "retained_exchange_real_primitives": 10752, + "retained_signed_exchanges": 448, + "retained_unit_complex_ADDs": 1344, + "total_monomial_maps": 1344 + }, + "negative_controls": { + "nonreciprocal_controller": 8, + "phase_mutations": 560, + "wrong_cover_direction": 112 + }, + "port_phase_polynomial_checks": 605248, + "program_sha256": "c87e99deeffa12b30b37f633c784118623aba1a4680ad3ae925d29be4f91a4d6", + "proof_sha256": "d57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad", + "scope": "Finite terminal and ordered raw controller. The local native words, complete owner schedule, recursive child hosting, map price, and precision are separate dependencies. The conditional native rank balance gives no positive kappa gain.", + "source_pins": { + "bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json": "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da", + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "encoded-controller/NORMALIZATION-PROGRAMS.json": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9" + }, + "status": "PASS_COMMON_COVER_INTEGRATED_TERMINAL" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md new file mode 100644 index 0000000000..8edd928852 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md @@ -0,0 +1,212 @@ +# A finite terminal for the common cover response + +This note gives a complete physical terminal for a common reciprocal +cover response. It does not require the response to commute with an +intrinsic port line. It contracts the two terminal line calls to one +rank-two child per X field. + +The common response and its stage phase maps are supplied by +`../../bridge-access-20261017/cycle-cover-response-20261018/`. +This terminal does not certify the fresh local native words, the global +owner schedule, or the complete scalar and precision invoice. Its native +rank is explicit. The resulting rank balance does not give a positive +kappa improvement. + +## 1. Coordinates and common response + +Let h be an orthogonal cover matrix on D=73 binary axes. Let q_p be the +odd intrinsic vector of port p. Write + + Q_(p,h)=C_(h q_p), q_(p,h)=Q_(p,h)^-1, + F_h=product_j C_(h e_j). + +Every C_v acts on the payload coordinates. For tensor depth lambda, +apply the same map to each payload column. The cover label h is separate +from the payload coordinates. + +The raw original input is (Qx,y). This is a coordinate convention; no +initial Q call is added. The local endpoints have the original frames: + + forward: (x,y) -> (x,y+E x), + backward: (x,y) -> (x-E^-1 y,y). + +The input and output native frames must be included in these equations. +In particular, Y has the inverse intrinsic line at its output. + +For each port, the pinned cycle L_p has order ten. It sends + + q_p -> v_0 -> v_1 -> ... -> v_8 -> q_p, + +where v_j for j>=1 is the first axis of fresh block j. These ten vectors +are orthonormal. The common logical response is + + (E f)_p(h)=f_p(h L_p), + (E^-1 f)_p(h)=f_p(h L_p^-1). (1) + +It does not change the payload values. Its physical realization at an +interior cut is a separate cover map with the phase correction in the +source packet. Equation (1) is common to all nine stages; equality of +local coefficient matrices alone would not establish this fact. + +## 2. The raw controller closes to an explicit code + +Use the retained m-pair controller: initial F0, then B and F on each +pair, the plus and minus bridges to the next pair, the idle jobs, the +descending final bridges, and the old terminal site. Every local F uses +E; every local B uses E^-1. No additional logical code is inserted. + +The exact logical output before the terminal is + + X_i=-E^-1 y_i, Y_i=E x_i. (2) + +For a direct proof, change variables to xbar=E x and ybar=y. The F and B +calls become the ordinary unit shears on (xbar,ybar). Every retained +bridge also becomes its ordinary unit bridge because the same E acts +on every X bank. The unit controller gives (-ybar,xbar). This proves +(2) for every m. All inputs are arbitrary. + +The checker also replays the exact pinned nineteen content events and +ten idle sites for m=4. It uses free integer powers of E. It does not use +the cycle relation E^10=I to obtain (2). + +In physical coordinates, put U=X_preterminal and V=Y_preterminal. Then + + U=-F E^-1 y, V=F q E x. (3) + +With the old terminal alone, the raw physical output code would be +diag(Q E Q^-1,E^-1). The first factor is not E. We do not move E across Q. + +## 3. The integrated physical terminal + +Define the FULL-frame maps + + M_E=F E F^-1, M_I=F E^-1 F^-1. + +Replace the old terminal line-square map and signed exchange by: + +1. V <- Q V. +2. V <- M_I V. +3. V <- Q V. +4. U <- M_E U. +5. (X,Y) <- (V,-U). + +Both line calls are positive. From (3), their ordered action gives + + V: F q E x -> F E x -> F x -> F Q x, + U: -F E^-1 y -> -F y. + +The final signed exchange therefore gives F times the raw original input +(Qx,y). No encoded state passes to an unchanged outer twiddle or product. +The terminal is valid for arbitrary x and y and for each tensor depth. + +## 4. Exact cover and phase recipes + +Let delta_p and epsilon_p be the source packet's +`FULL_E_output_translation` and `FULL_E_inverse_output_translation`. +They satisfy + + (M_E f)_p(h)=X_(h delta_p) f_p(h L_p), + (M_I f)_p(h)=X_(h epsilon_p) f_p(h L_p^-1). + +Here X_v denotes a payload translation. The checker verifies these +translations from the full Z4 phase polynomial on all 73 basis vectors +and all 2,628 pairs. The phase polynomial has degree at most two, so this +is a complete coefficient check, not a sample. It also verifies +L_p epsilon_p=delta_p. + +Since L_p^-1 q_p=v_8, the terminal has the following literal output form: + + X_new,p(h)=X_(h epsilon_p) C_(h q_p) C_(h v_8) + V_p(h L_p^-1), + Y_new,p(h)=-X_(h delta_p) U_p(h L_p). (4) + +Translations commute with both line transforms. The two line directions +are independent and orthogonal. Their product is one positive rank-two +native transform. + +For each port, choose an orthogonal binary basis matrix G_p whose first +columns are q_p and v_8. Two orthogonal transvections send e_0 to q_p +and fix v_8. A swap of input axes 1 and 65 then gives this basis. The +emitted recipe uses: + + right view: read cover h L_p^-1 and payload h G_p z; + child: apply C_e0 C_e1; + left view: z=G_p^-1 h^-1 w+G_p^-1 epsilon_p. + +These two views implement the first line of (4). The second line is one +cover/translation map followed by the retained signed exchange. No full +cover record, helper field, or new zero field is required by this +terminal. Array-map execution and recursive child hosting still use the +admitted map and child contracts. + +## 5. Finite terminal inventory + +For m pairs and n=112 ports per bank, the replacement terminal has: + +| Item | Count | +| --- | ---: | +| Rank-two native children | mn | +| Native rank mass | 2mn | +| Child wrapper maps | 2mn | +| FULL source cover/translation maps | mn | +| Signed bank exchanges | mn | + +For m=4, these are 448 rank-two children, rank mass 896, and 1,344 +monomial array maps. The signed exchange is the same as in the old +terminal. It can use three unit complex ADDs, or 24 real scalar +primitives per port pair. Thus its 10,752 real primitives per replica +are retained work, not a new surcharge. + +The old 448 line-square translation maps are removed. Relative to that +terminal lowering, there are 896 more monomial maps. The cover maps and +translations in (4) need no scalar multiplication. This inventory does +not include the recursive cost of the rank-two children, native map +execution, earlier local calls, idle jobs, or finite precision. + +Two rank-one calls per X field are an alternative implementation with +the same rank mass. The rank-two contraction reduces the child count. +It does not reduce native rank. + +## 6. Exact rank limit of this terminal + +After its cover permutation is removed, each X terminal block in (4) +has Fourier rank two. Left and right monomial maps preserve this rank. +For a one-field Clifford word, the Fourier rank of a product is at most +the sum of the Fourier ranks of its factors. Thus every terminal in this +word class needs total native rank at least two per X field. The emitted +rank-two child attains that bound. + +This is a bound for one-field Clifford terminal words. It does not rule +out a changed multi-field circuit or a change to an earlier local call. + +The fresh independent data paths use D-1 native rank per productive +field before this terminal. There are 2mn such fields. The terminal adds +2mn rank. Under that complete path and idle accounting, total native +rank is exactly 2mnD, the productive target rank. + +This equality cannot give a positive saving exponent merely by changing +the child partition. If every child width r is at most D and b>0, then + + r^(1-b) >= r D^-b. + +Summing at equal total rank gives native weight at least +2mn D^(1-b). Extra scalar or map work cannot improve this inequality. +The independent owner and budget packets must verify the complete path +accounting before this conclusion is applied to a hosted supplier. + +## 7. Validation and remaining work + +The checker pins the common cycle payload and the retained controller. +It checks the raw controller for one through eight pairs, the actual +four-pair recipe, all 112 cycle matrices and inverses, all FULL phase +polynomials, all two-axis child bases, and the signed terminal order. +Wrong line directions, wrong cover direction, a missing FULL translation, +and an omitted terminal line are negative controls. + +The proof supplies the all-m and all-tensor statements. Finite checks +support those proofs. Fresh local native emission, stage scheduling, +owner admission, the complete invoice, and precision are separate. + +No PR, commit, push, or publication is part of this work. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/FREEZE.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/FREEZE.json new file mode 100644 index 0000000000..b216669df3 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/FREEZE.json @@ -0,0 +1,16 @@ +{ + "commands_run": [ + "python3 -I -B check_common_terminal.py", + "python3 -O -I -B check_common_terminal.py" + ], + "files": { + "CHECKS.json": "27f222e13cc26291fe3d0dd25b1740029c906f5cbb080db79d9599fb262795b2", + "COMMON-TERMINAL.md": "d57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad", + "TERMINAL-PROGRAMS.json": "c87e99deeffa12b30b37f633c784118623aba1a4680ad3ae925d29be4f91a4d6", + "check_common_terminal.py": "4d28d8b98cf6de28e6eb2195e5ca1e461ab0aea5991a3aa700f2a1330fef5cfe" + }, + "future_PR_standard": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "publication": "Local only. No PR, commit, push, or publication.", + "scope": "The normal and optimized runs produce byte-identical program and receipt files. The raw controller, complete terminal phases, and literal child views pass. Local native words, full owner hosting, array-map execution cost, and precision remain separate.", + "status": "PASS_COMMON_COVER_INTEGRATED_TERMINAL" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/TERMINAL-PROGRAMS.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/TERMINAL-PROGRAMS.json new file mode 100644 index 0000000000..f45a6ae06f --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/TERMINAL-PROGRAMS.json @@ -0,0 +1,45500 @@ +{ + "input_contract": "U=-F E^-1 y; V=F Q^-1 E x; original raw input is (Qx,y)", + "inventory_per_replica": { + "FULL_source_maps": 448, + "child_wrapper_maps": 896, + "native_rank_mass": 896, + "net_added_monomial_maps": 896, + "new_full_cover_records": 0, + 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"bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json": "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da", + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "encoded-controller/NORMALIZATION-PROGRAMS.json": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9" + } +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py new file mode 100644 index 0000000000..6862791320 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py @@ -0,0 +1,274 @@ +"""Check the raw common-response controller and its finite terminal.""" + +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +N = 73 +UNIT = [1 << j for j in range(N)] +CYCLE = LANES / "bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json" +SCHEDULE = LANES / "encoded-controller/NORMALIZATION-PROGRAMS.json" +INTERFACE = LANES / "circuit-interface/INTERFACE.json" +PINS = { + CYCLE: "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da", + SCHEDULE: "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9", + INTERFACE: "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", +} + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def act(columns, value): + out = 0 + while value: + bit = value & -value + out ^= columns[bit.bit_length() - 1] + value ^= bit + return out + + +def transpose(columns): + return [sum(((columns[j] >> i) & 1) << j for j in range(N)) + for i in range(N)] + + +def compose(left, right): + return [act(left, column) for column in right] + + +def parity(value): + return value.bit_count() & 1 + + +def rank(columns): + pivots = {} + for value in columns: + while value: + lead = value.bit_length() - 1 + if lead in pivots: + value ^= pivots[lead] + else: + pivots[lead] = value + break + return len(pivots) + + +def transvection(vector, value): + return value ^ (vector if parity(vector & value) else 0) + + +def child_basis(q, last): + anchor = next(e for e in UNIT if e != 1 and e != last and not e & q) + v1, v2 = 1 ^ anchor, anchor ^ q + need(not parity(v1) and not parity(v2), "Both transvections are orthogonal") + columns = [transvection(v2, transvection(v1, e)) for e in UNIT] + columns[1], columns[65] = columns[65], columns[1] + inverse = transpose(columns) + need(columns[:2] == [q, last], "The child uses the two stated lines") + need(compose(columns, inverse) == compose(inverse, columns) == UNIT, + "The child basis is orthogonal") + return columns, inverse, [v1, v2] + + +def add_row(target, source, coefficient=1, shift=0): + out = dict(target) + for (input_row, exponent), value in source.items(): + key = (input_row, exponent + shift) + out[key] = out.get(key, 0) + coefficient * value + if not out[key]: + del out[key] + return out + + +def recipe(pairs): + events = [{"kind": "local", "stage": 0, "pair": 0, "reverse": False}] + for i in range(pairs): + s, t = 2 * i + 1, 2 * i + 2 + events.append({"kind": "local", "stage": s, "pair": i, "reverse": True}) + if i + 1 < pairs: + events.extend([ + {"kind": "idle", "pair": i + 1, "from": -1, "to": s}, + {"kind": "bridge", "dst": i, "src": i + 1, "coefficient": 1}, + ]) + events.append({"kind": "local", "stage": t, "pair": i, "reverse": False}) + if i + 1 < pairs: + events.extend([ + {"kind": "idle", "pair": i + 1, "from": s, "to": t}, + {"kind": "bridge", "dst": i, "src": i + 1, "coefficient": -1}, + ]) + events.extend({"kind": "idle", "pair": i, "from": 2 * i + 2, "to": 2 * pairs} + for i in range(pairs)) + events.extend({"kind": "bridge", "dst": i, "src": i - 1, "coefficient": 1} + for i in range(pairs - 1, 0, -1)) + events.append({"kind": "terminal", "pairs": pairs}) + return events + + +def run(pairs, events, backward_power=-1): + state = [{(j, 0): 1} for j in range(2 * pairs)] + for event in events: + if event["kind"] == "local": + x, y = 2 * event["pair"], 2 * event["pair"] + 1 + if event["reverse"]: + state[x] = add_row(state[x], state[y], -1, backward_power) + else: + state[y] = add_row(state[y], state[x], shift=1) + elif event["kind"] == "bridge": + d, s, c = event["dst"], event["src"], event["coefficient"] + state[2 * d] = add_row(state[2 * d], state[2 * s], c) + state[2 * s + 1] = add_row(state[2 * s + 1], state[2 * d + 1], -c) + return state + + +def controller_checks(actual): + need(actual == recipe(4), "The pinned nineteen content events and ten idle sites") + tests = [] + for pairs in range(1, 9): + wanted = [] + for i in range(pairs): + wanted.extend([{(2 * i + 1, -1): -1}, {(2 * i, 1): 1}]) + need(run(pairs, recipe(pairs)) == wanted, "All arbitrary controller inputs") + need(run(pairs, recipe(pairs), 1) != wanted, "A forward response is not its inverse") + tests.append({"pairs": pairs, "arbitrary_input_blocks": 4 * pairs * pairs}) + return tests + + +def terminal_record(record, ports): + p, q = record["port"], record["q"] + need(ports[p] == q, "The intrinsic direction is the actual supplier port") + left, inverse = record["L_columns"], record["L_inverse_columns"] + delta = record["FULL_E_output_translation"] + epsilon = record["FULL_E_inverse_output_translation"] + cycle = record["cycle_vectors"] + need(inverse == transpose(left), "The cover cycle is orthogonal") + need(compose(left, inverse) == compose(inverse, left) == UNIT, "Both cover inverse orders") + need([act(left, value) for value in cycle] == cycle[1:] + cycle[:1], "The exact cover cycle") + need(cycle[0] == q and cycle[-1] == 1 << 65, "The fixed final fresh axis") + need(all(parity(a & b) == int(i == j) + for i, a in enumerate(cycle) for j, b in enumerate(cycle)), "All ten cycle vectors") + power = list(UNIT) + for _ in range(10): + power = compose(left, power) + need(power == UNIT, "The cover cycle has order ten") + last = act(inverse, q) + need(last == cycle[-1], "The first terminal line is transported from the source cover") + need(act(left, epsilon) == delta, "Both FULL translation conventions") + g, gi, transvections = child_basis(q, last) + offset = act(gi, epsilon) + need(act(g, offset) == epsilon, "The left wrapper translation") + bblock = [(q if parity(q & e) else 0) ^ (last if parity(last & e) else 0) + for e in UNIT] + need(rank(bblock) == 2, "The terminal block has exact Fourier rank two") + + characters = [0] + UNIT + [UNIT[i] ^ UNIT[j] for i in range(N) for j in range(i)] + wrong = {key: None for key in ["omit_inverse_FULL_translation", "omit_forward_FULL_translation", + "use_q_twice", "omit_target_line", "omit_source_line"]} + for eta in characters: + phi = eta.bit_count() % 4 + phi_l = act(inverse, eta).bit_count() % 4 + phi_i = act(left, eta).bit_count() % 4 + pd, pe = 2 * parity(delta & eta), 2 * parity(epsilon & eta) + need((phi_l - phi - pd) % 4 == 0, "The full forward Z4 phase polynomial") + need((phi_i - phi - pe) % 4 == 0, "The full inverse Z4 phase polynomial") + line_q, line_last = parity(q & eta), parity(last & eta) + pre_x = (phi_i - line_last) % 4 + actual_x = (pe + line_q + line_last + pre_x) % 4 + target_x = (phi + line_q) % 4 + need(actual_x == target_x, "The complete X terminal equals F Q on raw X") + need((pd + phi_l) % 4 == phi, "The complete Y terminal equals F on raw Y") + values = { + "omit_inverse_FULL_translation": (line_q + line_last + pre_x) % 4 != target_x, + "omit_forward_FULL_translation": phi_l != phi, + "use_q_twice": (pe + 2 * line_q + pre_x) % 4 != target_x, + "omit_target_line": (pe + line_last + pre_x) % 4 != target_x, + "omit_source_line": (pe + line_q + pre_x) % 4 != target_x, + } + for key, failed in values.items(): + if failed and wrong[key] is None: + wrong[key] = eta + need(all(value is not None for value in wrong.values()), "All phase mutations fail") + need(compose(left, left) != UNIT, "The wrong cover direction does not restore the input address") + # The four translation coefficients are Gaussian integers divided by two. + source_stencil = {0: (0, 1), 1: (1, 0), 2: (1, 0), 3: (0, -1)} + target_stencil = {act(g, shift): value for shift, value in source_stencil.items()} + need(target_stencil == {0: (0, 1), q: (1, 0), last: (1, 0), q ^ last: (0, -1)}, + "The exact rank-two child kernel after both linear views") + return { + "port": p, "q": q, "second_native_line": last, + "X_child": { + "rank": 2, "sign": 1, + "right_view_cover_columns": inverse, + "right_view_payload_at_output_cover_h_columns": g, + "left_view_payload_columns_in_h_coordinates": gi, + "left_view_payload_offset": offset, + "basis_transvections_in_time_order": transvections, + "basis_input_axis_swap": [1, 65], + "output_translation_in_h_coordinates": epsilon, + }, + "Y_source_map": {"cover_columns": left, "payload_translation_in_h_coordinates": delta}, + "final_exchange": "(X,Y)=(processed_V,-processed_U)", + "negative_control_characters": wrong, + "wrong_cover_direction_residual_columns": compose(left, left), + "phase_coefficient_checks": len(characters), + } + + +def main(): + for path, pin in PINS.items(): + need(sha256(path.read_bytes()).hexdigest() == pin, "Pinned input: " + str(path)) + actual = [event for event in json.loads(SCHEDULE.read_bytes())["schedule"] + if event["kind"] in ("local", "idle", "bridge", "terminal")] + tests = controller_checks(actual) + ports = json.loads(INTERFACE.read_bytes())["ports"] + source = json.loads(CYCLE.read_bytes()) + need(len(ports) == len(source["records"]) == 112, "All 112 ports") + records = [terminal_record(record, ports) for record in source["records"]] + need([record["port"] for record in records] == list(range(112)), "Every port occurs once") + inventory = { + "pairs": 4, "ports_per_bank": 112, "rank_two_children": 448, + "native_rank_mass": 896, "child_wrapper_maps": 896, + "FULL_source_maps": 448, "total_monomial_maps": 1344, + "old_line_square_maps_removed": 448, "net_added_monomial_maps": 896, + "retained_signed_exchanges": 448, "retained_unit_complex_ADDs": 1344, + "retained_exchange_real_primitives": 10752, + "new_top_level_scalar_primitives_beyond_retained_exchange": 0, + "new_full_cover_records": 0, + } + payload = { + "schema": "common-cover-integrated-terminal-v1", + "input_contract": "U=-F E^-1 y; V=F Q^-1 E x; original raw input is (Qx,y)", + "output_contract": "(F Qx,F y), with no residual port or cover code", + "source_pins": {str(path.relative_to(LANES)): pin for path, pin in PINS.items()}, + "inventory_per_replica": inventory, + "records": records, + } + raw = (json.dumps(payload, sort_keys=True, indent=2) + "\n").encode() + (HERE / "TERMINAL-PROGRAMS.json").write_bytes(raw) + receipt = { + "status": "PASS_COMMON_COVER_INTEGRATED_TERMINAL", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "proof_sha256": sha256((HERE / "COMMON-TERMINAL.md").read_bytes()).hexdigest(), + "program_sha256": sha256(raw).hexdigest(), + "source_pins": payload["source_pins"], + "all_m_free_E_tests": tests, + "actual_content_events": sum(e["kind"] != "idle" for e in actual), + "actual_idle_sites": sum(e["kind"] == "idle" for e in actual), + "port_phase_polynomial_checks": 112 * 2 * (1 + 73 + 2628), + "exact_native_kernel_checks": 112, + "negative_controls": {"nonreciprocal_controller": 8, "phase_mutations": 560, + "wrong_cover_direction": 112}, + "inventory_per_replica": inventory, + "scope": "Finite terminal and ordered raw controller. The local native words, complete owner schedule, recursive child hosting, map price, and precision are separate dependencies. The conditional native rank balance gives no positive kappa gain.", + } + (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/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/CHECKS.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/CHECKS.json new file mode 100644 index 0000000000..3fe35d4b34 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/CHECKS.json @@ -0,0 +1,22 @@ +{ + "actual_port_checks": 112, + "checker_sha256": "50bb8f3470c758beb76444c9e875cee86bdd415610443f5fce9835956c899e72", + "proof_sha256": "5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3", + "scope": "A standalone one-field Clifford terminal for a port-diagonal orthogonal cover-only response with the stated first line cut. Fused earlier operations and broader response or circuit classes remain outside the claim.", + "small_dimension_checks": [ + { + "complete_character_checks": 48, + "dimension": 3, + "line_cases": 12, + "orthogonal_matrices": 6 + }, + { + "complete_character_checks": 23040, + "dimension": 5, + "line_cases": 5760, + "orthogonal_matrices": 720 + } + ], + "source_sha256": "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da", + "status": "PASS_COVER_ONLY_TERMINAL_RANK" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json new file mode 100644 index 0000000000..c0064f166c --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json @@ -0,0 +1,12 @@ +{ + "command_run": "python3 -I -B check_limit.py", + "files": { + "CHECKS.json": "79be122acd97d051a291143b44ab30a6e8df3159f1901c993afd75c10f85de17", + "LIMIT.md": "5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3", + "check_limit.py": "50bb8f3470c758beb76444c9e875cee86bdd415610443f5fce9835956c899e72" + }, + "future_PR_standard": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "publication": "Local only. No PR, commit, push, or publication.", + "scope": "A standalone one-field Clifford terminal for a port-diagonal orthogonal cover-only response with the stated first line cut. Fused earlier operations and broader response or circuit classes remain outside the claim.", + "status": "PASS_COVER_ONLY_TERMINAL_RANK" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md new file mode 100644 index 0000000000..2ed573d358 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md @@ -0,0 +1,64 @@ +# The line cut fixes the terminal rank for a cover-only response + +This result concerns a port-diagonal response that changes only the +orthogonal cover label. It does not concern all monomial responses or +all supplier circuits. + +Let q be an odd binary vector. Let v be an odd vector with q^T v=0. +Suppose the first native transfer reads a source in frame C_q and writes +a target in frame C_v. Let the common response be + + (E f)(h)=f(h L), + +where L is orthogonal and the logical payload action is the identity. +Exact matching of the line spaces requires + + L q=v. (1) + +An affine translation can correct a phase. It does not change (1). + +The raw common-response controller has preterminal state +(-F E^-1 y,F Q^-1 E x). To return FULL of the original raw input (Qx,y), +its X branch must apply Q F E^-1 F^-1 Q to the old Y branch. The FULL +conjugate F E^-1 F^-1 is a cover permutation and a translation: an +orthogonal matrix changes the full Z4 weight phase by an even linear +phase. Thus the terminal X branch, after its cover permutation and +translation are removed, is + + C_q C_w, where w=L^-1 q. (2) + +From orthogonality and (1), + + q^T w=(L q)^T q=v^T q=0. + +Both q and w have norm one. They are therefore distinct and independent. +The binary upper-right Clifford block of (2) is + + q q^T+w w^T. + +It has rank two. One positive rank-two native child implements it. A +one-field Clifford word with monomial views has total native rank at +least two, because the rank of a product is at most the sum of the +factor ranks and monomial views preserve rank. + +This conclusion holds for every orthogonal extension L of the initial +line map. Later flag choices cannot reduce this standalone terminal +rank. For 112 ports and four pairs, the terminal rank is at least 896. +The finite recipe in `../common-monomial-terminal-20261018/` attains +that rank for the actual ten-cycle extension. + +The result does not rule out an earlier native operation that absorbs +part of the terminal, a circuit that mixes fields, a logical response +with a nontrivial payload map, or a different initial native cut. It +does not prove a lower bound for multiplication algorithms. + +The proof is symbolic in L, q, and v. The checker separately enumerates +all orthogonal binary matrices in dimensions three and five and all +odd q that satisfy q^T Lq=0. It checks the FULL phase identity on every +character in those dimensions and checks the rank-two conclusion. It +also binds all 112 actual port cycles. These finite checks support the +proof; they are not the basis of the universal claim. + +No PR, commit, push, or publication is part of this work. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/check_limit.py b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/check_limit.py new file mode 100644 index 0000000000..ae52cfd607 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/encoded-controller/cover-line-terminal-limit-20261018/check_limit.py @@ -0,0 +1,105 @@ +"""Check the cover-only line-cut terminal rank.""" + +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parents[1] / "bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json" +PIN = "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da" + + +def need(condition, label): + if not condition: + raise ValueError(label) + + +def parity(value): + return value.bit_count() & 1 + + +def act(columns, value): + out = 0 + for i, column in enumerate(columns): + if value >> i & 1: + out ^= column + return out + + +def transpose(columns): + n = len(columns) + return [sum(((columns[j] >> i) & 1) << j for j in range(n)) for i in range(n)] + + +def rank(columns): + pivots = {} + for value in columns: + while value: + i = value.bit_length() - 1 + if i in pivots: + value ^= pivots[i] + else: + pivots[i] = value + break + return len(pivots) + + +def orthogonal_matrices(n, prefix=()): + if len(prefix) == n: + yield prefix + return + for vector in range(1, 1 << n): + if parity(vector) and all(not parity(vector & other) for other in prefix): + yield from orthogonal_matrices(n, prefix + (vector,)) + + +def check_line(columns, q): + v = act(columns, q) + need(not parity(q & v), "The first target line is orthogonal to q") + w = act(transpose(columns), q) + need(parity(q) == parity(w) == 1 and not parity(q & w), "Two odd orthogonal terminal lines") + block = [(q if q >> i & 1 else 0) ^ (w if w >> i & 1 else 0) + for i in range(len(columns))] + need(rank(block) == 2, "Exact terminal rank") + + +def main(): + need(sha256(SOURCE.read_bytes()).hexdigest() == PIN, "Actual cycle pin") + tests = [] + for n in (3, 5): + matrices = line_cases = phase_cases = 0 + for columns in orthogonal_matrices(n): + matrices += 1 + inverse = transpose(columns) + need([act(columns, v) for v in inverse] == [1 << i for i in range(n)], "Exact inverse") + delta = sum((((row.bit_count() - 1) // 2) & 1) << i + for i, row in enumerate(inverse)) + for character in range(1 << n): + need((act(inverse, character).bit_count() - character.bit_count() + - 2 * parity(delta & character)) % 4 == 0, "FULL phase is a translation") + phase_cases += 1 + for q in range(1, 1 << n): + if parity(q) and not parity(q & act(columns, q)): + check_line(columns, q) + line_cases += 1 + tests.append({"dimension": n, "orthogonal_matrices": matrices, + "line_cases": line_cases, "complete_character_checks": phase_cases}) + source = json.loads(SOURCE.read_bytes()) + for record in source["records"]: + need(act(record["L_columns"], record["q"]) == record["v0"], "Actual initial line cut") + check_line(record["L_columns"], record["q"]) + receipt = { + "status": "PASS_COVER_ONLY_TERMINAL_RANK", + "proof_sha256": sha256((HERE / "LIMIT.md").read_bytes()).hexdigest(), + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_sha256": PIN, "small_dimension_checks": tests, + "actual_port_checks": len(source["records"]), + "scope": "A standalone one-field Clifford terminal for a port-diagonal orthogonal cover-only response with the stated first line cut. Fused earlier operations and broader response or circuit classes remain outside the claim.", + } + (HERE / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/CHECKS.