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Notice + +The new campaign contributions and package files are supplied under the +repository's Apache-2.0 license. A copy is in [notices/LICENSE](notices/LICENSE). +Frozen source text, source pins, and existing attribution are unchanged. +Substantial OpenAI Codex assistance was used for the constructions, proofs, +independent agent checks, and this publication package. + +The rational grid comparison retains `notes/stopped-product-complex.tex` +from CrocSwap/integer-mult-bounds at commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. Its Git blob is +`4a9037137cd3158dbeca6d9e3b1881a599ebfcb5` and its SHA256 is +`4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a`. +It supplies the retained common odd-grid method. The retained source-pin +record is in [notices/ODD-GRID-SOURCE-PINS.json](notices/ODD-GRID-SOURCE-PINS.json). +The [retained upstream notice](notices/UPSTREAM-NOTICE) credits icekylinx +for the stopped product-ring construction and exact denominator grid, with +OpenAI GPT-6 Astra and Codex assistance. The new rational review proves the +exact domain and repeated-code height for this C16. It does not claim the retained grid method as new work. + +The original local proof files identify the source lanes for each new +result. Those records distinguish construction work from independent +checks. This package makes no claim that a finite certificate formally +verifies the complete multiplication theorem. + +The native construction uses the actual source core from +[PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133) at +`51eb9c4ee9e4722010d308aa3309e039d3940cc2` and the base/extra provider words +from [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148) at +`f2927a4b8afcf0701a6b945e14f30de1d94f5176`. The retained +[notice](notices/PR3133-NOTICE) and [credit record](notices/PR3133-CREDITS.md) +credit dcharb78 for the coupled folds and preserve the earlier contributor +lineage. The exact PR #3148 README credits Jeremy Diviney for its packing +exchange, integration, and verification. These are inherited inputs; this +package does not claim those constructions as new work. + +The native recipe tools descend from +[PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588) at +`8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`. Its +[notice](notices/PR2588-NOTICE) credits Cinna Davis for the dirty-borrowing +method, Rohan Arun for the new package work, and Jeremy Kothe and the named +predecessors for retained methods. It does not identify one person as the +author of every imported compiler file. 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{ + "bytes": 25416, + "path": "portable/check_signed_clean.py", + "sha256": "ec0fc10da3570981191420255c1bb30c2f26bfdb638137ae7077006f123f02ca" + }, + { + "bytes": 6945, + "path": "replay.py", + "sha256": "b75eb0f615c31b93130f0dcd986b794137ee3d9ded8cb9e8f6d237340ee87bb6" + } + ], + "schema": "centre-metric-encoders-package-v1", + "scope": "Finite-field coordinate theorem, actual unitary24 and signed16 encoders with local native words, general dyadic signed family, and rational16 grid limits. No kappa claim." +} diff --git a/research/centre-metric-encoders/PROOFS.md b/research/centre-metric-encoders/PROOFS.md new file mode 100644 index 0000000000..17449dfa89 --- /dev/null +++ b/research/centre-metric-encoders/PROOFS.md @@ -0,0 +1,27 @@ +# Proof and review index + +The source files below are unchanged. Old publication restrictions and +pending-review statements record their status at the time of the freeze. +Use this index for the current local review status. The package does not +change a frozen claim or its validation record. + +| Result | Proof | Decisive independent review | +| --- | --- | --- | +| Sharp original-reader coordinate bound | [Finite-field proof](frozen/root/UNITARY-CENTRE-FOOTPRINT-20261020.md); [array and recovery extension](frozen/root/UNITARY-FOOTPRINT-ARRAY-ADDENDUM-20261020.md) | [Footprint review](frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW.md) | +| Actual C24 matrix and scalar code | [C24 proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-24.md) | [Footprint review](frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW.md) | +| Eight complete C24 native services | [Native construction](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/UNITARY-CLEAN.md) | [Native review](frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/REVIEW.md); [complete component blocks](frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/BLOCK-DERIVATION.md) | +| Signed C, Cbar, and exact metric conversion | [C proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/SIGNED-SIXTEEN.md); [Cbar proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-COMPANION.md) | [Signed metric review](frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/REVIEW.md) | +| Thirty complete signed native services | [Native construction](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/SIGNED-CLEAN.md) | [Native review](frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/REVIEW.md) | +| General n=4+2^r scalar family and metric restriction | [General word and proof](frozen/root/SIGNED-METRIC-DYADIC-FAMILY-20261020.md); [family restriction](frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY.md) | [Word, cost, and restriction review](frozen/lanes/bridge-review-20261017/signed-family-review-20261020/REVIEW.md) | +| Rational C16 and exact grid growth | [Packing](frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/PACKING.md); [paid grid proof](frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/GRID-AND-POWERS.md) | [Exact grid and all-power review](frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/REVIEW.md) | + +The new replay retains all proof-relevant fields of every result receipt. +It compares the complete JSON bytes with the frozen receipts. The source +manifest records compressed and decompressed hashes. It also records why +each predecessor file is present. An imported arithmetic helper or source +receipt does not make the whole predecessor lane part of this result. + +The actual reciprocal response is a pinned input. Its [model proof](frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL.md) +and [model freeze](frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json) +are included. The encoder package does not depend on a moving PR head or +on the publication order of a separate reciprocal-response package. diff --git a/research/centre-metric-encoders/PROVENANCE.md b/research/centre-metric-encoders/PROVENANCE.md new file mode 100644 index 0000000000..e15a4b7030 --- /dev/null +++ b/research/centre-metric-encoders/PROVENANCE.md @@ -0,0 +1,64 @@ +# Source record + +The source campaign is `centre-encoding-campaign-20261014`. Each file under +`frozen/` is an exact copy from that campaign. [SOURCE-MANIFEST.json](SOURCE-MANIFEST.json) +records its original campaign path, SHA256, size, and reason for inclusion. +Compressed inputs also have a decompressed SHA256. The package includes +the closure required by the seven selected exact checks. It does not +include every producer prototype or every predecessor replay. + +The normal and optimized native reviews retain the exact source phases, +physical fields, endpoint adapters, and word bytes. The new replay uses +those bytes. It does not replace their pins with later upstream objects. +These local results are historical source-bound constructions, not the +current selected supplier. + +The publication context was checked on 2026-10-22 against upstream main +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. Its selected record names +[PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470), with +kappa 60403/20000000 = 0.00302015. The exact record is retained in +[SELECTED-CONTEXT.json](evidence/SELECTED-CONTEXT.json). That selection is +not an input to these checks. The package does not transplant its local +words into that construction or change its complete cost. + +## Portable entry point + +Six checks run their frozen source directly. The seventh uses +[portable/check_signed_clean.py](portable/check_signed_clean.py), a copy of +[the frozen signed-native checker](frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py). +Only its source-directory binding and absolute-source-path resolution +change. The resolver maps the single campaign path component to the local +frozen tree. It still checks every original payload digest. All arithmetic, +phase checks, endpoint checks, cost checks, and negative controls are +unchanged. The [exact diff](evidence/PORTABILITY.diff) records the change. + +The new [replay receipt](evidence/REPLAY.json) records both current checker +hashes. The runner uses Python file-access audit events to reject a read +outside the package, output directory, or Python runtime. This check does +not change a matrix, instruction, import, or producer result. Each result +must match its frozen receipt byte for byte. + +The root's earlier 32-coordinate proof and receipts remain as proof +ancestry for the finite-field theorem. The accepted actual construction +and native replay use C24. The rational C16 is the first actual packing, +not the later supported-packing extension. No source field is silently +substituted between these constructions. + +## Attribution and scope + +The root lane supplied the finite-field bound, array extension, general +signed-family word, and a separate exact engine. The new-core-transfer +lane supplied the actual C24 and signed-code constructions and native +words. The independent-review lane supplied the distinct C24 proof check +and the first rational packing. The bridge-access lane supplied the paid +rational word and grid analysis. The bridge-review lane supplied the +signed basis, matrix proof, and word/cost review. The native-review lane +supplied the independent native bindings, complete-block proof, rational +division-domain check, and all-power argument. The controller, oblique, +and earlier native packets supplied the actual readers and native inputs. +Substantial OpenAI Codex assistance was used throughout. + +[NOTICE.md](NOTICE.md) records the license and retained external source. +Human contributor credit must be based on source notices, not inferred +from the account that submits the package. Publication, GitHub link +verification, and rendered PR checks are separate from this local replay. diff --git a/research/centre-metric-encoders/README.md b/research/centre-metric-encoders/README.md new file mode 100644 index 0000000000..464c33db9e --- /dev/null +++ b/research/centre-metric-encoders/README.md @@ -0,0 +1,158 @@ +# Centre codes with unitary, signed, and rational metrics + +This package proves a sharp 24-coordinate bound for the original sixteen +readers in the Gaussian-dyadic unitary model. It gives an actual code and +complete local native words that attain 24. A different reciprocal reader +has a signed-metric code with sixteen coordinates. Thirty complete local +native words implement this code, its paid pair companion, and a separate +transpose interface. A general dyadic scalar construction and a rational-unitary +sixteen-coordinate comparison explain the representation limits. + +These results do not improve the complete kappa calculation. No complete +routed caller, terminal decoder, recursive host, finite map cost, or full +precision bound is supplied. Native rank mass is a local invoice. It is not +a multiplication exponent. + +Read the [proof and review index](PROOFS.md), the [source record](PROVENANCE.md), +and the [fresh replay receipt](evidence/REPLAY.json). + +## The two reader families + +| Reader | Euclidean Gram | Representation result | +| --- | --- | --- | +| Original sixteen rows V | diag(12 I8, 8 I8) | A Gaussian-dyadic unitary code needs at least 24 complex coordinates. The actual C24 attains 24. | +| Reciprocal sixteen rows L | diag(10 I8, 7 I8) | A Euclidean-unitary code also needs at least 24 coordinates, by reduction modulo five or seven. A signed-metric code uses sixteen. | + +For L, the signed Gram is diag(4 I8, 2 I8). The signed code stores the +rank-sixteen difference E-P. The difference E-I has rank thirty-two. +The physical P is a code on 32 ports, with 160 nonzero entries. It costs +728 real scalar primitives before address-view costs. + +The original-reader bound also covers arbitrary borrowed inputs, +nonlinear recovery, and unitary mixing of spatial and owner coordinates. +For arrays of N complex entries, the bound is 24N complex coordinates. +It counts capacity, not names of registers with unrestricted size. +A dyadic-unit output frame and a dyadic orthogonal input frame preserve +the bound. Promised zero inputs, approximate recovery, and general +nonunitary encodings are outside this theorem. + +## Exact local words and costs + +The standalone C24 code and its adjoint each cost 8052 real scalar +primitives. All eight complete native C24 services cost 16020. A complete +real-component block is treated as one complex-linear frame operation. +An individual component ADD need not preserve that frame. + +For the reciprocal readers, C K C^T=G and C^-T=G^-1 C K. The complete +dual conversion includes metric scales on both arbitrary input banks. +The original C transpose violates 32 ordinary support rows. A paid +80-scalar suffix gives the companion Cbar and repairs that support. +Cbar changes the selected coordinates. Recovery of the individual L rows +requires the paid selected-pair code. Only C and Cbar carry L in the sixteen +selected coordinates. Cbar transpose supplies a companion native interface; +its sixteen selected outputs do not decode L. +The raw selected dual of the Cbar-transpose service uses Cbar inverse. +Its metric-converted dual uses Cbar transpose. + +| Code | Forward or raw dual scalar cost | Metric-selected dual scalar cost | +| --- | ---: | ---: | +| C24 | 16020 | Not needed | +| Signed C | 9988 | 11252 | +| Signed Cbar | 10068 | 11284 | +| Cbar transpose interface | 10324 | 11156 | + +| Service | Q-entry profile | Q-entry mass | I-entry change | I-entry mass | +| --- | --- | ---: | --- | ---: | +| C24 | 1328 H1 + 64 H2 + 48 H3 + 24 H8 | 1792 | Replace 24 H8 by 24 H9 | 1816 | +| Signed code or transpose interface | 1392 H1 + 64 H2 + 48 H3 + 16 H8 | 1792 | Replace 16 H8 by 16 H9 | 1808 | + +All duals use the Q-entry profile. Each word acts on 640 arbitrary complex +inputs and preserves the 416 auxiliary roles. The words add no field, +private buffer, CLEAR, or odd division. The signed words have no new +spatial operator; every inherited phase and adapter is bound to its source. +The C24 check also replays eight distinct fresh H8 operators on all 512 +spatial columns. Neither result supplies a recursive helper host. + +## General signed family + +For every k=2^r and n=k+4, the scalar construction gives one centre output +and its metric-orthogonal complement. Its metric and inverse are dyadic. +The exact price in either direction is 86 for r=0, 96 for r=1, and +10kr+76+4r for r at least two. The instruction count is 3kr/2+12. + +The proof applies to all r. The checks for k=1,2,4,8,16,32,64 are exact +finite controls. The basis was supplied by the bridge-review lane and +checked by the root lane. The later bridge review checks the root's +word and cost. It is not a second independent proof of its own basis. +No general native row placement is claimed. + +## Rational sixteen-coordinate comparison + +The first rational unitary C16 packs the original V into sixteen +coordinates. Each complete scalar direction costs 5702 dyadic scalar +primitives, plus sixteen real multiplication-by-three scans and sixteen +real division-by-three scans. Odd scans remain separately priced. +One direction needs ternary height one and local binary height two. +Its complete word must remain contiguous at a common complex frame. + +For every positive integer m, h3(C16^m)=h3((C16*)^m)=m. This is a proved +all-power result. The nonzero trace of 3C16 modulo three prevents its +residue matrix from being nilpotent. A fixed dyadic-unit change of basis +or tensoring with an identity preserves the growth. A matched C16 then +C16* pair has prefix odd height one because the inverse word retraces +the first word. This does not give a uniform guard for unmatched calls. + +The exact quartet division domain is a congruence modulo three. The +check enumerates all 6561 residue inputs in each direction and accepts +729. The retained root-grid theorem requires a dyadic endpoint on every +role for each completed recursive child. C16 itself has no such endpoint. +All 96 ordinary diagonals of this C16 are nonzero, so this scalar packing +does not have the native realization used by C24. The later supported +packing extension is outside this package. + +## Reproduction + +Use Python 3.11 or later. No third-party library or network access is needed. +Run from this directory with a new output directory: + +```sh +python3 -I -B replay.py --output /tmp/centre-metric-encoders-replay +``` + +Expected final output: + +```text +PASS_CENTRE_METRIC_ENCODERS +``` + +The runner executes seven checks in normal and optimized Python, in +sequence. It compares each result with the frozen receipt and compares +both Python modes. It checks every immutable source hash before and +after the run. For compressed inputs it checks the decompressed payload +as well as the retained source bytes. It confines each check's file +access to this package, its output directory, and the Python runtime. +The command does not run the archived producer emitters or regenerate +their compressed containers. + +The negative controls reject damaged scalar words, wrong metric signs, +omitted target-bank metric scales, wrong dual chronology, wrong global +phases, and an insufficient rational division domain. The review files +state which controls belong to each result. No selected-frontier replay, +Lean formalization, or full recursive supplier check was run. + +## Open next questions + +A complete signed-code caller must supply route access, saved-record +restoration, and a paid terminal. Start with the explicit local input and +output maps in the signed native review. A count of selected coordinates +does not provide those operations. + +A recursive rational boundary type must control whole-state prefixes and +prove decoded child-entry types. Start with the matched C16/C16* case. +The all-power theorem blocks a constant ternary guard for unmatched +repetitions of this fixed C16. It makes no claim about products of +different stage codes. + +A general signed-family native construction needs physical row placement +and admissible support for every n=4+2^r. Start with the actual n=6 and n=8 +codes. 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The failed guessed path is retained as PR2588-NOTICE-SOURCE.json." +} diff --git a/research/centre-metric-encoders/evidence/PORTABILITY.diff b/research/centre-metric-encoders/evidence/PORTABILITY.diff new file mode 100644 index 0000000000..8970ae1c99 --- /dev/null +++ b/research/centre-metric-encoders/evidence/PORTABILITY.diff @@ -0,0 +1,25 @@ +--- frozen signed-native checker ++++ portable signed-native checker +@@ -9,7 +9,7 @@ + import importlib.util + import json + +-HERE = Path(__file__).resolve().parent ++HERE = Path(__file__).resolve().parents[1] / "frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020" + HELPER = HERE.parent / "row-capture-native-review-20261020/check.py" + PIN = "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84" + if sha256(HELPER.read_bytes()).hexdigest() != PIN: +@@ -327,7 +327,12 @@ + payload = json.loads(q.read(SOURCE/"run-normal/SIGNED-CLEAN.json.gz", PAYLOAD, True)) + need(len(payload["source_pins"]) == 12, "All twelve declared source pins") + for record in payload["source_pins"].values(): +- path = Path(record["path"]) ++ original_path = Path(record["path"]) ++ anchor = "centre-encoding-campaign-20261014" ++ need(original_path.parts.count(anchor) == 1, "Unique source campaign path") ++ relative = original_path.parts[original_path.parts.index(anchor)+1:] ++ need(relative and relative[0] == "lanes", "Source stays in the lane archive") ++ path = q.LANES.parent.joinpath(*relative) + q.read(path, record["sha256"], path.suffix == ".gz") + producer_receipt = json.loads(q.read(SOURCE/"run-normal/CHECKS.json", + "21e5ae1b7757429dac8ecc4c4238f7e7f1296bf3f6cb3b3c67b09166c22a79ca")) diff --git a/research/centre-metric-encoders/evidence/PROVIDER-NOTICE-VERIFICATION.json b/research/centre-metric-encoders/evidence/PROVIDER-NOTICE-VERIFICATION.json new file mode 100644 index 0000000000..1f3011b71c --- /dev/null +++ b/research/centre-metric-encoders/evidence/PROVIDER-NOTICE-VERIFICATION.json @@ -0,0 +1,24 @@ +{ + "status": "PASS_IMMUTABLE_GITHUB_NOTICE_READBACK", + "commit": "f2927a4b8afcf0701a6b945e14f30de1d94f5176", + "files": [ + { + "path": "research/coupled-carrier-cap740/vendor/PR3133-NOTICE", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/vendor/PR3133-NOTICE", + "git_blob_sha": "89c20926ea7f803718f751d95989d5a269908efd", + "computed_git_blob_sha": "89c20926ea7f803718f751d95989d5a269908efd", + "git_blob_matches": true, + "sha256": "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661", + "saved_path": "PR3148-VENDOR-NOTICE.txt" + }, + { + "path": "research/coupled-carrier-cap740/vendor/PR3133-CREDITS.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/vendor/PR3133-CREDITS.md", + "git_blob_sha": "24f00912d4ec829c3c8d2a8d086aa135664a124c", + "computed_git_blob_sha": "24f00912d4ec829c3c8d2a8d086aa135664a124c", + "git_blob_matches": true, + "sha256": "1d9d8f56d8899f55878e4cb2c4e052b22506444016a51c2e678773505f5189e6", + "saved_path": "PR3148-VENDOR-CREDITS.md" + } + ] +} diff --git a/research/centre-metric-encoders/evidence/REPLAY.json b/research/centre-metric-encoders/evidence/REPLAY.json new file mode 100644 index 0000000000..ff4f189dcf --- /dev/null +++ b/research/centre-metric-encoders/evidence/REPLAY.json @@ -0,0 +1,146 @@ +{ + "checks": [ + { + "check": "unitary_footprint", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result.json": "28db16426c29a8c5268bedfdde0e207c98db429d463b3e8a00ca1f8fdc5dfe08" + }, + "seconds": 4.544 + }, + { + "check": "unitary_footprint", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result.json": "28db16426c29a8c5268bedfdde0e207c98db429d463b3e8a00ca1f8fdc5dfe08" + }, + "seconds": 3.664 + }, + { + "check": "unitary_native", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/INPUTS.json": "2462a323f974b2417108a47aebc93974a8f2c94511252d67e47cb0debf0f6c11", + "result/REVIEW.json": "67fff6260e4ba02fc12322b31e3325de98f25ac52d35d29a6f53806677bca3bd" + }, + "seconds": 8.016 + }, + { + "check": "unitary_native", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/INPUTS.json": "2462a323f974b2417108a47aebc93974a8f2c94511252d67e47cb0debf0f6c11", + "result/REVIEW.json": "67fff6260e4ba02fc12322b31e3325de98f25ac52d35d29a6f53806677bca3bd" + }, + "seconds": 11.015 + }, + { + "check": "signed_metric", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/REVIEW-CHECKS.json": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b" + }, + "seconds": 4.599 + }, + { + "check": "signed_metric", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/REVIEW-CHECKS.json": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b" + }, + "seconds": 3.901 + }, + { + "check": "signed_native", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/INPUTS.json": "fa827c1a46d2f72325099cf1111a1a0d0aa65746baaee41b24588fa789a98797", + "result/REVIEW.json": "367b51faa030b534e2c547587a09d1ef30b8cc3cd05e5fd6283c62954b1a85c7" + }, + "seconds": 3.447 + }, + { + "check": "signed_native", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/INPUTS.json": "fa827c1a46d2f72325099cf1111a1a0d0aa65746baaee41b24588fa789a98797", + "result/REVIEW.json": "367b51faa030b534e2c547587a09d1ef30b8cc3cd05e5fd6283c62954b1a85c7" + }, + "seconds": 3.695 + }, + { + "check": "signed_family", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37" + }, + "seconds": 2.844 + }, + { + "check": "signed_family", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37" + }, + "seconds": 2.827 + }, + { + "check": "signed_family_review", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result.json": "bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba" + }, + "seconds": 3.265 + }, + { + "check": "signed_family_review", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result.json": "bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba" + }, + "seconds": 3.858 + }, + { + "check": "rational_grid", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/INPUTS.json": "5231e3f636b2e35456af9fb020950f3570f45daec9db9cd3fc88c2cb2ce8be23", + "result/REVIEW.json": "d929f05a9ad601007b046602ecd52ba4b2709fe8315e325475817eb9ece1c6d7" + }, + "seconds": 2.765 + }, + { + "check": "rational_grid", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/INPUTS.json": "5231e3f636b2e35456af9fb020950f3570f45daec9db9cd3fc88c2cb2ce8be23", + "result/REVIEW.json": "d929f05a9ad601007b046602ecd52ba4b2709fe8315e325475817eb9ece1c6d7" + }, + "seconds": 2.78 + } + ], + "frozen_sources_unchanged": true, + "immutable_inputs": 185, + "normal_optimized_equal": true, + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "portable_signed_checker_sha256": "ec0fc10da3570981191420255c1bb30c2f26bfdb638137ae7077006f123f02ca", + "python": "3.14.7", + "replay_sha256": "b75eb0f615c31b93130f0dcd986b794137ee3d9ded8cb9e8f6d237340ee87bb6", + "scope": "Exact local proofs, matrices, scalar words, native words, phases, invoices, and grid checks. No recursive supplier or kappa claim.", + "source_manifest_sha256": "71c42b6191c8f2fc6afdc3c79357352372a3d1911b79ef8a41130c0ef7a25b9e", + "status": "PASS_CENTRE_METRIC_ENCODERS" +} diff --git a/research/centre-metric-encoders/evidence/SELECTED-CONTEXT.json b/research/centre-metric-encoders/evidence/SELECTED-CONTEXT.json new file mode 100644 index 0000000000..aa2cb1b54d --- /dev/null +++ b/research/centre-metric-encoders/evidence/SELECTED-CONTEXT.json @@ -0,0 +1,91 @@ +{ + "applicability": "Historical local encoder constructions. The selected frontier is not an input to these exact checks and is unchanged.", + "checked_date": "2026-10-22", + "selected_record": { + "assumptions": [ + { + "id": "native_all_columns", + "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity." + }, + { + "id": "owned_erasure", + "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts." + }, + { + "id": "compiler", + "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract." + }, + { + "id": "precision_tape", + "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template." + }, + { + "id": "analytic_recovery", + "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework." + } + ], + "audited_source_head": "b9a13c1673e0e9697de410de16e8bbf3207a7363", + "certificate": "certificates/frontier4470/CLAIM.json", + "certificate_sha256": "d962932a6971b8f0054462c59f4ad699dcf3d1fbf886e1f856a6fa9e97491232", + "contributors": "docs/research/community-joint4470-contributors.md", + "decimal": "0.00302015", + "integration": "docs/research/pr-intake-evidence/pr4470/INTEGRATION.json", + "kappa": "60403/20000000", + "previous_kappa": "23/10000", + "previous_record": "certificates/checkpoints/frontier4359.json", + "proof": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md", + "proof_supplements": { + "docs/research/pr-intake-evidence/pr4359/PROOF-REVIEW.md": "7d67bb814285f7634029fbd378c6457156545f0b38858cc1c6ec34b68cd9d162", + "docs/research/pr-intake-evidence/pr4416/PROOF-REVIEW.md": "2c2bbe6fe1bab44778192118f27e59a0d23dbe02c47aa8a42845093f1ce46f49", + "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md": "5c111dd56beb53dc44ab727d96e1af03aaf50f3023d4342e2b0a89ede6cf585b", + "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c", + "notes/batched-complex-rows.tex": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c", + "notes/compact-control-movement.tex": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6", + "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54", + "notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511", + "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8", + "references/semantic-bulk/pr23/semantic-bulk-17-note.tex": "652242b05174bb776ffc6165af170df9c8cf220dbd0fc26c24d778f320dbabc8", + "research/e8-bit-carrier-skeleton/code/bit/export_records.py": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3", + "research/e8-bit-carrier-skeleton/code/nine/geometry.py": "36eeda3184bd009e89462b65c8725d10860c444f8da8f1f87e5f6e50120011ca", + "research/e8-bit-p111-tuned/code/gen_p3.py": "438b83f10d70ceca7cf78049420204b7de2dc61682f913c50a62596106ad84cd", + "research/e8-bit-p111-tuned/code/xcheck_p.py": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e", + "research/e8-bit-p111-tuned/tune/EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4", + "research/e8-bit-p111-tuned/tune/apply.py": "806ae4cb2648e4f05dcf56bd089891fd3ba33a6ee5fe76d3329e322c6770c1a1", + "research/e8-bit-p111-tuned/tune/wlib.py": "a37fdf3cdf5f62945c2a90193401c0e9edc9dd3cda8d8cb36a3b9c329ebe4dbc", + "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + "replay_mode": "fresh changed-construction replay with exact-source prior foundation review reuse", + "reproduce": "make frontier4470-verify", + "review": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md", + "scope": "Maintainer-reviewed conditional PR4470 construction. Inherited native/all-column, owned-erasure, whole-job, compiler, precision/tape, analytic, prime and recovery hypotheses remain. Uniform words are not materialized.", + "source_certificate": "research/joint-helper-lattice/RESULT.json", + "source_certificate_sha256": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21", + "source_manifest": "certificates/frontier4470-source.json", + "source_prs": [ + 4470, + 4447, + 4441, + 4440, + 4416, + 4433, + 4359, + 4268, + 3945, + 4085, + 2979, + 4076, + 4088, + 1673, + 1758, + 1786, + 23, + 555, + 589 + ], + "status": "Selected maintainer-reviewed conditional joint-helper construction; source-bound foundation reuse is explicit", + "validation": "docs/research/pr-intake-evidence/pr4470/VALIDATION.json" + }, + "selected_record_sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375", + "upstream_main": "b58ad9ef4d4e861b0eaa5dba41742bdc072dca51" +} diff --git a/research/centre-metric-encoders/evidence/SOURCE-LICENSE-CHECK.json b/research/centre-metric-encoders/evidence/SOURCE-LICENSE-CHECK.json new file mode 100644 index 0000000000..5b154ad53d --- /dev/null +++ b/research/centre-metric-encoders/evidence/SOURCE-LICENSE-CHECK.json @@ -0,0 +1,29 @@ +{ + "checks": [ + { + "equal": true, + "git_blob": "4a9037137cd3158dbeca6d9e3b1881a599ebfcb5", + "retained_path": "frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex", + "sha256": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_path": "notes/stopped-product-complex.tex" + }, + { + "equal": true, + "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64", + "retained_path": "notices/LICENSE", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_path": "LICENSE" + }, + { + "equal": true, + "git_blob": "59d8e0cf3102e15bd11db430838365531e2d7f18", + "retained_path": "notices/UPSTREAM-NOTICE", + "sha256": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd", + "source_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "source_path": "NOTICE" + } + ], + "status": "PASS_PINNED_SOURCE_AND_NOTICES" +} diff --git a/research/centre-metric-encoders/evidence/replay/rational_grid/normal/FILE-ACCESS.json b/research/centre-metric-encoders/evidence/replay/rational_grid/normal/FILE-ACCESS.json new file mode 100644 index 0000000000..d0c5e599dd --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/rational_grid/normal/FILE-ACCESS.json @@ -0,0 +1,40 @@ +[ + "frozen/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md", + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/FREEZE.json", + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/GRID-AND-POWERS.md", + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/actual-normal/CHECKS.json", + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/actual-normal/PACKING.json", + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/actual-optimized/CHECKS.json", + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/actual-optimized/PACKING.json", + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/check_packing.py", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/FREEZE.json", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/PRODUCER-REPLAY.json", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.json", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/check_review.py", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/producer-replay/A8-ODD-GRID-WORDS.json", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/producer-replay/A8-ODD-GRID.json", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/producer-replay/MINOR-FACTOR-WORDS.json", + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/producer-replay/MINOR-FACTORS.json", + "frozen/lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md", + "frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/FREEZE.json", + "frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/PACKING.md", + "frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/check_packing.py", + "frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal/CHECKS.json", + "frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal/PACKING.json.gz", + "frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-optimized/CHECKS.json", + 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It gives the +complete payload phase and the regular-cover owner map. + +This result supplies the stage boundary identities needed to carry the +same local nine-dimensional service to later stages. It does not make +the routed response constant. It does not supply a complete caller, +a new recursive host, a finite map cost, or an exponent. + +## Root quadratic refinement + +Fix an actual port with intrinsic unit vector q. The root chart is the +pinned orthonormal basis + +\[ +B=(q,b_1,\ldots,b_8) +\] + +of the first nine coordinates. Its q has Hamming weight 3 or 7. +For any unit vector v, define + +\[ +\beta(v)=\frac{|v|-1}{2}\pmod 2. +\] + +Put \(\beta_j=\beta(b_j)\) and + +\[ +\delta_0=q+\sum_{j=1}^{8}\beta_jb_j. +\tag{1} +\] + +The coefficient of q is one because its weight is 3 or 7. +Let \(C_v\) be the exact line transform with Fourier multiplier +\(i^{v\cdot z}\). Let \(X_v=C_v^2\) be the translation by v. +All these operators commute. If \(F_0\) is FULL on the root axes, then + +\[ +Q\prod_{j=1}^{8}C_{b_j}=X_{\delta_0}F_0,\qquad Q=C_q. +\tag{2} +\] + +To prove (2), compare the Z4 functions +\(\sum_{v\in B}(v\cdot z)\) and \(|z|\). Their difference has zero +quadratic part modulo four because B is orthonormal. Its linear part +is even. Evaluate it at each basis vector \(v\in B\): the value is +\(1-|v|=2\beta(v)\pmod4\). Thus the difference is +\(2\delta_0\cdot z\). This proves the full phase, including its sign. + +## The route and its two translations + +Let \(E_s=(e_{s,1},\ldots,e_{s,8})\) be the fresh coordinate block for +stage s, where \(1\leq s\leq T\). Define \(\rho_s\) to exchange +\(b_j\) with \(e_{s,j}\), for each j, and to fix q and all other fresh +blocks. This is an orthogonal involution. An explicit matrix is + +\[ +\rho_s=I+\sum_{j=1}^{8} + (b_j+e_{s,j})(b_j+e_{s,j})^{\mathsf T}. +\tag{3} +\] + +The eight vectors in the sum are isotropic and pairwise orthogonal. +Equation (3) therefore has the stated action on the complete +orthonormal basis. + +The two physical translations are + +\[ +\delta_{\rm in}(s)=\rho_s\delta_0 + =q+\sum_j\beta_je_{s,j},\qquad +\delta_{\rm out}(s)=\delta_0+\rho_s\delta_0. +\tag{4} +\] + +Let \(P_{\rho_s}\) be the payload address permutation. The entry map is +\(V_{\rm in}=X_{\delta_{\rm in}}P_{\rho_s}\). Its equivalent order is +\(P_{\rho_s}X_{\delta_0}\). The exit map is +\(V_{\rm out}=X_{\delta_{\rm out}}P_{\rho_s}\). +The exit translation is fixed by \(\rho_s\), so the exit map is its +own inverse. + +## Adjacent-stage identities + +Let \(F_\ell\) be FULL on the root and fresh blocks 1 through \(\ell\). +Let \(F_{{\rm ext},s}\) be FULL on fresh blocks 1 through s. +The exact adjacent identities are + +\[ +\begin{aligned} +V_{\rm in}(s)F_{s-1} + &=F_{{\rm ext},s}\,Q\,P_{\rho_s},\\ +V_{\rm in}(s)F_{s-1}q + &=F_{{\rm ext},s}\,P_{\rho_s},\\ +V_{\rm out}(s)F_s + &=F_sP_{\rho_s},\\ +V_{\rm out}(s)F_sq + &=F_sqP_{\rho_s}. +\end{aligned} +\tag{5} +\] + +For the first identity, conjugate (2) by \(P_{\rho_s}\). +The eight root-complement line factors become the fresh block s. +The other completed fresh blocks are fixed. The entry translation +in (4) cancels the translated factor in (2). +The second identity follows because \(\rho_s q=q\) and \(Qq=I\). + +For the third identity, the factors from both the root and fresh +block s are present. Exchanging these factors changes FULL by precisely +\(X_{\delta_0+\rho_s\delta_0}\), which the exit map cancels. +The fourth identity follows again from \(\rho_s q=q\). + +All remaining coordinates are spectators. None of these arguments +depends on T or on the number of preceding completed blocks. + +The same proof gives the complete access cones. A FULL field at level +\(\ell\geq s\) admits the stage-s exit map. A hole field \(F_\ell q\) +at level \(\ell` in +normal Python and in `python3 -O`; both payload and receipt must be +byte equal. + +The root charts, D25 records, and D73 records come from the actual +supplier access calculations. The retained-reader consequence uses +the complete forward service and its emitted inverse-adjoint. All +source hashes are explicit in the payload. This work uses AI assistance +and exact finite-field and Z4 computation. + +No PR or publication is authorized. Before any future PR description, +read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/FREEZE.json new file mode 100644 index 0000000000..d6d802be76 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/FREEZE.json @@ -0,0 +1,45 @@ +{ + "claims": { + "full_code_scalar": 5702, + "native_children": 0, + "positive_power_odd_height": "m for each positive m", + "prefix_binary_height": 2, + "prefix_odd_height": 1, + "real_divide_three_scans": 16, + "real_times_three_scans": 16, + "trace": [ + "11/6", + "7/6" + ], + "workspace_fields": 0 + }, + "files": { + "GRID-AND-POWERS.md": "aebb36eb7437b629e3449a95412a6886d45daee9cf3e2edd36ce9c6e1d2ae593", + "actual-normal/CHECKS.json": "f6037d8525db6e4ea33e18bdaadc00e7b5209e09f15f514b7ce5e8e80e750b67", + "actual-normal/PACKING.json": "1076d6e7b1c9d0fe1cf6c4d04130236ed8bed052b2f811c48f7e08b3ad7c11f5", + "actual-optimized/CHECKS.json": "f6037d8525db6e4ea33e18bdaadc00e7b5209e09f15f514b7ce5e8e80e750b67", + "actual-optimized/PACKING.json": "1076d6e7b1c9d0fe1cf6c4d04130236ed8bed052b2f811c48f7e08b3ad7c11f5", + "check_packing.py": "580aed984c339c6bf82a8292f8cad30217644ba3795d2d2fd2a0905614286fa8" + }, + "normal_optimized_byte_equal": true, + "not_claimed": [ + "native response realization", + "mixed-hole access", + "complete recursive child", + "complete supplier", + "kappa improvement" + ], + "publication": "No PR, commit, push, or publication is authorized.", + "source_payload_decompressed": "b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32", + "sources": { + "bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md": "5da866eb2802e8a30ea77d2f88877b5005a2eb04632514c897a426e76277db2e", + "independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md": "e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01", + "independent-review-20261017/odd-unitary-packing-20261020/FREEZE.json": "22769396f123964addb9024b2fda452148388c67868714b4121a8fe3bfb9d410", + "independent-review-20261017/odd-unitary-packing-20261020/run-normal/PACKING.json.gz": "dd9f9f053f929df31cf9ffbe8404256f9b34fdbd031162bd4b7873f7aaf70544", + "independent-review-20261017/reciprocal-centre-rank-review-20261018/ODD-GRID-COMPOSITION.md": "80f26788f706b5c3a3dbb3cd6bf9e0609e49d7f6384145e03daa9cbe9d3d4547", + "interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "native-escape-20261017/rational-code-admission-20261020/TYPED-CODE-POTENTIAL.md": "79d4c1b596528f1bc5cdb8bbe3da8edbda6a5c27bbca8fd7f4b6417bb6913f6c", + "new-core-transfer-20261017/low-displacement-20261020/check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8" + }, + "status": "FROZEN_PRODUCER_PASS_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/GRID-AND-POWERS.md b/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/GRID-AND-POWERS.md new file mode 100644 index 0000000000..7c97dd6e95 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/GRID-AND-POWERS.md @@ -0,0 +1,356 @@ +# Exact three-grid admission for the sixteen-coordinate unitary code + +The actual sixteen-coordinate code has a paid scalar implementation at +a proved common I or FULL cut. Each direction costs 5,702 old real +scalar units, sixteen real multiplications by three, and sixteen real +divisions by three. It uses no scratch field or native child. Every +prefix has at most one factor three and two binary factors in its +coefficient denominators. + +The code does not preserve the dyadic module on arbitrary inputs. +The preliminary dyadic code does not supply the required divisibility. +The retained common odd grid supplies it, with the root conversion, +added width, and local scans stated below. + +There is also an exact limit on reuse without matched types. For the +actual complete code C, + +```text +h_3(C^m) = h_3((C*)^m) = m, for every integer m >= 1. +``` + +Thus no bounded three-adic lattice is stable under both the actual +preliminary code and its packing factor. This does not exclude a caller +whose complete typed operations cancel their boundary codes. + +## Frozen inputs and scope + +The actual matrix is the first sixteen-coordinate packing in +`independent-review-20261017/odd-unitary-packing-20261020`. +Its decompressed `run-normal/PACKING.json.gz` has SHA256 +`b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32`. +Its source freeze is +`22769396f123964addb9024b2fda452148388c67868714b4121a8fe3bfb9d410`. + +That packet supplies the actual 112 by 112 matrices, the sixteen +original centre readers, the decoder, four packing quartets, and +literal dyadic preliminary words. It proves that C is unitary and +that the sixteen readers are obtained from sixteen output coordinates. +It does not supply a native implementation of the changed response. +In particular, all 96 ordinary diagonal entries of this C are nonzero. + +This packet copies the preliminary component words without change, +emits the rational packing words, and checks the complete result +against that frozen C on all 1,280 real input columns. The 528 complex +fields outside the 112 code fields remain unchanged. + +This C is not a modified extension of the later 24-coordinate native +code. No trace, support, or implementation result is transferred to +such an extension without its own matrix proof. + +The scalar tariff is pinned to +`new-core-transfer-20261017/low-displacement-20261020/check_response.py`, +SHA256 `c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8`. +As in the source component-word emitter, each real component has half +the cost of one complex instruction in that tariff. + +## The rational packing word + +Use the following two complex matrices and the permutation P with +output order `(0,2,1,3)`: + +```text +A = [[1, 1+i], [-1+i, 1]], +B = [[1-i, -i], [-i, 1+i]], +A* A = B* B = 3I. + +R = (1/3) diag(A*,A*) P diag(B,B) + = diag(A^-1,A^-1) P diag(B,B). +``` + +The last factorization has fewer odd scans than scaling all four +outputs separately. It first applies two B blocks, then the paid +middle exchange, then two A inverses. + +For two distinct complex data fields x and y, A has the word + +```text +x += (1+i)y +y *= 3 +y += (-1+i)x. +``` + +Its inverse is the reverse word, with subtraction and division by +three. To apply B, put `a=(1-i)/2` and `b=(1+i)/2`, then use + +```text +x += a y +x *= 1-i +y *= b +y *= 3 +y += a x. +``` + +No complex multiplication primitive is assumed. For `x=r+i s`, +multiplication by `1-i` uses + +```text +r += s; s *= 2; s -= r. +``` + +Multiplication by `(1+i)/2` uses + +```text +r -= s; s *= 2; s += r; r /= 2; s /= 2. +``` + +A complex ADD is expanded into its real component ADDs. Every +exchange uses three ADDs and a sign on each real component. The +inverse packing is the gatewise inverse of this literal word. + +One quartet costs 210 old real units, four real multiplication scans, +and four real division scans. The actual four disjoint quartets are + +```text +(0,71,27,78) +(53,41,111,37) +(20,47,7,63) +(57,104,46,110). +``` + +The four packings therefore cost 840 old units and 32 real odd scans +per direction. Their instruction count is 256. Every prefix has binary +height one and odd height one. The exact real coefficient row-sum +peaks are seven for the packing and six for its inverse. + +The preliminary word and its inverse each cost 4,862 old units. +Joining the correct words gives C and C*, each with 2,110 component +instructions and the stated 5,702 old units plus 32 odd scans. +The complete prefix row-sum peaks are 17 for C and 28/3 for C*. +Both have binary height two and odd height one. These are exact +instruction-boundary content bounds. They do not price primitive +ADD interiors, recursive children, or a full supplier's precision. + +## Exact divisibility domain + +Put `R0=Z[i,1/2]`. The integer Gaussian numerator N=3R has rank one +over the field `R0/(3)`, which is the field with nine elements. +For `x in R0^4`, the exact condition is + +```text +R x belongs to R0^4 +if and only if +x0 + ((1-i)/2)x1 - (1+i)x2 - x3 = 0 modulo 3. (1) +``` + +The first numerator row, divided by its nonzero first entry modulo +three, gives the row in (1). The other numerator rows are its +Gaussian multiples. The realified numerator has rank two modulo +three. Thus (1) is one Gaussian condition, or two real conditions. +The checker verifies that rank from the literal numerator. + +Each B word is dyadic before its odd multiplication. Each A inverse +has only one complex division, and all later operations are dyadic. +The two A inverse blocks have disjoint targets. Thus the literal +division domain agrees with the condition that its complete output +is dyadic; there is no hidden intermediate odd denominator of +higher order. + +The preliminary Cpre is a Gaussian-dyadic unit, with dyadic inverse. +Its values on the four packing fields can therefore be arbitrary. +For example, take the original input `Cpre* e_0`, where e_0 is the +first actual packing coordinate. That input is dyadic. Its value +before R is e_0, and R e_0 contains genuine thirds. A binary guard +cannot remove that factor. The checker also rejects the unscaled +arbitrary-input contract in both packing directions. + +A code-image argument can avoid a root factor only after the +actual input satisfies (1), and its counterpart for every quartet. +A caller must prove preservation of those congruences under all +intervening maps and all arbitrary borrowed columns. The fact that +the complete C is unitary does not prove this property. + +## Paid exact grid + +The retained model admits fixed odd arithmetic. The source method is +`interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex`, +in “One exact odd-denominator grid”. The explicit three-scan proof is +`independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md`, +SHA256 `e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01`. +Its borrowed-state and active-path argument is retained here. + +For a signed w-bit numerator, division by three reads bits from low +to high, starts with carry c=0, and uses + +```text +output bit a = (input bit b - c) mod 2, +next carry = (c + 3a - b)/2. +``` + +The carry stays in `{0,1,2}`. If s_in and s_out are the sign bits, +the quotient is exact precisely when `c_final=3 s_out-s_in`. +Multiplication writes `(3b+c) mod 2`, updates to +`floor((3b+c)/2)`, and checks `c_final=3 s_in-s_out`. +The allocation must prevent multiplication overflow. + +These operations overwrite the same record and need only finite +control. One real scan costs at most `4(w_g+1)` arithmetic-head +steps. Descriptor and record-counter work is separate. The checker +exhausts 8,188 signed division/multiplication cases, including +nonmultiples and overflow rejection. + +For n records in each complex array, one full code direction adds +at most `128 n(w_g+1)` arithmetic-head steps for its 32 odd scans, +in addition to 5,702 old scalar units and separate linear descriptor +work. Odd scans are not charged as old binary SCALE instructions. + +Suppose one finite parent has prefix odd height at most M after +every completed child is replaced by its exact Gaussian-dyadic +endpoint on all physical roles. If D bounds the recursive edge +depth, use + +```text +K = M(D+1), common grid = 2^-P / 3^K. +``` + +At the outer entrance, multiply the integer numerators of every +physical numeric stream by `3^K`. Include arbitrary borrowed data, +helpers, and numeric work streams. Do not scale addresses or tags. +All formats remain fixed during the computation. + +Every prefix then has an integer numerator on this grid. At a +literal division by three its input numerator is divisible by three. +A completed dyadic child does not add odd height, even on rational +input. The complete local word may contain the new code as a parent +operation, but calling it a parent operation does not prove the +complete parent's endpoint is dyadic. + +At the outer return, exact unscaling requires the intended +Gaussian-dyadic endpoint on all roles, including each borrowed role. +If N_real counts all real numeric records, the two outer conversions +cost at most + +```text +8 N_real K (w_g+1) arithmetic-head steps, +``` + +plus separate linear descriptor work. The added width is at most +`2K` bits. These conversions are required costs, not free changes +of notation. A new supplier must prove its actual depth, full +prefix guard, complete endpoint, and strict recurrence inequality. + +Matching rational boundary types are a further permitted case. +The proof in +`native-escape-20261017/rational-code-admission-20261020/TYPED-CODE-POTENTIAL.md` +applies to exact endpoints `C_out A C_in^-1` when all actual types +match and A is dyadic on the complete semantic state. The inverses +cancel in order. It does not require the codes to commute. A caller +must also prove its decoded child-entry types and its internal +prefix height. A code on 112 fields does not automatically restrict +to an admissible type for a recursive call on one field. + +## Exact power growth for the actual C + +Let K3 be the unramified quadratic extension `Q_3(i)`. The polynomial +`X^2+1` is irreducible modulo three, so three is inert in the +Gaussian integers. In K3, + +```text +v_3(a+ib) = min(v_3(a),v_3(b)) +``` + +for rational a and b. Normalize `|3|_3=1/3`. For a matrix use the +maximum absolute value of its entries. This norm is submultiplicative +and agrees with the induced coordinate maximum norm. + +The actual frozen matrix satisfies + +```text +h_3(C) = 1, +trace(C) = (11+7i)/6. +``` + +The trace has valuation minus one. In a finite extension containing +the eigenvalues, the non-Archimedean triangle inequality gives + +```text +3 = |trace(C)|_3 <= max_j |lambda_j|_3 <= ||C||_3 = 3. +``` + +The right inequality follows by applying C to an eigenvector whose +largest coordinate has norm one. Thus an eigenvalue has absolute +value exactly three. For every positive integer m, its eigenvector +and submultiplicativity give + +```text +3^m <= ||C^m||_3 <= ||C||_3^m = 3^m. +``` + +Therefore `h_3(C^m)=m`. The adjoint has conjugate trace and the same +entry norm, so the identical proof gives `h_3((C*)^m)=m`. +The checker recomputes the trace from the complete actual matrix +and checks the first four power heights. Those finite checks support +the theorem; the eigenvalue argument proves it for all m. + +A full lattice over the valuation ring is bounded above and below +by two scalar multiples of the coordinate lattice. If C preserved +such a lattice, its powers would be bounded in the coordinate norm. +The displayed equality excludes that possibility. Any lattice +stable under both Cpre and R would be stable under `C=R Cpre`. +It is therefore also excluded. + +The packing R alone is different: `R^4=I`, and its first three +powers have odd height one. A finite invariant lattice exists for +that finite group. This does not control its dyadic interleavings. +For example, set `S=diag(-1,1,1,1)`. The matrix `3RS` has Gaussian +rank one modulo three and trace `-2+2i`, which is nonzero there. +Its every positive power is nonzero modulo three. Hence +`h_3((RS)^m)=m` as well. + +Neither power result forbids a sequence of genuine matching code +transitions `C_t A_t C_s*`. Their intermediate types can cancel. +It forbids treating repeated unmatched complete C calls as a +bounded-height provider solely because each call is unitary. + +## Native access and remaining obligations + +At a current I cut, the scalar word acts in the existing common +body chart. At a completed FULL cut, the exact stage views gather +the 112 fields, apply the word, and undo the views. A conservative +count is 224 complete view maps per code application, or 448 +operations if route and translation are charged separately. +The source is +`bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md`. +The grid scalar commutes with those exact linear maps. + +This does not admit the code on a mixed or retired hole bank. +It does not make responses from different stages equal. The 96 +nonzero ordinary diagonals still need a changed native response +construction. The scalar code, the representation change, and +the native implementation are separate costs. + +No recursive host, changed supplier, complete exponent, or kappa +improvement is claimed. + +## Reproduction and credit + +Run `check_packing.py --out ` under both +`python3 -I -B` and `python3 -I -O -B`. The expected status is +`PASS_RATIONAL_PACKING_GRID`. Compare both output files byte for byte. + +The checks bind the frozen source and tariff, emit both packing +words, compose both complete codes, check all 1,280 real columns +and both inverse orders, test the exact signed scans, reject an +unscaled arbitrary input, compute the residue rank and prefix bills, +and reproduce the actual trace and four power heights. + +The independent-review lane found and froze the sixteen-coordinate +unitary packing and the dyadic preliminary words. This lane supplies +the paid packing words, the grid admission and divisibility limit, +and the actual-code power theorem. The retained rational-decoder +work supplies the fixed-odd scan and common-grid method. AI +assistance was used throughout. + +No PR, commit, push, or publication is authorized. 