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/CHECKS.json new file mode 100644 index 0000000000..3237944fef --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/CHECKS.json @@ -0,0 +1,826 @@ +{ + "checker_sha256": "a74cb8ea2464396d44cf86e9d87ca798f66009074facc28819f0a81f062838ec", + "controller": { + "actual_content_events": 19, + "actual_idle_sites": 10, + "arbitrary_input_blocks": 8, + "arithmetic": "Free Laurent integer coefficients; no cycle relation is used." + }, + "inventory_per_replica": { + "FULL_source_maps": 448, + "child_wrapper_maps": 896, + "native_rank_mass": 896, + "net_added_monomial_maps": 896, + "new_full_cover_records": 0, + "new_top_level_scalar_primitives_beyond_retained_exchange": 0, + "old_line_square_maps_removed": 448, + "pairs": 4, + "ports_per_bank": 112, + "rank_two_children": 448, + "retained_exchange_real_primitives": 10752, + "retained_signed_exchanges": 448, + "retained_unit_complex_ADDs": 1344, + "total_monomial_maps": 1344 + }, + "method": "Full Z4 polynomial coefficients and exact affine four-point Gaussian kernel; reverse columns for the pinned content schedule; no producer imports.", + "ports": [ + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 0 + }, + { + "both_cover_address_orders": true, + 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"native_fourier_rank": 2, + "port": 88 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 89 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 90 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 91 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 92 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 93 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 94 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 95 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 96 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 97 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 98 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 99 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 100 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 101 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 102 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 103 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 104 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 105 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 106 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 107 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 108 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 109 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 110 + }, + { + "both_cover_address_orders": true, + "complete_affine_kernel": true, + "complete_phase_polynomial": true, + "native_fourier_rank": 2, + "port": 111 + } + ], + "scope": "Finite terminal with admitted map and child operations. No recursive hosting, map-time price, complete supplier invoice, or precision certificate.", + "source_pins": { + "bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json": "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da", + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "encoded-controller/NORMALIZATION-PROGRAMS.json": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9", + "encoded-controller/common-monomial-terminal-20261018/CHECKS.json": "27f222e13cc26291fe3d0dd25b1740029c906f5cbb080db79d9599fb262795b2", + "encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md": "d57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad", + "encoded-controller/common-monomial-terminal-20261018/FREEZE.json": "e342c8d646a5c7cb5ee8cfd53d231c91a572b24894b9217a3a9533c00cce09f0", + "encoded-controller/common-monomial-terminal-20261018/TERMINAL-PROGRAMS.json": "c87e99deeffa12b30b37f633c784118623aba1a4680ad3ae925d29be4f91a4d6", + "encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py": "4d28d8b98cf6de28e6eb2195e5ca1e461ab0aea5991a3aa700f2a1330fef5cfe", + "encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json": "4103d8e89f10b8d8dcf7ba54c8e51cc6c685e36b9fff40ad86dc1d6bf532a427", + "encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md": "5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3" + }, + "status": "PASS_INDEPENDENT_COMMON_COVER_TERMINAL" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/FREEZE.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/FREEZE.json new file mode 100644 index 0000000000..733f5f4b06 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/FREEZE.json @@ -0,0 +1,12 @@ +{ + "files": { + "CHECKS.json": "24b6deefd0cae552127f158facc05b294af4f31ff25a04d0584603865f1a2de4", + "REPRODUCTION.json": "8f0abf468f7ef8b51ed47f61aa7ebd09d635fe547b9d5901ae22ffa5380931b7", + "REVIEW.md": "1ba6c4936fe98a983cc3485f49892b8ec1798efd96abb9bec428e7fe539b5e16", + "check_terminal.py": "a74cb8ea2464396d44cf86e9d87ca798f66009074facc28819f0a81f062838ec" + }, + "scope": "Finite terminal maps, exact phases, native inventory, and symbolic standalone line-cut rank bound. No complete supplier hosting, map price, or precision certificate.", + "source_line_limit_freeze_sha256": "4103d8e89f10b8d8dcf7ba54c8e51cc6c685e36b9fff40ad86dc1d6bf532a427", + "source_terminal_freeze_sha256": "e342c8d646a5c7cb5ee8cfd53d231c91a572b24894b9217a3a9533c00cce09f0", + "status": "FROZEN_INDEPENDENT_COMMON_COVER_TERMINAL_REVIEW" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/REPRODUCTION.json b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/REPRODUCTION.json new file mode 100644 index 0000000000..40b06f180f --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/REPRODUCTION.json @@ -0,0 +1,4 @@ +{ + "CHECKS.json": "24b6deefd0cae552127f158facc05b294af4f31ff25a04d0584603865f1a2de4", + "status": "PASS_NORMAL_AND_OPTIMIZED_IDENTICAL" +} diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/REVIEW.md b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/REVIEW.md new file mode 100644 index 0000000000..a334b16596 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/REVIEW.md @@ -0,0 +1,152 @@ +# Independent review of the common-cover terminal + +The finite terminal passes this review. It returns FULL of the raw input +`(Qx,y)` from the stated common-response controller. The cover address, +two positive line transforms, FULL translations, and final bank sign +are correct. The result uses admitted native children and array maps. +It does not supply their recursive hosting or complete execution cost. + +The source terminal proof is `COMMON-TERMINAL.md`, SHA-256 +`d57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad`, +in `encoded-controller/common-monomial-terminal-20261018/`. +The source program SHA-256 is +`c87e99deeffa12b30b37f633c784118623aba1a4680ad3ae925d29be4f91a4d6`. +The source freeze SHA-256 is +`e342c8d646a5c7cb5ee8cfd53d231c91a572b24894b9217a3a9533c00cce09f0`. +No source file was changed. No material proof error was found. + +The common-response controller has an all-pair proof. Put `a=Ex` and +`b=y`. Every local F becomes `b <- b+a`; every local B becomes +`a <- a-b`. Each retained bridge also has its unit-response form because +the same E acts on every X bank. This change of variables does not move +E across Q. + +For a direct induction, let `c_-1=0` and +`c_i=-b_i-c_(i-1)`. Just before B on pair i, its state is +`(a_i,b_i+c_(i-1)+a_i)`. B sets its X field to `c_i`. If there is a next +pair, the plus bridge, F, and minus bridge leave this pair at +`(c_i,a_i+a_(i+1))` and prepare the next Y field as +`b_(i+1)+c_i+a_(i+1)`. On the final pair, F leaves Y at `a_i`. +The descending final bridges therefore give X_i=`c_i+c_(i-1)=-b_i` +and Y_i=`a_i`. This proves the endpoint `(-E^-1 y,Ex)` for every pair +count and arbitrary inputs. The independent checker also uses reverse +columns to verify the actual pinned nineteen content events and ten +idle sites for four pairs. Its coefficients are free integer Laurent +polynomials in E; it does not use `E^10=I`. + +At the physical terminal input, + +`U=-F E^-1 y` and `V=F Q^-1 E x`. + +Let `M_I=F E^-1 F^-1` and `M_E=F E F^-1`. In time order, the V branch +uses `Q`, then `M_I`, then `Q`. Its value is successively `F E x`, +`F x`, and `F Q x`. The U branch uses `M_E` and becomes `-F y`. +The signed exchange gives `(F Q x,F y)`. This uses commutation of +payload line transforms with F. It makes no claim that E commutes +with Q. The same equations apply to every tensor coordinate copy. + +The literal cover maps agree with this order. At output cover h, the +V source is at `h L^-1`. Its intrinsic line is therefore `h L^-1 q`. +For every actual port, `L^-1 q=v_8`, with `v_8=2^65` in the binary +coordinate encoding. Thus the two positive lines are `h q` and +`h v_8`, not two copies of `h q`. The U source is at `h L`. The source +cover compositions with the preterminal E and E^-1 are both the +identity. All 112 actual cycle matrices and both inverse orders pass. + +The independent phase check uses full polynomial coefficients modulo +four, rather than the producer's character probes. For a binary +column matrix A, the polynomial `weight(A eta) mod 4` has linear +coefficient `weight(A e_i) mod 4` and quadratic coefficient +`2 (A e_i)^T (A e_j) mod 4`. All higher coefficients vanish modulo four. +For orthogonal A, the off-diagonal coefficients vanish, and every +linear coefficient is odd. Thus its difference from `weight(eta)` is +an even linear polynomial. It is exactly a payload translation, with +no constant phase. + +This calculation checks the complete forward and inverse FULL +translations in the source payload. It also checks every coefficient +of the final X and Y phase equations. In particular, +`L epsilon=delta`, with the output-coordinate convention used in the +literal maps. Omitting either FULL translation, using q twice, or +omitting either line gives a different phase polynomial. The wrong +cover direction gives a nonidentity address composition. + +The serialized child wrappers pass a separate affine address and +Gaussian kernel check. Their matrix G is orthogonal, its first columns +are `(q,v_8)`, and the stored inverse is exact in both orders. The two +stored even-vector transvections and the input-axis swap reconstruct +G exactly. If the output address is w, the wrappers read + +`V(h L^-1, w + h epsilon + h G tau)`, + +where tau runs over the four first-two-axis shifts of the rank-two +child. The four coefficients are `i/2, 1/2, 1/2, -i/2` at shifts +`0,q,v_8,q+v_8`, respectively. This is exactly the product `C_q C_v8`, +including its global phase. The checker verifies all affine address +coefficients and all four coefficients of this kernel. These are +complete finite descriptions of the maps on all `2^73` payload +addresses. Multiplication by an arbitrary orthogonal cover h preserves +the equations, so no equality of contents at different cover labels +is assumed. + +The terminal needs 448 positive rank-two children, native rank mass +896, 896 child wrapper maps, and 448 additional FULL cover/translation +maps per four-pair replica. The total map count is 1,344. The old +terminal's 448 line-square maps are removed, so the net map increase +is 896. The signed exchange remains `(X,Y)=(V,-U)`. Three unit complex +ADDs implement it: `U+=V`, `V-=U`, `U+=V`. Its 10,752 real primitives +are retained work. The new translations and cover permutations have +no scalar coefficient multiplications. This statement does not give +their finite address-execution time or the recursive cost of a child. + +The standalone rank claim is correct in its stated class. After +removal of the cover permutation and translation, the X branch has +binary upper-right Clifford block `q q^T+v_8 v_8^T`. It has rank two. +For a product of Clifford matrices, +`B_product=A_left B_right+B_left D_right`, so its rank is at most the +sum of the two B ranks. Monomial Clifford views have rank zero and +preserve B rank on the left or right. Thus a one-field Clifford word +needs total native rank at least two here. The emitted child attains +this bound. This does not bound a circuit that mixes fields or changes +an earlier native call. + +I also checked the symbolic proof in the separate frozen +`cover-line-terminal-limit-20261018/LIMIT.md`, SHA-256 +`5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3`. +For any orthogonal L with `Lq=v` and `q^T v=0`, put `w=L^-1 q`. +Then `q^T w=(Lq)^T q=0`, while q and w both have norm one. Hence they +are distinct. The same rank-two conclusion holds for every such L. +The actual 112 cycles satisfy these hypotheses. This rules out a +smaller standalone terminal merely from a different orthogonal +extension of the same cover-only line map. It does not rule out a +payload response, a different first cut, or fusion with an earlier +operation. I did not rerun that addendum's separate exhaustive +dimension-three and dimension-five enumeration. + +The native-moment conclusion remains conditional on the full path and +idle ledger. If the productive paths have total rank `2mn(D-1)` and +this terminal adds `2mn`, the total is `2mnD`. For `b>0` and each child +width `r<=D`, `r^(1-b)>=r D^-b`. Their total native weight is therefore +at least `2mn D^(1-b)`. A different partition of that same rank cannot +give a positive saving in this model. This review does not verify the +complete hosted path ledger or claim a lower bound for broader +supplier constructions. + +Run from the workspace root: + +```text +python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-terminal-review-20261018/check_terminal.py +python3 -O work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/common-terminal-review-20261018/check_terminal.py +``` + +Both runs print `PASS_INDEPENDENT_COMMON_COVER_TERMINAL` and produce +byte-identical receipts. The checker imports no producer module and +does not run the producer checker. `CHECKS.json` pins the inputs; +`REPRODUCTION.json` pins the equal receipts. + +The terminal is an exact finite operation under the stated map and +child contracts. Fresh local native words, whole-cover scheduling, +recursive workspace hosting, array-map execution cost, the complete +supplier invoice, and finite precision remain separate obligations. +No PR, push, publication, or commit was made. This review is +AI-assisted. diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/check_terminal.py b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/check_terminal.py new file mode 100644 index 0000000000..80d8b5e2fa --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/frozen/lanes/independent-review-20261017/common-terminal-review-20261018/check_terminal.py @@ -0,0 +1,238 @@ +#!/usr/bin/env python3 +"""Check common-cover terminal maps, complete phase coefficients, and cost scope.""" +from hashlib import sha256 +from pathlib import Path +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES/'encoded-controller/common-monomial-terminal-20261018' +N = 73 +UNIT = [1 << i for i in range(N)] +PINS = { + 'encoded-controller/common-monomial-terminal-20261018/FREEZE.json': + 'e342c8d646a5c7cb5ee8cfd53d231c91a572b24894b9217a3a9533c00cce09f0', + 'encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md': + 'd57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad', + 'encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py': + '4d28d8b98cf6de28e6eb2195e5ca1e461ab0aea5991a3aa700f2a1330fef5cfe', + 'encoded-controller/common-monomial-terminal-20261018/TERMINAL-PROGRAMS.json': + 'c87e99deeffa12b30b37f633c784118623aba1a4680ad3ae925d29be4f91a4d6', + 'encoded-controller/common-monomial-terminal-20261018/CHECKS.json': + '27f222e13cc26291fe3d0dd25b1740029c906f5cbb080db79d9599fb262795b2', + 'bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json': + '759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da', + 'encoded-controller/NORMALIZATION-PROGRAMS.json': + '7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9', + 'circuit-interface/INTERFACE.json': + '5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3', + 'encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json': + '4103d8e89f10b8d8dcf7ba54c8e51cc6c685e36b9fff40ad86dc1d6bf532a427', + 'encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md': + '5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3', +} + + +def need(test, label): + if not test: + raise ValueError(label) + + +def parity(value): + return value.bit_count() & 1 + + +def apply(columns, value): + out = 0 + for j, column in enumerate(columns): + if value >> j & 1: + out ^= column + return out + + +def compose(left, right): + return [apply(left, column) for column in right] + + +def transpose(columns): + return [sum(((column >> j) & 1) << i for i, column in enumerate(columns)) for j in range(N)] + + +def poly_sum(*terms): + out = {} + for coefficient, polynomial in terms: + for monomial, value in polynomial.items(): + new = (out.get(monomial, 0)+coefficient*value) % 4 + if new: + out[monomial] = new + else: + out.pop(monomial, None) + return out + + +def bit_phase(vector): + support = [j for j in range(N) if vector >> j & 1] + out = {(j,): 1 for j in support} + out.update({(i, j): 2 for j in support for i in support if i < j}) + return out + + +def full_phase(columns): + out = {(j,): column.bit_count() % 4 for j, column in enumerate(columns) if column.bit_count() % 4} + out.update({(i, j): 2 for j in range(N) for i in range(j) if parity(columns[i] & columns[j])}) + return out + + +def translation_phase(vector): + return {(j,): 2 for j in range(N) if vector >> j & 1} + + +def gmultiply(a, b): + return a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0] + + +def kernel_checks(record, cycle): + q = record['q'] + last = record['second_native_line'] + child = record['X_child'] + g = child['right_view_payload_at_output_cover_h_columns'] + gi = child['left_view_payload_columns_in_h_coordinates'] + offset = child['left_view_payload_offset'] + epsilon = cycle['FULL_E_inverse_output_translation'] + need(child['rank'] == 2 and child['sign'] == 1, 'One positive rank-two child') + need(len(g) == len(gi) == N and compose(g, gi) == compose(gi, g) == UNIT, 'Both payload view inverse orders') + need(gi == transpose(g), 'Orthogonal payload basis') + need(g[:2] == [q, last] and apply(g, offset) == epsilon, 'Exact child directions and output offset') + need(child['output_translation_in_h_coordinates'] == epsilon, 'Serialized output translation') + need(child['right_view_cover_columns'] == cycle['L_inverse_columns'], 'Actual source cover direction') + transvections = child['basis_transvections_in_time_order'] + need(len(transvections) == 2 and all(not parity(v) for v in transvections), 'Two orthogonal transvections') + reconstructed = list(UNIT) + for v in transvections: + reconstructed = [column ^ (v if parity(v & column) else 0) for column in reconstructed] + swap = child['basis_input_axis_swap'] + need(swap == [1, 65], 'Literal input-axis swap') + reconstructed[swap[0]], reconstructed[swap[1]] = reconstructed[swap[1]], reconstructed[swap[0]] + need(reconstructed == g, 'Literal basis construction') + need(parity(q) == parity(last) == 1 and not parity(q & last), 'Independent orthogonal native lines') + # The numerators below have a common denominator four. + one_line = ((1, 1), (1, -1)) + child_kernel = {mask: gmultiply(one_line[mask & 1], one_line[mask >> 1]) for mask in range(4)} + actual = {apply(g, mask) ^ apply(g, offset): value for mask, value in child_kernel.items()} + wanted = {epsilon: (0, 2), epsilon ^ q: (2, 0), + epsilon ^ last: (2, 0), epsilon ^ q ^ last: (0, -2)} + need(actual == wanted and len(actual) == 4, 'Complete translated Gaussian child kernel') + # Check every address coefficient of G(G^-1 w + offset + mask). + need(compose(g, gi) == UNIT, 'Address coefficients for every payload input') + for mask in range(4): + need(apply(g, offset ^ mask) == epsilon ^ (q if mask & 1 else 0) ^ (last if mask & 2 else 0), + 'Every affine child branch') + + +def controller_check(schedule): + events = [e for e in schedule if e['kind'] in ('local', 'idle', 'bridge', 'terminal')] + need(sum(e['kind'] != 'idle' for e in events) == 19 and sum(e['kind'] == 'idle' for e in events) == 10, + 'Pinned retained content and idle counts') + columns = [{(j, 0): 1} for j in range(8)] + + def add(target, source, coefficient, power=0): + for (output, exponent), value in list(columns[source].items()): + key = output, exponent+power + new = columns[target].get(key, 0)+coefficient*value + if new: + columns[target][key] = new + else: + columns[target].pop(key, None) + + for event in reversed(events): + if event['kind'] == 'local': + x, y = 2*event['pair'], 2*event['pair']+1 + if event['reverse']: + add(y, x, -1, -1) + else: + add(x, y, 1, 1) + elif event['kind'] == 'bridge': + d, s, value = 2*event['dst'], 2*event['src'], event['coefficient'] + add(s, d, value) + add(d+1, s+1, -value) + wanted = [] + for j in range(4): + wanted.extend([{(2*j+1, 1): 1}, {(2*j, -1): -1}]) + need(columns == wanted, 'Free Laurent reverse columns of the actual controller') + old = [e['event'] for e in schedule if e['kind'] == 'retained_physical_event' + and e['event']['kind'] == 'terminal_Y_translations'] + need(len(old) == 1 and old[0]['pairs'] == [0, 1, 2, 3], 'The old terminal has one line-square map per port pair') + return {'actual_content_events': 19, 'actual_idle_sites': 10, 'arbitrary_input_blocks': 8, + 'arithmetic': 'Free Laurent integer coefficients; no cycle relation is used.'} + + +def main(): + for relative, pin in PINS.items(): + need(sha256((LANES/relative).read_bytes()).hexdigest() == pin, 'Source pin '+relative) + payload = json.loads((SOURCE/'TERMINAL-PROGRAMS.json').read_bytes()) + cycles = json.loads((LANES/'bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json').read_bytes()) + ports = json.loads((LANES/'circuit-interface/INTERFACE.json').read_bytes())['ports'] + schedule = json.loads((LANES/'encoded-controller/NORMALIZATION-PROGRAMS.json').read_bytes())['schedule'] + controller = controller_check(schedule) + need(len(payload['records']) == len(cycles['records']) == len(ports) == 112, 'Every actual port') + plain_full = full_phase(UNIT) + report = [] + for p, (record, cycle) in enumerate(zip(payload['records'], cycles['records'])): + need(record['port'] == cycle['port'] == p and record['q'] == cycle['q'] == ports[p], 'Actual port binding') + q, last = record['q'], record['second_native_line'] + left, inverse = cycle['L_columns'], cycle['L_inverse_columns'] + delta, epsilon = cycle['FULL_E_output_translation'], cycle['FULL_E_inverse_output_translation'] + need(inverse == transpose(left) and compose(left, inverse) == compose(inverse, left) == UNIT, + 'Orthogonal cover permutation and both inverse orders') + need(apply(inverse, q) == last == 1 << 65 and apply(left, epsilon) == delta, 'Source line and translation order') + need(not parity(q & apply(left, q)) and parity(q & last) == parity(apply(left, q) & q), + 'The general line-cut rank theorem applies to this actual port') + need(compose(left, left) != UNIT, 'Wrong cover direction is detected') + sequence = cycle['cycle_vectors'] + need(len(sequence) == 10 and sequence[0] == q and sequence[-1] == last, + 'Ten actual cycle directions') + need([apply(left, v) for v in sequence] == sequence[1:]+sequence[:1], 'Literal cover cycle') + forward_phase = full_phase(inverse) + inverse_phase = full_phase(left) + need(poly_sum((1, plain_full), (-1, forward_phase)) == translation_phase(delta), + 'Complete forward FULL phase coefficients') + need(poly_sum((1, plain_full), (-1, inverse_phase)) == translation_phase(epsilon), + 'Complete inverse FULL phase coefficients') + line_q, line_last = bit_phase(q), bit_phase(last) + input_v = poly_sum((1, inverse_phase), (-1, line_last)) + terminal_x = poly_sum((1, translation_phase(epsilon)), (1, line_q), (1, line_last)) + need(poly_sum((1, input_v), (1, terminal_x)) == poly_sum((1, plain_full), (1, line_q)), + 'All X phase coefficients equal the raw FQ endpoint') + need(poly_sum((1, forward_phase), (1, translation_phase(delta))) == plain_full, + 'All Y phase coefficients equal the raw F endpoint') + need(record['Y_source_map'] == {'cover_columns': left, 'payload_translation_in_h_coordinates': delta}, + 'Literal Y cover and translation map') + need(record['final_exchange'] == '(X,Y)=(processed_V,-processed_U)', 'Exact final bank sign') + need(delta and epsilon, 'Omitted FULL translations change every port map') + need(poly_sum((1, input_v), (1, translation_phase(epsilon)), (2, line_q)) + != poly_sum((1, plain_full), (1, line_q)), 'Using the same line twice is rejected') + need(poly_sum((1, input_v), (1, translation_phase(epsilon)), (1, line_q)) + != poly_sum((1, plain_full), (1, line_q)), 'Omitting the source line is rejected') + need(poly_sum((1, input_v), (1, translation_phase(epsilon)), (1, line_last)) + != poly_sum((1, plain_full), (1, line_q)), 'Omitting the target line is rejected') + kernel_checks(record, cycle) + report.append({'port': p, 'complete_phase_polynomial': True, 'complete_affine_kernel': True, + 'native_fourier_rank': 2, 'both_cover_address_orders': True}) + inventory = {'pairs': 4, 'ports_per_bank': 112, 'rank_two_children': 448, 'native_rank_mass': 896, + 'child_wrapper_maps': 896, 'FULL_source_maps': 448, 'total_monomial_maps': 1344, + 'old_line_square_maps_removed': 448, 'net_added_monomial_maps': 896, + 'retained_signed_exchanges': 448, 'retained_unit_complex_ADDs': 1344, + 'retained_exchange_real_primitives': 10752, + 'new_top_level_scalar_primitives_beyond_retained_exchange': 0, 'new_full_cover_records': 0} + need(payload['inventory_per_replica'] == inventory, 'Exact finite map and native inventory') + result = {'status': 'PASS_INDEPENDENT_COMMON_COVER_TERMINAL', 'source_pins': PINS, + 'controller': controller, 'ports': report, 'inventory_per_replica': inventory, + 'method': 'Full Z4 polynomial coefficients and exact affine four-point Gaussian kernel; reverse columns for the pinned content schedule; no producer imports.', + 'scope': 'Finite terminal with admitted map and child operations. No recursive hosting, map-time price, complete supplier invoice, or precision certificate.', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest()} + (HERE/'CHECKS.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(result['status']) + + +if __name__ == '__main__': + main() diff --git a/research/ordered-centre-interfaces/annexes/common-cover-terminal/notices/LICENSE b/research/ordered-centre-interfaces/annexes/common-cover-terminal/notices/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/common-cover-terminal/notices/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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No complete path, owner, map-price, recursive, or precision replay."} + (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/ordered-centre-interfaces/annexes/reciprocal-controller/ANNEX-MANIFEST.json b/research/ordered-centre-interfaces/annexes/reciprocal-controller/ANNEX-MANIFEST.json new file mode 100644 index 0000000000..33c9e023f9 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/ANNEX-MANIFEST.json @@ -0,0 +1,82 @@ +{ + "appendix": "reciprocal-controller", + "files": { + "PROOF.md": { + "bytes": 2484, + "sha256": "833d7ebcc5e122b3828db8348bf84d7169cd606918a9c63adb792b92c28e8e88" + }, + "PUBLICATION.md": { + "bytes": 823, + "sha256": "96d1c62230149287e75b3d0536f700d25eda71def25b453ec7afa6a1d36278c0" + }, + "README.md": { + "bytes": 1105, + "sha256": "f629ab61f188cbec33b0b1d77c09194b3f88c7c2040b3b6c4f37cdd0f8f3d3ad" + }, + "REVIEW.json": { + "bytes": 1021, + "sha256": "71376cb12dfe4cbbf85bf6adeced3d1d615b0181a018140336d9d2f7f19abf11" + }, + "REVIEW.md": { + "bytes": 3878, + "sha256": "e2bbfe48658b27c760a813ae59e4caf2da7faca198fc694f799ec27e8606e064" + }, + "SOURCES.json": { + "bytes": 2336, + "sha256": "e67b85e2de213e39cd038bc9fe35bec8696fd421ecf65132311ace25228df39f" + }, + "TASK.json": { + "bytes": 639, + "sha256": "602097a7c32df2e23f097ebfaab5653947302aff51507d359429a5e0cddfc249" + }, + "VALIDATION.json": { + "bytes": 1558, + "sha256": "a51c751cc5eb6f43a3d2c96eb51f2de9798526edd89a03713ffbbc36e6a0c124" + }, + "frozen/lanes/circuit-interface/INTERFACE.json": { + "bytes": 23232, + "sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3" + }, + "frozen/lanes/encoded-controller/NORMALIZATION-PROGRAMS.json": { + "bytes": 58263, + "sha256": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9" + }, + "frozen/lanes/encoded-controller/reciprocal-response-20261018/CHECKS.json": { + "bytes": 6660, + "sha256": "f76f36816359223609ecf506a2a1daad97caed96c08b0cea080d537016486b3e" + }, + "frozen/lanes/encoded-controller/reciprocal-response-20261018/FREEZE.json": { + "bytes": 506, + "sha256": "92470e66e90fc5026fe36ddf8d0922090f524530b492b5257a5dc2a6e1fcd3a9" + }, + "frozen/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md": { + "bytes": 11844, + "sha256": "5facaac62ec417bae33690fa645150774d3820eb17be9e5033e779840f9821d5" + }, + "frozen/lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py": { + "bytes": 10138, + "sha256": "b9cf8869932a356f0884bdb861c1a5b567c338b0e4174c7619829d2fdc599d61" + }, + "frozen/lanes/oblique-native-20261017/interior-cut/UNIT-MODE-CANDIDATE.json": { + "bytes": 24371, + "sha256": "d61d7447a499973afe49b7e422c51070262fc83229a82b7ff0ebb0238605d2fd" + }, + "replay.py": { + "bytes": 2891, + "sha256": "c5b6abbe8d9704adfaea980c77f4f34fee78ae2367bf1e2e88bed59ca79b7697" + }, + "validation/normal.log": { + "bytes": 36, + "sha256": "dae4e127dfe668492e80dec40468b347fb22ac1726c226486f8baaf1930c8261" + }, + "validation/optimized.log": { + "bytes": 36, + "sha256": "dae4e127dfe668492e80dec40468b347fb22ac1726c226486f8baaf1930c8261" + } + }, + "frozen_input_files": 7, + "schema": "accepted-support-proof-appendix-v1", + "scope": "All-m varying routed reciprocal responses close with 4m+1 typed code factors under the stated native and code-access premises; the common-response specialization has 2m+2 factors.", + "total_bytes_excluding_manifest": 151821, + "total_files_excluding_manifest": 18 +} diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/PROOF.md b/research/ordered-centre-interfaces/annexes/reciprocal-controller/PROOF.md new file mode 100644 index 0000000000..8234b617ab --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/PROOF.md @@ -0,0 +1,47 @@ +# A conditional controller for varying reciprocal responses + +Fix m>=1 pairs. At stage s, assume exact native calls + +```text +F_s(x,y)=(x,y+E_s x), +B_s(x,y)=(x-E_s^-1 y,y), +``` + +with the original physical input and output types and full restoration of +all arbitrary helper contents. Each E_s is an invertible operator on the +complete routed bank. Equal local coefficient matrices do not imply equal +routed E_s. The current historical transpose call does not establish this +reciprocal native premise. + +Use the retained sequence F0, then B_(2i+1), F_(2i+2) for each pair i, +with its plus/minus inter-pair bridges and final descending bridges. Insert: + +1. E0 on Y0 before F0; E1^-1 on X0 after F0; E0^-1 on Y0 before B1. +2. E_(s+1)^-1 E_s on active X after each B_s. +3. E_(s+1)^-1 on the next X at its first FULL cut before the plus bridge. +4. E_(t+1)^-1 E_t on that next X after the minus bridge at even stage t. +5. E_(2i+2) on every retired X after idle tails and before final bridges. + +Items 3 and 4 occur only when a next pair exists. There are 4m+1 code +factors. These are required operators at specified cuts, not a native-cost +count. Before each B_s, active X has code E_s^-1 and active Y is plain. +The backward call preserves this code. Item 2 changes it to the next +forward inverse code. Item 3 makes the two X bridge codes equal. The +forward response cancels that code on Y, and item 4 prepares the next +backward stage. Item 5 removes all retired X codes before the final +bridges. The complete content endpoint is (-y_i,x_i) for every pair. + +With W=diag(Q,I), V=diag(I,Q^-1), J0=[[0,-I],[I,0]], and retained terminal +A=[[0,Q^2],[-I,0]], direct multiplication gives A V J0=W. Thus the old +physical terminal is valid under the stated native phase contracts. +No E_s is commuted through Q. If all routed E_s equal one E, the transition +products are identities and the displayed construction has 2m+2 factors. +This is not an optimality claim. + +The [unchanged full proof](frozen/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md) +gives the typed four-pair table and the ordered three-call equations. +The [independent review](REVIEW.md) checks the all-m argument. The replay +checks the original free-word verifier for one through eight pairs and its +controls. Reciprocal native words, future and past code access, paid views, +owner schedules, precision, and complete supplier cost remain premises or +open obligations. No complete kappa improvement follows. diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/PUBLICATION.md b/research/ordered-centre-interfaces/annexes/reciprocal-controller/PUBLICATION.md new file mode 100644 index 0000000000..02a6eee5d8 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/PUBLICATION.md @@ -0,0 +1,7 @@ +The [varying-response controller appendix](PROOF.md) adds an independently reviewed all-pair construction for reciprocal routed responses. With `m` pairs, `4m+1` code factors at explicitly typed cuts restore the raw `(-y_i,x_i)` content endpoint and the retained physical terminal. A common routed response reduces this construction to `2m+2` factors. These counts are conditional code placements, not native costs. Exact reciprocal native words, future and past code access, restoration, and complete pricing remain required. The original free-word checker passes for one through eight pairs in normal Python and with `-O`. + +```sh +python3 -I -B research/ordered-centre-interfaces/annexes/reciprocal-controller/replay.py --out /tmp/reciprocal-controller-replay +``` + +Expected final line: `PASS_SCOPED_SUPPORT_PROOF_REPLAY`. diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/README.md b/research/ordered-centre-interfaces/annexes/reciprocal-controller/README.md new file mode 100644 index 0000000000..2440217869 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/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/reciprocal-controller-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/ordered-centre-interfaces/annexes/reciprocal-controller/REVIEW.json b/research/ordered-centre-interfaces/annexes/reciprocal-controller/REVIEW.json new file mode 100644 index 0000000000..4e8443bccd --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/REVIEW.json @@ -0,0 +1,15 @@ +{ + "accepted_proof_wrapper_sha256": "833d7ebcc5e122b3828db8348bf84d7169cd606918a9c63adb792b92c28e8e88", + "claim": "All-m varying routed reciprocal responses close with 4m+1 typed code factors under the stated native and code-access premises; the common-response specialization has 2m+2 factors.", + "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": "e2bbfe48658b27c760a813ae59e4caf2da7faca198fc694f799ec27e8606e064", + "source_manifest_sha256": "e67b85e2de213e39cd038bc9fe35bec8696fd421ecf65132311ace25228df39f", + "status": "ACCEPT_SCOPED_SUPPORT_APPENDIX", + "target_package": "ordered-centre-interfaces", + "validation_sha256": "a51c751cc5eb6f43a3d2c96eb51f2de9798526edd89a03713ffbbc36e6a0c124" +} diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/REVIEW.md b/research/ordered-centre-interfaces/annexes/reciprocal-controller/REVIEW.md new file mode 100644 index 0000000000..1108c3976f --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/REVIEW.md @@ -0,0 +1,65 @@ +# Independent review of the varying-response controller + +Verdict: accept the existing all-m reciprocal controller as a conditional +appendix. The historical producer freeze remains unchanged. This review +supplies a separate proof check; it does not infer correctness from that +freeze. The reviewer read PR-DESCRIPTION-STANDARD.md. + +First check the unit-response network. Let x_m=0 and w_-1=0. Immediately +before the backward call on pair i, its X value is x_i and its Y value is +x_i+y_i+w_(i-1). The backward call leaves w_i=-y_i-w_(i-1) in X. The plus +bridge adds x_(i+1). The forward call leaves x_i+x_(i+1) in retired Y. +The minus bridge restores w_i in retired X and prepares the next Y as +x_(i+1)+y_(i+1)+w_i. These equations prove the recurrence for every pair. +The descending final bridges give w_i+w_(i-1)=-y_i. On Y they subtract +the already reduced x_i from x_(i-1)+x_i. The endpoint is (-y_i,x_i). + +For general routed E_s, compare each physical content row with that ideal +network. After F0 and the first X code, X0 is E1^-1 x0 and Y0 is +E0(y0+x0). The pre-B1 Y factor removes E0. At each subsequent B_s the +active X is E_s^-1 times the ideal value and active Y is plain. The call +therefore produces E_s^-1 times the ideal difference. Left multiplication +by E_(s+1)^-1 E_s gives the required next X code, without any commutation. +The next X preparation gives equal codes on the two bridge operands. +F_(s+1) cancels its inverse code in the Y update. The minus bridge is +therefore valid, and the next transition prepares the following B call. +Final X decoding precedes every descending full bridge. This is an all-m +induction on arbitrary independent inputs. + +There are three initial factors, m active-X transitions, m-1 next-X +preparations, m-1 next-X transitions, and m final decodings: 4m+1 in total. +A common routed E removes the 2m-1 transition factors and leaves 2m+2. +The note's different three-factor one-pair identity is also valid; neither +factor count is asserted to be minimal. + +The general three-call equations have the stated product order. Vanishing +of the final X-from-x block forces b1=E1 a0 E0^-1. The Y-from-x block then +forces b2=a0^-1 E1^-1. The Y-from-y block forces a1=E2^-1 a0^-1. Finally, +the X-from-y block forces a2=b0^-1 E0 E2. These deductions also prove +necessity under the stated invertibility assumptions. They do not permit +reversal of a stage transition. + +The terminal equation A V J0=W is direct block multiplication. It uses +Q^2 Q^-1=Q and introduces no E/Q commutation. The uncoded common-E +endpoint is diag(Q E Q^-1,E^-1) relative to the raw input. The actual +564 off-diagonal source entries have distinct port directions, so the +retained character witnesses distinguish each paired intrinsic line. +No untyped scalar decoder is supplied by this observation. + +The unchanged source checker was read and run from copied closures in +normal Python and with -O. Both complete receipts match the frozen receipt +byte for byte. It checks all input blocks for one through eight pairs, +common and varying free ordered symbols, all 19 retained content events, +ten idle sites, the terminal equations, all 564 source witnesses, and +six mutations that remove a code or reverse a transition. It imports no +producer proof engine. The finite cases supplement the induction; they +do not replace it. + +This result is useful beyond the parent package's one-pair residual-code +identity because it supplies an explicit all-pair placement with varying +stage operators and a raw physical endpoint. Its stronger endpoint uses +stronger access premises, including future-stage products at specified +completed-X cuts. It does not establish those premises. In particular, +a native transpose response is not a native inverse response. No new +native construction, source access, owner admission, map price, precision, +or complete multiplication exponent is proved. diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/SOURCES.json b/research/ordered-centre-interfaces/annexes/reciprocal-controller/SOURCES.json new file mode 100644 index 0000000000..ece25def96 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/SOURCES.json @@ -0,0 +1,41 @@ +{ + "frozen_files": { + "lanes/circuit-interface/INTERFACE.json": { + "bytes": 23232, + "sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "source": "work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json" + }, + "lanes/encoded-controller/NORMALIZATION-PROGRAMS.json": { + "bytes": 58263, + "sha256": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9", + "source": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/NORMALIZATION-PROGRAMS.json" + }, + "lanes/encoded-controller/reciprocal-response-20261018/CHECKS.json": { + "bytes": 6660, + "sha256": "f76f36816359223609ecf506a2a1daad97caed96c08b0cea080d537016486b3e", + "source": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/CHECKS.json" + }, + "lanes/encoded-controller/reciprocal-response-20261018/FREEZE.json": { + "bytes": 506, + "sha256": "92470e66e90fc5026fe36ddf8d0922090f524530b492b5257a5dc2a6e1fcd3a9", + "source": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/FREEZE.json" + }, + "lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md": { + "bytes": 11844, + "sha256": "5facaac62ec417bae33690fa645150774d3820eb17be9e5033e779840f9821d5", + "source": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md" + }, + "lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py": { + "bytes": 10138, + "sha256": "b9cf8869932a356f0884bdb861c1a5b567c338b0e4174c7619829d2fdc599d61", + "source": "work/centre-encoding-campaign-20261014/lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py" + }, + "lanes/oblique-native-20261017/interior-cut/UNIT-MODE-CANDIDATE.json": { + "bytes": 24371, + "sha256": "d61d7447a499973afe49b7e422c51070262fc83229a82b7ff0ebb0238605d2fd", + "source": "work/centre-encoding-campaign-20261014/lanes/oblique-native-20261017/interior-cut/UNIT-MODE-CANDIDATE.json" + } + }, + "schema": "support-proof-appendix-sources-v1", + "scope": "Unchanged proof and check inputs. Historical receipts retain their original status." +} diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/TASK.json b/research/ordered-centre-interfaces/annexes/reciprocal-controller/TASK.json new file mode 100644 index 0000000000..2eb1769012 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/TASK.json @@ -0,0 +1,9 @@ +{ + "arguments": [], + "expected": "frozen/lanes/encoded-controller/reciprocal-response-20261018/CHECKS.json", + "id": "reciprocal-controller", + "location": "workspace", + "receipt": "lanes/encoded-controller/reciprocal-response-20261018/CHECKS.json", + "scope": "The unchanged producer free-word check for one through eight pairs, ordered three-call equations, typed source schedule, and physical terminal. The separate independent proof review proves the all-m statement. Native reciprocal and code-access contracts remain premises.", + "script": "lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py" +} diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/VALIDATION.json b/research/ordered-centre-interfaces/annexes/reciprocal-controller/VALIDATION.json new file mode 100644 index 0000000000..25018fdbac --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/VALIDATION.json @@ -0,0 +1,35 @@ +{ + "appendix": "reciprocal-controller", + "comparison": "Both complete receipt files match exact bytes.", + "runner_sha256": "c5b6abbe8d9704adfaea980c77f4f34fee78ae2367bf1e2e88bed59ca79b7697", + "runs": [ + { + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-B", + "/private/tmp/reciprocal-controller-review-20261022-a/normal/lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py" + ], + "elapsed_seconds": 0.097, + "exit_code": 0, + "mode": "normal", + "receipt_sha256": "f76f36816359223609ecf506a2a1daad97caed96c08b0cea080d537016486b3e" + }, + { + "command": [ + "/opt/homebrew/opt/python@3.14/bin/python3.14", + "-I", + "-B", + "-O", + "/private/tmp/reciprocal-controller-review-20261022-a/optimized/lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py" + ], + "elapsed_seconds": 0.066, + "exit_code": 0, + "mode": "optimized", + "receipt_sha256": "f76f36816359223609ecf506a2a1daad97caed96c08b0cea080d537016486b3e" + } + ], + "scope": "The unchanged producer free-word check for one through eight pairs, ordered three-call equations, typed source schedule, and physical terminal. The separate independent proof review proves the all-m statement. 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The actual local backward word is E^T, not E^-1. No new native transfer, owner fit, outer twiddle, price, or kappa claim." +} diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/FREEZE.json b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/FREEZE.json new file mode 100644 index 0000000000..1cd8c02506 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/FREEZE.json @@ -0,0 +1,9 @@ +{ + "status": "FROZEN_PRODUCER_PASS", + "files": { + "RECIPROCAL-CONTROLLER.md": "5facaac62ec417bae33690fa645150774d3820eb17be9e5033e779840f9821d5", + "check_reciprocal_controller.py": "b9cf8869932a356f0884bdb861c1a5b567c338b0e4174c7619829d2fdc599d61", + "CHECKS.json": "f76f36816359223609ecf506a2a1daad97caed96c08b0cea080d537016486b3e" + }, + "scope": "Ordered controller and phase theorem with explicit reciprocal native and code-cut premises. No native transfer or complete supplier admission." +} diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md new file mode 100644 index 0000000000..19b10c0cd1 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/RECIPROCAL-CONTROLLER.md @@ -0,0 +1,265 @@ +# A controller for reciprocal native responses + +This note gives a complete ordered content controller for reciprocal +responses. It includes the original phase terminal. It also lists each +additional code operation and its required cut. Thus a native construction +can test a finite set of access conditions. + +The current interior packet proves a forward response E and a backward +response E^T. It does not prove a backward response E^-1. This note does +not identify these two matrices. Its new construction has an explicit +reciprocal-response premise. + +## 1. Required local contract + +Let X and Y be arbitrary productive banks. Each bank has 112 fields with +the complete cover and payload coordinates. At stage s, let E_s be an +invertible operator on this whole bank space. In the original logical +frames, assume that the following native words are available: + + F_s(x,y) = (x, y + E_s x), + B_s(x,y) = (x - E_s^-1 y, y). + +Only F at even stages and B at odd stages is needed. Each native word must +restore every arbitrary helper and every private field according to its +own contract. Both words must have the original X-line/Y-hole input and +output frames. An inverse as an abstract matrix does not meet this premise. + +The E_s in this note is the routed operator on the complete bank. Equality +of two local 112-by-112 coefficient matrices is not sufficient to give +E_s=E_t. The cover routes are part of this equality. + +Code operations such as X<-E_t^-1 E_s X also need an implementation. +Sections 3 and 5 state their locations. No new child count is assigned to +an operation merely because the matrix is invertible. + +## 2. The retained scalar controller + +Use m pairs and 2m+1 local calls. First apply F0 to pair zero. For each +i=0,...,m-1, apply B_(2i+1) and then F_(2i+2) to pair i. If a next pair +exists, put a plus bridge before this F and a minus bridge after it: + + plus: X_i += X_(i+1), Y_(i+1) -= Y_i, + minus: X_i -= X_(i+1), Y_(i+1) += Y_i. + +The next X bank reaches FULL at the preceding odd stage before the plus +bridge. It reaches the next even level before the minus bridge. Keep the +old idle native jobs at those sites. + +After the local calls, keep the old idle tails. In descending i order, +apply the final full bridges + + X_i += X_(i-1), Y_(i-1) -= Y_i. + +For unit local responses, this word gives (-y_i,x_i) on every pair. +One proof uses the values before the final bridges. Put w_-1=0. The +completed X values obey w_i=-y_i-w_(i-1). The retired Y values are +x_i+x_(i+1), with x_m=0. The descending bridges give -y_i and x_i. + +For m=4, the checker reads the pinned source recipe directly. It verifies +all 19 content events and all ten idle sites. It does not replace the +source recipe with an unrelated network. + +## 3. A complete code placement for arbitrary E_s + +Use the local responses from section 1. Insert the following operations +in the listed order. Every multiplication below acts on the left. + +1. Before F0, apply Y0<-E0 Y0. After F0, apply X0<-E1^-1 X0. +2. Immediately before B1, apply Y0<-E0^-1 Y0. +3. After each B_s, where s=2i+1, apply + X_i<-E_(s+1)^-1 E_s X_i. +4. At the first FULL cut of the next idle X bank, before the plus bridge, + apply X_(i+1)<-E_(s+1)^-1 X_(i+1). +5. After the minus bridge at stage t=2i+2, apply + X_(i+1)<-E_(t+1)^-1 E_t X_(i+1). +6. After the old idle tails and before the final descending bridges, + apply X_i<-E_(2i+2) X_i for every pair. + +Steps 4 and 5 are absent for the last pair. There are 4m+1 code factors. +The exact four-pair table is in CHECKS.json. The table separates a Y entry +stage from a completed X level. + +### Ordered proof + +Compare the changed state with the unit-response network in section 2. +After step 1, X0 carries code E1^-1 and Y0 carries code E0. Step 2 removes +the Y code. Thus B1 subtracts the correct ideal Y from the coded X. + +Before B_s, the active X carries E_s^-1 and the active Y is plain. The +backward call gives E_s^-1(x-y), with Y unchanged. Step 3 changes this X +code to E_(s+1)^-1. Step 4 gives the same code to the next X bank. Both +parts of the plus bridge therefore act on the correct ideal contents. + +At F_(s+1), its response cancels the X code. Its Y output is the ideal +sum, with no residual code. The X code remains E_(s+1)^-1. Both parts of +the minus bridge are valid. Step 5 changes the next X code to the inverse +required by its next backward call. This proves the invariant by induction. + +Each retired X bank has code E_(2i+2)^-1. Step 6 removes all these codes +before the final bridges. Those bridges now act on plain ideal contents. +The complete preterminal endpoint is exactly + + X_i=-y_i, Y_i=x_i. (1) + +This proof treats all X and Y inputs as independent. No input, query, or +helper baseline is set to zero. The native helper contracts remain a +separate premise; the code factors act only on productive banks. + +## 4. Common routed response: ten code factors for four pairs + +If every global E_s is one common operator E, the two transition factors +in steps 3 and 5 are identities. The construction needs only 2m+2 code +factors. For four pairs these are: + +| Code | Cut | Number | +| --- | --- | ---: | +| E on Y0 | Original I input before F0 | 1 | +| E^-1 on X0 | FULL after F0 | 1 | +| E^-1 on Y0 | Current I entrance before B1 | 1 | +| E^-1 on each next X | First FULL cuts, levels 1,3,5 | 3 | +| E on every X | Final FULL, before the three tail bridges | 4 | + +After B1, all X banks that take part in a bridge carry E^-1 and all Y +banks are plain. This is why every original bridge can remain unchanged. +The final X decoding is at FULL. There is no Y-hole terminal decoding. + +If E and E^-1 have admitted scalar/cover graph circuits at these cuts, +these factors need no additional native child. Their scalar work, views, +temporary fields, and precision are still part of the supplier bill. +The note does not supply such a circuit or bill for the actual E_s. + +There is also a shorter one-pair identity. In chronological order, use + + F_E; + B_(E^-1), then X<-E^-1 X; + Y<-E^-1 Y, F_E, then X<-E^2 X. + +Its output is (-y,x). The three code factors are at a completed X cut, +a current Y input, and a completed X cut. This is an ordered identity +for one common routed response. It does not authorize repeated native +calls on one stage, nor does it prove that repeated calls advance new axes. + +## 5. The exact stage-access obligation + +The general construction places most unresolved work on completed X. +Its first tests in the actual four-pair word are: + +| Code | Required cut | Issue not removed by invertibility | +| --- | --- | --- | +| E1^-1 | X0 FULL at level0 | A future-stage code | +| E0^-1 | Y0 current entrance at stage1 | A past-stage Y code | +| E2^-1 E1 | X0 FULL after B1, level1 | A future-stage transition | +| E2^-1 | X1 first FULL, level1 | A future-stage preparation | +| E3^-1 E2 | X1 FULL after the minus bridge, level2 | A future-stage transition | +| E4^-1 E3; E4^-1 | Active and idle X at level3 | The next transition and preparation | +| E5^-1 E4 | Next X at level4 | A future-stage transition | +| E6^-1 E5; E6^-1 | Active and idle X at level5 | The next transition and preparation | +| E7^-1 E6 | Next X at level6 | A future-stage transition | +| E8^-1 E7 | Active X at level7 | The last transition | +| E2,E4,E6,E8 | Final FULL at level8 | Past/current code circuits | + +This is a finite construction hypothesis. An implementation can use a +different circuit for a product; it need not execute its factors +separately. The table does not claim that these products are free. + +The three-call calculation also gives an exact test for other wrappers. +Write the forward wrappers as pre-Y b0/post-X a0 and pre-Y b2/post-X a2. +Write the backward wrappers as pre-Y b1/post-X a1. For arbitrary +invertible a0,b0, closure to (-y,x) is equivalent to + + b1 = E1 a0 E0^-1, + a1 = E2^-1 a0^-1, + b2 = a0^-1 E1^-1, + a2 = b0^-1 E0 E2. (2) + +These equations follow by setting all four ordered endpoint blocks to +the target blocks. They show where a different boundary choice moves a +code. A future E2 in a1 cannot be dropped because the desired endpoint +has a dyadic inverse. + +## 6. The physical terminal + +Let Q be the diagonal intrinsic port-line operator and q=Q^-1. The raw +original input is W(x,y), with W=diag(Q,I). Before the old terminal, the +physical frames are F V, with V=diag(I,q). Suppress the common F in the +following equation. The retained terminal is + + A = [[0,Q^2],[-I,0]]. + +Let J0=[[0,-I],[I,0]]. Then the exact physical equation is + + A V J0 = W. (3) + +Consequently (1), together with the stated native phase contract, gives +the original FULL transform on the raw original inputs. No E crosses Q +in this proof. No encoded representation passes into an unchanged outer +twiddle or pointwise product. + +In contrast, substitute a common E into the raw controller and omit the +codes in section 4. The logical endpoint is + + [[0,-E^-1],[E,0]]. + +After the old terminal, its code relative to the raw original inputs is + + diag(Q E Q^-1, E^-1). (4) + +The first code is not E. It cannot be decoded by an untyped FULL scalar +E^-1 operation. The actual interior E has 564 nonzero entries, all off +the diagonal. All 112 port directions are distinct. For each nonzero +entry e_pr, a one-column Fourier character separates Q_p from Q_r. +Thus every nonzero entry supplies a nonzero commutator term with Q. +The checker verifies these 564 actual-source witnesses. It does not use +the older H-response obstruction as a substitute. + +Leaving (4) as an outer representation needs a new contract. With an +unchanged twiddle T, the input and output codes must satisfy the exact +intertwining equation C_out T=T C_in. A common code must commute with T. +The pointwise product also needs its own encoded multiplication identity. +A matrix inverse alone proves neither condition. A changed terminal or +encoded outer operation can be useful, but its execution and price must +be supplied separately. + +## 7. Complementary centre responses + +The root's separate construction uses RK=14I and a centre projection P: + + E = I-K[I-(12/13)P]R, + E^-1 = I-K[I-(12/13)(I-P)]R. + +This is a reciprocal pair over a ring that contains 1/13. Its native +emission and centre-child bill belong to the root's separate packet. +The controller proof above applies if its stated global and cut +conditions hold. It does not require a dyadic-only coefficient ring. + +For every such P, both centre eigenvalues differ from one. Hence + + im(I-E_s) = im(K_s). + +A change of P cannot make two global E_s equal when their routed K_s +images differ. It changes the centre splitting, not the response image. +This observation does not rule out a paid transition or a changed native +response. It only prevents a false use of the common-E corollary. + +## 8. Verification and remaining work + +Run one process from the campaign directory: + + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -I -B lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py + +Expected output: + + PASS_RECIPROCAL_RESPONSE_CONTROLLER + +The checker uses free ordered invertible symbols. It checks every input +block for one through eight pairs, the common and distinct-stage cases, +the general three-call identity, the exact retained recipe, equation (3), +and equation (4). Mutation controls remove required codes and reverse a +transition order. It reads the actual interior matrix for the Q tests. +It does not import or run another lane's proof engine. + +The induction proves the all-m statement. The finite checks do not replace +that proof. The complete supplier still needs reciprocal native words, +the stated cut circuits, owner admission, all scalar/native/precision +costs, and recursive hosting. No complete kappa improvement is claimed. diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py new file mode 100644 index 0000000000..5f1ba0e468 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/encoded-controller/reciprocal-response-20261018/check_reciprocal_controller.py @@ -0,0 +1,252 @@ +"""Check the ordered reciprocal controller and its physical terminal.""" + +from fractions import Fraction +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +ONE = {(): 1} +ZERO = {} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def normalize(word): + out = [] + for name, exponent in word: + if out and out[-1][0] == name: + exponent += out.pop()[1] + if name == "Q": + exponent %= 4 + if exponent: + out.append((name, exponent)) + return tuple(out) + + +def letter(name, exponent=1): + return {normalize(((name, exponent),)): 1} + + +def add(a, b, sign=1): + out = dict(a) + for word, value in b.items(): + out[word] = out.get(word, 0) + sign * value + if not out[word]: + del out[word] + return out + + +def mul(a, b): + out = {} + for wa, ca in a.items(): + for wb, cb in b.items(): + out = add(out, {normalize(wa + wb): ca * cb}) + return out + + +def identity(n): + return [[ONE if i == j else ZERO for j in range(n)] for i in range(n)] + + +def product(a, b): + out = [[ZERO for _ in b[0]] for _ in a] + for i, row in enumerate(a): + for j in range(len(b[0])): + for k in range(len(b)): + out[i][j] = add(out[i][j], mul(row[k], b[k][j])) + return out + + +def row_code(state, row, code): + state[row] = [mul(code, cell) for cell in state[row]] + + +def row_add(state, target, source, sign=1, code=ONE): + state[target] = [add(a, mul(code, b), sign) + for a, b in zip(state[target], state[source])] + + +def recipe(m): + out = [{"kind": "local", "stage": 0, "pair": 0, "reverse": False}] + for i in range(m): + s, t = 2 * i + 1, 2 * i + 2 + out.append({"kind": "local", "stage": s, "pair": i, "reverse": True}) + if i + 1 < m: + out.extend([ + {"kind": "idle", "pair": i + 1, "from": -1, "to": s}, + {"kind": "bridge", "dst": i, "src": i + 1, "coefficient": 1}]) + out.append({"kind": "local", "stage": t, "pair": i, "reverse": False}) + if i + 1 < m: + out.extend([ + {"kind": "idle", "pair": i + 1, "from": s, "to": t}, + {"kind": "bridge", "dst": i, "src": i + 1, "coefficient": -1}]) + out.extend({"kind": "idle", "pair": i, "from": 2 * i + 2, "to": 2 * m} + for i in range(m)) + out.extend({"kind": "bridge", "dst": i, "src": i - 1, "coefficient": 1} + for i in range(m - 1, 0, -1)) + out.append({"kind": "terminal", "pairs": m}) + return out + + +def run(m, common=False, control=None): + state, placements = identity(2 * m), [] + + def e(stage, exponent=1): + return letter("E" if common else "E" + str(stage), exponent) + + def code(row, op, cut, level): + placements.append({"row": row, "cut": cut, + "completed_X_level" if row % 2 == 0 else "current_Y_stage": level, + "operator": [[[name, power] for name, power in word] + for word in op]}) + if control != cut: + row_code(state, row, op) + + code(1, e(0), "initial_Y_before_F0", 0) + for event in recipe(m): + kind = event["kind"] + if kind == "local": + s, i = event["stage"], event["pair"] + x, y = 2 * i, 2 * i + 1 + if s == 0: + row_add(state, y, x, code=e(0)) + code(x, e(1, -1), "X_after_F0", 0) + elif event["reverse"]: + if s == 1: + code(y, e(0, -1), "Y_before_B1", 1) + row_add(state, x, y, -1, e(s, -1)) + transition = mul(e(s + 1, -1), e(s)) + if control == "reverse_B_transition_order": + transition = mul(e(s), e(s + 1, -1)) + code(x, transition, "X_after_B" + str(s), s) + else: + row_add(state, y, x, code=e(s)) + elif kind == "idle" and event["from"] == -1: + i, s = event["pair"], event["to"] + code(2 * i, e(s + 1, -1), "first_idle_X" + str(i), s) + elif kind == "idle" and event["to"] == 2 * m: + i = event["pair"] + code(2 * i, e(2 * i + 2), "final_FULL_X" + str(i), 2 * m) + elif kind == "bridge": + dst, src, c = event["dst"], event["src"], event["coefficient"] + row_add(state, 2 * dst, 2 * src, c) + row_add(state, 2 * src + 1, 2 * dst + 1, -c) + if c == -1: + t = 2 * dst + 2 + code(2 * src, mul(e(t + 1, -1), e(t)), + "next_X_after_minus" + str(t), t) + elif kind == "terminal": + pass + return state, placements + + +def rotation(m): + out = [[ZERO for _ in range(2 * m)] for _ in range(2 * m)] + for i in range(m): + out[2 * i][2 * i + 1] = {(): -1} + out[2 * i + 1][2 * i] = ONE + return out + + +def triple(): + e0, e1, e2 = [letter("E" + str(i)) for i in range(3)] + a0, b0 = letter("A"), letter("B") + b1 = mul(mul(e1, a0), letter("E0", -1)) + a1 = mul(letter("E2", -1), letter("A", -1)) + b2 = mul(letter("A", -1), letter("E1", -1)) + a2 = mul(mul(letter("B", -1), e0), e2) + f0 = [[a0, ZERO], [e0, b0]] + b = [[a1, mul(mul(a1, letter("E1", -1)), b1)], [ZERO, b1]] + b[0][1] = {w: -c for w, c in b[0][1].items()} + f2 = [[a2, ZERO], [e2, b2]] + need(product(f2, product(b, f0)) == rotation(1), "General ordered triple") + e, ei = letter("E"), letter("E", -1) + f = [[ONE, ZERO], [e, ONE]] + middle = [[ei, {(("E", -2),): -1}], [ZERO, ONE]] + last = [[letter("E", 2), ZERO], [e, ei]] + need(product(last, product(middle, f)) == rotation(1), "Three-code common triple") + + +def main(): + schedule_path = LANES / "encoded-controller/NORMALIZATION-PROGRAMS.json" + schedule_bytes = schedule_path.read_bytes() + need(sha256(schedule_bytes).hexdigest() == + "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9", + "Retained schedule pin") + actual = [e for e in json.loads(schedule_bytes)["schedule"] + if e["kind"] in ("local", "idle", "bridge", "terminal")] + need(actual == recipe(4), "Exact retained 19-event word and 10 idle sites") + tests = [] + for m in range(1, 9): + for common in (False, True): + state, placements = run(m, common) + need(state == rotation(m), "All arbitrary input blocks") + need(len(placements) == 4 * m + 1, "General factor count") + nonidentity = sum(p["operator"] != [[]] for p in placements) + need(nonidentity == (2 * m + 2 if common else 4 * m + 1), + "Nonidentity factor count") + tests.append({"pairs": m, "common_response": common, + "blocks_checked": (2 * m) ** 2, + "nonidentity_codes": nonidentity}) + for control in ("Y_before_B1", "X_after_B1", "first_idle_X1", + "next_X_after_minus2", "final_FULL_X0", + "reverse_B_transition_order"): + need(run(4, False, control)[0] != rotation(4), "Mutation: " + control) + triple() + q, qi, q2 = letter("Q"), letter("Q", -1), letter("Q", 2) + terminal = [[ZERO, q2], [{(): -1}, ZERO]] + v, w = [[ONE, ZERO], [ZERO, qi]], [[q, ZERO], [ZERO, ONE]] + need(product(terminal, product(v, rotation(1))) == w, + "Physical terminal has the exact original W input") + raw = [[ZERO, {(("E", -1),): -1}], [letter("E"), ZERO]] + raw_code = product(terminal, product(v, product(raw, [[qi, ZERO], [ZERO, ONE]]))) + need(raw_code == [[mul(q, mul(letter("E"), qi)), ZERO], + [ZERO, letter("E", -1)]], "Uncorrected physical code") + need(mul(q, letter("E")) != mul(letter("E"), q), "No Q/E commutation") + candidate_path = LANES / "oblique-native-20261017/interior-cut/UNIT-MODE-CANDIDATE.json" + interface_path = LANES / "circuit-interface/INTERFACE.json" + need(sha256(candidate_path.read_bytes()).hexdigest() == + "d61d7447a499973afe49b7e422c51070262fc83229a82b7ff0ebb0238605d2fd", + "Actual interior response pin") + need(sha256(interface_path.read_bytes()).hexdigest() == + "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "Actual port interface pin") + candidate = json.loads(candidate_path.read_bytes()) + ports = json.loads(interface_path.read_bytes())["ports"] + entries = [(i, int(j), Fraction(c)) for i, row in enumerate(candidate["J"]) + for j, c in row.items() if Fraction(c)] + need(len(entries) == 564 and all(i != j for i, j, c in entries), + "Actual response support") + need(len(set(ports)) == 112, "Distinct actual port directions") + witnesses = [] + for i, j, c in entries: + difference = ports[i] ^ ports[j] + bit = (difference & -difference).bit_length() - 1 + need(((ports[i] >> bit) & 1) != ((ports[j] >> bit) & 1), + "An actual one-column character separates each coupling") + witnesses.append([i, j, str(c), bit]) + receipt = { + "status": "PASS_RECIPROCAL_RESPONSE_CONTROLLER", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_pins": {str(p.relative_to(LANES)): sha256(p.read_bytes()).hexdigest() + for p in (schedule_path, candidate_path, interface_path)}, + "tests": tests, + "actual_four_pair_placements": run(4)[1], + "actual_noncommuting_entries": len(witnesses), + "first_noncommuting_entry": witnesses[0], + "physical_endpoint": "A V J = W; no residual code when every stated factor is implemented", + "unwrapped_common_response_endpoint": "diag(Q E Q^-1,E^-1)", + "scope": "Ordered content theorem and exact phase equation. The actual local backward word is E^T, not E^-1. No new native transfer, owner fit, outer twiddle, price, or kappa claim." + } + (HERE / "CHECKS.json").write_text(json.dumps(receipt, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/oblique-native-20261017/interior-cut/UNIT-MODE-CANDIDATE.json b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/oblique-native-20261017/interior-cut/UNIT-MODE-CANDIDATE.json new file mode 100644 index 0000000000..dfe7d30192 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/frozen/lanes/oblique-native-20261017/interior-cut/UNIT-MODE-CANDIDATE.json @@ -0,0 +1,1863 @@ +{ + "J": [ + { + "15": "1", + "2": "1", + "25": "1", + "53": "1", + "70": "1", + "76": "1", + "78": "1", + "87": "1", + "91": "1", + "99": "1" + }, + { + "75": "1", + "82": "1", + "86": "-1/2", + "93": "1/2" + }, + { + "20": "-1/2", + "46": "1/2", + "76": 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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/ordered-centre-interfaces/annexes/reciprocal-controller/validation/normal.log b/research/ordered-centre-interfaces/annexes/reciprocal-controller/validation/normal.log new file mode 100644 index 0000000000..70bda496cb --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/validation/normal.log @@ -0,0 +1 @@ +PASS_RECIPROCAL_RESPONSE_CONTROLLER diff --git a/research/ordered-centre-interfaces/annexes/reciprocal-controller/validation/optimized.log b/research/ordered-centre-interfaces/annexes/reciprocal-controller/validation/optimized.log new file mode 100644 index 0000000000..70bda496cb --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/reciprocal-controller/validation/optimized.log @@ -0,0 +1 @@ +PASS_RECIPROCAL_RESPONSE_CONTROLLER diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/BASE-PRESERVATION-CHECK.json b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/BASE-PRESERVATION-CHECK.json new file mode 100644 index 0000000000..8eda8a9e63 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/BASE-PRESERVATION-CHECK.json @@ -0,0 +1,7 @@ +{ + "changed": [], + "manifest_payload_files_checked": 139, + "manifest_sha256": "a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9", + "scope": "Checks all pre-existing payload hashes in PACKAGE-SHA256.json. The annex is additive and has its own manifest.", + "status": "PASS_EXISTING_MANIFEST_PAYLOAD_UNCHANGED" +} diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/BODY-CLAIM-CHECK.json b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/BODY-CLAIM-CHECK.json new file mode 100644 index 0000000000..a9a7317436 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/BODY-CLAIM-CHECK.json @@ -0,0 +1,15 @@ +{ + "commands_and_expected_status_match_runner": true, + "commit_placeholder": "COMMIT", + "file": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/ordered-centre-common-terminal-body-addendum.template.md", + "limitations_and_no_complete_kappa_improvement_present": true, + "mathematical_claims_match_reviewed_annex": true, + "not_checked": [ + "Final publication commit links", + "GitHub rendered Markdown", + "Published body and rendered readback" + ], + "scope": "Read the complete addendum draft. 