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"1/2" + ], + [ + "scale", + 31, + null, + "1/2" + ], + [ + "odd", + 30, + null, + "3" + ], + [ + "odd", + 31, + null, + "3" + ], + [ + "add", + 30, + 28, + "1/2" + ], + [ + "add", + 30, + 29, + "1/2" + ], + [ + "add", + 31, + 28, + "-1/2" + ], + [ + "add", + 31, + 29, + "1/2" + ], + [ + "add", + 26, + 28, + "1" + ], + [ + "add", + 28, + 26, + "-1" + ], + [ + "add", + 26, + 28, + "1" + ], + [ + "scale", + 28, + null, + "-1" + ], + [ + "add", + 27, + 29, + "1" + ], + [ + "add", + 29, + 27, + "-1" + ], + [ + "add", + 27, + 29, + "1" + ], + [ + "scale", + 29, + null, + "-1" + ], + [ + "add", + 31, + 29, + "1" + ], + [ + "add", + 31, + 28, + "-1" + ], + [ + "add", + 30, + 29, + "1" + ], + [ + "add", + 30, + 28, + "1" + ], + [ + "odd", + 31, + null, + "1/3" + ], + [ + "odd", + 30, + null, + "1/3" + ], + [ + "add", + 29, + 31, + "-1" + ], + [ + "add", + 29, + 30, + "-1" + ], + [ + "add", + 28, + 31, + "1" + ], + [ + "add", + 28, + 30, + "-1" + ], + [ + "add", + 27, + 25, + "1" + ], + [ + "add", + 27, + 24, + "-1" + ], + [ + "add", + 26, + 25, + "1" + ], + [ + "add", + 26, + 24, + "1" + ], + [ + "odd", + 27, + null, + "1/3" + ], + [ + "odd", + 26, + null, + "1/3" + ], + [ + "add", + 25, + 27, + "-1" + ], + [ + "add", + 25, + 26, + "-1" + ], + [ + "add", + 24, + 27, + "1" + ], + [ + "add", + 24, + 26, + "-1" + ] + ] + } +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/check_packing.py b/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/check_packing.py new file mode 100644 index 0000000000..7a07731b60 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/check_packing.py @@ -0,0 +1,393 @@ +#!/usr/bin/env python3 +"""Check the exact packing word and its odd-grid requirements.""" + +import argparse +from collections import Counter +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.parents[1] +SOURCE = LANES / "independent-review-20261017/odd-unitary-packing-20261020/run-normal/PACKING.json.gz" +SOURCE_PIN = "b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32" +PRICE = LANES / "new-core-transfer-20261017/low-displacement-20261020/check_response.py" +PRICE_PIN = "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8" + + +def need(value, message): + if not value: + raise ValueError(message) + + +def eye(n): + return [{i: F(1)} for i in range(n)] + + +def add(row, other, c): + for j, value in other.items(): + row[j] = row.get(j, F(0)) + c * value + if not row[j]: + del row[j] + + +def product(a, b): + result = [] + for row in a: + out = {} + for k, value in row.items(): + add(out, b[k], value) + result.append(out) + return result + + +def transpose(a): + out = [{} for _ in a] + for i, row in enumerate(a): + for j, value in row.items(): + out[j][i] = value + return out + + +def scaled(a, c): + return [{j: c * value for j, value in row.items() if c * value} + for row in a] + + +def realify(a): + out = [{} for _ in range(2 * len(a))] + for i, row in enumerate(a): + for j, (x, y) in enumerate(row): + for target, source, c in ( + (2 * i, 2 * j, x), (2 * i, 2 * j + 1, -y), + (2 * i + 1, 2 * j, y), (2 * i + 1, 2 * j + 1, x)): + if c: + out[target][source] = F(c) + return out + + +def direct_sum(a, count): + n = len(a) + return [{j + k * n: c for j, c in row.items()} + for k in range(count) for row in a] + + +def realify_sparse(a, n=1280): + out = eye(n) + for i, row in enumerate(a): + out[2 * i], out[2 * i + 1] = {}, {} + for j, (x, y) in row.items(): + j, x, y = int(j), F(x), F(y) + for target, source, c in ( + (2 * i, 2 * j, x), (2 * i, 2 * j + 1, -y), + (2 * i + 1, 2 * j, y), (2 * i + 1, 2 * j + 1, x)): + if c: + out[target][source] = c + return out + + +def heights(a): + binary = odd = 0 + for row in a: + for c in row.values(): + d, h2, h3 = c.denominator, 0, 0 + while d % 2 == 0: + d //= 2 + h2 += 1 + while d % 3 == 0: + d //= 3 + h3 += 1 + need(d == 1, "Only two and three occur in denominators") + binary, odd = max(binary, h2), max(odd, h3) + return binary, odd + + +def add_complex(word, target, source, re, im): + for a, b, c in ((0, 0, re), (0, 1, -im), (1, 0, im), (1, 1, re)): + if c: + word.append(["add", 2 * target + a, 2 * source + b, str(c)]) + + +def scale_alpha(word, port): + x, y = 2 * port, 2 * port + 1 + word += [["add", x, y, "-1"], ["scale", y, None, "2"], + ["add", y, x, "1"], ["scale", x, None, "1/2"], + ["scale", y, None, "1/2"]] + + +def scale_one_minus_i(word, port): + x, y = 2 * port, 2 * port + 1 + word += [["add", x, y, "1"], ["scale", y, None, "2"], + ["add", y, x, "-1"]] + + +def odd_scale(word, port, c): + for bit in (0, 1): + word.append(["odd", 2 * port + bit, None, str(c)]) + + +def factor_a(word, x, y): + add_complex(word, x, y, F(1), F(1)) + odd_scale(word, y, F(3)) + add_complex(word, y, x, F(-1), F(1)) + + +def factor_b(word, x, y): + add_complex(word, x, y, F(1, 2), F(-1, 2)) + scale_one_minus_i(word, x) + scale_alpha(word, y) + odd_scale(word, y, F(3)) + add_complex(word, y, x, F(1, 2), F(-1, 2)) + + +def inverse_word(word): + return [[op, target, source, + str(-F(c) if op == "add" else 1 / F(c))] + for op, target, source, c in reversed(word)] + + +def swap_complex(word, x, y): + for bit in (0, 1): + a, b = 2 * x + bit, 2 * y + bit + word += [["add", a, b, "1"], ["add", b, a, "-1"], + ["add", a, b, "1"], ["scale", b, None, "-1"]] + + +def packing_word(offset): + word, a_word = [], [] + for x, y in ((offset, offset + 1), (offset + 2, offset + 3)): + factor_b(word, x, y) + factor_a(a_word, x, y) + swap_complex(word, offset + 1, offset + 2) + return word + inverse_word(a_word) + + +def scalar_price(op, c): + a, b = abs(c.numerator), c.denominator + need(a and b & (b - 1) == 0, "A dyadic old scalar coefficient") + if op == "scale": + need(a & (a - 1) == 0, "A signed binary scale") + return abs(a.bit_length() - b.bit_length()) + int(c < 0) + return 1 + a.bit_length() + a.bit_count() + b.bit_length() + + +def replay(word, n=1280, active_components=32): + state = eye(n) + price = 0 + scan = Counter() + peak = F(1) + binary = odd = 0 + for op, target, source, value in word: + c = F(value) + need(0 <= target < active_components, "Only declared data components change") + if op == "add": + need(source != target and 0 <= source < active_components, + "Distinct data components") + add(state[target], state[source], c) + else: + need(op in ("scale", "odd"), "A scalar operation") + state[target] = {j: c * v for j, v in state[target].items()} + if op == "odd": + need(c in (3, F(1, 3)), "A fixed three scan") + scan[str(c)] += 1 + else: + price += scalar_price(op, c) + peak = max(peak, sum(abs(v) for v in state[target].values())) + h2, h3 = heights([state[target]]) + binary, odd = max(binary, h2), max(odd, h3) + return state, {"old_real_scalar": price, "real_odd_scans": dict(scan), + "instructions": len(word), "prefix_real_row_norm": str(peak), + "binary_height": binary, "odd_height": odd} + + +def mod_three(c): + need(c.denominator % 3, "A dyadic residue exists") + return c.numerator * pow(c.denominator, -1, 3) % 3 + + +def rank_three(matrix): + a = [[mod_three(row.get(j, F(0))) for j in range(len(matrix))] + for row in matrix] + rank = 0 + for j in range(len(a[0])): + pivot = next((i for i in range(rank, len(a)) if a[i][j]), None) + if pivot is None: + continue + a[rank], a[pivot] = a[pivot], a[rank] + a[rank] = [x * pow(a[rank][j], -1, 3) % 3 for x in a[rank]] + for i in range(len(a)): + if i != rank and a[i][j]: + c = a[i][j] + a[i] = [(x - c * y) % 3 for x, y in zip(a[i], a[rank])] + rank += 1 + return rank, a + + +def signed_scan(n, width, divide): + bits = [(n % (1 << width) >> j) & 1 for j in range(width)] + carry, output = 0, 0 + for j, b in enumerate(bits): + if divide: + a = (b - carry) % 2 + carry = (carry + 3 * a - b) // 2 + else: + a, carry = (3 * b + carry) % 2, (3 * b + carry) // 2 + need(0 <= carry < 3, "The fixed carry range") + output |= a << j + sn, sq = bits[-1], (output >> (width - 1)) & 1 + signed = output - sq * (1 << width) + valid = carry == (3 * sq - sn if divide else 3 * sn - sq) + return valid, signed + + +def scan_checks(): + count = 0 + for width in range(1, 12): + for n in range(-(1 << (width - 1)), 1 << (width - 1)): + valid, value = signed_scan(n, width, True) + need(valid == (n % 3 == 0), "The exact division domain") + if valid: + need(value == n // 3, "The signed quotient") + valid, value = signed_scan(n, width, False) + fits = -(1 << (width - 1)) <= 3 * n < 1 << (width - 1) + need(valid == fits, "The multiplication overflow test") + if valid: + need(value == 3 * n, "The signed product") + count += 2 + return count + + +def integer_word(word, root_scale): + binary = replay(word)[1]["binary_height"] + state = [[int(i == j) * root_scale * 2 ** binary for j in range(32)] + for i in range(32)] + for op, target, source, value in word: + c = F(value) + candidate = ([F(x) + c * y for x, y in zip(state[target], state[source])] + if op == "add" else [c * x for x in state[target]]) + if any(x.denominator != 1 for x in candidate): + return False + state[target] = [int(x) for x in candidate] + return True + + +def serialized(matrix): + return [{str(j): str(v) for j, v in sorted(row.items())} for row in matrix] + + +def actual_code(word, inverse, r): + raw = gzip.decompress(SOURCE.read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_PIN, "The frozen actual packing source") + need(sha256(PRICE.read_bytes()).hexdigest() == PRICE_PIN, "The scalar tariff source") + source = json.loads(raw) + need(realify_sparse(source["packing"], 8) == r, "The same four-field packing") + ports = sum(source["packing_ports"], []) + need(len(ports) == len(set(ports)) == 16, "Four disjoint actual quartets") + + def placed(instructions): + return [[op, 2 * ports[target // 2] + target % 2, + None if old is None else 2 * ports[old // 2] + old % 2, c] + for op, target, old, c in instructions] + + code = source["precode_words"]["precode"] + placed(word) + adjoint = placed(inverse) + source["precode_words"]["precode_adjoint"] + expected = realify_sparse(source["code"]) + fw, report = replay(code, active_components=224) + bw, inverse_report = replay(adjoint, active_components=224) + need(fw == expected, "The actual full code on all1280 real input columns") + need(bw == transpose(expected), "The actual full adjoint on all1280 columns") + need(product(fw, bw) == product(bw, fw) == eye(1280), + "The actual complete code restores arbitrary data and borrowed state") + trace = [sum((F(row.get(str(i), ["0", "0"])[k]) + for i, row in enumerate(source["code"])), F(0)) for k in (0, 1)] + need(trace == [F(11, 6), F(7, 6)], "The exact nonintegral three-adic trace") + small = expected[:224] + matrix, powers = eye(224), [] + for exponent in range(1, 5): + matrix = product(small, matrix) + need(heights(matrix)[1] == exponent, "The first four actual power heights") + powers.append({"power": exponent, "odd_height": exponent}) + precode_inverse = realify_sparse(source["precode_adjoint"], 224) + witness = [row.get(2 * ports[0], F(0)) for row in precode_inverse] + need(heights([{i: c for i, c in enumerate(witness) if c}])[1] == 0, + "A dyadic input gives the failing first packing basis vector") + need(heights([r[0]])[1] == 1, "That unscaled input has a genuine third") + return {"source": str(SOURCE.relative_to(LANES)), "source_sha256": SOURCE_PIN, + "packing_ports": source["packing_ports"], + "words": {"code": code, "adjoint": adjoint}}, { + "code": report, "adjoint": inverse_report, + "trace": list(map(str, trace)), "power_checks": powers, + "all_positive_power_odd_height": "m, by the trace and spectral-radius proof", + "untouched_complex_fields": 528, "full_real_columns": 1280} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + a = realify([[(1, 0), (1, 1)], [(-1, 1), (1, 0)]]) + b = realify([[(1, -1), (0, -1)], [(0, -1), (1, 1)]]) + need(product(transpose(a), a) == scaled(eye(4), 3), "A* A = 3I") + need(product(transpose(b), b) == scaled(eye(4), 3), "B* B = 3I") + p = eye(8) + p[2], p[4], p[3], p[5] = p[4], p[2], p[5], p[3] + numerator = product(product(direct_sum(transpose(a), 2), p), direct_sum(b, 2)) + r = scaled(numerator, F(1, 3)) + need(product(transpose(r), r) == product(r, transpose(r)) == eye(8), + "Both exact unitary orders") + word = sum((packing_word(4 * block) for block in range(4)), []) + inverse = inverse_word(word) + expected = direct_sum(r, 4) + eye(1280)[32:] + forward, fw = replay(word) + backward, bw = replay(inverse) + need(forward == expected, "All 1280 real columns of the forward word") + need(backward == transpose(expected), "All 1280 real columns of the inverse") + need(product(forward, backward) == product(backward, forward) == eye(1280), + "Both full inverse orders with arbitrary borrowed columns") + rank, reduced = rank_three(numerator) + need(rank == 2, "Two real, or one Gaussian, residue constraints per block") + need(integer_word(word, 3) and integer_word(inverse, 3), + "One paid root factor gives integer prefixes in each direction") + need(not integer_word(word, 1) and not integer_word(inverse, 1), + "The unscaled arbitrary input contract fails") + need(replay(word + inverse)[0] == eye(1280), "Exact complete restoration") + need(integer_word(word + inverse, 3), "One root factor for the restored pair") + powers, matrix = [], eye(8) + for exponent in range(1, 13): + matrix = product(r, matrix) + powers.append({"power": exponent, "odd_height": heights(matrix)[1]}) + need(product(product(r, r), product(r, r)) == eye(8), "The packing has order four") + sign = eye(8) + sign[0], sign[1] = {0: F(-1)}, {1: F(-1)} + signed_numerator = product(numerator, sign) + need(rank_three(signed_numerator)[0] == 2, "The signed residue has Gaussian rank one") + signed_trace = [sum((signed_numerator[2 * i + k].get(2 * i, F(0)) + for i in range(4)), F(0)) for k in (0, 1)] + need(signed_trace == [F(-2), F(2)], "The nonzero signed residue trace") + damaged = [event for i, event in enumerate(word) if i != 0] + need(replay(damaged)[0] != expected, "An omitted scalar gate is rejected") + program = {"A_real": serialized(a), "B_real": serialized(b), + "R_real": serialized(r), "numerator_real": serialized(numerator), + "residue_reduced_rows": reduced[:rank], + "words": {"packing": word, "inverse": inverse}} + actual, actual_report = actual_code(word, inverse, r) + program["actual_code"] = actual + receipt = {"status": "PASS_RATIONAL_PACKING_GRID", + "packing": fw, "inverse": bw, "residue_rank_real": rank, + "full_real_columns": 1280, "untouched_complex_fields": 624, + "signed_scan_cases": scan_checks(), "repeated_packing": powers, + "signed_interleaving_trace": list(map(str, signed_trace)), + "actual_code": actual_report} + for name, data in (("PACKING.json", program), ("CHECKS.json", receipt)): + raw = (json.dumps(data, sort_keys=True, indent=2) + "\n").encode() + (args.out / name).write_bytes(raw) + print(name, sha256(raw).hexdigest()) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json new file mode 100644 index 0000000000..30776ef158 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/FREEZE.json @@ -0,0 +1,15 @@ +{ + "files": { + "GENERAL-READER.md": "b8fb7892bc351fb3f872b81526e3f6b3c311525942a1283413e3e14b86313e9a", + "PEER-REVIEW.md": "428f1085e7c4cba5f178c09309b23b16f7a8569cbc58cc2ea1ad62cb0fbfa977", + "REPRODUCTION.json": "798531c4347439aca79fcf4f52f1209eabc8982f154ce1ee7aa5fbd53fd35cce", + "REVIEW.md": "da80ad6a9ad957fa4de2f7a81d5d6e3a573947b1d8a32057ae4d5300dee0f42c", + "check_review.py": "c1caa97a3929c3750e6e663c2d7429297a1e50e7a835264ee7ecde17c47f0b7e", + "normal/REVIEW-CHECKS.json": "18226da65a8eb6e07f716d328451107e97c8905c2c429edfe54608310e97e1a9", + "optimized/REVIEW-CHECKS.json": "18226da65a8eb6e07f716d328451107e97c8905c2c429edfe54608310e97e1a9" + }, + "producer_dual_freeze_sha256": "92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455", + "producer_reuse_freeze_sha256": "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf", + "schema": "independent-fixed-reader-review-freeze-v1", + "scope": "Independent D25 query, carrier phase and typed dual review. Complete native integration and supplier admission are separate." +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/GENERAL-READER.md b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/GENERAL-READER.md new file mode 100644 index 0000000000..841cd48bc5 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/GENERAL-READER.md @@ -0,0 +1,111 @@ +# A reusable query for an arbitrary old reader + +This theorem extends the fixed-reader factorization from the +bridge-access lane. It uses ordered operators. It does not assume +that spatial maps commute. + +Let X and Z be modules over the coefficient ring. Let J insert a centre +module into X, and let P select it, so \(PJ=I\). Suppose the current +reader and response satisfy + +\[ +L_tJ=I,\qquad E_t=I+A_tL_t. +\] + +Put \(B_t=L_t-P\) and \(C_t=I+JB_t\). Since \(B_tJ=0\), the code is a +unit with \(C_t^{-1}=I-JB_t\). Let \(L_s:X\to Z\) be any old reader. +Define + +\[ +W=L_sJ,\qquad B_s=L_s-WP,\qquad M=L_sE_tJ. +\] + +Then \(B_sJ=0\), and + +\[ +\boxed{L_sE_tC_t^{-1}=B_s-WB_t+MP.} +\] + +To prove the identity, keep the order of all factors: + +\[ +\begin{aligned} +E_tC_t^{-1} + &=(I+A_tL_t)(I-JB_t)\\ + &=I-JB_t+A_t(L_t-B_t)\\ + &=I-JB_t+A_tP. +\end{aligned} +\] + +Multiplication by \(L_s\), followed by +\(L_s=B_s+WP\) and \(M=W+L_sA_t\), gives the stated identity. + +The following six-step query therefore works for arbitrary independent +X and Z inputs: + +1. Add \(B_sX\) to Z. +2. Add \(WPX\) to Z. +3. Apply \(C_t\) to X. +4. Subtract the new \(WPX\) from Z. +5. Add \(MPX\) to Z. +6. Apply \(C_t^{-1}\) to X. + +The resulting map is + +\[ +(X,Z)\longmapsto(X,Z+L_sE_tX). +\] + +In particular, steps 2 and 4 contribute \(-WB_tX_{\rm initial}\), +and step 5 contributes \(ML_tX_{\rm initial}\). Each X field is +restored. Z keeps its arbitrary baseline. An inverse of E is never +used. Neither invertibility of E nor a zero selected block of E is +required. + +The map W is a service obligation. It must act additively on Z, and its +access and implementation must be priced. An in-place application of W +to an existing centre value does not by itself give this additive +service. No inverse of W is required by the theorem. + +The theorem is a query identity. It does not by itself make \(L_s\) +a unit encoding of a complete target bank. Such an encoding requires +a unit completion of \(L_s\). If the centre width and the ordinary +coordinates R stay the same, this completion is +\(\left[\begin{smallmatrix}W&B_s\\0&I\end{smallmatrix}\right]\). +It is a unit exactly when W is a unit on the centre space. A completion +with different ordinary coordinates changes the interface and needs +its own implementation. The query identity itself also permits singular W. +In the actual normalized case +\(L_sJ=I\), W is I and \(C_s=I+J(L_s-P)\) gives that completion. The +two W services are then plain same-port copies. Only this case has +the actual 11,168-scalar and 2,064-map invoice in `REVIEW.md`. + +The independent checker includes a finite example with two-dimensional +blocks + +\[ +T=\begin{bmatrix}0&1\\1&0\end{bmatrix},\quad +W=\begin{bmatrix}1&1\\0&1\end{bmatrix},\quad +S=\begin{bmatrix}2&1\\-1&0\end{bmatrix},\quad +A=\begin{bmatrix}-1&0\\0&1\end{bmatrix}. +\] + +Take \(L_t=[I,T]\), \(L_s=[W,S]\), and + +\[ +E_t=\begin{bmatrix}I+A&AT\\0&I\end{bmatrix}. +\] + +Here E is singular, its selected block is nonzero, and \(WT\ne TW\). +The six-step query passes all six independent input columns. The word +with plain copies in place of W fails. This example tests the removed +hypotheses. The ordered proof above applies to all modules and maps +with the stated types. + +This theorem does not emit a new native response family. It does not +provide a new complete supplier or a change to the selected frontier. +The actual native frame and access conditions remain those in the +separate D25 review. + +No publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/PEER-REVIEW.md b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/PEER-REVIEW.md new file mode 100644 index 0000000000..2859baa83a --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/PEER-REVIEW.md @@ -0,0 +1,27 @@ +# Peer check of the added consequences + +The bridge-access producer checked the new consequences on 2026-10-20. +This check concerns the new theorem and norm argument. It does not +serve as independent approval of that producer's original query. + +The producer accepted the arbitrary-reader identity and the two +additive W services. The producer requested one qualification: +with the same ordinary coordinates, the completed bank code is +\(\left[\begin{smallmatrix}W&B_s\\0&I\end{smallmatrix}\right]\), so it +is a unit exactly when W is a unit. `GENERAL-READER.md` now states +this condition. A different completion changes the interface. + +The producer also accepted the sharp norm argument on the regular +cover. At a fixed owner h, different route matrices A give different +owners \(hA\). The payload view for each route must also be retained. +The checked maps use the unique FULL conjugate \(\Psi_t(A)\), so this +condition holds. The claim concerns emitted scalar and map boundaries. +It excludes quotient covers, internal scalar arithmetic, and native +child interiors. + +The producer confirmed the chronology of pair \((0,2)\): reader zero +has been carried through physical level one. It is not a skipped +physical advance. + +All producer freezes remain unchanged. The later native dispatcher +has a separate freeze and is outside this review. diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..1ac718edf9 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REPRODUCTION.json @@ -0,0 +1,11 @@ +{ + "commands": [ + "python3 check_review.py --output normal", + "python3 -O check_review.py --output optimized" + ], + "normal_optimized_byte_equal": true, + "python": "3.14.7 (main, Aug 5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]", + "receipt_sha256": "18226da65a8eb6e07f716d328451107e97c8905c2c429edfe54608310e97e1a9", + "schema": "independent-fixed-reader-reproduction-v1", + "status": "PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL" +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REVIEW.md new file mode 100644 index 0000000000..e21b9062e8 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/REVIEW.md @@ -0,0 +1,283 @@ +# Independent review of the fixed-reader query + +The forward query is correct for all three declared D25 pairs. The +literal query restores all 112 source fields. It preserves each arbitrary +target baseline and all 416 outside fields. Its price is 11,168 real +scalar primitives and 2,064 monomial map calls. It uses no native child +and no extra field. + +The sixteen positive H8 carrier phase identities and the retained path +conditions pass independent checks. These results do not verify an +integrated native reuse word. The complete supplier, map price, child +hosting, and recursive precision remain separate. + +The separate typed inverse-adjoint lemma is correct. This review also +emits its late query in memory and checks its exact map on all 640 +arbitrary input columns. This is a check of the late query, not a complete +native backward service. + +## Frozen inputs and method + +The forward source is +`../../bridge-access-20261017/row-capture-access-20261020/REUSE-FREEZE.json`, +SHA-256 +`41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf`. +The separate dual source is `DUAL-FREEZE.json` in that directory, +SHA-256 +`92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455`. +The checker validates both freezes and their files before it starts. +It also validates the earlier formation freeze. + +`check_review.py` imports no producer code. It uses exact rational +arithmetic and a separate Z4 polynomial representation. It reads the +actual rank-sixteen native response, row-capture word, and D25 views. +The receipt records their full hashes. + +The review derives \(L=V_P^{-1}V\) from the actual factorization +\(E=I+UV\). The selected minor has determinant 16. The resulting L equals +the emitted reader. The review checks \(LJ=I\), \(E[P,P]=0\), +\(E=I+AL\), and both orders of the code inverse. Here J inserts the +sixteen selected fields and \(A=(E-I)J\). + +Both native providers have the same retained path count. The review +removes 128 H1 events and 122 scalar events that write selected Y. +No retained event reads these selected Y fields. No forward scalar +event feeds Y into X. The last source event is 2638. After the retained +sweep, all source fields are FULL, and the selected Y fields retain +their input type. + +## The algebra needs no inverse response + +Let P select the coordinates that J inserts, so \(PJ=I\). This P is +an operator; in the actual coordinate notation it is \(J^{\mathsf T}\). +Let + +\[ +L_tJ=I,\quad B_t=L_t-P,\quad +C_t=I+JB_t,\quad E_t=I+A_tL_t. +\] + +Then \(B_tJ=0\), so \(C_t^{-1}=I-JB_t\). Direct ordered +multiplication gives + +\[ +E_tC_t^{-1}=I-JB_t+A_tP. +\] + +For a normalized old reader \(L_sJ=I\), put \(B_s=L_s-P\) and +\(M=L_sE_tJ\). It follows that + +\[ +L_sE_tC_t^{-1}=B_s-B_t+MP. +\] + +The six steps in the producer follow: + +1. Add \(B_sX\) to the selected target bank. +2. Add \(PX\) to that bank. +3. Apply \(C_t\) to X. +4. Subtract the new \(PX\) from that bank. +5. Add \(MPX\) to that bank. +6. Apply \(C_t^{-1}\) to X. + +Steps 2 and 4 add \(-B_tX_{\rm initial}\). Step 5 adds +\(ML_tX_{\rm initial}\). Their sum with step 1 is +\(L_sE_tX_{\rm initial}\). The target baseline has coefficient I at +the endpoint. This argument does not commute operators at two stages. + +Neither \(E_t[P,P]=0\) nor invertibility of \(E_t\) is needed for this +identity. The former is a property of the actual inexpensive middle +query. It is not a hypothesis of the general factorization. + +`GENERAL-READER.md` records a separate extension to an arbitrary old +reader. It replaces the two copies by a paid map \(W=L_sJ\). +The actual invoice in this review applies only to \(W=I\). + +## Actual owner paths and source chronology + +The checker reconstructs all 336 D25 routes from the native q values +and the actual orthogonal chart rule. It checks the canonical Z4 +phase identities with a separate coefficient representation. The +canonical operator model itself is inherited from the source supplier +and the earlier formation and D25 reviews. + +The checked reader/service pairs are \((0,1),(0,2),(1,2)\). In each +case the physical level before service t is \(t-1\). The label s +identifies a retained reader. Thus \((0,2)\) assumes that reader \(L_0\) +was carried through stage one. It does not mean a physical jump from +level zero to stage two. + +At the adjacent entry, a selected FULL target becomes its positive +intrinsic line \(Q_p\), with the common exterior retained. An ordinary +hole target becomes I with the same exterior. The checker verifies +448 source/target FULL-to-Q identities and 224 hole-to-I identities +over all ports. It also verifies 672 past/current FULL view identities. +Omission of the positive intrinsic line gives a different phase. + +Each carrier uses eight orthogonal axes perpendicular to its actual +q, plus an explicit output translation. The full phase polynomial is +that of \(F_9Q_p^{-1}\), with no constant phase. All sixteen carriers +pass. The opposite intrinsic sign fails. + +For a term of \(L_sE_t\), the route is + +\[ +\rho_{s,p}\rho_{s,j}\rho_{t,j}\rho_{t,r}. +\] + +The independent multiplication retains this exact order. It combines +terms only if both the input field and the complete route agree. +There are 3,808 terms per pair. Restriction to the selected source +fields gives 696 terms. The first two pairs use 216 distinct middle +routes; the last pair uses 696. + +Every route A is orthogonal and fixes all uncompleted axes. At the +completed level t, its actual view is + +\[ +\Psi_t(A)=F_{9+8t}P_AF_{9+8t}^{-1} + =X_{\delta_A}P_A. +\] + +The checker verifies the entire Z4 difference polynomial and the +inverse translation \(A^{-1}\delta_A\). The map is a single owner and +payload map: the owner read is \(h\mapsto hA\), and the payload map +expresses that source chart in the target chart. + +The review expands the complete literal query. It applies each old +view, code view, temporary source map, scalar gate, and restoration map +in order. Its matrix is compared with the direct \(L_sE_t\) product on +all 640 arbitrary input columns. There is no zero baseline assumption. +The retained X rows are available only after the complete cover sweep. + +Two negative controls test route order. Commuting the middle stage +factors fails for \((1,2)\). Replacing an inverse source map by a second +copy of its forward map also fails. Stage zero is the identity, so it +cannot supply the first negative control. + +## Price and sharper local bounds + +The literal query gives: + +| Part | Real scalar primitives | Monomial maps | +| --- | ---: | ---: | +| Old complement query | 1,760 | 224 | +| Two copies | 256 | 0 | +| Current code and inverse | 3,520 | 448 | +| Middle query | 5,632 | 1,392 | +| Total | 11,168 | 2,064 | + +The middle uses 456 additions with coefficient -1 and 240 with +coefficient +1. It uses eight pairs of scales by 4 and 1/4. +The retained native word has scalar price 6,456. With sixteen H8 +carriers, its prospective profile is + +\[ +1392H_1+64H_2+48H_3+16H_8, +\] + +of total native rank 1,792. The prospective retained-word-plus-query +scalar price is 17,624. These counts do not include a finite price for +the 2,064 query maps, native wrappers, ordinary boundary maps, or +recursive hosting. + +The producer's conservative forward bounds, 972 and binary height 3, +are valid. Exact coefficient cancellation gives stronger bounds at +each emitted scalar or map boundary: + +| Late query | Maximum coefficient row sum | Maximum binary denominator height | +| --- | ---: | ---: | +| Forward | 448 | 2 | +| Inverse-adjoint | \(43/2\) | 3 | + +These values hold for all three pairs. The receipt gives the first +maximal row and exact denominator witnesses. For example, a forward +prefix contains a coefficient -1/4, and a dual prefix contains 1/8. +Thus the indicated coefficient heights cannot be reduced. + +Here the row sum also gives the sharp physical sup norm on the +regular cover. Each coefficient is attached to an input field and a +route A. At a fixed output owner h, distinct A give distinct source +owners \(hA\). The payload view for a given A is uniquely \(\Psi_t(A)\) +and is monomial. Therefore equal field/route terms can be combined +exactly, and the remaining independent source locations can take the +signs that attain the row sum. This statement uses the regular cover. +It does not assert sharpness on a quotient cover. + +The bounds concern complete emitted gates. They do not bound the +internal arithmetic states of a lowered scalar instruction, a native +child, or a recursive caller. They do not supply a complete precision +certificate. + +## The typed inverse-adjoint + +Let \(Q_P\) be the positive intrinsic line on the selected target +fields, with I on the other target fields. Let \(H_R\) be the inverse +intrinsic line on the ordinary target fields, with I on the selected +fields. Put + +\[ +F_{\rm in}=\operatorname{diag}(Q,Q_P),\qquad +F_{\rm out}=\operatorname{diag}(F,FH_R),\qquad A=C_sE_t. +\] + +The exterior factors and cover views belong to these unitary frames. +For an integrated forward word, the physical operator is + +\[ +U=F_{\rm out} +\begin{bmatrix}I&0\\A&I\end{bmatrix}F_{\rm in}^{-1}. +\] + +For a chronological word \(U=G_n\cdots G_1\), its inverse-adjoint is +\(G_n^{-*}\cdots G_1^{-*}\). Thus the chronological gate order stays +the same. Unitary native and monomial gates stay the same. An ADD +\(b\leftarrow b+ca\) becomes \(a\leftarrow a-\overline c b\), and a +real unit SCALE becomes its reciprocal. Therefore + +\[ +U^{-*}=F_{\rm out} +\begin{bmatrix}I&-E_t^*C_s^*\\0&I\end{bmatrix} +F_{\rm in}^{-1}. +\] + +This is an adjoint response, not a reciprocal response. It retains +the selected \(Q_P\) input type. + +The late dual query is checked independently by this gate transform. +It implements \(X\leftarrow X-E_t^*L_s^*Y_P\), retains every selected +Y baseline at its endpoint, and leaves ordinary Y and outside fields +unchanged. Its maps have the same order, and it reads only the FULL +selected Y fields. The complete route in each adjoint coefficient is +the inverse of the forward route. The price is unchanged. The +different prefix bounds are computed separately. + +This proves the conditional circuit lemma and the emitted late query. +It does not replace the missing integrated native forward and backward +replays. It also does not provide a controller that accepts these +boundary types. + +## Reproduction and credit + +Run from this directory: + +```text +python3 check_review.py --output normal +python3 -O check_review.py --output optimized +``` + +Both commands must print +`PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL`. +The two `REVIEW-CHECKS.json` files must be byte equal. + +The bridge-access lane supplied the fixed-reader factorization, literal +D25 query, and typed dual lemma. The controller lane supplied the +normalized row capture. The new-core-transfer lane supplied the +rank-sixteen native response. This review supplies independent route, +phase, map-order, and arbitrary-input checks. It adds the arbitrary-reader +form and the sharper local prefix bounds. The bridge-access author +separately checked the regular-cover norm argument and the weaker +algebraic hypotheses. AI research agents produced these local records. + +No publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/check_review.py b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/check_review.py new file mode 100644 index 0000000000..d06084e8c0 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/check_review.py @@ -0,0 +1,680 @@ +"""Check the fixed-reader query without producer code imports.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from functools import cache +import gzip +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +PRODUCER = LANES / "bridge-access-20261017/row-capture-access-20261020" +UNIT = tuple(1 << i for i in range(25)) +PIVOTS = (0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23) +PSET = set(PIVOTS) +REUSE_PIN = "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf" +DUAL_PIN = "92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455" +PINS = { + "capture": ( + "controller-followthrough-20261017/row-capture-20261020/" + "run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7", + ), + "native": ( + "new-core-transfer-20261017/low-displacement-20261020/" + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + ), + "views": ( + "bridge-access-20261017/matched-stage-access-20261018/" + "DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), +} + + +def require(test, message): + if not test: + raise ValueError(message) + + +def digest(raw): + return sha256(raw).hexdigest() + + +def pinned_json(path, pin, compressed=False): + raw = path.read_bytes() + if compressed: + raw = gzip.decompress(raw) + require(digest(raw) == pin, "Pin: " + str(path)) + return json.loads(raw) + + +def put(row, key, value): + value += row.get(key, F(0)) + if value: + row[key] = value + else: + row.pop(key, None) + + +def sparse(raw): + return [{int(j): F(v) for j, v in row.items() if F(v)} for row in raw] + + +def eye(n): + return [{i: F(1)} for i in range(n)] + + +def matmul(a, b): + result = [] + for row in a: + out = {} + for j, value in row.items(): + for k, other in b[j].items(): + put(out, k, value * other) + result.append(out) + return result + + +def invert(a): + n = len(a) + rows = [[a[i].get(j, F(0)) for j in range(n)] + + [F(i == j) for j in range(n)] for i in range(n)] + determinant = F(1) + for j in range(n): + p = next((i for i in range(j, n) if rows[i][j]), None) + require(p is not None, "The pivot minor is a unit over Q") + if p != j: + rows[j], rows[p] = rows[p], rows[j] + determinant = -determinant + value = rows[j][j] + determinant *= value + rows[j] = [v / value for v in rows[j]] + for i in range(n): + if i != j and rows[i][j]: + value = rows[i][j] + rows[i] = [x - value * y for x, y in zip(rows[i], rows[j])] + return [{j: v for j, v in enumerate(row[n:]) if v} for row in rows], determinant + + +def scalar_word(rows, word): + result = [dict(row) for row in rows] + for op, dst, src, value in word: + value = F(value) + if op == "scale": + result[dst] = {j: value * v for j, v in result[dst].items()} + else: + require(op == "add" and src != dst, "Scalar ADD") + for j, v in result[src].items(): + put(result[dst], j, value * v) + return result + + +def apply(a, vector): + result = 0 + while vector: + bit = vector & -vector + result ^= a[bit.bit_length() - 1] + vector ^= bit + return result + + +@cache +def product(a, b): + return tuple(apply(a, x) for x in b) + + +def transpose(a): + return tuple(sum(((a[j] >> i) & 1) << j for j in range(25)) + for i in range(25)) + + +def route_product(*args): + result = UNIT + for a in args: + result = product(result, a) + return result + + +def dot(a, b): + return (a & b).bit_count() & 1 + + +def chart(q): + hole = next(i for i in range(9) if not (q >> i) & 1) + vector = q ^ (1 << hole) + order = list(range(9)) + order[0], order[hole] = order[hole], order[0] + basis = tuple((1 << i) ^ (vector if (vector >> i) & 1 else 0) + for i in order) + UNIT[9:] + require(basis[0] == q and product(transpose(basis), basis) == UNIT, + "Independent port chart") + return basis + + +def route(q, stage): + if not stage: + return UNIT + basis = chart(q) + swaps = [basis[j + 1] ^ UNIT[9 + 8 * (stage - 1) + j] for j in range(8)] + return tuple(x ^ xor(v for v in swaps if dot(v, x)) for x in UNIT) + + +def xor(values): + result = 0 + for value in values: + result ^= value + return result + + +@cache +def line_phase(vector, exponent): + exponent %= 4 + linear = tuple(exponent if (vector >> i) & 1 else 0 for i in range(25)) + quadratic = 0 + if exponent & 1: + for i in range(25): + if (vector >> i) & 1: + for j in range(i + 1, 25): + if (vector >> j) & 1: + quadratic ^= 1 << (25 * i + j) + return linear, quadratic + + +ZERO_PHASE = ((0,) * 25, 0) + + +def add_phase(a, b): + return tuple((x + y) % 4 for x, y in zip(a[0], b[0])), a[1] ^ b[1] + + +def minus_phase(a): + return tuple(-x % 4 for x in a[0]), a[1] + + +def sum_phase(terms): + result = ZERO_PHASE + for vector, exponent in terms: + result = add_phase(result, line_phase(vector, exponent)) + return result + + +@cache +def full_phase(level, a=UNIT): + return sum_phase((a[j], 1) for j in range(9 + 8 * level)) + + +def phase_translation(phase): + require(phase[1] == 0 and all(x % 2 == 0 for x in phase[0]), + "The phase difference is a translation") + return sum((x // 2) << i for i, x in enumerate(phase[0])) + + +def routed_matrix(rows, targets, stage, routes): + return [{(r, product(routes[stage, p], routes[stage, r])): value + for r, value in row.items()} + for p, row in zip(targets, rows)] + + +def multiply_routed(a, b): + result = [] + for row in a: + out = {} + for (j, ra), value in row.items(): + for (k, rb), other in b[j].items(): + put(out, (k, product(ra, rb)), value * other) + result.append(out) + return result + + +def real_price(op, value): + value = F(value) + numerator, denominator = abs(value.numerator), value.denominator + require(numerator and denominator & (denominator - 1) == 0, "Dyadic coefficient") + if op == "scale": + require(numerator & (numerator - 1) == 0, "Dyadic unit scale") + return 2 * (abs(numerator.bit_length() - denominator.bit_length()) + (value < 0)) + return 2 * (3 + numerator.bit_length() - 1 + numerator.bit_count() + + denominator.bit_length() - 1) + + +def replay(operations, dual=False): + rows = [{(i, UNIT): F(1)} for i in range(640)] + bounds = [F(1)] * 640 + grid = [0] * 640 + peak, height = F(1), 0 + exact_peak, exact_height = F(1), 0 + norm_witness = None + height_witness = None + bill = Counter() + for index, (op, dst, src, value) in enumerate(operations): + if op == "map": + rows[dst] = {(j, product(value, a)): c for (j, a), c in rows[dst].items()} + bill["maps"] += 1 + continue + if dual and op == "add": + dst, src, value = src, dst, -value + elif dual and op == "scale": + value = 1 / value + bill["real_scalar"] += real_price(op, value) + if op == "scale": + rows[dst] = {j: value * v for j, v in rows[dst].items()} + bounds[dst] *= abs(value) + grid[dst] = max(0, grid[dst] + value.denominator.bit_length() + - abs(value.numerator).bit_length()) + else: + for j, v in rows[src].items(): + put(rows[dst], j, value * v) + bounds[dst] += abs(value) * bounds[src] + grid[dst] = max(grid[dst], grid[src] + value.denominator.bit_length() - 1) + peak, height = max(peak, bounds[dst]), max(height, grid[dst]) + current_norm = sum(abs(v) for v in rows[dst].values()) + current_height = max((v.denominator.bit_length() - 1 for v in rows[dst].values()), + default=0) + if current_norm > exact_peak: + exact_peak = current_norm + norm_witness = {"event_index": index, "target": dst, + "coefficient_terms": len(rows[dst]), + "coefficient_census": dict(Counter(str(c) for c in rows[dst].values()))} + if current_height > exact_height: + exact_height = current_height + (origin, a), coefficient = next( + (key, c) for key, c in rows[dst].items() + if c.denominator.bit_length() - 1 == current_height) + height_witness = {"event_index": index, "target": dst, + "origin": origin, "route": a, "coefficient": str(coefficient)} + return rows, dict(bill), peak, height, { + "coefficient_row_sum_peak": str(exact_peak), + "coefficient_binary_height": exact_height, + "norm_witness": norm_witness, "height_witness": height_witness} + + +def isolation(word, ports): + selected = {112 + p for p in PIVOTS} + frames = list(word["start"]) + require(len(frames) == len(word["final"]) == 640, "All literal input fields") + require(set(word["frames"][1]) == set(UNIT[:9]), "Literal local FULL frame") + require(all(word["frames"][frames[p]] == [ports[p]] for p in range(112)), + "The literal source lines are the actual model ports") + for p in PIVOTS: + frames[112 + p] = frames[p] + initial = list(frames) + count = Counter() + native = Counter() + last_x = None + for i, event in enumerate(word["events"]): + op = event[0] + dst = event[1] if op == "native" else event[1][1] + if dst < 112: + last_x = i + if dst in selected: + count["removed_" + op] += 1 + if op == "native": + require(event[4] == 1, "Removed selected children have rank one") + continue + if op == "native": + _, dst, old, new, rank, _ = event + require(frames[dst] == old, "Retained native frame") + frames[dst] = new + native[rank] += 1 + else: + require(op == "scalar", "Retained event kind") + _, (kind, dst, src, coefficient), frame = event + require(src not in selected, "The retained word does not read selected Y") + require(frames[dst] == frame and (src is None or frames[src] == frame), + "Retained scalar frames") + require(not (dst < 112 and src is not None and src >= 112), + "The source word does not read target fields") + count["retained_scalar"] += real_price(kind, F(coefficient)) + require(count == {"removed_native": 128, "removed_scalar": 122, + "retained_scalar": 6456}, "Native deletion and scalar invoice") + require(last_x == 2638 and len(word["events"]) == 2640, "The complete source cut") + require(all(frames[p] == 1 for p in range(112)), "All source fields are FULL") + require(all(frames[t] == initial[t] for t in selected), "Selected Q fields are retained") + require(all(frames[i] == word["final"][i] for i in range(640) if i not in selected), + "Other final frames") + require(all(word["start"][i] == word["final"][i] for i in range(224, 640)), + "Outside frame endpoints") + require(native == {1: 1392, 2: 64, 3: 48}, "Retained child census") + native[8] += 16 + require(sum(k * n for k, n in native.items()) == 1792, "Prospective native mass") + return {"deletion": dict(count), "last_source_event": last_x, + "prospective_native_profile": dict(native), "prospective_native_mass": 1792} + + +def general_reader_example(): + t = [{1: F(1)}, {0: F(1)}] + w = [{0: F(1), 1: F(1)}, {1: F(1)}] + b = [{0: F(2), 1: F(1)}, {0: F(-1)}] + a = [{0: F(-1)}, {1: F(1)}] + selected_e = [{}, {1: F(2)}] + m = matmul(w, selected_e) + computed_selected = eye(2) + for row, correction in zip(computed_selected, a): + for j, value in correction.items(): + put(row, j, value) + require(computed_selected == selected_e and not selected_e[0] and bool(selected_e[1]), + "The selected response is nonzero and singular") + require(matmul(w, t) != matmul(t, w), "The general reader example does not commute") + + def mv(matrix, vector): + return [sum(value * vector[j] for j, value in row.items()) for row in matrix] + + def add(left, right, sign=1): + return [x + sign * y for x, y in zip(left, right)] + + wrong_copy = False + for column in range(6): + initial = [F(i == column) for i in range(6)] + xp, xr, z = initial[:2], initial[2:4], initial[4:] + ex_p = add(mv(selected_e, xp), mv(matmul(a, t), xr)) + desired = add(z, add(mv(w, ex_p), mv(b, xr))) + z = add(z, mv(b, xr)) + z = add(z, mv(w, xp)) + changed = add(xp, mv(t, xr)) + z = add(z, mv(w, changed), -1) + z = add(z, mv(m, changed)) + restored = add(changed, mv(t, xr), -1) + require(restored == xp and z == desired, "The arbitrary-reader six-step identity") + wrong = add(initial[4:], mv(b, xr)) + wrong = add(wrong, xp) + wrong = add(wrong, changed, -1) + wrong = add(wrong, mv(m, changed)) + wrong_copy |= wrong != desired + require(wrong_copy, "A nonidentity W cannot be replaced by two plain copies") + return {"arbitrary_input_columns": 6, "E_is_singular": True, + "E_selected_block_is_nonzero": True, "W_and_B_t_do_not_commute": True, + "plain_copy_negative_control": "fails"} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, default=HERE / "normal") + args = parser.parse_args() + frozen = pinned_json(PRODUCER / "REUSE-FREEZE.json", REUSE_PIN) + for name, pin in frozen["files"].items(): + require(digest((PRODUCER / name).read_bytes()) == pin, "Producer file: " + name) + formation = pinned_json(PRODUCER / "FREEZE.json", frozen["formation_freeze_sha256"]) + for name, pin in formation["files"].items(): + require(digest((PRODUCER / name).read_bytes()) == pin, "Formation file: " + name) + dual = pinned_json(PRODUCER / "DUAL-FREEZE.json", DUAL_PIN) + require(digest((PRODUCER / "DUAL.md").read_bytes()) == dual["proof_sha256"], + "The dual proof pin") + require(dual["reuse_freeze_sha256"] == REUSE_PIN, "The dual dependency pin") + sources = {name: pinned_json(LANES / path, pin, path.endswith(".gz")) + for name, (path, pin) in PINS.items()} + capture, native, views = (sources[k] for k in ("capture", "native", "views")) + emitted = json.loads((PRODUCER / "reuse-normal/REUSE-PROGRAM.json").read_bytes()) + require(tuple(capture["pivots"]) == tuple(emitted["pivots"]) == PIVOTS, "Pivots") + model = native["model"] + e, u, v = (sparse(model[k]) for k in ("response", "correction_U", "correction_V")) + expected_e = eye(112) + for row, correction in zip(expected_e, matmul(u, v)): + for j, value in correction.items(): + put(row, j, value) + require(e == expected_e == sparse(capture["response"]), "The actual E = I + UV") + vp = [{j: row[p] for j, p in enumerate(PIVOTS) if p in row} for row in v] + vpi, vp_det = invert(vp) + reader = matmul(vpi, v) + require(reader == sparse(capture["centre_reader"]), "Independent reader derivation") + require(all({j: value for j, value in row.items() if j in PSET} == {p: F(1)} + for row, p in zip(reader, PIVOTS)), "LJ = I") + require(all(not (set(e[p]) & PSET) for p in PIVOTS), "E[P,P] = 0") + a = [{j: e[i].get(p, F(0)) - F(i == p) + for j, p in enumerate(PIVOTS) if e[i].get(p, F(0)) != F(i == p)} + for i in range(112)] + reconstructed_e = eye(112) + for row, correction in zip(reconstructed_e, matmul(a, reader)): + for j, value in correction.items(): + put(row, j, value) + require(reconstructed_e == e, "E = I + A L") + code = eye(112) + inverse = eye(112) + for p, row in zip(PIVOTS, reader): + code[p] = dict(row) + for r, value in row.items(): + if r != p: + inverse[p][r] = -value + require(code == sparse(capture["code"]) and inverse == sparse(capture["code_inverse"]), + "Independent capture maps") + require(matmul(code, inverse) == matmul(inverse, code) == eye(112), "Both inverse orders") + for key, target in (("scalar_word", code), ("inverse_scalar_word", inverse)): + require(scalar_word(eye(112), capture[key]) == target, "Literal capture word: " + key) + require(sum(real_price(op, F(c)) for op, _, _, c in capture[key]) == 1760, + "Capture price: " + key) + require(all(dst in PSET and (src is None or src not in PSET) + for _, dst, src, _ in capture[key]), "Complement-only capture word") + provider_checks = {name: isolation(value["forward"], model["ports"]) + for name, value in native["providers"].items()} + records = {(r["stage"], r["port"]): r for r in views["entries"]} + require(set(records) == {(s, p) for s in range(3) for p in range(112)}, + "All actual D25 views") + routes = {} + phase_checks = Counter() + for (stage, p), record in records.items(): + q = model["ports"][p] + require(record["q"] == q, "Actual native q") + rho = route(q, stage) + routes[stage, p] = rho + require(rho == tuple(record["route_columns"]), "Independent D25 route") + require(product(rho, rho) == UNIT and transpose(rho) == rho + and apply(rho, q) == q, "Route properties") + align = record["literal_stage_alignment"] + for level in range(stage, 3): + actual = add_phase(full_phase(level, rho), line_phase(align["exit_X"], 2)) + require(actual == full_phase(level), "Past-reader FULL view") + phase_checks["full_views"] += 1 + require(align["exit_X"] == align["exit_Y"], "Equal physical output translations") + if stage: + exterior = sum_phase((UNIT[j], 1) for j in range(9, 9 + 8 * stage)) + for name in ("entry_X", "entry_Y"): + actual = add_phase(full_phase(stage - 1, rho), + line_phase(apply(rho, align[name]), 2)) + expected = add_phase(exterior, line_phase(q, 1)) + require(actual == expected and actual != exterior, + "An adjacent physical FULL entry has the positive intrinsic line") + phase_checks["adjacent_full_to_Q"] += 1 + ordinary = add_phase(actual, line_phase(q, -1)) + require(ordinary == exterior, "An adjacent hole entry has the identity type") + phase_checks["adjacent_hole_to_I"] += 1 + carrier_checks = [] + for rec in emitted["carrier_recipes"]: + p, q = rec["port"], model["ports"][rec["port"]] + basis = tuple(rec["basis_columns"]) + expected_basis = chart(q)[1:9] + chart(q)[:1] + UNIT[9:] + require(basis == expected_basis and rec["q"] == q and rec["rank"] == 8, + "Actual H8 carrier basis") + require(tuple(rec["inverse_columns"]) == transpose(basis) + and product(transpose(basis), basis) == UNIT, "Carrier orthogonality") + desired = add_phase(full_phase(0), line_phase(q, -1)) + implemented = add_phase(sum_phase((b, 1) for b in basis[:8]), + line_phase(rec["output_translation"], 2)) + require(implemented == desired, "Exact H8 carrier phase") + require(implemented != add_phase(full_phase(0), line_phase(q, 1)), + "Negative control: the opposite intrinsic sign fails") + carrier_checks.append({"port": p, "q": q, "translation": rec["output_translation"]}) + require({c["port"] for c in carrier_checks} == PSET, "All sixteen carriers") + pair_checks = [] + for pair in emitted["pairs"]: + s, t = pair["reader_stage"], pair["service_stage"] + ls = routed_matrix(reader, PIVOTS, s, routes) + lt = routed_matrix(reader, PIVOTS, t, routes) + et = routed_matrix(e, range(112), t, routes) + direct = multiply_routed(ls, et) + middle = [{key: value for key, value in row.items() if key[0] in PSET} + for row in direct] + require(sum(map(len, direct)) == 3808 and sum(map(len, middle)) == 696, + "Independent owner-path counts") + prefix = 9 + 8 * t + route_table = pair["middle_routes"] + for record in route_table: + a, ai = tuple(record["columns"]), tuple(record["inverse_columns"]) + require(ai == transpose(a) and product(a, ai) == product(ai, a) == UNIT, + "The source map inverse") + require(a[prefix:] == UNIT[prefix:], "Every uncompleted axis is fixed") + delta = phase_translation(add_phase(full_phase(t), minus_phase(full_phase(t, a)))) + reverse_delta = phase_translation( + add_phase(full_phase(t), minus_phase(full_phase(t, ai)))) + require(record["FULL_translation"] == delta + and record["inverse_FULL_translation"] == reverse_delta + and reverse_delta == apply(ai, delta), "Complete map and inverse phases") + for label, stage in (("old_reader_views", s), ("current_code_views", t)): + require({rec["port"] for rec in pair[label]} == set(range(112)), "All FULL views") + for rec in pair[label]: + require(tuple(rec["route_columns"]) == routes[stage, rec["port"]] + and rec["translation"] == + records[stage, rec["port"]]["literal_stage_alignment"]["exit_X"], + "Emitted FULL view") + require(pair["old_reader_view_ports"] == + {"X": sorted(set(range(112)) - PSET), "Y": list(PIVOTS)}, "Old reader fields") + operations = [] + part_invoices = [] + + def scalar(op, dst, src, coefficient): + operations.append((op, dst, src, F(coefficient))) + + def maps(stage, ports, offset): + for p in ports: + operations.append(("map", offset + p, None, routes[stage, p])) + + def mark(name, begin): + part = operations[begin:] + part_invoices.append({ + "part": name, + "maps": sum(op == "map" for op, _, _, _ in part), + "real_scalar": sum(real_price(op, value) for op, _, _, value in part + if op != "map"), + }) + + begin = len(operations) + ordinary = sorted(set(range(112)) - PSET) + maps(s, ordinary, 0) + maps(s, PIVOTS, 112) + for op, p, r, value in capture["scalar_word"]: + scalar(op, 112 + p, r, value) + maps(s, ordinary, 0) + maps(s, PIVOTS, 112) + mark("old_complement", begin) + begin = len(operations) + for p in PIVOTS: + scalar("add", 112 + p, p, 1) + mark("first_copy", begin) + begin = len(operations) + maps(t, range(112), 0) + for op, p, r, value in capture["scalar_word"]: + scalar(op, p, r, value) + maps(t, range(112), 0) + mark("current_code", begin) + begin = len(operations) + for p in PIVOTS: + scalar("add", 112 + p, p, -1) + mark("second_copy", begin) + begin = len(operations) + middle_rows = [{} for _ in PIVOTS] + pindex = {p: i for i, p in enumerate(PIVOTS)} + integer_census = Counter() + for op, p, r, value, route_id in pair["middle_query"]: + value = F(value) + if op == "scale": + require(r is None and route_id is None, "Middle scale format") + middle_rows[pindex[p]] = { + key: value * v for key, v in middle_rows[pindex[p]].items()} + scalar(op, 112 + p, None, value) + else: + require(op == "mapped_add_restore" and p in PSET and r in PSET, + "The middle query reads existing centres") + require(value.denominator == 1, "The middle ADD is integral") + integer_census[str(value)] += 1 + a = tuple(route_table[route_id]["columns"]) + ai = tuple(route_table[route_id]["inverse_columns"]) + put(middle_rows[pindex[p]], (r, a), value) + operations.append(("map", r, None, a)) + scalar("add", 112 + p, r, value) + operations.append(("map", r, None, ai)) + require(middle_rows == middle, "The emitted middle query equals the independent product") + mark("middle", begin) + begin = len(operations) + maps(t, range(112), 0) + for op, p, r, value in capture["inverse_scalar_word"]: + scalar(op, p, r, value) + maps(t, range(112), 0) + mark("current_inverse", begin) + actual, bill, peak, height, exact_prefix = replay(operations) + expected = [{(i, UNIT): F(1)} for i in range(640)] + for p, row in zip(PIVOTS, direct): + for key, value in row.items(): + put(expected[112 + p], key, value) + require(actual == expected, "All 640 arbitrary input columns of the complete query") + require(bill == {"maps": 2064, "real_scalar": 11168} + and peak == 972 and height == 3, "Independent complete query invoice and bounds") + require(exact_prefix["coefficient_row_sum_peak"] == "448" + and exact_prefix["coefficient_binary_height"] == 2, + "Sharper forward bounds at emitted gate boundaries") + actual_dual, dual_bill, dual_peak, dual_height, exact_dual_prefix = replay( + operations, dual=True) + expected_dual = [{(i, UNIT): F(1)} for i in range(640)] + for p, row in zip(PIVOTS, direct): + for (r, a), value in row.items(): + put(expected_dual[r], (112 + p, transpose(a)), -value) + require(actual_dual == expected_dual, "All 640 input columns of the literal late dual query") + require(dual_bill == bill, "The dual query keeps the invoice") + require(exact_dual_prefix["coefficient_row_sum_peak"] == "43/2" + and exact_dual_prefix["coefficient_binary_height"] == 3, + "Sharper dual bounds at emitted gate boundaries") + unordered = [{} for _ in PIVOTS] + for row_index, (p, row) in enumerate(zip(PIVOTS, reader)): + for j, value in row.items(): + for r, other in e[j].items(): + wrong = route_product(routes[s, p], routes[t, j], + routes[s, j], routes[t, r]) + put(unordered[row_index], (r, wrong), value * other) + if s: + require(unordered != direct, "Negative control: inner stage factors cannot commute") + first_map = next((record for record in route_table + if tuple(record["columns"]) != tuple(record["inverse_columns"])), None) + require(first_map is not None, "Negative control has a noninvolutive map") + require(product(tuple(first_map["columns"]), tuple(first_map["columns"])) != UNIT, + "Negative control: repeat of the forward source map does not restore") + pair_checks.append({ + "reader_stage": s, "physical_level_before_service": t - 1, "service_stage": t, + "direct_paths": sum(map(len, direct)), "selected_paths": sum(map(len, middle)), + "distinct_middle_maps": len(route_table), + "middle_integer_census": dict(integer_census), "parts": part_invoices, + "query_invoice": bill, "triangle_prefix_bound": str(peak), "binary_height_bound": height, + "exact_prefix": exact_prefix, + "all_input_columns": 640, "unchanged_outside_fields": 416, + "dual_query_all_input_columns": 640, + "dual_triangle_prefix_bound": str(dual_peak), "dual_binary_height_bound": dual_height, + "dual_exact_prefix": exact_dual_prefix, + "ordered_factor_negative_control": "fails" if s else "stage zero is identity", + "wrong_inverse_map_negative_control": "fails", + }) + require({(r["reader_stage"], r["service_stage"]) for r in pair_checks} == + {(0, 1), (0, 2), (1, 2)}, "All three pairs") + output = { + "status": "PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL", + "checker_sha256": digest(Path(__file__).read_bytes()), + "producer_reuse_freeze_sha256": REUSE_PIN, + "producer_dual_freeze_sha256": DUAL_PIN, + "source_pins": PINS, "pivot_minor_determinant": str(vp_det), + "providers": provider_checks, "phase_checks": dict(phase_checks), + "H8_carriers": carrier_checks, "pairs": pair_checks, + "general_reader_example": general_reader_example(), + "producer_code_imported": False, + "complete_native_integration_checked": False, + "complete_supplier_claimed": False, + } + args.output.mkdir(parents=True, exist_ok=True) + raw = (json.dumps(output, indent=2, sort_keys=True) + "\n").encode() + (args.output / "REVIEW-CHECKS.json").write_bytes(raw) + print(output["status"]) + print(digest(raw)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/normal/REVIEW-CHECKS.