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"88b8afc8f12f0863dfad34bbb4933523db681223c7b6ab4be0d61244a4684b9a" +} diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/PROOF-REVIEW.md b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/PROOF-REVIEW.md new file mode 100644 index 0000000000..5740076525 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/PROOF-REVIEW.md @@ -0,0 +1,96 @@ +# Common-cover terminal proof review + +The terminal and its standalone rank bound pass this proof review. The +construction uses admitted native children and monomial array maps. It +does not provide a complete supplier, map-execution price, owner schedule, +or precision certificate. This is a separate OpenAI Codex agent review, +not independent human review or a formal proof. + +The reviewer read the workspace PR description standard. The coordinator +retains the final PR, pinned-link, rendering, and readback checks. + +## Ordered physical map + +The common response must be the same operator `E` at every local call. +Changing variables to `a=Ex`, `b=y` gives the unit-response controller, +including its bridges. Its final content is `(-E^-1 y,Ex)` for every +positive pair count. The induction in the historical independent review +is valid. It does not use the ten-cycle relation or commute `E` with `Q`. + +At the physical cut, `U=-F E^-1 y` and `V=F Q^-1 E x`. The V branch +applies `Q`, then `F E^-1 F^-1`, then `Q`. This gives `F Q x`. +The U branch applies `F E F^-1` and gives `-F y`. The signed exchange +therefore returns `(F Q x,F y)`. The argument uses commutation of `F` +with payload line transforms. It requires no commutation of `E` with +the port-dependent `Q`. + +For each port, the inverse cover source is `h L^-1`. Its line direction +is `h L^-1 q`, which is `h v8` in the actual cycle. Thus the two positive +lines are `h q` and `h v8`. They are not two copies of `h q`. The other +branch uses source cover `h L`. The exact FULL translations remain in +both branches. + +The independent checker uses the full coefficients of the phase +polynomial modulo four. The phase has degree at most two. Hence the +coefficient check covers all payload addresses; it is not a sample of +the `2^73` addresses. The exact four-point Gaussian kernel also fixes +the scalar phase: the coefficients at `0,q,v8,q+v8` are +`i/2,1/2,1/2,-i/2`. The orthogonal matrix `G`, its two inverse orders, +its translations, and its literal cover source agree with this kernel. +The wrong cover direction, repeated line, omitted line, and omitted +FULL translation controls distinguish the incorrect maps. + +## Sharpness and cost class + +For any admitted orthogonal extension with `Lq=v` and `q^T v=0`, set +`w=L^-1 q`. Then `q^T w=(Lq)^T q=0`. Both vectors have norm one, so +they are distinct and independent. The terminal Fourier block +`q q^T+w w^T` has rank two. Monomial Clifford maps preserve this rank. +For a product, `B=A_left B_right+B_left D_right`, so rank is at most +the sum of the factor ranks. Thus a standalone one-field Clifford +terminal needs total native rank at least two. The emitted child +attains the bound. + +This lower bound does not cover a circuit that mixes fields, fuses an +earlier native call, changes the first line cut, or gives the logical +response a nontrivial payload action. In particular, it is not a +general terminal or multiplication lower bound. + +For four pairs and 112 ports, the inventory is 448 rank-two children, +native rank mass 896, 896 child wrapper maps, and 448 FULL source maps. +There are 1,344 monomial maps in total. Removing the old 448 line-square +maps gives 896 additional maps. The 448 signed exchanges retain their +1,344 unit complex ADDs and 10,752 real primitives. These are counts, +not a complete finite execution price. + +The native-moment conclusion has a further premise: the complete +productive path and idle ledger must have rank `2mn(D-1)` before the +terminal. With this premise, the terminal gives total rank `2mnD`. +For `r<=D` and `b>0`, `r^(1-b)>=r D^-b`. Repartitioning the same rank +cannot give a positive native saving. This review does not verify the +full hosted path ledger. This dimension-73 common-response terminal is +distinct from the two dimension-25 one-pair terminals in the parent +package. + +## Fresh execution + +The advertised runner was copied to +`/tmp/common-cover-terminal-independent-20261022` and run from `/tmp`: + +```sh +python3 -I -B /tmp/common-cover-terminal-independent-20261022/replay.py --out /tmp/common-cover-terminal-independent-results-20261022 +``` + +It passed the independent terminal checker and the line-limit checker +in normal Python and with `-O`. All four receipts matched their frozen +bytes. The finite limit check enumerated the stated dimensions three +and five and bound all 112 actual port cycles. This finite enumeration +supports the symbolic argument; it does not replace it. + +All 18 frozen source files match their campaign originals. The runner +uses only these local inputs and the Python standard library. It makes +fresh copies and leaves the source bytes unchanged. The original +producer emission, complete native and owner histories, admitted map +execution, recursive child hosting, complete price, and precision were +not replayed. No source rewrite, runtime patch, or fragile workaround +was introduced. diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REPLAY.json b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REPLAY.json new file mode 100644 index 0000000000..b04fd42013 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REPLAY.json @@ -0,0 +1,44 @@ +{ + "checks": [ + { + "check": "terminal", + "equal_frozen_bytes": true, + "mode": "normal", + "receipt_sha256": "24b6deefd0cae552127f158facc05b294af4f31ff25a04d0584603865f1a2de4", + "seconds": 0.46, + "status": "PASS_INDEPENDENT_COMMON_COVER_TERMINAL" + }, + { + "check": "terminal", + "equal_frozen_bytes": true, + "mode": "optimized", + "receipt_sha256": "24b6deefd0cae552127f158facc05b294af4f31ff25a04d0584603865f1a2de4", + "seconds": 0.473, + "status": "PASS_INDEPENDENT_COMMON_COVER_TERMINAL" + }, + { + "check": "rank_limit", + "equal_frozen_bytes": true, + "mode": "normal", + "receipt_sha256": "79be122acd97d051a291143b44ab30a6e8df3159f1901c993afd75c10f85de17", + "seconds": 0.294, + "status": "PASS_COVER_ONLY_TERMINAL_RANK" + }, + { + "check": "rank_limit", + "equal_frozen_bytes": true, + "mode": "optimized", + "receipt_sha256": "79be122acd97d051a291143b44ab30a6e8df3159f1901c993afd75c10f85de17", + "seconds": 0.226, + "status": "PASS_COVER_ONLY_TERMINAL_RANK" + } + ], + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "python": "3.14.7", + "runner_sha256": "88b8afc8f12f0863dfad34bbb4933523db681223c7b6ab4be0d61244a4684b9a", + "scope": "Exact common-cover terminal and finite controls for its standalone rank theorem. No complete path, owner, map-price, recursive, or precision replay.", + "source_count": 18, + "source_manifest_sha256": "6abfc84724acd10302ca60ac6d29720b7329db329ac55ff8e46bb88e03a915ed", + "sources_unchanged": true, + "status": "PASS_COMMON_COVER_TERMINAL_ANNEX" +} diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REVIEW.json b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REVIEW.json new file mode 100644 index 0000000000..8c33a6480e --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REVIEW.json @@ -0,0 +1,235 @@ +{ + "accepted_scope": [ + "Exact common-response terminal in dimension 73 with the declared operator order and FULL translations", + "Sharp rank two for the admitted standalone one-field Clifford terminal class with orthogonal cover-only response", + "Component inventory for four pairs and 112 ports", + "Conditional native-moment statement with its complete productive and idle ledger premise" + ], + "annex_manifest_sha256": "b6af12d53e4f4c91db4c051ae2a42d52d48fd9b8598a5d88d2c7401a690ec35c", + "base_preservation": { + "changed": [], + "manifest_payload_files_checked": 139, + "manifest_sha256": "a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9", + "scope": "Checks all pre-existing payload hashes in PACKAGE-SHA256.json. The annex is additive and has its own manifest.", + "status": "PASS_EXISTING_MANIFEST_PAYLOAD_UNCHANGED" + }, + "body_claim_check": { + "commands_and_expected_status_match_runner": true, + "commit_placeholder": "COMMIT", + "file": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/ordered-centre-common-terminal-body-addendum.template.md", + "limitations_and_no_complete_kappa_improvement_present": true, + "mathematical_claims_match_reviewed_annex": true, + "not_checked": [ + "Final publication commit links", + "GitHub rendered Markdown", + "Published body and rendered readback" + ], + "scope": "Read the complete addendum draft. 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hosting", + "Precision certificate", + "Complete kappa calculation" + ], + "package": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/ordered-centre-interfaces/annexes/common-cover-terminal", + "payload_files": 34, + "proof_review": { + "path": "PROOF-REVIEW.md", + "sha256": "a766cbebca890f237c2c3420c255d86ccca99680c3f33040fe931b70b4be77eb" + }, + "publication_not_performed": true, + "review_evidence_sha256": { + "BASE-PRESERVATION-CHECK.json": "b64f77fc2bfeee861098523273be7db49871af992f2f6110fb3ccb00a334a0f8", + "BODY-CLAIM-CHECK.json": "87f179522043babe906b17ad91fdbdb6e811716e78e2154633607ddca099eec1", + "CAMPAIGN-SOURCE-CHECK.json": "bc81ab09ea7ccb3a8d1e7a07325ab9265ba68c6865a3b070ae985e24d255652b", + "FINAL-ANNEX-INTEGRITY.json": "2aaa54771973c3458a8b539a9c4c588a6ad3963bbc8bdf069f82986a0df0e57d", + "INITIAL-INPUT-HASHES.json": "a67a292d99f9c7cba9527b28c83072ad3936b83698c00e214ca352af0404ff1d", + "PROOF-REVIEW.md": "a766cbebca890f237c2c3420c255d86ccca99680c3f33040fe931b70b4be77eb", + "REPLAY.json": "e798223ce0e32f238d12d8cf1e084967f2178fcb2472023fea56a85619f88a0f", + "REVIEW.md": "9dcc172fdc11a7b6b5ae37f6727f76c801ce8f226202895c25dcddedf7a5c344", + "SOURCE-PROOF-PINS.json": "eeb1ca70e5346f51f69c49db25b621812a008076b3587417ba716df1475835c2", + "replay-logs/rank_limit/normal/CHECKS.json": "79be122acd97d051a291143b44ab30a6e8df3159f1901c993afd75c10f85de17", + "replay-logs/rank_limit/normal/stdout.log": "a8ae5a5c3f2415282a01232ca6522f2477316acfd1280c1ada0c63e990ee7ecb", + "replay-logs/rank_limit/optimized/CHECKS.json": "79be122acd97d051a291143b44ab30a6e8df3159f1901c993afd75c10f85de17", + "replay-logs/rank_limit/optimized/stdout.log": "a8ae5a5c3f2415282a01232ca6522f2477316acfd1280c1ada0c63e990ee7ecb", + "replay-logs/terminal/normal/CHECKS.json": "24b6deefd0cae552127f158facc05b294af4f31ff25a04d0584603865f1a2de4", + "replay-logs/terminal/normal/stdout.log": "4b6db02fdd2d56b46df33fff874db8dbe4a91ed7926ddd6f9823b85e835ea833", + "replay-logs/terminal/optimized/CHECKS.json": "24b6deefd0cae552127f158facc05b294af4f31ff25a04d0584603865f1a2de4", + "replay-logs/terminal/optimized/stdout.log": "4b6db02fdd2d56b46df33fff874db8dbe4a91ed7926ddd6f9823b85e835ea833" + }, + "review_kind": "Bounded proof, scope, source, and publication-package review; not human review or formal proof", + "reviewer": "Separate OpenAI Codex agent reciprocal_package", + "status": "PASS_INDEPENDENT_ANNEX_REVIEW", + "summary": { + "path": "REVIEW.md", + "sha256": "9dcc172fdc11a7b6b5ae37f6727f76c801ce8f226202895c25dcddedf7a5c344" + }, + "total_bytes_including_manifest": 4028700, + "total_files_including_manifest": 35 +} diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REVIEW.md b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REVIEW.md new file mode 100644 index 0000000000..3a6fdb7592 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/REVIEW.md @@ -0,0 +1,57 @@ +# Common-cover terminal annex review + +Status: `PASS_INDEPENDENT_ANNEX_REVIEW`. + +The final annex passes this separate OpenAI Codex agent review. No material +proof, scope, source, or replay defect was found. This is not a human review +or a formal proof. The [proof review](PROOF-REVIEW.md) states the checked +operator order, phase, rank argument, costs, and limits. + +The exact common-response terminal and the sharp rank-two result apply to +the declared orthogonal, cover-only response and standalone one-field +Clifford terminal class. The rank bound does not cover field mixing, +fusion with an earlier call, a different first line cut, or an added +payload action. The dimension-73 construction is distinct from the +dimension-25 one-pair terminals in the parent package. The conditional +native-moment statement retains its complete-path ledger premise. + +The [fresh relocated replay](REPLAY.json) ran the independent terminal +checker and the finite rank-limit checker in normal Python and with `-O`. +All four receipts matched their frozen bytes. The command was run from +`/tmp` with Python 3.14.7 and one sequential child process: + +```sh +python3 -I -B /tmp/common-cover-terminal-independent-20261022/replay.py --out /tmp/common-cover-terminal-independent-results-20261022 +``` + +Expected and observed status: `PASS_COMMON_COVER_TERMINAL_ANNEX`. +The phase check includes the complete degree-two polynomial modulo four +and the exact four-point Gaussian kernel. The rank-limit check includes +the stated dimension-three and dimension-five finite controls and all +112 actual cycles. The symbolic rank proof has the wider stated scope. + +The [final integrity check](FINAL-ANNEX-INTEGRITY.json) binds manifest +`b6af12d53e4f4c91db4c051ae2a42d52d48fd9b8598a5d88d2c7401a690ec35c`: +34 payload files plus the manifest, 4,028,700 bytes in total. All 20 files +used in the fresh replay are unchanged. All 18 frozen sources match their +[campaign originals](CAMPAIGN-SOURCE-CHECK.json). The final additions are +documentation, notices, license, and retained evidence. All local links +in the final README and notice resolve in the package. + +The [base preservation check](BASE-PRESERVATION-CHECK.json) verifies all +139 payload hashes in the existing parent manifest. The parent manifest +hash is `a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9`. +The annex has its own manifest and does not require a base-source edit. +The final notice names the campaign source lanes, retains the parent +source notices and Apache-2.0 license, and states the AI assistance. + +No complete native or owner history, admitted array-map execution price, +recursive child hosting, precision certificate, or complete kappa +calculation ran in this annex review. The inventory of 448 rank-two +children, rank mass 896, and 1,344 monomial maps is not a complete finite +execution price. The annex gives no complete kappa improvement. + +The workspace PR description standard was read. Final commit links, +GitHub rendering, same-PR edits, and published readback remain with the +coordinator. No source rewrite, runtime patch, or fragile workaround was +introduced in this review. diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/SOURCE-PROOF-PINS.json b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/SOURCE-PROOF-PINS.json new file mode 100644 index 0000000000..1dae868600 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/SOURCE-PROOF-PINS.json @@ -0,0 +1,14 @@ +{ + "files": { + "lanes/encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md": "d57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad", + "lanes/encoded-controller/common-monomial-terminal-20261018/FREEZE.json": "e342c8d646a5c7cb5ee8cfd53d231c91a572b24894b9217a3a9533c00cce09f0", + "lanes/encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py": "4d28d8b98cf6de28e6eb2195e5ca1e461ab0aea5991a3aa700f2a1330fef5cfe", + "lanes/encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json": "4103d8e89f10b8d8dcf7ba54c8e51cc6c685e36b9fff40ad86dc1d6bf532a427", + "lanes/encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md": "5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3", + "lanes/encoded-controller/cover-line-terminal-limit-20261018/check_limit.py": "50bb8f3470c758beb76444c9e875cee86bdd415610443f5fce9835956c899e72", + "lanes/independent-review-20261017/common-terminal-review-20261018/FREEZE.json": "d75a1b7d9138f9f79971157c322ff38b2368054a6eb17e60ba43512a990a0c63", + "lanes/independent-review-20261017/common-terminal-review-20261018/REVIEW.md": "1ba6c4936fe98a983cc3485f49892b8ec1798efd96abb9bec428e7fe539b5e16", + "lanes/independent-review-20261017/common-terminal-review-20261018/check_terminal.py": "a74cb8ea2464396d44cf86e9d87ca798f66009074facc28819f0a81f062838ec" + }, + "scope": "Source proof and checker reads before publication-annex review. This is not a fresh execution receipt." +} diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/rank_limit/normal/CHECKS.json b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/rank_limit/normal/CHECKS.json new file mode 100644 index 0000000000..3fe35d4b34 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/rank_limit/normal/CHECKS.json @@ -0,0 +1,22 @@ +{ + "actual_port_checks": 112, + "checker_sha256": "50bb8f3470c758beb76444c9e875cee86bdd415610443f5fce9835956c899e72", + "proof_sha256": "5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3", + "scope": "A standalone one-field Clifford terminal for a port-diagonal orthogonal cover-only response with the stated first line cut. 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No recursive hosting, map-time price, complete supplier invoice, or precision certificate.", + "source_pins": { + "bridge-access-20261017/cycle-cover-response-20261018/CYCLE-COVER-PROGRAMS.json": "759f85673b0fda9ba4ff7312c18c80f8a8b72a3ad0a7b1192a8d08571d0095da", + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "encoded-controller/NORMALIZATION-PROGRAMS.json": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9", + "encoded-controller/common-monomial-terminal-20261018/CHECKS.json": "27f222e13cc26291fe3d0dd25b1740029c906f5cbb080db79d9599fb262795b2", + "encoded-controller/common-monomial-terminal-20261018/COMMON-TERMINAL.md": "d57d298a6b5394270fa2360d15d867b406f7fbc5e69d62829b978edda29b05ad", + "encoded-controller/common-monomial-terminal-20261018/FREEZE.json": "e342c8d646a5c7cb5ee8cfd53d231c91a572b24894b9217a3a9533c00cce09f0", + "encoded-controller/common-monomial-terminal-20261018/TERMINAL-PROGRAMS.json": "c87e99deeffa12b30b37f633c784118623aba1a4680ad3ae925d29be4f91a4d6", + "encoded-controller/common-monomial-terminal-20261018/check_common_terminal.py": "4d28d8b98cf6de28e6eb2195e5ca1e461ab0aea5991a3aa700f2a1330fef5cfe", + "encoded-controller/cover-line-terminal-limit-20261018/FREEZE.json": "4103d8e89f10b8d8dcf7ba54c8e51cc6c685e36b9fff40ad86dc1d6bf532a427", + "encoded-controller/cover-line-terminal-limit-20261018/LIMIT.md": "5e71f90893fafd7e85a7fd49617f6982dfada8079e1223a29135bb957f0707c3" + }, + "status": "PASS_INDEPENDENT_COMMON_COVER_TERMINAL" +} diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/terminal/normal/stdout.log b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/terminal/normal/stdout.log new file mode 100644 index 0000000000..144265da52 --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/terminal/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_COMMON_COVER_TERMINAL diff --git a/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/terminal/optimized/CHECKS.json b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/terminal/optimized/CHECKS.json new file mode 100644 index 0000000000..3237944fef --- /dev/null +++ b/research/publication-reviews/ordered-centre-interfaces/common-terminal-review/replay-logs/terminal/optimized/CHECKS.json @@ -0,0 +1,826 @@ +{ + "checker_sha256": "a74cb8ea2464396d44cf86e9d87ca798f66009074facc28819f0a81f062838ec", + "controller": { + "actual_content_events": 19, + "actual_idle_sites": 10, + "arbitrary_input_blocks": 8, + "arithmetic": "Free Laurent integer coefficients; no cycle relation is used." + }, + "inventory_per_replica": { + "FULL_source_maps": 448, + "child_wrapper_maps": 896, + "native_rank_mass": 896, + "net_added_monomial_maps": 896, + "new_full_cover_records": 0, + 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All earlier 234 package files and three prior annexes remain unchanged." +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/NOTICE.md b/research/ordered-centre-interfaces/annexes/access-algebra/NOTICE.md new file mode 100644 index 0000000000..a04ca9eb8a --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/NOTICE.md @@ -0,0 +1,34 @@ +# Source credit and license + +The bridge-access lane supplied the future D73 bridge program and its +proof. The controller-followthrough lane supplied the arbitrary matched +bridge theorem and partner-retirement proof. The bridge-review lane +supplied the independent access, controller, and partner checks. Its +partner review proves the weaker selected-data hypotheses, the joint +inverse, and the direct terminal endpoint guard. + +The earlier cover-algebra lane supplied the future-Y and past-X phase +theorem. The circuit-interface lane supplied the actual query matrix. +The interface-proof review supplied the historical owner and helper +phase context. The complete 1094 archive supplies the actual phase +recipes, canonical word, and owner schedule. The controller's signed +bipartite response supplies the current-chart principal units. The +native-escape proof is retained for the raw physical ADD convention. +Its native emitter is not a new result or replay of this annex. + +The partner peer check verifies the extension in the independent review. +It is not an independent native implementation review. Native partner-F16 +emission, new local-word admission, and a full decoder are outside this +package addition. + +The [source manifest](SOURCES.json) binds all exact copies. The unchanged +[source notice](notices/NOTICE), [license](notices/LICENSE), and +[parent notice](../../NOTICE.md) retain the historical contributor credit. +No prior provider, packing, compiler, or supplier result is claimed as new. +New wrapper material uses Apache-2.0. + +Substantial OpenAI Codex assistance was used for the research, proofs, +checks, and extraction. Separate agents supplied the proof and its +review. No independent human review is claimed. Copied source files, +notices, and licenses remain byte-exact. Historical pending-review or +local-only text is retained as a record of the original freeze. diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/PROOF.md b/research/ordered-centre-interfaces/annexes/access-algebra/PROOF.md new file mode 100644 index 0000000000..1bf4d5a221 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/PROOF.md @@ -0,0 +1,184 @@ +# Proof map and scope + +The two accepted packets address different obligations. The future bridge +proves a native access component and an ordered controller identity. +Partner retirement proves local algebra and principal-unit conditions. +Neither packet supplies a complete new supplier. + +## Future D73 bridge + +The [access proof](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.md) +and [independent review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/REVIEW.md) +use the actual eight selected ports and 104 ordinary ports. The actual +minor gives `R_A^T R_A=4I`. For `B=R_A^-1 R_U`, there are 416 nonzero +coefficients, each a signed half, with 52 per selected row. The bridge +adds the following map from a distinct source bank to a target bank: + +```text +c U_t = c D_t^-1 [[0,-B],[0,I]] D_t, c in {-1,1}. +``` + +First add each ordinary source to its same-port ordinary target. Then +align 104 ordinary sources and eight selected targets, apply the 416 +half ADDs, and undo the 112 views. Selected source fields are not read. +No input needs to be zero, and no source is discarded. + +For a port chart `[q,b_1,...,b_8]`, the route rho_t exchanges the eight +b axes with the coordinates of the future block E_t. Put +`beta_j=(weight(b_j)-1)/2 mod 2`. The future-Y translation after the +route is `q+lift_t(beta)`. For completed level h=t, the X translation is `sum beta_j*b_j+lift_t(beta)` and +preserves the completed X frame. The independent check compares every +coefficient modulo four, including the constant. These equalities +tensor to every positive width. + +The physical view A and logical content route D have different roles: +`A_(q,t) T_(q,h)=F_common D_(q,t)`. Relabeling a frame does not execute +the view. The checker binds the exact translations to the actual DATA +adapters and checks the two bank maps on all 224 arbitrary input columns. + +All 96 Y cuts and 48 descending X cuts are derived from the actual event +order across 16 replicas. Every update has 104 distinct source families +and 112 distinct target families, with no source-target alias. Each +cover route is a bijection. Both views finish within the update. The +ledger covers all 69,120 helper jobs and 7,526 idle suffixes. Its mixed +policy retains all 512 selected FULL exceptions. Selected source fields +with the extra line are not read, and each selected target is still in +the required earlier phase. + +One update costs `104*8+416*10=4,992` real scalar primitives and 224 +affine maps. Its largest intermediate row one-norm is 27, with at most +one added binary denominator bit. These are component quantities. A +changed local word still needs its own content, frame, phase, and +arbitrary-helper proof. + +## Arbitrary matched controller coefficients + +The [general bridge proof](frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/GENERAL-BRIDGES.md) +uses units A_i, G_i, C and arbitrary linear maps P_i, W_i, T_i, V. +Put U_i=I-P_i and E_i=G_i A_i. The local B map and its inverse are + +```text +B_i(x,y) = (U_i A_i x-y, y+P_i A_i x), +B_i^-1(w,v) = (A_i^-1(w+v), U_i v-P_i w). +``` + +No idempotence is needed here. Use the exact ordered preparation, plus-Y +bridge W, forward call, subtraction, minus-Y bridge T, and idle-X reset +in the source proof. The final descending X tail must use the same W. +For `z_i=sum_(j>=i) (-1)^(j-i) x_j`, the endpoint is + +```text +Y_i = E_i x_i, X_i = -y_i + (H x)_i, +(H x)_0 = C^-1 (U_0 A_0-V) z_0, +(H x)_i = U_i A_i z_i + W_(i-1) A_(i-1) z_(i-1) + - T_(i-1) E_(i-1) x_(i-1), i>0. +``` + +The descending tail cancels the preceding active Y input before that +X value is changed. Its remaining terms use P_i+U_i=I in their original +order. This proves the formula for every positive pair count. + +If P_i is idempotent, the two independent suffix variables show that +later query preservation holds if and only if + +```text +P_i W_(i-1)=0, P_i T_(i-1)=0, i>0. +``` + +No relation between consecutive projections is required. Pair zero +instead needs `P_0 C^-1(U_0 A_0-V)=0`. In the signed specialization the +proof uses only the same-stage relation `B_s D_s=13I`; it does not +commute graphs at different stages. Query preservation still does not +provide the original selected X suffixes needed by the response formula. +The first code and complete decoder remain separate obligations. + +## Ordered partner retirement + +The [partner proof](frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.md) +and its [independent review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.md) +use disjoint selected sets S and T, each of size eight in the actual +packet. Let U be the complement of S and V the complement of T. +The intrinsic line at port p is Q_p, with inverse q_p. Graph entries +retain their stage, source, target, and operator order. + +For arbitrary physical input `(Qh,d)`, the exact prefix and exchanges +give `z_S=d_S`, `z_U=h_U+d_U`, and + +```text +Y_T = z_T, Y_V = q_V (J_t z)_V, +X_V = hat_h_V, X_T = h_T + q_T (J_t w)_T, +hat_h_S = Q_S h_S, hat_h_U = h_U, +w_T = z_T, w_V = hat_h_V. +``` + +These cancellations need no inverse of J_t. Reversible ordinary +preparation needs J_t[V,V] to be a unit. The weaker preceding-stage +hypotheses are + +```text +h_S = p_S + q_S b, d_S = Q_S a, +h_U = p_U-v, d_U = v, +p_U = H_s^-1 (u-D_s Q_S a), +``` + +where H_s is a unit and p_S is any data-only linear function. Then +`z_S=Q_S a` and `z_U=p_U`, so all 112 borrowed coefficients vanish +from Y. No relation between J_s and J_t is needed for that cancellation. + +Let K_s have identity rows on S and rows `[D_s,H_s]` on U. Let R_t +have identity rows on T and rows of J_t on V. The physical Y code is + +```text +E = diag(I_T,q_V) R_t K_s^-1 diag(Q_S,I_U). +``` + +It is a unit when H_s and J_t[V,V] are units. J_s, J_t, their selected +principal blocks, and the original selected data coefficient need not +be units. The full ordinary blocks in the actual current chart each +have size 104 and determinant 2^60. Their dyadic inverses pass in both +orders. The 40-port large-component determinant is 1/16; the separate +64-port block supplies determinant 2^64. The full gauge must be kept. + +Put `D=diag(I_S,-I_U)` and `N=P_T q_T J_t[T,V] P_V`. Disjoint row and +column supports give N^2=0. The borrowed coefficient in X is therefore + +```text +G_b = (I+N)D, G_b^-1 = D(I-N). +``` + +For any X data coefficient C, the complete local map +`X=Cx+G_b y, Y=Ex` is a unit: + +```text +x = E^-1 Y, y = G_b^-1 (X-C E^-1 Y). +``` + +This does not remove a separate global controller requirement on C. +The optional eight-query correction acts on the full state. It cannot +be priced as only an inverse of the borrowed coefficient. + +The initial selected ADD is a raw physical common-address operation. +Its fields have different logical frames. Q remains in the operator +coefficient; no inverse Q is executed by normalization notation. The +retained [boundary model](frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/RAW-SELECTED-BACKWARD.md) +states that convention. This annex does not replay its native emitter. + +## Endpoint and implementation limits + +The physical retired code E is not FULL x. The direct FULL-data route +uses 104 normalization lines and eight final lines: 112. To reach the +required hole qx endpoint instead, the last powers are q_S^2 on S and +q_U on U. Thus the direct route uses 104 normalization lines, 104 +demotion lines, and eight even-line monomial maps. The 208-line count +is not a lower bound on every decoder and is not a global construction. + +The sixteen-line prefix count excludes its sixteen ADDs, the complete +ordinary gauge, routes, phases, and helper obligations. The separate +partner-F16 literal emission is not independently admitted here. Formal +operator tokens do not prove physical inter-stage access. The native +implementation must transport each block inverse consistently and bind +the same-port Q views before using the retired-code formula. Complete +finite precision, scalar and array-map cost, storage, recursive hosting, +and supplier admission remain open. No kappa improvement is claimed. diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/README.md b/research/ordered-centre-interfaces/annexes/access-algebra/README.md new file mode 100644 index 0000000000..30b4fdcea2 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/README.md @@ -0,0 +1,103 @@ +# Future bridge access and partner-retirement algebra + +This annex preserves two distinct accepted results. It does not give a +complete new local word, terminal decoder, supplier, or kappa improvement. +Read the [proof map](PROOF.md), [source pins](SOURCES.json), and +[source credit](NOTICE.md). + +The future D73 bridge has an exact access program at all 144 stated cuts +of the pinned historical schedule: 96 Y bridges and 48 descending X +tail updates. One update costs 4,992 real scalar primitives and 224 +affine array-map applications. It adds no recursive native child, +private field, or live field. The array maps are not free. The matched +controller theorem permits arbitrary plus-Y coefficient W when the +final X tail uses the same W. Its endpoint identity holds for every +positive pair count without commutation or idempotence of P. With +idempotent P, later query preservation holds exactly when both incoming +bridge coefficients vanish after left multiplication by the current P. +The first response has a separate condition. + +The partner-retirement theorem is ordered local algebra. It cancels all +112 arbitrary borrowed input coefficients from physical Y. The resulting +Y code and the X borrowed coefficient are units under the stated ordinary +principal-unit hypotheses. The preceding selected data coefficient can +be arbitrary. The complete ordinary gauge has 104 ports; its 64-port +component must not be omitted. The physical retirement code is not FULL +original data. A direct route to FULL data uses 112 lines. The direct +route to the required hole endpoint uses 208 lines and eight even-line +monomial maps. These are route counts, not universal lower bounds or +a complete terminal invoice. + +The unchanged [bridge access proof](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.md) +and [matched controller proof](frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/GENERAL-BRIDGES.md) +have a joint [independent review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/REVIEW.md). +The unchanged [partner proof](frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.md) +has a separate [independent review](frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.md) +that proves the weaker hypotheses, joint inverse, and terminal endpoint +guard. Native partner-F16 emission is a separate producer result. It is +not certified by this annex. + +## Replay + +Use Python 3.10 or later and the standard library. Keep at least 3 GiB +free and use one process. From this annex directory, run: + +```sh +python3 -I -B replay.py --out /tmp/ordered-access-algebra +``` + +The output directory must be new and outside the annex. Its parent must +exist. The final line must be: + +```text +PASS_ORDERED_ACCESS_ALGEBRA_ANNEX +``` + +The wrapper runs three unchanged independent checkers in normal and +optimized Python, in sequence. Each run uses a fresh local layout. +The copied runtime receipt is removed before execution, so the checker +must produce it again. Every complete receipt must equal its frozen +bytes. All source hashes are checked before and after the run. Only +the generated runtime copies are removed; logs and receipts remain. +The annex can run from a copy outside the workspace without Git or +network access. No producer checker or native emitter is imported. + +The access check verifies all 4,032 future-Y and 4,032 past-X phase +identities, both scalar signs on 224 arbitrary input columns, and the +complete owner/helper phase ledger under uniform and mixed retirement. +The controller check uses free ordered words for pair counts one through +eight. The proof covers all positive pair counts. The partner check +uses all 224 local and all 224 original data/borrowed columns, both full +104-port principal blocks, and both inverse orders. Negative controls +reject missing or misordered translations, the wrong tail coefficient, +an early idle-X reset, omitted selected Q, an omitted ordinary gauge, +and moving q through a graph entry. The first-response control confirms +that the later query criterion does not settle pair zero. + +The 34 exact source/license copies close these checks and retain their +proofs, freezes, receipts, peer qualification, and physical boundary +context. Producer scripts appear only where a source pin or freeze +requires their bytes. They are not run. Earlier pending-review and +local-only text is preserved; the later accepted reviews govern this +annex. All 234 earlier package files, including the rank-completions +annex, remain unchanged. This annex has its own ANNEX-MANIFEST.json. + +## Component prices and open obligations + +| Component | Exact local quantity | Excluded work | +| --- | --- | --- | +| One future bridge | 104 complex unit ADDs and 416 complex half ADDs; 4,992 real scalar primitives; 224 affine maps; row one-norm 27; at most one added denominator bit. | Packed map price and complete controller growth. | +| Matched T=W bridge subtotal | 804,864 real scalar primitives and 32,256 affine maps. | Initial triangle, idle-X preparation/reset, first code, final C inverse, new local words, and decoder. | +| T=0 bridge subtotal | 565,248 real scalar primitives and 21,504 affine maps. | The same excluded controller work. | +| Partner prefix | Sixteen positive native lines and sixteen unit ADDs, plus the complete ordinary gauge. | Literal native emission, all access/phase obligations, and full price. | +| Optional partner X correction | Eight inverse-line graph queries. | Scalar query, restore, access, and storage cost. | + +Both bridge subtotals include the 96 retained full-X bank writes. The +bridge result inherits the arbitrary-helper endpoint contract. It does +not prove a changed local word. Partner principal units are checked in +one current chart. A routed implementation must transport each block +and its inverse consistently and identify the same-port Q views between +stages. Formal route tokens do not prove those physical identifications. +Finite precision, full map and cover prices, helper leases, global +controller admission, recursive hosting, and a complete supplier remain +separate obligations. diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/SOURCES.json b/research/ordered-centre-interfaces/annexes/access-algebra/SOURCES.json new file mode 100644 index 0000000000..a737141777 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/SOURCES.json @@ -0,0 +1,260 @@ +{ + "existing_manifests": { + "PACKAGE-SHA256.json": "a215deb84824b4549ced931b702fd16bc5af8978b3b5e46efba5ae475f36fac9", + "annexes/common-cover-terminal/ANNEX-MANIFEST.json": "b6af12d53e4f4c91db4c051ae2a42d52d48fd9b8598a5d88d2c7401a690ec35c", + "annexes/rank-completions/ANNEX-MANIFEST.json": "c0bef4e01dc09282457234f5b3b2ff6f986c68cb38bb7607e5a30724460115ae", + "annexes/reciprocal-controller/ANNEX-MANIFEST.json": 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The identities tensor to every positive width.", + "unchanged_original_helper_jobs": 69120, + "unchanged_original_idle_suffixes": 7526, + "uniform_schedule": { + "all_bridge_frame_pairs": 32256, + "future_Y_cuts": 96, + "helper_jobs": 69120, + "idle_events": 160, + "idle_suffixes": 7526, + "local_calls": 144, + "past_X_tail_cuts": 48, + "preterminal_endpoints": 16, + "terminal_events": 16 + } +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.md b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.md new file mode 100644 index 0000000000..7ac3fec377 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/ACCESS.md @@ -0,0 +1,223 @@ +# Future projection bridges in the actual supplier + +The future projection in the new retirement controller has a legal native +implementation at both Y bridge cuts. The same coefficient has a legal +implementation in the final descending X triangle. These operations need +no new recursive native child and no private field. + +This resolves the bridge access question for the oblique projection return. +It does not complete the output decoder or admit a new supplier. The new +array maps and scalar work remain part of that supplier's finite invoice. +The result uses the earlier future-Y and past-X theorem in +`../cover-algebra/BRIDGES.md`. It binds that theorem to the new sparse +coefficient, all actual cuts, and the mixed retirement frames. + +## Coefficient and literal operations + +Use the actual selected ports + +```text +A = [0,7,20,27,36,46,57,111], +U = the other 104 ports, +B = R_A^-1 R_U. +``` + +The source matrix has `R_A^T R_A=4I`. Thus B has 416 nonzero entries, each +equal to `+1/2` or `-1/2`. Each of its eight rows has 52 entries. Let D_t be +the actual portwise stage-t cover route. The required operators are + +```text +P_t = D_t^-1 [[I,B],[0,0]] D_t, +U_t = I-P_t = D_t^-1 [[0,-B],[0,I]] D_t. +``` + +For distinct source and target banks, the update `target += c U_t source`, +where c is +1 or -1, has this literal word: + +1. For each ordinary port p, add `c source_p` to `target_p` at the old + equal same-port frame. +2. Put the 104 ordinary source fields and the eight selected target fields + in the exact stage-t view below. +3. For each nonzero B_ap, add `-c B_ap source_p` to `target_a`. +4. Undo all 112 views in their inverse order. + +The word never reads a selected source. The ordinary source fields remain +unchanged. No source field aliases a target field. There is no CLEAR, COPY, +or assumption that a data or borrowed field starts at zero. The scalar +replay checks all 224 arbitrary bank input columns. Unrelated fields have +the identity map because the word does not access them. + +The payload `BRIDGE-PROGRAMS.json.gz` contains the two signed 520-ADD words, +the full 73-column binary matrix and translation for each view, and each +physical family at all 144 scheduled cuts. Its canonical uncompressed hash +is in `ACCESS.json`. The array view is an actual monomial operation. A frame +label without that operation does not implement this word. + +## Exact future-Y view + +Write E_j for the eight-coordinate block j, and write U_h for the first +`9+8h` coordinates. At completed level h the physical Y frame at port q is + +```text +T_Y(q,h) = F_(U_h) C_q^-1. +``` + +Let `[q,b_1,...,b_8]` be the actual orthonormal port chart. The stage route +rho_t fixes q, swaps each b_j with its coordinate in E_t, and fixes the +other external blocks. For t>h it sends the Y subspace to + +```text +E_1 + ... + E_h + E_t. +``` + +This subspace does not depend on q. Its exact phase also aligns. Define + +```text +beta_j = (weight(b_j)-1)/2 modulo 2, +delta_Y(q,t) = q + lift_t(beta). +``` + +Apply rho_t first and then the translation delta_Y in invocation +coordinates. This gives the operator identity + +```text +A_(q,t) T_Y(q,h) = F_(E_1+...+E_h+E_t) D_(q,t). +``` + +The right D acts on logical content. The physical left A includes the +translation; the two are not interchangeable. In the original owner +coordinates the translation is `rho_t delta_Y`. This is exactly the +serialized `DATA-PHASES.stage_alignment[t].entry_Y`. In particular the +translation is valid before the immediately preceding stage is complete. +It is independent of h throughout h d rho_t(q)` is a bijection of the cover. +Thus each aligned source and each selected target occurs once in its +complete bridge sweep. Source and target pair IDs differ. A source cannot +alias a target in another invocation. The forward and inverse views finish +within the sweep. They introduce no borrowed-state restoration debt and +no storage cohort. + +## Exact component invoice + +One `U_t` update uses 104 complex unit ADDs and 416 complex signed-half +ADDs. Under the inherited real primitive convention, its scalar bound is + +```text +104*8 + 416*10 = 4,992. +``` + +It uses at most 224 additional affine array-map applications: one view and +one inverse on 112 fields. These maps include the explicit translation. +They are charged separately from scalar primitives. There is no recursive +native child, private field, new live field, or physical stock increase. +The largest intermediate scalar row 1-norm is exactly 27. One bridge adds +at most one binary denominator bit; it has no odd division. + +For `T_i=W_i=U_(s_i+2)`, the 96 Y updates and 48 X tails use 718,848 real +scalar primitives and 32,256 new affine map applications. The 96 retained +ordinary full X bank bridges add 86,016 real primitives. The complete +bridge subtotal is 804,864. It is a per-cover macro invoice in the same +convention as the source local words. + +For `T_i=0`, omit the 48 minus-Y words. The corresponding complete bridge +subtotal is 565,248 real primitives and 21,504 new affine map applications. +Both variants have zero native profile delta. Neither number is a complete +controller cost. A finite compiler must charge the array maps, combine the +growth bounds with the local words, and check the full recursion. + +## Verification and limits + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/check_bridge_access.py +``` + +Expected output begins with: + +```text +PASS_ACTUAL_FUTURE_PROJECTION_BRIDGES +``` + +The checker uses pinned current-supplier archive members and the actual R +matrix. It does not import a producer. It checks the bridge on arbitrary +inputs, exact phases, the actual complete source schedule, and the mixed +selected exception. Independent review of this packet is pending. + +The result discharges a specific access obligation in the generalized +projection controller. It does not implement a terminal decoder, complete +the finite precision or array-map invoice, or change kappa. It builds on +the prior cover-algebra phase theorem and the independent operator and +owner reviews listed by hash in the receipt. This work used substantial +OpenAI Codex assistance under the user's direction. + +No PR, push, or commit is authorized. 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b/research/ordered-centre-interfaces/annexes/access-algebra/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/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/ACCESS-REVIEW.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/ACCESS-REVIEW.json new file mode 100644 index 0000000000..fad9bf4045 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/ACCESS-REVIEW.json @@ -0,0 +1,66 @@ +{ + "archive_members": { + "phases": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "template": "2acf02b418078e37090495c601fe550448751d4f35912757b13a1f778efc7760", + "word": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219" + }, + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "checker_sha256": "30784728fb419da22ee17a577fd4abf1706988f242feed0693104b4b4a5535f9", + "native_children_delta": 0, + "payload_sha256": "57e2f089e0dd9f363603fc0278612b8ae8b98956a7422aa41fbd592922213abc", + "phase_cases": { + "X": 4032, + "Y": 4032 + }, + "private_fields_delta": 0, + "scalar": { + "affine_maps_per_update": 224, + "input_columns_per_sign": 224, + "maximum_row_one_norm": "27", + "real_scalar_per_update": 4992, + "signs": 2 + }, + "schedules": { + "False": { + "X_tail": 48, + "Y_bridge": 96, + "helper_jobs": 69120, + "idle_events": 160, + "idle_suffixes": 7526, + "local_calls": 144, + "preterminal": 16, + "retired_helper_jobs": 0, + "retired_idle_suffixes": 0, + "terminal": 16 + }, + "True": { + "X_tail": 48, + "Y_bridge": 96, + "helper_jobs": 69120, + "idle_events": 160, + "idle_suffixes": 7526, + "local_calls": 144, + "preterminal": 16, + "retired_helper_jobs": 1126, + "retired_idle_suffixes": 118, + "terminal": 16 + } + }, + "scope": "Bridge macro admission only. New local maps, idle-X codes, decoder, finite map costs and recursion remain separate.", + "source_pins": { + "bridge-access-20261017/ACCESS.json": "33944a0fe4587aa1ae939dd9861ad7d4c2b7c523dcf05f88fc404e4eeff8c7e8", + "bridge-access-20261017/ACCESS.md": "7fbce6a85b3704293e87ce11b8cd0add2f70f9781e2ade516ffd5fd5c29c6b58", + "bridge-access-20261017/check_bridge_access.py": "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111", + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json": "8b8c4d814b44c2fc42cf9ad995f8451512309fcfc46bea9317ebe4b4d79e8a4d" + }, + "status": "PASS_INDEPENDENT_FUTURE_BRIDGE_ACCESS", + "total_T_equals_W": { + "affine_maps": 32256, + "real_scalar": 804864 + }, + "total_T_zero": { + "affine_maps": 21504, + "real_scalar": 565248 + } +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/CONTROLLER-REVIEW.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/CONTROLLER-REVIEW.json new file mode 100644 index 0000000000..2aaa1b1e42 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/CONTROLLER-REVIEW.json @@ -0,0 +1,151 @@ +{ + "cases": [ + { + "endpoint_words": 5, + "pairs": 1, + "policy": "arbitrary" + }, + { + "endpoint_words": 15, + "pairs": 2, + "policy": "arbitrary" + }, + { + "endpoint_words": 28, + "pairs": 3, + "policy": "arbitrary" + }, + { + "endpoint_words": 44, + "pairs": 4, + "policy": "arbitrary" + }, + { + "endpoint_words": 63, + "pairs": 5, + "policy": "arbitrary" + }, + { + "endpoint_words": 85, + "pairs": 6, + "policy": "arbitrary" + }, + { + "endpoint_words": 110, + "pairs": 7, + "policy": "arbitrary" + }, + { + "endpoint_words": 138, + "pairs": 8, + "policy": "arbitrary" + }, + { + "endpoint_words": 5, + "pairs": 1, + "policy": "future_zero" + }, + { + "endpoint_words": 16, + "pairs": 2, + "policy": "future_zero" + }, + { + "endpoint_words": 31, + "pairs": 3, + "policy": "future_zero" + }, + { + "endpoint_words": 50, + "pairs": 4, + "policy": "future_zero" + }, + { + "endpoint_words": 73, + "pairs": 5, + "policy": "future_zero" + }, + { + "endpoint_words": 100, + "pairs": 6, + "policy": "future_zero" + }, + { + "endpoint_words": 131, + "pairs": 7, + "policy": "future_zero" + }, + { + "endpoint_words": 166, + "pairs": 8, + "policy": "future_zero" + }, + { + "endpoint_words": 5, + "pairs": 1, + "policy": "future_matched" + }, + { + "endpoint_words": 18, + "pairs": 2, + "policy": "future_matched" + }, + { + "endpoint_words": 35, + "pairs": 3, + "policy": "future_matched" + }, + { + "endpoint_words": 56, + "pairs": 4, + "policy": "future_matched" + }, + { + "endpoint_words": 81, + "pairs": 5, + "policy": "future_matched" + }, + { + "endpoint_words": 110, + "pairs": 6, + "policy": "future_matched" + }, + { + "endpoint_words": 143, + "pairs": 7, + "policy": "future_matched" + }, + { + "endpoint_words": 180, + "pairs": 8, + "policy": "future_matched" + } + ], + "checker_sha256": "3022521a7bc6a9e5f56d0aa1750eaefb1065ecbb2d8f83ceeb80c41878f0b169", + "controls": { + "early_idle_X_reset": 21, + "first_response_not_automatic": 16, + "wrong_tail_coefficient": 21 + }, + "method": "Free noncommutative words; only adjacent unit cancellations, specified idempotence, and B_s D_s = 13 I.", + "open_obligations": [ + "Native local maps and idle-X code changes", + "First response", + "Complete decoder", + "Finite maps, precision, stock and recursion" + ], + "proof_scope": "The induction proves all positive pair counts. The executable word checks cover m=1 through 8.", + "signed_kernel": { + "cross_stage_commutations": 0, + "relations_used": [ + "B_s D_s = 13 I" + ], + "stages": 3 + }, + "source_pins": { + "controller-followthrough-20261017/CHECKS.json": "6d35a2b2e92d0775874e50cd89a071dc5a02f575e8d58d04880a31167bf94af7", + "controller-followthrough-20261017/GENERAL-BRIDGES.md": "1871ff4f98ccc23e31221146f4be0012229ba2af64847353d42f0329842b59bf", + "controller-followthrough-20261017/check_general_bridges.py": "c4e2a92865a92deaa06bf70ef1d0aa4b717571e2ced49a5575cd1346b2490837" + }, + "status": "PASS_INDEPENDENT_MATCHED_CONTROLLER" +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/FREEZE.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/FREEZE.json new file mode 100644 index 0000000000..6b080d942d --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "ACCESS-REVIEW.json": "6d2bff6956a677a2b8d6ebfc864dfaee6b485db2b9cc3611bb26e755ad59c225", + "CONTROLLER-REVIEW.json": "e64bcc0c56a590051bdb8802ed8715534d6ea238566a2a8d4ae9111b9bfd0b7c", + "PRODUCER-ACCESS-REPLAY.json": "33944a0fe4587aa1ae939dd9861ad7d4c2b7c523dcf05f88fc404e4eeff8c7e8", + "PRODUCER-PROGRAM-REPLAY.json.gz": "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f", + "REVIEW.md": "f113fc735e179b08704a8772ba81140ed34d70239be30d2c2561f9ed73ca5c20", + "check_access_review.py": "30784728fb419da22ee17a577fd4abf1706988f242feed0693104b4b4a5535f9", + "check_controller_review.py": "3022521a7bc6a9e5f56d0aa1750eaefb1065ecbb2d8f83ceeb80c41878f0b169" + }, + "no_pr_commit_or_push": true, + "producer_replay_matches": true, + "status": "PASS_INDEPENDENT_BRIDGE_AND_CONTROLLER_REVIEW" +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/PRODUCER-ACCESS-REPLAY.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/PRODUCER-ACCESS-REPLAY.json new file mode 100644 index 0000000000..d74f021131 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/PRODUCER-ACCESS-REPLAY.json @@ -0,0 +1,103 @@ +{ + "archive_sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6", + "checker_sha256": "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111", + "complete_T_equals_W_bridge_invoice": { + "U_updates": 144, + "live_delta": 0, + "native_profile_delta": {}, + "new_affine_view_maps": 32256, + "physical_stock_delta": 0, + "real_scalar_bound": 718848, + "retained_X_real_scalar_bound": 86016, + "retained_X_unit_adds": 10752, + "total_real_scalar_bound": 804864 + }, + "complete_T_zero_bridge_invoice": { + "U_updates": 96, + "live_delta": 0, + "native_profile_delta": {}, + "new_affine_view_maps": 21504, + "physical_stock_delta": 0, + "real_scalar_bound": 479232, + "retained_X_real_scalar_bound": 86016, + "total_real_scalar_bound": 565248 + }, + "mixed_retired_selected_fields_not_read": 512, + "mixed_schedule": { + "all_bridge_frame_pairs": 32256, + "future_Y_cuts": 96, + "helper_jobs": 69120, + "idle_events": 160, + "idle_suffixes": 7526, + "local_calls": 144, + "past_X_tail_cuts": 48, + "preterminal_endpoints": 16, + "terminal_events": 16 + }, + "new_native_children": 0, + "new_private_fields": 0, + "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" + ], + "payload_sha256": 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b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/REVIEW.md @@ -0,0 +1,248 @@ +# Independent review of the future projection bridges + +The two reviewed results pass. The future projection bridge has an exact +native access program at each stated cut in the pinned supplier schedule. +The matched controller identity permits this bridge coefficient without a +right-absorption hypothesis. No material defect was found in the pinned +claims. + +This is a component and algebra review. It does not admit a new supplier or +improve kappa. In particular, it does not supply the output decoder, prove +the new local content maps, or price the complete finite implementation. + +## Reviewed sources + +The source pins are in `ACCESS-REVIEW.json` and `CONTROLLER-REVIEW.json`. +The two proof files reviewed here are: + +- `../bridge-access-20261017/ACCESS.md`, SHA-256 + `7fbce6a85b3704293e87ce11b8cd0add2f70f9781e2ade516ffd5fd5c29c6b58`. +- `../controller-followthrough-20261017/GENERAL-BRIDGES.md`, SHA-256 + `1871ff4f98ccc23e31221146f4be0012229ba2af64847353d42f0329842b59bf`. + +The source archive has SHA-256 +`f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6`. +The review reads its actual phase recipes, full owner schedule, and local +canonical word. It reads the pinned R matrix from the earlier interface +receipt. It does not import either producer checker. + +## Exact access identity + +Write `q,b_1,...,b_8` for a port's actual orthonormal chart in the initial +nine-dimensional block. The review obtains these columns from the source +idle recipe. It builds `rho_t` by exchanging `b_j` with the corresponding +coordinate of block `E_t`, while fixing q and the other external blocks. +This construction is independent of the producer's transvection formula. +It gives an orthogonal involution on all 73 coordinates. + +The Fourier phase of Y at completed level h is + +```text +phi_Y(q,h)(z) = sum_(j<9+8h) z_j - mod 4. +``` + +Here each binary dot product is first evaluated as zero or one. Its +integer polynomial modulo four is + +```text + = sum_(j in supp(v)) z_j + - 2 sum_(j + = sum_(e_j in E_1+...+E_h+E_t) z_j mod 4. +``` + +For h>=t, the X identity is + +```text +phi_X(h)(rho_t z) + 2 + = phi_X(h)(z) mod 4. +``` + +The constants are zero. These are full quadratic identities, not only +equalities of their polar subspaces. They hold in all 4,032 future-Y cases +and all 4,032 past-X cases. Omitting the translation fails in all 8,064 +cases. Applying the Y translation on the wrong side of the route fails +in all 4,032 Y cases. The exact identities tensor to every positive width. + +The review compares the two translations with the actual `entry_Y` and +`exit_X` source adapters. Thus the logical route in this program is the +same route used by the local supplier. In operator notation the physical +view satisfies `A_(q,t) T_(q,h)=F_common D_(q,t)`. The D on the right acts +on content. It is not the full physical view A on the left. + +The actual selected minor gives `R_A^T R_A=4I`. The review also verifies +`R R^T=56I`, and hence `B B^T=13I` for `B=R_A^-1 R_U`. The actual B has +416 nonzero half coefficients, with 52 per selected row. For distinct banks, +the program first adds each ordinary source to its same-port ordinary +target. It then aligns the 104 ordinary sources and eight selected targets, +applies the 416 selected-target half ADDs, and undoes each view. Therefore +it adds + +```text +c D_t^-1 [[0,-B],[0,I]] D_t source +``` + +to the target. The same-port ordinary prefix equals the diagonal ordinary +part of this expression because its two routes cancel. The cross-port +suffix uses the common frame just proved. Both signs are checked on every +one of the 224 arbitrary bank input columns. No source value is discarded. +The eight selected sources are unchanged and are never read. Unrelated +fields are not accessed. + +## Actual cuts and borrowed state + +The review derives each cut from the source event and pair orientation. It +does not infer the Y level only from a bridge counter. The plus-Y word is +after the odd backward call; the minus-Y word is after its even forward +call. In both cases its target odd stage is still in the future. The final +X words run in descending target order 3, 2, 1 before the terminal exchange. +All X fields then have the exact completed F73 frame. + +The source audit covers all 16 replicas. It verifies 96 Y cuts, 48 X tail +cuts, and the full physical family list of each payload cut. Each update +has 104 distinct source families and 112 distinct target families, with no +source-target alias. Each port's route is a bijection of the full cover. +Thus a complete sweep does not introduce an alias through another cover +index. Both views of each field finish inside the update. + +The helper audit uses each actual idle recipe to recover its native axes. +It checks every helper's strict source window, owner, width, and route +descriptor. The helper and suffix axes partition each original idle child +exactly once. The complete phase ledger covers all 144 local calls, +69,120 complete helper jobs, 7,526 suffixes, and 160 idle events. + +The mixed ledger retains the extra selected q-line after each of the 64 +retiring forward pairs. It checks all 512 selected FULL exceptions, +including their 1,126 later helper jobs and 118 idle suffixes. At a minus +bridge the selected source may have this extra line; the word does not +read it. Every selected target belongs to a pair that has not retired and +still has the required old Y phase. No later active call consumes a +retired selected field. + +This ledger uses the inherited arbitrary-helper endpoint contract. It does +not require a helper or a data bank to start at zero. It also does not +re-prove a changed local word. A new local word must still establish its +claimed data content, endpoint frames, phases, and arbitrary-helper action. + +## Matched controller proof + +The local B map is invertible even when P is not idempotent. For +`w=(I-P)Ax-y` and `v=y+PAx`, its inverse is + +```text +x=A^-1(w+v), y=(I-P)v-Pw. +``` + +The identity uses only `(I-P)+P=I`. Let eta_i be the Y input to this map. +After B, define + +```text +w_i=U_i A_i z_i-eta_i, +v_i=eta_i+P_i A_i z_i. +``` + +The prepared next X supplies `A_i z_(i+1)`. Thus the intervening F map +outputs `r_i=G_i A_i(z_i+z_(i+1))=E_i x_i`. The subsequent subtraction +restores w_i. The next Y input is exactly + +```text +eta_(i+1)=y_(i+1)-W_i eta_i-W_i P_i A_i z_i+T_i r_i. +``` + +In descending order the tail adds `W_i w_i` to the next X before w_i is +changed. The two eta_i terms cancel. The remaining preceding-stage terms +are `W_i(P_i+U_i)A_i z_i=W_i A_i z_i`. This proves the stated endpoint for +every positive pair count, with no commutation or idempotence assumption. +The separate first response is + +```text +H_0=C^-1(U_0 A_0-V)z_0. +``` + +If P_i is idempotent, the later projected response equals + +```text +(P_i W_(i-1) A_(i-1)-P_i T_(i-1) E_(i-1)) z_(i-1) + -P_i T_(i-1) E_(i-1) z_i. +``` + +The suffix map from x to z is a unit triangular map. Its two displayed +suffix variables are therefore independent. Since E and A are units, the +expression is identically zero if and only if +`P_i T_(i-1)=0` and `P_i W_(i-1)=0`. This proves necessity as well as +sufficiency. It is equivalent to factoring both maps on the left through +`U_i=I-P_i`. It imposes no relation between consecutive projections. +At pair zero the condition is instead +`P_0 C^-1(U_0 A_0-V)=0`; it is not automatic. + +The independent executable check uses free noncommutative operator words. +It checks m=1 through 8 for arbitrary P, W, T and for both future-projection +choices. Only adjacent inverse pairs and the stated projection relation +are reduced. All 24 endpoint cases pass. All 42 controls that change the +tail coefficient or reset idle X too early fail. The first-response control +fails in all 16 future-projection cases, as it must. + +For the signed specialization the check uses only `B_s D_s=13I`. It does +not commute graphs from different stages. It proves both signed inverse +orders, `P_s A_s=-Pi`, `U_s A_s=A_s+Pi`, and the response + +```text +H_(i,U)=(D_(s_(i-1))-D_(s_i))(z_i)_A + -D_(t_(i-1))(r_(i-1))_A, +H_(i,A)=-B_(s_i) H_(i,U). +``` + +This formula still contains original selected X suffixes. Preservation of +the original Y query does not itself make those X values available. + +## Cost and remaining scope + +One bridge has 104 complex unit ADDs and 416 complex half ADDs. Its inherited +real primitive bound is `104*8+416*10=4,992`. Its maximum intermediate row +one-norm is exactly 27. It adds at most one binary denominator bit. It uses +224 affine array maps, no new recursive native child, and no private field. + +The matched `T=W` subtotal is 804,864 scalar primitives and 32,256 new +affine maps. The `T=0` subtotal is 565,248 scalar primitives and 21,504 new +affine maps. Both include the 96 retained full-X bridge writes. These are +the subtotals for the stated schedule replacements. They exclude the +initial X suffix triangle, the idle-X A preparation and reset, the first +C/V code, the final C inverse, the new local words, and the decoder. A +literal initial triangle alone has 5,376 complex unit ADDs across the 16 +replicas, or 43,008 real primitives under the inherited convention. + +No affine array map is declared free. The complete compiler must price +those maps and their storage access, combine all growth and denominator +bounds, and check the recursive supplier. The zero native delta for this +component does not establish a zero supplier cost or a new kappa value. + +## Reproduction + +Run from the workspace root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_access_review.