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/normal/REVIEW-CHECKS.json new file mode 100644 index 0000000000..00610f175c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/normal/REVIEW-CHECKS.json @@ -0,0 +1,635 @@ +{ + "H8_carriers": [ + { + "port": 0, + "q": 11, + "translation": 15 + }, + { + "port": 27, + "q": 38, + "translation": 39 + }, + { + "port": 36, + "q": 146, + "translation": 147 + }, + { + "port": 111, + "q": 191, + "translation": 255 + }, + { + "port": 20, + "q": 161, + "translation": 163 + }, + { + "port": 7, + "q": 21, + "translation": 23 + }, + { + "port": 57, + "q": 56, + "translation": 57 + }, + { + "port": 46, + "q": 140, + "translation": 141 + }, + { + "port": 1, + "q": 19, + "translation": 23 + }, + { + "port": 3, + "q": 67, + "translation": 71 + }, + { + "port": 6, + "q": 13, + "translation": 15 + }, + { + "port": 8, + "q": 37, + "translation": 39 + }, + { + "port": 17, + "q": 81, + "translation": 83 + }, + { + "port": 18, + "q": 145, + "translation": 147 + }, + { + "port": 24, + "q": 385, + "translation": 387 + }, + { + "port": 23, + "q": 321, + "translation": 323 + } + ], + "checker_sha256": "c1caa97a3929c3750e6e663c2d7429297a1e50e7a835264ee7ecde17c47f0b7e", + "complete_native_integration_checked": false, + "complete_supplier_claimed": false, + "general_reader_example": { + "E_is_singular": true, + "E_selected_block_is_nonzero": true, + "W_and_B_t_do_not_commute": true, + "arbitrary_input_columns": 6, + "plain_copy_negative_control": "fails" + }, + "pairs": [ + { + "all_input_columns": 640, + "binary_height_bound": 3, + "direct_paths": 3808, + "distinct_middle_maps": 216, + "dual_binary_height_bound": 3, + "dual_exact_prefix": { + "coefficient_binary_height": 3, + "coefficient_row_sum_peak": "43/2", + "height_witness": { + "coefficient": "1/8", + "event_index": 3160, + "origin": 112, + "route": [ + 3584, + 3086, + 2574, + 1550, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 11, + 7, + 16, + 32, + 64, + 128, + 256, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 0 + }, + "norm_witness": { + "coefficient_census": { + "-1/2": 1, + "-1/4": 8, + "-1/8": 30, + "1": 1, + "1/2": 4, + "1/4": 24, + "1/8": 50 + }, + "coefficient_terms": 118, + "event_index": 3253, + "target": 21 + } + }, + "dual_query_all_input_columns": 640, + "dual_triangle_prefix_bound": "53", + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "448", + "height_witness": { + "coefficient": "-1/4", + "event_index": 1185, + "origin": 0, + "route": [ + 1034, + 1036, + 1, + 1030, + 16, + 32, + 64, + 128, + 256, + 512, + 14, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 112 + }, + "norm_witness": { + "coefficient_census": { + "-1": 148, + "-1/2": 198, + "-2": 17, + "-3/2": 14, + "1": 40, + "1/2": 186, + "2": 3, + "3/2": 2, + "4": 1 + }, + "coefficient_terms": 609, + "event_index": 1123, + "target": 112 + } + }, + "middle_integer_census": { + "-1": 456, + "1": 240 + }, + "ordered_factor_negative_control": "stage zero is identity", + "parts": [ + { + "maps": 224, + "part": "old_complement", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "first_copy", + "real_scalar": 128 + }, + { + "maps": 224, + "part": "current_code", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "second_copy", + "real_scalar": 128 + }, + { + "maps": 1392, + "part": "middle", + "real_scalar": 5632 + }, + { + "maps": 224, + "part": "current_inverse", + "real_scalar": 1760 + } + ], + "physical_level_before_service": 0, + "query_invoice": { + "maps": 2064, + "real_scalar": 11168 + }, + "reader_stage": 0, + "selected_paths": 696, + "service_stage": 1, + "triangle_prefix_bound": "972", + "unchanged_outside_fields": 416, + "wrong_inverse_map_negative_control": "fails" + }, + { + "all_input_columns": 640, + "binary_height_bound": 3, + "direct_paths": 3808, + "distinct_middle_maps": 216, + "dual_binary_height_bound": 3, + "dual_exact_prefix": { + "coefficient_binary_height": 3, + "coefficient_row_sum_peak": "43/2", + "height_witness": { + "coefficient": "1/8", + "event_index": 3160, + "origin": 112, + "route": [ + 917504, + 786446, + 655374, + 393230, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216, + 512, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 11, + 7, + 16, + 32, + 64, + 128, + 256 + ], + "target": 0 + }, + "norm_witness": { + "coefficient_census": { + "-1/2": 1, + "-1/4": 8, + "-1/8": 30, + "1": 1, + "1/2": 4, + "1/4": 24, + "1/8": 50 + }, + "coefficient_terms": 118, + "event_index": 3253, + "target": 21 + } + }, + "dual_query_all_input_columns": 640, + "dual_triangle_prefix_bound": "53", + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "448", + "height_witness": { + "coefficient": "-1/4", + "event_index": 1185, + "origin": 0, + "route": [ + 262154, + 262156, + 1, + 262150, + 16, + 32, + 64, + 128, + 256, + 512, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 131072, + 14, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 112 + }, + "norm_witness": { + "coefficient_census": { + "-1": 148, + "-1/2": 198, + "-2": 17, + "-3/2": 14, + "1": 40, + "1/2": 186, + "2": 3, + "3/2": 2, + "4": 1 + }, + "coefficient_terms": 609, + "event_index": 1123, + "target": 112 + } + }, + "middle_integer_census": { + "-1": 456, + "1": 240 + }, + "ordered_factor_negative_control": "stage zero is identity", + "parts": [ + { + "maps": 224, + "part": "old_complement", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "first_copy", + "real_scalar": 128 + }, + { + "maps": 224, + "part": "current_code", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "second_copy", + "real_scalar": 128 + }, + { + "maps": 1392, + "part": "middle", + "real_scalar": 5632 + }, + { + "maps": 224, + "part": "current_inverse", + "real_scalar": 1760 + } + ], + "physical_level_before_service": 1, + "query_invoice": { + "maps": 2064, + "real_scalar": 11168 + }, + "reader_stage": 0, + "selected_paths": 696, + "service_stage": 2, + "triangle_prefix_bound": "972", + "unchanged_outside_fields": 416, + "wrong_inverse_map_negative_control": "fails" + }, + { + "all_input_columns": 640, + "binary_height_bound": 3, + "direct_paths": 3808, + "distinct_middle_maps": 696, + "dual_binary_height_bound": 3, + "dual_exact_prefix": { + "coefficient_binary_height": 3, + "coefficient_row_sum_peak": "43/2", + "height_witness": { + "coefficient": "1/8", + "event_index": 3160, + "origin": 112, + "route": [ + 656384, + 787456, + 917504, + 394240, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216, + 512, + 14, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 11, + 7, + 16, + 32, + 64, + 128, + 256 + ], + "target": 0 + }, + "norm_witness": { + "coefficient_census": { + "-1/2": 1, + "-1/4": 8, + "-1/8": 30, + "1": 1, + "1/2": 4, + "1/4": 24, + "1/8": 50 + }, + "coefficient_terms": 118, + "event_index": 3253, + "target": 21 + } + }, + "dual_query_all_input_columns": 640, + "dual_triangle_prefix_bound": "53", + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "448", + "height_witness": { + "coefficient": "-1/4", + "event_index": 1185, + "origin": 0, + "route": [ + 262154, + 262153, + 4, + 262147, + 16, + 32, + 64, + 128, + 256, + 512, + 11, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 131072, + 1024, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 112 + }, + "norm_witness": { + "coefficient_census": { + "-1": 148, + "-1/2": 198, + "-2": 17, + "-3/2": 14, + "1": 40, + "1/2": 186, + "2": 3, + "3/2": 2, + "4": 1 + }, + "coefficient_terms": 609, + "event_index": 1123, + "target": 112 + } + }, + "middle_integer_census": { + "-1": 456, + "1": 240 + }, + "ordered_factor_negative_control": "fails", + "parts": [ + { + "maps": 224, + "part": "old_complement", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "first_copy", + "real_scalar": 128 + }, + { + "maps": 224, + "part": "current_code", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "second_copy", + "real_scalar": 128 + }, + { + "maps": 1392, + "part": "middle", + "real_scalar": 5632 + }, + { + "maps": 224, + "part": "current_inverse", + "real_scalar": 1760 + } + ], + "physical_level_before_service": 1, + "query_invoice": { + "maps": 2064, + "real_scalar": 11168 + }, + "reader_stage": 1, + "selected_paths": 696, + "service_stage": 2, + "triangle_prefix_bound": "972", + "unchanged_outside_fields": 416, + "wrong_inverse_map_negative_control": "fails" + } + ], + "phase_checks": { + "adjacent_full_to_Q": 448, + "adjacent_hole_to_I": 224, + "full_views": 672 + }, + "pivot_minor_determinant": "16", + "producer_code_imported": false, + "producer_dual_freeze_sha256": "92ffceb625c3a97745892bb0f06a1140e9031ca3dc8085417d54cde9cc61f455", + "producer_reuse_freeze_sha256": "41d689596777344268bca937bb2e7fea302bfff443590aa42e46788409e563bf", + "providers": { + "base": { + "deletion": { + "removed_native": 128, + "removed_scalar": 122, + "retained_scalar": 6456 + }, + "last_source_event": 2638, + "prospective_native_mass": 1792, + "prospective_native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + } + }, + "extra": { + "deletion": { + "removed_native": 128, + "removed_scalar": 122, + "retained_scalar": 6456 + }, + "last_source_event": 2638, + "prospective_native_mass": 1792, + "prospective_native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + } + } + }, + "source_pins": { + "capture": [ + "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7" + ], + "native": [ + "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" + ], + "views": [ + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + ] + }, + "status": "PASS_INDEPENDENT_FIXED_READER_QUERY_AND_TYPED_DUAL" +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/optimized/REVIEW-CHECKS.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/optimized/REVIEW-CHECKS.json new file mode 100644 index 0000000000..00610f175c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/optimized/REVIEW-CHECKS.json @@ -0,0 +1,635 @@ +{ + "H8_carriers": [ + { + "port": 0, + "q": 11, + "translation": 15 + }, + { + "port": 27, + "q": 38, + "translation": 39 + }, + { + "port": 36, + "q": 146, + "translation": 147 + }, + { + "port": 111, + "q": 191, + "translation": 255 + }, + { + "port": 20, + "q": 161, + "translation": 163 + }, + { + "port": 7, + "q": 21, + "translation": 23 + }, + { + "port": 57, + "q": 56, + "translation": 57 + }, + { + "port": 46, + "q": 140, + "translation": 141 + }, + { + "port": 1, + "q": 19, + "translation": 23 + }, + { + "port": 3, + "q": 67, + "translation": 71 + }, + { + "port": 6, + "q": 13, + "translation": 15 + }, + { + "port": 8, + "q": 37, + "translation": 39 + }, + { + "port": 17, + "q": 81, + "translation": 83 + }, + { + "port": 18, + "q": 145, + "translation": 147 + }, + { + "port": 24, + "q": 385, + "translation": 387 + }, + { + "port": 23, + "q": 321, + "translation": 323 + } + ], + "checker_sha256": "c1caa97a3929c3750e6e663c2d7429297a1e50e7a835264ee7ecde17c47f0b7e", + "complete_native_integration_checked": false, + "complete_supplier_claimed": false, + "general_reader_example": { + "E_is_singular": true, + "E_selected_block_is_nonzero": true, + "W_and_B_t_do_not_commute": true, + "arbitrary_input_columns": 6, + "plain_copy_negative_control": "fails" + }, + "pairs": [ + { + "all_input_columns": 640, + "binary_height_bound": 3, + "direct_paths": 3808, + "distinct_middle_maps": 216, + "dual_binary_height_bound": 3, + "dual_exact_prefix": { + "coefficient_binary_height": 3, + "coefficient_row_sum_peak": "43/2", + "height_witness": { + "coefficient": "1/8", + "event_index": 3160, + "origin": 112, + "route": [ + 3584, + 3086, + 2574, + 1550, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 11, + 7, + 16, + 32, + 64, + 128, + 256, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 0 + }, + "norm_witness": { + "coefficient_census": { + "-1/2": 1, + "-1/4": 8, + "-1/8": 30, + "1": 1, + "1/2": 4, + "1/4": 24, + "1/8": 50 + }, + "coefficient_terms": 118, + "event_index": 3253, + "target": 21 + } + }, + "dual_query_all_input_columns": 640, + "dual_triangle_prefix_bound": "53", + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "448", + "height_witness": { + "coefficient": "-1/4", + "event_index": 1185, + "origin": 0, + "route": [ + 1034, + 1036, + 1, + 1030, + 16, + 32, + 64, + 128, + 256, + 512, + 14, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 112 + }, + "norm_witness": { + "coefficient_census": { + "-1": 148, + "-1/2": 198, + "-2": 17, + "-3/2": 14, + "1": 40, + "1/2": 186, + "2": 3, + "3/2": 2, + "4": 1 + }, + "coefficient_terms": 609, + "event_index": 1123, + "target": 112 + } + }, + "middle_integer_census": { + "-1": 456, + "1": 240 + }, + "ordered_factor_negative_control": "stage zero is identity", + "parts": [ + { + "maps": 224, + "part": "old_complement", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "first_copy", + "real_scalar": 128 + }, + { + "maps": 224, + "part": "current_code", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "second_copy", + "real_scalar": 128 + }, + { + "maps": 1392, + "part": "middle", + "real_scalar": 5632 + }, + { + "maps": 224, + "part": "current_inverse", + "real_scalar": 1760 + } + ], + "physical_level_before_service": 0, + "query_invoice": { + "maps": 2064, + "real_scalar": 11168 + }, + "reader_stage": 0, + "selected_paths": 696, + "service_stage": 1, + "triangle_prefix_bound": "972", + "unchanged_outside_fields": 416, + "wrong_inverse_map_negative_control": "fails" + }, + { + "all_input_columns": 640, + "binary_height_bound": 3, + "direct_paths": 3808, + "distinct_middle_maps": 216, + "dual_binary_height_bound": 3, + "dual_exact_prefix": { + "coefficient_binary_height": 3, + "coefficient_row_sum_peak": "43/2", + "height_witness": { + "coefficient": "1/8", + "event_index": 3160, + "origin": 112, + "route": [ + 917504, + 786446, + 655374, + 393230, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216, + 512, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 11, + 7, + 16, + 32, + 64, + 128, + 256 + ], + "target": 0 + }, + "norm_witness": { + "coefficient_census": { + "-1/2": 1, + "-1/4": 8, + "-1/8": 30, + "1": 1, + "1/2": 4, + "1/4": 24, + "1/8": 50 + }, + "coefficient_terms": 118, + "event_index": 3253, + "target": 21 + } + }, + "dual_query_all_input_columns": 640, + "dual_triangle_prefix_bound": "53", + "exact_prefix": { + "coefficient_binary_height": 2, + "coefficient_row_sum_peak": "448", + "height_witness": { + "coefficient": "-1/4", + "event_index": 1185, + "origin": 0, + "route": [ + 262154, + 262156, + 1, + 262150, + 16, + 32, + 64, + 128, + 256, + 512, + 1024, + 2048, + 4096, + 8192, + 16384, + 32768, + 65536, + 131072, + 14, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "target": 112 + }, + "norm_witness": { + "coefficient_census": { + "-1": 148, + "-1/2": 198, + "-2": 17, + "-3/2": 14, + "1": 40, + "1/2": 186, + "2": 3, + "3/2": 2, + "4": 1 + }, + "coefficient_terms": 609, + "event_index": 1123, + "target": 112 + } + }, + "middle_integer_census": { + "-1": 456, + "1": 240 + }, + "ordered_factor_negative_control": "stage zero is identity", + "parts": [ + { + "maps": 224, + "part": "old_complement", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "first_copy", + "real_scalar": 128 + }, + { + "maps": 224, + "part": "current_code", + "real_scalar": 1760 + }, + { + "maps": 0, + "part": "second_copy", + "real_scalar": 128 + }, + { + "maps": 1392, + "part": "middle", + "real_scalar": 5632 + }, + { + "maps": 224, + "part": "current_inverse", + "real_scalar": 1760 + } + ], + "physical_level_before_service": 1, + "query_invoice": { + "maps": 2064, + "real_scalar": 11168 + }, + "reader_stage": 0, + "selected_paths": 696, + "service_stage": 2, + "triangle_prefix_bound": "972", + "unchanged_outside_fields": 416, + "wrong_inverse_map_negative_control": "fails" + }, + { + "all_input_columns": 640, + "binary_height_bound": 3, + "direct_paths": 3808, + "distinct_middle_maps": 696, + "dual_binary_height_bound": 3, + "dual_exact_prefix": { + "coefficient_binary_height": 3, + "coefficient_row_sum_peak": "43/2", + "height_witness": { + "coefficient": "1/8", + "event_index": 3160, + "origin": 112, + "route": [ + 656384, + 787456, + 917504, + 394240, + 1048576, + 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The fixtures check the invariant and its necessary hypotheses.", + "recursive_grid_fixtures": [ + { + "completed_nodes": 1, + "maximum_height": 1, + "odd": 3, + "recursive_edges": 0 + }, + { + "completed_nodes": 1, + "maximum_height": 1, + "odd": 45045, + "recursive_edges": 0 + }, + { + "completed_nodes": 3, + "maximum_height": 2, + "odd": 3, + "recursive_edges": 1 + }, + { + "completed_nodes": 3, + "maximum_height": 2, + "odd": 45045, + "recursive_edges": 1 + }, + { + "completed_nodes": 7, + "maximum_height": 3, + "odd": 3, + "recursive_edges": 2 + }, + { + "completed_nodes": 7, + "maximum_height": 3, + "odd": 45045, + "recursive_edges": 2 + }, + { + "completed_nodes": 15, + "maximum_height": 4, + "odd": 3, + "recursive_edges": 3 + }, + { + "completed_nodes": 15, + "maximum_height": 4, + "odd": 45045, + "recursive_edges": 3 + }, + { + "completed_nodes": 31, + "maximum_height": 5, + "odd": 3, + "recursive_edges": 4 + }, + { + "completed_nodes": 31, + "maximum_height": 5, + "odd": 45045, + "recursive_edges": 4 + }, + { + "completed_nodes": 63, + "maximum_height": 6, + "odd": 3, + "recursive_edges": 5 + }, + { + "completed_nodes": 63, + "maximum_height": 6, + "odd": 45045, + "recursive_edges": 5 + } + ], + "signed_scan_checks": [ + { + "directions": 2, + "odd": 3, + "signed_inputs": 8190 + }, + { + "directions": 2, + "odd": 5, + "signed_inputs": 8190 + }, + { + "directions": 2, + "odd": 7, + "signed_inputs": 8190 + }, + { + "directions": 2, + "odd": 9, + "signed_inputs": 8190 + }, + { + "directions": 2, + "odd": 11, + "signed_inputs": 8190 + }, + { + "directions": 2, + "odd": 13, + "signed_inputs": 8190 + } + ], + "source_freezes": { + "FREEZE-A8-ODD-GRID.json": "97f00c72bc3baeb4ce3ca91b91d9e46d7978d7ec502bee77845f5484731bb086", + "FREEZE-MINOR-FACTORS.json": "de05cc545581deadbe855e6ae214c9cda79a6b20add92948d066a95756ed4219" + }, + "status": "PASS_INDEPENDENT_ODD_GRID_AND_MINOR_FACTORS", + "structural": { + "A8_nullity": 8, + "A8_rank": 104, + "R_E_K": "12 I8", + "R_U_R_U_transpose": "52 I8", + "content_singular_k": 1, + "minor_Gram_checks": 896, + "ordinary_singular_k": 13 + }, + "wrong_scatter_controls": 66 +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md new file mode 100644 index 0000000000..555f0dd6b9 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md @@ -0,0 +1,339 @@ +# Independent review of the odd grid and complete-minor factors + +The A8 scalar factor and common-grid theorem pass this review. The general +complete-minor family also passes. These results remove an arithmetic +restriction of the dyadic emitter. They do not remove the A8 content +kernel, establish a new owner schedule, or prove a complete supplier. + +The accepted scope is exact scalar computation on arbitrary inputs at a +legal common-frame cut. One existing owned C0 suffices. The new divisions +are separate fixed odd-division scans. They are not old dyadic SCALEs or +new H1 children. Recursive use requires exact Gaussian-dyadic completed +children on all data and arbitrary helper columns, one root conversion of +all numeric streams, and a separately proved final dyadic endpoint. + +## Sources and independent checks + +The producer packets are +[A8-ODD-GRID.md](../../independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md) +and +[GENERAL-MINOR-FACTORS.md](../../independent-review-20261017/odd-grid-a8-20261017/GENERAL-MINOR-FACTORS.md). +Their frozen source hashes are in [REVIEW.json](REVIEW.json). The review +checks each frozen file before use. It also checks the actual new-core +interface hash, the retained model source SHA256 and Git blob identities, +and the four pinned PR source Git blobs. It does not claim a new live +GitHub refresh or a rerun of the PR3423 and PR3406 executable suites. + +The actual source is the eight-row R matrix in +`new-core-transfer-20261017/INTERFACE.json`, SHA256 +`c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746`. +The review derives its Gram matrices from those entries. It does not use +an abstract matrix with only the desired dimensions. + +The independent checker imports no producer module. It replays each +literal word as dense integer basis columns on a fixed exact grid. It +checks divisibility before each binary scale and each odd division. This +differs from the producer's Fraction-row replay. It checks every input +column, including arbitrary C0, every stored prefix, the final matrices, +and the complete scalar invoice. The three A8 baseline words and all 69 +family factors pass. The 66 nonempty family words each reject a changed +scatter sign. + +The checker also verifies signed division and multiplication on 49,140 +inputs over the six odd divisors. An independent modular inverse checks +each division output. Twelve recursive fixtures check the active-chain +height invariant and its failure for completed rational children. Those +fixtures support the proof below; they do not substitute for it. + +## Actual Gram matrices and the A8 inverse + +The first selected minor has ports +`[0,7,20,27,36,46,57,111]`. Let U be its 104-port complement. Every row of +R has 56 signed unit entries. Every row restricted to U has 52. Direct +calculation gives + +```text +R_U R_U^T = 52I_8, +K = R^T/4, +H = I_U-R_U^T R_U/4, +H^-1 = I_U-R_U^T R_U/48. +``` + +If `P=R_U^T R_U`, then `P^2=52P`. The P coefficient in either inverse +product is `-1/4-1/48+52/192=0`. Thus both inverse orders hold on arbitrary +ordinary inputs. H acts by -12 on the eight-dimensional query image and +by one on its complement. + +Modulo three, `R_U K_U=13I=I`. The eight K_U columns are independent, and +`H K_U=-12K_U=0`. Thus the old dyadic ring obstruction is real. Extending +the exact arithmetic to division by three removes this obstruction. +It does not change the source native operators. + +For row r_i, the inverse computes the complete query `r_i X` in C0, +divides it by 16 and three, then subtracts `r_i^T C0` from ordinary X. +The different row updates have zero cross products. Their product is the +stated inverse. The upper correction after that inverse is fused by +scattering through all entries of R_i instead. Its exact ordered map is + +```text +X_U' = X_U-R_U^T R_U X_U/48, +X_A' = X_A-R_A^T R_U X_U/48. +``` + +The selected scatter does not enter any later query. It therefore leaves +the cancellation and prefix-divisibility proof unchanged. The initial +C0 value has no effect, because C0 is owned and is cleared. No borrowed +data field is cleared or assumed zero. + +## All complete-minor unions + +The actual 112 columns partition into fourteen disjoint eight-port minors. +The review verifies all fourteen identities `R_Aj R_Aj^T=4I_8` and all +four-unit-per-row support counts. For any union S of k such minors, + +```text +R_U K_U = (14-k)I_8, +E = diag(-I_S,I_U), +R E K = (14-2k)I_8, +d = k-13. +``` + +These individual minor identities prove the assertion for every union; +there is no need to infer it from the first-k examples. + +For `k!=13`, direct rank-eight multiplication gives + +```text +H_k^-1 = I_U+K_U R_U/d, +A_k = E+K R/d. +``` + +For `k!=1,13`, the content inverse is + +```text +A_k^-1 = E+E K R E/(k-1). +``` + +For example, the nonidentity coefficient in `A_k A_k^-1` is proportional +to `d+(k-1)+(14-2k)=0`. The same identity proves the reverse order. This +proof retains the order of E, K and R. It does not commute a selected Q +operator through them. + +For A_k, first apply E, query `R_i E`, and scatter through `R_i^T`. For +its inverse, first apply E, query R_i, and scatter through `E R_i^T`. +For distinct row indices, `R_i E R_j^T=0`. Therefore earlier row updates +do not change a later complete query. This proves the two content words +as well as the ordinary words. The literal all-column checks agree with +these formulas. + +At k=0, the ordinary inverse and A_0 are the J inverse. Its odd divisor +is thirteen. At k=14, the ordinary space is empty. Its three ordinary +factor words are identities that do not use or clear C0. The content +maps are `A_14=-J` and `A_14^-1=-J^-1`. These endpoints are consistent +with both the formulas and the literal words. + +The two singular cases have different causes. At k=13, the complement +is one complete square minor. Hence `R_U^T R_U=4I_8`, so H_13 is zero +on all eight ordinary fields. No coefficient extension inverts it. +At k=1, `R E K=12I_8` and + +```text +A_1 E K=0, +E A_1=I-E K R/12. +``` + +The second matrix is a projector with trace 104. The checker separately +multiplies its dense integer numerator by itself and checks the trace. +Thus A_1 has rank 104 and nullity exactly eight over Q. Its kernel is +the image of E K. The explicit selected input Q is invertible and cannot +remove these kernel channels. A controller that needs A_1 inverse remains +invalid. A controller may use the retained selected Y information, but +must prove and price that use. + +## Prefix denominators and one C0 + +Write a factor's scalar denominator as `2^t o`, with o odd. Each row +query is completed before it is scaled or divided. A complete later query +equals that row's query on the module input, because all preceding row +updates cancel. It therefore has no new odd denominator. A partial query +can have denominator o from an earlier scatter, but it is not divided +while partial. The division adds one factor o to the complete query. +Scattering that value cannot add a second factor. This proves that every +prefix has an odd denominator dividing o relative to the module input, +including inputs that already have an odd denominator from a parent. + +The A8 inverse has t=4 and o=3. Its eight divisions together add at most +one ternary level, not eight. Across the full family, `t<=5` and +`o` belongs to `{1,3,5,7,9,11,13}`. The divisor nine means two ternary +levels. The binary argument is the same: a complete query cancels the +prior factor before another scale occurs. + +The family words use one initial CLEAR and one after each of the eight +rows, for nine CLEARs. The first CLEAR discards only the arbitrary owned +C0 input. Between rows C0 is zero and stays in the common frame. At exit +it is zero and can return to its private empty-frame convention. No +nonzero value is relabelled. The A8 baseline retains sixteen CLEARs; +the separate family packet removes the seven adjacent duplicate CLEARs. + +For any union of minors, each data-prefix row has 1-norm at most +`1+8*56/4=113`. A partial query has at most 56 terms, so its row 1-norm +is at most 6328. Unit-ADD arithmetic temporaries are at most 12656 times +the input magnitude, below `2^14` times that magnitude. The smaller +exact first-k norms in the receipt also pass the independent replay. +This is a factor guard, not a completed supplier precision constant. + +## Exact record scans + +For an odd o, division reads a bit b from least to most significant, +writes `a=(b-c) mod 2`, and sets `c'=(c+oa-b)/2`. The carry starts at +zero and remains in `0,...,o-1`. Summing the bit recurrence gives + +```text +o Q_unsigned = N_unsigned+2^w c_final. +``` + +For sign bits s_N and s_Q, exact signed division is equivalent to +`c_final=o s_Q-s_N`. On a valid input the quotient fits in the signed +width. The scan overwrites its input and needs only finite carry and sign +control. A nonmultiple must fail; numerator one is a decisive control. + +Multiplication uses `a=(ob+c) mod 2` and `c'=floor((ob+c)/2)`. Its signed +test is `c_final=o s_N-s_output`. The allocated guard prevents overflow. +Both scans preserve the record layout. The stated bound of `4(w_g+1)` +arithmetic-head steps per scan covers traversal, positioning and return. +Descriptor and record-counter work is additional linear work. The old +scalar price is not assigned to these scans. + +## Recursive common grid and cost + +The retained +[stopped-product source](../../interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex) +explicitly implements this method with odd divisor 21. It includes root +dyadic inputs, arbitrary dirty auxiliaries, exact Gaussian-dyadic completed +children, active-chain denominator accumulation, and outer unscaling. +The new packet applies that existing method to the factors above. + +Fix a finite parent word with at most M odd factors. Let L be an odd +multiple of each factor's o. A completed child must have an exact +Gaussian-dyadic matrix on every data and arbitrary helper column. It then +preserves any existing odd denominator of its input. Only unfinished +calls can add odd factors. A live chain of at most D+1 nodes adds at most +`K=M(D+1)` factors L. + +At the root, choose one grid `2^-P/L^K` and multiply all padded numeric +numerators by `L^K`. This includes arbitrary borrowed values and all +numeric work streams. It does not scale addresses or descriptors. Any +nonzero numeric literal must use this representation. No local division +or recursive entry changes the format. The binary guard P must cover the +new complete event list. + +Every intermediate is then on the chosen grid. In particular, immediately +before each /o scan, the encoded numerator is divisible by o, because its +exact quotient is also on that grid. This is a consequence of the root +dyadic-input invariant. It is false for arbitrary integer numerators on +the finest grid. It is also false if completed children retain an odd +denominator and one counts only live depth. The independent fixtures check +both failure modes. + +At the final outer return, the proved Gaussian-dyadic endpoint implies +that each numeric numerator is divisible by `L^K`. Exact unscaling gives +the required original encoding, including every borrowed role's declared +endpoint. This conclusion needs the actual final semantic proof. A local +factor or denominator calculation does not supply it. + +For A8, use L=3. Both root conversions cost at most +`8 N K(w_g+1)` arithmetic-head steps, plus linear descriptor work, and +add at most 2K numerator bits. For the full family, a uniform choice is + +```text +L=45045=3^2*5*7*11*13 < 2^16. +``` + +It uses six prime scans for each multiplication or division by L. Both +root conversions cost at most `48 N K(w_g+1)`, plus descriptor work, +and add at most 16K bits. Here N counts all real numeric records, not +only active data. A factor with odd division adds sixteen real scans, +or at most `64 n(w_g+1)` arithmetic-head steps for n complex entries +per field, plus the retained linear stream work. + +If every child has at most `48e/73` axes, two recursive edges reduce the +axis count by more than half. Thus `D<=2 ceil(log2(d+1))` is safe. +Fixed M gives logarithmic extra width and `O(V log d)` root work. An +exact completed u-axis child adds at most u binary denominator bits and +row-norm factor `2^u`. A finite complete parent can therefore use the +stated linear guard recurrence once its own constants a and b are +calculated. This establishes a way to obtain the guard. It does not +establish those constants for an unspecified new controller. + +The common scalar scale commutes with exact linear native operators. +The conclusion does not apply to a rounded native operation without a +separate exactness proof. The read PR3423/PR3406 sources impose Newton +module and source-divisibility conditions in their own setting. PR3423 +also explicitly obtains the coefficient map `E^-1 A E` and exhibits +its difference from A. Those results neither ban odd grids here nor +prepare arbitrary dirty payloads for free. Their executable suites were +not rerun for this review. + +## Complete component invoices + +The independent literal recount gives the retained A8 baseline: + +| Factor | Old real primitives | Real /3 scans | CLEARs | +| --- | ---: | ---: | ---: | +| H | 6,720 | 0 | 16 | +| H inverse | 6,752 | 16 | 16 | +| Fused inverse and upper correction | 7,008 | 16 | 16 | + +All use zero new native children at the legal common-frame cuts. Their +maximum stored row 1-norms are 121, 52 and 52. The nine-CLEAR family words +subtract fourteen old primitives from each A8 row. The corresponding +S40 costs are 4,658, 4,706 and 5,986, with no odd scan. Its content map +and inverse cost 7,346 and 7,330. + +For the whole family, let `t=v2(4|k-13|)` and +`u=v2(4|k-1|)`. The nonempty word prices are + +```text +H_k: 7218-512k, +H_k inverse: 7186-512k+16t, +Fused: 7186-256k+16t, +A_k: 7186+16k+16t, +A_k inverse: 7186+16k+16u. +``` + +Each nontrivial odd divisor adds sixteen real scans. The independent +recount verifies every one of these formulas and every local assembly +sum in the producer table. Those assembly sums consume the prior +164,514-scalar core, its rank mass 5073, the stated physical exchange +prices, and the fourteen-scalar C1-through-C7 cleanup. They do not count +as a literal native transfer or a controller replay in this review. + +## Reproduction and conclusion + +Run from the workspace root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/check_review.py +``` + +Expected status: + +```text +PASS_INDEPENDENT_ODD_GRID_AND_MINOR_FACTORS +``` + +The independent checker ran successfully. Both producer checkers also ran +with separate output paths in this review directory. Their two receipts +and two literal-word files match the frozen source bytes exactly, as +recorded in [PRODUCER-REPLAY.json](PRODUCER-REPLAY.json). + +No material defect remains in +the stated scalar and representation claims. The native local-word +transfer is reviewed in a separate lane. Complete phases and owners, +recursive hosting, the final dyadic endpoint, the complete binary guard, +and the supplier moment remain necessary for a complete construction. +No new kappa value follows from this packet alone. + +This review used substantial OpenAI Codex assistance. No PR, commit, push, +or publication was made. Before a future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/check_review.py b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/check_review.py new file mode 100644 index 0000000000..8e603e9c40 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/check_review.py @@ -0,0 +1,364 @@ +"""Review the odd-grid factors with integer-grid basis columns.""" + +from collections import Counter +from fractions import Fraction +from hashlib import sha1, sha256 +import json +from math import gcd, lcm +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / "independent-review-20261017/odd-grid-a8-20261017" +INTERFACE = LANES / "new-core-transfer-20261017/INTERFACE.json" +INTERFACE_PIN = "c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746" +FREEZES = { + "FREEZE-A8-ODD-GRID.json": "97f00c72bc3baeb4ce3ca91b91d9e46d7978d7ec502bee77845f5484731bb086", + "FREEZE-MINOR-FACTORS.json": "de05cc545581deadbe855e6ae214c9cda79a6b20add92948d066a95756ed4219", +} +C = 112 +N = 113 + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def split(n): + t = 0 + while n % 2 == 0: + n //= 2 + t += 1 + return t, n + + +def sources(): + for name, digest in FREEZES.items(): + raw = (SOURCE / name).read_bytes() + require(sha256(raw).hexdigest() == digest, name) + data = json.loads(raw) + for path, pin in data["files"].items(): + content = (SOURCE / path).read_bytes() + if isinstance(pin, dict): + require(len(content) == pin["bytes"], path + " byte count") + pin = pin["sha256"] + require(sha256(content).hexdigest() == pin, path) + require(sha256(INTERFACE.read_bytes()).hexdigest() == INTERFACE_PIN, "Actual R pin") + pins = json.loads((SOURCE / "SOURCE-PINS.json").read_text()) + for item in pins["sources"]: + raw = (SOURCE / item["local_copy"]).read_bytes() + require(sha256(raw).hexdigest() == item["sha256"], "Model source SHA256") + require(sha1(b"blob " + str(len(raw)).encode() + b"\0" + raw).hexdigest() == item["git_blob"], "Model Git blob") + pr_pins = json.loads((SOURCE / "sources/GITHUB-PINS.json").read_text()) + for item in pr_pins: + raw = (SOURCE / "sources" / item["local"]).read_bytes() + require(sha1(b"blob " + str(len(raw)).encode() + b"\0" + raw).hexdigest() == item["git_blob"], "Pinned PR Git blob") + rows = json.loads(INTERFACE.read_text())["R"] + r = [[Fraction(row.get(str(p), 0)) for p in range(112)] for row in rows] + require(len(r) == 8 and all(x in (-1, 0, 1) for row in r for x in row), "Signed unit R") + r = [[int(x) for x in row] for row in r] + require(all(sum(x != 0 for x in row) == 56 for row in r), "Actual row support") + report = json.loads((SOURCE / "MINOR-FACTORS.json").read_text()) + minors = report["minors"] + require(len(minors) == 14 and sorted(p for minor in minors for p in minor) == list(range(112)), "Complete minor partition") + for minor in minors: + require(len(minor) == 8, "Eight columns per minor") + for i in range(8): + require(sum(r[i][p] != 0 for p in minor) == 4, "Four signed units per minor row") + for j in range(8): + require(sum(r[i][p] * r[j][p] for p in minor) == (4 if i == j else 0), "Actual minor Gram 4I") + g = [[sum(r[i][p] * r[i][q] for i in range(8)) for q in range(112)] for p in range(112)] + return r, g, minors, report, pins, pr_pins + + +def endpoint(g, selected, kind, denominator): + ordinary = set(range(112)) - selected + k = len(selected) // 8 + out = [[0] * N for _ in range(N)] + for p in range(112): + out[p][p] = denominator * (-1 if kind.startswith("content") and p in selected else 1) + for q in range(112): + if kind == "H": + coefficient = Fraction(-g[p][q], 4) if p in ordinary and q in ordinary else 0 + elif kind == "inverse": + coefficient = Fraction(g[p][q], 4 * (k - 13)) if p in ordinary and q in ordinary else 0 + elif kind == "fused": + coefficient = Fraction(g[p][q], 4 * (k - 13)) if q in ordinary else 0 + elif kind == "content": + coefficient = Fraction(g[p][q], 4 * (k - 13)) + else: + sign = (-1 if p in selected else 1) * (-1 if q in selected else 1) + coefficient = Fraction(sign * g[p][q], 4 * (k - 1)) + value = denominator * coefficient + require(Fraction(value).denominator == 1, "Endpoint fits the chosen integer grid") + out[p][q] += int(value) + return out + + +def execute(word, denominator, odd, clear_count): + state = [[denominator if i == j else 0 for j in range(N)] for i in range(N)] + counts = Counter() + old_cost = 0 + max_norm_numerator = denominator + binary_height = 0 + odd_denominator = 1 + divisions = [] + changed_coefficients = 0 + for position, event in enumerate(word): + kind, target = event[:2] + require(0 <= target < N, "Declared target") + counts[kind] += 1 + if kind == "clear": + require(target == C, "Only the owned accumulator is cleared") + state[C] = [0] * N + old_cost += 2 + elif kind == "add": + source, coefficient = event[2], Fraction(event[3]) + require(0 <= source < N and source != target and coefficient in (-1, 1), "Distinct unit ADD") + sign = int(coefficient) + state[target] = [a + sign * b for a, b in zip(state[target], state[source])] + old_cost += 8 + elif kind == "scale": + q = Fraction(event[2]) + require(target == C or q == -1, "Only signs on data") + require(abs(q.numerator) == 1 and q.denominator & (q.denominator - 1) == 0, "Signed binary SCALE") + require(all(v % q.denominator == 0 for v in state[target]), "Exact binary scale on every encoded basis column") + state[target] = [v // q.denominator * q.numerator for v in state[target]] + old_cost += 2 * ((q.denominator.bit_length() - 1) + (q.numerator < 0)) + else: + require(kind == "divide_odd" and target == C and event[2] == odd and odd > 1, "Distinct fixed odd-division opcode") + before_odd = lcm(*(split(denominator // gcd(abs(v), denominator))[1] for v in state[C])) + require(before_odd == 1, "The complete query cancels prior local odd denominators") + require(all(v % odd == 0 for v in state[C]), "Every encoded basis numerator is divisible at the scan") + state[C] = [v // odd for v in state[C]] + divisions.append(position) + max_norm_numerator = max(max_norm_numerator, sum(abs(v) for v in state[target])) + for v in state[target]: + if not v: + continue + binary, local_odd = split(denominator // gcd(abs(v), denominator)) + binary_height = max(binary_height, binary) + odd_denominator = lcm(odd_denominator, local_odd) + require(odd % local_odd == 0, "At most one stated odd denominator at every prefix") + changed_coefficients += 1 + if word: + require(counts["clear"] == clear_count and not any(state[C]), "Owned C0 clears and final zero") + require(all(row[C] == 0 for row in state), "No output depends on initial owned C0") + return state, { + "old_real_primitives": old_cost, + "real_odd_scans": 2 * len(divisions), + "events": dict(counts), + "additional_binary_height": binary_height, + "prefix_odd_denominator_divides": odd_denominator, + "max_row_l1": str(Fraction(max_norm_numerator, denominator)), + "encoded_coefficient_checks": changed_coefficients, + "division_sites": divisions, + } + + +def compare(receipt, producer, baseline=False): + fields = { + "old_real_primitives": "old_real_primitives", + "real_odd_scans": "real_division_by_3_scans" if baseline else "real_odd_scans", + "additional_binary_height": "binary_height" if baseline else "additional_binary_height", + "max_row_l1": "max_coefficient_row_l1" if baseline else "max_row_l1", + "events": "event_counts" if baseline else "events", + } + for ours, theirs in fields.items(): + require(receipt[ours] == producer[theirs], "Independent receipt field " + ours) + + +def factor_checks(g, minors, family): + words = json.loads((SOURCE / "A8-ODD-GRID-WORDS.json").read_text()) + reports = json.loads((SOURCE / "A8-ODD-GRID.json").read_text()) + selected = set(minors[0]) + baseline = {} + for name, kind in [("H", "H"), ("H_inverse", "inverse"), ("H_inverse_fused_upper", "fused")]: + den, odd = (4, 1) if kind == "H" else (48, 3) + actual, receipt = execute(words[name], den, odd, 16) + require(actual == endpoint(g, selected, kind, den), "A8 full basis endpoint") + compare(receipt, reports["local_factors"][name], True) + require(receipt["old_real_primitives"] == {"H": 6720, "inverse": 6752, "fused": 7008}[kind], "A8 baseline invoice") + baseline[name] = receipt + all_words = json.loads((SOURCE / "MINOR-FACTOR-WORDS.json").read_text()) + all_receipts, controls = {}, 0 + for k in range(15): + selected = set(p for minor in minors[:k] for p in minor) + if k == 13: + ordinary = set(range(112)) - selected + require(all(g[p][q] == (4 if p == q else 0) for p in ordinary for q in ordinary), "H13 is zero on all ordinary fields") + continue + case = {} + for kind, word in all_words[str(k)].items(): + den = 4 if kind == "H" else 4 * abs(k - (1 if kind == "content_inverse" else 13)) + if not word: + require(k == 14 and kind in ["H", "inverse", "fused"], "Only the empty ordinary identities") + den = 1 + binary, odd = split(den) + actual, receipt = execute(word, den, odd, 9) + want = endpoint(g, selected, kind, den) + if not word: + want[C][C] = den + require(actual == want, "Family full basis endpoint: " + str(k) + " " + kind) + compare(receipt, family["cases"][str(k)][kind]) + closed_cost = { + "H": 7218 - 512 * k, + "inverse": 7186 - 512 * k + 16 * binary, + "fused": 7186 - 256 * k + 16 * binary, + "content": 7186 + 16 * k + 16 * binary, + "content_inverse": 7186 + 16 * k + 16 * binary, + }[kind] if word else 0 + require(receipt["old_real_primitives"] == closed_cost + and receipt["real_odd_scans"] == (16 if word and odd > 1 else 0), "Independent closed invoice") + if word: + require(receipt["additional_binary_height"] <= 5, "Uniform binary height") + require(Fraction(receipt["max_row_l1"]) <= 6328, "Uniform prefix norm") + first_scatter = next(i for i, e in enumerate(word) if e[0] == "add" and e[1] != C) + wrong = [list(e) for e in word] + wrong[first_scatter][3] = str(-Fraction(wrong[first_scatter][3])) + try: + bad, _ = execute(wrong, den, odd, 9) + except ValueError as error: + require(str(error) in { + "Exact binary scale on every encoded basis column", + "The complete query cancels prior local odd denominators", + "Every encoded basis numerator is divisible at the scan", + "At most one stated odd denominator at every prefix"}, "Expected mutation rejection") + else: + require(bad != want, "Wrong scatter changes the exact endpoint") + controls += 1 + case[kind] = receipt + predicted = family["cases"][str(k)]["predicted_local"] + require(predicted["balanced_F_old"] == 164514 + 416 * k + 14 + case["H"]["old_real_primitives"] + and predicted["balanced_B_old"] == 164514 + 208 * k + 14 + case["inverse"]["old_real_primitives"] + and predicted["fused_B_old"] == 164514 + 208 * k + 14 + case["fused"]["old_real_primitives"], + "Conditional local assembly sums") + all_receipts[str(k)] = case + require(sum(len(c) for c in all_receipts.values()) == 69 and controls == 66, "All factor and mutation cases") + return baseline, all_receipts, controls + + +def structural_checks(r, g, minors): + a = set(minors[0]) + e = [-1 if p in a else 1 for p in range(112)] + for i in range(8): + for j in range(8): + require(sum(r[i][p] * r[j][p] for p in range(112) if p not in a) == (52 if i == j else 0), "Actual A8 Gram 52I") + require(sum(r[i][p] * e[p] * r[j][p] for p in range(112)) == (48 if i == j else 0), "R E K=12I") + # Multiply the scaled projector independently as dense integer matrices. + projector = [[48 * (p == q) - e[p] * g[p][q] for q in range(112)] for p in range(112)] + columns = list(zip(*projector)) + require(all(sum(x * y for x, y in zip(row, col)) == 48 * projector[p][q] + for p, row in enumerate(projector) for q, col in enumerate(columns)), "E A8 is a projector over Q") + require(sum(projector[p][p] for p in range(112)) == 48 * 104, "Projector trace and rank 104") + for p in range(112): + for i in range(8): + require(sum(projector[p][q] * e[q] * r[i][q] for q in range(112)) == 0, "Its kernel is the independent eight-channel E K image") + return {"R_U_R_U_transpose": "52 I8", "R_E_K": "12 I8", "A8_rank": 104, "A8_nullity": 8, + "ordinary_singular_k": 13, "content_singular_k": 1, "minor_Gram_checks": 14 * 64} + + +def bit_scan(number, width, odd, inverse): + source = number % (1 << width) + carry = 0 + output = 0 + for i in range(width): + bit = (source >> i) & 1 + if inverse: + value = (bit - carry) & 1 + carry = (carry + odd * value - bit) // 2 + else: + value, carry = (odd * bit + carry) & 1, (odd * bit + carry) // 2 + require(0 <= carry < odd, "Finite scan carry bound") + output |= value << i + input_sign = (source >> (width - 1)) & 1 + output_sign = (output >> (width - 1)) & 1 + valid = carry == (odd * output_sign - input_sign if inverse else odd * input_sign - output_sign) + return valid, output - (1 << width) * output_sign + + +def scan_checks(): + odds = [3, 5, 7, 9, 11, 13] + results = [] + for odd in odds: + count = 0 + for width in range(1, 13): + modulus = 1 << width + inverse_modulus = pow(odd, -1, modulus) + lo, hi = -modulus // 2, modulus // 2 + for number in range(lo, hi): + valid, quotient = bit_scan(number, width, odd, True) + require(quotient % modulus == (number * inverse_modulus) % modulus, "Independent modular quotient") + require(valid == (number % odd == 0) and (not valid or quotient * odd == number), "Signed exact division at all tested inputs") + good, product = bit_scan(number, width, odd, False) + require(good == (lo <= number * odd < hi) and (not good or product == number * odd), "Signed multiplication and guard test") + count += 1 + require(not bit_scan(1, 12, odd, True)[0], "Unconverted finest-grid numerator fails") + results.append({"odd": odd, "signed_inputs": count, "directions": 2}) + require(lcm(*odds) == 45045 and 45045 < 2**16 and 45045 == 3 * 3 * 5 * 7 * 11 * 13, "Uniform root divisor and six scans") + return results + + +def recursive_grid_check(depth, odd): + scale = odd ** (depth + 1) + rows = [[scale, 0], [0, scale]] + peak_height = 0 + calls = 0 + + def visit(remaining): + nonlocal peak_height, calls, rows + calls += 1 + saved = [list(r) for r in rows] + rows[0] = [a + b for a, b in zip(rows[0], rows[1])] + require(all(v % odd == 0 for v in rows[0]), "Active-chain grid divisibility") + rows[0] = [v // odd for v in rows[0]] + for row in rows: + for v in row: + d, h = scale // gcd(abs(v), scale), 0 + while d > 1: + require(d % odd == 0, "Fixture denominator power") + d //= odd + h += 1 + peak_height = max(peak_height, h) + if remaining: + visit(remaining - 1) + visit(remaining - 1) + rows[0] = [odd * a - b for a, b in zip(rows[0], rows[1])] + require(rows == saved, "Every complete child restores both arbitrary columns") + + visit(depth) + require(rows == [[scale, 0], [0, scale]] and peak_height == depth + 1, "Dyadic outer endpoint and depth-only height") + # Three completed rational children defeat a depth-one height budget. + wrong = odd**2 + for _ in range(2): + require(wrong % odd == 0, "Rational-endpoint control setup") + wrong //= odd + require(wrong % odd != 0, "Completed rational children require another bound") + return {"recursive_edges": depth, "completed_nodes": calls, "odd": odd, "maximum_height": peak_height} + + +def main(): + r, g, minors, family, pins, pr_pins = sources() + structural = structural_checks(r, g, minors) + baseline, factors, mutations = factor_checks(g, minors, family) + scans = scan_checks() + recursive = [recursive_grid_check(depth, odd) for depth in range(6) for odd in [3, 45045]] + out = {"status": "PASS_INDEPENDENT_ODD_GRID_AND_MINOR_FACTORS", "source_freezes": FREEZES, + "interface_sha256": INTERFACE_PIN, "model_sources": pins["sources"], "pinned_pr_sources": pr_pins, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "method": "Dense integer-grid basis replay, exact divisibility at every opcode, independent formula endpoints, and dense projector multiplication. No producer module is imported.", + "formal_input_columns": 113, "structural": structural, "A8_baseline": baseline, + "minor_factors": factors, "wrong_scatter_controls": mutations, + "signed_scan_checks": scans, "recursive_grid_fixtures": recursive, + "proof_scope": "The source-backed active-chain proof covers general recursion. The fixtures check the invariant and its necessary hypotheses.", + "limits": ["Only common-frame scalar factors are reviewed here", "No new native recipe or H1 child is inserted by these words", "Complete local transfer is a separate review", "Binary guard constants, hosting, final dyadic endpoint and full supplier moment remain separate"]} + (HERE / "REVIEW.json").write_text(json.dumps(out, sort_keys=True, indent=2) + "\n") + print(out["status"]) + print(json.dumps({"factors": 69, "A8_baselines": 3, "columns": 113, "mutations": mutations, + "signed_scan_inputs": sum(s["signed_inputs"] for s in scans), "recursive_fixtures": len(recursive)}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/producer-replay/A8-ODD-GRID-WORDS.