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_controller_review.py +``` + +The expected status lines are `PASS_INDEPENDENT_FUTURE_BRIDGE_ACCESS` and +`PASS_INDEPENDENT_MATCHED_CONTROLLER`. The access producer was also replayed +with separate output paths. Its receipt and uncompressed program match the +pinned originals byte for byte. The controller producer was inspected but +was not rerun, because its output path is fixed to its frozen source lane. +The independent free-word checker supplies the controller reproduction. + +This review credits the prior cover-algebra phase theorem, the interface +operator review, the original complex-mode owner review, the new bridge +program, and the new controller proof. The source pins preserve those +dependencies. This work used OpenAI Codex assistance under the user's +direction. No PR, commit, or push is authorized. Before any future PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_access_review.py b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_access_review.py new file mode 100644 index 0000000000..006c1c3ece --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_access_review.py @@ -0,0 +1,358 @@ +"""Review the future bridge program from pinned supplier data.""" + +from collections import Counter, defaultdict +from fractions import Fraction as F +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 = { + "bridge-access-20261017/ACCESS.md": "7fbce6a85b3704293e87ce11b8cd0add2f70f9781e2ade516ffd5fd5c29c6b58", + "bridge-access-20261017/ACCESS.json": "33944a0fe4587aa1ae939dd9861ad7d4c2b7c523dcf05f88fc404e4eeff8c7e8", + "bridge-access-20261017/check_bridge_access.py": "9510c5624dfb51d98767728084851e4ee75a135e6d7b546569a47fe458485111", + "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3", + "interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json": "8b8c4d814b44c2fc42cf9ad995f8451512309fcfc46bea9317ebe4b4d79e8a4d", +} +A = [0, 7, 20, 27, 36, 46, 57, 111] +U = [p for p in range(112) if p not in A] +E = [1 << i for i in range(73)] + + +def require(condition, label): + if not condition: + raise ValueError(label) + + +def read_sources(): + require(sha256(ARCHIVE.read_bytes()).hexdigest() == ARCHIVE_PIN, "Archive pin") + for name, pin in PINS.items(): + require(sha256((LANES / name).read_bytes()).hexdigest() == pin, name) + data = {} + with tarfile.open(ARCHIVE) as stream: + for name, (member, pin) in MEMBERS.items(): + raw = stream.extractfile(member).read() + require(sha256(raw).hexdigest() == pin, member) + data[name] = json.loads(gzip.decompress(raw) if member.endswith(".gz") else raw) + return data + + +@cache +def parity_polynomial(v): + """Expand binary parity as an integer polynomial modulo four.""" + bits = [j for j in range(73) if (v >> j) & 1] + out = {(j,): 1 for j in bits} + out.update({(j, k): 2 for i, j in enumerate(bits) for k in bits[i + 1:]}) + return out + + +def append_phase(out, vector, coefficient=1): + for term, value in parity_polynomial(vector).items(): + new = (out.get(term, 0) + coefficient * value) % 4 + if new: + out[term] = new + else: + out.pop(term, None) + + +def phase(terms): + out = {} + for v, c in terms: + append_phase(out, v, c) + return out + + +@cache +def boundary(q, level, side): + if level < 0: + return phase([(q, 1)] if side == 0 else []) + return phase([(v, 1) for v in E[:9 + 8 * level]] + ([(q, -1)] if side else [])) + + +def action(columns, value): + out = 0 + for i, column in enumerate(columns): + if (value >> i) & 1: + out ^= column + return out + + +def stage_route(q, basis, t): + """Build the map by its action on the supplied orthonormal basis.""" + block = E[9 + 8 * (t - 1):9 + 8 * t] + fixed = [q] + [v for v in E[9:] if v not in block] + pairs = list(zip(basis, block)) + list(zip(block, basis)) + [(v, v) for v in fixed] + columns = [] + for coordinate in E: + value = 0 + for old, new in pairs: + if (old & coordinate).bit_count() % 2: + value ^= new + columns.append(value) + require([action(columns, c) for c in columns] == E, "Involutive route") + return columns + + +def phase_review(recipes, payload): + views = {(v["port"], v["stage"], v["side"]): v for v in payload["views"]} + require(len(views) == len(payload["views"]) == 1792, "All unique views") + counts = Counter() + for p, recipe in enumerate(recipes): + q = recipe["q"] + b = recipe["idle_children"][0]["orthogonal_axes"][:8] + chart = [q] + b + E[9:] + require(all((v & w).bit_count() % 2 == (i == j) + for i, v in enumerate(chart) for j, w in enumerate(chart)), "Source basis") + beta = [((v.bit_count() - 1) // 2) % 2 for v in b] + for t in range(1, 9): + rho = stage_route(q, b, t) + lifted = sum(beta[j] * E[9 + 8 * (t - 1) + j] for j in range(8)) + local = 0 + for j in range(8): + if beta[j]: + local ^= b[j] + deltas = {"Y": q ^ lifted, "X": local ^ lifted} + require(action(rho, recipe["stage_alignment"][t]["entry_Y"]) == deltas["Y"], "Supplier Y gauge") + require(recipe["stage_alignment"][t]["exit_X"] == deltas["X"], "Supplier X gauge") + for side, delta in deltas.items(): + v = views[p, t, side] + require(v["route_columns"] == rho and v["translation_after_route"] == delta + and v["translation_before_route"] == action(rho, delta), "Literal affine view") + for h in range(9): + side = "Y" if h < t else "X" + terms = [(action(rho, v), 1) for v in E[:9 + 8 * h]] + if side == "Y": + terms.append((q, -1)) + common = phase([(v, 1) for v in E[9:9 + 8 * h] + E[9 + 8 * (t - 1):9 + 8 * t]]) + else: + common = boundary(q, h, 0) + old = phase(terms) + corrected = dict(old) + append_phase(corrected, deltas[side], 2) + require(corrected == common, "Every exact phase coefficient") + require(old != common, "Omitted translation control") + if side == "Y": + wrong = dict(old) + append_phase(wrong, action(rho, deltas[side]), 2) + require(wrong != common, "Wrong route order control") + counts[side] += 1 + require(counts == {"Y": 4032, "X": 4032}, "All phase cone cases") + return dict(counts) + + +def scalar_review(payload): + interface = json.loads((LANES / "circuit-interface/INTERFACE.json").read_bytes()) + r = [[F(row.get(str(p), 0)) for p in range(112)] for row in interface["R"]] + require(all(sum(r[i][p] * r[j][p] for p in range(112)) == 56 * (i == j) + for i in range(8) for j in range(8)), "Actual centre Gram matrix") + require(all(sum(r[k][a] * r[k][b] for k in range(8)) == 4 * (a == b) + for a in A for b in A), "Actual selected minor") + b = {(a, p): sum(r[k][a] * r[k][p] for k in range(8)) / 4 for a in A for p in U} + b = {key: value for key, value in b.items() if value} + require(len(b) == 416 and set(map(abs, b.values())) == {F(1, 2)}, "Actual half coefficients") + require(Counter(a for a, p in b) == {a: 52 for a in A}, "Actual selected row support") + require(all(sum(b.get((a, p), 0) * b.get((c, p), 0) for p in U) == 13 * (a == c) + for a in A for c in A), "Actual B D equals thirteen identity") + for sign in [-1, 1]: + program = payload["scalar_words"][str(sign)] + require(len(program) == 520, "Literal word length") + rows = [{i: F(1)} for i in range(224)] + max_norm = F(1) + for index, (op, target, source, coefficient) in enumerate(program): + coefficient = F(coefficient) + require(op == "add" and source in U and target >= 112, "Only ordinary sources") + if index < 104: + require(target == 112 + source and coefficient == sign, "Old-frame same-port prefix") + else: + require(target - 112 in A and coefficient == -sign * b[target - 112, source], "Aligned sparse suffix") + for j, value in rows[source].items(): + rows[target][j] = rows[target].get(j, 0) + coefficient * value + max_norm = max(max_norm, sum(abs(v) for v in rows[target].values())) + expected = [{i: F(1)} for i in range(224)] + for p in U: + expected[112 + p][p] = F(sign) + for (a, p), value in b.items(): + expected[112 + a][p] = -sign * value + require(rows == expected and max_norm == 27, "All arbitrary bank input columns") + return {"signs": 2, "input_columns_per_sign": 224, "maximum_row_one_norm": "27", + "real_scalar_per_update": 104 * 8 + 416 * 10, "affine_maps_per_update": 2 * (104 + 8)} + + +def family(replica, pair, side, port): + return replica * 896 + pair * 224 + side * 112 + port + + +def schedule_review(data, payload, mixed): + template, word, recipes = data["template"], data["word"], data["phases"]["recipes"] + events, calls = template["execution_schedule"], template["calls"] + positions = {e["time"]: i for i, e in enumerate(events) if e["kind"] == "local_cover_sweep"} + ends = {(e["replica"], child): (i, e, side) for i, e in enumerate(events) + if e["kind"] == "idle_cover_sweep" for side, child in enumerate(e["child_indices"])} + jobs, suffixes, covered = defaultdict(list), defaultdict(list), defaultdict(list) + touches = 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) + for job in template["hosting"]["pooled_slots"]: + end, idle, side = ends[job["owner_replica"], job["child"]] + p, role = job["port"], 224 + job["helper"] + f = family(job["owner_replica"], idle["pair"], side, p) + width = len(word["frames"][word["final"][role]]) - len(word["frames"][word["start"][role]]) + axes = recipes[p]["idle_children"][job["child"]]["orthogonal_axes"][job["offset"]:job["offset"] + width] + source_pos = positions[job["time"]] + release = max([-1] + [i for i in touches[job["owner_replica"], idle["pair"]] if i < end]) + require(release < source_pos < end and len(axes) == width == job["width"], "Strict source helper window") + first = 9 + 8 * idle["from_level"] + job["offset"] + indices = list(range(first, first + width)) + spectators = [j for j in range(73) if j not in indices][:9 - width] + descriptor = [3, job["child"], job["offset"]] if width == 9 else [4, job["child"], job["offset"], width, spectators] + require(job["family"] == f and calls[job["time"]]["owners"][role] == [f, descriptor], "Unchanged helper route") + covered[job["owner_replica"], job["child"], p].extend(axes) + jobs[job["time"]].append((f, axes)) + for job in template["idle_children"]: + end, idle, side = ends[job["replica"], job["child"]] + p = job["port"] + axes = recipes[p]["idle_children"][job["child"]]["orthogonal_axes"][job["pending_offset"]:] + f = family(job["replica"], idle["pair"], side, p) + require(job["family"] == f and len(axes) == job["rank"], "Unchanged idle suffix") + covered[job["replica"], job["child"], p].extend(axes) + suffixes[end].append((f, axes)) + for (rep, child), (end, idle, side) in ends.items(): + for p in range(112): + axes = recipes[p]["idle_children"][child]["orthogonal_axes"] + require(Counter(covered[rep, child, p]) == Counter(axes) and len(axes) == len(set(axes)), "Exact native axis partition") + state = [dict(boundary(recipes[f % 112]["q"], -1, (f // 112) % 2)) for f in range(14336)] + retired, counts, cuts, tail_order = set(), Counter(), [], defaultdict(list) + + def complete(rep, pair, level): + for side in [0, 1]: + for p in range(112): + f = family(rep, pair, side, p) + want = dict(boundary(recipes[p]["q"], level, side)) + if f in retired: + append_phase(want, recipes[p]["q"]) + require(state[f] == want, "Complete source bank phase") + + for position, event in enumerate(events): + kind, rep = event["kind"], event.get("replica") + if kind == "local_cover_sweep": + c = calls[event["time"]] + stage, pair = c["stage"], c["pair"] + require(c["orientation"] == ("backward" if stage % 2 else "forward") + and pair == max(0, (stage - 1) // 2), "Actual pair and local orientation") + require(len(c["owners"]) == len({o[0] for o in c["owners"]}) == 704, "No local owner alias") + complete(rep, pair, stage - 1) + for side in [0, 1]: + for p in range(112): + f = family(rep, pair, side, p) + require(c["owners"][112 * side + p] == [f, [1, stage, p]] and f not in retired, "Original active owner route") + state[f] = dict(boundary(recipes[p]["q"], stage, side)) + if mixed and side == 1 and p in A and stage in [2, 4, 6, 8]: + retired.add(f) + append_phase(state[f], recipes[p]["q"]) + for f, axes in jobs[event["time"]]: + for axis in axes: + append_phase(state[f], axis) + counts["helper_jobs"] += 1 + counts["retired_helper_jobs"] += int(f in retired) + complete(rep, pair, stage) + counts["local_calls"] += 1 + elif kind == "idle_cover_sweep": + for f, axes in suffixes[position]: + for axis in axes: + append_phase(state[f], axis) + counts["idle_suffixes"] += 1 + counts["retired_idle_suffixes"] += int(f in retired) + for side, child in enumerate(event["child_indices"]): + for p in range(112): + f = family(rep, event["pair"], side, p) + append_phase(state[f], recipes[p]["idle_children"][child]["translation_after"], 2) + complete(rep, event["pair"], event["to_level"]) + counts["idle_events"] += 1 + elif kind == "bridge": + tail = event["src"] < event["dst"] + if tail: + src, dst, side = event["src"], event["dst"], 0 + level, sign = 8, 1 + counts["X_tail"] += 1 + tail_order[rep].append(dst) + else: + src, dst, side = event["dst"], event["src"], 1 + level = 2 * src + 1 + int(event["coefficient"] == -1) + sign = -event["coefficient"] + counts["Y_bridge"] += 1 + require(calls[event["time"]]["pair"] == src + and calls[event["time"]]["stage"] == level, "Y bridge follows its specified local call") + stage = 2 * dst + 1 + require(dst == src + 1 and (stage <= level if tail else level < stage), "Actual bridge cone") + sources = [family(rep, src, side, p) for p in U] + targets = [family(rep, dst, side, p) for p in range(112)] + require(len(set(sources + targets)) == 216, "No bridge family alias") + for p in U: + require(state[family(rep, src, side, p)] == state[family(rep, dst, side, p)] + == boundary(recipes[p]["q"], level, side), "Same-port ordinary frame") + for p in A: + f = family(rep, dst, side, p) + require(f not in retired and state[f] == boundary(recipes[p]["q"], level, side), "Selected target frame") + cuts.append(dict(position=position, source_event=event["source_event"], replica=rep, + source_pair=src, target_pair=dst, side="X" if tail else "Y", stage=stage, + completed_level=level, sign=sign, source_ordinary_families=sources, + target_families=targets, aligned_source_ports=U, aligned_target_ports=A, + scalar_word_key=str(sign), new_affine_view_maps=224, + retained_X_bridge=not tail, removed_Y_tail=tail)) + elif kind == "terminal_Y_translations": + for pair in range(4): + complete(rep, pair, 8) + counts["preterminal"] += 1 + elif kind == "terminal": + counts["terminal"] += 1 + else: + require(kind in ["bank_padding_cover_sweep", "translate_every_live_family"], "Known event") + require(cuts == payload["cuts"], "Every literal program cut") + require(len(tail_order) == 16 and all(v == [3, 2, 1] for v in tail_order.values()), "Descending X tails") + require(counts["Y_bridge"] == 96 and counts["X_tail"] == 48 + and counts["helper_jobs"] == 69120 and counts["idle_suffixes"] == 7526, "Full schedule counts") + require(len(retired) == (512 if mixed else 0), "All selected exceptions") + return dict(counts) + + +def main(): + data = read_sources() + raw = gzip.decompress((LANES / "bridge-access-20261017/BRIDGE-PROGRAMS.json.gz").read_bytes()) + payload = json.loads(raw) + require(sha256(raw).hexdigest() == "57e2f089e0dd9f363603fc0278612b8ae8b98956a7422aa41fbd592922213abc", "Literal payload pin") + phases = phase_review(data["phases"]["recipes"], payload) + scalar = scalar_review(payload) + schedules = {str(mixed): schedule_review(data, payload, mixed) for mixed in [False, True]} + receipt = dict(status="PASS_INDEPENDENT_FUTURE_BRIDGE_ACCESS", source_pins=PINS, + archive_sha256=ARCHIVE_PIN, archive_members={k: p for k, (_, p) in MEMBERS.items()}, + payload_sha256=sha256(raw).hexdigest(), checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), + phase_cases=phases, scalar=scalar, schedules=schedules, + total_T_equals_W=dict(real_scalar=144 * 4992 + 96 * 112 * 8, affine_maps=144 * 224), + total_T_zero=dict(real_scalar=96 * 4992 + 96 * 112 * 8, affine_maps=96 * 224), + native_children_delta=0, private_fields_delta=0, + scope="Bridge macro admission only. New local maps, idle-X codes, decoder, finite map costs and recursion remain separate.") + (HERE / "ACCESS-REVIEW.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + print(json.dumps({"phase_cases": phases, "schedule": schedules["True"]}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_controller_review.py b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_controller_review.py new file mode 100644 index 0000000000..0ff6fc5047 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/check_controller_review.py @@ -0,0 +1,186 @@ +"""Check the matched controller with free operator words.""" + +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +PINS = { + "controller-followthrough-20261017/GENERAL-BRIDGES.md": "1871ff4f98ccc23e31221146f4be0012229ba2af64847353d42f0329842b59bf", + "controller-followthrough-20261017/CHECKS.json": "6d35a2b2e92d0775874e50cd89a071dc5a02f575e8d58d04880a31167bf94af7", + "controller-followthrough-20261017/check_general_bridges.py": "c4e2a92865a92deaa06bf70ef1d0aa4b717571e2ced49a5575cd1346b2490837", +} +ONE, ZERO = {(): 1}, {} + + +def require(condition, label): + if not condition: + raise ValueError(label) + + +def symbol(name, index=0, inverse=0): + return {((name, index, inverse),): 1} + + +def plus(a, b, scale=1): + result = dict(a) + for word, coefficient in b.items(): + value = result.get(word, 0) + scale * coefficient + if value: + result[word] = value + else: + result.pop(word, None) + return result + + +def normalize(word, projections): + stack, scalar = [], 1 + for token in word: + if stack and token[:2] == stack[-1][:2] and token[2] and token[2] == -stack[-1][2]: + stack.pop() + elif projections and stack and token == stack[-1] and token[0] == "P": + continue + elif stack and stack[-1][0] == "B" and token[0] == "D" and stack[-1][1] == token[1]: + stack.pop() + scalar *= 13 + else: + stack.append(token) + return tuple(stack), scalar + + +def times(a, b, projections=False): + result = {} + for left, c in a.items(): + for right, d in b.items(): + word, scale = normalize(left + right, projections) + value = result.get(word, 0) + c * d * scale + if value: + result[word] = value + else: + result.pop(word, None) + return result + + +def replay(m, policy, mutation=None): + p = [symbol("P", i) for i in range(m)] + a = [symbol("A", i, 1) for i in range(m)] + ai = [symbol("A", i, -1) for i in range(m)] + g = [symbol("G", i, 1) for i in range(m)] + u = [plus(ONE, x, -1) for x in p] + w = [symbol("W", i) if policy == "arbitrary" else u[i + 1] for i in range(m - 1)] + t = [symbol("T", i) if policy == "arbitrary" else (ZERO if policy == "future_zero" else u[i + 1]) + for i in range(m - 1)] + projections = policy != "arbitrary" + mul = lambda x, y: times(x, y, projections) + c, ci, v = symbol("C", inverse=1), symbol("C", inverse=-1), symbol("V") + original_x, original_y = [symbol("x", i) for i in range(m)], [symbol("y", i) for i in range(m)] + x, y = list(original_x), list(original_y) + for i in range(m - 2, -1, -1): + x[i] = plus(x[i], x[i + 1], -1) + z = list(x) + y[0] = plus(mul(c, y[0]), mul(v, x[0])) + for i in range(m): + ax, old_y = mul(a[i], x[i]), y[i] + x[i], y[i] = plus(mul(u[i], ax), old_y, -1), plus(old_y, mul(p[i], ax)) + if i + 1 < m: + x[i + 1] = mul(a[i], x[i + 1]) + x[i] = plus(x[i], x[i + 1]) + y[i + 1] = plus(y[i + 1], mul(w[i], y[i]), -1) + y[i] = mul(g[i], plus(x[i], y[i])) + if i + 1 < m: + if mutation == "early_reset": + x[i + 1] = mul(ai[i], x[i + 1]) + x[i] = plus(x[i], x[i + 1], -1) + y[i + 1] = plus(y[i + 1], mul(t[i], y[i])) + if mutation != "early_reset": + x[i + 1] = mul(ai[i], x[i + 1]) + for i in range(m - 1, 0, -1): + x[i] = plus(x[i], mul(u[i - 1] if mutation == "wrong_tail" else w[i - 1], x[i - 1])) + x[0] = mul(ci, x[0]) + e = [mul(g[i], a[i]) for i in range(m)] + h = [mul(ci, mul(plus(mul(u[0], a[0]), v, -1), z[0]))] + for i in range(1, m): + response = plus(mul(mul(u[i], a[i]), z[i]), mul(mul(w[i - 1], a[i - 1]), z[i - 1])) + response = plus(response, mul(mul(t[i - 1], e[i - 1]), original_x[i - 1]), -1) + h.append(response) + expected_x = [plus(h[i], original_y[i], -1) for i in range(m)] + expected_y = [mul(e[i], original_x[i]) for i in range(m)] + if mutation: + require((x, y) != (expected_x, expected_y), "Mutation must fail: " + mutation) + else: + require(x == expected_x and y == expected_y, "Free noncommuting endpoint identity") + if projections: + require(all(mul(p[i], h[i]) == ZERO for i in range(1, m)), "Every later query is preserved") + require(mul(p[0], h[0]) != ZERO, "First response is a separate condition") + return {"pairs": m, "policy": policy, "endpoint_words": sum(map(len, x + y))} + + +def matrix_add(a, b, scale=1): + return [[plus(x, y, scale) for x, y in zip(ra, rb)] for ra, rb in zip(a, b)] + + +def matrix_mul(a, b): + rows = [] + for row in a: + out = [] + for col in zip(*b): + value = ZERO + for left, right in zip(row, col): + value = plus(value, times(left, right)) + out.append(value) + rows.append(out) + return rows + + +def signed_kernel_review(): + identity = [[ONE, ZERO], [ZERO, ONE]] + pi = [[ONE, ZERO], [ZERO, ZERO]] + s, a, p, u = {}, {}, {}, {} + for stage in [1, 2, 3]: + b, d = symbol("B", stage), symbol("D", stage) + nb, nd = plus(ZERO, b, -1), plus(ZERO, d, -1) + s[stage] = [[plus(ZERO, ONE, -1), nb], [nd, plus(ONE, times(d, b), -1)]] + a[stage] = [[plus(ZERO, ONE, 12), nb], [nd, ONE]] + p[stage] = [[ONE, b], [ZERO, ZERO]] + u[stage] = matrix_add(identity, p[stage], -1) + require(matrix_mul(s[stage], a[stage]) == matrix_mul(a[stage], s[stage]) == identity, "Both signed inverses") + require(matrix_mul(p[stage], a[stage]) == matrix_add([[ZERO, ZERO], [ZERO, ZERO]], pi, -1), "Original selected return") + require(matrix_mul(u[stage], a[stage]) == matrix_add(a[stage], pi), "Return factor") + previous_x = [[symbol("xpA")], [symbol("xpU")]] + next_z = [[symbol("ziA")], [symbol("ziU")]] + previous_z = matrix_add(previous_x, next_z, -1) + r = matrix_mul(matrix_mul(s[2], a[1]), previous_x) + h = matrix_add(matrix_mul(matrix_mul(u[3], a[3]), next_z), matrix_mul(matrix_mul(u[3], a[1]), previous_z)) + h = matrix_add(h, matrix_mul(u[3], r), -1) + ordinary = plus(times(plus(symbol("D", 1), symbol("D", 3), -1), next_z[0][0]), times(symbol("D", 2), r[0][0]), -1) + require(h[1][0] == ordinary, "Exact signed ordinary response") + require(h[0][0] == plus(ZERO, times(symbol("B", 3), ordinary), -1), "Exact signed selected response") + require(matrix_mul(p[3], h) == [[ZERO], [ZERO]], "Actual oblique query preservation") + return {"stages": 3, "relations_used": ["B_s D_s = 13 I"], "cross_stage_commutations": 0} + + +def main(): + for path, pin in PINS.items(): + require(sha256((LANES / path).read_bytes()).hexdigest() == pin, path) + cases = [replay(m, policy) for policy in ["arbitrary", "future_zero", "future_matched"] for m in range(1, 9)] + for policy in ["arbitrary", "future_zero", "future_matched"]: + for m in range(2, 9): + replay(m, policy, "early_reset") + replay(m, policy, "wrong_tail") + signed = signed_kernel_review() + receipt = dict(status="PASS_INDEPENDENT_MATCHED_CONTROLLER", source_pins=PINS, + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), cases=cases, + controls={"early_idle_X_reset": 21, "wrong_tail_coefficient": 21, + "first_response_not_automatic": 16}, signed_kernel=signed, + method="Free noncommutative words; only adjacent unit cancellations, specified idempotence, and B_s D_s = 13 I.", + proof_scope="The induction proves all positive pair counts. The executable word checks cover m=1 through 8.", + open_obligations=["Native local maps and idle-X code changes", "First response", "Complete decoder", "Finite maps, precision, stock and recursion"]) + (HERE / "CONTROLLER-REVIEW.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + print(json.dumps({"free_word_cases": len(cases), "mutation_controls": 42, "signed_kernel": signed}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/FREEZE.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/FREEZE.json new file mode 100644 index 0000000000..257d7769f0 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/FREEZE.json @@ -0,0 +1,16 @@ +{ + "artifacts": { + "PRODUCER-REPLAY.json": "214a499b891c1fbfec947931b8ad71db027c04959ee2b14e200b33336b5589d3", + "REVIEW.json": "10dde09c440205d6b82149090b9d21db84251b3726823543efb9008e57a0af17", + "REVIEW.md": "1d2875499b36f31b11dbbe974b2ee681632144968b92732c36264efe783ceb95", + "check_review.py": "2722239283424e3e125c03f8de563b98cd8d8e747f4cac1707cbf3f9bfb888ad", + "replay_producer.py": "9a7856870a8786d8a7734d6fc587d92052b25652e0ac02897491b4fabeb84950" + }, + "boundary_model_proof_sha256": "3121f637184a369bba9959fa8a66e9dbf9186580c2dc957f35c5a7609ee5aad1", + "producer_freeze_sha256": "ee4c11882ab042f3101b8ccc21e33cfae0348e48af77dcd1667757b94c403af6", + "publication": "No PR, commit, push or publication.", + "reviewer": "bridge_review", + "scope": "Ordered local retirement, all224 original columns, full104-port principal units, exact source inverse, weaker selected-data hypothesis, and direct terminal endpoint guard. Native emission and global access/decoder remain separate.", + "status": "ACCEPTED_LOCAL_ORDERED_THEOREM", + "validation": "Independent original-column checker and unchanged producer replay passed under python3 -I -B -O." +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/PEER-CHECK.md b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/PEER-CHECK.md new file mode 100644 index 0000000000..4b82fd737b --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/PEER-CHECK.md @@ -0,0 +1,15 @@ +# Peer check of the weaker retirement hypotheses + +The controller-followthrough worker independently checked the extension +in `REVIEW.md`, SHA256 +`1d2875499b36f31b11dbbe974b2ee681632144968b92732c36264efe783ceb95`. +The check confirmed that Y depends only on d_S and h_U+d_U, so any +data-only p_S cancels. It confirmed N^2=0 from the disjoint row and +column supports, the source inverse D(I-N), and the stated joint inverse +for every X data coefficient C when E and G_b are units. + +The worker also confirmed the distinctions between local invertibility, +global controller conditions, raw physical prefix ADDs, and the direct +208-line hole endpoint. No material issue was found. This is a peer +check of the new theorem extension, not a native implementation review. +The original review freeze remains unchanged. diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/PRODUCER-REPLAY.