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/producer-replay/A8-ODD-GRID-WORDS.json new file mode 100644 index 0000000000..c2985f02fc --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/producer-replay/A8-ODD-GRID-WORDS.json @@ -0,0 +1 @@ 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Literal native transfer, full controller, and complete supplier cost remain separate.", + "signed_scan_checks": [ + { + "odd_divisor": 3, + "signed_inputs": 2046, + "transition_cases": 6 + }, + { + "odd_divisor": 5, + "signed_inputs": 2046, + "transition_cases": 10 + }, + { + "odd_divisor": 7, + "signed_inputs": 2046, + "transition_cases": 14 + }, + { + "odd_divisor": 9, + "signed_inputs": 2046, + "transition_cases": 18 + }, + { + "odd_divisor": 11, + "signed_inputs": 2046, + "transition_cases": 22 + }, + { + "odd_divisor": 13, + "signed_inputs": 2046, + "transition_cases": 26 + } + ], + "status": "PASS_ALL_COMPLETE_MINOR_SCALAR_FACTORS", + "uniform_odd_multiple": 45045 +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/FREEZE.json new file mode 100644 index 0000000000..6df47602e9 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "REVIEW.md": "d68faf6def55a1af01423bce205b91735c7b882d9b4029d6c0991fae5ebd2425", + "check_family_review.py": "ffd8501205d60b795a99a02fd56995afd2ddc71a2b44c7ce237ca2c853d7b487", + "normal.json": "bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba", + "optimized.json": "bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba" + }, + "normal_optimized_byte_identical": true, + "scope": "Independent review of root word/cost and oblique metric classification. This lane supplied the basis; no second independent basis-review claim.", + "status": "FROZEN_WORD_COST_AND_CLASSIFICATION_REVIEW" +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/REVIEW.md new file mode 100644 index 0000000000..ab73374437 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/REVIEW.md @@ -0,0 +1,165 @@ +# Review of the general signed-family word and restrictions + +The root's complete scalar word, exact price, and prefix bounds are +correct. The oblique lane's diagonal-metric classification and +rank-two-per-block lower bound are also correct. The general basis +was first supplied by this review lane. Thus this is an independent +check of the root's word and cost, not an independent second review +of this lane's own basis. + +The checked sources are: + +- [Root proof](../../../root/SIGNED-METRIC-DYADIC-FAMILY-20261020.md), + SHA256 `c19042d37e37921de9a67fbdaf262305811190f7e886f199b89a09f2c044667a`. +- [Root checker](../../../root/check_signed_metric_family.py), + SHA256 `9daacf3e3f5683477235824a18afb92b09aad42c5ac297862aa1d2c7c5dea9fa`. +- [Family restrictions](../../oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY.md), + SHA256 `d5764b5fd29ccd897a7a666b22d8e77bdca415f65072d44974b0ff7b70f37e43`. + Its separate freeze is + `a6088c38e984e7c4f15fb462d0cb89ac2c73cb2b6bbba0501513c236b32107b1`. + +## Scalar word + +Put \(k=2^r\), \(n=k+4\), and use the root's coordinate order. +After the Walsh transform and the first two-field butterfly, the +named fields hold \(S,T,d,b,c\). The six instructions then give + +\[ + S=v=S_{\rm old}-b_{\rm old},\qquad + T=\ell=-T_{\rm old}-v, +\] + +and + +\[ + b=-b_{\rm old}-(k/2)\ell-((k+2)/4)v + =(k/2)T_{\rm old}-b_{\rm old}+((k-2)/4)v=w'. +\] + +The final butterfly gives \(v+w'\) and \(v-w'\). This proves the +word implements the stated basis for every \(r\). Each instruction +is invertible on arbitrary input contents. Reverse order with +inverse instructions therefore gives the complete inverse without +a zero target or an extra field. + +There are \(kr/2\) Walsh butterflies and two further butterflies. +Each costs 20 real primitives. The four unit/sign instructions in +the middle cost 20. The other two ADD coefficients are \(k/2\) and +\((k+2)/4\). + +For \(r\ge2\), their prices are \(2r+6\) and \(2r+10\). For \(r=0\) +they cost 10 and 16; for \(r=1\) they cost 8 and 8. Thus the total +price, in either direction, is + +\[ + 86\ (r=0),\qquad 96\ (r=1),\qquad 10kr+76+4r\ (r\ge2). +\] + +The instruction count is \(3kr/2+12\). The tariff charges the +non-power-of-two dyadic ADD coefficient by its complete numerator +bit length and population count. It is not priced as a unit ADD. + +## Prefix bounds + +At the end of the initial Walsh and pair blocks, the row one-norm +is at most \(\max(k,2)\). Relative to those inputs, the middle +S and T rows have norms at most two and three. Its b row has norm +at most + +\[ + 1+(k/2)3+((k+2)/4)2=2k+2. +\] + +The last butterfly has prefix norm at most \(4k+4\): the doubled +row gives that bound, and the final subtraction gives \(v-w'\). +This proves the root's forward bound +\(4(k+1)\max(k,2)\). + +For the inverse, the first inverse butterfly has prefix norm at +most two and completed norm one. In the three-field inverse, +the b row is bounded by \(1+(k+2)/4+k/2\); the T row by two; and +the restored S row by one plus the b bound. All are at most +\(k+5\) for \(k\ge1\). Every remaining inverse butterfly has +prefix norm at most two and completed norm one. Completed stages +therefore do not multiply the bound repeatedly. This proves +the inverse bound \(2(k+5)\). + +The forward word introduces denominators only in the two middle +ADDs, at height at most two. In reverse, the first inverse +butterfly adds one binary division. The middle block can add +at most two more. The disjoint inverse Walsh and pair parts add +at most \(\max(r,1)\). Thus the stated inverse height +\(\max(r,1)+3\) is valid. These are scalar-word bounds only. + +## Diagonal-metric classification + +For the reciprocal family, write \(m=n-4>0\) and let +\(D=\operatorname{diag}(d_0,\ldots,d_{n-3},e,f)\). +The last column of E has one unit entry in row b. Its norm +equation gives \(e=f\). The ordinary column norm equations give + +\[ + \sum_jd_j+m^2f=2d_i. +\] + +Thus every \(d_i=d\). Since there are \(m+2\) such entries, +these equations give \(m(d+mf)=0\), and hence \(e=f=-d/m\). +The known metric identity proves sufficiency. The entire space +of invariant diagonal metrics is therefore the scalar multiples +of \(J\). + +A nonsingular real such metric is indefinite. If all its entries +are units of \(\mathbb Z[1/2]\), their ratio \(m\) must be a +signed power of two. Since \(m>0\), it is \(2^r\). Conversely, +that condition makes both J and its inverse diagonal dyadic units. +The criterion is exact for this family. + +The excluded small dimensions matter. At \(n=3\), this family is +a three-cycle and permits a positive diagonal metric. At \(n=4\), +the off-diagonal equations force the ordinary weights to zero; +the remaining two weights agree. Such a metric is singular. + +## Minimum displacement and scope + +If \(A=I+vw^T\) has zero diagonal, then \(v_iw_i=-1\) and +\(w^Tv=-n\). For \(n\ge3\) in characteristic zero, its inverse +has diagonal \((n-2)/(n-1)\), which is nonzero. Thus an invertible +response and its inverse cannot both have zero diagonal with +\(\operatorname{rank}(A-I)<2\). + +The family E attains rank two in each block. Rank 32 is therefore +sharp for the stated direct sum of sixteen independent blocks. +The proof does not give a rank-32 bound for coupled 112-port +responses or a changed baseline. In particular, \(E-P\) has +rank sixteen and is the quantity captured by the signed code. + +## Checks and attribution + +[check_family_review.py](check_family_review.py) imports this lane's +frozen exact arithmetic, not producer code. It constructs the +basis from \(v,w'\), replays the complete word and inverse on +arbitrary inputs, and checks both inverse orders, the Gram, +determinant square, exact cost, and bounds for \(k=1,\ldots,64\) +in powers of two. Five additional input fields remain unchanged. +A deleted gate fails. + +A separate calculation builds every coefficient equation for a +diagonal invariant metric, for \(n=5,\ldots,24\). It verifies +nullity one, reciprocal zero diagonals, and both displacement +ranks. These checks support the all-size proofs above. + +Run in normal Python and in `python3 -O`, with separate +`--output` files. The expected status is +`PASS_SIGNED_FAMILY_WORD_AND_METRIC_CLASSIFICATION`. +The receipts must match. + +The root lane supplied the combined scalar word and its prices. +This lane supplied the underlying basis and this word review. +The oblique lane supplied the metric classification and sharp +blockwise restriction. AI assistance was used. + +No general native row placement, phase recipe, caller, host, +or supplier bound is proved here. Publication is coordinated by +the parent; this lane does not create a PR. Before a PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/check_family_review.py b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/check_family_review.py new file mode 100644 index 0000000000..45df6ed108 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/check_family_review.py @@ -0,0 +1,169 @@ +"""Check the general scalar word and the diagonal-metric classification.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +ROOT = LANES.parent / "root" +PREVIOUS = HERE.parent / "signed-metric-review-20261020" +MODEL = LANES / "oblique-native-20261017/signed-metric-reciprocal-20261020" +PINS = { + "SIGNED-METRIC-DYADIC-FAMILY-20261020.md": "c19042d37e37921de9a67fbdaf262305811190f7e886f199b89a09f2c044667a", + "check_signed_metric_family.py": "9daacf3e3f5683477235824a18afb92b09aad42c5ac297862aa1d2c7c5dea9fa", + "signed-metric-family-normal.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37", + "signed-metric-family-optimized.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37", +} +PRIOR_PIN = "b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762" +FAMILY_PIN = "a6088c38e984e7c4f15fb462d0cb89ac2c73cb2b6bbba0501513c236b32107b1" + + +def need(test, reason): + if not test: + raise ValueError(reason) + + +def freeze(path, pin): + raw = path.read_bytes() + need(sha256(raw).hexdigest() == pin, "Freeze pin") + for name, value in json.loads(raw)["files"].items(): + need(sha256((path.parent / name).read_bytes()).hexdigest() == value, "Frozen file") + + +freeze(PREVIOUS / "FREEZE.json", PRIOR_PIN) +spec = importlib.util.spec_from_file_location("own_signed_review", PREVIOUS / "check_review.py") +old = importlib.util.module_from_spec(spec) +spec.loader.exec_module(old) +r = old.r + + +def replay(word, n): + rows = r.eye(n) + cost, height, peak = 0, 0, F(1) + for op, target, source, value in word: + if op == "add": + for j, c in rows[source].items(): + r.put(rows[target], j, value * c) + a, b = abs(value.numerator), value.denominator + cost += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + else: + need(op == "scale", "Scalar grammar") + rows[target] = {j: value * c for j, c in rows[target].items()} + cost += 2 * (abs(old.dyadic_exponent(value)) + (value < 0)) + peak = max(peak, sum(map(abs, rows[target].values()))) + for c in rows[target].values(): + d = c.denominator + need(d & (d - 1) == 0, "Odd prefix denominator") + height = max(height, d.bit_length() - 1) + return rows, dict(cost=cost, height=height, peak=str(peak), instructions=len(word)) + + +def build_word(k): + gates = [] + def h(a, b): + gates.extend((("add", a, b, F(1)), ("scale", b, None, F(-2)), + ("add", b, a, F(1)))) + for bit in range(k.bit_length() - 1): + mask = 1 << bit + for left in range(k): + if not left & mask: + h(left, left | mask) + h(k, k + 1) + gates.extend((("add", 0, k + 2, F(-1)), ("add", k, 0, F(1)), + ("scale", k, None, F(-1)), ("add", k + 2, k, F(k, 2)), + ("add", k + 2, 0, F(k + 2, 4)), ("scale", k + 2, None, F(-1)))) + h(0, k + 2) + return gates + + +def closed(k): + n = k + 4 + a = [{} for _ in range(n)] + for i in range(1, k): + a[i] = {j: F(1 if (i & j).bit_count() % 2 == 0 else -1) for j in range(k)} + s = {j: F(1) for j in range(k)} + v = dict(s) + r.put(v, k + 2, F(-1)) + w = {k: F(k, 2), k + 1: F(k, 2), k + 2: F(-1)} + for j, value in v.items(): + r.put(w, j, F(k - 2, 4) * value) + for j in set(v) | set(w): + r.put(a[0], j, v.get(j, 0) + w.get(j, 0)) + r.put(a[k + 2], j, v.get(j, 0) - w.get(j, 0)) + a[k] = {j: F(-1) for j in range(k + 2)} + a[k][k + 2] = F(1) + a[k + 1] = {k: F(1), k + 1: F(-1)} + a[-1] = {n - 1: F(1)} + return a + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, default=HERE / "normal.json") + args = parser.parse_args() + for name, pin in PINS.items(): + need(sha256((ROOT / name).read_bytes()).hexdigest() == pin, "Root source pin") + freeze(MODEL / "FAMILY-FREEZE.json", FAMILY_PIN) + samples = [] + for power in range(7): + k, n = 2**power, 2**power + 4 + word = build_word(k) + fw, fb = replay(word, n + 5) + inverse = [(op, t, s, -c if op == "add" else 1 / c) for op, t, s, c in reversed(word)] + bw, bb = replay(inverse, n + 5) + c = closed(k) + need(fw[:n] == c and fw[n:] == bw[n:] == r.eye(n + 5)[n:], "All arbitrary inputs") + need(r.matmul(fw, bw) == r.matmul(bw, fw) == r.eye(n + 5), "Both inverse orders") + g = old.diagonal([-2 * k] + [k] * (k - 1) + [2, 2, 2 * k, -k]) + metric = old.diagonal([1] * (k + 2) + [-k, -k]) + need(r.matmul(c, r.matmul(metric, old.transpose(c, n))) == g, "Signed Gram") + _, determinant = r.invert(c) + need(determinant**2 == 16 * k**k, "Determinant square") + bill = 86 if power == 0 else 96 if power == 1 else 10 * k * power + 76 + 4 * power + need(fb["cost"] == bb["cost"] == bill, "Closed exact price") + need(fb["instructions"] == bb["instructions"] == 3 * k * power // 2 + 12, "Instruction count") + need(F(fb["peak"]) <= 4 * (k + 1) * max(k, 2) and F(bb["peak"]) <= 2 * (k + 5), + "General prefix norm bounds") + need(fb["height"] <= 2 and bb["height"] <= max(power, 1) + 3, "General height bounds") + need(replay(word[1:], n + 5)[0] != fw, "Deleted gate control") + samples.append(dict(k=k, forward=fb, inverse=bb)) + metric_samples = [] + for n in range(5, 25): + model = old.local_model(n) + e = model["E"] + equations = [] + for a in range(n): + for b in range(a, n): + eq = {i: e[i].get(a, 0) * e[i].get(b, 0) for i in range(n)} + eq = {i: value for i, value in eq.items() if value} + if a == b: + r.put(eq, a, F(-1)) + if eq: + equations.append(eq) + need(old.rank(equations, n) == n - 1, "Exact diagonal-metric nullity one") + need(old.rank(old.difference(e, r.eye(n)), n) == 2 + and old.rank(old.difference(e, model["P"]), n) == 1, "Both displacement ranks") + need(all(not matrix[i].get(i) for matrix in (e, model["inverse_E"]) for i in range(n)), + "Reciprocal zero diagonals") + metric_samples.append(dict(n=n, diagonal_metric_dimension=1, identity_rank=2, P_rank=1)) + output = dict( + status="PASS_SIGNED_FAMILY_WORD_AND_METRIC_CLASSIFICATION", + checker_sha256=sha256(Path(__file__).read_bytes()).hexdigest(), + root_source_pins=PINS, family_freeze_sha256=FAMILY_PIN, prior_review_freeze_sha256=PRIOR_PIN, + word_samples=samples, metric_samples=metric_samples, + scope="Independent word/cost and family classification review. This lane supplied the underlying basis.", + native_geometry_or_supplier_claim=False, + ) + raw = (json.dumps(output, sort_keys=True, indent=2) + "\n").encode() + args.output.write_bytes(raw) + print(output["status"]) + print(sha256(raw).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/normal.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/normal.json new file mode 100644 index 0000000000..aab8b71b99 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/normal.json @@ -0,0 +1,243 @@ +{ + "checker_sha256": "ffd8501205d60b795a99a02fd56995afd2ddc71a2b44c7ce237ca2c853d7b487", + "family_freeze_sha256": "a6088c38e984e7c4f15fb462d0cb89ac2c73cb2b6bbba0501513c236b32107b1", + "metric_samples": [ + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 5 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 6 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 7 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 8 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 9 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 10 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 11 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 12 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 13 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 14 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 15 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 16 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 17 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 18 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 19 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 20 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 21 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 22 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 23 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 24 + } + ], + "native_geometry_or_supplier_claim": false, + "prior_review_freeze_sha256": "b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762", + "root_source_pins": { + "SIGNED-METRIC-DYADIC-FAMILY-20261020.md": "c19042d37e37921de9a67fbdaf262305811190f7e886f199b89a09f2c044667a", + "check_signed_metric_family.py": "9daacf3e3f5683477235824a18afb92b09aad42c5ac297862aa1d2c7c5dea9fa", + "signed-metric-family-normal.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37", + "signed-metric-family-optimized.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37" + }, + "scope": "Independent word/cost and family classification review. This lane supplied the underlying basis.", + "status": "PASS_SIGNED_FAMILY_WORD_AND_METRIC_CLASSIFICATION", + "word_samples": [ + { + "forward": { + "cost": 86, + "height": 2, + "instructions": 12, + "peak": "4" + }, + "inverse": { + "cost": 86, + "height": 3, + "instructions": 12, + "peak": "3" + }, + "k": 1 + }, + { + "forward": { + "cost": 96, + "height": 0, + "instructions": 15, + "peak": "6" + }, + "inverse": { + "cost": 96, + "height": 2, + "instructions": 15, + "peak": "3" + }, + "k": 2 + }, + { + "forward": { + "cost": 164, + "height": 1, + "instructions": 24, + "peak": "15" + }, + "inverse": { + "cost": 164, + "height": 4, + "instructions": 24, + "peak": "4" + }, + "k": 4 + }, + { + "forward": { + "cost": 328, + "height": 1, + "instructions": 48, + "peak": "45" + }, + "inverse": { + "cost": 328, + "height": 5, + "instructions": 48, + "peak": "13/2" + }, + "k": 8 + }, + { + "forward": { + "cost": 732, + "height": 1, + "instructions": 108, + "peak": "153" + }, + "inverse": { + "cost": 732, + "height": 6, + "instructions": 108, + "peak": "25/2" + }, + "k": 16 + }, + { + "forward": { + "cost": 1696, + "height": 1, + "instructions": 252, + "peak": "561" + }, + "inverse": { + "cost": 1696, + "height": 7, + "instructions": 252, + "peak": "49/2" + }, + "k": 32 + }, + { + "forward": { + "cost": 3940, + "height": 1, + "instructions": 588, + "peak": "2145" + }, + "inverse": { + "cost": 3940, + "height": 8, + "instructions": 588, + "peak": "97/2" + }, + "k": 64 + } + ] +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/optimized.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/optimized.json new file mode 100644 index 0000000000..aab8b71b99 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-family-review-20261020/optimized.json @@ -0,0 +1,243 @@ +{ + "checker_sha256": "ffd8501205d60b795a99a02fd56995afd2ddc71a2b44c7ce237ca2c853d7b487", + "family_freeze_sha256": "a6088c38e984e7c4f15fb462d0cb89ac2c73cb2b6bbba0501513c236b32107b1", + "metric_samples": [ + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 5 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 6 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 7 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 8 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 9 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 10 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 11 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 12 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 13 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 14 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 15 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 16 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 17 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 18 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 19 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 20 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 21 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 22 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 23 + }, + { + "P_rank": 1, + "diagonal_metric_dimension": 1, + "identity_rank": 2, + "n": 24 + } + ], + "native_geometry_or_supplier_claim": false, + "prior_review_freeze_sha256": "b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762", + "root_source_pins": { + "SIGNED-METRIC-DYADIC-FAMILY-20261020.md": "c19042d37e37921de9a67fbdaf262305811190f7e886f199b89a09f2c044667a", + "check_signed_metric_family.py": "9daacf3e3f5683477235824a18afb92b09aad42c5ac297862aa1d2c7c5dea9fa", + "signed-metric-family-normal.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37", + "signed-metric-family-optimized.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37" + }, + "scope": "Independent word/cost and family classification review. This lane supplied the underlying basis.", + "status": "PASS_SIGNED_FAMILY_WORD_AND_METRIC_CLASSIFICATION", + "word_samples": [ + { + "forward": { + "cost": 86, + "height": 2, + "instructions": 12, + "peak": "4" + }, + "inverse": { + "cost": 86, + "height": 3, + "instructions": 12, + "peak": "3" + }, + "k": 1 + }, + { + "forward": { + "cost": 96, + "height": 0, + "instructions": 15, + "peak": "6" + }, + "inverse": { + "cost": 96, + "height": 2, + "instructions": 15, + "peak": "3" + }, + "k": 2 + }, + { + "forward": { + "cost": 164, + "height": 1, + "instructions": 24, + "peak": "15" + }, + "inverse": { + "cost": 164, + "height": 4, + "instructions": 24, + "peak": "4" + }, + "k": 4 + }, + { + "forward": { + "cost": 328, + "height": 1, + "instructions": 48, + "peak": "45" + }, + "inverse": { + "cost": 328, + "height": 5, + "instructions": 48, + "peak": "13/2" + }, + "k": 8 + }, + { + "forward": { + "cost": 732, + "height": 1, + "instructions": 108, + "peak": "153" + }, + "inverse": { + "cost": 732, + "height": 6, + "instructions": 108, + "peak": "25/2" + }, + "k": 16 + }, + { + "forward": { + "cost": 1696, + "height": 1, + "instructions": 252, + "peak": "561" + }, + "inverse": { + "cost": 1696, + "height": 7, + "instructions": 252, + "peak": "49/2" + }, + "k": 32 + }, + { + "forward": { + "cost": 3940, + "height": 1, + "instructions": 588, + "peak": "2145" + }, + "inverse": { + "cost": 3940, + "height": 8, + "instructions": 588, + "peak": "97/2" + }, + "k": 64 + } + ] +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/FREEZE.json new file mode 100644 index 0000000000..f8deae37b8 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "REVIEW.md": "79ffc65f3037d00a03fbfa99e0a24ab3c889412602be21a022399ad59f8599f1", + "check_review.py": "415a45c0475f0d6499d77e0b41b695596ddb99536c60e5ec9859fd564f8edf0f", + "normal/REVIEW-CHECKS.json": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b", + "optimized/REVIEW-CHECKS.json": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b" + }, + "normal_optimized_byte_identical": true, + "scope": "Actual signed112 model; original and paired16 code matrices and scalar words; no native service, routed caller, host or supplier claim.", + "status": "FROZEN_INDEPENDENT_REVIEW_PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/REVIEW.md new file mode 100644 index 0000000000..2e746db2c8 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/REVIEW.md @@ -0,0 +1,307 @@ +# Independent review of the signed metric and sixteen-reader code + +The actual 112-port response and both scalar codes pass this review. +The signed metric permits a dyadic code with sixteen centre fields. +The new pair suffix also makes the transpose fit the native support +conditions. These are exact local results. This review does not certify +a native service, a routed caller, a recursive host, or a supplier bound. + +## Sources and method + +The review pins these producer freezes: + +| Packet | Freeze SHA256 | +| --- | --- | +| Reciprocal model | `9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7` | +| Original sixteen-reader code | `8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2` | +| Pair-closed companion | `810508791ea43aecaaf894c3cb50a8170d3e6f1f8e52684e274cda16c2c2db57` | + +The source proofs are +[MODEL.md](../../oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL.md), +[SIGNED-SIXTEEN.md](../../new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/SIGNED-SIXTEEN.md), +and [PAIRED-COMPANION.md](../../new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-COMPANION.md). + +[check_review.py](check_review.py) imports no producer code. It uses +the exact sparse fraction engine from this lane's frozen +[query review](../fixed-reader-reuse-review-20261020/FREEZE.json). +It constructs each response and code from the formulas below, then +compares all matrices with the pinned packets. It reconstructs the +physical pair matrix from the actual pair list. It checks the actual +port labels, all sixteen blocks, and every physical support entry. + +The scalar replay starts with 640 independent complex input fields. +Each field is an independent symbolic variable. The check therefore +covers arbitrary data and borrowed fields, not only zero work fields. +The complete code words leave the other 528 fields unchanged. The +two-bank reference words leave the other 416 fields unchanged. + +## The reciprocal response + +Let \(n=k+4\). In the coordinate order +\((a_0,\ldots,a_{n-3},b,c)\), set + +\[ + u=(1^{n-2},k,0)^T,\qquad \ell=(-1^{n-2},1,0),\qquad + R=I+u\ell,\qquad E=PR, +\] + +where \(P\) exchanges \(b,c\). Let + +\[ + J=\operatorname{diag}(1^{n-2},-1/k,-1/k),\qquad K=J^{-1}. +\] + +Then \(\ell u=-2\), \(Ju=-\ell^T\), and \(u^TJu=2\). +Expansion gives + +\[ + R^2=I,\qquad R^TJR=J,\qquad P^TJP=J. +\] + +It follows that + +\[ + E^{-1}=RP,\qquad E^TJE=J,\qquad E^{-T}=JEK. +\] + +The order \(RP\) in the inverse is required. In general \(E^2\ne I\). +The displayed formulas give zero diagonal for both \(E\) and \(E^{-1}\). +Each block has \(\operatorname{rank}(E-P)=1\) and +\(\operatorname{rank}(E-I)=2\). + +The actual response has eight six-mode blocks and eight eight-port +blocks. Thus the two ranks are sixteen and thirty-two. The sixteen +readers encode \(E-P\). They do not encode \(E-I\) in sixteen fields. + +## The physical chart + +Let \(H\) be the 24 actual pair codes on the large 48-port sector. +It is the identity on the small 64-port sector. Each pair satisfies +\(H_{\rm pair}^TH_{\rm pair}=2I\). Physical matrices are +\(H^{-1}AH\), where \(A\) is the mode matrix. + +The scale in \(H^TH\) is constant on the whole large sector. All +mode matrices preserve the large and small sectors. The input metric +is constant on each physical pair. These facts, rather than similarity +alone, preserve the transpose metric identity. The physical \(J\) is +diagonal, with 80 entries \(1\), sixteen entries \(-1/2\), and sixteen +entries \(-1/4\). + +The check confirms both physical zero diagonals and every orthogonal +port-label support condition. Physical \(P\) is the identity on 80 +fields and acts only on the other 32. It has 160 nonzero entries and +is not a field permutation. Its complete common-frame word costs 728 +real scalar primitives. This price does not include address views. + +## The local code and its inverse + +For \(n=6\), use these rows in order: + +\[ + \ell,\quad a_2-a_3,\quad a_0-a_1,\quad c,\quad + a_0+a_1-a_2-a_3,\quad \sum_{j=0}^3a_j-2b. +\] + +For \(n=8\), use: + +\[ +\begin{split} + \ell,\quad &a_4+a_5-b/2,\quad a_4-a_5,\quad c,\quad + a_0-a_1,\quad a_2-a_3,\\ + &a_0+a_1-a_2-a_3,\quad + \sum_{j=0}^3a_j+2a_4+2a_5-2b. +\end{split} +\] + +Call the direct sum of these matrices \(C_m\). Direct row products +give the local \(K\)-Grams + +\[ + G_6=\operatorname{diag}(2,2,2,-2,4,-4),\qquad + G_8=\operatorname{diag}(2,1,2,-4,2,2,4,-4). +\] + +Both local determinants are \(-8\). Each ordinary row annihilates +\(u\), and its diagonal entry is zero. The centre row is \(\ell\). +Thus \(C_mR=ZC_m\), where \(Z\) negates the sixteen centre positions. +Each displayed Gram entry is a dyadic unit. The identity +\(C_m^{-1}=K C_m^T G_m^{-1}\) proves a dyadic inverse. + +For the original physical code, let \(H_{\mathrm{ord}}^{-1}\) undo +the pair codes only on ordinary pairs. Then + +\[ + C=H_{\mathrm{ord}}^{-1}C_mH,\qquad + CKC^T=G,\qquad + C^{-1}=KC^TG^{-1},\qquad C^{-T}=G^{-1}CK. +\] + +The actual ordinary pairs have equal Gram entries. Hence \(G\) is +physical and diagonal. The selected rows are exactly the sixteen +source readers \(L\), in the source order. Their weighted Gram is + +\[ + LKL^T=\operatorname{diag}(4I_8,2I_8). +\] + +The factor four on the first eight rows comes from the physical +pair transform. The check does not replace it by two. + +## The paid pair suffix + +Let \(H_{\mathrm{sel}}\) be \(H\) on the four selected large pairs +and the identity elsewhere. The companion code is + +\[ + \bar C=H_{\mathrm{sel}}^{-1}C=H^{-1}C_mH. +\] + +The supplied suffix implements \(H_{\mathrm{sel}}^{-1}\) in 13 +instructions, at a cost of 80 real scalar primitives. It changes +the selected readers by an invertible pair code. It leaves all +ordinary rows unchanged. The individual readers are recovered by +the paid matrix \(H_{\mathrm{sel}}\); recovery is not free. + +The complete native charts satisfy + +\[ + H\bar C H^{-1}=C_m,\qquad + H\bar C^T H^{-1}=C_m^T. +\] + +For the second identity use that \(H^TH\) commutes with \(C_m^T\). +Both matrices have zero ordinary diagonals and the admitted local +mode support. In contrast, the original \(HC^TH^{-1}\) has 32 +ordinary rows outside their mode blocks. The suffix resolves this +specific support defect. + +The companion Gram \(\bar G=\bar C K\bar C^T\) is diagonal. +Its sixteen selected entries are all two. The check proves + +\[ + \bar C^{-1}=K\bar C^T\bar G^{-1},\qquad + \bar C^T\bar G^{-1}\bar C=J +\] + +and both inverse orders. These conditions permit a separate native +construction to use the transpose code. This review certifies its +scalar word and support; it does not substitute them for a native +phase check. + +## Complete scalar prices and bounds + +All listed prices include pair changes, signs, scales, and exchanges. +The norms and binary heights are exact maxima at scalar instruction +boundaries. They are not bounds on internal native-child arithmetic. + +| Word | Real scalar primitives | Prefix row one-norm | Binary height | +| --- | ---: | ---: | ---: | +| Original \(C\) | 5564 | 24 | 3 | +| Original \(C^{-1}\) | 5564 | 9 | 3 | +| Original literal \(C^{-T}\) | 5564 | 5 | 3 | +| Original diagonal construction of \(C^{-T}\) | 6092 | 32 | 3 | +| Companion \(\bar C\) | 5644 | 24 | 3 | +| Companion \(\bar C^T\) | 5644 | 8 | 3 | +| Companion \(\bar C^{-1}\) | 5644 | 10 | 3 | +| Companion \(\bar C^{-T}\) | 5644 | 6 | 3 | + +Each companion word has 752 instructions and uses no extra field. +No prefix uses an odd denominator. + +## Arbitrary target baselines in the clean dual + +Let \(S\) project onto the selected fields and \(T=I-S\). The complete +clean reference map is + +\[ + F_C=\begin{pmatrix}TC&-S\\C&T\end{pmatrix},\qquad + F_C^{-T}=\begin{pmatrix}TC^{-T}&-I\\SC^{-T}&T\end{pmatrix}. +\] + +The exact diagonal conversion is + +\[ + \operatorname{diag}(G,G)F_C^{-T} + \operatorname{diag}(J,G^{-1}) + = + \begin{pmatrix}TC&-I\\SC&T\end{pmatrix}. +\] + +This follows from \(C^{-T}=G^{-1}CK\), and from the fact that +diagonal \(G\) commutes with \(S,T\). The result holds for arbitrary +inputs in both banks. In particular, it retains each ordinary target +baseline with coefficient \(-1\) in the first bank and \(+1\) in the +second bank. Both input banks have a metric factor. + +The independent replay forms the literal chronological inverse- +adjoint of the scalar word. It then applies the exact pre and post +scales. It also checks conjugation by the selected-bank exchange. +The complete metric wrappers cost 1264 real primitives before fusion. +Deleting the input metric scales on the target bank makes the map +incorrect. This two-bank price is distinct from the 320-primitives +one-bank conversion in the reciprocal model. + +## What changes in the coordinate obstruction + +The new raw physical reader has Euclidean Gram + +\[ + LL^T=\operatorname{diag}(10I_8,7I_8). +\] + +It has row rank sixteen modulo each of 3, 5, and 7. Its Gram rank +is sixteen modulo 3, but eight modulo 5 or 7. Thus the old modulo-3 +instance must not be applied to this new reader without change. + +The general coordinate obstruction still applies to a Euclidean +unitary code. A subspace of dimension \(r\), with restricted Gram +rank \(s\), in a nondegenerate space of dimension \(m\) must satisfy +\(m\ge 2r-s\). Its radical has dimension \(r-s\), lies in the +orthogonal complement, and that complement has dimension \(m-r\). +Apply this argument modulo 5 or 7. A real dyadic orthogonal code +requires at least 24 output coordinates for this reader. + +For a Gaussian dyadic unitary code, use realification. The two real +copies have row rank 32 and Gram rank 16. Thus \(2m\ge64-16\), so +at least 24 complex coordinates are required. This assumes exact +read access through the supported output coordinates, as in the +[coordinate theorem](../../../root/UNITARY-CENTRE-FOOTPRINT-20261020.md). + +The sixteen-field code does not satisfy the Euclidean-unitary +hypothesis. It preserves a signed metric between two diagonal +coordinate metrics. Its weighted reader Gram is a dyadic unit. +This is the precise escape from the unitary obstruction. + +## Reproduction, limits, and credit + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/signed-metric-review-20261020/check_review.py --output +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/signed-metric-review-20261020/check_review.py --output +``` + +The expected status is +`PASS_INDEPENDENT_SIGNED_METRIC_AND_SIXTEEN_CENTRES`. +Both modes must give the same receipt bytes. The check includes +negative controls for a deleted code ADD, a deleted inverse ADD, +the changed raw reader after the pair suffix, a changed metric sign, +and omitted target metric scales. + +The checker also verifies the proposed general one-centre Gram for +seven sizes \(k=1,2,4,8,16,32,64\). These checks are regression data. +The separate all-size proof and word are not part of this freeze. + +The root lane supplied the signed reciprocal family. The oblique +lane bound its actual response. The new-core-transfer lane supplied +the sparse local bases, scalar words, and paid pair suffix. This +review independently derives the matrices, checks all scalar +columns, and identifies the modulo-5 and modulo-7 unitary bounds. +AI assistance was used. + +Native phases, routed source access, saved-record restoration, +recursive hosting, finite-precision guards, and the complete supplier +cost remain separate obligations. No selected bound changes here. +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/check_review.py b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/check_review.py new file mode 100644 index 0000000000..e40a765aba --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/check_review.py @@ -0,0 +1,507 @@ +"""Check the signed metric and the actual one-centre completion.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent.parent +OLD = HERE.parent / "fixed-reader-reuse-review-20261020" +MODEL = LANES / "oblique-native-20261017/signed-metric-reciprocal-20261020" +CODE = LANES / "new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020" +MODEL_FREEZE = "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7" +MODEL_PIN = "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0" +CODE_FREEZE = "8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2" +CODE_PIN = "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c" +PAIRED_FREEZE = "810508791ea43aecaaf894c3cb50a8170d3e6f1f8e52684e274cda16c2c2db57" +PAIRED_PIN = "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1" +OLD_PIN = "d8d782ecc13fdd2d26380fc4b047fc6d6781417ec694fdd3dea910dce04c2e2a" + + +def need(test, reason): + if not test: + raise ValueError(reason) + + +def read(path, pin, compressed=False): + raw = path.read_bytes() + if compressed: + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Source pin: " + str(path)) + return json.loads(raw) + + +def freeze(path, pin): + value = read(path, pin) + for name, expected in value["files"].items(): + raw = (path.parent / name).read_bytes() + pin = expected["sha256"] if isinstance(expected, dict) else expected + need(sha256(raw).hexdigest() == pin, "Frozen file: " + name) + if isinstance(expected, dict) and "decompressed_sha256" in expected: + need(sha256(gzip.decompress(raw)).hexdigest() == expected["decompressed_sha256"], + "Frozen decompressed file: " + name) + return value + + +freeze(OLD / "FREEZE.json", OLD_PIN) +spec = importlib.util.spec_from_file_location("independent_signed_metric_math", OLD / "check_review.py") +r = importlib.util.module_from_spec(spec) +spec.loader.exec_module(r) + + +def transpose(a, columns): + result = [{} for _ in range(columns)] + for i, row in enumerate(a): + for j, value in row.items(): + result[j][i] = value + return result + + +def diagonal(values): + return [{i: F(value)} for i, value in enumerate(values)] + + +def difference(a, b): + out = [dict(row) for row in a] + for row, source in zip(out, b): + for p, value in source.items(): + r.put(row, p, -value) + return out + + +def rank(a, columns): + state = [dict(row) for row in a] + pivot = 0 + for j in range(columns): + found = next((i for i in range(pivot, len(state)) if state[i].get(j)), None) + if found is None: + continue + state[pivot], state[found] = state[found], state[pivot] + divisor = state[pivot][j] + state[pivot] = {q: c / divisor for q, c in state[pivot].items()} + for i in range(pivot + 1, len(state)): + value = state[i].get(j, F(0)) + for q, c in state[pivot].items(): + r.put(state[i], q, -value * c) + pivot += 1 + return pivot + + +def modular_rank(a, columns, prime): + state = [{j: (v.numerator * pow(v.denominator, -1, prime)) % prime for j, v in row.items()} + for row in a] + pivot = 0 + for j in range(columns): + found = next((i for i in range(pivot, len(state)) if state[i].get(j)), None) + if found is None: + continue + state[pivot], state[found] = state[found], state[pivot] + reciprocal = pow(state[pivot][j], -1, prime) + state[pivot] = {q: value * reciprocal % prime for q, value in state[pivot].items()} + for i in range(pivot + 1, len(state)): + value = state[i].get(j, 0) + for q, coefficient in state[pivot].items(): + state[i][q] = (state[i].get(q, 0) - value * coefficient) % prime + pivot += 1 + return pivot + + +def install(a, local, ports): + for p, row in zip(ports, local): + a[p] = {ports[j]: value for j, value in row.items()} + + +def local_model(n): + k = n - 4 + u = [F(1)] * (n - 2) + [F(k), F(0)] + ell = [F(-1)] * (n - 2) + [F(1), F(0)] + reflection = r.eye(n) + for i, value in enumerate(u): + for j, coefficient in enumerate(ell): + r.put(reflection[i], j, value * coefficient) + permutation = r.eye(n) + permutation[-2], permutation[-1] = permutation[-1], permutation[-2] + metric = diagonal([1] * (n - 2) + [F(-1, k)] * 2) + metric_inverse = diagonal([1] * (n - 2) + [-k] * 2) + response = r.matmul(permutation, reflection) + inverse = r.matmul(reflection, permutation) + need(sum(a * b for a, b in zip(u, ell)) == -2, "Reflection scalar") + need(r.matmul(reflection, reflection) == r.eye(n), "Local reflection") + need(r.matmul(response, inverse) == r.matmul(inverse, response) == r.eye(n), "Local reciprocal orders") + need(r.matmul(transpose(response, n), r.matmul(metric, response)) == metric, "Local signed metric") + return dict(E=response, inverse_E=inverse, R=reflection, P=permutation, J=metric, inverse_J=metric_inverse) + + +def local_code(n): + def row(*terms): + out = {} + for indices, value in terms: + for j in indices: + r.put(out, j, F(value)) + return out + ell = row((range(n - 2), -1), ([n - 2], 1)) + if n == 6: + rows = [ell, row(([2], 1), ([3], -1)), row(([0], 1), ([1], -1)), + row(([5], 1)), row(([0, 1], 1), ([2, 3], -1)), + row((range(4), 1), ([4], -2))] + gram = [2, 2, 2, -2, 4, -4] + else: + need(n == 8, "Actual local block size") + rows = [ell, row(([4, 5], 1), ([6], F(-1, 2))), + row(([4], 1), ([5], -1)), row(([7], 1)), + row(([0], 1), ([1], -1)), row(([2], 1), ([3], -1)), + row(([0, 1], 1), ([2, 3], -1)), + row((range(4), 1), ([4, 5], 2), ([6], -2))] + gram = [2, 1, 2, -4, 2, 2, 4, -4] + return rows, diagonal(gram) + + +def dyadic_exponent(value): + value = abs(value) + need(value and value.numerator & (value.numerator - 1) == 0 + and value.denominator & (value.denominator - 1) == 0, "A signed power of two") + return value.numerator.bit_length() - value.denominator.bit_length() + + +def replay(word, count=640): + state = r.eye(count) + bill, peak, height = 0, F(1), 0 + for op, target, source, coefficient in word: + c = F(coefficient) + exponent = dyadic_exponent(c) + need(0 <= target < count, "Target range") + if op == "add": + need(0 <= source < count and source != target, "Independent source") + for j, value in state[source].items(): + r.put(state[target], j, c * value) + bill += 8 + 2 * abs(exponent) + else: + need(op == "scale" and source is None, "Scale grammar") + state[target] = {j: c * value for j, value in state[target].items()} + bill += 2 * (abs(exponent) + (c < 0)) + peak = max(peak, sum(abs(c) for c in state[target].values())) + for value in state[target].values(): + d = value.denominator + need(d & (d - 1) == 0, "No odd denominator at any prefix") + height = max(height, d.bit_length() - 1) + return state, {"scalar_primitives": bill, "row_sum_peak": str(peak), "binary_height": height, + "input_columns": count, "instructions": len(word)} + + +def inverse_word(word): + return [[op, target, source, str(-F(c) if op == "add" else 1 / F(c))] + for op, target, source, c in reversed(word)] + + +def inverse_adjoint_word(word): + return [["add", source, target, str(-F(c))] if op == "add" + else [op, target, source, str(1 / F(c))] + for op, target, source, c in word] + + +def direct_clean(c, selected): + out = r.eye(224) + for p in range(112): + if p in selected: + out[p] = {112 + p: F(-1)} + out[112 + p] = dict(c[p]) + else: + out[p] = dict(c[p]) + for j, value in c[p].items(): + r.put(out[112 + p], j, value) + return out + + +def general_completion(power): + k, n = 2**power, 2**power + 4 + c = r.eye(n) + for i in range(k): + c[i] = {j: F((-1) ** ((i & j).bit_count())) for j in range(k)} + alpha = F(k - 2, 4) + c[0] = {j: 1 + alpha for j in range(k)} + c[0].update({k: F(k, 2), k + 1: F(k, 2), k + 2: -2 - alpha}) + c[k] = {j: F(-1) for j in range(k + 2)} + c[k][k + 2] = F(1) + c[k + 1] = {k: F(1), k + 1: F(-1)} + c[k + 2] = {j: 1 - alpha for j in range(k)} + c[k + 2].update({k: F(-k, 2), k + 1: F(-k, 2), k + 2: alpha}) + c = [{j: value for j, value in row.items() if value} for row in c] + model = local_model(n) + g = diagonal([-2 * k] + [k] * (k - 1) + [2, 2, 2 * k, -k]) + need(r.matmul(c, r.matmul(model["inverse_J"], transpose(c, n))) == g, + "General one-centre diagonal Gram") + signed = [dict(row) for row in c] + signed[k] = {j: -value for j, value in c[k].items()} + need(r.matmul(c, model["R"]) == signed, "General ordinary rows are fixed") + return {"n": n, "k": k, "centre_coordinate": k, "gram": [str(row[i]) for i, row in enumerate(g)], + "determinant_squared": str(16 * k**k)} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, default=HERE / "normal") + args = parser.parse_args() + freeze(MODEL / "MODEL-FREEZE.json", MODEL_FREEZE) + freeze(CODE / "FREEZE.json", CODE_FREEZE) + freeze(CODE / "PAIRED-FREEZE.json", PAIRED_FREEZE) + model = read(MODEL / "model-normal-v2/RESPONSE.json.gz", MODEL_PIN, True) + code = read(CODE / "run-v2-normal/SIGNED-SIXTEEN.json.gz", CODE_PIN, True) + paired = read(CODE / "paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz", PAIRED_PIN, True) + for relative, pin in model["source_pins"].values(): + read(LANES / relative, pin, relative.endswith(".gz")) if relative.endswith((".json", ".gz")) else \ + need(sha256((LANES / relative).read_bytes()).hexdigest() == pin, "Model arithmetic source") + cyclic_path, cyclic_pin = model["source_pins"]["cyclic"] + cyclic = read(LANES / cyclic_path, cyclic_pin) + need(model["ports"] == cyclic["ports"] and model["pair_codes"] == cyclic["pair_codes"], + "Pinned actual physical pair geometry") + h = r.eye(112) + for pair in model["pair_codes"]: + ports = pair["ports"] + install(h, [{j: F(c) for j, c in enumerate(row) if c} for row in pair["matrix"]], ports) + hi, _ = r.invert(h) + need(h == r.sparse(model["pair_code"]) and hi == r.sparse(model["pair_code_inverse"]), + "Independent actual pair transform") + modes = {name: r.eye(112) for name in ("E", "inverse_E", "R", "P", "J", "inverse_J")} + cm, gm = r.eye(112), r.eye(112) + all_ports, centres, special = [], [], [] + local_reports = {} + for block in model["blocks"]: + ports = block["ports"] + all_ports += ports + centres.append(ports[0]) + special += ports[-2:] + if len(ports) == 6: + need(set(ports) == set(cyclic["cyclic_carriers"][block["vertex"]]), "Actual six-mode component") + else: + need(all((model["ports"][p] & model["ports"][q]).bit_count() % 2 == (p == q) + for p in ports for q in ports), "Actual orthonormal eight-clique") + local = local_model(len(ports)) + c, g = local_code(len(ports)) + need(r.matmul(c, r.matmul(local["inverse_J"], transpose(c, len(ports)))) == g, + "Independently constructed local code Gram") + ci, determinant = r.invert(c) + need(determinant == -8 and r.matmul(ci, c) == r.eye(len(ports)), "Local dyadic inverse") + for name, matrix in local.items(): + install(modes[name], matrix, ports) + install(cm, c, ports) + install(gm, g, ports) + local_reports[str(len(ports))] = {"determinant": str(determinant), + "gram": [str(row[i]) for i, row in enumerate(g)]} + need(sorted(all_ports) == list(range(112)) and centres == model["centre_ports"] == code["centre_ports"], + "Complete sixteen-block partition") + selected = set(centres) + for pair in model["pair_codes"]: + p, q = pair["ports"] + need((p in selected) == (q in selected), "Complete selected physical pairs") + need(modes["J"][p][p] == modes["J"][q][q], "Input metric pair closure") + need(gm[p][p] == gm[q][q], "Output Gram pair closure") + physical = {name: r.matmul(hi, r.matmul(a, h)) for name, a in modes.items()} + need(all(modes[name] == r.sparse(model["mode"][name]) + and physical[name] == r.sparse(model["physical"][name]) for name in modes), + "Every independently derived physical model matrix") + e, ei, reflection, permutation, j, k = (physical[name] for name in modes) + need(r.matmul(transpose(e, 112), r.matmul(j, e)) == j, "Actual signed metric") + need(transpose(ei, 112) == r.matmul(j, r.matmul(e, k)), "Actual inverse-adjoint conversion") + need(Counter(row[i] for i, row in enumerate(j)) == {F(1): 80, F(-1, 2): 16, F(-1, 4): 16}, + "Physical metric weights") + need(all(not a[p].get(p) for a in (e, ei) for p in range(112)), "Both physical response diagonals") + need(all((model["ports"][p] & model["ports"][q]).bit_count() % 2 == 0 + for p, row in enumerate(e) for q in row), "Actual orthogonal physical response support") + support = [p for p in range(112) if permutation[p] != {p: F(1)}] + need(support == sorted(special) and len(support) == 32 + and sum(map(len, permutation)) == 160, "Paid P support and non-monomial census") + need(rank(difference(reflection, r.eye(112)), 112) == 16 + and rank(difference(e, r.eye(112)), 112) == 32, "Both displacement ranks") + ordinary_hi = r.eye(112) + for p in range(112): + if p not in selected: + ordinary_hi[p] = hi[p] + c = r.matmul(ordinary_hi, r.matmul(cm, h)) + g = r.matmul(c, r.matmul(k, transpose(c, 112))) + need(c == r.sparse(code["code"]) and cm == r.sparse(code["mode_code"]), "Actual physical one-centre code") + need(r.matmul(c, transpose(c, 112)) != r.eye(112) + and r.matmul(transpose(e, 112), e) != r.eye(112), "The code and response are not Euclidean unitary") + need(all(set(row) == {p} for p, row in enumerate(g)), "Physical diagonal output Gram") + need(g == r.sparse(code["output_metric"]) and k == r.sparse(code["input_metric"]), "Exact K and G") + gi = diagonal([1 / row[p] for p, row in enumerate(g)]) + ci = r.matmul(k, r.matmul(transpose(c, 112), gi)) + cd = r.matmul(gi, r.matmul(c, k)) + need(r.matmul(c, ci) == r.matmul(ci, c) == r.eye(112) + and ci == r.sparse(code["inverse"]) + and cd == transpose(ci, 112) == r.sparse(code["inverse_adjoint"]), "Both complete inverse identities") + zc = [{q: (-1 if p in selected else 1) * value for q, value in row.items()} + for p, row in enumerate(c)] + need(r.matmul(c, reflection) == zc and zc == r.sparse(code["coded_reflection"]), + "The code diagonalizes the reflection") + need([c[p] for p in centres] == r.sparse(model["reflection_L"]) + and [g[p][p] for p in centres] == [F(4)] * 8 + [F(2)] * 8, "Physical reader normalization") + readers = [c[p] for p in centres] + euclidean_gram = r.matmul(readers, transpose(readers, 112)) + need(euclidean_gram == diagonal([10] * 8 + [7] * 8), "The new Euclidean reader Gram") + prime_ranks = {} + for prime in (3, 5, 7): + a, gram_rank = modular_rank(readers, 112, prime), modular_rank(euclidean_gram, 16, prime) + need(a == 16 and gram_rank == (16 if prime == 3 else 8), "Actual odd-prime ranks") + prime_ranks[str(prime)] = {"reader_rank": a, "gram_rank": gram_rank, + "complex_unitary_coordinate_bound": 2 * a - gram_rank} + cn = r.matmul(h, r.matmul(c, hi)) + need(cn == r.sparse(code["native_code"]), "Actual native coordinate code") + need(all(not c[p].get(p) and not cn[p].get(p) for p in range(112) if p not in selected), + "Every ordinary physical and native diagonal") + groups = [set(block["ports"]) for block in model["blocks"]] + need(all(any(p in group and set(cn[p]) <= group for group in groups) + for p in range(112) if p not in selected), "Ordinary native support remains in its mode block") + reports = {} + expected = dict(physical, inverse_adjoint_E=transpose(ei, 112), metric_inverse_adjoint_E=transpose(ei, 112)) + for name, word in model["scalar_words"].items(): + state, reports["model/" + name] = replay(word) + need(state[:112] == expected[name] and state[112:] == r.eye(640)[112:], "All640 model word columns") + expected = {"code": c, "inverse": ci, "literal_inverse_adjoint": cd, "diagonal_inverse_adjoint": cd} + for name, word in code["scalar_words"].items(): + state, reports["code/" + name] = replay(word) + need(state[:112] == expected[name] and state[112:] == r.eye(640)[112:], "All640 code word columns") + need(reports["code/code"]["scalar_primitives"] == reports["code/inverse"]["scalar_primitives"] == 5564, + "Complete C and inverse costs") + need(reports["code/code"]["row_sum_peak"] == "24" + and reports["code/inverse"]["row_sum_peak"] == "9" + and reports["code/code"]["binary_height"] == reports["code/inverse"]["binary_height"] == 3, + "Exact C and inverse prefix bounds") + for name in ("code", "inverse"): + word = code["scalar_words"][name] + index = next(i for i, gate in enumerate(word) if gate[0] == "add") + wrong, _ = replay(word[:index] + word[index + 1:]) + need(wrong[:112] != expected[name], "Deleted ADD control: " + name) + wrong_c = r.matmul(hi, r.matmul(cm, h)) + need([wrong_c[p] for p in centres] != readers, "The full left inverse pair code changes the readers") + wrong_j = [dict(row) for row in j] + wrong_j[special[0]][special[0]] *= -1 + need(r.matmul(transpose(e, 112), r.matmul(wrong_j, e)) != wrong_j, + "One changed metric sign fails") + fw = list(code["scalar_words"]["code"]) + fw += [["add", 112 + p, p, "1"] for p in range(112) if p not in selected] + for p in centres: + fw += [["add", 112 + p, p, "1"], ["add", p, 112 + p, "-1"], ["add", 112 + p, p, "1"]] + state, reports["clean/forward_scalar"] = replay(fw) + need(state[:224] == direct_clean(c, selected) == r.sparse(code["clean_maps"]["forward"]) + and state[224:] == r.eye(640)[224:], "Arbitrary clean inputs and416 outside fields") + pre, post = (code["clean_metric_wrappers"][name] for name in ("pre", "post")) + def diagonal_word(a, offset=0): + return [["scale", offset + p, None, str(row[p])] for p, row in enumerate(a) if row[p] != 1] + need(pre == diagonal_word(j) + diagonal_word(gi, 112) + and post == diagonal_word(g) + diagonal_word(g, 112), "Exact metric signs and baseline banks") + converted = pre + inverse_adjoint_word(fw) + post + state, reports["clean/converted_scalar"] = replay(converted) + target = r.eye(224) + for p in range(112): + if p in selected: + target[p] = {112 + p: F(-1)} + target[112 + p] = dict(c[p]) + else: + target[p] = dict(c[p]) + r.put(target[p], 112 + p, F(-1)) + need(state[:224] == target == r.sparse(code["clean_maps"]["converted_inverse_adjoint"]) + and state[224:] == r.eye(640)[224:], "Full metric-converted inverse-adjoint on arbitrary inputs") + missing_target_pre = [gate for gate in pre if gate[1] < 112] + inverse_adjoint_word(fw) + post + wrong, _ = replay(missing_target_pre) + need(wrong[:224] != target, "The target metric input scales cannot be omitted") + def exchange(field): + if field is None: + return None + return field + 112 if field in selected else (field - 112 if field - 112 in selected else field) + swapped_word = [[op, exchange(t), exchange(s), value] for op, t, s, value in converted] + swapped_target = [{exchange(q): value for q, value in target[exchange(p)].items()} for p in range(224)] + state, reports["clean/selected_conjugate"] = replay(swapped_word) + need(state[:224] == swapped_target == r.sparse(code["clean_maps"]["selected_conjugate"]) + and state[224:] == r.eye(640)[224:], "Complete selected-bank conjugation") + _, wrapper_bill = replay(pre + post) + need(wrapper_bill["scalar_primitives"] == 1264, "Both-bank metric wrapper price") + cbar = r.matmul(hi, r.matmul(cm, h)) + cbar_t = transpose(cbar, 112) + gbar = r.matmul(cbar, r.matmul(k, cbar_t)) + need(all(set(row) == {p} for p, row in enumerate(gbar)), "Paired output metric is diagonal") + gbar_i = diagonal([1 / row[p] for p, row in enumerate(gbar)]) + cbar_i = r.matmul(k, r.matmul(cbar_t, gbar_i)) + cbar_it = transpose(cbar_i, 112) + paired_matrices = {"code": cbar, "transpose": cbar_t, "inverse": cbar_i, + "inverse_transpose": cbar_it, "input_metric": k, + "input_metric_inverse": j, "output_metric": gbar, + "output_metric_inverse": gbar_i} + need(all(value == r.sparse(paired[name]) for name, value in paired_matrices.items()), + "Every paired code and metric matrix") + need(r.matmul(cbar, cbar_i) == r.matmul(cbar_i, cbar) == r.eye(112) + and r.matmul(cbar_t, r.matmul(gbar_i, cbar)) == j, + "Both paired inverse orders and transpose metric contract") + selected_h, selected_hi = r.eye(112), r.eye(112) + for p in centres: + selected_h[p], selected_hi[p] = h[p], hi[p] + need(selected_h == r.sparse(paired["centre_recovery"]) + and r.matmul(selected_hi, c) == cbar + and r.matmul(selected_h, cbar) == c, "Paid exact reader recovery") + need([gbar[p][p] for p in centres] == [F(2)] * 16, "All paired centre norms are two") + need([cbar[p] for p in range(112) if p not in selected] + == [c[p] for p in range(112) if p not in selected], "Ordinary rows are unchanged") + need(r.matmul(cbar, reflection) + == [{q: (-1 if p in selected else 1) * value for q, value in row.items()} + for p, row in enumerate(cbar)], "Paired reflection diagonalization") + suffix, reports["paired/selected_pair_suffix"] = replay(paired["selected_pair_inverse_word"]) + need(suffix[:112] == selected_hi and suffix[112:] == r.eye(640)[112:] + and reports["paired/selected_pair_suffix"]["scalar_primitives"] == 80, + "The selected pair suffix is fully paid") + need(paired["scalar_words"]["code"] + == code["scalar_words"]["code"] + paired["selected_pair_inverse_word"], + "Literal original code plus selected pair suffix") + old_native_t = r.matmul(h, r.matmul(transpose(c, 112), hi)) + bad_rows = [p for p in range(112) if p not in selected + and not any(p in group and set(old_native_t[p]) <= group for group in groups)] + need(len(bad_rows) == 32, "The original transpose fails 32 ordinary support rows") + for name, matrix in (("code", cbar), ("transpose", cbar_t)): + native = r.matmul(h, r.matmul(matrix, hi)) + need(native == r.sparse(paired["native_codes"][name]) + == (cm if name == "code" else transpose(cm, 112)), "Paired native chart identity") + need(all(not matrix[p].get(p) and not native[p].get(p) + and any(p in group and set(native[p]) <= group for group in groups) + for p in range(112) if p not in selected), + "Both paired ordinary diagonals and mode supports") + for name, word in paired["scalar_words"].items(): + state, report = replay(word) + reports["paired/" + name] = report + need(state[:112] == paired_matrices[name] and state[112:] == r.eye(640)[112:], + "All640 paired code word columns") + need(report["scalar_primitives"] == 5644 and report["binary_height"] == 3 + and report["instructions"] == 752, "Complete paired word invoice") + need(report["row_sum_peak"] + == {"code": "24", "transpose": "8", "inverse": "10", "inverse_transpose": "6"}[name], + "Exact paired prefix row norm") + result = { + "status": "PASS_INDEPENDENT_SIGNED_METRIC_AND_SIXTEEN_CENTRES", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "model_freeze_sha256": MODEL_FREEZE, "model_payload_sha256": MODEL_PIN, + "code_freeze_sha256": CODE_FREEZE, "code_payload_sha256": CODE_PIN, "local_codes": local_reports, + "paired_freeze_sha256": PAIRED_FREEZE, "paired_payload_sha256": PAIRED_PIN, + "physical_metric_census": dict(Counter(str(row[p]) for p, row in enumerate(j))), + "output_metric_census": dict(Counter(str(row[p]) for p, row in enumerate(g))), + "reflection_rank": 16, "response_minus_identity_rank": 32, "P_support": 32, "P_nonzero": 160, + "euclidean_reader_gram": [10] * 8 + [7] * 8, "odd_prime_ranks": prime_ranks, + "negative_controls": ["deleted_code_ADD", "deleted_inverse_ADD", "full_left_pair_inverse", + "changed_metric_sign", "omitted_target_metric_input"], + "reports": reports, "clean_metric_wrapper_scalar": 1264, + "paired_output_metric_census": dict(Counter(str(row[p]) for p, row in enumerate(gbar))), + "old_transpose_ordinary_support_failures": bad_rows, + "general_power_two_examples": [general_completion(power) for power in range(7)], + "producer_code_imported": False, "native_service_claimed": False, + } + args.output.mkdir(parents=True, exist_ok=True) + raw = (json.dumps(result, sort_keys=True, indent=2) + "\n").encode() + (args.output / "REVIEW-CHECKS.json").write_bytes(raw) + print(result["status"]) + print(sha256(raw).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/normal/REVIEW-CHECKS.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/normal/REVIEW-CHECKS.json new file mode 100644 index 0000000000..2a6e6b3e6c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/normal/REVIEW-CHECKS.json @@ -0,0 +1,479 @@ +{ + "P_nonzero": 160, + "P_support": 32, + "checker_sha256": "415a45c0475f0d6499d77e0b41b695596ddb99536c60e5ec9859fd564f8edf0f", + "clean_metric_wrapper_scalar": 1264, + "code_freeze_sha256": "8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2", + "code_payload_sha256": "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c", + "euclidean_reader_gram": [ + 10, + 10, + 10, + 10, + 10, + 10, + 10, + 10, + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 7 + ], + "general_power_two_examples": [ + { + "centre_coordinate": 1, + "determinant_squared": "16", + "gram": [ + "-2", + "2", + "2", + "2", + "-1" + ], + "k": 1, + "n": 5 + }, + { + "centre_coordinate": 2, + "determinant_squared": "64", + "gram": [ + "-4", + "2", + "2", + "2", + "4", + "-2" + ], + "k": 2, + "n": 6 + }, + { + "centre_coordinate": 4, + "determinant_squared": "4096", + "gram": [ + "-8", + "4", + "4", + "4", + "2", + "2", + "8", + "-4" + ], + "k": 4, + "n": 8 + }, + { + "centre_coordinate": 8, + "determinant_squared": "268435456", + "gram": [ + "-16", + "8", + "8", + "8", + "8", + "8", + "8", + "8", + "2", + "2", + "16", + "-8" + ], + "k": 8, + "n": 12 + }, + { + "centre_coordinate": 16, + "determinant_squared": "295147905179352825856", + "gram": [ + "-32", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "2", + "2", + "32", + "-16" + ], + "k": 16, + "n": 20 + }, + { + "centre_coordinate": 32, + "determinant_squared": "23384026197294446691258957323460528314494920687616", + "gram": [ + "-64", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "2", + "2", + "64", + "-32" + ], + "k": 32, + "n": 36 + }, + { + "centre_coordinate": 64, + "determinant_squared": "630432099142311667396464641602297820881275828327447146687172694467931548343955369782628260078158650252906047844909056", + "gram": [ + "-128", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "2", + "2", + "128", + "-64" + ], + "k": 64, + "n": 68 + } + ], + "local_codes": { + "6": { + "determinant": "-8", + "gram": [ + "2", + "2", + "2", + "-2", + "4", + "-4" + ] + }, + "8": { + "determinant": "-8", + "gram": [ + "2", + "1", + "2", + "-4", + "2", + "2", + "4", + "-4" + ] + } + }, + "model_freeze_sha256": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7", + "model_payload_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "native_service_claimed": false, + "negative_controls": [ + "deleted_code_ADD", + "deleted_inverse_ADD", + "full_left_pair_inverse", + "changed_metric_sign", + "omitted_target_metric_input" + ], + "odd_prime_ranks": { + "3": { + "complex_unitary_coordinate_bound": 16, + "gram_rank": 16, + "reader_rank": 16 + }, + "5": { + "complex_unitary_coordinate_bound": 24, + "gram_rank": 8, + "reader_rank": 16 + }, + "7": { + "complex_unitary_coordinate_bound": 24, + "gram_rank": 8, + "reader_rank": 16 + } + }, + "old_transpose_ordinary_support_failures": [ + 2, + 9, + 11, + 13, + 14, + 15, + 16, + 21, + 25, + 37, + 41, + 42, + 44, + 47, + 51, + 52, + 53, + 61, + 63, + 71, + 72, + 76, + 79, + 81, + 87, + 89, + 90, + 92, + 94, + 105, + 106, + 110 + ], + "output_metric_census": { + "-2": 8, + "-4": 24, + "1": 8, + "2": 48, + "4": 24 + }, + "paired_freeze_sha256": "810508791ea43aecaaf894c3cb50a8170d3e6f1f8e52684e274cda16c2c2db57", + "paired_output_metric_census": { + "-2": 8, + "-4": 24, + "1": 8, + "2": 56, + "4": 16 + }, + "paired_payload_sha256": "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1", + "physical_metric_census": { + "-1/2": 16, + "-1/4": 16, + "1": 80 + }, + "producer_code_imported": false, + "reflection_rank": 16, + "reports": { + "clean/converted_scalar": { + "binary_height": 3, + "input_columns": 640, + "instructions": 1227, + "row_sum_peak": "13", + "scalar_primitives": 7980 + }, + "clean/forward_scalar": { + "binary_height": 3, + "input_columns": 640, + "instructions": 883, + "row_sum_peak": "24", + "scalar_primitives": 6716 + }, + "clean/selected_conjugate": { + "binary_height": 3, + "input_columns": 640, + "instructions": 1227, + "row_sum_peak": "13", + "scalar_primitives": 7980 + }, + "code/code": { + "binary_height": 3, + "input_columns": 640, + "instructions": 739, + "row_sum_peak": "24", + "scalar_primitives": 5564 + }, + "code/diagonal_inverse_adjoint": { + "binary_height": 3, + "input_columns": 640, + "instructions": 875, + "row_sum_peak": "32", + "scalar_primitives": 6092 + }, + "code/inverse": { + "binary_height": 3, + "input_columns": 640, + "instructions": 739, + "row_sum_peak": "9", + "scalar_primitives": 5564 + }, + "code/literal_inverse_adjoint": { + "binary_height": 3, + "input_columns": 640, + "instructions": 739, + "row_sum_peak": "5", + "scalar_primitives": 5564 + }, + "model/E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 480, + "row_sum_peak": "44", + "scalar_primitives": 3308 + }, + "model/P": { + "binary_height": 1, + "input_columns": 640, + "instructions": 116, + "row_sum_peak": "4", + "scalar_primitives": 728 + }, + "model/R": { + "binary_height": 1, + "input_columns": 640, + "instructions": 416, + "row_sum_peak": "38", + "scalar_primitives": 2892 + }, + "model/inverse_E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 480, + "row_sum_peak": "44", + "scalar_primitives": 3308 + }, + "model/inverse_adjoint_E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 480, + "row_sum_peak": "14", + "scalar_primitives": 3308 + }, + "model/metric_inverse_adjoint_E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 544, + "row_sum_peak": "56", + "scalar_primitives": 3628 + }, + "paired/code": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "24", + "scalar_primitives": 5644 + }, + "paired/inverse": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "10", + "scalar_primitives": 5644 + }, + "paired/inverse_transpose": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "6", + "scalar_primitives": 5644 + }, + "paired/selected_pair_suffix": { + "binary_height": 1, + "input_columns": 640, + "instructions": 13, + "row_sum_peak": "2", + "scalar_primitives": 80 + }, + "paired/transpose": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "8", + "scalar_primitives": 5644 + } + }, + "response_minus_identity_rank": 32, + "status": "PASS_INDEPENDENT_SIGNED_METRIC_AND_SIXTEEN_CENTRES" +} diff --git a/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/optimized/REVIEW-CHECKS.json b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/optimized/REVIEW-CHECKS.json new file mode 100644 index 0000000000..2a6e6b3e6c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/optimized/REVIEW-CHECKS.json @@ -0,0 +1,479 @@ +{ + "P_nonzero": 160, + "P_support": 32, + "checker_sha256": "415a45c0475f0d6499d77e0b41b695596ddb99536c60e5ec9859fd564f8edf0f", + "clean_metric_wrapper_scalar": 1264, + "code_freeze_sha256": "8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2", + "code_payload_sha256": "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c", + "euclidean_reader_gram": [ + 10, + 10, + 10, + 10, + 10, + 10, + 10, + 10, + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 7 + ], + "general_power_two_examples": [ + { + "centre_coordinate": 1, + "determinant_squared": "16", + "gram": [ + "-2", + "2", + "2", + "2", + "-1" + ], + "k": 1, + "n": 5 + }, + { + "centre_coordinate": 2, + "determinant_squared": "64", + "gram": [ + "-4", + "2", + "2", + "2", + "4", + "-2" + ], + "k": 2, + "n": 6 + }, + { + "centre_coordinate": 4, + "determinant_squared": "4096", + "gram": [ + "-8", + "4", + "4", + "4", + "2", + "2", + "8", + "-4" + ], + "k": 4, + "n": 8 + }, + { + "centre_coordinate": 8, + "determinant_squared": "268435456", + "gram": [ + "-16", + "8", + "8", + "8", + "8", + "8", + "8", + "8", + "2", + "2", + "16", + "-8" + ], + "k": 8, + "n": 12 + }, + { + "centre_coordinate": 16, + "determinant_squared": "295147905179352825856", + "gram": [ + "-32", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "16", + "2", + "2", + "32", + "-16" + ], + "k": 16, + "n": 20 + }, + { + "centre_coordinate": 32, + "determinant_squared": "23384026197294446691258957323460528314494920687616", + "gram": [ + "-64", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "32", + "2", + "2", + "64", + "-32" + ], + "k": 32, + "n": 36 + }, + { + "centre_coordinate": 64, + "determinant_squared": "630432099142311667396464641602297820881275828327447146687172694467931548343955369782628260078158650252906047844909056", + "gram": [ + "-128", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", + "64", 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"full_left_pair_inverse", + "changed_metric_sign", + "omitted_target_metric_input" + ], + "odd_prime_ranks": { + "3": { + "complex_unitary_coordinate_bound": 16, + "gram_rank": 16, + "reader_rank": 16 + }, + "5": { + "complex_unitary_coordinate_bound": 24, + "gram_rank": 8, + "reader_rank": 16 + }, + "7": { + "complex_unitary_coordinate_bound": 24, + "gram_rank": 8, + "reader_rank": 16 + } + }, + "old_transpose_ordinary_support_failures": [ + 2, + 9, + 11, + 13, + 14, + 15, + 16, + 21, + 25, + 37, + 41, + 42, + 44, + 47, + 51, + 52, + 53, + 61, + 63, + 71, + 72, + 76, + 79, + 81, + 87, + 89, + 90, + 92, + 94, + 105, + 106, + 110 + ], + "output_metric_census": { + "-2": 8, + "-4": 24, + "1": 8, + "2": 48, + "4": 24 + }, + "paired_freeze_sha256": "810508791ea43aecaaf894c3cb50a8170d3e6f1f8e52684e274cda16c2c2db57", + "paired_output_metric_census": { + "-2": 8, + "-4": 24, + "1": 8, + "2": 56, + "4": 16 + }, + "paired_payload_sha256": "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1", + "physical_metric_census": { + "-1/2": 16, + "-1/4": 16, + "1": 80 + }, + "producer_code_imported": false, + "reflection_rank": 16, + "reports": { + "clean/converted_scalar": { + "binary_height": 3, + "input_columns": 640, + "instructions": 1227, + "row_sum_peak": "13", + "scalar_primitives": 7980 + }, + "clean/forward_scalar": { + "binary_height": 3, + "input_columns": 640, + "instructions": 883, + "row_sum_peak": "24", + "scalar_primitives": 6716 + }, + "clean/selected_conjugate": { + "binary_height": 3, + "input_columns": 640, + "instructions": 1227, + "row_sum_peak": "13", + "scalar_primitives": 7980 + }, + "code/code": { + "binary_height": 3, + "input_columns": 640, + "instructions": 739, + "row_sum_peak": "24", + "scalar_primitives": 5564 + }, + "code/diagonal_inverse_adjoint": { + "binary_height": 3, + "input_columns": 640, + "instructions": 875, + "row_sum_peak": "32", + "scalar_primitives": 6092 + }, + "code/inverse": { + "binary_height": 3, + "input_columns": 640, + "instructions": 739, + "row_sum_peak": "9", + "scalar_primitives": 5564 + }, + "code/literal_inverse_adjoint": { + "binary_height": 3, + "input_columns": 640, + "instructions": 739, + "row_sum_peak": "5", + "scalar_primitives": 5564 + }, + "model/E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 480, + "row_sum_peak": "44", + "scalar_primitives": 3308 + }, + "model/P": { + "binary_height": 1, + "input_columns": 640, + "instructions": 116, + "row_sum_peak": "4", + "scalar_primitives": 728 + }, + "model/R": { + "binary_height": 1, + "input_columns": 640, + "instructions": 416, + "row_sum_peak": "38", + "scalar_primitives": 2892 + }, + "model/inverse_E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 480, + "row_sum_peak": "44", + "scalar_primitives": 3308 + }, + "model/inverse_adjoint_E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 480, + "row_sum_peak": "14", + "scalar_primitives": 3308 + }, + "model/metric_inverse_adjoint_E": { + "binary_height": 1, + "input_columns": 640, + "instructions": 544, + "row_sum_peak": "56", + "scalar_primitives": 3628 + }, + "paired/code": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "24", + "scalar_primitives": 5644 + }, + "paired/inverse": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "10", + "scalar_primitives": 5644 + }, + "paired/inverse_transpose": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "6", + "scalar_primitives": 5644 + }, + "paired/selected_pair_suffix": { + "binary_height": 1, + "input_columns": 640, + "instructions": 13, + "row_sum_peak": "2", + "scalar_primitives": 80 + }, + "paired/transpose": { + "binary_height": 3, + "input_columns": 640, + "instructions": 752, + "row_sum_peak": "8", + "scalar_primitives": 5644 + } + }, + "response_minus_identity_rank": 32, + 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The current dyadic scalar +emitter does not have this operation, but the retained fixed-tape model +already permits fixed odd divisors on a common exact grid. Thus the +modulo-three obstruction applies to that emitter's coefficient ring. It +is not an obstruction to the required computation. + +This note gives a scalar word for the actual A8 block, its fused upper +correction, and a complete representation rule for recursive use. The +fused word uses one existing private array, 7,008 old real scalar +primitives, and 16 real division-by-three scans. It adds no native child +at a legal common-frame cut. It has odd denominator height one at every +prefix. These are new finite statements about this block. The common +odd-grid method is retained prior work. + +The result does not supply the complete controller, its owners, or its +phase proof. In particular, the fused original-X response still has an +eight-dimensional kernel. The retained selected Y values are necessary +for the complete two-bank map. No new complete kappa value is claimed. + +## Source binding + +The actual interface is `../../new-core-transfer-20261017/INTERFACE.json`, +SHA256 `c6ca09711622ce4ad236f78cc28c03b6c46808a9d91cfc1722ff4fe371f38746`. +The checker verifies this pin before it reads R. The clean core, its full +native phase review, and the raw selected boundary convention are reviewed +in the parent directory's `NEW-CORE-LOGICAL-REVIEW.md`, +`NEW-CORE-NATIVE-REVIEW.md`, and `NEW-RAW-REVIEW.md`. + +The source model was fetched again at commit +`6f100d4bb5083f8c35d96fd95a539811c62f245c`. The following files have the +same Git blob identities as the prior rational-decoder source packet: + +- [The fixed-tape model](https://github.com/CrocSwap/integer-mult-bounds/blob/6f100d4bb5083f8c35d96fd95a539811c62f245c/upstream/build/sections/02-streams.tex). +- [The exact recursive contract and guard](https://github.com/CrocSwap/integer-mult-bounds/blob/6f100d4bb5083f8c35d96fd95a539811c62f245c/upstream/build/sections/05-layers.tex). +- [The retained common odd grid](https://github.com/CrocSwap/integer-mult-bounds/blob/6f100d4bb5083f8c35d96fd95a539811c62f245c/notes/stopped-product-complex.tex), in "One exact odd-denominator grid". + +The retained grid proof uses division by 21. It scales all root dyadic +inputs and dirty auxiliaries once. It proves the depth bound from the +Gaussian-dyadic endpoint of each completed child. Its exactness argument +also applies to division by three. + +The local campaign predecessor is +`../../interface-proof/rational-decoder/RATIONAL-DECODER.md`. That note +gives the exact signed scan, a one-accumulator J inverse, and the root-grid +cost. Its independent review is +`../../temporal-reuse/RATIONAL-DECODER-REVIEW.md`. The A8 factor below uses +the same arithmetic method on the actual ordinary block. It does not +claim to introduce fixed odd division or common grids. + +## The actual block and its inverse + +Let + + A = [0,7,20,27,36,46,57,111], U = {0,...,111} minus A. + +The pinned interface gives an 8 by 112 signed matrix R. Each row has 56 +nonzero entries. Write R_U for its 104 ordinary columns, and put + + K = R^T/4, H = I_U - K_U R_U. + +The checker derives, from the pinned entries, + + R_U R_U^T = 52 I_8, R_U K_U = 13 I_8. + +Each row of R_U has 52 entries, each equal to +1 or -1. Hence + + H^-1 = I_U - K_U R_U/12 = I_U - R_U^T R_U/48. (1) + +For P=R_U^T R_U, the identity P^2=52P proves both inverse orders. In fact +the coefficient of P in (I-P/4)(I-P/48) is +`-1/4 -1/48 +52/(4*48)=0`. The same calculation proves the other order. +The eigenvalue on the eight-dimensional query image is -12 for H and +-1/12 for its inverse. The eigenvalue on ker(R_U) is one. + +The failure of H to be a dyadic unit is exact: modulo three, the eight +columns of K_U are independent kernel channels. Equation (1) removes +this obstruction over Z[1/2,1/3]. It does not change the native source +operators or treat an odd division as an admitted old SCALE. + +## One private accumulator + +Use the already owned private C0 array. For each row r_i of R_U, perform +the following steps in order: + + C0 = 0 + C0 += r_i[p] * X_p for each nonzero ordinary entry p + C0 *= 1/16 + C0 /= 3 exact signed numerator division + X_p -= r_i[p] * C0 for each nonzero ordinary entry p + C0 = 0 + +All eight rows use the same array. Distinct rows are orthogonal, so the +rank-one updates have zero cross product. Their product is exactly (1). +All other fields are unchanged. C0 ends at zero and has no dependence on +its arbitrary initial value. This is an owned-array construction. It +does not permit the erasure of an arbitrary borrowed helper. + +To apply H, use the same query and scatter with `C0 *= 1/4`, and omit the +division by three. Its row updates also have zero cross product. + +Suppose that k complete inverse rows have already run. The complete next +query r_i X equals r_i times the module input, since each earlier term +contains r_i r_j^T=0. A partial query can have one new factor of three in +its denominator. The complete query has none. Division occurs only after +the complete query. The new scatter therefore adds at most one factor. +This proves the odd-height-one bound at every prefix, including partial +queries and partial scatters. It holds relative to any existing input +height, including rational inputs from an unfinished parent. + +The same argument bounds the additional binary denominator height by four +for the inverse and by two for H. Partial queries do not receive another +scale until the complete orthogonal cancellation has occurred. + +## Fuse the completed-X upper correction + +The raw selected backward boundary needs, after H^-1 on ordinary X, + + X_A += K_A R_U X_U. + +All these X fields are at the same completed full frame. Since +`R_U H^-1 = -R_U/12`, the combined map on the initial completed X is + + X_U' = X_U - R_U^T R_U X_U/48, + X_A' = X_A - R_A^T R_U X_U/48. (2) + +Thus the inverse loop can scatter through all 56 entries of the full row +R_i, instead of only its 52 ordinary entries. Each query still reads only +ordinary X. Its orthogonality and denominator proof are unchanged. +Selected writes do not enter later queries. + +This order matters. The upper correction uses the final ordinary X, and +(2) is the ordered product of that upper map with H^-1. The checker +verifies this product on all 112 data columns. It does not move a line +operator Q through R, K, or H. + +For the raw backward formula, write the original input as x=(a,u), +y=(b,v), and put q=Q^-1 on selected fields. The retained physical input +convention has selected X=Q a. The raw backward core, before its old +postlower correction, gives + + X_U = u - J_US Q a - H v, + X_A = q b - J_AA Q a - J_AU v, + Y_A = Q a, Y_U = v. + +Apply (2). The borrowed-y response of completed X becomes `diag(q,-I)`. +In particular, arbitrary ordinary borrowed v is restored with coefficient +-I; it need not be zero, divisible by three, or a previously computed +centre. The common-grid conversion below supplies the integer divisibility +for every such input. + +Let E=diag(-I_A,I_U). Apart from the explicit input Q, the fused response +of X to original x is + + A_X = E - K R/12. + +The actual matrix has `R E K=12I_8`. Therefore `A_X E K=0`, and +`E A_X=I-E K R/12` is a rank-104 projector. The nullity is exactly eight. +Division by three does not remove this content kernel. The full two-bank +map still has the selected original content in Y_A. A controller that +requires A_X^-1 cannot use this A8 word. A controller that uses the +retained selected Y must prove that use explicitly. + +## Literal invoice and finite guard + +The old scalar price is used without modification. A complex unit ADD +costs eight real primitives; a positive complex `1/4` SCALE costs four; +`1/16` costs eight; CLEAR costs two. A complex odd division is two separate +real scans. It is not assigned an old primitive price. + +| Factor | Unit ADDs | SCALEs | CLEARs | Old real primitives | Real /3 scans | +| --- | ---: | ---: | ---: | ---: | ---: | +| H | 832 | 8 | 16 | 6720 | 0 | +| H^-1 | 832 | 8 | 16 | 6752 | 16 | +| H^-1 with upper correction | 864 | 8 | 16 | 7008 | 16 | + +All three rows use no new native child. The H input word is legal on the +ordinary Y fields at frame I. The inverse and fused words are legal on +completed X at FULL. C0 must be cleared and assigned the same frame before +its query; all operations in one factor then use that frame. No nonzero +private value is relabelled. The scalar packet contains no native frame +transition. A complete transferred word must check these lifetime facts. + +An exact Fraction-row calculation covers all 113 input columns: +112 data fields and arbitrary C0. It obtains the following maximum row +1-norms over every stored scalar prefix: + +| Factor | Maximum row 1-norm | New binary height | New odd height | +| --- | ---: | ---: | ---: | +| H | 121 | 2 | 0 | +| H^-1 | 52 | 4 | 1 | +| Fused inverse | 52 | 4 | 1 | + +The row norms bound stored magnitudes relative to the maximum input field +magnitude. Primitive unit ADD temporaries are bounded by twice the larger +operand bound. The SCALEs and exact division decrease magnitude. Thus +256 times the input bound suffices for H scalar arithmetic, and 128 times +the input bound suffices for either inverse. The signed division carry is +at most two. These are finite factor bounds. They do not assert that the +old complete supplier's precision constant is unchanged. + +When added to the independently reviewed 164514-scalar core, the two +selected exchanges for F cost 416 and the one selected exchange for B +costs 208. Clearing the seven other owned fields costs 14. Thus the +predicted complete local bills are + + balanced F: 171664 old real primitives, + fused B: 171744 old real primitives plus 16 real /3 scans. + +Both retain native mass 5073. These sums are predictions for the literal +transfer. This packet does not claim to have replayed those complete new +words. Their emitter, helpers, phase bindings, and frame checks remain a +separate verification step. + +## Exact signed division and root preparation + +Use one signed w-bit two's-complement numerator. Starting at its least +significant bit, read b, write a, and update the finite carry c by + + a = (b-c) mod 2, c' = (c+3a-b)/2, c starts at 0. + +The six possible input-bit/carry transitions preserve `0 <= c < 3`. +Summation gives `3 Q_unsigned = N_unsigned + 2^w c_final`. With input +and output sign bits s_N,s_Q, the signed quotient is exact precisely when + + c_final = 3 s_Q - s_N. + +This condition rejects nonmultiples. On a valid division the quotient +cannot overflow. The numerator is overwritten in place. Carry and sign +flags need only finite control. There is no second numerical array. +At most `4(w+1)` arithmetic-head steps cover a move to the low end, the +computation traversal, delimiters, and return. Retained descriptor and +record-counter work is an additional O(w+1) per record. The coefficient +four is not claimed for that separate layer. + +Multiplication by three writes `(3b+c) mod 2` and updates +`c'=floor((3b+c)/2)`. Its signed final test is +`c_final=3s_N-s_output`. The preallocated guard prevents overflow. The +same arithmetic-head scan bound applies. Both algorithms preserve the +common record format. The checker exhausts all signed inputs at widths +one through twelve, as a check of the general invariant, and rejects the +unscaled numerator one. + +## Recursive common-grid theorem + +Assume a fixed finite parent word has M inverse-factor occurrences. Assume +all other local operations are Gaussian dyadic. Replace each completed +recursive child by its exact linear endpoint on every data and arbitrary +helper column. Assume each such endpoint is Gaussian dyadic. Let D bound +the number of recursive edges in any live call chain. Put + + K_3 = M(D+1), S = 3^K_3, common grid = 2^-P/S. (3) + +P is a binary guard for the new complete word. At the outer boundary, +multiply the padded integer numerator of every physical numeric stream by +S. This includes arbitrary borrowed data, helpers, and numeric work +streams. Private zeros remain zero. Address fields, tags, and descriptors +are not numeric payloads and are not scaled. Any numeric literal must be +written in the same representation. The factors here write only zero. + +No denominator tag is added. No stream changes format at a local +division, recursive entry, or return. A common scalar S commutes with +every exact linear native operator, so the encoded computation represents +the same operator. This statement does not apply to an unproved rounded +version of that operator. + +Each finite parent prefix adds at most M to the odd denominator height. +The height-one factor proof allows this count per inverse occurrence, +instead of eight counts for its eight divisions. Gaussian-dyadic +operations cannot add odd height. A completed Gaussian-dyadic child also +cannot add odd height, even when its input already has an odd denominator. +Only unfinished calls add height. Their chain has at most D+1 nodes. Thus +all intermediates lie on (3), and every /3 scan receives an integer +numerator divisible by three. + +This proof starts with arbitrary dyadic root values scaled by S. It does +not start with arbitrary integer numerators on the finest grid. The latter +claim would be false, as numerator one shows. It also does not permit a +completed recursive child to retain an uncancelled rational normalization. +Repeated completed children with endpoint x/3 can increase odd height +beyond any bound that counts only active depth. Such a construction needs +a different global denominator bound. + +At the completed outer return, require the exact intended +Gaussian-dyadic endpoint on all physical roles. Every numerator is then +divisible by S. Divide all physical numeric streams by three K_3 times. +This restores the original encoding of arbitrary borrowed values under +their stipulated endpoint operation. There is no new approximation error +and no new tolerance premise. The inherited final truncation occurs only +after this exact unscaling. + +If N counts all real numeric records and w_g is the guarded common width, +both outer conversions together cost at most + + 8 N K_3 (w_g+1) + +arithmetic-head steps. Descriptor and counter work adds +`O(N K_3 (w_g+1))`. The additional numerator width is at most `2K_3` bits, +since `3^K_3 < 2^(2K_3)` for positive K_3. One local inverse factor on n +complex entries per field adds at most `64 n (w_g+1)` arithmetic-head +steps for its sixteen real scans, plus the retained linear stream work. +Its old scalar invoice is separate and remains in the table above. + +For the retained 73-axis recurrence with largest child at most 48e/73, +`2*48^2 < 73^2` gives `D <= 2 ceil(log2(d+1))`. Fixed M therefore adds +O(log d) bits and O(V log d) outer work. The local scans add O(V) finite +node work. The same positive complex-power slack absorbs the outer log +factor. This statement preserves a strict exponent once its complete +supplier moment is proved; it does not supply that missing moment. + +A full guard can be constructed as in the retained proof. Give each local +scalar primitive a finite magnitude and denominator-height charge, and +use the exact bound above for each factor. Completed u-axis children add +at most u binary denominator bits and a factor `2^u` in row norm. A +finite parent with total child rank s and largest child ratio rho<1 has +a prefix bound of the form + + A(e) <= A(rho e) + a e + b, + +where a and b are explicit constants from its complete event list. For +e>=1, `(a+b)e/(1-rho)` is a linear inductive majorant, with a fixed base +allowance. The additional `2K_3` numerator bits in (3) are logarithmic. +Thus O(p) records suffice in the retained parameter family. The complete +controller must calculate its own a,b and binary P. A cancellation-based +bound for a different old whole word cannot be copied without that check. + +Replacing /3 by a dyadic approximation alone is not this extension. The +checker replaces it by 85/256 and proves that composition with H does not +restore arbitrary inputs exactly. This rejects that direct substitution. +It does not exclude a separately proved reversible rounded construction. + +## What the recent Newton-code results do and do not require + +[PR3423](https://github.com/CrocSwap/integer-mult-bounds/pull/3423) and +[PR3406](https://github.com/CrocSwap/integer-mult-bounds/pull/3406) were +refreshed and their pinned proof files were read. Exact heads, paths, and +Git blob identities are in `sources/GITHUB-PINS.json`. Their executable +suites were not rerun for this audit. + +Their actual P104 code is `B_9=E Z[i]^512`, where +`E=[[1,0],[1,1+i]]^tensor9`. The proved source Clifford alphabet preserves +this module. The signed-floor pair is exact on its stated domain. The +real initial Y banks must also satisfy the appropriate fourfold +divisibility before quarter reads. These are source-domain obligations, +not free preparation of arbitrary dirty payloads. + +The [PR3423 consumer proof](https://github.com/CrocSwap/integer-mult-bounds/blob/15d28c4de37dc47ea07cd7173c8b318fca7a4d75/research/p104-newton-interfaces/CONSUMER.md) +states the resulting coefficient map as `E^-1 A E`, and checks a case +where it differs from A. A caller must bind that changed interface. The +common scalar grid in (3) has `S^-1 A S=A` for every exact linear A. It +therefore avoids that non-scalar interface change, but pays root scaling, +extra width, exact scans, and all unchanged native operations. Neither +Newton theorem imposes a ban on odd rational intermediates in the retained +exact machine model. Their fixed P104 bill also does not replace the bill +for the changed PR3133 core used here. + +## Reproduction and remaining work + +Run one process from the workspace root: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-grid-a8-20261017/check_a8_odd_grid.py --out /tmp/A8-ODD-GRID-REPLAY.json +``` + +Expected status: `PASS_A8_EXACT_ODD_GRID_NORMALIZATION`. +The checker writes the boundary words next to its chosen receipt. Compare +both files to the frozen packet. It verifies all formal input columns, +both H inverse orders, the fused order, every prefix denominator bound, +all local bills, the exact X-content kernel, and signed record arithmetic. +Controls reject an omitted division, an approximate inverse, and a root +numerator outside the stated representation contract. + +The next required check is the literal transfer onto both new native +providers, with all helper and private columns, legal frames, and native +phase pins. A complete supplier must then use the retained selected +content, bind the controller, host all private state, prove every owner +endpoint, and calculate the complete moment and precision. These tasks +are not certified by this local packet. An independent reviewer must also +review this new factor and its grid argument; the producing lane's older +independent reviews do not review its own new construction. + +The actual raw selected mechanism and minor block identities come from +the native-escape and new-core-transfer lanes. The scalar scan and grid +method come from the credited retained sources and prior rational-decoder +work. OpenAI Codex assisted the derivation, implementation, and source +audit. No human review, maintainer selection, PR, push, or publication +commit is claimed. diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/FREEZE.json new file mode 100644 index 0000000000..28c9580be4 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/FREEZE.json @@ -0,0 +1,20 @@ +{ + "commands": [ + "python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-unitary-packing-20261020/check_packing.py --out work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal", + "python3 -O work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-unitary-packing-20261020/check_packing.py --out work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-optimized" + ], + "files": { + "PACKING.md": "f13ee61b7dab8f63da2ef03808d1cc3cd0365ca00aafc9c70893f0f15c6340d4", + "check_packing.py": "2ce5a49f66b3e8acd1d2a822ea77c0e9257c82214331d897ba6d6d83899d6cef", + "run-normal/CHECKS.json": "142f254b16b880bfc4237266d044a8bf781f546c9322a31682d73341624acc46", + "run-normal/PACKING.json.gz": "dd9f9f053f929df31cf9ffbe8404256f9b34fdbd031162bd4b7873f7aaf70544", + "run-optimized/CHECKS.json": "142f254b16b880bfc4237266d044a8bf781f546c9322a31682d73341624acc46", + "run-optimized/PACKING.json.gz": "dd9f9f053f929df31cf9ffbe8404256f9b34fdbd031162bd4b7873f7aaf70544" + }, + "normal_optimized_bytes_equal": true, + "payload_decompressed_sha256": "b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32", + "publication": "No PR, commit, push or publication. Before a future PR description read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.", + "schema": "actual-odd-unitary-packing-freeze-v1", + "scope": "Actual sixteen-coordinate unitary matrix and paid dyadic precode. Packing word, odd-grid admission, native support and recursive caller are separate.", + "status": "FROZEN_DISTINCT_REVIEW_PENDING" +} diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/PACKING.md b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/PACKING.md new file mode 100644 index 0000000000..9369bb2332 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/PACKING.md @@ -0,0 +1,241 @@ +# Sixteen unitary centre outputs with divisor three + +The actual sixteen centre readers admit a Gaussian rational unitary +code on 112 ports whose decoder uses exactly sixteen output fields. +Its entries have denominators dividing a power of two times three. +No entry needs a second factor of three. + +The sixteen-coordinate count is the ordinary rank minimum. In +contrast, a unitary code with no factor of three in its denominators +needs at least 24 output fields. Thus the factor three changes the +possible coordinate interfaces. This is a representation theorem +and an actual matrix construction. It is not a native supplier. + +The dyadic part of the construction has a complete scalar word and +inverse. Each costs 4,862 real scalar primitives and uses no extra +field. The final four small packing matrices still need their +separate component words, paid division scans, and grid admission. +Those obligations are assigned to the bridge-access lane. + +## Pinned input + +The actual reader V and response E come from +`new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/twenty-four-v2-normal/UNITARY-24.json.gz`. +Its decompressed digest is +`9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c`. + +The actual pair matrices and signed mode blocks come from +`signed-probe/METRIC-COMPLETION.json.gz` in the same source directory. +Its decompressed digest is +`88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e`. + +The matrix and scalar arithmetic is imported from the preceding +independent review with digest +`a834f297f9cc82de9b29f4cd17ac762ed371d9a0b13bbac25b3430d2f87de25e`. +No producer interpreter is imported. All source geometry is retained. + +## A dyadic preliminary code + +Let alpha=(1+i)/2. On each actual physical pair, the real pair matrix +H has H*H=2I. Thus alpha H is Gaussian dyadic and unitary. +Apply these normalized pair matrices on the 48 large ports. + +In each signed six-mode block, first apply its recorded input signs. +Apply H4/2 to the first four stored coordinates, where H4 is the +four-point Walsh matrix. Apply alpha H2 to the last two. The two +sum outputs occur at the first and fifth stored ports. + +The corresponding actual physical centre reader has coefficients + +```text +2(1-i), -2i +``` + +on those two outputs. To verify the normalization, the original +reader is d^T H. The normalized pair input is alpha H x. +The four-mode sum has decoder coefficient 2/alpha, and the two-mode +sum has decoder coefficient 1/alpha^2. These are exactly the two +displayed coefficients. + +On each small eight-port clique, use ((1+i)/4) H8. Its centre +reader is 2(1-i) times the first output. Let Cpre be this complete +dyadic unitary code. It has sixteen large sum outputs and eight +small sum outputs. + +This preliminary code differs from the native-compatible +24-coordinate code. It is chosen to make the odd packing explicit. +It does not inherit that code's zero-diagonal support. + +## A four-field packing matrix + +Define + +```text +A = [[1,1+i],[-1+i,1]], +B = [[1-i,-i],[-i,1+i]]. +``` + +Direct multiplication gives A A*=B B*=3I. Let P reorder four +coordinates as (0,2,1,3), and put + +```text +R = (1/3) diag(A*,A*) P diag(B,B). (1) +``` + +Then R is unitary. Its only non-dyadic divisor is three. Moreover, + +```text +[2A,0] R + = [[2(1-i),-2i,0,0], + [0,0,2(1-i),-2i]]. (2) +``` + +Indeed, multiplication by the first block of A cancels A*/3. +The first two rows of P diag(B,B) are the first row of each +copy of B. This proves (2) without a square root or an extension +of the scalar field. + +Pair the eight large readers in their stored order. For each pair, +apply R to its four preliminary sum outputs. The new first two +outputs recover both readers through the decoder 2A. Their other +two outputs retain independent information. + +Embed these four disjoint R matrices into a 112-port unitary +Rall. Define + +```text +C16 = Rall Cpre. +``` + +The eight small sum outputs are unchanged. The centre decoder +therefore uses eight large outputs and eight small outputs. +The exact payload includes all four port lists, Cpre, Rall through +its disjoint factors, C16, C16*, and the complete decoder. + +## Exact scope of the representation change + +The full actual matrices satisfy + +```text +C16 C16* = C16* C16 = I, +T16 = V C16*, +T16 C16 = V. +``` + +The union of the supports of T16 has exactly sixteen coordinates. +The other 96 response rows satisfy + +```text +(C16 E)_R96 = (C16)_R96. +``` + +These identities were checked on every matrix entry. They do not +permit the other independent coordinates to be discarded. +All 96 ordinary rows in this particular assignment have nonzero +diagonal. The current off-diagonal native grammar therefore does +not implement this matrix merely from its centre count. + +Every entry of C16 and C16* has binary denominator height at most +two and three-denominator height at most one. Some entries have a +factor three, so the distinction is real. + +The lower bound from the preceding footprint theorem applies more +widely than the dyadic ring. It applies over every Gaussian +rational coefficient ring whose denominators are invertible modulo +three. The unitary encoder remains invertible after reduction, and +the actual real reader ranks remain 32 and 16. Thus a unitary +sixteen-coordinate encoder must contain a denominator divisible +by three. Other odd primes alone cannot remove this obstruction. + +On the other hand, the rank of V over Q(i) is sixteen. No invertible +linear code with arbitrary inputs can recover those readers from +fewer than sixteen complex coordinates. Construction (1) reaches +that bound with a single factor three in each endpoint coefficient. + +This establishes a sharp coordinate change between the two stated +coefficient classes. It is not a lower bound for nonunitary codes, +approximate recovery, promised zero inputs, or a different output +interface. + +## Paid dyadic word + +The literal Cpre word uses the actual signed pair matrices. +A real two-field Hadamard map is implemented as + +```text +x <- x+y +y <- -2y +y <- y+x. +``` + +The signs from the actual pair matrices are paid before and after +that word. Walsh4 and Walsh8 are products of these pair words. +All permutations are fixed by the displayed port order; none is +inserted as a free circuit operation. + +Multiplication by alpha uses the real-component word + +```text +r <- r-s +s <- 2s +s <- s+r +r <- r/2 +s <- s/2. +``` + +The inverse word reverses each component operation and its +coefficient. Each direction has 1,854 component instructions +and costs 4,862 real scalar primitives. Both directions pass +all 1,280 real input columns. The 528 outside complex fields +are unchanged and remain arbitrary. + +The Cpre word has real-component prefix one-norm bound 16. +Its inverse has bound 8. Both have maximum binary denominator +height two. These bounds do not include the four rational +packing words. + +## Access, division, and reuse obligations + +The code and these scalar words are stated at one common type, +such as current I or completed FULL. They cannot be applied +across unequal holes without a separate access proof. +The code generally does not commute with the port-dependent Q. + +For arbitrary dyadic input, divisibility by three is not promised. +The dyadic unitary Cpre is onto the dyadic input module, so its +four-field carrier inputs can be arbitrary dyadic values. +A component implementation must use an exact paid division +contract or a sufficient common input grid. + +The bridge-access lane is checking the literal R and R* words, +code-image divisibility, root-grid cost, and restoration. +This packet claims none of those checks. The fact that C16* +is the exact inverse does not by itself price division scans +or prove a complete recursive grid. + +The two scalar types, native responses, full phase lowering, +borrowed-state hosting, recursive entrance, and final code +removal remain open. There is no complete supplier or +integer-multiplication improvement in this packet. + +## Reproduction and credit + +Run into two new directories: + +```text +python3 check_packing.py --out +python3 -O check_packing.py --out +``` + +Both runs must report `PASS_ACTUAL_ODD_UNITARY_PACKING`. +The freeze records their exact payload and receipt comparison. + +The root lane supplied the footprint question and emphasized +representation changes. The core lane supplied the actual +reader and pair geometry. This lane derived the explicit +norm-three packing, its physical binding, and the dyadic +precode word. AI assistance was used throughout. + +No PR, commit, push, or publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/check_packing.py b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/check_packing.py new file mode 100644 index 0000000000..7cbd61088b --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/check_packing.py @@ -0,0 +1,244 @@ +"""Construct the actual sixteen-coordinate unitary code with odd divisor three.""" + +import argparse +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +HELPER = HERE.parent / "unitary-footprint-review-20261020/check_review.py" +HELPER_PIN = "a834f297f9cc82de9b29f4cd17ac762ed371d9a0b13bbac25b3430d2f87de25e" +SOURCE = HERE.parents[1] / "new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020" +PLACEMENT_PIN = "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e" +CODE_PIN = "9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c" + + +def need(value, label): + if not value: + raise ValueError(label) + + +def serialize(matrix): + return [{str(j): [str(x), str(y)] for j, (x, y) in sorted(row.items())} + for row in matrix] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + need(sha256(HELPER.read_bytes()).hexdigest() == HELPER_PIN, "Independent arithmetic pin") + spec = importlib.util.spec_from_file_location("packing_arithmetic", HELPER) + g = importlib.util.module_from_spec(spec) + spec.loader.exec_module(g) + placement = json.loads(g.read_pinned( + SOURCE / "signed-probe/METRIC-COMPLETION.json.gz", PLACEMENT_PIN)) + source = json.loads(g.read_pinned( + SOURCE / "twenty-four-v2-normal/UNITARY-24.json.gz", CODE_PIN)) + h = g.rows(placement["pair_code"], True) + v, e = g.rows(source["original_centre_readers"]), g.rows(source["response"]) + large = [block for block in placement["mode_blocks"] if block["kind"] == "large6"] + small = [block for block in placement["mode_blocks"] if block["kind"] == "small8"] + large_ports = {p for block in large for p in block["ports"]} + alpha, beta = (F(1,2), F(1,2)), (F(1,4), F(1,4)) + normalized_pair = [{j: g.times(alpha, x) if i in large_ports else x for j, x in row.items()} + for i, row in enumerate(h)] + need(g.product(normalized_pair, g.adjoint(normalized_pair, 112)) == g.eye(112), + "Actual Gaussian dyadic unitary pair encoder") + mode = g.eye(112) + word = [] + + def cadd(target, source_field, value): + for component in (0, 1): + word.append(["add", 2*target+component, 2*source_field+component, str(value)]) + + def cscale(target, value): + for component in (0, 1): + word.append(["scale", 2*target+component, None, str(value)]) + + def c_alpha(target): + x, y = 2*target, 2*target+1 + word.extend([["add", x, y, "-1"], ["scale", y, None, "2"], + ["add", y, x, "1"], ["scale", x, None, "1/2"], + ["scale", y, None, "1/2"]]) + + def raw_hadamard(a, b): + cadd(a, b, 1) + cscale(b, -2) + cadd(b, a, 1) + + def walsh(ports): + bit = 1 + while bit < len(ports): + for j in range(len(ports)): + if not j & bit: + raw_hadamard(ports[j], ports[j | bit]) + bit *= 2 + + pairs = sorted({tuple(sorted(h[p])) for p in large_ports}) + need(len(pairs) == 24 and all(len(pair) == 2 for pair in pairs), "Actual24 physical pairs") + for a, b in pairs: + aa, bb, cc, dd = [h[x][y][0] for x, y in ((a,a),(a,b),(b,a),(b,b))] + need(all(x in (-1, 1) for x in (aa,bb,cc,dd)), "Signed Hadamard pair") + sign = cc / aa + need(dd == -bb*sign, "Pair sign factor") + if aa < 0: + cscale(a, -1) + if bb < 0: + cscale(b, -1) + raw_hadamard(a, b) + if sign < 0: + cscale(b, -1) + c_alpha(a) + c_alpha(b) + large_carriers = [] + for block in large: + ports, signs = block["ports"], block["signs"] + for port, sign in zip(ports, signs): + if sign < 0: + cscale(port, -1) + for i in range(4): + mode[ports[i]] = { + ports[j]: (F(signs[j] * (-1 if (i & j).bit_count() % 2 else 1), 2), F(0)) + for j in range(4)} + for i in range(2): + mode[ports[4+i]] = { + ports[4+j]: g.times(alpha, (F(signs[4+j] * (-1 if i*j else 1)), F(0))) + for j in range(2)} + walsh(ports[:4]) + for port in ports[:4]: + cscale(port, F(1,2)) + raw_hadamard(ports[4], ports[5]) + c_alpha(ports[4]) + c_alpha(ports[5]) + large_carriers.append([ports[0], ports[4]]) + small_carriers = [] + for block in small: + ports = block["ports"] + for i, port in enumerate(ports): + mode[port] = { + ports[j]: g.times(beta, (F(-1 if (i & j).bit_count() % 2 else 1), F(0))) + for j in range(8)} + walsh(ports) + for port in ports: + c_alpha(port) + cscale(port, F(1,2)) + small_carriers.append(ports[0]) + cpre = g.product(mode, normalized_pair) + cprei = g.adjoint(cpre, 112) + need(g.product(cpre, cprei) == g.product(cprei, cpre) == g.eye(112), "Precode unitary orders") + decoder_pre = g.product(v, cprei) + wanted_pre = [{ports[0]: (F(2),F(-2)), ports[1]: (F(0),F(-2))} + for ports in large_carriers] + wanted_pre += [{port: (F(2),F(-2))} for port in small_carriers] + need(decoder_pre == wanted_pre, "Actual preliminary centre coefficients") + inverse_word = [[op, target, source_field, str(-F(value) if op == "add" else 1/F(value))] + for op, target, source_field, value in reversed(word)] + reports = {} + for name, instructions, matrix in (("precode", word, cpre), ("precode_adjoint", inverse_word, cprei)): + need(all(0 <= x[1] < 224 and (x[0] == "scale" or 0 <= x[2] < 224) for x in instructions), + "Arbitrary528 outside complex fields stay fixed") + expected = g.realify(matrix, 112) + need(g.pullback(instructions) == expected, "All1280 precode real input columns") + forward, bounds = g.prefix_bounds(instructions) + need(forward == expected, "Precode prefix replay") + reports[name] = {"instructions": len(instructions), + "scalar": sum(map(g.tariff, instructions)), **bounds} + + a = [{0:(F(1),F(0)),1:(F(1),F(1))}, + {0:(F(-1),F(1)),1:(F(1),F(0))}] + b = [{0:(F(1),F(-1)),1:(F(0),F(-1))}, + {0:(F(0),F(-1)),1:(F(1),F(1))}] + three = [{j:(F(3),F(0))} for j in range(2)] + need(g.product(a,g.adjoint(a,2)) == g.product(b,g.adjoint(b,2)) == three, + "Two integer Gaussian norm-three factors") + + def doubled(matrix): + return [{j+2*block:x for j,x in row.items()} for block in range(2) for row in matrix] + + permutation = [{j:g.ONE} for j in (0,2,1,3)] + numerator = g.product(g.product(doubled(g.adjoint(a,2)), permutation), doubled(b)) + packing = [{j:g.times((F(1,3),F(0)),x) for j,x in row.items()} for row in numerator] + packing_inverse = g.adjoint(packing,4) + need(g.product(packing,packing_inverse) == g.product(packing_inverse,packing) == g.eye(4), + "Packing unitary products") + target = [{j:g.times((F(2),F(0)),x) for j,x in row.items()} for row in a] + old_readers = [{j+2*i:g.times((F(2),F(0)),x) for j,x in b[0].items()} for i in range(2)] + need(g.product(target,packing) == old_readers, "Exact four-to-two packing equation") + global_packing = g.eye(112) + pack_ports, selected = [], list(small_carriers) + for i in range(0,8,2): + ports = large_carriers[i]+large_carriers[i+1] + pack_ports.append(ports) + selected.extend(ports[:2]) + for row, port in zip(packing, ports): + global_packing[port] = {ports[j]:x for j,x in row.items()} + c = g.product(global_packing,cpre) + ci = g.adjoint(c,112) + decoder = g.product(v,ci) + need(g.product(c,ci) == g.product(ci,c) == g.eye(112), "Complete sixteen-output unitary") + need(set().union(*(set(row) for row in decoder)) == set(selected) and len(set(selected)) == 16, + "Exact sixteen-coordinate footprint") + need(g.product(decoder,c) == v, "Actual complete reader recovery") + ce = g.product(c,e) + ordinary = set(range(112))-set(selected) + need(all(c[p] == ce[p] for p in ordinary), "All96 ordinary response rows") + odd_height = binary_height = 0 + for matrix in (c,ci): + for row in matrix: + for z in row.values(): + for coefficient in z: + denominator = coefficient.denominator + two = three_power = 0 + while denominator % 2 == 0: + two += 1 + denominator //= 2 + while denominator % 3 == 0: + three_power += 1 + denominator //= 3 + need(denominator == 1 and three_power <= 1, "Only one factor three in endpoint entries") + binary_height, odd_height = max(binary_height,two), max(odd_height,three_power) + need(odd_height == 1, "The odd factor is present") + payload = { + "schema":"actual-sixteen-coordinate-odd-unitary-v1", + "selected_ports":sorted(selected), "ordinary_ports":sorted(ordinary), + "large_precode_carriers":large_carriers, "small_precode_carriers":small_carriers, + "packing_ports":pack_ports, "packing_order":"diag(B,B), P, diag(A*,A*), scalar1/3", + "packing_integer_A":serialize(a), "packing_integer_B":serialize(b), + "packing_numerator":serialize(numerator), "packing":serialize(packing), + "packing_adjoint":serialize(packing_inverse), "packing_target_decoder":serialize(target), + "precode":serialize(cpre), "precode_adjoint":serialize(cprei), + "precode_words":{"precode":word,"precode_adjoint":inverse_word}, + "code":serialize(c), "code_adjoint":serialize(ci), + "original_readers":serialize(v), "decoder":serialize(decoder), + "coded_response":serialize(ce), + "source_pins":{"independent_arithmetic":HELPER_PIN,"actual_24_code":CODE_PIN, + "actual_placement":PLACEMENT_PIN}, + "scope":"Actual common-frame matrices and paid dyadic precode only. Packing component word, grid admission, native support and caller are separate.", + } + encoded = (json.dumps(payload,sort_keys=True,separators=(",",":"))+"\n").encode() + (args.out/"PACKING.json.gz").write_bytes(gzip.compress(encoded,mtime=0)) + receipt = { + "status":"PASS_ACTUAL_ODD_UNITARY_PACKING", + "payload_decompressed_sha256":sha256(encoded).hexdigest(), + "source_pins":payload["source_pins"], "arbitrary_real_precode_columns":1280, + "unchanged_outside_complex_fields":528, "precode_words":reports, + "complete_code_selected_fields":16, "ordinary_response_equal_rows":96, + "complete_code_maximum_binary_denominator_height":binary_height, + "complete_code_maximum_three_denominator_height":odd_height, + "ordinary_code_nonzero_diagonals":sum(p in c[p] for p in ordinary), + "packing_component_word_emitted":False, "complete_native_service":False, + "recursive_grid_contract_admitted":False, "new_owned_fields":0, + } + (args.out/"CHECKS.json").write_text(json.dumps(receipt,sort_keys=True,indent=2)+"\n") + print(receipt["status"]) + print(json.dumps(reports,sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..3428da40c3 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal/CHECKS.json @@ -0,0 +1,34 @@ +{ + "arbitrary_real_precode_columns": 1280, + "complete_code_maximum_binary_denominator_height": 2, + "complete_code_maximum_three_denominator_height": 1, + "complete_code_selected_fields": 16, + "complete_native_service": false, + "new_owned_fields": 0, + "ordinary_code_nonzero_diagonals": 96, + "ordinary_response_equal_rows": 