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/PRODUCER-REPLAY.json new file mode 100644 index 0000000000..cf5865e2e2 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/PRODUCER-REPLAY.json @@ -0,0 +1,7 @@ +{ + "frozen_source_bytes_preserved": true, + "identical_receipt_sha256": "a493c96135c1f038ed4181ffedb64545fc561763a621a7c48c215b2f5db3e55e", + "producer_freeze_sha256": "ee4c11882ab042f3101b8ccc21e33cfae0348e48af77dcd1667757b94c403af6", + "replay_checker_sha256": "9a7856870a8786d8a7734d6fc587d92052b25652e0ac02897491b4fabeb84950", + "status": "PASS_UNCHANGED_PRODUCER_REPLAY" +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.json new file mode 100644 index 0000000000..63a4d8bfba --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.json @@ -0,0 +1,37 @@ +{ + "arbitrary_selected_data_coefficient_passed": true, + "borrowed_columns_cancelled_from_Y": 112, + "checker_sha256": "2722239283424e3e125c03f8de563b98cd8d8e747f4cac1707cbf3f9bfb888ad", + "direct_FULL_x_decoder_native_lines": 112, + "direct_hole_qx_decoder_even_line_maps": 8, + "direct_hole_qx_decoder_native_lines": 208, + "full_principal_block_sizes": [ + 104, + 104 + ], + "full_principal_determinants": [ + "1152921504606846976", + "1152921504606846976" + ], + "local_input_columns": 224, + "negative_controls": [ + "omit_selected_Q", + "omit_ordinary_gauge", + "commute_q_through_graph" + ], + "optional_X_inverse_queries": 8, + "original_data_and_borrowed_columns": 224, + "prefix_positive_lines": 16, + "producer_freeze_sha256": "ee4c11882ab042f3101b8ccc21e33cfae0348e48af77dcd1667757b94c403af6", + "retired_X_ordered_sha256": "aebd6c5b07d1adba79b8801b8451278a4237dd7a2368bb92855a42a179e30c31", + "retired_Y_ordered_sha256": "fcb40ee425e9892d93ae5e89a2a6e87fc6e261186069a10ebb07d79c4513b350", + "row_code_determinants": [ + "1152921504606846976", + "1152921504606846976" + ], + "scope": "Ordered local theorem and full principal-unit check. Native emission, access, inter-stage binding and global terminal price remain separate.", + "selected_h_columns_absent_from_Y": 8, + "source_X_ordered_sha256": "3895c69188fd23fed1bdf4801de41efa14d34fc05098487161fb1d9e19103212", + "source_payload_decompressed_sha256": "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee", + "status": "PASS_INDEPENDENT_PARTNER_RETIREMENT" +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.md b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.md new file mode 100644 index 0000000000..dbb66d5f60 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/REVIEW.md @@ -0,0 +1,187 @@ +# Independent review of partner retirement + +The ordered local theorem is accepted. It cancels all 112 arbitrary +borrowed inputs from the retired Y bank. The Y bank contains an +invertible code of the original data. The X coefficient of the borrowed +inputs is also invertible. These statements hold without commuting a +line operator through a graph entry. + +The reviewed producer freeze is +`ee4c11882ab042f3101b8ccc21e33cfae0348e48af77dcd1667757b94c403af6` +in `controller-followthrough-20261017/partner-retirement-20261018`. +Its proof has SHA256 +`904950ea0121db197b8ce2142707e67981888a2499349ba1fb3ff069720b049d`. +The signed native response has decompressed SHA256 +`0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee`. + +This review proves the local algebra and checks its principal-unit +hypotheses. It does not certify the native prefix, inter-stage access, +helper leases, a global controller, or a terminal decoder. Those require +the separate literal implementation and cost packets. + +## Independent ordered derivation + +Let S and T be disjoint port sets. Put U = complement(S), +V = complement(T), and R = complement(S union T). The proof works for +any sizes of S and T. The actual packet has |S| = |T| = 8. + +Let Q_p be an invertible operator on port p, and let q_p be its inverse. +Let J_t have arbitrary linear operator entries. Products retain their +order. Before the prefix, the physical input is (Qh,d). + +After the prefix, define hat_h_S = Q_S h_S and hat_h_U = h_U. The X +input to the raw word is Q hat_h. The selected Y input on T is +Q_T z_T, where z_S = d_S and z_U = h_U+d_U. On V, the Y input is + + J_t[V,V] (z_V - hat_h_V). + +The initial T exchange therefore gives the raw word normalized X +content w_T = z_T and w_V = hat_h_V. For V, the raw Y output is + + q_V (J_t[V,V](z_V-hat_h_V) + (J_t w)_V) + = q_V (J_t z)_V. + +For T it is h_T + q_T(J_t w)_T. The final T exchange gives + + Y_T = z_T, Y_V = q_V(J_t z)_V, + X_V = hat_h_V, X_T = h_T + q_T(J_t w)_T. + +No inverse of J_t is used. The cancellations occur with the same +ordered graph entries. This proves the local identities even if the +graph entries are unrelated noncommuting operators. To implement the +ordinary precode reversibly, J_t[V,V] must be a unit. + +## Weaker backward hypotheses and joint invertibility + +The preceding stage need only provide + + h_S = p_S + q_S b, d_S = Q_S a, + h_U = p_U - v, d_U = v, + p_U = H_s^-1 (u - D_s Q_S a), + +where H_s is a unit and p_S is any data-only linear function. In +particular, the formula for p_S from A_s is not needed. Substitution +gives z_S = Q_S a and z_U = p_U. All borrowed terms cancel from z. +No relation between J_s and J_t is needed for this cancellation. + +Let K_s have identity rows on S and rows [D_s,H_s] on U. Let R_t have +identity rows on T and rows of J_t on V. In block order these are +triangular, with ordinary diagonal blocks H_s and J_t[V,V]. Therefore +the original-data to physical-Y map is the unit + + E = diag(I_T,q_V) R_t K_s^-1 diag(Q_S,I_U). (1) + +This statement needs both ordinary blocks to be units. It does not +need J_s, J_t, their selected principal blocks, or A_s to be units. + +Write D = diag(I_S,-I_U) and + + N = P_T q_T J_t[T,V] P_V. + +The borrowed coefficient in X is G_b = (I+N)D. Since V is the complement +of T, N has source columns only in V and target rows only in T. +Thus N^2 = 0 without a commutation assumption. Its exact inverse is + + G_b^-1 = D (I-N). + +This gives X_S = b, X_R = -v_R, and + + X_T = -v_T + q_T(J_t[T,S]b - J_t[T,R]v_R). + +There is a further consequence. Write the complete local map as + + X = C x + G_b y, Y = E x. + +Since E and G_b are units, this joint map is a unit for every C: + + x = E^-1 Y, + y = G_b^-1 (X - C E^-1 Y). + +Hence the local retirement operation does not require its X data +coefficient to be invertible. This does not remove a separate global +controller requirement for that coefficient, if a controller imposes +one. It does identify which hypotheses this retirement theorem uses. + +The optional correction uses w_T = Y_T and w_V = X_V, all in FULL. +Subtract q_T(J_t w)_T from X_T. The result is hat_h on every port. +Its borrowed coefficient is D. This correction acts on the full state; +it is not just a change to the borrowed coefficient. A direct version +needs eight inverse-line queries, plus their scalar, access, restore, +and storage obligations. + +## Actual response and complete column checks + +The independent checker uses exact fractions and operator words in +execution order. It reduces adjacent powers of the same Q only. Route +tokens retain their stage, source, and target. It imports no producer +code. It checks all 224 independent local input columns and then builds +the preceding backward data coefficient from the original 112 inputs. +It checks all 224 original data and borrowed columns again. + +Every borrowed coefficient in Y is zero. The exact X source matrix, +its ordered inverse, and the optional eight-query correction pass. An +arbitrary new selected data coefficient leaves Y unchanged. Omitting +the selected positive Q, omitting the ordinary gauge, or moving q +through a graph entry fails. The generic local map has no coefficient +of any h_S input in Y, which proves independence from every p_S. + +Both complete ordinary blocks have size 104 and determinant 2^60. +Their inverses are dyadic, and both inverse orders pass. The row codes +K_s and R_t also have determinant 2^60. The checker verifies G^2 = I, +GJ = JG, and G(S) = T directly from the pinned scalar response, after +extending G by the identity on its separate 64-port block. + +The 40-port large-component gauge from the S8 packet is not the whole +104-port ordinary gauge. Its determinant is 1/16. The separate 64-port +negative-Hadamard block supplies determinant 2^64 and must also be +implemented and priced. The native emitter has been asked to bind +the complete 104-port gauge and its inverse. + +The principal-unit calculation is in one current chart. To apply it +to routed operator blocks, the implementation must transport a block +and its inverse consistently. It must also identify the preceding and +current same-port Q views before using (1). Independent formal route +tokens in the algebra do not establish those physical identifications. + +## Terminal endpoint guard + +The retired physical Y is (1), not a FULL copy of x. A direct decoder +can first apply Q_V to its 104 hole fields. In the common FULL view, +R_t^-1 followed by K_s gives diag(Q_S,I_U)x. + +To obtain FULL x from there needs q_S on eight fields. This is the +104 + 8 = 112 native-line count. It does not reach the required qx +hole endpoint. + +For that endpoint, the remaining operator is q_S^2 on S and q_U on U. +For the actual intrinsic rank-one C frames, q_S^2 is monomial. Thus +this direct route has 104 normalization lines, 104 demotion lines, and +eight even-line monomial maps: 208 native lines in total. Its scalar +codes, routes, monomial maps, precision, and hosting still need a full +invoice. The count is not a lower bound on all possible decoders and +is not itself a global terminal construction. + +The 16-line prefix count likewise covers only eight positive Q lines +on S and eight on T. Its sixteen ADDs and the complete ordinary gauge +must be included. The initial Y_S -= X_S is a raw physical array ADD; +the two fields do not have the same logical frame. Literal access and +frame bookkeeping must use that physical interpretation. At each fixed +local address z it is the update Y_p[z] -= X_p[z]. Q remains in the +operator coefficient. Defining the changed native X input as q times +the changed physical array does not execute an inverse Q for free. +This is the same explicit boundary model described in +`native-escape-20261017/RAW-SELECTED-BACKWARD.md`. The new literal emitter +must still bind its own addresses and retain the complete coefficient. + +Run the independent check with one process: + + python3 -I -B -O check_review.py + +Expected result: + + PASS_INDEPENDENT_PARTNER_RETIREMENT + +No frozen producer file was changed. No PR, commit, push, or publication +was made. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. +This review and its checker were produced with AI assistance. diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/check_review.py b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/check_review.py new file mode 100644 index 0000000000..838e355297 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/check_review.py @@ -0,0 +1,296 @@ +"""Check the partner interface with exact ordered operator columns.""" + +from collections import defaultdict +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +CHECKER_SHA = sha256(Path(__file__).read_bytes()).hexdigest() +LANES = HERE.parents[1] +PRODUCER = LANES / "controller-followthrough-20261017/partner-retirement-20261018" +SOURCE = LANES / "controller-followthrough-20261017/bipartite-eight-20261018" +FREEZE = "ee4c11882ab042f3101b8ccc21e33cfae0348e48af77dcd1667757b94c403af6" +PAYLOAD = "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee" + + +def need(test, message): + if not test: + raise ValueError(message) + + +def combine(*terms): + result = defaultdict(F) + for coefficient, row in terms: + for key, value in row.items(): + result[key] += coefficient * value + return {key: value for key, value in result.items() if value} + + +def symbol(column): + return {(column, ()): F(1)} + + +def op(row, token): + """Append an operator in execution order. Reduce adjacent Q powers only.""" + result = defaultdict(F) + for (column, word), value in row.items(): + if word and token[0] == word[-1][0] == "Q" and token[1] == word[-1][1]: + power = token[2] + word[-1][2] + next_word = word[:-1] + (("Q", token[1], power),) if power else word[:-1] + else: + next_word = word + (token,) + result[column, next_word] += value + return {key: value for key, value in result.items() if value} + + +def q(row, port, power): + return op(row, ("Q", port, power)) + + +def graph(matrix, vector, targets=None, sources=None, stage="t"): + targets = range(len(matrix)) if targets is None else targets + allowed = set(range(len(matrix))) if sources is None else set(sources) + result = {} + for row in targets: + parts = [] + for column, value in matrix[row].items(): + if column in allowed: + expression = vector[column] + if row != column: + expression = op(expression, ("route", stage, row, column)) + parts.append((value, expression)) + result[row] = combine(*parts) + return result + + +def physical_word(matrix, selected, partner, h, d, bad=None): + n = len(matrix) + outside = sorted(set(range(n)) - set(partner)) + x = {p: q(h[p], p, 1) for p in range(n)} + y = dict(d) + for p in selected: + y[p] = combine((1, y[p]), (-1, x[p])) + if bad != "omit_selected_Q": + for p in selected: + x[p] = q(x[p], p, 1) + for p in partner: + y[p] = q(y[p], p, 1) + y[p] = combine((1, y[p]), (1, x[p])) + if bad != "omit_ordinary_gauge": + y.update(graph(matrix, y, outside, outside)) + for p in partner: + x[p], y[p] = y[p], x[p] + normalized = {p: q(x[p], p, -1) for p in range(n)} + response = graph(matrix, normalized) + y = {p: q(combine((1, y[p]), (1, response[p])), p, -1) for p in range(n)} + x = normalized + for p in partner: + x[p], y[p] = y[p], x[p] + return x, y + + +def expected(matrix, selected, partner, h, d): + n = len(matrix) + selected, partner = set(selected), set(partner) + z = {p: d[p] if p in selected else combine((1, h[p]), (1, d[p])) for p in range(n)} + hhat = {p: q(h[p], p, 1) if p in selected else h[p] for p in range(n)} + w = {p: z[p] if p in partner else hhat[p] for p in range(n)} + jz, jw = graph(matrix, z), graph(matrix, w) + y = {p: z[p] if p in partner else q(jz[p], p, -1) for p in range(n)} + x = {p: combine((1, h[p]), (1, q(jw[p], p, -1))) if p in partner else hhat[p] + for p in range(n)} + return x, y, z + + +def mm(left, right): + out = [] + for row in left: + result = defaultdict(F) + for middle, a in row.items(): + for column, b in right[middle].items(): + result[column] += a*b + out.append({column: value for column, value in result.items() if value}) + return out + + +def eye(n): + return [{j: F(1)} for j in range(n)] + + +def sub(matrix, ports): + index = {p: i for i, p in enumerate(ports)} + return [{index[j]: value for j, value in matrix[p].items() if j in index} for p in ports] + + +def inverse(matrix): + n = len(matrix) + left, right = [dict(row) for row in matrix], eye(n) + determinant = F(1) + for column in range(n): + pivot = next(i for i in range(column, n) if left[i].get(column)) + if pivot != column: + left[column], left[pivot] = left[pivot], left[column] + right[column], right[pivot] = right[pivot], right[column] + determinant = -determinant + value = left[column][column] + determinant *= value + left[column] = {j: a/value for j, a in left[column].items()} + right[column] = {j: a/value for j, a in right[column].items()} + for i in range(n): + if i != column and left[i].get(column): + value = left[i][column] + left[i] = combine((1, left[i]), (-value, left[column])) + right[i] = combine((1, right[i]), (-value, right[column])) + need(left == eye(n), "Exact elimination reached the identity") + need(mm(matrix, right) == mm(right, matrix) == eye(n), "Both inverse orders") + return right, determinant + + +def embed(matrix, ports, n): + result = [{} for _ in range(n)] + for i, p in enumerate(ports): + result[p] = {ports[j]: value for j, value in matrix[i].items()} + return result + + +def digest(vector): + serial = [[(column, word, str(value)) for (column, word), value in sorted(vector[p].items(), key=repr)] + for p in sorted(vector)] + return sha256(json.dumps(serial, separators=(",", ":")).encode()).hexdigest() + + +def main(): + need(sha256((PRODUCER/"FREEZE.json").read_bytes()).hexdigest() == FREEZE, "Frozen theorem pin") + for name, pin in json.loads((PRODUCER/"FREEZE.json").read_text())["files"].items(): + need(sha256((PRODUCER/name).read_bytes()).hexdigest() == pin, "Frozen producer artifact: " + name) + raw = gzip.decompress((SOURCE/"BIPARTITE-EIGHT-PROGRAM.json.gz").read_bytes()) + need(sha256(raw).hexdigest() == PAYLOAD, "Exact signed native payload") + packet = json.loads(raw) + j = [{int(k): F(v) for k, v in row.items()} for row in packet["response"]] + n = len(j) + selected, partner = packet["selected_ports"], packet["partner_ports"] + s, t = set(selected), set(partner) + u, v = sorted(set(range(n))-s), sorted(set(range(n))-t) + rest = sorted(set(range(n))-s-t) + need(n == 112 and len(s) == len(t) == 8 and not s&t, "The disjoint actual port sets") + hs, ht = sub(j, u), sub(j, v) + hsi, hsdet = inverse(hs) + hti, htdet = inverse(ht) + need(hsdet == htdet == F(2**60), "Full 104-port principal determinants") + need(all(a.denominator & (a.denominator-1) == 0 for matrix in (hsi, hti) for row in matrix for a in row.values()), + "Both complete principal inverses are dyadic") + g = [{int(k): F(a) for k, a in row.items()} for row in packet["signed_monomial"]] + for p in packet["small_ports"]: + need(not g[p], "Stored G is restricted to the large component") + g[p] = {p:F(1)} + need(mm(g, g) == eye(n) and mm(g, j) == mm(j, g), "Exact signed relabeling symmetry") + need({next(iter(g[p])) for p in selected} == t, "The symmetry sends S to T") + ks = [{p:F(1)} if p in s else dict(j[p]) for p in range(n)] + rt = [{p:F(1)} if p in t else dict(j[p]) for p in range(n)] + ksi, kdet = inverse(ks) + rti, rdet = inverse(rt) + need(kdet == rdet == hsdet, "Both row codes are complete dyadic units") + need(mm(mm(ks, rti), mm(rt, ksi)) == eye(n), "The common-view logical decoder inverse") + + h = {p:symbol(p) for p in range(n)} + d = {p:symbol(n+p) for p in range(n)} + x0, y0 = physical_word(j, selected, partner, h, d) + xe, ye, _ = expected(j, selected, partner, h, d) + need((x0, y0) == (xe, ye), "All 224 independent local input columns") + need(all(column not in s for row in y0.values() for column, _ in row), + "The selected h columns are absent for unrestricted local inputs") + + # Build the preceding backward data coefficient from original inputs. + # Distinct route symbols keep stage-s products in their original order. + a = {p:q(symbol(p), p, 1) if p in s else symbol(p) for p in range(n)} + da = graph(j, a, u, selected, stage="s") + residual = {p:combine((1, symbol(p)), (-1, da[p])) for p in u} + p_data = graph(embed(hsi, u, n), residual, u, u, stage="s_inverse") + first = graph(j, a, selected, selected, stage="s") + cross = graph(j, p_data, selected, u, stage="s") + p_data.update({p:combine((-1, first[p]), (-1, cross[p])) for p in selected}) + h = {p:combine((1, p_data[p]), (1, q(symbol(n+p), p, -1))) if p in s + else combine((1, p_data[p]), (-1, symbol(n+p))) for p in range(n)} + d = {p:a[p] if p in s else symbol(n+p) for p in range(n)} + x, y = physical_word(j, selected, partner, h, d) + xe, ye, z = expected(j, selected, partner, h, d) + need((x, y) == (xe, ye), "All 224 original data and borrowed input columns") + clean_z = {p:a[p] if p in s else p_data[p] for p in range(n)} + need(z == clean_z, "The data-only z identity") + need(all(column < n for row in y.values() for column, _ in row), "Every borrowed coefficient in Y is zero") + source = {p:{key:value for key, value in row.items() if key[0] >= n} for p, row in x.items()} + diagonal = {p:symbol(n+p) if p in s else combine((-1, symbol(n+p))) for p in range(n)} + cross = graph(j, diagonal, partner, v) + expected_source = {p:combine((1, diagonal[p]), (1, q(cross[p], p, -1))) if p in t else diagonal[p] + for p in range(n)} + need(source == expected_source, "Complete unit triangular borrowed-source code") + inverse_source = dict(source) + source_query = graph(j, source, partner, v) + for p in partner: + inverse_source[p] = combine((1, inverse_source[p]), (-1, q(source_query[p], p, -1))) + need(inverse_source == diagonal, "The source coefficient has the stated ordered inverse") + mixed = {p:y[p] if p in t else x[p] for p in range(n)} + query = graph(j, mixed, partner) + corrected = dict(x) + for p in partner: + corrected[p] = combine((1, corrected[p]), (-1, q(query[p], p, -1))) + need(corrected == {p:q(h[p], p, 1) if p in s else h[p] for p in range(n)}, + "The optional eight-query correction on all original columns") + wrong_query = graph(j, {p:q(mixed[p], p, -1) for p in range(n)}, partner) + need(wrong_query != {p:q(query[p], p, -1) for p in partner}, + "An inverse line cannot be moved through a graph entry") + + # The selected data term need not be the term supplied by A_s. + for p in selected: + arbitrary = op(symbol(p), ("unrestricted_selected_data_map", p)) + h[p] = combine((1, arbitrary), (1, q(symbol(n+p), p, -1))) + _, weaker_y = physical_word(j, selected, partner, h, d) + need(weaker_y == y, "The retired code is independent of the selected data coefficient") + for mutation in ("omit_selected_Q", "omit_ordinary_gauge"): + _, bad_y = physical_word(j, selected, partner, h, d, bad=mutation) + need(bad_y != y, "Mutation must fail: " + mutation) + + # A common-view decoder gives D_QS x. The required hole endpoint is q x. + line_exponents = {p:1 if p in s else 0 for p in range(n)} + terminal_inverse_lines = {p:1 + line_exponents[p] for p in range(n)} + need(sum(a == 1 for a in terminal_inverse_lines.values()) == 104 + and sum(a == 2 for a in terminal_inverse_lines.values()) == 8, + "Final demotion needs 104 odd line powers and eight even powers") + terminal_native = len(v) + sum(a % 2 for a in terminal_inverse_lines.values()) + full_x_native = len(v) + len(s) + need((terminal_native, full_x_native) == (208, 112), "Hole and FULL endpoint counts differ") + need(sha256(Path(__file__).read_bytes()).hexdigest() == CHECKER_SHA, "Checker bytes stayed fixed") + receipt = { + "status":"PASS_INDEPENDENT_PARTNER_RETIREMENT", + "producer_freeze_sha256": FREEZE, + "source_payload_decompressed_sha256": PAYLOAD, + "checker_sha256": CHECKER_SHA, + "local_input_columns":224, + "original_data_and_borrowed_columns":224, + "borrowed_columns_cancelled_from_Y":112, + "selected_h_columns_absent_from_Y":len(s), + "full_principal_block_sizes":[len(u),len(v)], + "full_principal_determinants":[str(hsdet),str(htdet)], + "row_code_determinants":[str(kdet),str(rdet)], + "prefix_positive_lines":len(s)+len(t), + "optional_X_inverse_queries":len(t), + "direct_FULL_x_decoder_native_lines":full_x_native, + "direct_hole_qx_decoder_native_lines":terminal_native, + "direct_hole_qx_decoder_even_line_maps":len(s), + "retired_X_ordered_sha256":digest(x), + "retired_Y_ordered_sha256":digest(y), + "source_X_ordered_sha256":digest(source), + "arbitrary_selected_data_coefficient_passed":True, + "negative_controls":["omit_selected_Q","omit_ordinary_gauge","commute_q_through_graph"], + "scope":"Ordered local theorem and full principal-unit check. Native emission, access, inter-stage binding and global terminal price remain separate.", + } + (HERE/"REVIEW.json").write_text(json.dumps(receipt,indent=2,sort_keys=True)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/replay_producer.py b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/replay_producer.py new file mode 100644 index 0000000000..39011a5671 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/partner-retirement-review-20261018/replay_producer.py @@ -0,0 +1,49 @@ +"""Reproduce the frozen local theorem receipt without changing its files.""" + +from hashlib import sha256 +import json +from pathlib import Path +import runpy +from unittest.mock import patch + + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parents[1] / "controller-followthrough-20261017/partner-retirement-20261018" +FREEZE = "ee4c11882ab042f3101b8ccc21e33cfae0348e48af77dcd1667757b94c403af6" + + +def main(): + if sha256((SOURCE/"FREEZE.json").read_bytes()).hexdigest() != FREEZE: + raise ValueError("Frozen theorem pin") + pins = json.loads((SOURCE/"FREEZE.json").read_text())["files"] + before = {name:(SOURCE/name).read_bytes() for name in pins} + for name, raw in before.items(): + if sha256(raw).hexdigest() != pins[name]: + raise ValueError("Frozen producer artifact: " + name) + output = {} + + def write_text(path, text, *args, **kwargs): + if path != SOURCE/"PARTNER-RETIREMENT.json": + raise ValueError("Unexpected producer output") + output[path.name] = text.encode() + return len(text) + + with patch.object(Path, "write_text", write_text): + runpy.run_path(str(SOURCE/"check_partner_retirement.py"), run_name="__main__") + if output != {"PARTNER-RETIREMENT.json":before["PARTNER-RETIREMENT.json"]}: + raise ValueError("Producer receipt is not byte-identical") + if any((SOURCE/name).read_bytes() != raw for name, raw in before.items()): + raise ValueError("A frozen producer file changed") + receipt = { + "status":"PASS_UNCHANGED_PRODUCER_REPLAY", + "producer_freeze_sha256":FREEZE, + "identical_receipt_sha256":sha256(output["PARTNER-RETIREMENT.json"]).hexdigest(), + "replay_checker_sha256":sha256(Path(__file__).read_bytes()).hexdigest(), + "frozen_source_bytes_preserved":True, + } + (HERE/"PRODUCER-REPLAY.json").write_text(json.dumps(receipt,indent=2,sort_keys=True)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json 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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/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/CHECKS.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/CHECKS.json new file mode 100644 index 0000000000..e9eada8e90 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/CHECKS.json @@ -0,0 +1,140 @@ +{ + "status": "PASS_GENERAL_MATCHED_BRIDGES", + "checker_sha256": "c4e2a92865a92deaa06bf70ef1d0aa4b717571e2ced49a5575cd1346b2490837", + "proof_sha256": "1871ff4f98ccc23e31221146f4be0012229ba2af64847353d42f0329842b59bf", + "source_pins": { + "encoded-controller/PROJECTION-RETIREMENT.md": "8345762fb9cad9366dcd0f6bff8723e306877d1b4a5523e969c3894cb547b3b3", + "interface-proof/projection-retirement-review/REVIEW.md": "54a69b9b040d0c28ec5b08203ab72aed1a369495f101014023bdd6a330394759", + "encoded-controller/SELECTED-SOURCE-RETIREMENT.md": "69a9b6a2ef615fe1c0cb051f5b8be6ac51042efc77eee78c864978f40f21b92f", + "interface-proof/selected-source-retirement-review/REVIEW.md": "98080b5bdb16e41ab06e14c13a2577fff71c86fe70b3a5f242fb5597f7e2b0d9" + }, + "tests": [ + { + "pairs": 1, + "family": "general", + "endpoint_blocks": 4 + }, + { + "pairs": 2, + "family": "general", + "endpoint_blocks": 16 + }, + { + "pairs": 3, + "family": "general", + "endpoint_blocks": 36 + }, + { + "pairs": 4, + "family": "general", + "endpoint_blocks": 64 + }, + { + "pairs": 5, + "family": "general", + "endpoint_blocks": 100 + }, + { + "pairs": 6, + "family": "general", + "endpoint_blocks": 144 + }, + { + "pairs": 1, + "family": "non_idempotent", + "endpoint_blocks": 4 + }, + { + "pairs": 2, + "family": "non_idempotent", + "endpoint_blocks": 16 + }, + { + "pairs": 3, + "family": "non_idempotent", + "endpoint_blocks": 36 + }, + { + "pairs": 4, + "family": "non_idempotent", + "endpoint_blocks": 64 + }, + { + "pairs": 5, + "family": "non_idempotent", + "endpoint_blocks": 100 + }, + { + "pairs": 6, + "family": "non_idempotent", + "endpoint_blocks": 144 + }, + { + "pairs": 1, + "family": "future_zero", + "endpoint_blocks": 4 + }, + { + "pairs": 2, + "family": "future_zero", + "endpoint_blocks": 16 + }, + { + "pairs": 3, + "family": "future_zero", + "endpoint_blocks": 36 + }, + { + "pairs": 4, + "family": "future_zero", + "endpoint_blocks": 64 + }, + { + "pairs": 5, + "family": "future_zero", + "endpoint_blocks": 100 + }, + { + "pairs": 6, + "family": "future_zero", + "endpoint_blocks": 144 + }, + { + "pairs": 1, + "family": "future_matched", + "endpoint_blocks": 4 + }, + { + "pairs": 2, + "family": "future_matched", + "endpoint_blocks": 16 + }, + { + "pairs": 3, + "family": "future_matched", + "endpoint_blocks": 36 + }, + { + "pairs": 4, + "family": "future_matched", + "endpoint_blocks": 64 + }, + { + "pairs": 5, + "family": "future_matched", + "endpoint_blocks": 100 + }, + { + "pairs": 6, + "family": "future_matched", + "endpoint_blocks": 144 + } + ], + "signed_specializations": 5, + "method": "Exact Fraction matrices; direct event replay and independent endpoint formula; no producer imports.", + "controls": [ + "Wrong final bridge coefficient", + "Early idle-X reset" + ], + "scope": "Ordered algebra only. The proof covers all positive pair counts. Separate native bridge and local-word contracts are required. No complete decoder or kappa claim." +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/GENERAL-BRIDGES.md b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/GENERAL-BRIDGES.md new file mode 100644 index 0000000000..02808881e7 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/GENERAL-BRIDGES.md @@ -0,0 +1,189 @@ +# Matched bridges for changing return projections + +The projection-return controller permits an arbitrary plus-Y coefficient. +The final X triangle must use the same coefficient. This removes the +right-absorption condition from the earlier controller. It also identifies +the coefficient choices that preserve each original Y query. + +This note extends `encoded-controller/PROJECTION-RETIREMENT.md` and its +independent review in `interface-proof/projection-retirement-review`. The +source files are unchanged. `CHECKS.json` records their SHA-256 pins. + +## Ordered controller + +Let there be `m>=1` pairs in a common module. Let `A_i`, `G_i`, and `C` be +units. Let `P_i`, `W_i`, `T_i`, and `V` be linear maps. Put `U_i=I-P_i`. +The maps `P_i` need not be projections for the endpoint identity below. + +Use the local maps + +``` +B_i(x,y) = (U_i A_i x-y, y+P_i A_i x), +F_i(x,y) = (x, G_i(x+y)). +``` + +Their inverses are + +``` +B_i^-1(w,v) = (A_i^-1(w+v), U_i v-P_i w), +F_i^-1(w,v) = (w,G_i^-1 v-w). +``` + +Form `z_i=sum_(j>=i) (-1)^(j-i) x_j`, with `z_m=0`. Thus +`x_i=z_i+z_(i+1)`. First change Y0 to `C y0+V z0`. At each pair, run B_i. +If there is a next pair, do the following operations in order: + +1. Change next X from `z_(i+1)` to `A_i z_(i+1)`. +2. Add next X to active X. +3. Subtract `W_i` times active Y from next Y. +4. Run F_i on the active pair. +5. Subtract next X from active X. +6. Add `T_i` times active Y to next Y. +7. Change next X back by `A_i^-1`. + +At the last pair, only B and F are needed. In descending pair order apply +`X_i += W_(i-1) X_(i-1)`. Then apply `C^-1` to X0. + +Set `E_i=G_i A_i`. The endpoint is + +``` +Y_i = E_i x_i, +X_i = -y_i + (H x)_i, + +(H x)_0 = C^-1(U_0 A_0-V) z_0, +(H x)_i = U_i A_i z_i + W_(i-1) A_(i-1) z_(i-1) + - T_(i-1) E_(i-1) x_(i-1), i>0. (1) +``` + +After the signed terminal, the map is `[[E,0],[-H,I]]`. Its inverse is +`[[E^-1,0],[H E^-1,I]]`. These are ordered operator identities. + +### Proof + +Let eta_i be the active Y input to B_i. Its two outputs are + +``` +w_i = U_i A_i z_i-eta_i, +v_i = eta_i+P_i A_i z_i. +``` + +Their sum is `A_i z_i`. The temporary next-X addition therefore gives +`r_i=G_i A_i(z_i+z_(i+1))=E_i x_i` after F. The subtraction restores w_i. +The next input is + +``` +eta_(i+1) = y_(i+1)-W_i eta_i-W_i P_i A_i z_i+T_i r_i. +``` + +The descending X triangle adds `W_i w_i` before w_i is changed. Its two +terms with eta_i cancel. Its two terms with A_i z_i add to +`W_i(P_i+U_i) A_i z_i=W_i A_i z_i`. This proves (1), including every +original Y input. The first pair follows from its stated initial code. +The proof uses neither idempotence nor commutation of different maps. + +## Exact query-preservation criterion + +Now assume `P_i^2=P_i`. For each `i>0`, + +``` +P_i(Hx)_i = P_i W_(i-1) A_(i-1) z_(i-1) + -P_i T_(i-1) E_(i-1)(z_(i-1)+z_i). (2) +``` + +The two suffix variables `z_(i-1)` and `z_i` are independent. Both A and E +are units. Thus (2) vanishes for every input if and only if + +``` +P_i W_(i-1)=0, P_i T_(i-1)=0. (3) +``` + +Equivalently, `W_(i-1)=U_i Z_(i-1)` and +`T_(i-1)=U_i Z'_(i-1)` for some linear maps Z and Z'. No relation between +P_i and P_(i-1) is needed. In particular, both choices + +``` +W_i=U_(i+1), T_i=0, +W_i=U_(i+1), T_i=U_(i+1) +``` + +preserve the original query: `P_i X_i=-P_i y_i` for `i>0`. The same property +at pair zero requires its explicit first response to vanish under P0. It +does not follow from the later-pair argument. + +The old choice `W_i=U_i` forces right absorption to remove its preceding +history term. It is one member of a larger family. The proof above does not +invalidate the earlier theorem within that fixed coefficient family. + +## Actual signed kernel + +Use the selected and ordinary split. In the actual construction, + +``` +Pi = [[I,0],[0,0]], +S_s = [[-I,-B_s],[-D_s,I-D_s B_s]], +A_s = S_s^-1 = [[12I,-B_s],[-D_s,I]], +B_s D_s = 13I, +P_s = [[I,B_s],[0,0]], U_s = [[0,-B_s],[0,I]]. +``` + +Then `P_s A_s=-Pi` and `U_s A_s=A_s+Pi`. The local return is + +``` +((A_s+Pi)x-y, y-Pi x). +``` + +It uses the actual original selected input in the returned Y value. Its +literal native implementation and arbitrary-helper proof are separate. + +For pair i put `s_i=2i+1`, `t_i=2i+2`, and +`E_i=S_(t_i) A_(s_i)`. Choose `W_i=T_i=U_(s_(i+1))`. +For `i>0`, write `r_(i-1)=E_(i-1) x_(i-1)` and `a_j=(x_j)_A`. Its ordinary +response is + +``` +(H x)_(i,U) = (D_(s_(i-1))-D_(s_i)) (z_i)_A + -D_(t_(i-1)) (r_(i-1))_A. (4) +``` + +Its selected response is `-B_(s_i)(Hx)_(i,U)`. To check (4), use + +``` +(E_i x)_U = x_U-D_(s_i) x_A+D_(t_i)(E_i x)_A. +``` + +This follows by subtracting `S_(s_i) A_(s_i) x=x` from +`S_(t_i) A_(s_i) x=E_i x`. Substitute it in (1) and use +`z_(i-1)+z_i=x_(i-1)`. No D graph commutes through another graph. + +The choice `T_i=0` preserves the query but leaves an additional dense +ordinary input term. Thus query preservation alone does not establish a +cheap endpoint decoder. Formula (4) still needs original selected X suffixes. +The preserved original Y query is a baseline value, not a clean X record. + +## Native and claim scope + +The future-graph access proof is in `bridge-access-20261017`. It treats both +Y bridge signs with coefficient U at the next odd stage, and the same +coefficient in the final completed-X triangle. Its receipt is a separate +dependency. The endpoint proof here does not replace its owner, phase, or +literal map checks. Changed selected FULL retirements must satisfy their +own local and later-helper contracts. + +The present result removes a specific algebraic restriction and gives a +family with scalar future-Y bridges. It does not supply a complete decoder, +the first response, a native stock bound, a full recursive invoice, or a +new kappa value. Original selected-input acquisition remains an open issue +for the unchanged retired E outputs. + +Run from the workspace root: + +``` +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/check_general_bridges.py +``` + +The expected result is `PASS_GENERAL_MATCHED_BRIDGES`. The checker uses exact +rational matrices and a direct event replay. It checks arbitrary returns, +noncommuting varying projections, both query-preserving choices, and the +signed-kernel identity. Finite checks support the proof for all pair counts. +The work was prepared with substantial OpenAI Codex assistance. 