96, + "packing_component_word_emitted": false, + "payload_decompressed_sha256": "b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32", + "precode_words": { + "precode": { + "binary_height": 2, + "instructions": 1854, + "prefix_one_norm": "16", + "scalar": 4862 + }, + "precode_adjoint": { + "binary_height": 2, + "instructions": 1854, + "prefix_one_norm": "8", + "scalar": 4862 + } + }, + "recursive_grid_contract_admitted": false, + "source_pins": { + "actual_24_code": "9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c", + "actual_placement": "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e", + "independent_arithmetic": "a834f297f9cc82de9b29f4cd17ac762ed371d9a0b13bbac25b3430d2f87de25e" + }, + "status": "PASS_ACTUAL_ODD_UNITARY_PACKING", + "unchanged_outside_complex_fields": 528 +} diff --git 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a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/ODD-GRID-COMPOSITION.md b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/ODD-GRID-COMPOSITION.md new file mode 100644 index 0000000000..1823209221 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/ODD-GRID-COMPOSITION.md @@ -0,0 +1,195 @@ +# A common odd grid for unfinished parent operations + +The reciprocal E and G maps have coefficients with denominator 13. This +does not require the recursive native children to have rational endpoint +maps. E and G can be local operations in a parent word. The theorem below +states the condition under which a depth bound still pays for all such +denominators. A rational local endpoint is not, by that fact alone, an +admitted completed recursive child. + +## Coefficient theorem + +Put A=Z[i,1/2]. Represent a complete finite machine state by its numeric +fields, including all arbitrary borrowed fields. Add zero and private +fields as needed. Maps in this statement are exact linear maps on that +full state. Permutations, copies, clears of owned private fields, and +Gaussian-dyadic native operations have matrices over A. + +Consider a finite recursive computation with these hypotheses: + +1. At most L invocations are active at the same time. Count the root and + the current leaf in L. +2. Each invocation has a finite parent word. In that word, replace each + completed recursive child by its full endpoint map. Each such map has + coefficients in A, on every permitted data and arbitrary helper input. +3. Apart from child calls, the local factors have coefficients in + 13^-h A, with h a nonnegative integer. The sum of these h values in one + parent word is at most D. This bound also covers an operation stopped + at any scalar prefix. A stronger proved bound on all local prefixes + can be used instead of this sum. +4. All initial numeric values are dyadic. A separate binary guard and + magnitude bound are valid for this new complete word. + +Then every global prefix matrix has entries in + + 13^(-D L) A. (1) + +Different bounds D_j at different active levels give the more precise +bound 13^(-sum_j D_j) A. An initial odd denominator height h_0 adds h_0 +to the exponent. The bound depends on the active path, not on the total +number of completed child calls. + +To prove (1), stop the execution at any event. Contract each completed +child call to its exact full endpoint matrix over A. The remaining +unfinished invocations form one active path. At each level, the executed +part of its parent word adds at most D to the denominator height. In a +product of matrices, the height is at most the sum of the heights of the +factors. Adding entries cannot increase this bound. Thus the total is at +most D L. This proof uses no commutation between different local maps. + +A completed child may receive values with denominator 13 from its parent. +An A-linear endpoint does not add a new factor of 13 to those values. +Its own unfinished prefixes are covered by the next active level. The +claim therefore remains valid on rational inputs from an unfinished +parent, provided its exact full-column endpoint identity is valid there. +An exact linear identity over A has that scalar extension. A rounded or +input-restricted implementation needs a separate argument. + +## Exact encoded execution + +Let H=D L. Choose the binary unit 2^-P from a guard for the complete new +word. Use the common grid + + 2^-P 13^-H Z[i]. (2) + +At the outer boundary, multiply the padded integer numerator of every +physical numeric stream by 13^H. Include arbitrary borrowed data and +helpers. Private zeros remain zero. Do not scale addresses, tags, or +descriptors. Any nonzero numeric literal must use the same encoding. +The present linear words need only zero literals. + +The initial states here are arbitrary dyadic values with this root +encoding. They are not arbitrary integer numerators on the finest grid. +That stronger claim is false: the finest-grid numerator one cannot be +divided exactly by 13. + +Every algebraic prefix lies on (2), by (1) and the separate binary guard. +At a literal division by 13, the algebraic state after the operation +therefore also has an integer numerator. Its input numerator is divisible +by 13. Induction over the literal events shows that the integer scans +implement the rational word exactly. This is not an approximation claim. +The scalar root encoding commutes with every exact linear native map. + +At the outer return, suppose the complete intended endpoint on all +physical roles has coefficients in A. Every final numerator is then +divisible by 13^H. Exact unscaling restores the original encoding of all +numeric fields, including the stipulated borrowed-state output. Final +truncation can occur after this unscaling under the separate original +error proof. No new rounding error or tolerance is introduced by (2). +Without a dyadic root endpoint, this unscaling conclusion does not follow. + +The endpoint hypothesis is essential for a bound based only on depth. +Three consecutive completed children with endpoint x/13 can create +denominator height three at depth two. More such calls give unbounded +height at the same depth. If a changed controller exposes E or G as a +completed recursive provider with this rational endpoint, it needs a +different denominator theorem. Calling these maps local parent operations +does not by itself prove that the complete parent endpoint is dyadic. + +## Signed scan and price + +For a w-bit signed numerator N, start at its low bit with carry c=0. +For each input bit b, write a and update c by + + a=(b-c) mod 2, c'=(c+13a-b)/2. (3) + +The carry stays in {0,...,12}. After w bits, summing the bit equations +gives 13 Q_unsigned=N_unsigned+2^w c_final. If s_N and s_Q are the +two sign bits, the signed quotient is exact if and only if + + c_final=13 s_Q-s_N. (4) + +The quotient of an exactly divisible signed input cannot overflow its +input width. Formula (3) needs finite control and one scan; it does not +need another numeric array. Multiplication uses output bit +(13b+c) mod 2 and next carry floor((13b+c)/2). Its final signed test is +c_final=13s_N-s_output. The allocated magnitude guard prevents overflow. + +These scans have O(w) arithmetic-head cost. The retained record and +descriptor work has a separate O(w) cost per record. The prior common-grid +packet gives the same finite-control construction for division by three; +changing the fixed carry set to thirteen states does not change the scan +order. This statement does not assign an old scalar-primitive price to a +new odd division. + +If w is the guarded numerator width before the common odd scale, the +extra width is at most + + ceil(H log2(13)) <= 4H. (5) + +This is an odd-denominator overhead. It is in addition to the binary and +magnitude guard for the changed word. For S real numeric records, root +conversion and final unscaling by repeated fixed scans cost + + O(S H (w+H)). (6) + +Each local real division by 13 costs O(w+H). All numeric streams that +need conversion belong in S, including arbitrary borrowed storage. +Descriptor, owner, routing, and hosting costs are still part of the +complete construction. Equations (5) and (6) do not pay for an omitted +controller or a native frame transition. + +For a fixed finite parent word, D is constant. If its recursion depth is +O(log N), the extra width is O(log N). If its guarded word width is at +least proportional to H and V=S w, the outer conversion cost is O(V H). +An exponent claim also needs the full recurrence and its strict slack. +This theorem supplies neither a new moment bound nor a kappa value. + +## Application to the actual reciprocal family + +The actual coordinate projection P gives + + E=I+K((12/13)P-I)R, + G=I+K((12/13)(I-P)-I)R. + +Each is a fixed rational local map. Each has an endpoint denominator of +height at most one. The actual source has ||R||_infinity=56 and +||K||_infinity=1. Thus each endpoint has row-sum norm at most 57. +These endpoint facts do not bound every native implementation prefix. +One may use the literal number of /13 factors as a conservative D once +the complete word, its helpers, and its legal input states are checked. + +The native H1 and H8 children can keep their original exact dyadic maps. +The parent can use E and G between such calls under hypotheses 1--4. +For a complete controller, it remains necessary to prove its ordered +endpoint, every borrowed-state output, the binary and magnitude guard, +and its actual recursive bill. In particular, EG=I in one scalar chart +does not prove cancellation of physical maps that contain port-dependent +q operators or changes of chart. + +## Validation and prior work + +`check_grid.py` exhausts all signed inputs at widths one through fourteen +for both fixed scans. It checks five nested test trees on all eight +independent input columns using integer numerators only. Every completed +child is a dyadic shear. Rational reciprocal centre scales surround two +child calls. The tree checks all divisions, every child endpoint, the +active-path bound, and final unscaling. Separate controls reject an +unscaled finest-grid input, repeated rational child endpoints, and early +unscaling. These tests support the general proof above. They are not a +native supplier or controller implementation. + +The retained common odd-grid source is +`../../interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex`, +SHA256 `4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a`. +The local predecessor is +`../odd-grid-a8-20261017/A8-ODD-GRID.md`, SHA256 +`e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01`. +The prior peer review is +`../../bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md`, +SHA256 `0eee1c869ba6c1c5e75075bc9dbae3324468a27a6b0dd45cd16e4f7973f9eb05`. +This note states the same method for 13 and for explicit rational parent +operations. It does not claim to introduce common odd grids. + +This work used OpenAI Codex under the user's direction. It remains local. +No publication is authorized. diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/FREEZE.json new file mode 100644 index 0000000000..3659fc1614 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/FREEZE.json @@ -0,0 +1,17 @@ +{ + "commands": [ + "python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/unitary-footprint-review-20261020/check_review.py --out work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-NORMAL.json", + "python3 -O work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/unitary-footprint-review-20261020/check_review.py --out work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-OPTIMIZED.json" + ], + "files": { + "REVIEW-NORMAL.json": "28db16426c29a8c5268bedfdde0e207c98db429d463b3e8a00ca1f8fdc5dfe08", + "REVIEW-OPTIMIZED.json": "28db16426c29a8c5268bedfdde0e207c98db429d463b3e8a00ca1f8fdc5dfe08", + "REVIEW.md": "62fb5a91437d183c401571177dccfe93dbd0503000520708c2fd2d8bfddb9a7d", + "check_review.py": "a834f297f9cc82de9b29f4cd17ac762ed371d9a0b13bbac25b3430d2f87de25e" + }, + "normal_optimized_bytes_equal": true, + "publication": "No PR, commit, push or publication. Before a future PR description read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.", + "schema": "unitary-footprint-and-24-code-independent-review-v1", + "scope": "Finite-field coordinate theorem, actual24-field Gaussian dyadic unitary matrix, and full common-frame scalar words. No native/service/caller claim.", + "status": "PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-NORMAL.json b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-NORMAL.json new file mode 100644 index 0000000000..4a40e76590 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-NORMAL.json @@ -0,0 +1,59 @@ +{ + "arbitrary_real_input_columns": 1280, + "attained_selected_fields": 24, + "component_words": { + "code": { + "binary_height": 3, + "instructions": 2418, + "prefix_one_norm": "16", + "scalar": 8052 + }, + "inverse_and_adjoint": { + "binary_height": 2, + "instructions": 2418, + "prefix_one_norm": "28", + "scalar": 8052 + } + }, + "imports_producer_or_root_checker": false, + "lower_bound_complex_fields": 24, + "lower_bound_real_coordinates": 48, + "native_phases_or_complete_service_reviewed": false, + "native_target_path_census_reviewed": false, + "new_owned_fields": 0, + "ordinary_equal_rows": 88, + "producer_source_pins": { + "TWENTY-FOUR-FREEZE.json": "3fda436c0390fb8ef2ee72b4d9fe6ccbfc0ea994208f4d962bb9f43960af7a82", + "UNITARY-24.md": "420e5d4eb13c43bfbd41614c7a686db49e1091bf06ed26039f231323208461a6", + "signed-probe/METRIC-COMPLETION.json.gz": "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e", + "twenty-four-v2-normal/UNITARY-24.json.gz": "9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c", + "unitary-v2-normal/UNITARY-COMPLETION.json.gz": "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428" + }, + "reader_Gram": [ + "12", + "12", + "12", + "12", + "12", + "12", + "12", + "12", + "8", + "8", + "8", + "8", + "8", + "8", + "8", + "8" + ], + "real_mod_three_Gram_rank": 16, + "real_mod_three_row_rank": 32, + "recursive_caller_admitted": false, + "root_source_pins": { + "root/UNITARY-CENTRE-FOOTPRINT-20261020.md": "464628f0966138a9f95c34d26abeed214ab38720916fb1214820dd62e998f0a0", + "root/UNITARY-FOOTPRINT-FREEZE-20261020.json": "9ec2cb0f38210cf95246991f9637c036c7e5489cfc9ad78b7075213d9ca3ba75" + }, + "status": "PASS_UNITARY_FOOTPRINT_AND_24_CODE_REVIEW", + "unchanged_outside_complex_fields": 528 +} diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-OPTIMIZED.json b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-OPTIMIZED.json new file mode 100644 index 0000000000..4a40e76590 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-OPTIMIZED.json @@ -0,0 +1,59 @@ +{ + "arbitrary_real_input_columns": 1280, + "attained_selected_fields": 24, + "component_words": { + "code": { + "binary_height": 3, + "instructions": 2418, + "prefix_one_norm": "16", + "scalar": 8052 + }, + "inverse_and_adjoint": { + "binary_height": 2, + "instructions": 2418, + "prefix_one_norm": "28", + "scalar": 8052 + } + }, + "imports_producer_or_root_checker": false, + "lower_bound_complex_fields": 24, + "lower_bound_real_coordinates": 48, + "native_phases_or_complete_service_reviewed": false, + "native_target_path_census_reviewed": false, + "new_owned_fields": 0, + "ordinary_equal_rows": 88, + "producer_source_pins": { + "TWENTY-FOUR-FREEZE.json": "3fda436c0390fb8ef2ee72b4d9fe6ccbfc0ea994208f4d962bb9f43960af7a82", + "UNITARY-24.md": "420e5d4eb13c43bfbd41614c7a686db49e1091bf06ed26039f231323208461a6", + "signed-probe/METRIC-COMPLETION.json.gz": "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e", + "twenty-four-v2-normal/UNITARY-24.json.gz": "9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c", + "unitary-v2-normal/UNITARY-COMPLETION.json.gz": "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428" + }, + "reader_Gram": [ + "12", + "12", + "12", + "12", + "12", + "12", + "12", + "12", + "8", + "8", + "8", + "8", + "8", + "8", + "8", + "8" + ], + "real_mod_three_Gram_rank": 16, + "real_mod_three_row_rank": 32, + "recursive_caller_admitted": false, + "root_source_pins": { + "root/UNITARY-CENTRE-FOOTPRINT-20261020.md": "464628f0966138a9f95c34d26abeed214ab38720916fb1214820dd62e998f0a0", + "root/UNITARY-FOOTPRINT-FREEZE-20261020.json": "9ec2cb0f38210cf95246991f9637c036c7e5489cfc9ad78b7075213d9ca3ba75" + }, + "status": "PASS_UNITARY_FOOTPRINT_AND_24_CODE_REVIEW", + "unchanged_outside_complex_fields": 528 +} diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW.md new file mode 100644 index 0000000000..b70d4c671c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW.md @@ -0,0 +1,180 @@ +# Independent review of the 24-coordinate unitary code + +The finite-field lower bound and the actual 24-coordinate matrix +pass this review. The complete common-frame scalar words also pass. +The proof applies to Gaussian dyadic unitary codes, and more generally +to real dyadic orthogonal codes. It does not give a lower bound for +all encodings or for native implementation cost. + +The reviewed root proof is +`root/UNITARY-CENTRE-FOOTPRINT-20261020.md`, digest +`464628f0966138a9f95c34d26abeed214ab38720916fb1214820dd62e998f0a0`. +The actual 24-coordinate source is +`lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/TWENTY-FOUR-FREEZE.json`, +digest +`3fda436c0390fb8ef2ee72b4d9fe6ccbfc0ea994208f4d962bb9f43960af7a82`. +The source proof has digest +`420e5d4eb13c43bfbd41614c7a686db49e1091bf06ed26039f231323208461a6`. +The decompressed matrix and word payload has digest +`9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c`. + +The checker in this review imports no root or producer arithmetic, +matrix code, or interpreter. It reads the frozen matrices, geometry, +and literal component instructions. All source digests are checked +before and after the computation. + +## The lower bound + +Let A have entries in Z[1/2]. Suppose A has row rank r modulo an +odd prime p, and A A^T has rank s modulo p. Let U be orthogonal +over Z[1/2]. Suppose the exact required vector A x can be recovered +from m coordinates of U x, for every x. + +Set y=U x. Every y is possible. The required vector is A U^T y. +If recovery ignores a coordinate of y, the corresponding column +of A U^T must be zero. This argument also applies to a recovery +routine that was not declared linear. + +Reduce T=A U^T to its m used columns and then reduce modulo p. +It has row rank r because U remains invertible. Its Gram matrix +is A A^T and has rank s. The row space W therefore has radical +R of dimension r-s. The ambient coordinate pairing is +nondegenerate, so R-perpendicular has dimension m-r+s. Since +W is contained in R-perpendicular, + +```text +r <= m-r+s, and hence m >= 2r-s. +``` + +This argument does not assume that the pairing on W is +nondegenerate. Its radical is the reason for the extra coordinates. + +Appending arbitrary borrowed inputs appends zero columns to A. +It changes neither rank. Orthogonality of the extended U still +makes every encoded y possible. Thus arbitrary borrowed inputs +cannot defeat this bound. A promised zero input is a different +hypothesis; it is not covered. + +The review reconstructs all 16 actual centre rows from the signed +mode blocks and the actual pair matrix. It obtains + +```text +V V* = diag(12 I8,8 I8), +rank_F3(V)=16. +``` + +The real form A has rank 32 modulo 3. Its Gram has rank 16. +The bound is therefore 48 real coordinates, or 24 complete +complex fields. These ranks were computed directly with exact +modular elimination, in addition to the block derivation. + +For Gaussian dyadic unitary codes, realification gives a real +dyadic orthogonal code. The same proof also permits arbitrary +real dyadic orthogonal mixing of real and imaginary components; +complex linearity is not required for that stronger statement. + +## Arrays and physical frames + +For N complex entries in each field, use the reader V tensor I_N. +The real ranks modulo 3 are 32N and 16N. This proves a bound of +48N real coordinates, or 24 arrays of N complex entries. The code +may mix ports, spatial entries, and owner indices. For arrays of +different sizes, the bound concerns total coordinate capacity. + +Let A be this real reader, and replace it by L A U. If U is dyadic +orthogonal and both L and L^-1 are dyadic, then + +```text +(L A U)(L A U)^T = L (A A^T) L^T. +``` + +Both relevant ranks modulo 3 are unchanged. The complex statement +requires a Gaussian dyadic unitary U and a Gaussian dyadic L whose +inverse is also Gaussian dyadic. Merely being invertible over +the rational numbers is insufficient: L=3I illustrates the +difference. This condition must be kept explicit in any use of +the frame extension. + +These are exact finite-dimensional statements. They do not bound +approximate recovery, odd-denominator codes, nonunitary codes, +native calls, or the complete recursive cost. + +## Independent reconstruction of the 24-coordinate code + +The large 48-port block is identical to the pinned 32-coordinate +code. The review does not infer that an unnormalized pair matrix +is unitary. It checks its inverse explicitly and verifies both +unitary products of the resulting full physical code. + +For each actual small clique, the review builds the stated eight +Haar rows independently. Their squared norms are +`8,8,4,4,2,2,2,2`. The factors `(1+i)/4`, `1/2`, and `(1+i)/2` +give unit rows with zero pairwise inner products. + +For v=(1,1,-1,0,-1,0,0,0), the matrix +`R=I-v v^T/2` is an orthogonal involution because v^T v=4. +It fixes the sum because v^T 1=0. After multiplication by R, +the output assignment `(0,1,5,3,2,7,6,4)` makes each of the +seven contrast rows omit its assigned input coordinate. + +This independently constructed matrix agrees entry by entry +with the saved physical matrix. The direct checks establish: + +* Both unitary product orders and the saved adjoint. +* The full decoder T=V C*, its exact support of 24 fields, and T C=V. +* All 88 ordinary identities `(C E)_R=C_R`. +* Every ordinary diagonal in the physical and native mode bases. +* Exactly eight nonzero code diagonals, all at selected small ports. +* Every mode transfer remaining inside its original vertex or clique. +* Gaussian dyadic coefficients throughout these matrices. + +The selected set has 16 physical large ports and one port from +each of the eight small cliques. The large reader supports overlap; +counting four physical coordinates per large row would double-count +their common selected set. + +The construction attains the coordinate bound. Its eight selected +diagonals still need the proposed selected FULL paths. It does not +give an all-hole zero-diagonal code. + +## Literal scalar words + +The review pulls every active real output covector backwards +through the literal component word. This differs from the +producer's forward sparse-row computation. It obtains the exact +real matrix of C or C* on all 224 active real coordinates. + +No instruction reads or writes any of the other 1,056 real +coordinates. This proves the full 1,280-column map with arbitrary +outside inputs. No zero field is assumed. + +A second forward computation checks every instruction prefix. +Each word has 2,418 instructions and costs 8,052 real scalar +primitives under the source tariff. The code has prefix +one-norm bound 16 and binary denominator height 3. The adjoint +has bounds 28 and 2. The saved adjoint word is exactly the +reverse sequence of inverse component operations. + +A deleted ADD is rejected separately in each direction. Both +normal and optimized runs give +`PASS_UNITARY_FOOTPRINT_AND_24_CODE_REVIEW` with identical receipts. +The commands and file digests are recorded in this review's freeze. + +## Scope of acceptance + +There is no material defect in the reviewed matrix, common-frame +word, or finite-field theorem. The array and frame extension is +accepted with the explicit inverse-in-the-dyadic-ring condition +stated above. + +The target-path removal census, replacement native service, +phases inside new native calls, source access at unequal hole +types, inverse-adjoint service, routed caller, helper host, and +full precision proof are outside this review. The native review +worker has those implementation obligations. Neither the +footprint bound nor a scalar code invoice pays them. + +The source bytes were preserved. AI assistance was used. No PR, +commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/check_review.py b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/check_review.py new file mode 100644 index 0000000000..761a52e713 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/check_review.py @@ -0,0 +1,323 @@ +"""Check the actual unitary code and the coordinate bound without producer code.""" + +import argparse +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +CAMPAIGN = HERE.parents[2] +SOURCE = CAMPAIGN / "lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020" +PINS = { + "root/UNITARY-FOOTPRINT-FREEZE-20261020.json": + "9ec2cb0f38210cf95246991f9637c036c7e5489cfc9ad78b7075213d9ca3ba75", + "root/UNITARY-CENTRE-FOOTPRINT-20261020.md": + "464628f0966138a9f95c34d26abeed214ab38720916fb1214820dd62e998f0a0", +} +LOCAL_PINS = { + "TWENTY-FOUR-FREEZE.json": "3fda436c0390fb8ef2ee72b4d9fe6ccbfc0ea994208f4d962bb9f43960af7a82", + "UNITARY-24.md": "420e5d4eb13c43bfbd41614c7a686db49e1091bf06ed26039f231323208461a6", + "twenty-four-v2-normal/UNITARY-24.json.gz": + "9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c", + "unitary-v2-normal/UNITARY-COMPLETION.json.gz": + "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428", + "signed-probe/METRIC-COMPLETION.json.gz": + "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e", +} +ZERO = (F(0), F(0)) +ONE = (F(1), F(0)) + + +def need(test, label): + if not test: + raise ValueError(label) + + +def plus(a, b): + return a[0] + b[0], a[1] + b[1] + + +def times(a, b): + return a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0] + + +def conjugate(a): + return a[0], -a[1] + + +def put(row, j, value): + result = plus(row.get(j, ZERO), value) + if result == ZERO: + row.pop(j, None) + else: + row[j] = result + + +def rows(raw, real=False): + return [{int(j): (F(v), F(0)) if real else tuple(map(F, v)) + for j, v in row.items()} for row in raw] + + +def eye(n): + return [{j: ONE} for j in range(n)] + + +def adjoint(a, columns): + out = [{} for _ in range(columns)] + for i, row in enumerate(a): + for j, x in row.items(): + out[j][i] = conjugate(x) + return out + + +def product(a, b): + out = [] + for row in a: + result = {} + for j, x in row.items(): + for k, y in b[j].items(): + put(result, k, times(x, y)) + out.append(result) + return out + + +def realify(a, columns): + out = [{} for _ in range(2 * len(a))] + for i, row in enumerate(a): + for j, (x, y) in row.items(): + for target, source, value in ( + (2*i, 2*j, x), (2*i, 2*j+1, -y), + (2*i+1, 2*j, y), (2*i+1, 2*j+1, x)): + if value: + out[target][source] = value + need(all(j < 2 * columns for row in out for j in row), "Real column range") + return out + + +def rank_mod_three(a, columns): + a = [[int(row.get(j, 0).numerator) * pow(int(row.get(j, F(0)).denominator), -1, 3) % 3 + for j in range(columns)] for row in a] + pivot = 0 + for j in range(columns): + found = next((k for k in range(pivot, len(a)) if a[k][j]), None) + if found is None: + continue + a[pivot], a[found] = a[found], a[pivot] + a[pivot] = [(x * pow(a[pivot][j], -1, 3)) % 3 for x in a[pivot]] + for k in range(pivot + 1, len(a)): + value = a[k][j] + if value: + a[k] = [(x - value*y) % 3 for x, y in zip(a[k], a[pivot])] + pivot += 1 + if pivot == len(a): + break + return pivot + + +def tariff(event): + op, _, _, raw = event + value = F(raw) + a, b = abs(value.numerator), value.denominator + need(b & (b - 1) == 0, "Dyadic component coefficient") + if op == "add": + return 3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1 + need(op == "scale" and a and a & (a - 1) == 0, "Binary component scale") + return abs(a.bit_length() - b.bit_length()) + int(value < 0) + + +def pullback(word): + """Propagate each output covector backwards through the literal word.""" + out = [] + for output in range(224): + row = {output: F(1)} + for op, target, source, raw in reversed(word): + coefficient = F(raw) + if target not in row: + continue + if op == "scale": + row[target] *= coefficient + else: + need(op == "add" and source != target, "A distinct ADD source") + value = row.get(source, F(0)) + coefficient * row[target] + if value: + row[source] = value + else: + row.pop(source, None) + out.append(row) + return out + + +def prefix_bounds(word): + a = [{j: F(1)} for j in range(224)] + norm, height = F(1), 0 + for op, target, source, raw in word: + coefficient = F(raw) + if op == "scale": + a[target] = {j: coefficient*x for j, x in a[target].items()} + else: + row = dict(a[target]) + for j, x in a[source].items(): + value = row.get(j, F(0)) + coefficient*x + if value: + row[j] = value + else: + row.pop(j, None) + a[target] = row + norm = max(norm, sum(map(abs, a[target].values()), F(0))) + height = max(height, max((x.denominator.bit_length()-1 for x in a[target].values()), default=0)) + return a, {"prefix_one_norm": str(norm), "binary_height": height} + + +def read_pinned(path, pin): + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Source digest: " + str(path)) + return raw + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + need(not args.out.exists(), "New output file") + for name, pin in PINS.items(): + read_pinned(CAMPAIGN / name, pin) + raw = {name: read_pinned(SOURCE / name, pin) for name, pin in LOCAL_PINS.items()} + source = json.loads(raw["twenty-four-v2-normal/UNITARY-24.json.gz"]) + old = json.loads(raw["unitary-v2-normal/UNITARY-COMPLETION.json.gz"]) + placement = json.loads(raw["signed-probe/METRIC-COMPLETION.json.gz"]) + c, ci = rows(source["code"]), rows(source["inverse_and_adjoint"]) + v, e = rows(source["original_centre_readers"]), rows(source["response"]) + h, hi = rows(placement["pair_code"], True), rows(placement["pair_code_inverse"], True) + need(product(h, hi) == product(hi, h) == eye(112), "Actual pair inverse") + need(ci == adjoint(c, 112), "Literal adjoint") + need(product(c, ci) == product(ci, c) == eye(112), "Both unitary products") + need(v == rows(old["original_centre_readers"]), "Unchanged actual readers") + need(e == rows(old["response"]), "Unchanged actual response") + + rebuilt_v, owner = [], {} + for index, block in enumerate(placement["mode_blocks"]): + ports = block["ports"] + for port in ports: + need(port not in owner, "Disjoint native mode blocks") + owner[port] = index + if block["kind"] == "large6": + local = [{p: (F(s), F(0)) for p, s in zip(ports, block["signs"])}] + rebuilt_v += product(local, h) + else: + rebuilt_v.append({p: ONE for p in ports}) + need(rebuilt_v == v, "Readers derived from actual block and pair geometry") + gram = product(v, adjoint(v, 112)) + desired = [{j: (F(12 if j < 8 else 8), F(0))} for j in range(16)] + need(gram == desired, "Actual reader Gram") + rv, rg = realify(v, 112), realify(gram, 16) + real_rank, real_gram_rank = rank_mod_three(rv, 224), rank_mod_three(rg, 32) + need((real_rank, real_gram_rank) == (32, 16), "Actual real modulo-three ranks") + need(rank_mod_three([{j: x for j, (x, _) in row.items()} for row in v], 112) == 16, + "Actual complex modulo-three row rank") + + rebuilt_c = rows(old["code"]) + reflection_vector = [1, 1, -1, 0, -1, 0, 0, 0] + reflection = [{j: (F(i == j)-F(reflection_vector[i]*reflection_vector[j], 2), F(0)) + for j in range(8) if F(i == j)-F(reflection_vector[i]*reflection_vector[j], 2)} + for i in range(8)] + need(product(reflection, reflection) == eye(8), "Small reflection involution") + need(product([{j: ONE for j in range(8)}], reflection) == [{j: ONE for j in range(8)}], + "Reflection fixes the centre") + haar = [[1,1,1,1,1,1,1,1], [1,1,1,1,-1,-1,-1,-1], + [1,1,-1,-1,0,0,0,0], [0,0,0,0,1,1,-1,-1], + [1,-1,0,0,0,0,0,0], [0,0,1,-1,0,0,0,0], + [0,0,0,0,1,-1,0,0], [0,0,0,0,0,0,1,-1]] + normalizers = [(F(1,4),F(1,4))]*2 + [(F(1,2),F(0))]*2 + [(F(1,2),F(1,2))]*4 + normalized = [{j: times((F(x), F(0)), normalizers[i]) for j, x in enumerate(row) if x} + for i, row in enumerate(haar)] + local = product(normalized, reflection) + assignment = [0,1,5,3,2,7,6,4] + small = [b for b in placement["mode_blocks"] if b["kind"] == "small8"] + small_ports = {p for block in small for p in block["ports"]} + selected = set(old["selected_full_ports"]) - small_ports + for block in small: + ports = block["ports"] + selected.add(ports[0]) + for row, target in zip(local, assignment): + rebuilt_c[ports[target]] = {ports[j]: x for j, x in row.items()} + need(rebuilt_c == c, "Independent Haar/reflection construction on actual ports") + need(selected == set(source["selected_full_ports"]) and len(selected) == 24, + "Actual selected coordinate set") + ordinary = set(range(112))-selected + need(ordinary == set(source["ordinary_ports"]) and len(ordinary) == 88, + "Actual ordinary coordinate set") + ce = product(c, e) + mode, mode_ce = product(product(h, c), hi), product(product(h, ce), hi) + need(ce == rows(source["coded_response"]), "Complete coded response") + need(mode == rows(source["mode_code"]) and mode_ce == rows(source["mode_coded_response"]), + "Actual mode conjugations") + need(all(ce[p] == c[p] for p in ordinary), "All88 ordinary rows") + for matrix in (c, ce, mode, mode_ce): + need(all(p not in matrix[p] for p in ordinary), "Every ordinary diagonal") + need(sum(p in c[p] for p in range(112)) == 8, "Eight selected diagonal exceptions") + need(all(owner[i] == owner[j] for matrix in (mode, mode_ce) + for i, row in enumerate(matrix) for j in row), "Native block support") + decoder = product(v, ci) + need(decoder == rows(source["centre_decoder"]), "Exact saved decoder") + need(set().union(*(set(row) for row in decoder)) == selected, "Exact24 coordinate support") + need(product(decoder, c) == v, "Complete centre recovery") + need(all(x.denominator & (x.denominator-1) == 0 + for matrix in (c, ci, ce, decoder) for row in matrix for z in row.values() for x in z), + "Every coefficient is Gaussian dyadic") + + reports = {} + words = source["component_words"] + for name, matrix in (("code", c), ("inverse_and_adjoint", ci)): + word = words[name] + need(all(0 <= event[1] < 224 and + (event[0] == "scale" or 0 <= event[2] < 224) for event in word), + "All528 outside complex fields are untouched") + expected = realify(matrix, 112) + backward = pullback(word) + need(backward == expected, "Every real output covector") + forward, bounds = prefix_bounds(word) + need(forward == backward, "Distinct forward prefix computation") + cost = sum(map(tariff, word)) + need(cost == 8052 and len(word) == 2418, "Full real scalar invoice") + mutation = list(word) + del mutation[next(i for i, event in enumerate(mutation) if event[0] == "add")] + need(pullback(mutation) != expected, "Deleted component ADD rejected") + reports[name] = {"instructions": len(word), "scalar": cost, **bounds} + reverse = [[op, target, source_field, str(-F(value) if op == "add" else 1/F(value))] + for op, target, source_field, value in reversed(words["code"])] + need(words["inverse_and_adjoint"] == reverse, "Literal inverse instruction order") + need(reports["code"]["prefix_one_norm"] == "16" and reports["code"]["binary_height"] == 3, + "Code prefix bounds") + need(reports["inverse_and_adjoint"]["prefix_one_norm"] == "28" and + reports["inverse_and_adjoint"]["binary_height"] == 2, "Adjoint prefix bounds") + for name, pin in PINS.items(): + read_pinned(CAMPAIGN / name, pin) + for name, pin in LOCAL_PINS.items(): + read_pinned(SOURCE / name, pin) + receipt = { + "status": "PASS_UNITARY_FOOTPRINT_AND_24_CODE_REVIEW", + "root_source_pins": PINS, "producer_source_pins": LOCAL_PINS, + "imports_producer_or_root_checker": False, + "reader_Gram": ["12"]*8+["8"]*8, + "real_mod_three_row_rank": real_rank, "real_mod_three_Gram_rank": real_gram_rank, + "lower_bound_real_coordinates": 2*real_rank-real_gram_rank, + "lower_bound_complex_fields": (2*real_rank-real_gram_rank)//2, + "attained_selected_fields": len(selected), "ordinary_equal_rows": len(ordinary), + "arbitrary_real_input_columns": 1280, "unchanged_outside_complex_fields": 528, + "component_words": reports, "new_owned_fields": 0, + "native_target_path_census_reviewed": False, + "native_phases_or_complete_service_reviewed": False, + "recursive_caller_admitted": False, + } + args.out.parent.mkdir(parents=True, exist_ok=True) + args.out.write_text(json.dumps(receipt, sort_keys=True, indent=2)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex b/research/centre-metric-encoders/frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex new file mode 100644 index 0000000000..4a9037137c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex @@ -0,0 +1,137 @@ +\subsection{All-disjoint retained centers} +Use two factors $h=24$. For triple inputs write $G=\sum_TX_T$, +$T_i=\sum_{T\ni i}X_T$, and retain all $A_i=G-T_i$. +Each input triple avoids exactly 21 points, so +\[ + \sum_{i=1}^{24}A_i=21G,\qquad G=\frac1{21}\sum_i A_i. +\] +For a target triple $S$ the central correction is +\[ + G-\frac12\sum_{i\in S}A_i + =\frac{\sum_{i\in S}T_i-G}{2}. +\] +An input triple meeting $S$ in $j$ points has central coefficient +$(j-1)/2$. Adding half the disjoint sum and subtracting half the +intersection-two sum leaves coefficient one exactly when $j=3$. +The scalar source-to-scatter transfer is therefore the identity. +The transparent old-value subtraction and new-value addition use this +identity only on fresh contributions and restore arbitrary old values. + +The base-two paired exclusion and aligned pair-star producer retains +nested binary labels: common-pair supports have their orthonormal triple +span, other ordinary sums have their coordinate cover. Each retained +$A_i$ has the nondegenerate coordinate hyperplane excluding $i$, +of dimension 23. Hence all copied-center arguments and general +nondegenerate binary residuals of the preceding proof apply. The +selected local counts are +\[ + v=2024,\quad c_h=45764,\quad q_h=8120,\quad + |\mathcal M|=8966,\quad R=44918,\quad\ell=552. +\] +The old internal histogram, starting at rank zero, is +\begin{small}\begin{align*} +[&8930,49042,30844,15972,11883,8272,6399,4356,6682,2263,\\ + &5109,1808,5317,1733,5391,1757,4908,3290,6233,4363,\\ + &4056,264,564,24,24]. +\end{align*}\end{small} +It has rank mass $24R+2\ell$. Replace 24 rank-24 original transitions +by 24 rank-one transitions; all rank-23 copied transforms remain. +The new mass is $24R+\ell$. + +\subsection{Physical endpoints and strict complex moment} +The copied-center two-stage complex contract in +\path{notes/copied-centers-complex.tex} is unchanged by the scalar +center decoding. For the tensor triple line $U$, let +$T=C_U$, $F=C_I$, $E=C_{U^\perp}=FT^{-1}$. +The two data outputs are $A=-Fy$ and $B=FT^{-2}x+Ey$. +Add $T^{-1}$ applied to a copy of $A$ into $B$, paying one rank-one +child per data pair. The inherited input/output $Z$ phases and +$i^{9f}$ scalar normalize $FT^{-2}$ to $F$; sign and bank corrections +complete the exact tensor $C$. Auxiliary source/sink operators remain +$C_{D_0}$ and $FC_{D_0}$ in the second stage. Every original role +therefore returns the exact selected-axis tensor operation on arbitrary +inputs. This algebraic statement holds over $\mathbb Q(i)$ as well as +over Gaussian dyadics. + +With $m_c=576$, $N_c=v^2=4096576$, $B_c=vR=90914032$, put +\[ + W_c=2N_c+2B_c=190021216,\quad L_c=2v\ell=2234496, +\] +\[ + s_c=W_cm_c-N_c+L_c=109450358336,\qquad N_c-L_c=1862080. +\] +The complete list is $2B_c$ width-552 auxiliary exteriors, +$2N_c$ width-529 data macros, $2vH'_r$ width-$r$ internal children, +$4N_c$ width-23 data fronts, and $N_c$ width-one endpoint copies. +These disjoint classes include both kinds of paid copies and sum to +$s_c$. All binary residuals, including alternating forms, use the retained +one-child Gauss normal form with paid bit adapters and unit phases. +At $a_c=1949/25000000$ the exact rational enclosure gives +\[ + \sum_r\frac{n_r}{W_c}(r/m_c)^{1-a_c} + <1-1.3338373969\times10^{-10}. +\] + +\subsection{One exact odd-denominator grid} +The only new odd divisor is 21. Let $d$ bound the root axis count, +$D$ bound its maximum complex recursion depth, and $G_0$ bound the +number of grouped scalar operations per node. Choose +\[ + K=G_0(D+1),\qquad \text{common grid }2^{-P}21^{-K}. +\] +Root inputs and arbitrary dirty auxiliaries start Gaussian dyadic. +Multiply their integer numerators by $21^K$ once at the outer boundary. +Every local coefficient contains at most one factor 21 in its denominator, +so a local finite program adds at most $G_0$ to the odd-denominator +exponent. A completed $u$-axis child has Gaussian-dyadic coefficients +and therefore preserves its input's existing odd-denominator exponent; +it adds no new odd factor. Only the active chain of unfinished calls +can accumulate new factors. Its length is at most $D+1$, proving that +all intermediates lie on the common grid and every local division by +21 is an exact integer division of its encoded numerator. + +This divisibility claim uses the root dyadic-input invariant, not an +assumption about arbitrary numerators on the finest grid. Internal values +may have odd denominators. They are neither rounded nor re-encoded when +a child returns. At the completed outer return the operator is the exact +Gaussian-dyadic tensor on root dyadic inputs, so the final numerators +are divisible by $21^K$; exact unscaling restores dyadic encoding. + +Since the largest child is $552<576$, $D=O(\log d)$ and +$K=O(\log d)$ with fixed constants. Constant-divisor long division +is linear in numerator length. Initial and final scaling by $K$ +successive constant multiplications/divisions cost $O(V\log d)$ and +occur only at the outer boundary. The extra numerator length is +$O(\log d)$, preserving the retained $O(p)$ word bound. This overhead +is subordinate to the positive-power complex layer bound. + +For explicit semantic constants use +\[ + g_h=4(c_h+v)+10v+4hv+4h^2+8h+8=408200, +\] +\[ + G_0=N_c+2v(g_h+2h)=1656684480, +\] +where endpoint additions and copied-center scalar work are included. +The complete child contributes at most $u$ binary denominator bits +and row-norm factor $2^u$, with no additional odd exponent. A local +21-division contributes fewer than five denominator-height bits, +covered by the fixed scalar charge. Set +\[ +\begin{aligned} + E_0&=64(W_c+m_c+G_0+1)^3=403063477262941121443761178688,\\ + \mathcal E&=2G_0W_c^2+8s_c+4W_c+4+32m_c\\ + &=119639333593035096270287748> i & 1), + key=lambda i: (adjacent[i] & possible).bit_count(), default=0) + todo = possible & ~adjacent[pivot] + while todo: + bit = todo & -todo + i = bit.bit_length() - 1 + todo -= bit + visit(chosen | bit, possible & adjacent[i], excluded & adjacent[i]) + possible -= bit + excluded |= bit + + visit(0, (1 << n) - 1, 0) + return [[ports[i] for i in range(n) if mask >> i & 1] for mask in sorted(result)] + + +def encoded(rows): + return [{str(p): str(c) for p, c in sorted(row.items())} for row in rows] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = read(next(name for name in PINS if "CYCLIC" in name)) + matching = read(next(name for name in PINS if "MATCHED" in name)) + selected, small = matching["selected_ports"], matching["small_ports"] + selected_set = set(selected) + q = cyclic["ports"] + h = identity(112) + codes = [] + for pair in cyclic["pair_codes"]: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + h[a], h[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)} + if aa != 1: + codes.append(["scale", a, None, str(aa)]) + codes.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + hi = transpose(h, 112) + for p in cyclic["affected_ports"]: + hi[p] = {k: v / 2 for k, v in hi[p].items()} + need(product(h, hi) == identity(112), "Actual pair inverse") + mode = identity(112) + mode_inverse = identity(112) + mode_u, mode_v = [{} for _ in range(112)], [] + mode_word, assignments = [], [] + for vertex, group in enumerate(cyclic["cyclic_carriers"]): + chosen = [p for p in group if selected_set.intersection(map(int, cyclic["mode_rows"][str(p)]))] + rest = [p for p in group if p not in chosen] + need(len(chosen) == 2 and len(rest) == 4, "Two selected modes per vertex") + order = chosen + rest + signs = [1, 1 if vertex % 2 == 0 else -1, 1, 1, 1, 1] + e = [{j: F((i == j) - 1) for j in range(4) if i != j} | {4: F(1)} + for i in range(4)] + e += [{5: F(1)}, {0: F(-2), 1: F(-2), 2: F(-2), 3: F(-2), 4: F(3)}] + swap = [0, 1, 2, 3, 5, 4] + ei = [{swap[j]: c for j, c in e[swap[i]].items()} for i in range(6)] + need(product(e, ei) == product(ei, e) == identity(6), "Six-mode reciprocal pair") + for i, p in enumerate(order): + mode[p] = {order[j]: c * signs[i] * signs[j] for j, c in e[i].items()} + mode_inverse[p] = {order[j]: c * signs[i] * signs[j] for j, c in ei[i].items()} + offset = len(mode_v) + local_u = [[1, 0]] * 4 + [[0, 1], [2, -1]] + local_v = [[-1, -1, -1, -1, 1, 0], [0, 0, 0, 0, -1, 1]] + for i, p in enumerate(order): + mode_u[p].update({offset + j: F(value * signs[i]) + for j, value in enumerate(local_u[i]) if value}) + mode_v.extend([{order[j]: F(value * signs[j]) for j, value in enumerate(row) if value} + for row in local_v]) + a, b, c = order[:4], order[4], order[5] + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(-signs[i])]) + for i, p in enumerate(a): + mode_word.append(["add", p, b, str(signs[i])]) + mode_word.append(["scale", b, None, "-1"]) + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(signs[i])]) + mode_word.extend([["add", b, c, "1"], ["add", c, b, "-1"], + ["add", b, c, "1"], ["scale", c, None, "-1"]]) + assignments.append({"vertex": vertex, "ordered_carriers_a_b_c": order, "signs": signs}) + need(replay(mode_word)[0] == mode, "In-place rank-two mode code") + response, response_inverse = product(hi, product(mode, h)), product(hi, product(mode_inverse, h)) + u, v = product(hi, mode_u), product(mode_v, h) + small_word = [] + need(sorted(p for group in CLIQUES for p in group) == sorted(small), "Exact disjoint64 cover") + for group in CLIQUES: + k = len(group) + need(k in (3, 5), "Dyadic clique size") + need(all((q[p] & q[r]).bit_count() % 2 == int(p == r) + for p in group for r in group), "Actual orthonormal clique") + for p in group: + response[p] = {r: F(-1) for r in group if r != p} + response_inverse[p] = {r: F(int(p == r)) - F(1, k - 1) for r in group} + u[p] = {len(v): F(-1)} + v.append({p: F(1) for p in group}) + a, rest = group[0], group[1:] + small_word.extend([["add", a, p, "1"] for p in rest]) + small_word.extend([["add", p, a, "-1"] for p in rest]) + small_word.append(["scale", a, None, str(1 - k)]) + small_word.extend([["add", a, p, "-1"] for p in rest]) + word = codes + mode_word + inverse_word(codes) + small_word + common_words = {"E": word, "inverse_E": inverse_word(word), + "transpose_E": transpose_word(word), + "inverse_transpose_E": transpose_word(inverse_word(word))} + expected = {"E": response, "inverse_E": response_inverse, + "transpose_E": transpose(response, 112), + "inverse_transpose_E": transpose(response_inverse, 112)} + word_receipts = {} + for name, gates in common_words.items(): + actual, maximum = replay(gates) + need(actual == expected[name], "Full112 scalar code " + name) + need(replay(gates + inverse_word(gates))[0] == identity(112), "Both code orders " + name) + word_receipts[name] = {"real_scalar_primitives": price(gates), + "prefix_row_l1_bound": str(maximum), "owned_fields": 0} + need(product(response, response_inverse) == product(response_inverse, response) == identity(112), + "Full112 reciprocal products") + correction = [dict(row) for row in response] + for i in range(112): + add(correction[i], {i: F(-1)}) + need(product(u, v) == correction and rank(u, 30) == rank(v, 112) == 30, + "Exact full rank30 correction factor") + l = restrict(response, selected) + li = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_inverse"]] + old_l = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_block"]] + need(l == restrict(response_inverse, selected) == old_l, "Both selected blocks retain L") + need(product(l, li) == identity(8), "Selected inverse") + ordinary = sorted(set(range(112)) - selected_set) + p = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(selected) + if response_inverse[r].get(s)} for r in ordinary] + n = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(ordinary) + if response_inverse[r].get(s)} for r in selected] + ordinary_inverse = restrict(response_inverse, ordinary) + for row, update in zip(ordinary_inverse, product(product(p, li), n)): + add(row, update, -1) + ordinary_block = restrict(response, ordinary) + need(product(ordinary_block, ordinary_inverse) == product(ordinary_inverse, ordinary_block) + == identity(104), "Both ordinary104 inverse orders") + need(all(not c.denominator & (c.denominator - 1) + for row in ordinary_inverse for c in row.values()), "Dyadic ordinary inverse") + maxima = maximal_cliques(small, q) + histogram = Counter(map(len, maxima)) + need(histogram == {4: 896, 8: 64}, "Exhaustive maximal clique census") + # A separate exhaustive extension pass checks the absence of a ninth vertex. + need(all(not any(p not in clique and all(not (q[p] & q[r]).bit_count() % 2 for r in clique) + for p in small) for clique in maxima), "Each reported clique is maximal") + receipt = { + "status": "PASS_LOW_DISPLACEMENT_RESPONSE", + "source_pins": PINS, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "correction_rank_large48": 16, "correction_rank_small64": 14, "correction_rank_full112": 30, + "selected_determinant": str(determinant(l)), + "full_determinant": str(determinant(response)), + "ordinary104_determinant": str(determinant(ordinary_block)), + "small_clique_sizes": dict(sorted(Counter(map(len, CLIQUES)).items())), + "all_maximal_small_clique_sizes": dict(sorted(histogram.items())), + "common_frame_scalar_codes": word_receipts, + "scope": "Exact port matrices, principal units, scalar codes and geometry. Native phases and terminal access are separate.", + } + payload = { + "source_pins": PINS, "ports": q, "selected_ports": selected, "ordinary_ports": ordinary, + "large_ports": cyclic["affected_ports"], "small_ports": small, + "vertex_assignments": assignments, "mode_response": encoded(mode), + "mode_inverse": encoded(mode_inverse), "small_cliques": CLIQUES, + "response": encoded(response), "response_inverse": encoded(response_inverse), + "correction_U": encoded(u), "correction_V": encoded(v), + "selected_block": encoded(l), "selected_inverse": encoded(li), + "ordinary_inverse": encoded(ordinary_inverse), "common_frame_words": common_words, + "maximal_small_cliques": maxima, + } + raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode() + (args.out / "RESPONSE-PROGRAM.json").write_bytes(raw) + receipt["payload_sha256"] = sha256(raw).hexdigest() + (args.out / "RESPONSE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py new file mode 100644 index 0000000000..532c8709eb --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py @@ -0,0 +1,279 @@ +#!/usr/bin/env python3 +"""Emit and check the native rank-thirty response on the actual ports.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + ("plain", "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"), + "new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json": + ("plain", "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c"), + "new-core-transfer-20261017/low-displacement-20261020/check_response.py": + ("plain", "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"), + "new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz": + ("decompressed", "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa"), + "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py": + ("plain", "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962"), + "interface-proof/verify_native_lift.py": + ("plain", "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b"), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(relative): + mode, pin = PINS[relative] + raw = (LANES / relative).read_bytes() + if mode == "decompressed": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Source pin " + relative) + return raw + + +def load_module(name, relative): + read(relative) + spec = importlib.util.spec_from_file_location(name, LANES / relative) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +r = load_module("low_response", "new-core-transfer-20261017/low-displacement-20261020/check_response.py") +compiler = load_module("low_compiler", "new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py") +phase = load_module("low_phase", "interface-proof/verify_native_lift.py") + + +def basis(vectors): + rows = list(dict.fromkeys(vectors)) + count = 0 + for bit in range(8, -1, -1): + found = next((i for i in range(count, len(rows)) if rows[i] >> bit & 1), None) + if found is None: + continue + rows[count], rows[found] = rows[found], rows[count] + for i in range(len(rows)): + if i != count and rows[i] >> bit & 1: + rows[i] ^= rows[count] + count += 1 + return tuple(rows[:count]) + + +def rows(value): + return [{int(p): F(c) for p, c in row.items()} for row in value] + + +def verify_word(word, response, direction): + current = list(word["start"]) + state = [{i: F(1)} for i in range(len(current))] + maximum = F(1) + scalar_word = [] + for event in word["events"]: + if event[0] == "native": + _, field, old, new, rank, key = event + need(current[field] == old, "Literal native entry frame") + need(len(basis(word["frames"][old] + word["frames"][new])) == len(word["frames"][new]), + "Literal nested native edge") + need(rank == len(word["frames"][new]) - len(word["frames"][old]) + == word["native_recipes"][key]["rank"], "Literal native rank") + current[field] = new + else: + need(event[0] == "scalar", "Literal event grammar") + gate, frame = event[1:] + op, target, origin, coefficient = gate + c = F(coefficient) + need(current[target] == frame, "Literal scalar target frame") + if op == "scale": + state[target] = {p: c * v for p, v in state[target].items() if c * v} + else: + need(op == "add" and target != origin and current[origin] == frame, + "Literal scalar source frame") + r.add(state[target], state[origin], c) + maximum = max(maximum, sum(abs(v) for v in state[target].values())) + scalar_word.append(gate) + expected = [{i: F(1)} for i in range(len(current))] + for target, row in enumerate(response): + if direction == "forward": + r.add(expected[112 + target], row) + else: + for origin, coefficient in row.items(): + r.add(expected[origin], {112 + target: -coefficient}) + need(state == expected and current == word["final"], "All640 columns and final frames") + profile = Counter(event[4] for event in word["events"] if event[0] == "native") + return {"all_input_columns": len(current), "untouched_arbitrary_fields": len(current) - 224, + "owned_fields": 0, "private_fields": 0, "native_profile": dict(sorted(profile.items())), + "native_mass": sum(k * v for k, v in profile.items()), "native_children": sum(profile.values()), + "real_scalar_primitives": r.price(scalar_word), "prefix_row_l1_bound": str(maximum), + "native_side_map_bound": 2 * sum(profile.values()), "endpoint_maps": 224} + + +def make_word(cyclic, model, direction): + frames = deepcopy(cyclic["frames"]) + indices = {tuple(frame): i for i, frame in enumerate(frames)} + small = set(model["small_ports"]) + current = list(cyclic["start"]) + events = [] + mode = rows(model["mode_response"]) + by_parameter = {record["id"]: record for record in cyclic["parameters"]} + transfer_records = [] + for event in cyclic["programs"][direction]: + kind = event[0] + if kind == "native": + _, field, old, new, rank = event + if field % 112 in small: + need(field < 224, "Only data fields receive native progress") + continue + need(current[field] == old, "Pinned cyclic native frame") + current[field] = new + events.append(["native", field, old, new, rank, str(old) + ":" + str(new)]) + elif kind == "parameter_add": + _, target, origin, parameter, sign, frame = event + record = by_parameter[parameter] + carriers = cyclic["cyclic_carriers"][record["vertex"]] + c = sign * mode[carriers[record["row"]]].get(carriers[record["column"]], F(0)) + if c: + transfer_records.append({"part": "large48", "event": len(events), + "coefficient": str(c), "parameter": parameter}) + events.append(["scalar", ["add", target, origin, str(c)], frame]) + else: + need(kind in ("add", "scale"), "Pinned cyclic scalar grammar") + _, target, origin, coefficient, frame = event + events.append(["scalar", [kind, target, origin, coefficient], frame]) + + def frame(vectors): + vectors = basis(vectors) + if vectors not in indices: + indices[vectors] = len(frames) + frames.append(list(vectors)) + return indices[vectors] + + def native(field, new): + old = current[field] + if old == new: + return + need(len(basis(frames[old] + frames[new])) == len(frames[new]), "Clique nested edge") + events.append(["native", field, old, new, len(frames[new]) - len(frames[old]), + str(old) + ":" + str(new)]) + current[field] = new + + q = cyclic["ports"] + for group in model["small_cliques"]: + k = len(group) + for depth in range(1, k): + for i, p in enumerate(group): + native(p, frame(q[group[(i + j) % k]] for j in range(depth))) + native(112 + p, frame(q[group[(i - j) % k]] for j in range(1, depth + 1))) + for i, p in enumerate(group): + target_port = group[(i + depth) % k] + need(current[p] == current[112 + target_port], "Every clique transfer has equal frames") + target, origin, coefficient = ((112 + target_port, p, "-1") if direction == "forward" + else (p, 112 + target_port, "1")) + transfer_records.append({"part": "small64", "event": len(events), + "source_port": p, "target_port": target_port, + "coefficient": coefficient}) + events.append(["scalar", ["add", target, origin, coefficient], current[p]]) + for p in group: + native(p, cyclic["final"][p]) + native(112 + p, cyclic["final"][112 + p]) + need(current == cyclic["final"], "Full native frame completion") + return {"frames": frames, "start": cyclic["start"], "final": cyclic["final"], + "events": events, "transfer_records": transfer_records} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = json.loads(read("independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json")) + model = json.loads(read("new-core-transfer-20261017/low-displacement-20261020/run-normal/RESPONSE-PROGRAM.json")) + core = json.loads(read("new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz")) + for provider, data in core["providers"].items(): + need(data["canonical"]["ports"] == cyclic["ports"], "Pinned provider directions " + provider) + need(len(data["canonical"]["start"]) == 632, "Pinned live-field count " + provider) + words = {direction: make_word(cyclic, model, direction) for direction in ("forward", "backward")} + need(words["forward"]["frames"] == words["backward"]["frames"], "Both directions use the same actual frames") + frames = words["forward"]["frames"] + edge_pairs = sorted({(event[2], event[3]) for word in words.values() + for event in word["events"] if event[0] == "native"}) + recipes = {} + for i, (old, new) in enumerate(edge_pairs): + operation = compiler.canonical_frame(9, tuple(frames[old])).adjoint().then( + compiler.canonical_frame(9, tuple(frames[new]))) + record, _ = compiler.lower_child(operation) + need(record["rank"] == len(frames[new]) - len(frames[old]), "Fresh native rank") + phase.equal(phase.recipe(record), phase.adjoint(phase.frame(frames[old], 9)) + + phase.frame(frames[new], 9), "Fresh native phase " + str((old, new))) + recipes[str(old) + ":" + str(new)] = record + if (i + 1) % 100 == 0: + print("Native phases", i + 1, "/", len(edge_pairs), flush=True) + endpoints = [] + for p, q in enumerate(cyclic["ports"]): + for role in ("source", "target"): + conventional = (compiler.cgate(9, q) if role == "source" + else compiler.cgate(9, q, -1).then(compiler.fourier(9))) + circuit = (("C", q, 1),) if role == "source" else (("C", q, -1),) + phase.fourier(9) + frame = cyclic["start"][p] if role == "source" else cyclic["final"][112 + p] + operation = conventional.adjoint().then(compiler.canonical_frame(9, tuple(frames[frame]))) + record, _ = compiler.lower_child(operation) + need(record["rank"] == 0, "Endpoint adapter is monomial") + phase.equal(phase.recipe(record), phase.adjoint(circuit) + phase.frame(frames[frame], 9), + "Fresh conventional endpoint " + str((role, p))) + endpoints.append({"port": p, "role": role, "frame": frame, **record}) + reports = {} + for direction, word in words.items(): + word["native_recipes"] = recipes + word["endpoint_adapters"] = endpoints + reports[direction] = verify_word(word, rows(model["response"]), direction) + need(reports["forward"]["native_profile"] == {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}, + "Complete profile") + need(reports["forward"]["native_mass"] == 1792 and reports["forward"]["real_scalar_primitives"] == 5288, + "Complete local invoice") + # Deletion of one nonzero transfer must change the complete content map. + bad = deepcopy(words["forward"]) + del bad["events"][bad["transfer_records"][0]["event"]] + try: + verify_word(bad, rows(model["response"]), "forward") + except ValueError: + pass + else: + raise ValueError("The missing transfer control was accepted") + payload = {"schema": "low-displacement-native-v1", "source_pins": PINS, + "response": model["response"], "common_frame_words": model["common_frame_words"], + "selected_ports": model["selected_ports"], "small_cliques": model["small_cliques"], + "providers": {provider: words for provider in core["providers"]}} + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for provider, directions in saved["providers"].items(): + for direction, word in directions.items(): + need(verify_word(word, rows(saved["response"]), direction) == reports[direction], + "Serialized provider replay " + provider + " " + direction) + (args.out / "NATIVE-PROGRAM.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = {"status": "PASS_LOW_DISPLACEMENT_NATIVE", "source_pins": PINS, + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "fresh_native_phase_checks": len(recipes), "fresh_endpoint_phase_checks": len(endpoints), + "reports": reports, "same_geometry_both_providers_checked": True, + "negative_control": "one nonzero transfer omitted and rejected", + "scope": "Complete local data shears and exact phases. Helpers are unchanged; their progress, recursive hosting, routed codes and terminal remain open."} + (args.out / "NATIVE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..10606e5e975b74a86921422158d1967b7ba22069 GIT binary patch literal 142430 zcmYIu18`-{^LCt#ZF_HQ+qP}nwr$(l*tRz|H@34IWAoj8fAz2L)~QoC^r6 z(>+5J^9|(R5A5rz*RI}_!Hat|w*VBH5Lcq)4aR-6VRz5IBXo)w{3eie4CF?;&WIyEF5Nk<@R?v zx}2ZN9HE|gDy-bx;@n%u&dm8e3(8%x25CWe&xWm?c8(h 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Read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md before any future PR description.", + "schema": "unitary-24-coordinate-freeze-v1", + "scope": "Actual24-coordinate Gaussian dyadic unitary code and scalar implementation. Native path isolation is checked; full native service and routed caller remain separate.", + "status": "PRODUCER_FROZEN_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-24.md b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-24.md new file mode 100644 index 0000000000..df8b951e6f --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-24.md @@ -0,0 +1,153 @@ +# A unitary centre code with 24 output coordinates + +The actual sixteen centre readers can be recovered from 24 output +coordinates of a Gaussian dyadic unitary code C on 112 ports. +The other 88 rows of C E equal the same rows of C. Each of these +88 rows has zero diagonal in the actual native mode basis. + +The code and its adjoint each have a complete scalar word. Each word +costs 8,052 real scalar primitives and uses no extra field or odd +division. Both words pass all 1,280 real input columns. These columns +represent 640 arbitrary complex fields; the 528 fields outside the +code remain unchanged. + +This packet proves the code, its scalar words, and its native support. +It also checks that the 24 selected target paths can be removed from +each pinned forward provider without a retained read of a removed +target. A complete replacement native word and a routed caller are +separate constructions. + +## The eight-port change + +Keep the large six-mode codes from the pinned 32-coordinate packet. +They use sixteen selected physical outputs and preserve the actual +physical pair closure. Change only the eight disjoint small blocks. + +On one small block use the unnormalized Haar rows + +```text +h0 = (1,1,1,1,1,1,1,1) +h1 = (1,1,1,1,-1,-1,-1,-1) +h2 = (1,1,-1,-1,0,0,0,0) +h3 = (0,0,0,0,1,1,-1,-1) +h4 = (1,-1,0,0,0,0,0,0) +h5 = (0,0,1,-1,0,0,0,0) +h6 = (0,0,0,0,1,-1,0,0) +h7 = (0,0,0,0,0,0,1,-1). +``` + +Normalize rows 0 and 1 by beta=(1+i)/4, rows 2 and 3 by 1/2, +and rows 4 through 7 by alpha=(1+i)/2. The normalized rows are +orthonormal. + +Put v=(1,1,-1,0,-1,0,0,0) and R=I-v v^T/2. Since v^T v=4, +R is a real dyadic orthogonal involution. Since v^T 1=0, +R fixes the centre reader. Apply R to the input of the Haar code. + +Assign Haar rows 0 through 7 to output positions + +```text +(0,1,5,3,2,7,6,4). +``` + +Each noncentre row now omits its assigned input coordinate. Thus +its diagonal entry is zero. The first row is still beta times +the all-one reader. The complete block code is unitary, and + +```text +1^T x = (2-2i) out_0. +``` + +Only one output field is needed for this small-block centre. +The field contains a normalized centre; the other seven fields +retain the independent contrast information. + +## The actual 112-port code + +Use the stored order of each pinned small clique. Its first port +is the one selected output. The large part and its actual pair +code remain as in the 32-coordinate packet. No abstract new port +placement is used. + +The exact full matrices satisfy + +```text +C* C = C C* = I, +C^-* = C, +(C E)_R88 = C_R88. +``` + +Let V contain the sixteen original centre readers. The stored +decoder is T=V C*. Every row of T uses only the selected 24 +coordinates, and T C=V. The eight large readers use four physical +coordinates each. The eight small readers use one each. The large +supports overlap in their two complete physical pair matchings; +their union has sixteen ports. + +The code has eight nonzero diagonal entries, all at the selected +small ports. All 88 ordinary diagonals vanish for both C and C E +in both the native mode basis and the physical basis. Every mode +entry stays in an original six-mode vertex or small clique. + +This support permits an ordinary-row response C_R88 in the existing +off-diagonal grammar. It does not permit an all-hole response C: +the eight selected small diagonals are real exceptions. + +## Literal scalar words and target paths + +The program copies the closed large-port part of the frozen +32-coordinate component word. On each small block it then applies +the real reflection, the paid Haar row word with its stated output +assignment, and the explicit complex normalizations. + +Every row exchange in the real factor word is paid. The complex +normalizations use only real component ADDs and signed binary +scales. The factor beta uses the alpha word followed by a binary +half scale on each component. No complex multiply primitive is +assumed. + +The code and its inverse each contain 2,418 component instructions +and cost 8,052 real scalar primitives. The exact local +real-component row one-norm reaches 16 for C and 28 for C*. +The additional binary denominator heights are three and two, +respectively. These are instruction-boundary bounds; they do not +include a recursive child or rounding error. + +For each actual forward provider, remove every event whose target +is a selected Y field. This removes 380 events, including 192 +rank-one native calls. No retained event reads a removed selected +Y field. This is an exact path-isolation check, not a complete +replacement service. A new service must still add the selected +FULL progress, retune the ordinary scalar transfers, apply the +source code at a common FULL cut, and verify its complete endpoint. + +## Validation and scope + +The checker verifies both unitary orders, the complete centre +decoder, all ordinary row and diagonal identities, Gaussian dyadic +coefficients, native block support, and both provider path censuses. +Both scalar words pass all 1,280 real columns. A missing component +ADD is rejected in each direction. Their full real-component +inverse composition also passes. + +Run into new directories: + +```text +python3 check_twenty_four.py --out +python3 -O check_twenty_four.py --out +``` + +Normal and optimized payloads and receipts are byte-identical. +Independent review is separate. This packet does not prove a +complete supplier, recursive hosting, or a final cost improvement. + +The root lane proposed the 24-coordinate lower-bound target and +the earlier positive unitary normalization. This lane found the +small dyadic reflection and output assignment, bound the actual +ports, and emitted the paid scalar words. The original native and +controller packets supply the centre readers and transfer supports. +AI assistance was used throughout. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-COMPLETION.md b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-COMPLETION.md new file mode 100644 index 0000000000..8fbf7836f6 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-COMPLETION.md @@ -0,0 +1,227 @@ +# A unitary completion of the actual centre readers + +The actual rank-sixteen centre readers admit a Gaussian dyadic unitary +completion C on all 112 ports. Both C and C* have zero diagonal in the +actual native mode basis. They also have zero diagonal in the physical +port basis. + +All sixteen original centre readers can be recovered from a fixed set +of 32 output coordinates of C. Each large reader uses four of these +physical output coordinates. Each small reader uses two. No ordinary +output coordinate is needed for this recovery. + +The complete scalar code and its inverse each cost 5,460 real scalar +primitives. They use no extra field. Both pass all 1,280 independent real +input columns, which represent 640 arbitrary complex fields. The 528 +fields outside the code remain unchanged. + +This packet proves a code, its scalar implementation, its centre +information, and its native support conditions. It does not emit a +changed native service or prove a routed caller. + +## The actual basis and reader blocks + +The pinned native response has eight six-mode blocks and eight +eight-port blocks. In each block its response is + +```text +E_block = I - d d^T, +``` + +where each entry of d is a sign. The eight-port blocks have d=1. +The exact physical pair code H acts on the 48 large ports. Its 24 +two-by-two matrices satisfy H_pair* H_pair=2I. It acts as identity +on the 64 small ports. + +The pinned placement payload includes the actual port list, block +assignment, and pair matrices. The unitary payload includes the port +list and reader matrix V. No new abstract placement replaces these +data. + +Put alpha=(1+i)/2. A signed six-mode block uses the names +(p,c,n,t,a,b) from the stored matching placement. First put +z_j=d_j x_j. Its code is + +```text +out_p = (z_c+z_t+z_a+z_b)/2, +out_c = alpha (z_p+z_n), +out_n = (z_b+z_c-z_a-z_t)/2, +out_t = alpha (z_p-z_n), +out_a = alpha (z_b-z_c), +out_b = alpha (z_a-z_t). +``` + +The four-coordinate sum, its contrast, and two pair differences form +an orthonormal basis on those four coordinates. The two-coordinate +sum and difference form an orthonormal basis on the other two +coordinates. Here |alpha|^2=1/2. The full block is therefore unitary. +Each output row omits its own input coordinate, so its diagonal is +zero. + +The original centre reader of this block is + +```text +d^T x = 2 out_p + (1-i) out_c. +``` + +The centre is distributed over two output coordinates. This is why +the construction does not need a single normalized row of squared +length six. + +For an eight-port block, split its stored ports into two groups of +four. Use the normalized sum, two pair differences, and one contrast +on each group. Put each group's four output rows in the other +group's four output locations. The two sum outputs are + +```text +out_p = -sum(right)/2, out_c = sum(left)/2. +``` + +Thus the block is unitary and has zero diagonal. Its centre reader +is 2(out_c-out_p). The six other rows are the normalized differences +and contrasts, each with zero sum. + +## Physical pair closure + +The two distinguished mode outputs per large block form two disjoint +perfect matchings in the actual eight-vertex pair graph. Their union +is closed under the physical pair code. The chosen 32 physical output +ports are serialized in `selected_full_ports`. + +Let C_mode be the direct sum of the sixteen block codes. Define + +```text +C = H^-1 C_mode H. +``` + +The factor H*H is 2I on all 48 large modes and I on the small modes. +The mode code preserves these two sets. These constant factors +therefore cancel when the physical adjoint is taken. It follows that + +```text +C* C = C C* = I, C^-* = C. +``` + +The checker verifies both identities on all 112 physical columns. +It does not treat the unnormalized pair matrix H as unitary. + +The two modes of a physical pair belong to different six-mode +vertices. The mode code has no entries between those vertices and +has zero diagonal within each vertex. Conjugation by the pair code +therefore preserves the zero diagonal. The checker also verifies +this directly on the physical matrix. + +## Centre information and the ordinary rows + +Let P32 be the selected output set and R80 its complement. The +payload stores the exact decoder + +```text +T = V C*. +``` + +Every row of T is supported on P32, and exact multiplication gives +T C=V. This is a statement about available centre information. It is +not an instruction to discard the other independent coordinates. + +Every ordinary mode row r has r d=0 in its block. Hence + +```text +r E_block = r. +``` + +The selected pair closure transfers this statement to physical +ports. The full exact matrix check gives + +```text +(C E)_R80 = C_R80. +``` + +The ordinary diagonal is zero for both responses. The complete +response C has zero diagonal on all 112 modes. Its adjoint has the +same property. Every nonzero off-diagonal entry stays inside the +original six-mode vertex or eight-port clique. These are the +existing native transfer supports. + +This creates two different native construction targets: + +* Response CE uses the same 80 ordinary rows as C. Its exceptional + rows can use the 32 selected FULL paths and a late FULL query. +* Response C needs no diagonal override in the native mode basis. + It can be tested in the existing off-diagonal grammar. + +These support statements do not price retuned native ADDs, compile +new complete native words, or prove that a current code can replace +an old code at a hole phase. Those are separate obligations. + +## Complete scalar implementation + +The program applies the actual H pair word, the sixteen real +unnormalized Haar blocks, the row normalizations, and the inverse H +pair word. The two selected rows of each small block use a paid +three-ADD signed rotation. No field permutation is free. + +The complex factor alpha has an explicit real-component word. +For a field with real and imaginary parts (r,s), execute + +```text +r -= s; +s *= 2; +s += r; +r /= 2; +s /= 2. +``` + +The result is ((r-s)/2,(r+s)/2) in terms of the original values. +Its price is eleven real scalar primitives under the source tariff. +The program uses only real ADDs and signed power-of-two scales. +There are no odd divisions, extra fields, or implicit complex +multiply primitives. + +The serialized words use component index 2p for the real part of +field p and 2p+1 for its imaginary part. The code and its inverse +each have 1,778 component instructions and cost 5,460 real scalar +primitives. Each inverse instruction is emitted in the exact reverse +order with its inverse coefficient. + +The largest real-component row one-norm at an instruction boundary +is 16 for C and 28 for C*. The additional binary denominator height +is two. These are exact local bounds. They do not include a +recursive child or rounding error. + +The code accepts arbitrary field values at one common physical +type, such as current I or completed FULL. Its scalar word cannot +be applied across unequal hole types without an additional access +proof. In particular, C_t C_s^-1 is not assumed free. + +## Checks, reproduction, and credit + +Both unitary product orders, both physical zero diagonals, the +ordinary-row equality, and the full centre-decoder identity pass. +Every matrix entry is Gaussian dyadic. The literal component word +and inverse pass all 1,280 real columns, including 1,056 unchanged +outside components. A missing component ADD is rejected in both +directions. The saved programs are replayed. + +Run in new output directories: + +```text +python3 check_unitary.py --out +python3 -O check_unitary.py --out +``` + +The normal and optimized payloads and receipts are byte-identical. +The earlier signed-metric construction remains as a pinned placement +dependency. It is not substituted for the new positive unitary code. + +The root lane proposed the distributed positive unitary normalization. +This lane supplied the actual matching placement, physical basis +binding, zero-diagonal output assignment, scalar words, and complete +checks. The controller and native response packets supplied the +centre readers and the six-mode and clique supports. The cover lane +is studying the caller that uses the primal and inverse-adjoint code. +AI assistance was used throughout. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-FREEZE.json new file mode 100644 index 0000000000..3fd49f6816 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/UNITARY-FREEZE.json @@ -0,0 +1,50 @@ +{ + "files": { + "UNITARY-COMPLETION.md": "ae558d4ee9e5205435612b9548881f6bdf64e2065f47ca8cb94e3fd393495090", + "check_completion.py": "854d8be88966bfdd279f9e208927f21c34d4e3fe09a19be2b7d180334f178084", + "check_unitary.py": "45edfdf2a3e62557b1809ed6280b27d0afc411704fd1c572ab7295759d40127a", + "signed-probe/CHECKS.json": "fa62da09a88a50af828fcf2858073a0786049c132af2d33ec14aa70ce2221e41", + "signed-probe/METRIC-COMPLETION.json.gz": "a4a0ed5d7a927673dbc103377c0fa5ed375ad495b43f051956d2251872dcb099", + "unitary-v2-normal/CHECKS.json": "1c8ff0812baa43befc3c079e027568f666479c26f6a68330a2cd673ff0f80cbe", + "unitary-v2-normal/UNITARY-COMPLETION.json.gz": "ab0b61e8e1f530769b6e2f70c1d37798b23f0d5ccb2ea2f6a905bf235938ae58", + "unitary-v2-optimized/CHECKS.json": "1c8ff0812baa43befc3c079e027568f666479c26f6a68330a2cd673ff0f80cbe", + "unitary-v2-optimized/UNITARY-COMPLETION.json.gz": "ab0b61e8e1f530769b6e2f70c1d37798b23f0d5ccb2ea2f6a905bf235938ae58" + }, + "inputs": [ + { + "decompressed_sha256": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "name": "arithmetic", + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py", + "sha256": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8" + }, + { + "decompressed_sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "name": "native", + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "sha256": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b" + }, + { + "decompressed_sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "name": "cyclic", + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + }, + { + "decompressed_sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7", + "name": "reader", + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json", + "sha256": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7" + }, + { + "name": "gaussian_arithmetic", + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/root/check_sign_metric_involutions_20261020.py", + "sha256": "4c053a9fbc5da82ec1ef39c6740256f3fc0f6d5784df630130b1110a7efae863" + } + ], + "normal_optimized_bytes_equal": true, + "payload_decompressed_sha256": "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428", + "publication": "No PR, commit, push or publication. Read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md before any future PR description.", + "schema": "unitary-centre-completion-freeze-v1", + "scope": "Exact Gaussian dyadic unitary code, centre decoder, scalar words and native support. No changed native service, routed caller, recursive host or complete supplier claim.", + "status": "PRODUCER_FROZEN_INDEPENDENT_REVIEW_PENDING" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_completion.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_completion.py new file mode 100644 index 0000000000..3d0d13d384 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_completion.py @@ -0,0 +1,325 @@ +#!/usr/bin/env python3 +"""Build a row-complete code with physical diagonal metrics.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[2] +PINS = { + "arithmetic": (HERE.parent / "check_response.py", + "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"), + "native": (HERE.parent / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"), + "cyclic": (LANES / "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"), + "reader": (LANES / "controller-followthrough-20261017/row-capture-20261020/run-normal/ROW-CAPTURE.json", + "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7"), +} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source " + name) + return raw + + +read("arithmetic") +spec = importlib.util.spec_from_file_location("metric_completion_arithmetic", PINS["arithmetic"][0]) +r = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = r +spec.loader.exec_module(r) + + +def rows(value): + return [{int(j): F(c) for j, c in row.items() if F(c)} for row in value] + + +def unit(x): + x = abs(x) + return bool(x) and (x.numerator & (x.numerator - 1) == 0 + and x.denominator & (x.denominator - 1) == 0) + + +def scale_row(a, c): + return {j: c * v for j, v in a.items() if c * v} + + +def factor(matrix, ports): + """Reduce a small dyadic matrix and reverse the paid row steps.""" + a = [dict(row) for row in matrix] + reduction = [] + + def add(i, j, c): + if c: + r.add(a[i], a[j], c) + reduction.append(["add", ports[i], ports[j], str(c)]) + + def scale(i, c): + if c != 1: + need(unit(c), "Only signed power-of-two scales are used") + a[i] = scale_row(a[i], c) + reduction.append(["scale", ports[i], None, str(c)]) + + for j in range(len(ports)): + candidates = [i for i in range(j, len(ports)) if unit(a[i].get(j, F(0)))] + need(candidates, "A dyadic pivot exists") + pivot = min(candidates, key=lambda i: (i != j, len(a[i]), abs(a[i][j]))) + if pivot != j: + add(j, pivot, 1) + add(pivot, j, -1) + add(j, pivot, 1) + scale(pivot, -1) + scale(j, 1 / a[j][j]) + for i in range(len(ports)): + if i != j: + add(i, j, -a[i].get(j, F(0))) + need(a == r.identity(len(ports)), "The complete block reduction") + return r.inverse_word(reduction) + + +def matchings(edges, remaining=tuple(range(8))): + if not remaining: + yield [] + return + a = remaining[0] + for b in remaining[1:]: + key = tuple(sorted((a, b))) + if key in edges: + rest = tuple(v for v in remaining if v not in (a, b)) + for tail in matchings(edges, rest): + yield [key] + tail + + +def replay(word, n=112): + a = r.identity(n) + peak, height = F(1), 0 + for op, target, source, coefficient in word: + coefficient = F(coefficient) + if op == "add": + need(target != source, "Distinct ADD fields") + r.add(a[target], a[source], coefficient) + else: + need(op == "scale" and unit(coefficient), "Dyadic unit scale") + a[target] = scale_row(a[target], coefficient) + peak = max(peak, sum(abs(v) for v in a[target].values())) + for value in a[target].values(): + d = value.denominator + need(d & (d - 1) == 0, "No odd content denominator") + height = max(height, d.bit_length() - 1) + return a, {"scalar": r.price(word), "prefix_row_one_norm": str(peak), + "binary_height": height, "instructions": len(word)} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + native = json.loads(read("native")) + model = native["model"] + cyclic = json.loads(read("cyclic")) + reader = json.loads(read("reader")) + pairs = cyclic["pair_codes"] + old_centres = reader["pivots"] + centre_set = set(old_centres) + large = set(model["large_ports"]) + pair_by_edge = {tuple(sorted(pair["vertices"])): pair for pair in pairs} + p0 = {edge for edge, pair in pair_by_edge.items() if set(pair["ports"]) <= centre_set} + q_ports = {2, 25, 13, 51, 11, 63, 42, 105} + q = {edge for edge, pair in pair_by_edge.items() if set(pair["ports"]) <= q_ports} + need(len(p0) == len(q) == 4 and not p0 & q, "Two disjoint selected matchings") + remaining = set(pair_by_edge) - p0 - q + found = None + for n in matchings(remaining): + for t in matchings(remaining - set(n)): + found = (set(n), set(t)) + break + if found: + break + need(found is not None, "Two further disjoint actual matchings") + n_edges, t_edges = found + labels = {"centre": p0, "contrast": q, "negative": n_edges, "negative_difference": t_edges} + assignment = {} + for vertex in range(8): + assignment[vertex] = {} + for label, edges in labels.items(): + edge = next(e for e in edges if vertex in e) + pair = pair_by_edge[edge] + assignment[vertex][label] = pair["ports"][pair["vertices"].index(vertex)] + H, Hinv = r.identity(112), r.identity(112) + hword = [] + for pair in pairs: + pp, matrix = pair["ports"], pair["matrix"] + local = [{j: F(c) for j, c in enumerate(row) if c} for row in matrix] + for i, port in enumerate(pp): + H[port] = {pp[j]: c for j, c in local[i].items()} + Hinv[port] = {pp[j]: F(matrix[j][i], 2) for j in range(2) if matrix[j][i]} + hword += factor(local, pp) + need(r.product(H, Hinv) == r.product(Hinv, H) == r.identity(112), "The actual physical pair code") + Cm, Jm, Gm = r.identity(112), r.identity(112), r.identity(112) + block_records, mode_word, exceptional = [], [], set() + for block in model["vertex_assignments"]: + vertex, pp, signs = block["vertex"], block["ordered_carriers_a_b_c"], block["signs"] + roles = assignment[vertex] + p, c, n, t = [roles[k] for k in ("centre", "contrast", "negative", "negative_difference")] + a, b = sorted(set(pp) - {p, c, n, t}) + template = { + p: {j: 1 for j in pp}, + c: {j: (2 if j in (p, n) else 1) for j in pp}, + n: {b: 1, c: 1, a: -1, t: -1}, + t: {p: 1, n: -1}, + a: {b: 1, c: -1}, + b: {a: 1, t: -1}, + } + sign = dict(zip(pp, signs)) + for port in pp: + Cm[port] = {j: F(value * sign[j]) for j, value in template[port].items()} + Jm[port] = {port: F(-1 if port in (p, n) else 1)} + norms = {p: 2, c: -4, n: 4, t: -2, a: 2, b: 2} + for port, norm in norms.items(): + Gm[port] = {port: F(norm)} + local = [{pp.index(j): value for j, value in Cm[port].items()} for port in pp] + mode_word += factor(local, pp) + exceptional.update((p, c)) + block_records.append({"kind": "large6", "vertex": vertex, "ports": pp, + "roles": {**roles, "pair_difference_a": a, "pair_difference_b": b}, + "signs": signs, "row_norms": norms}) + for i, pp in enumerate(model["small_cliques"]): + left, right = pp[:4], pp[4:] + p, c = left[0], right[0] + template = {p: {j: 1 for j in pp}, + c: {j: (1 if j in left else -1) for j in pp}} + norms = {p: 8, c: 8} + for group, outputs in ((left, right[1:]), (right, left[1:])): + x0, x1, x2, x3 = group + patterns = [{x0: 1, x1: -1}, {x2: 1, x3: -1}, + {x0: 1, x1: 1, x2: -1, x3: -1}] + for output, pattern, norm in zip(outputs, patterns, (2, 2, 4)): + template[output], norms[output] = pattern, norm + for port in pp: + Cm[port] = {j: F(value) for j, value in template[port].items()} + Gm[port] = {port: F(norms[port])} + local = [{pp.index(j): value for j, value in Cm[port].items()} for port in pp] + mode_word += factor(local, pp) + exceptional.update((p, c)) + block_records.append({"kind": "small8", "index": i, "ports": pp, + "centre": p, "contrast": c, "row_norms": norms}) + need(r.product(r.product(Cm, Jm), r.transpose(Cm, 112)) == Gm, "Every exact mode metric") + C = r.product(r.product(Hinv, Cm), H) + J = r.product(r.product(Hinv, Jm), H) + G = r.product(r.product(Hinv, Gm), H) + need(all(set(row) == {i} and abs(row[i]) == 1 for i, row in enumerate(J)), "Physical J is diagonal signs") + need(all(set(row) == {i} and unit(row[i]) for i, row in enumerate(G)), "Physical G is diagonal dyadic units") + Gi = [{i: 1 / row[i]} for i, row in enumerate(G)] + Cinv = r.product(r.product(J, r.transpose(C, 112)), Gi) + Cdual = r.product(r.product(Gi, C), J) + need(r.product(C, Cinv) == r.product(Cinv, C) == r.identity(112), "Both actual112 inverse orders") + need(Cdual == r.transpose(Cinv, 112), "Physical inverse-adjoint identity") + need(r.product(r.product(C, J), r.transpose(C, 112)) == G, "Actual physical metric") + E = rows(model["response"]) + CE = r.product(C, E) + Em = r.product(r.product(H, E), Hinv) + CEm = r.product(Cm, Em) + need(len(exceptional) == 32 and centre_set <= exceptional, "The actual32 exceptional ports") + need(all((CEm[p].get(p, 0) != 0) == (p in exceptional) for p in range(112)), + "Exactly32 mode diagonal exceptions") + need(all(set(pair["ports"]) <= exceptional or not set(pair["ports"]) & exceptional for pair in pairs), + "Complete physical pair closure") + need(all(not CE[p].get(p, 0) for p in set(range(112)) - exceptional), + "Every ordinary physical response diagonal is zero") + V = rows(model["correction_V"]) + centre_rows = [C[p] for p in old_centres] + need(r.rank(centre_rows, 112) == r.rank(V, 112) == r.rank(centre_rows + V, 112) == 16, + "The exact old centre rowspace") + code_word = hword + mode_word + r.inverse_word(hword) + inverse_word = r.inverse_word(code_word) + dual_word = [["scale", p, None, str(J[p][p])] for p in range(112) if J[p][p] != 1] + dual_word += code_word + dual_word += [["scale", p, None, str(Gi[p][p])] for p in range(112) if Gi[p][p] != 1] + words = {"code": code_word, "inverse": inverse_word, "inverse_adjoint": dual_word} + expected = {"code": C, "inverse": Cinv, "inverse_adjoint": Cdual} + reports = {} + for name, word in words.items(): + actual, report = replay(word, 640) + need(actual[:112] == expected[name] and actual[112:] == r.identity(640)[112:], + "All640 scalar columns and528 arbitrary outside fields") + reports[name] = report + native_audit = {} + for provider, data in native["providers"].items(): + forward = data["forward"] + selected_fields = {112 + p for p in exceptional} + removed = [] + kept = [] + for i, event in enumerate(forward["events"]): + target = event[1] if event[0] == "native" else event[1][1] + if target in selected_fields: + removed.append(event) + else: + if event[0] == "scalar" and event[1][0] == "add": + need(event[1][2] not in selected_fields, "No retained event reads a removed target") + kept.append(event) + old = Counter(event[4] for event in kept if event[0] == "native") + profile_q = old + Counter({8: 32}) + profile_i = old + Counter({9: 32}) + need(Counter(event[4] for event in removed if event[0] == "native") == {1: 256}, + "Exactly256 old native target steps are removed") + native_audit[provider] = { + "removed_events": len(removed), "removed_native_profile": {"1": 256}, + "line_entry_profile": dict(sorted(profile_q.items())), + "line_entry_mass": sum(k * v for k, v in profile_q.items()), + "formation_profile": dict(sorted(profile_i.items())), + "formation_mass": sum(k * v for k, v in profile_i.items()), + "scope": "Path-removal census only. Retuned transfer weights, new native phases, late queries and full native replay remain open.", + } + payload = { + "schema": "physical-diagonal-metric-completion-v1", + "source_pins": {k: {"path": str(v[0]), "sha256": v[1]} for k, v in PINS.items()}, + "ports": model["ports"], "centre_ports": old_centres, + "exceptional_ports": sorted(exceptional), "ordinary_ports": sorted(set(range(112)) - exceptional), + "mode_blocks": block_records, "matchings": {k: sorted(v) for k, v in labels.items()}, + "pair_code": r.encoded(H), "pair_code_inverse": r.encoded(Hinv), + "mode_code": r.encoded(Cm), "code": r.encoded(C), "inverse": r.encoded(Cinv), + "inverse_adjoint": r.encoded(Cdual), "input_metric": r.encoded(J), "output_metric": r.encoded(G), + "response": model["response"], "coded_response": r.encoded(CE), + "mode_response": r.encoded(Em), "mode_coded_response": r.encoded(CEm), "scalar_words": words, + "identity": "C J C^T=G; C^(-T)=G^(-1) C J. Both physical metrics are diagonal dyadic units.", + "scope": "Complete scalar code and exact native-support census. No changed native service or routed caller is claimed.", + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for name, word in saved["scalar_words"].items(): + need(replay(word, 640)[0][:112] == expected[name], "Serialized scalar code") + (args.out / "METRIC-COMPLETION.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_PHYSICAL_DIAGONAL_METRIC_COMPLETION", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "all_matrix_columns": 112, "all_scalar_columns": 640, "centre_rank": 16, + "exceptional_rows": len(exceptional), "ordinary_rows": 80, + "input_metric_counts": dict(Counter(str(row[i]) for i, row in enumerate(J))), + "output_metric_counts": dict(Counter(str(row[i]) for i, row in enumerate(G))), + "reports": reports, "native_path_census": native_audit, "scope": payload["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_twenty_four.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_twenty_four.py new file mode 100644 index 0000000000..c6664782ef --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_twenty_four.py @@ -0,0 +1,196 @@ +#!/usr/bin/env python3 +"""Build a unitary centre code with 24 output coordinates.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +HELPER = HERE / "check_unitary.py" +HELPER_PIN = "45edfdf2a3e62557b1809ed6280b27d0afc411704fd1c572ab7295759d40127a" +SOURCE = HERE / "unitary-v2-normal/UNITARY-COMPLETION.json.gz" +SOURCE_PIN = "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428" + + +def need(value, message): + if not value: + raise ValueError(message) + + +need(sha256(HELPER.read_bytes()).hexdigest() == HELPER_PIN, "Pinned unitary helper") +spec = importlib.util.spec_from_file_location("unitary_twenty_four_source", HELPER) +u = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = u +spec.loader.exec_module(u) +b, g = u.b, u.g + + +def rows(value): + return [{int(j): (F(x), F(y)) for j, (x, y) in row.items()} for row in value] + + +def small_block(): + vector = [1, 1, -1, 0, -1, 0, 0, 0] + reflection = [{j: F(int(i == j)) - F(vector[i] * vector[j], 2) + for j in range(8) + if F(int(i == j)) - F(vector[i] * vector[j], 2)} + for i in range(8)] + haar = [ + [1, 1, 1, 1, 1, 1, 1, 1], + [1, 1, 1, 1, -1, -1, -1, -1], + [1, 1, -1, -1, 0, 0, 0, 0], + [0, 0, 0, 0, 1, 1, -1, -1], + [1, -1, 0, 0, 0, 0, 0, 0], + [0, 0, 1, -1, 0, 0, 0, 0], + [0, 0, 0, 0, 1, -1, 0, 0], + [0, 0, 0, 0, 0, 0, 1, -1], + ] + output = [0, 1, 5, 3, 2, 7, 6, 4] + norm = [8, 8, 4, 4, 2, 2, 2, 2] + ordered = [{} for _ in range(8)] + factors, norms = {}, {} + for row, target, squared_norm in zip(haar, output, norm): + ordered[target] = {j: F(x) for j, x in enumerate(row) if x} + factors[target] = ((F(1, 4), F(1, 4)) if squared_norm == 8 else + (F(1, 2), F(1, 2)) if squared_norm == 2 else + (F(1, 2), F(0))) + norms[target] = squared_norm + real_product = b.r.product(ordered, reflection) + code = [{j: g.times(g.real(x), factors[i]) for j, x in row.items()} + for i, row in enumerate(real_product)] + need(sum(vector) == 0 and sum(x * x for x in vector) == 4, "The reflection fixes the centre") + need(b.r.product(reflection, reflection) == b.r.identity(8), "The real reflection is an involution") + need(g.multiply(code, g.adjoint(code, 8)) == g.multiply(g.adjoint(code, 8), code) == g.eye(8), + "Both small-block unitary identities") + need(all(i not in code[i] for i in range(1, 8)), "All seven ordinary diagonals vanish") + need(code[0] == {j: (F(1, 4), F(1, 4)) for j in range(8)}, "The sole centre row") + return code, reflection, ordered, norms, vector, output + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + raw = gzip.decompress(SOURCE.read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_PIN, "Pinned physical 32-coordinate code") + source = json.loads(raw) + placement = json.loads(gzip.decompress(u.SOURCE.read_bytes())) + native = json.loads(b.read("native")) + large = set(native["model"]["large_ports"]) + C, Cm = rows(source["code"]), rows(source["mode_code"]) + E = rows(source["response"]) + V = rows(source["original_centre_readers"]) + block, reflection, haar, norms, vector, output = small_block() + selected = set(source["selected_full_ports"]) & large + word = [] + for event in source["component_words"]["code"]: + target = event[1] // 2 + if target in large: + need(event[2] is None or event[2] // 2 in large, "The copied large word is closed") + word.append(event) + blocks = [] + for record in placement["mode_blocks"]: + if record["kind"] == "large6": + continue + ports = record["ports"] + selected.add(ports[0]) + for i, p in enumerate(ports): + C[p] = {ports[j]: z for j, z in block[i].items()} + Cm[p] = dict(C[p]) + local_word = u.components(b.factor(reflection, ports) + b.factor(haar, ports)) + for i, p in enumerate(ports): + local_word += u.component_scale(p, 2 if norms[i] == 8 else norms[i]) + if norms[i] == 8: + local_word += [["scale", 2 * p, None, "1/2"], + ["scale", 2 * p + 1, None, "1/2"]] + word += local_word + blocks.append({"ports": ports, "centre": ports[0], "component_word": local_word}) + Ci = g.adjoint(C, 112) + ordinary = set(range(112)) - selected + CE = g.multiply(C, E) + decoder = g.multiply(V, Ci) + need(len(selected) == 24, "Exactly 24 centre coordinates") + need(g.multiply(C, Ci) == g.multiply(Ci, C) == g.eye(112), "Both physical unitary orders") + need(all(C[p] == CE[p] and p not in C[p] for p in ordinary), "All88 ordinary rows and diagonals") + need(all(set(row) <= selected for row in decoder) and g.multiply(decoder, C) == V, + "All sixteen original readers use the 24 coordinates") + for matrix in (C, Ci, CE, decoder): + for row in matrix: + for value in row.values(): + need(all(x.denominator & (x.denominator - 1) == 0 for x in value), + "Every coefficient is Gaussian dyadic") + mode_response = rows(source["mode_response"]) + CEm = g.multiply(Cm, mode_response) + need(all(p not in Cm[p] and p not in CEm[p] for p in ordinary), "All ordinary mode diagonals") + allowed = {} + for record in placement["mode_blocks"]: + for p in record["ports"]: + allowed[p] = set(record["ports"]) + need(all(set(row) <= allowed[p] for p, row in enumerate(Cm)), "The native block support") + inverse = b.r.inverse_word(word) + reports = {} + for name, instructions, matrix in (("code", word, C), ("inverse_and_adjoint", inverse, Ci)): + actual, report = u.replay(instructions) + need(actual == u.realify(matrix), "All1280 real columns and528 external complex fields") + damaged = list(instructions) + del damaged[next(i for i, event in enumerate(damaged) if event[0] == "add")] + need(u.replay(damaged)[0] != actual, "A missing component ADD is rejected") + reports[name] = report + need(b.r.product(u.realify(C), u.realify(Ci)) == b.r.identity(1280), + "The full real-component inverse composition") + path_census = {} + for name, provider in native["providers"].items(): + events = provider["forward"]["events"] + removed = [] + kept = [] + for event in events: + target = event[1] if event[0] == "native" else event[1][1] + (removed if target in {112 + p for p in selected} else kept).append(event) + need(all(event[0] != "scalar" or event[1][2] not in {112 + p for p in selected} + for event in kept), "No retained event reads a removed target") + profile = Counter(event[4] for event in removed if event[0] == "native") + need(profile == Counter({1: 192}), "Exactly192 removed rank-one target advances") + path_census[name] = {"removed_events": len(removed), "removed_native_profile": dict(profile), + "retained_reads_of_selected_target": 0} + payload = { + "schema": "physical-unitary-24-coordinate-centre-code-v1", + "source_payload_decompressed_sha256": SOURCE_PIN, + "helper_sha256": HELPER_PIN, + "source_pins": source["source_pins"], + "selected_full_ports": sorted(selected), "ordinary_ports": sorted(ordinary), + "code": g.serialize(C), "inverse_and_adjoint": g.serialize(Ci), + "mode_code": g.serialize(Cm), "response": g.serialize(E), + "coded_response": g.serialize(CE), "mode_coded_response": g.serialize(CEm), + "original_centre_readers": g.serialize(V), "centre_decoder": g.serialize(decoder), + "small_reflection_vector": vector, "small_output_assignment": output, + "small_blocks": blocks, + "component_words": {"code": word, "inverse_and_adjoint": inverse}, + "scope": "Exact unitary code,24-coordinate centre recovery, scalar words and native path/support census. Complete native code and routed caller remain open.", + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + (args.out / "UNITARY-24.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_ACTUAL_UNITARY_24_COORDINATE_CODE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "all_real_columns": 1280, "all_complex_fields": 640, "unchanged_external_complex_fields": 528, + "selected_full_rows": 24, "ordinary_rows": 88, "reports": reports, + "centre_decoder_supports": [len(row) for row in decoder], + "code_diagonal_exceptions": [p for p in range(112) if p in C[p]], + "coded_response_diagonal_exceptions": [p for p in range(112) if p in CE[p]], + "path_census": path_census, "scope": payload["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_unitary.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_unitary.py new file mode 100644 index 0000000000..8e8c0cd666 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_unitary.py @@ -0,0 +1,213 @@ +#!/usr/bin/env python3 +"""Build a dyadic unitary code with distributed centre rows.""" + +import argparse +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +HELPER = HERE / "check_completion.py" +HELPER_PIN = "854d8be88966bfdd279f9e208927f21c34d4e3fe09a19be2b7d180334f178084" +GAUSSIAN = HERE.parents[3] / "root/check_sign_metric_involutions_20261020.py" +GAUSSIAN_PIN = "4c053a9fbc5da82ec1ef39c6740256f3fc0f6d5784df630130b1110a7efae863" +SOURCE = HERE / "signed-probe/METRIC-COMPLETION.json.gz" +SOURCE_PIN = "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e" + + +def load(path, pin, name): + if sha256(path.read_bytes()).hexdigest() != pin: + raise ValueError("Pinned helper " + name) + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +b = load(HELPER, HELPER_PIN, "unitary_real_code") +g = load(GAUSSIAN, GAUSSIAN_PIN, "unitary_gaussian_arithmetic") +need = b.need + + +def gaussian(real_rows): + return [{j: g.real(v) for j, v in row.items()} for row in real_rows] + + +def realify(matrix, n=640): + out = b.r.identity(2 * n) + for p, row in enumerate(matrix): + out[2 * p], out[2 * p + 1] = {}, {} + for j, (x, y) in row.items(): + for target, source, coefficient in ( + (2 * p, 2 * j, x), (2 * p, 2 * j + 1, -y), + (2 * p + 1, 2 * j, y), (2 * p + 1, 2 * j + 1, x)): + if coefficient: + out[target][source] = coefficient + return out + + +def components(word): + out = [] + for op, target, source, coefficient in word: + for bit in (0, 1): + out.append([op, 2 * target + bit, + None if source is None else 2 * source + bit, coefficient]) + return out + + +def component_scale(port, norm): + x, y = 2 * port, 2 * port + 1 + if norm == 4: + return [["scale", x, None, "1/2"], ["scale", y, None, "1/2"]] + need(norm == 2, "A pair or four-field Haar row") + return [["add", x, y, "-1"], ["scale", y, None, "2"], + ["add", y, x, "1"], ["scale", x, None, "1/2"], + ["scale", y, None, "1/2"]] + + +def replay(word): + result, report = b.replay(word, 1280) + need(report["scalar"] % 2 == 0, "The real-component tariff is integral") + report["scalar"] //= 2 + return result, report + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + raw = gzip.decompress(SOURCE.read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_PIN, "The exact block placement") + source = json.loads(raw) + native = json.loads(b.read("native")) + cyclic = json.loads(b.read("cyclic")) + H, Hi = gaussian(b.rows(source["pair_code"])), gaussian(b.rows(source["pair_code_inverse"])) + real_mode = b.r.identity(112) + mode = g.eye(112) + modes, normalization = [], [] + for block in source["mode_blocks"]: + pp = block["ports"] + rotation = [] + if block["kind"] == "large6": + v = block["roles"] + p, c, n, t, a, z = [v[k] for k in + ("centre", "contrast", "negative", "negative_difference", + "pair_difference_a", "pair_difference_b")] + template = { + p: {c: 1, t: 1, a: 1, z: 1}, + c: {p: 1, n: 1}, + n: {z: 1, c: 1, a: -1, t: -1}, + t: {p: 1, n: -1}, + a: {z: 1, c: -1}, + z: {a: 1, t: -1}, + } + norms = {p: 4, c: 2, n: 4, t: 2, a: 2, z: 2} + sign = dict(zip(pp, block["signs"])) + else: + p, c = block["centre"], block["contrast"] + left, right = pp[:4], pp[4:] + template = {p: {j: 1 for j in left}, c: {j: 1 for j in right}} + norms = {p: 4, c: 4} + for group, outputs in ((left, right[1:]), (right, left[1:])): + x0, x1, x2, x3 = group + patterns = [{x0: 1, x1: -1}, {x2: 1, x3: -1}, + {x0: 1, x1: 1, x2: -1, x3: -1}] + for output, row, norm in zip(outputs, patterns, (2, 2, 4)): + template[output], norms[output] = row, norm + sign = {j: 1 for j in pp} + rotation = [["add", c, p, "1"], ["add", p, c, "-1"], ["add", c, p, "1"]] + for port in pp: + real_mode[port] = {j: F(value * sign[j]) for j, value in template[port].items()} + coefficient = (F(1, 2), F(1, 2) if norms[port] == 2 else F(0)) + mode[port] = {j: g.times(g.real(value), coefficient) + for j, value in real_mode[port].items()} + normalization += component_scale(port, norms[port]) + local = [{pp.index(j): value for j, value in real_mode[port].items()} for port in pp] + modes += b.factor(local, pp) + rotation + if rotation: + real_mode[p], real_mode[c] = b.scale_row(real_mode[c], F(-1)), real_mode[p] + mode[p], mode[c] = {j: g.neg(value) for j, value in mode[c].items()}, mode[p] + need(g.multiply(mode, g.adjoint(mode, 112)) == g.multiply(g.adjoint(mode, 112), mode) == g.eye(112), + "Both exact mode unitary identities") + C = g.multiply(g.multiply(Hi, mode), H) + Ci = g.adjoint(C, 112) + need(g.multiply(C, Ci) == g.multiply(Ci, C) == g.eye(112), "Both physical unitary orders") + E = gaussian(b.rows(native["model"]["response"])) + CE = g.multiply(C, E) + Em = g.multiply(g.multiply(H, E), Hi) + CEm = g.multiply(mode, Em) + selected = set(source["exceptional_ports"]) + ordinary = set(range(112)) - selected + need(all(C[p] == CE[p] for p in ordinary), "All80 ordinary response rows are unchanged") + need(all(p not in mode[p] and p not in CEm[p] for p in ordinary), "Ordinary mode diagonals vanish") + need(all(p not in C[p] and p not in CE[p] for p in ordinary), "Ordinary physical diagonals vanish") + need(all(p not in mode[p] and p not in C[p] for p in range(112)), + "The full code has zero mode and physical diagonal") + need({p for p in range(112) if p in CEm[p]} <= selected, "Response exceptions are selected") + V = gaussian(b.rows(native["model"]["correction_V"])) + decoder = g.multiply(V, Ci) + need(all(set(row) <= selected for row in decoder), "All old centre readers use only32 FULL outputs") + need(g.multiply(decoder, C) == V, "The exact original centre information") + hword = [] + for pair in cyclic["pair_codes"]: + local = [{j: F(c) for j, c in enumerate(row) if c} for row in pair["matrix"]] + hword += b.factor(local, pair["ports"]) + word = components(hword) + components(modes) + normalization + components(b.r.inverse_word(hword)) + inverse = b.r.inverse_word(word) + words = {"code": word, "inverse_and_adjoint": inverse} + reports = {} + for name, instructions in words.items(): + expected = C if name == "code" else Ci + actual, report = replay(instructions) + need(actual == realify(expected), "All1280 real columns and1056 outside components") + wrong = list(instructions) + del wrong[next(i for i, event in enumerate(wrong) if event[0] == "add")] + need(replay(wrong)[0] != realify(expected), "A missing component ADD is rejected") + reports[name] = report + for value in (C, Ci, CE, decoder): + for row in value: + for z in row.values(): + for x in z: + need(x.denominator & (x.denominator - 1) == 0, "Every matrix entry is Gaussian dyadic") + payload = { + "schema": "physical-unitary-distributed-centre-code-v1", + "source_pins": {"real_helper": HELPER_PIN, "gaussian_helper": GAUSSIAN_PIN, + "placement_payload_decompressed": SOURCE_PIN, **source["source_pins"]}, + "ports": source["ports"], "selected_full_ports": sorted(selected), "ordinary_ports": sorted(ordinary), + "code": g.serialize(C), "inverse_and_adjoint": g.serialize(Ci), + "mode_code": g.serialize(mode), "response": g.serialize(E), "coded_response": g.serialize(CE), + "mode_response": g.serialize(Em), "mode_coded_response": g.serialize(CEm), + "original_centre_readers": g.serialize(V), "full_carrier_centre_decoder": g.serialize(decoder), + "component_words": words, "component_index": "2*p is real;2*p+1 is imaginary.", + "identity": "C*=C^-1 and C^-*=C. Every ordinary row of C E equals the same row of C.", + "scope": "Exact unitary scalar code,32-carrier centre decoding and zero mode diagonal. Changed native typed service and routed caller remain open.", + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for name, instructions in saved["component_words"].items(): + need(replay(instructions)[1] == reports[name], "Serialized component word") + (args.out / "UNITARY-COMPLETION.