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[projection(i+1) if kind != "non_idempotent" else add(projection(i+1), I) for i in range(m)] + w = [unit(i+3) if kind in ("general", "non_idempotent") else add(I, p[i+1], -1) for i in range(m-1)] + t = [unit(-i-4) if kind in ("general", "non_idempotent") else (ZERO if kind == "future_zero" else w[i]) for i in range(m-1)] + c, v = unit(3), [[F(2), F(-3)], [F(5), F(7)]] + state = run(a, g, p, w, t, c, v) + e, h = formulas(a, g, p, w, t, c, v) + terminal, inverse = identity_blocks(m), identity_blocks(m) + for i in range(m): + for j in range(2*m): + need(state[2*i+1][j] == (e[i] if j == 2*i else ZERO), "Retired output") + expected = h[i][j//2] if j % 2 == 0 else (add(ZERO, I, -1) if j == 2*i+1 else ZERO) + need(state[2*i][j] == expected, "Completed output") + terminal[2*i][2*i], inverse[2*i][2*i] = e[i], inv(e[i]) + for j in range(m): + terminal[2*i+1][2*j] = add(ZERO, h[i][j], -1) + inverse[2*i+1][2*j] = mul(h[i][j], inv(e[j])) + if i and kind.startswith("future"): + need(mul(p[i], h[i][j]) == ZERO, "Future projection removes selected response") + need(block_product(terminal, inverse) == identity_blocks(m), "Right inverse") + need(block_product(inverse, terminal) == identity_blocks(m), "Left inverse") + if m > 1: + need(run(a, g, p, w, t, c, v, "early_reset") != state, "Early reset control") + need(run(a, g, p, w, t, c, v, "old_tail") != state, "Unmatched tail control") + return {"pairs": m, "family": kind, "endpoint_blocks": (2*m)**2} + + +def signed_checks(): + pi = [[F(1), F(0)], [F(0), F(0)]] + for i in range(1, 6): + bs, ds, bt, dt = F(13*i), F(1, i), F(13*(i+1)), F(1, i+1) + a = [[F(12), -bs], [-ds, F(1)]] + s = [[F(-1), -bs], [-ds, F(1)-ds*bs]] + st = [[F(-1), -bt], [-dt, F(1)-dt*bt]] + p = [[F(1), bs], [F(0), F(0)]] + pt = [[F(1), bt], [F(0), F(0)]] + need(mul(s, a) == I and mul(a, s) == I, "Signed inverse") + need(mul(p, a) == add(ZERO, pi, -1), "Original selected return") + need(mul(p, p) == p, "Oblique projection") + need(mul(add(I, p, -1), a) == add(a, pi), "Cheap return factor") + e = mul(st, a) + need(e[1] == [F(0)-ds+dt*e[0][0], F(1)+dt*e[0][1]], "Ordinary E graph") + need(mul(pt, a) == add(ZERO, mul(pi, e), -1), "Productive query quotient") + return 5 + + +def main(): + tests = [check_case(m, kind) for kind in ("general", "non_idempotent", "future_zero", "future_matched") for m in range(1, 7)] + signed = signed_checks() + root = HERE.parent + sources = [root / "encoded-controller/PROJECTION-RETIREMENT.md", root / "interface-proof/projection-retirement-review/REVIEW.md", root / "encoded-controller/SELECTED-SOURCE-RETIREMENT.md", root / "interface-proof/selected-source-retirement-review/REVIEW.md"] + receipt = { + "status": "PASS_GENERAL_MATCHED_BRIDGES", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "proof_sha256": sha256((HERE / "GENERAL-BRIDGES.md").read_bytes()).hexdigest(), + "source_pins": {str(p.relative_to(root)): sha256(p.read_bytes()).hexdigest() for p in sources}, + "tests": tests, + "signed_specializations": signed, + "method": "Exact Fraction matrices; direct event replay and independent endpoint formula; no producer imports.", + "controls": ["Wrong final bridge coefficient", "Early idle-X reset"], + "scope": "Ordered algebra only. The proof covers all positive pair counts. Separate native bridge and local-word contracts are required. No complete decoder or kappa claim." + } + (HERE / "CHECKS.json").write_text(json.dumps(receipt, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/FREEZE.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/FREEZE.json new file mode 100644 index 0000000000..109e0c5f81 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "PARTNER-RETIREMENT.json": "a493c96135c1f038ed4181ffedb64545fc561763a621a7c48c215b2f5db3e55e", + "PARTNER-RETIREMENT.md": "904950ea0121db197b8ce2142707e67981888a2499349ba1fb3ff069720b049d", + "check_partner_retirement.py": "f3de220fc8d020ad6346a60193703957d46c7589d7281dcd419c27cd6c667999" + }, + "normal_optimized_receipts_identical": true, + "scope": "Ordered local content theorem only; native emission and global terminal remain open", + "source_payload_decompressed_sha256": "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee" +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.json b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.json new file mode 100644 index 0000000000..dc48d9a663 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.json @@ -0,0 +1,39 @@ +{ + "X_ordered_polynomial_sha256": "bf176e400712c2dd38992c48ecbf3e84c522cb9added440d2fa9433797cdc25a", + "Y_ordered_polynomial_sha256": "8f461eca41e4a3bf45f9cd286c59b5bf1ec7333b59375b99354b7b7ec62dcb20", + "borrowed_source_fields_cancelled_from_Y": 112, + "checker_sha256": "f3de220fc8d020ad6346a60193703957d46c7589d7281dcd419c27cd6c667999", + "generic_input_fields": 224, + "mutation_controls_rejected": [ + "omit_positive_Q_on_selected_X" + ], + "optional_X_correction_extra_H1_queries": 8, + "ordinary_ports": 104, + "partner_ports": [ + 20, + 27, + 53, + 57, + 72, + 94, + 105, + 111 + ], + "proposed_extra_H1_children": 16, + "retired_FULL_fields": 8, + "retired_hole_fields": 104, + "scope": "Ordered local content identity, source unit, and pinned principal-unit applicability; no native implementation or supplier decoder claim", + "selected_ports": [ + 0, + 7, + 15, + 36, + 42, + 46, + 79, + 89 + ], + "source_payload_decompressed_sha256": "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee", + "source_unit_ordered_polynomial_sha256": "33705c3aa2c8cd1616297cae0215c4fa05e5b739f47efa4503b70b3b2bb6ede8", + "status": "PASS_PARTNER_RETIREMENT_ORDERED_CONTENT" +} diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.md b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.md new file mode 100644 index 0000000000..b821ec5eeb --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/PARTNER-RETIREMENT.md @@ -0,0 +1,203 @@ +# Data-only retirement into a partner code + +This packet proves an ordered local interface. It changes the selected +output set from `S` to its partner set `T`. It cancels all arbitrary +borrowed inputs from the retired Y bank. Eight values leave in the FULL +frame, and 104 values leave in their hole frames. The retired code is a +unit. No original-data record bank is used. + +The proposed forward prefix uses 16 additional rank-one native lines. +This is an operation count, not a complete native invoice. The literal +forward word, inter-stage binding, helper leases, global controller, +and terminal decoder remain separate obligations. + +## Pinned local response and notation + +Use the response and selected set in +`../bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz`. Its +decompressed SHA256 is +`0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee`. + +The selected set is `S=[0,7,15,36,42,46,79,89]`. Its partner set is +`T=[20,27,53,57,72,94,105,111]`. The sets are disjoint. Let `U` be the +complement of S, `V` the complement of T, and `R` the complement of +`S union T`. There are 112 ports. + +Write `Q_p` for the intrinsic line operator at port p, and `q_p` for its +inverse. A current-entry X field is physically `Q_p h_p`. A current-entry +Y field is physically `d_p`. Remove only the common exterior operator +from these formulas. A completed X field has content `X_p`; a completed +Y field has physical content `q_p Y_p` in that exterior. A selected +completed Y field can instead carry a value in FULL. + +All matrix products have their displayed order. A graph entry of `J_t` +includes its actual stage-t port route. The proof does not move a Q +operator across a graph entry. The same-port intrinsic Q is fixed by its +stage route, as checked in the existing access packets. + +## The partner prefix + +On arbitrary current input `(Qh,d)`, use this order: + +1. For p in S, set `Y_p <- Y_p - X_p`. +2. For p in S, apply the positive line `Q_p` to physical `X_p`. +3. For p in T, apply the positive line `Q_p` to physical `Y_p`, then set + `Y_p <- Y_p + X_p`. +4. Apply `H_t^(T)=J_t[V,V]` to the current Y fields in V. +5. Run the raw forward word with the selected physical exchanges on T. + +Steps 2 and 3 use eight positive lines each. Steps 1 and 3 use sixteen +unit ADD operations. Step 4 acts on current-entry Y fields in their +common I view. It is not a future-stage query on X. + +Define + +```text +z_S = d_S, +z_U = h_U + d_U. +``` + +Then the completed physical Y output, with the common exterior removed, +is exactly + +```text +Y_T = z_T (FULL), +Y_V = q_V (J_t z)_V (hole frames). (1) +``` + +To prove (1), consider the input to the raw forward word. On S, its +logical X is `Q_S h_S`, while the Y vector before the ordinary gauge is +`d_S-Q_S h_S`. Their sum is `d_S`. On R, their sum is `h_R+d_R`. On T, +the selected Y input is `Q_T(h_T+d_T)`, so the physical exchange gives +the raw word logical X equal to `z_T`. The ordinary Y output is therefore +`J_t[V,T] z_T + J_t[V,V] z_V`. The final selected exchange returns `z_T` +in FULL. Each cancellation is between adjacent equal operators. + +For the complete X output, put + +```text +hat_h_S = Q_S h_S, +hat_h_U = h_U, +w_T = z_T, +w_V = hat_h_V. +``` + +The exact output is + +```text +X_V = hat_h_V, +X_T = h_T + q_T (J_t w)_T. (2) +``` + +These identities do not require J or any principal block to be a unit. +The ordinary precode is reversible when `H_t^(T)` is a unit. + +## Composition with the diagonal backward interface + +Let the preceding backward stage be s. Write its response as + +```text +J_s = [[L_s, B_s], [D_s, H_s]] +``` + +in the S/U split. Its diagonal borrowed interface on original data +`x=(a,u)` and arbitrary borrowed state `y=(b,v)` has + +```text +p = A_s (Q_S a,u), +h_S = p_S + q_S b, +h_U = p_U - v, +d_S = Q_S a, +d_U = v, +p_U = H_s^-1 (u-D_s Q_S a). +``` + +Substitution into (1) gives the data-only vector + +```text +z_S = Q_S a, +z_U = H_s^-1 (u-D_s Q_S a). (3) +``` + +Thus every coefficient of every original borrowed field is zero in Y. +The cancellation holds for arbitrary borrowed state. It does not use a +clean record or a known baseline. + +Let `K_s` have identity rows on S and the rows of `J_s` on U. Let `R_t` +have identity rows on T and the rows of `J_t` on V. Then + +```text +(Q_S a,u) = K_s z, +retired logical row code = R_t z. +``` + +Both row codes are units if `H_s` and `H_t^(T)` are units. Their +determinants, in the corresponding block orders, are those of these +ordinary principal blocks. The physical row code also includes q on V. +This factor must remain in any terminal decoder. + +For the pinned response, extend G by the identity on the separate +64-port block. Then `G^2=I`, `GJ=JG`, and `G(S)=T`. Signed port +relabeling therefore takes the S ordinary principal block to the T +ordinary principal block. The first has a proved dyadic inverse; the +second does as well. This is a statement in a single current chart. +It does not identify the globally routed responses at distinct stages. + +## The complete borrowed-source response + +The data-free part of (2) is + +```text +X_S = b, +X_R = -v_R, +X_T = -v_T + q_T [J_t[T,S] b - J_t[T,R] v_R]. (4) +``` + +This is a unit triangular source code. Subtract +`q_T J_t[T,V] X_V` from its T component to obtain `(b,-v)`. This +subtraction is only an inverse of the source coefficient. Applied to +the full state, it also changes its data coefficient. + +A stronger optional correction uses the actual completed values: + +```text +X_T <- X_T - q_T (J_t w)_T, +w_T = completed FULL Y_T, +w_V = completed FULL X_V. (5) +``` + +Then all X output is `(Q_S h_S,h_U)`, and its source part is exactly +`(b,-v)`. Equation (5) needs eight inverse-line graph queries in a direct +FULL implementation, in addition to its scalar query and restore work. +No native cost for (5) is hidden in the 16-line prefix count. + +## Verification and remaining work + +The checker executes the physical prefix, the T exchanges, and the raw +physical forward matrix. It uses exact rational coefficients and free +ordered operator words. Only adjacent inverse powers of the same Q are +reduced. Every nontrivial graph edge retains its stage, source, and +target as a formal route token. No cross-stage identity or Q commutation +is used. + +It checks the full 224-input local map, all 112 borrowed source +coefficients, (4), the source inverse, and (5). A control that omits the +positive Q on selected X fails. It also checks G and J directly from the +pinned native payload. Run: + +```text +python3 work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/check_partner_retirement.py +python3 -O work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/check_partner_retirement.py +``` + +Both commands must print `PASS_PARTNER_RETIREMENT_ORDERED_CONTENT` and +produce an identical receipt. This proves the ordered local content +identity. It does not prove a native implementation, a complete supplier, +or an improvement in kappa. In particular, decoding (1) into the required +physical `q x` endpoint is open. A 104-field normalization is not by +itself a complete terminal decoder. + +This is AI-assisted research. It uses the signed response and principal +gauges from the controller lane, the physical boundary interfaces from +the new-core-transfer lane, and the route and frame checks from the +bridge-access lane. diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/check_partner_retirement.py b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/check_partner_retirement.py new file mode 100644 index 0000000000..471fd7a7f7 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/partner-retirement-20261018/check_partner_retirement.py @@ -0,0 +1,206 @@ +#!/usr/bin/env python3 +"""Check the ordered partner-retirement interface on the pinned response.""" + +from collections import defaultdict +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 / "bipartite-eight-20261018" +PAYLOAD_SHA = "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee" + + +def need(value, message): + if not value: + raise RuntimeError(message) + + +def add(*terms): + out = defaultdict(F) + for coefficient, expression in terms: + for word, value in expression.items(): + out[word] += coefficient * value + return {word: value for word, value in out.items() if value} + + +def symbol(name, port): + return {((name, port),): F(1)} + + +def operator(token, expression): + out = defaultdict(F) + for word, coefficient in expression.items(): + new = (token,) + word + if token[0] == "Q" and word[0][0] == "Q" and token[1] == word[0][1]: + exponent = token[2] + word[0][2] + new = (("Q", token[1], exponent),) + word[1:] if exponent else word[1:] + out[new] += coefficient + return {word: value for word, value in out.items() if value} + + +def line(port, exponent, expression): + return operator(("Q", port, exponent), expression) + + +def route(stage, target, source, expression): + if target == source: + return expression + return operator(("route", stage, target, source), expression) + + +def graph(rows, values, targets=None, sources=None): + targets = range(len(rows)) if targets is None else targets + allowed = set(range(len(rows))) if sources is None else set(sources) + out = {} + for target in targets: + out[target] = add(*[(coefficient, route("t", target, source, values[source])) + for source, coefficient in rows[target].items() if source in allowed]) + return out + + +def word(rows, selected, partner, h, d, omit_s_line=False): + n = len(rows) + outside = sorted(set(range(n)) - set(partner)) + x = {p: line(p, 1, h[p]) for p in range(n)} + y = dict(d) + for p in selected: + y[p] = add((1, y[p]), (-1, x[p])) + if not omit_s_line: + x[p] = line(p, 1, x[p]) + for p in partner: + y[p] = add((1, line(p, 1, y[p])), (1, x[p])) + ordinary = graph(rows, y, outside, outside) + y.update(ordinary) + for p in partner: + x[p], y[p] = y[p], x[p] + normalized_x = {p: line(p, -1, x[p]) for p in range(n)} + response = graph(rows, normalized_x) + x = normalized_x + y = {p: line(p, -1, add((1, y[p]), (1, response[p]))) for p in range(n)} + for p in partner: + x[p], y[p] = y[p], x[p] + return x, y + + +def sparse_product(left, right): + out = [] + for row in left: + result = defaultdict(F) + for middle, a in row.items(): + for column, b in right[middle].items(): + result[column] += a * b + out.append({column: value for column, value in result.items() if value}) + return out + + +def digest_expressions(values): + serial = [[(repr(word), str(value)) for word, value in sorted(values[p].items(), key=lambda v: repr(v[0]))] + for p in sorted(values)] + return sha256(json.dumps(serial, separators=(",", ":")).encode()).hexdigest() + + +def main(): + raw = gzip.decompress((SOURCE / "BIPARTITE-EIGHT-PROGRAM.json.gz").read_bytes()) + need(sha256(raw).hexdigest() == PAYLOAD_SHA, "Pinned signed response changed") + payload = json.loads(raw) + rows = [{int(p): F(v) for p, v in row.items()} for row in payload["response"]] + monomial = [{int(p): F(v) for p, v in row.items()} for row in payload["signed_monomial"]] + n = len(rows) + for p in payload["small_ports"]: + need(not monomial[p], "The stored G has zero support on the small block") + monomial[p] = {p: F(1)} + selected, partner = payload["selected_ports"], payload["partner_ports"] + sset, tset = set(selected), set(partner) + ordinary = set(range(n)) - sset + outside = set(range(n)) - tset + rest = ordinary - tset + need(n == 112 and len(sset) == len(tset) == 8 and not sset & tset, + "The source has two disjoint eight-port sets") + need(all(len(row) == 1 and next(iter(row.values())) in (1, -1) for row in monomial), + "G is a signed permutation on all ports") + identity = [{p: F(1)} for p in range(n)] + need(sparse_product(monomial, monomial) == identity, "G squared is the identity") + need(sparse_product(rows, monomial) == sparse_product(monomial, rows), "J and G commute") + need({next(iter(monomial[p])) for p in selected} == tset, "G takes S to T") + + h = {p: symbol("h", p) for p in range(n)} + d = {p: symbol("d", p) for p in range(n)} + x, y = word(rows, selected, partner, h, d) + z = {p: d[p] if p in sset else add((1, h[p]), (1, d[p])) for p in range(n)} + jz = graph(rows, z) + expected_y = {p: z[p] if p in tset else line(p, -1, jz[p]) for p in range(n)} + need(y == expected_y, "The complete ordered Y endpoint is the stated code") + modified_h = {p: line(p, 1, h[p]) if p in sset else h[p] for p in range(n)} + input_response = dict(modified_h) + input_response.update({p: z[p] for p in partner}) + jinput = graph(rows, input_response) + expected_x = {p: add((1, h[p]), (1, line(p, -1, jinput[p]))) if p in tset else modified_h[p] + for p in range(n)} + need(x == expected_x, "The complete ordered X endpoint is the stated map") + + p_data = {p: symbol("p", p) for p in range(n)} + a = {p: symbol("a", p) for p in selected} + b = {p: symbol("b", p) for p in selected} + v = {p: symbol("v", p) for p in ordinary} + h = {p: add((1, p_data[p]), (1, line(p, -1, b[p]))) if p in sset + else add((1, p_data[p]), (-1, v[p])) for p in range(n)} + d = {p: line(p, 1, a[p]) if p in sset else v[p] for p in range(n)} + x, y = word(rows, selected, partner, h, d) + z = {p: line(p, 1, a[p]) if p in sset else p_data[p] for p in range(n)} + jz = graph(rows, z) + need(y == {p: z[p] if p in tset else line(p, -1, jz[p]) for p in range(n)}, + "The retired Y code contains no borrowed input") + need(not any(word[-1][0] in ("b", "v") for expression in y.values() for word in expression), + "All 112 borrowed source columns vanish from retired Y") + source_x = {p: {word: value for word, value in expression.items() if word[-1][0] in ("b", "v")} + for p, expression in x.items()} + diagonal_source = {p: b[p] if p in sset else add((-1, v[p])) for p in range(n)} + graph_source = graph(rows, diagonal_source, partner, outside) + expected_source = {p: add((1, diagonal_source[p]), (1, line(p, -1, graph_source[p]))) + if p in tset else diagonal_source[p] for p in range(n)} + need(source_x == expected_source, "The source map is the stated unit triangular map") + undone = dict(source_x) + current_query = graph(rows, source_x, partner, outside) + for p in partner: + undone[p] = add((1, undone[p]), (-1, line(p, -1, current_query[p]))) + need(undone == diagonal_source, "One selected graph shear inverts the source code") + corrected = dict(x) + query_input = dict(x) + query_input.update({p: y[p] for p in partner}) + complete_query = graph(rows, query_input, partner) + for p in partner: + corrected[p] = add((1, corrected[p]), (-1, line(p, -1, complete_query[p]))) + need(corrected == {p: line(p, 1, h[p]) if p in sset else h[p] for p in range(n)}, + "The optional eight-query correction returns the unchanged ordinary X") + + _, bad_y = word(rows, selected, partner, h, d, omit_s_line=True) + need(bad_y != y, "The missing S phase mutation must fail") + receipt = { + "status": "PASS_PARTNER_RETIREMENT_ORDERED_CONTENT", + "scope": "Ordered local content identity, source unit, and pinned principal-unit applicability; no native implementation or supplier decoder claim", + "source_payload_decompressed_sha256": PAYLOAD_SHA, + "selected_ports": selected, + "partner_ports": partner, + "ordinary_ports": len(ordinary), + "generic_input_fields": 224, + "borrowed_source_fields_cancelled_from_Y": 112, + "retired_FULL_fields": 8, + "retired_hole_fields": 104, + "proposed_extra_H1_children": 16, + "optional_X_correction_extra_H1_queries": 8, + "Y_ordered_polynomial_sha256": digest_expressions(y), + "X_ordered_polynomial_sha256": digest_expressions(x), + "source_unit_ordered_polynomial_sha256": digest_expressions(source_x), + "mutation_controls_rejected": ["omit_positive_Q_on_selected_X"], + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + } + (HERE / "PARTNER-RETIREMENT.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/cover-algebra/BRIDGES.md b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/cover-algebra/BRIDGES.md new file mode 100644 index 0000000000..fda782ac93 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/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/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/interface-proof/ORIGINAL-COMPLEX-MODES-REVIEW.json b/research/ordered-centre-interfaces/annexes/access-algebra/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/ordered-centre-interfaces/annexes/access-algebra/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/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/RAW-SELECTED-BACKWARD.md b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/RAW-SELECTED-BACKWARD.md new file mode 100644 index 0000000000..5776b529b1 --- /dev/null +++ b/research/ordered-centre-interfaces/annexes/access-algebra/frozen/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/RAW-SELECTED-BACKWARD.md @@ -0,0 +1,182 @@ +# A physical selected exchange in the backward word + +This local construction carries each original selected X input into its +productive Y output. It uses eight new rank-one children. It does not keep +the old logical contents of the selected X or ordinary Y outputs. An +explicit unit code retains that information. A global controller must +use or remove this code before the construction can replace a supplier. + +The literal word has 210,714 real scalar primitives and native mass 5,530. +It restores all 480 arbitrary helper arrays. It clears the eight owned +private outputs. One existing owned array, C0, serves all new copies in +sequence. No additional array is used. An optional block adds eight more +rank-one children and changes the ordinary X output to `x_U-y_U`. The +optional total is 214,922 real scalar primitives and native mass 5,538. +These are local invoices. No complete supplier or kappa claim is made. + +## Operators and local contract + +Use the selected set + +```text +A = [0, 7, 20, 27, 36, 46, 57, 111]. +``` + +Its complement U has 104 ports. The source matrix R and `K=R^T/4` give + +```text +J = [[0, -B], [-D, I-DB]], BD=13I. +``` + +At the local input, physical X_p is `Q_p x_p`, and physical Y_p is `y_p`. +Here Q_p is the exact positive line operator C_qp. At the local output, +physical X_p is `F x'_p`, and physical Y_p is `F Q_p^-1 y'_p`. The full +operator F commutes with each Q_p. These are the existing local endpoints. +Write `x=(a,u)` and `y=(b,v)`, with selected components first. Put + +```text +r = Q_A^-1 b. +``` + +The operator order is part of this definition. In particular, the proof +does not commute Q_A through B or D. + +## Literal construction + +First form `r_a` in C0 from each unchanged selected Y input. Apply the exact +inverse line to the copy. Subtract `D[:,a] r_a` from ordinary Y, then clear +C0. This gives the physical common-address update + +```text +Y_U <- v-D Q_A^-1 b. +``` + +The source C0 after the child and the target Y field have different logical +frame labels. Their ADD is a physical ADD at the same local addresses. Its +operator Q_A^-1 remains in the data code. It is not removed by a frame label +change or an uncharged inverse. A verifier that permits only equal logical +frame labels cannot validate this block without an explicit operator code. + +Next exchange physical X_a and Y_a for each selected port. Each exchange is +three unit ADDs followed by one negative SCALE. This is an exact exchange +of arbitrary physical arrays. In logical input coordinates it gives + +```text +X_A <- Q_A^-1 b, Y_A <- Q_A a. +``` + +All ordinary X fields are unchanged. Then execute the byte-exact clean-J +backward core. Finally, at the complete FULL X boundary, apply `L(-D)`: +subtract D times selected X from ordinary X. + +The full logical result is + +```text +X_A = Bv-12r, +X_U = u-v+D Q_A a, +Y_A = Q_A a, +Y_U = v-Dr. +``` + +Indeed, the clean backward core has map `(X,Y)->(X-JY,Y)`. Its selected X +row is `r+B(v-Dr)=Bv-12r`. Its ordinary X row before the final lower shear +is `u-v+D Q_A a+DBv-12Dr`. The lower shear removes its final two terms. +These identities use `BD=13I` and do not require any other relation. + +The physical selected Y output is exactly + +```text +F Q_A^-1 Q_A a = F a. +``` + +Thus the original selected input is present in productive FULL Y. No +original-input record cohort is required for this local statement. + +## The remaining unit code + +The other selected X and ordinary Y values form the unit + +```text +(X_A,Y_U) = U(B) L(-D) (r,v). +``` + +Its direct inverse is + +```text +r = X_A-B Y_U, +v = Y_U+D r, +b = Q_A r. +``` + +No division by 12 or 13 is used. The first inverse operation reads the +ordinary Y fields, whose physical operators are different holes. Its +algebraic formula is not a free native decoder. A useful controller must +route this code, cancel it, or provide and price its native inverse. + +For the optional ordinary correction, copy each physical selected Y output +`F a_a` into C0. Apply the positive Q_a line and subtract D times that copy +from completed ordinary X. This removes `D Q_A a`. The output is then +`X_U=u-v`. It costs eight rank-one children. C0 is cleared after every copy. + +## Checks and source pins + +Run + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/emit_raw_selected_backward.py +``` + +The first line is + +```text +PASS_RAW_SELECTED_BACKWARD_LOCAL_OPERATOR +``` + +The checker replays every retained scalar event on all 712 formal input +columns. Its operator words cancel only adjacent Q and Q^-1 pairs. It does +not use commutation between different Q operators or between Q, B, and D. +It checks every retained scalar frame and native frame transition. It +checks arbitrary helper restoration, all owned-private outputs, both +local formulas, and the displayed source-code inverse. The boundary +interpreter uses physical common-address ADDs, not equal-logical-frame +ADDs. Five mutation controls reject omitted or wrongly signed blocks. + +The sixteen signed line recipes are checked on every one of the 512 +spatial basis columns: 8,192 exact Gaussian columns. Both wrappers, their +addresses, their translations, and all scalar phase fields are included. +The complete unchanged core native proof is inherited. It is not replayed +as a new 712-array physical Gaussian operator in this packet. + +The payload pins are: + +```text +clean-J core, decompressed: +fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877 +canonical word, compressed: +16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219 +source matrix receipt: +5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3 +signed line recipe packet, decompressed: +17122a343fb8a3dd804b2d7042d523aa209d0684447cdba63d84cc5561b6144f +``` + +`RAW-SELECTED-BACKWARD.json` pins the emitted word and this checker. The +old core cost is recalculated from its literal scalar events. The new +scalar parts are 4,208 for the input code, 208 for the physical exchanges, +and 4,160 for the final lower shear. The optional correction costs 4,208. +Each new line has two monomial wrappers. The uncorrected native profile +adds eight rank-one children to the old profile. + +The remaining obligations are an independent review, the actual inter-call +views and controller, new child hosting, and the complete recursive scalar, +storage, and precision invoice. The old canonical-frame obstruction does +not apply because the new physical ADDs cross its declared logical frame +classes. This escape does not establish that the desired final supplier +can decode the resulting unit code within its budget. + +The coordinating lane proposed the input code and the final lower shear. +This lane supplied the physical selected exchange and the independent local +operator replay. The clean-J and exact native recipes are prior campaign +results. Research and verification used OpenAI Codex under the user's +direction. No independent human review is claimed. 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