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_PHYSICAL_UNITARY_CENTRE_COMPLETION", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "all_complex_columns": 640, "all_real_columns": 1280, "unchanged_other_complex_fields": 528, + "selected_full_rows": len(selected), "ordinary_rows": len(ordinary), + "centre_decoder_row_supports": [len(row) for row in decoder], + "code_diagonal_exceptions": sorted(p for p in range(112) if p in C[p]), + "coded_response_diagonal_exceptions": sorted(p for p in range(112) if p in CE[p]), + "reports": reports, "scope": payload["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/CHECKS.json new file mode 100644 index 0000000000..e51d683cde --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/CHECKS.json @@ -0,0 +1,86 @@ +{ + "all_matrix_columns": 112, + "all_scalar_columns": 640, + "centre_rank": 16, + "exceptional_rows": 32, + "input_metric_counts": { + "-1": 16, + "1": 96 + }, + "native_path_census": { + "base": { + "formation_mass": 1824, + "formation_profile": { + "1": 1264, + "2": 64, + "3": 48, + "9": 32 + }, + "line_entry_mass": 1792, + "line_entry_profile": { + "1": 1264, + "2": 64, + "3": 48, + "8": 32 + }, + "removed_events": 500, + "removed_native_profile": { + "1": 256 + }, + "scope": "Path-removal census only. Retuned transfer weights, new native phases, late queries and full native replay remain open." + }, + "extra": { + "formation_mass": 1824, + "formation_profile": { + "1": 1264, + "2": 64, + "3": 48, + "9": 32 + }, + "line_entry_mass": 1792, + "line_entry_profile": { + "1": 1264, + "2": 64, + "3": 48, + "8": 32 + }, + "removed_events": 500, + "removed_native_profile": { + "1": 256 + }, + "scope": "Path-removal census only. Retuned transfer weights, new native phases, late queries and full native replay remain open." + } + }, + "ordinary_rows": 80, + "output_metric_counts": { + "-2": 8, + "-4": 8, + "2": 56, + "4": 24, + "8": 16 + }, + "payload_decompressed_sha256": "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e", + "producer_sha256": "854d8be88966bfdd279f9e208927f21c34d4e3fe09a19be2b7d180334f178084", + "reports": { + "code": { + "binary_height": 2, + "instructions": 711, + "prefix_row_one_norm": "30", + "scalar": 5104 + }, + "inverse": { + "binary_height": 3, + "instructions": 711, + "prefix_row_one_norm": "18", + "scalar": 5104 + }, + "inverse_adjoint": { + "binary_height": 3, + "instructions": 839, + "prefix_row_one_norm": "30", + "scalar": 5520 + } + }, + "scope": "Complete scalar code and exact native-support census. 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/dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/unitary-v2-normal/CHECKS.json @@ -0,0 +1,76 @@ +{ + "all_complex_columns": 640, + "all_real_columns": 1280, + "centre_decoder_row_supports": [ + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 2 + ], + "code_diagonal_exceptions": [], + "coded_response_diagonal_exceptions": [ + 0, + 1, + 2, + 3, + 6, + 7, + 8, + 11, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 27, + 36, + 40, + 46, + 51, + 57, + 58, + 59, + 60, + 63, + 64, + 65, + 66, + 103, + 111 + ], + "ordinary_rows": 80, + "payload_decompressed_sha256": "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428", + "producer_sha256": "45edfdf2a3e62557b1809ed6280b27d0afc411704fd1c572ab7295759d40127a", + "reports": { + "code": { + "binary_height": 2, + "instructions": 1778, + "prefix_row_one_norm": "16", + "scalar": 5460 + }, + "inverse_and_adjoint": { + "binary_height": 2, + "instructions": 1778, + "prefix_row_one_norm": "28", + "scalar": 5460 + } + }, + "scope": "Exact unitary scalar code,32-carrier centre decoding and zero mode diagonal. 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zV_(7TBKAXJ@!jE_m7>Fr?)VR!+O6FKPh%=w;~MksFq_SCb`R9S@`K&Y&u6N$TkHj* zd-a)GGod<~mI1Cd!T)Fh7bg5*Vfytcq6bBF``X0l$PN_&dcfLhY8ua;L{by5z` zMO6Gn6=rWnftv}itZ~8kuMI_WbT*v2d*^kPwbomaswb^AP`r*AQB$+q3))$;nf{W& zSqy}KzR9&6TzTks)tmA9!M@?XZE0m|MFgKth+Qi18;ts``(>3`m57$dpcv+64!%eQ z9XkJ1{ymu9iu>E4S(U=p$Hj5$tLxoP!QCxBs_X$d9>nsYkXJV{1{SG1m}%Z{bgl4G zlV+UPP@m!2+n5a@ZlzlEQ72X;I0n-TI>F3 z7G<*6bRP!^iSYBz)>~Bc_Am{Uk@(%a(++NpJcLIa1Z_%PXzqKW>RdvabZ6wz}4x9W=fUIyo9V zzj)VrcDBzMeAGC3KFDbjm~fDDT6RC}bTh}jj_7>d?5Irr+X>70c#B0 +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/emit_signed_clean.py --out +``` + +The expected status is `PASS_COMPLETE_SIGNED_SIXTEEN_NATIVE`. +Normal and optimized payloads and receipts match byte for byte. +Independent native review is a separate validation step. + +The root lane supplied the reciprocal reflection family. +The oblique lane fixed its physical metric and placement. +The cover lane supplied the full diagonal-dual identity. +The bridge access lane requested the transpose interface. +The prior native and review lanes supplied the unchanged +spatial recipes. This lane supplied the complete retuned words, +pair-closed code, and local checks. AI assistance was used. + +This packet does not allocate the 416 auxiliary roles as a +cache. It does not provide routed composition, a terminal +decoder, recursive child hosting, a finite-precision proof, +or a complete supplier improvement. + +No PR, commit, push, or publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/emit_signed_clean.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/emit_signed_clean.py new file mode 100644 index 0000000000..befd9f5475 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/emit_signed_clean.py @@ -0,0 +1,375 @@ +#!/usr/bin/env python3 +"""Emit complete clean interfaces for the signed sixteen-field codes.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +PARENT = HERE.parent +LANES = PARENT.parents[1] +PINS = { + "helper": (PARENT / "signed-sixteen-20261020/check_signed_sixteen.py", + "7befca24a7e3fd9afccfda3f494d2a515361fdf7575751d3b690f380a6681b82"), + "code": (PARENT / "signed-sixteen-20261020/run-v2-normal/SIGNED-SIXTEEN.json.gz", + "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c"), + "code_freeze": (PARENT / "signed-sixteen-20261020/FREEZE.json", + "8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2"), + "paired": (PARENT / "signed-sixteen-20261020/paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz", + "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1"), + "paired_freeze": (PARENT / "signed-sixteen-20261020/PAIRED-FREEZE.json", + "810508791ea43aecaaf894c3cb50a8170d3e6f1f8e52684e274cda16c2c2db57"), + "native_helper": (PARENT / "emit_native.py", + "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745"), + "native": (PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"), + "formation": (PARENT / "row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz", + "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c"), + "prefix": (PARENT / "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz", + "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e"), + "native_review": (LANES / "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json", + "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c"), + "formation_review": (LANES / "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json", + "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"), + "prefix_review": (LANES / "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"), +} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned input " + name) + return raw + + +def module(name, key): + read(key) + spec = importlib.util.spec_from_file_location(name, PINS[key][0]) + value = importlib.util.module_from_spec(spec) + sys.modules[name] = value + spec.loader.exec_module(value) + return value + + +m = module("signed_clean_code", "helper") +n = module("signed_clean_native", "native_helper") +b, r = m.b, m.r + + +def verify(word, expected): + state, frames = r.identity(640), list(word["start"]) + peak, height = F(1), 0 + for event in word["events"]: + if event[0] == "native": + _, p, old, new, rank, key = event + need(frames[p] == old, "The exact native entrance frame") + need(len(n.basis(word["frames"][old] + word["frames"][new])) + == len(word["frames"][new]), "The native frame inclusion") + need(rank == len(word["frames"][new]) - len(word["frames"][old]) + == word["native_recipes"][key]["rank"], "The exact native rank") + frames[p] = new + continue + need(event[0] == "scalar", "Only scalar and native events are used") + op, p, q, raw = event[1] + value, frame = F(raw), event[2] + need(frames[p] == frame, "The scalar target frame") + if op == "add": + need(p != q and frames[q] == frame, "The common scalar frame") + r.add(state[p], state[q], value) + else: + need(op == "scale" and b.unit(value), "A signed dyadic-unit scale") + state[p] = b.scale_row(state[p], value) + peak = max(peak, sum(abs(v) for v in state[p].values())) + for v in state[p].values(): + denominator = v.denominator + need(not denominator & (denominator - 1), "Every content coefficient is dyadic") + height = max(height, denominator.bit_length() - 1) + need(frames == word["final"], "Every final frame") + need(state == expected + r.identity(640)[224:], "All640 independent complex inputs") + need(state[224:] == r.identity(640)[224:], "All416 arbitrary auxiliary fields") + profile = Counter(e[4] for e in word["events"] if e[0] == "native") + direct = sum(e[0] == "native" and e[5] == "direct-full" for e in word["events"]) + price = lambda events: r.price([e[1] for e in events if e[0] == "scalar"]) + return { + "all_input_columns": 640, "unchanged_arbitrary_auxiliaries": 416, + "native_profile": dict(sorted(profile.items())), + "native_mass": sum(k * v for k, v in profile.items()), + "native_children": sum(profile.values()), + "native_side_map_upper_bound": 2 * (sum(profile.values()) - direct), + "input_views": len(word["input_views"]), "output_views": len(word["output_views"]), + "scalar": price(word["events"]), + "scalar_stages": {name: price(word["events"][start:end]) + for name, (start, end) in word["stage_ranges"].items()}, + "content_row_one_norm": str(peak), "binary_height": height, + "owned_fields": 0, "private_fields": 0, "odd_divisions": 0, + } + + +def conjugate(matrix, permutation): + result = [{} for _ in matrix] + for p, row in enumerate(matrix): + result[permutation[p]] = {permutation[j]: v for j, v in row.items()} + return result + + +def dual_word(source, permutation): + result = deepcopy(source) + for event in result["events"]: + if event[0] == "native": + event[1] = permutation[event[1]] + else: + op, p, q, c = event[1] + event[1] = ([op, permutation[q], permutation[p], str(-F(c))] if op == "add" + else [op, permutation[p], None, str(1 / F(c))]) + for key in ("start", "final"): + result[key] = [source[key][permutation[p]] for p in range(640)] + need(result[key] == source[key], "The selected endpoint frames are symmetric") + for view in result["input_views"]: + view["field"] = permutation[view["field"]] + result["input_views"].sort(key=lambda v: v["field"]) + original = {view["field"]: view for view in source["input_views"]} + for view in result["input_views"]: + need(all(view[k] == original[view["field"]][k] + for k in ("port", "frame", "left", "right", "rank")), + "The complete input adapter stays on its actual same-port field") + need(all(permutation[112 + v["port"]] == 112 + v["port"] + for v in result["output_views"]), "Every ordinary output view is fixed") + result["wire_permutation"] = {str(p): q for p, q in enumerate(permutation) if p != q} + return result + + +def wrap_metric(word, pre, post, permutation): + result = deepcopy(word) + def bind(tape, frames): + return [["scalar", [op, permutation[p], None, c], frames[permutation[p]]] + for op, p, q, c in tape] + prefix, suffix = bind(pre, result["start"]), bind(post, result["final"]) + events = result["events"] + result["events"] = prefix + events + suffix + result["stage_ranges"] = { + "metric_input": [0, len(prefix)], + **{name: [start + len(prefix), end + len(prefix)] + for name, (start, end) in result["stage_ranges"].items()}, + "metric_output": [len(prefix) + len(events), len(result["events"])], + } + return result + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for name in PINS: + read(name) + first, paired = json.loads(read("code")), json.loads(read("paired")) + native, formation, prefix = [json.loads(read(name)) for name in ("native", "formation", "prefix")] + cyclic = json.loads(b.read("cyclic")) + parameters = {x["id"]: x for x in cyclic["parameters"]} + selected = set(first["centre_ports"]) + selected_fields = {112 + p for p in selected} + old_mode = b.rows(native["model"]["mode_response"]) + old_physical = b.rows(native["model"]["response"]) + identity = list(range(640)) + permutation = list(identity) + for p in selected: + permutation[p], permutation[112 + p] = 112 + p, p + families = { + "individual": (first["code"], first["inverse"], first["native_code"], + first["scalar_words"]["code"], first["input_metric_inverse"], first["output_metric"]), + "paired": (paired["code"], paired["inverse"], paired["native_codes"]["code"], + paired["scalar_words"]["code"], paired["input_metric_inverse"], paired["output_metric"]), + "paired_transpose": (paired["transpose"], paired["inverse_transpose"], paired["native_codes"]["transpose"], + paired["scalar_words"]["transpose"], paired["output_metric"], paired["input_metric_inverse"]), + } + providers, reports, family_data = {}, {}, {} + for family, (raw_code, raw_inverse, raw_mode, tape, raw_J, raw_G) in families.items(): + C, Ci, mode = b.rows(raw_code), b.rows(raw_inverse), b.rows(raw_mode) + J, G = b.rows(raw_J), b.rows(raw_G) + Gi = [{p: 1 / row[p]} for p, row in enumerate(G)] + pre = m.diagonal_word(J) + m.diagonal_word(Gi, 112) + post = m.diagonal_word(G) + m.diagonal_word(G, 112) + scalar_forward = m.literal_clean_word(tape, sorted(selected)) + forward = m.clean_map(C, selected) + inverse = b.replay(r.inverse_word(scalar_forward), 224)[0] + need(r.product(forward, inverse) == r.product(inverse, forward) == r.identity(224), + "Both complete content inverse orders") + literal_dual = r.transpose(inverse, 224) + converted = b.replay(pre + r.transpose_word(r.inverse_word(scalar_forward)) + post, 224)[0] + expected = { + "forward_I": forward, "forward_Q": forward, + "inverse_adjoint_Q": literal_dual, + "selected_conjugate_Q": conjugate(literal_dual, permutation[:224]), + "metric_selected_conjugate_Q": conjugate(converted, permutation[:224]), + } + formula = r.identity(224) + w = r.product(C, [{112 + p if p in selected else p: F(1)} for p in range(112)]) + for p in range(112): + formula[p] = dict(w[p]) + if p in selected: + formula[112 + p] = {p: F(-1)} + else: + r.add(formula[p], {112 + p: F(1)}, -1) + need(formula == expected["metric_selected_conjugate_Q"], "The metric-converted Bswap formula") + family_data[family] = { + "code": raw_code, "inverse": raw_inverse, "native_code": raw_mode, + "metric_input_inverse": raw_J, "metric_output": raw_G, + "metric_pre_word": pre, "metric_post_word": post, + "content_maps": {name: r.encoded(value) for name, value in expected.items()}, + } + providers[family], reports[family] = {}, {} + for provider, directions in native["providers"].items(): + original = directions["forward"] + prior_formation, prior_prefix = formation["providers"][provider], prefix["providers"][provider] + transfers = {item["event"]: item for item in original["transfer_records"]} + kept, retained, removed, retunings = [], [], [], [] + for index, event in enumerate(original["events"]): + target = event[1] if event[0] == "native" else event[1][1] + if target in selected_fields: + removed.append(index) + continue + if event[0] == "scalar" and event[1][0] == "add": + need(event[1][2] not in selected_fields, "No retained read of a removed target") + retained.append(index) + changed = deepcopy(event) + if index in transfers: + record = transfers[index] + if record["part"] == "large48": + parameter = parameters[record["parameter"]] + ports = cyclic["cyclic_carriers"][parameter["vertex"]] + p, j = ports[parameter["row"]], ports[parameter["column"]] + old_coefficient = old_mode[p][j] + else: + p, j = record["target_port"], record["source_port"] + old_coefficient = old_physical[p][j] + need(p not in selected and changed[1][0] == "add", "An ordinary transfer slot") + value = F(changed[1][3]) * mode[p].get(j, F(0)) / old_coefficient + changed[1][3] = str(value) + retunings.append({"original_event": index, "mode_target": p, "mode_source": j, + "coefficient": str(value)}) + if not value: + continue + kept.append(changed) + removed_profile = Counter(original["events"][i][4] for i in removed + if original["events"][i][0] == "native") + need(len(removed) == 250 and removed_profile == {1: 128}, "The full sixteen-path removal census") + used = {e[5] for e in kept if e[0] == "native"} + recipes = {key: deepcopy(original["native_recipes"][key]) for key in used} + source_views = {v["port"]: v for v in prior_formation["input_views"]} + output_views = [deepcopy(v) for v in prior_formation["output_views"] if v["port"] not in selected] + need(len(output_views) == 96, "Every ordinary output view") + providers[family][provider], reports[family][provider] = {}, {} + for entry in ("I", "Q"): + word = { + "frames": deepcopy(original["frames"]), "start": list(original["start"]), + "final": list(original["final"]), "events": deepcopy(kept), + "native_recipes": deepcopy(recipes), + "input_views": [{**deepcopy(v), "field": p} for p, v in sorted(source_views.items())], + "output_views": deepcopy(output_views), "retained_original_event_indices": retained, + "removed_original_event_indices": removed, "transfer_retunings": retunings, + "stage_ranges": {"retained_retuned_core": [0, len(kept)]}, + } + begin = len(word["events"]) + for p in sorted(selected): + if entry == "I": + key, old, rank = "direct-full", 0, 9 + recipe = prior_formation["native_recipes"]["capture-full"] + else: + key, old, rank = "capture-line:" + str(p), original["start"][p], 8 + recipe = prior_prefix["native_recipes"][key] + word["start"][112 + p] = old + word["input_views"].append({**deepcopy(source_views[p]), "field": 112 + p, + "role": "selected_target"}) + word["native_recipes"][key] = deepcopy(recipe) + word["events"].append(["native", 112 + p, old, 1, rank, key]) + word["final"][112 + p] = 1 + word["stage_ranges"]["selected_progress"] = [begin, len(word["events"])] + begin = len(word["events"]) + word["events"].extend([["scalar", deepcopy(gate), 1] for gate in tape]) + word["stage_ranges"]["source_code"] = [begin, len(word["events"])] + begin = len(word["events"]) + for p in sorted(selected): + word["events"].extend([["scalar", ["add", 112 + p, p, "1"], 1], + ["scalar", ["add", p, 112 + p, "-1"], 1], + ["scalar", ["add", 112 + p, p, "1"], 1]]) + word["stage_ranges"]["signed_selected_exchanges"] = [begin, len(word["events"])] + word["input_views"].sort(key=lambda v: v["field"]) + name = "forward_" + entry + report = verify(word, expected[name]) + need(report["native_profile"] == {1: 1392, 2: 64, 3: 48, 9 if entry == "I" else 8: 16}, + "The complete sixteen-field native profile") + providers[family][provider][name], reports[family][provider][name] = word, report + for name, perm in (("inverse_adjoint_Q", identity), ("selected_conjugate_Q", permutation)): + word = dual_word(providers[family][provider]["forward_Q"], perm) + providers[family][provider][name] = word + reports[family][provider][name] = verify(word, expected[name]) + name = "metric_selected_conjugate_Q" + word = wrap_metric(providers[family][provider]["selected_conjugate_Q"], pre, post, permutation) + providers[family][provider][name] = word + reports[family][provider][name] = verify(word, expected[name]) + print(json.dumps({"family": family, "provider": provider, + "scalar": {name: result["scalar"] for name, result in reports[family][provider].items()}}, + sort_keys=True), flush=True) + payload = { + "schema": "complete-signed-sixteen-clean-native-v1", + "source_pins": {name: {"path": str(path), "sha256": pin} for name, (path, pin) in PINS.items()}, + "selected_ports": sorted(selected), "ports": native["model"]["ports"], + "families": family_data, "providers": providers, + "physical_contract": { + "input_I": "X=Q x; selectedY=z; ordinaryY=v.", + "input_Q": "X=Q x; selectedY=Q_P z; ordinaryY=v.", + "output": "AllX and selectedY have F9; ordinaryY has F9 q_R.", + "forward": "Put w=Cx. X=(-z,w_R); Y=(w_P,v+w_R).", + "raw_selected_dual": "Put w=C^-T(z,u). X=(w_P,w_R-v); Y=(-a,v).", + "metric_selected_dual": "Put w=C(z,u). X=(w_P,w_R-v); Y=(-a,v).", + "scope": "Complete local native words and local invoices. Routed composition, terminal decoding, recursive hosting, precision and supplier cost remain separate.", + }, + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for family, variants in saved["providers"].items(): + for provider, words in variants.items(): + for name, word in words.items(): + expected = b.rows(saved["families"][family]["content_maps"][name]) + need(verify(word, expected) == reports[family][provider][name], "Every complete serialized word") + bad = deepcopy(saved["providers"]["individual"]["base"]["metric_selected_conjugate_Q"]) + first_scale = next(e for e in bad["events"] if e[0] == "scalar" and e[1][0] == "scale") + first_scale[1][3] = str(-F(first_scale[1][3])) + try: + verify(bad, b.rows(saved["families"]["individual"]["content_maps"]["metric_selected_conjugate_Q"])) + except ValueError: + pass + else: + raise ValueError("A wrong metric sign was accepted") + (args.out / "SIGNED-CLEAN.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_COMPLETE_SIGNED_SIXTEEN_NATIVE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "complete_words": 30, "reports": reports, "fresh_phase_operators": 0, + "phase_scope": "Every exact native recipe and endpoint adapter is inherited by equality from independently reviewed source records.", + "negative_control": "A wrong diagonal metric sign is rejected.", + "scope": payload["physical_contract"]["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps({"status": receipt["status"], "payload": receipt["payload_decompressed_sha256"]}), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/run-normal/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..3f8c4887c8 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/run-normal/CHECKS.json @@ -0,0 +1,852 @@ +{ + "complete_words": 30, + "fresh_phase_operators": 0, + "negative_control": "A wrong diagonal metric sign is rejected.", + "payload_decompressed_sha256": "aa5c064837350c50928c984e03a3d7dffb5ab37da4510dc75607ced6166be797", + "phase_scope": "Every exact native recipe and endpoint adapter is inherited by equality from independently reviewed source records.", + "producer_sha256": "0ebb48e55bb32b67e85126df8ca1bdc1cc296df319e9c608bcd9eace4081050e", + "reports": { + "individual": { + "base": { + "forward_I": { + "all_input_columns": 640, + "binary_height": 3, + "content_row_one_norm": "26", + "input_views": 112, + "native_children": 1520, + "native_mass": 1808, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "9": 16 + }, + "native_side_map_upper_bound": 3008, + "odd_divisions": 0, + "output_views": 96, + "owned_fields": 0, + "private_fields": 0, + "scalar": 9988, + "scalar_stages": { + "retained_retuned_core": 4040, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_code": 5564 + }, + "unchanged_arbitrary_auxiliaries": 416 + }, + "forward_Q": { + "all_input_columns": 640, + "binary_height": 3, + "content_row_one_norm": "26", + "input_views": 128, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "output_views": 96, + "owned_fields": 0, + "private_fields": 0, + "scalar": 9988, + "scalar_stages": { + "retained_retuned_core": 4040, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_code": 5564 + }, + "unchanged_arbitrary_auxiliaries": 416 + }, + "inverse_adjoint_Q": { + "all_input_columns": 640, + "binary_height": 3, + "content_row_one_norm": "8", + "input_views": 128, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "output_views": 96, + "owned_fields": 0, + "private_fields": 0, + "scalar": 9988, + "scalar_stages": { + "retained_retuned_core": 4040, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_code": 5564 + }, + "unchanged_arbitrary_auxiliaries": 416 + }, + "metric_selected_conjugate_Q": { + "all_input_columns": 640, + "binary_height": 5, + "content_row_one_norm": "13", + "input_views": 128, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "odd_divisions": 0, + "output_views": 96, + "owned_fields": 0, + 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b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/FREEZE.json @@ -0,0 +1,15 @@ +{ + "files": { + "SIGNED-SIXTEEN.md": "82dc62c95fa9166dbe729a1beb5c522333f80ca9d5d70bf3f41e1aeefa4b6423", + "check_signed_sixteen.py": "7befca24a7e3fd9afccfda3f494d2a515361fdf7575751d3b690f380a6681b82", + "run-v2-normal/CHECKS.json": "6ae8129ac615b9592d613042551d08504973be5b05051ddda8e27de916918d8a", + "run-v2-normal/SIGNED-SIXTEEN.json.gz": "c3beaf9d548b8616e10cf18c4709dcb8f11c40630832500eb901cf4545b56b0b", + "run-v2-optimized/CHECKS.json": "6ae8129ac615b9592d613042551d08504973be5b05051ddda8e27de916918d8a", + "run-v2-optimized/SIGNED-SIXTEEN.json.gz": "c3beaf9d548b8616e10cf18c4709dcb8f11c40630832500eb901cf4545b56b0b" + }, + "independent_review": "pending", + "normal_optimized_byte_identical": true, + "payload_decompressed_sha256": "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c", + "scope": "Exact signed-metric16 scalar code and native support; no native service or complete supplier claim.", + "status": "FROZEN_PRODUCER_PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-COMPANION.md b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-COMPANION.md new file mode 100644 index 0000000000..57d94e3b73 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-COMPANION.md @@ -0,0 +1,62 @@ +# A pair-closed signed code and its transpose + +The first signed code leaves the selected large readers uncombined. +Its transpose has 32 ordinary mode rows outside the original vertex +blocks. The old transfer grammar does not admit those rows directly. + +This packet applies the inverse of the four selected physical pair +codes as a paid suffix. If the first code is `C`, define + +```text +Cbar = H_P^-1 C = H^-1 C_m H. +``` + +The suffix costs 80 real scalar primitives in 13 instructions. +Both `Cbar` and `Cbar^T` now have zero ordinary diagonals and the +original six-mode or eight-port block support. This statement is +checked on the actual 112-port matrices. + +The sixteen centre readers are retained in the selected row space. +Apply the actual selected pair code `H_P` to recover them. The +packet includes that recovery matrix. It does not count that +recovery as free when a caller needs the individual readers. + +The input metric `K` stays unchanged. For `Gbar=Cbar K Cbar^T`, +the eight large centre norms are now two. All physical entries of +`Gbar` remain diagonal dyadic units. Therefore + +```text +Cbar^-1 = K Cbar^T Gbar^-1, +Cbar^T Gbar^-1 Cbar = K^-1. +``` + +The second identity is the signed-metric contract for the +transpose code. A native clean service for that code can have +a literal inverse-adjoint whose mixed-source block is +`Cbar^-1`. This packet proves its scalar and support conditions; +it does not itself emit the native service. + +All four complete words pass on 640 independent complex fields. +The other 528 fields remain unchanged. + +| Word | Real scalar primitives | Instructions | Prefix row one-norm | Binary height | +| --- | ---: | ---: | ---: | ---: | +| Cbar | 5644 | 752 | 24 | 3 | +| Cbar transpose | 5644 | 752 | 8 | 3 | +| Cbar inverse | 5644 | 752 | 10 | 3 | +| Cbar inverse-transpose | 5644 | 752 | 6 | 3 | + +The checker is [check_paired_companion.py](check_paired_companion.py). +It pins the [first signed-code freeze](FREEZE.json). +Run it with `python3 -I -B` and `--out `. +The expected status is `PASS_PAIRED_SIGNED_SIXTEEN_CODE`. +The normal and `-O` outputs must match byte for byte. + +The bridge access lane requested the transpose service. This lane +found the actual support defect and supplied the paid pair suffix. +AI assistance was used. No routed inverse cancellation, terminal +decoder, or supplier improvement is asserted. + +No PR, commit, push, or publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-FREEZE.json new file mode 100644 index 0000000000..3f9b2cad18 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/PAIRED-FREEZE.json @@ -0,0 +1,15 @@ +{ + "files": { + "PAIRED-COMPANION.md": "0e481a50c821683041032663ebb67fd4fdca42c355e3926a9e36589842f94fb5", + "check_paired_companion.py": "2951594157080c07a90a9f2bb799c50c037a383c9d01c44a79ceaa0ef65be09b", + "paired-normal/CHECKS.json": "c48300c2e195b107522d167ec09e85d6d7874274298dee363d831846a9cf723c", + "paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz": "d31ddebdde5225c8dbae7f1a2899bb7d6bd598f1a6f8b59c3e05933cee17092e", + "paired-optimized/CHECKS.json": "c48300c2e195b107522d167ec09e85d6d7874274298dee363d831846a9cf723c", + "paired-optimized/PAIRED-SIGNED-SIXTEEN.json.gz": "d31ddebdde5225c8dbae7f1a2899bb7d6bd598f1a6f8b59c3e05933cee17092e" + }, + "independent_review": "pending", + "normal_optimized_byte_identical": true, + "payload_decompressed_sha256": "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1", + "scope": "Pair-closed signed code and transpose scalar words and exact native support; native service not yet asserted.", + "status": "FROZEN_PRODUCER_PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/SIGNED-SIXTEEN.md b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/SIGNED-SIXTEEN.md new file mode 100644 index 0000000000..645b87da28 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/SIGNED-SIXTEEN.md @@ -0,0 +1,251 @@ +# One signed-metric carrier for each reflection centre + +This packet gives a complete 112-field scalar code. It stores the 16 +independent readers of the new reciprocal response in 16 existing +fields. The code, its inverse, and its inverse-adjoint use only real +dyadic arithmetic. They use no extra field and no odd division. + +The physical input and output metrics are diagonal signed powers of +two. Thus a diagonal correction converts the inverse-adjoint code to +the primal code. This correction does not mix fields that have +different spatial frames. + +This is a code for the rank-16 difference `E-P`. It is not a +rank-16 code for `E-I`. The actual physical `P` is a paid field code, +not a free permutation. + +## Source and exact blocks + +The source is the actual +[reciprocal model](../../../oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz), +with decompressed SHA256 +`df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0`. +It fixes every port, pair code, block, sign, and metric. +The [checker](check_signed_sixteen.py) pins that file and the exact +arithmetic helper. The source model has eight blocks of size six +and eight blocks of size eight. + +For a block of size `n=m+2`, write its fields as +`(a0,...,a(m-1),b,c)`. Put + +```text +K = J^-1 = diag(1,...,1,-(m-2),-(m-2)), +u = (1,...,1,m-2,0)^T, +l = (-1,...,-1,1,0), +R = I + u l. +``` + +Then `l u=-2`, `K l^T=-u`, and `l K l^T=2`. +It follows that `R^2=I` and `R K R^T=K`. +The mode permutation `P` exchanges `b` and `c`, and `E=P R`. + +Use the following rows in the stated output order. Here +`s=a0+...+a(m-1)`. + +| Output | Six-mode row | Eight-mode row | +| --- | --- | --- | +| a0 | `-s+b` | `-s+b` | +| a1 | `a2-a3` | `a4+a5-b/2` | +| a2 | `a0-a1` | `a4-a5` | +| a3 | `c` | `c` | +| a4 | — | `a0-a1` | +| a5 | — | `a2-a3` | +| b | `a0+a1-a2-a3` | `a0+a1-a2-a3` | +| c | `s-2b` | `a0+a1+a2+a3+2a4+2a5-2b` | + +Let these block matrices be `C_m`. Direct row products give + +```text +n=6: C_m K C_m^T = diag(2,2,2,-2,4,-4); +n=8: C_m K C_m^T = diag(2,1,2,-4,2,2,4,-4). +``` + +Both determinants are `-8`. The first row is `l`. Every other row +annihilates `u` and has a zero diagonal entry. Thus the first row +changes sign under `R`; every other row is fixed. + +These identities also give an explicit inverse over the dyadic +ring. If the displayed Gram matrix is `G_m`, then +`C_m^-1=K C_m^T G_m^-1`. No appeal to numerical conditioning or to +an invertible rational matrix is needed. + +## Actual physical pair code + +Let `H` be the pinned pair code on the 48 large ports. It is the +identity on the other 64 ports. On each large pair, `H H^T=2I`. +The chosen large-block order is + +```text +(centre, pair_difference_a, pair_difference_b, + negative_difference, contrast, negative). +``` + +The centre, negative-difference, contrast, and negative positions +each form complete physical pair matchings. The other two +positions both have output norm two. Therefore the mode input and +output metrics are constant on every ordinary physical pair. + +Let `H_R^-1` undo `H` on the ordinary pairs and act as the identity +on the selected pairs. Define + +```text +C = H_R^-1 C_m H. +``` + +This choice keeps each selected large row equal to its individual +reader `l H`; it does not mix the two centre readers in one pair. +The selected small row is `l`. + +The exact selected ports, in reader order, are + +```text +0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23. +``` + +Let physical `K=H^-1 K_m H`. It is diagonal. The checker proves + +```text +C K C^T = G, +C^-1 = K C^T G^-1, +C^-T = G^-1 C K. +``` + +The physical `K` has 80 entries `1`, 16 entries `-2`, and 16 entries +`-4`. The physical `G` has the following entries: + +| Value | Count | +| --- | ---: | +| -4 | 24 | +| -2 | 8 | +| 1 | 8 | +| 2 | 48 | +| 4 | 24 | + +The eight large centre norms are four. The eight small centre +norms are two. All 16 selected rows equal the source's actual +`reflection_L` rows, in the same order. + +With `Z` equal to `-1` on the selected fields and `1` elsewhere, + +```text +C R = Z C, +C R C^-1 = Z, +C P E = C R. +``` + +The last identity keeps the order of all factors. It does not +identify `C E` with `C`. + +## Native support + +The checker verifies every ordinary diagonal of both `C` and +`C R`, in the physical chart and in the actual native mode chart. +All are zero. Every ordinary mode row stays within its original +six-mode vertex or eight-port clique. + +Consequently the complete dense cyclic/clique transfer grammar +has a slot for every required ordinary transfer of `C` or `C R`. +This is a support statement. It does not by itself emit a new +native word, prove a target phase, or price a changed endpoint. +In particular, a native word for `E=P R` cannot be reinterpreted +as a word for `R` without a separate operation. + +The proposed clean service emits the ordinary response `C_R` +directly, removes the 16 selected target paths, advances those +targets to FULL, applies `C` to the completed source bank, and +performs the selected signed exchanges. A complete native +emission must check this sequence separately. + +## Complete scalar words and price + +The word applies the actual 24 pair codes, then the 16 block +codes, then undoes the pair code on the 20 ordinary pairs. +The block factorization uses only dyadic-unit pivots. Every row +exchange, ADD, sign, and scale is present in the word. + +All words pass exact replay on 640 independent complex fields. +The 528 fields outside the coded bank remain unchanged. + +| Word | Real scalar primitives | Instructions | Prefix row one-norm | Binary height | +| --- | ---: | ---: | ---: | ---: | +| C | 5564 | 739 | 24 | 3 | +| C inverse | 5564 | 739 | 9 | 3 | +| Literal inverse-adjoint | 5564 | 739 | 5 | 3 | +| K, then C, then G inverse | 6092 | 875 | 32 | 3 | + +These are exact scalar-word bounds. They do not include the +internal arithmetic of a recursive native child or rounding. +All events are complex-linear real scalar operations. Each +event is valid at a common complex spatial frame. + +## Diagonal conversion of the complete clean dual + +Write the two banks as `x=(a,u)` and `y=(z,v)`, with the first +coordinate set equal to the selected 16 fields. Define + +```text +w = Cx; +F_C(x,y) = ((-z,w_R),(w_P,v+w_R)). +``` + +This map accepts arbitrary `x` and `y`; no baseline is zero. +For `D(G)=diag(G,G)`, the exact complete identity is + +```text +D(G) F_C^-T diag(J,G^-1)(x,y) + = ((-z,w_R-v),(w_P,v)). +``` + +The checker proves this identity on all 640 independent fields +using the literal same-order inverse-transpose of the clean +scalar word. It does not transpose a desired endpoint and +assume that the implementation follows. + +Conjugate by the selected-bank exchange at both endpoints. +The result is + +```text +w = C(z,u); +Bswap_C(x,y) = ((w_P,w_R-v),(-a,v)). +``` + +The two metric wrappers cost 1264 real scalar primitives before +any fusion. Each wrapper scales one field at a time. Thus it +commutes with that field's spatial frame. It does not require a +common frame across distinct fields. + +This scalar identity does not grant the selected-bank exchange +at arbitrary native endpoints. The intended Q-entry native +service has equal Q frames on the two selected inputs and equal +FULL frames on the two selected outputs. A complete native +packet must bind that fact and every adapter to its field. + +## Reproduction, credit, and limits + +Run from the workspace root, with fresh output directories: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_signed_sixteen.py --out +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_signed_sixteen.py --out +``` + +The expected status is `PASS_SIGNED_SIXTEEN_COMPLETION`. +Normal and optimized payloads and receipts match byte for byte. + +The root lane supplied the reciprocal reflection family. The +oblique lane bound its actual physical placement and metric. +The bridge review lane supplied a distinct signed-metric basis +and a general extension. The cover lane derived the complete +clean-dual conversion. This lane supplied the stated sparse +bases, paid physical code, and exact replay. AI assistance was +used. + +This packet supplies a full scalar code and exact native +support. It leaves the changed native service, routed caller, +terminal decoder, finite-precision guard, recursive helper +hosting, and complete supplier cost open. It does not allocate +the 416 auxiliary roles as a free centre cache. + +No PR, commit, push, or publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_paired_companion.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_paired_companion.py new file mode 100644 index 0000000000..7a55b27ba6 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_paired_companion.py @@ -0,0 +1,139 @@ +#!/usr/bin/env python3 +"""Check the pair-closed code and its native transpose support.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +PINS = { + "helper": (HERE / "check_signed_sixteen.py", + "7befca24a7e3fd9afccfda3f494d2a515361fdf7575751d3b690f380a6681b82"), + "source": (HERE / "run-v2-normal/SIGNED-SIXTEEN.json.gz", + "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c"), + "freeze": (HERE / "FREEZE.json", + "8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2"), +} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned input " + name) + return raw + + +read("helper") +spec = importlib.util.spec_from_file_location("paired_signed_code", PINS["helper"][0]) +m = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = m +spec.loader.exec_module(m) +b, r = m.b, m.r + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for name in PINS: + read(name) + source = json.loads(read("source")) + model = json.loads(m.read("response")) + H, Hi = b.rows(source["pair_code"]), b.rows(source["pair_code_inverse"]) + K, J = b.rows(source["input_metric"]), b.rows(source["input_metric_inverse"]) + selected = set(source["centre_ports"]) + selector_inverse = r.identity(112) + extra = [] + for pair in model["pair_codes"]: + if set(pair["ports"]) <= selected: + ports = pair["ports"] + local = [{j: F(c) for j, c in enumerate(row) if c} for row in pair["matrix"]] + extra += r.inverse_word(b.factor(local, ports)) + for p in ports: + selector_inverse[p] = dict(Hi[p]) + C = r.product(selector_inverse, b.rows(source["code"])) + need(C == r.product(r.product(Hi, b.rows(source["mode_code"])), H), + "The complete physical pair conjugation") + Ct = r.transpose(C, 112) + G = r.product(r.product(C, K), Ct) + need(all(set(row) == {p} and b.unit(row[p]) for p, row in enumerate(G)), + "The new physical metric is diagonal") + Gi = [{p: 1 / row[p]} for p, row in enumerate(G)] + Ci = r.product(r.product(K, Ct), Gi) + Cti = r.transpose(Ci, 112) + need(r.product(C, Ci) == r.product(Ci, C) == r.identity(112), "Both code inverse orders") + need(r.product(r.product(Ct, Gi), C) == J, "The transpose metric identity") + groups = [set(block["ports"]) for block in model["blocks"]] + codes = {"code": C, "transpose": Ct} + native_codes = {} + for name, matrix in codes.items(): + native = r.product(r.product(H, matrix), Hi) + native_codes[name] = native + need(all(not matrix[p].get(p, 0) and not native[p].get(p, 0) + and any(p in group and set(native[p]) <= group for group in groups) + for p in range(112) if p not in selected), + "Every ordinary row has native block support and zero diagonal") + recovery = r.identity(112) + for p in selected: + recovery[p] = dict(H[p]) + need([r.product(recovery, C)[p] for p in source["centre_ports"]] + == b.rows(model["reflection_L"]), "The complete centre recovery") + word = source["scalar_words"]["code"] + extra + words = {"code": word, "transpose": r.transpose_word(word), + "inverse": r.inverse_word(word), + "inverse_transpose": r.transpose_word(r.inverse_word(word))} + expected = {"code": C, "transpose": Ct, "inverse": Ci, "inverse_transpose": Cti} + reports = {} + for name, tape in words.items(): + actual, report = b.replay(tape, 640) + need(actual[:112] == expected[name] and actual[112:] == r.identity(640)[112:], + "All640 exact columns of each complete word") + reports[name] = report + payload = { + "schema": "paired-signed-sixteen-code-v1", + "source_pins": {name: {"path": str(path), "sha256": pin} for name, (path, pin) in PINS.items()}, + "centre_ports": source["centre_ports"], "ordinary_ports": source["ordinary_ports"], + "blocks": model["blocks"], "pair_code": source["pair_code"], + "pair_code_inverse": source["pair_code_inverse"], + "code": r.encoded(C), "transpose": r.encoded(Ct), + "inverse": r.encoded(Ci), "inverse_transpose": r.encoded(Cti), + "native_codes": {name: r.encoded(matrix) for name, matrix in native_codes.items()}, + "input_metric": r.encoded(K), "input_metric_inverse": r.encoded(J), + "output_metric": r.encoded(G), "output_metric_inverse": r.encoded(Gi), + "centre_recovery": r.encoded(recovery), "selected_pair_inverse_word": extra, + "scalar_words": words, + "scope": "Complete pair-closed scalar code, its transpose, and exact native support. No native service or routed caller is asserted.", + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + (args.out / "PAIRED-SIGNED-SIXTEEN.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_PAIRED_SIGNED_SIXTEEN_CODE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "all_input_columns": 640, "unchanged_outside_fields": 528, + "selected_fields": 16, "selected_pair_inverse_price": r.price(extra), + "reports": reports, + "output_metric_counts": dict(Counter(str(row[p]) for p, row in enumerate(G))), + "scope": payload["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_signed_sixteen.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_signed_sixteen.py new file mode 100644 index 0000000000..a6ba406a19 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_signed_sixteen.py @@ -0,0 +1,281 @@ +#!/usr/bin/env python3 +"""Check a complete code with one signed-metric carrier per centre.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[2] +PINS = { + "arithmetic": ( + HERE.parent / "metric-completion-20261020/check_completion.py", + "854d8be88966bfdd279f9e208927f21c34d4e3fe09a19be2b7d180334f178084"), + "response": ( + LANES / "oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz", + "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0"), +} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned source " + name) + return raw + + +read("arithmetic") +spec = importlib.util.spec_from_file_location("signed_sixteen_arithmetic", PINS["arithmetic"][0]) +b = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = b +spec.loader.exec_module(b) +r = b.r + + +def local_code(n): + if n == 6: + dense = [ + [-1, -1, -1, -1, 1, 0], + [0, 0, 1, -1, 0, 0], + [1, -1, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 1], + [1, 1, -1, -1, 0, 0], + [1, 1, 1, 1, -2, 0], + ] + gram = [2, 2, 2, -2, 4, -4] + else: + need(n == 8, "The actual six-mode and eight-mode blocks") + dense = [ + [-1, -1, -1, -1, -1, -1, 1, 0], + [0, 0, 0, 0, 1, 1, F(-1, 2), 0], + [0, 0, 0, 0, 1, -1, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 1], + [1, -1, 0, 0, 0, 0, 0, 0], + [0, 0, 1, -1, 0, 0, 0, 0], + [1, 1, -1, -1, 0, 0, 0, 0], + [1, 1, 1, 1, 2, 2, -2, 0], + ] + gram = [2, 1, 2, -4, 2, 2, 4, -4] + matrix = [{j: F(c) for j, c in enumerate(row) if c} for row in dense] + return matrix, [{i: F(c)} for i, c in enumerate(gram)] + + +def diagonal_word(matrix, offset=0): + return [["scale", offset + i, None, str(row[i])] + for i, row in enumerate(matrix) if row[i] != 1] + + +def clean_map(code, centres): + selected = set(centres) + matrix = r.identity(224) + for p in range(112): + if p in selected: + matrix[p] = {112 + p: F(-1)} + matrix[112 + p] = dict(code[p]) + else: + matrix[p] = dict(code[p]) + matrix[112 + p] = {112 + p: F(1)} + r.add(matrix[112 + p], code[p], 1) + return matrix + + +def literal_clean_word(code_word, centres): + word = list(code_word) + selected = set(centres) + for p in range(112): + if p not in selected: + word.append(["add", 112 + p, p, "1"]) + for p in centres: + word.extend([["add", 112 + p, p, "1"], + ["add", p, 112 + p, "-1"], + ["add", 112 + p, p, "1"]]) + return word + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + source = json.loads(read("response")) + centres = source["centre_ports"] + selected = set(centres) + need(len(selected) == 16, "Sixteen actual centre fields") + H = b.rows(source["pair_code"]) + Hi = b.rows(source["pair_code_inverse"]) + K = b.rows(source["physical"]["inverse_J"]) + J = b.rows(source["physical"]["J"]) + R = b.rows(source["physical"]["R"]) + E = b.rows(source["physical"]["E"]) + P = b.rows(source["physical"]["P"]) + Km = b.rows(source["mode"]["inverse_J"]) + Cm, Gm = r.identity(112), r.identity(112) + mode_word, blocks = [], [] + for block in source["blocks"]: + ports = block["ports"] + local, gram = local_code(len(ports)) + local_k = r.restrict(Km, ports) + need(r.product(r.product(local, local_k), r.transpose(local, len(ports))) == gram, + "The exact local diagonal metric") + u = [F(v) for v in block["u"]] + need(all(sum(c * u[j] for j, c in row.items()) == (F(-2) if i == 0 else F(0)) + for i, row in enumerate(local)), "The centre and ordinary actions on u") + need(all(not local[i].get(i, 0) for i in range(1, len(ports))), + "Every ordinary local diagonal is zero") + for i, p in enumerate(ports): + Cm[p] = {ports[j]: c for j, c in local[i].items()} + Gm[p] = {p: gram[i][i]} + word = b.factor(local, ports) + mode_word += word + blocks.append({ + **block, "code": r.encoded(local), "metric": r.encoded(gram), + "determinant": str(r.determinant(local)), + "scalar_word": word, "scalar_price": r.price(word), + }) + hword, ordinary_hword = [], [] + for pair in source["pair_codes"]: + ports = pair["ports"] + matrix = [{j: F(c) for j, c in enumerate(row) if c} + for row in pair["matrix"]] + word = b.factor(matrix, ports) + hword += word + need(not set(ports) & selected or set(ports) <= selected, + "Selected physical pairs are complete") + if not set(ports) & selected: + ordinary_hword += word + Horinv = r.identity(112) + for p in range(112): + if p not in selected: + Horinv[p] = dict(Hi[p]) + C = r.product(r.product(Horinv, Cm), H) + Ct = r.transpose(C, 112) + G = r.product(r.product(C, K), Ct) + need(all(set(row) == {p} and b.unit(row[p]) for p, row in enumerate(G)), + "The physical output metric is diagonal with dyadic units") + need(all(set(row) == {p} and b.unit(row[p]) for p, row in enumerate(K)), + "The physical input metric is diagonal with dyadic units") + Gi = [{p: 1 / row[p]} for p, row in enumerate(G)] + Ci = r.product(r.product(K, Ct), Gi) + Cd = r.product(r.product(Gi, C), K) + need(r.product(C, Ci) == r.product(Ci, C) == r.identity(112), + "Both full physical inverse orders") + need(Cd == r.transpose(Ci, 112), "The exact inverse-adjoint identity") + L = b.rows(source["reflection_L"]) + need([C[p] for p in centres] == L, "The sixteen stored centre readers") + need(r.rank(L, 112) == 16, "All sixteen independent centre readers") + CR = r.product(C, R) + ZC = [b.scale_row(row, -1 if p in selected else 1) for p, row in enumerate(C)] + need(CR == ZC, "The completed code diagonalizes the reflection") + need(r.product(r.product(C, P), E) == CR, "The ordered C P E identity") + Cnative = r.product(r.product(H, C), Hi) + CRnative = r.product(r.product(H, CR), Hi) + need(all(not C[p].get(p, 0) and not CR[p].get(p, 0) + and not Cnative[p].get(p, 0) and not CRnative[p].get(p, 0) + for p in range(112) if p not in selected), "Every ordinary native and physical diagonal is zero") + mode_groups = [set(block["ports"]) for block in source["blocks"]] + need(all(any(p in group and set(Cnative[p]) <= group for group in mode_groups) + for p in range(112) if p not in selected), "All ordinary transfers use their admitted mode block") + code_word = hword + mode_word + r.inverse_word(ordinary_hword) + inverse_word = r.inverse_word(code_word) + literal_dual = r.transpose_word(r.inverse_word(code_word)) + wrapped_dual = diagonal_word(K) + code_word + diagonal_word(Gi) + words = { + "code": code_word, "inverse": inverse_word, + "literal_inverse_adjoint": literal_dual, + "diagonal_inverse_adjoint": wrapped_dual, + } + expected = {"code": C, "inverse": Ci, "literal_inverse_adjoint": Cd, + "diagonal_inverse_adjoint": Cd} + reports = {} + for name, word in words.items(): + actual, report = b.replay(word, 640) + need(actual[:112] == expected[name] and actual[112:] == r.identity(640)[112:], + "All640 input columns and528 unchanged outside fields") + reports[name] = report + fm = clean_map(C, centres) + fw = literal_clean_word(code_word, centres) + need(b.replay(fw, 640)[0][:224] == fm, "The complete scalar clean map") + fd = r.transpose_word(r.inverse_word(fw)) + pre = diagonal_word(J) + diagonal_word(Gi, 112) + post = diagonal_word(G) + diagonal_word(G, 112) + converted = pre + fd + post + converted_map = r.identity(224) + for p in range(112): + if p in selected: + converted_map[p] = {112 + p: F(-1)} + converted_map[112 + p] = dict(C[p]) + else: + converted_map[p] = dict(C[p]) + r.add(converted_map[p], {112 + p: F(1)}, -1) + converted_map[112 + p] = {112 + p: F(1)} + need(b.replay(converted, 640)[0][:224] == converted_map, + "The complete diagonal-converted clean inverse-adjoint") + swap = {p: 112 + p for p in selected} + swap.update({112 + p: p for p in selected}) + conjugated = [[op, swap.get(t, t), swap.get(s, s) if s is not None else None, c] + for op, t, s, c in converted] + bmap = r.identity(224) + mixed = [{(112 + p if p in selected else p): F(1)} for p in range(112)] + w = r.product(C, mixed) + for p in range(112): + bmap[p] = dict(w[p]) + if p in selected: + bmap[112 + p] = {p: F(-1)} + else: + r.add(bmap[p], {112 + p: F(1)}, -1) + need(b.replay(conjugated, 640)[0][:224] == bmap, + "The complete selected-bank conjugate with diagonal metric conversion") + payload = { + "schema": "signed-sixteen-complete-centre-code-v1", + "source_pins": {name: {"path": str(path), "sha256": pin} for name, (path, pin) in PINS.items()}, + "centre_ports": centres, "ordinary_ports": sorted(set(range(112)) - selected), + "blocks": blocks, "pair_code": source["pair_code"], + "pair_code_inverse": source["pair_code_inverse"], + "mode_code": r.encoded(Cm), "code": r.encoded(C), "inverse": r.encoded(Ci), + "inverse_adjoint": r.encoded(Cd), "native_code": r.encoded(Cnative), + "coded_reflection": r.encoded(CR), "native_coded_reflection": r.encoded(CRnative), + "input_metric": r.encoded(K), "input_metric_inverse": r.encoded(J), + "output_metric": r.encoded(G), "output_metric_inverse": r.encoded(Gi), + "reflection_readers": source["reflection_L"], + "scalar_words": words, + "clean_metric_wrappers": {"pre": pre, "post": post}, + "clean_maps": {"forward": r.encoded(fm), "converted_inverse_adjoint": r.encoded(converted_map), + "selected_conjugate": r.encoded(bmap)}, + "scope": "Complete scalar code and exact native support. Native service, routed caller, recursive precision and hosting remain separate.", + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + need(b.replay(saved["scalar_words"]["code"], 640)[0][:112] == C, "Serialized code replay") + (args.out / "SIGNED-SIXTEEN.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_SIGNED_SIXTEEN_COMPLETION", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), + "centre_count": 16, "ordinary_count": 96, "all_matrix_columns": 112, + "all_scalar_columns": 640, "all_clean_columns": 640, + "reports": reports, "metric_wrapper_price": r.price(pre + post), + "input_metric_counts": dict(Counter(str(row[p]) for p, row in enumerate(K))), + "output_metric_counts": dict(Counter(str(row[p]) for p, row in enumerate(G))), + "local_determinants": dict(Counter(block["determinant"] for block in blocks)), + "scope": payload["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/paired-normal/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/paired-normal/CHECKS.json new file mode 100644 index 0000000000..fff17341bf --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/paired-normal/CHECKS.json @@ -0,0 +1,43 @@ +{ + "all_input_columns": 640, + "output_metric_counts": { + "-2": 8, + "-4": 24, + "1": 8, + "2": 56, + "4": 16 + }, + "payload_decompressed_sha256": "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1", + "producer_sha256": "2951594157080c07a90a9f2bb799c50c037a383c9d01c44a79ceaa0ef65be09b", + "reports": { + "code": { + "binary_height": 3, + "instructions": 752, + "prefix_row_one_norm": "24", + "scalar": 5644 + }, + "inverse": { + "binary_height": 3, + "instructions": 752, + "prefix_row_one_norm": "10", + "scalar": 5644 + }, + "inverse_transpose": { + "binary_height": 3, + "instructions": 752, + "prefix_row_one_norm": "6", + "scalar": 5644 + }, + "transpose": { + "binary_height": 3, + "instructions": 752, + "prefix_row_one_norm": "8", + "scalar": 5644 + } + }, + "scope": "Complete pair-closed scalar code, its transpose, and exact native support. No native service or routed caller is asserted.", + "selected_fields": 16, + "selected_pair_inverse_price": 80, + "status": "PASS_PAIRED_SIGNED_SIXTEEN_CODE", + "unchanged_outside_fields": 528 +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..17f390cb0e03e4538574b1c11cb7d4622453baeb GIT binary patch literal 17741 zcmZsCV{|4>v~_G}V%xUOiESqn+s4Fs;wPEdwry)-+qOA3@49z=zrOx)*6OaV+WVZ^ zUA3y}G*L7R$bT2uze_*;xJ~KA&5nRjrRhnUBd*oB=8<7RPh(HJ-kV&KwJoO3B&MaBy%?aZrz$JZiQAd_PO3J+?o0zi+O( zT{bt*JFcCDKBo@{Qb#5>J?5t;-k;~UuVcE-5B{b7JHPI}zS{Ehba`#DITw-_y6*1q z`FHa&Kp`LS^>BMT@$uC?(L7N$QSG9CRr1R}eY?HO{C(Qa;p6r0E|d(r}n_ 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Read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md before any future PR description.", + "schema": "unitary-24-clean-native-freeze-v1", + "scope": "Complete local native clean unitary interface and its literal inverse-adjoint. Routed composition, recursive hosting, precision and complete supplier cost remain separate.", + "status": "PRODUCER_FROZEN_INDEPENDENT_NATIVE_REVIEW_PENDING" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/UNITARY-CLEAN.md b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/UNITARY-CLEAN.md new file mode 100644 index 0000000000..e69aea4d8c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/UNITARY-CLEAN.md @@ -0,0 +1,251 @@ +# A complete clean unitary centre interface + +The actual 24-coordinate unitary code now has complete native forward, +inverse-adjoint, and selected-conjugate interfaces. The packet emits +eight words: two forward entry types and two dual words for each of +the base and extra providers. + +Every word costs 16,020 real scalar primitives. The Q-entry words have +native profile + +```text +1328 H1 + 64 H2 + 48 H3 + 24 H8, +``` + +with 1,464 children and rank mass 1,792. The I-entry forward replaces +the 24 H8 calls by 24 H9 calls, for rank mass 1,816. Each word +accepts all 640 independent complex inputs and restores the 416 +arbitrary helper fields. No extra field or odd division is used. + +These are complete local native interfaces. They do not establish a +routed caller, a recursive helper host, a precision bound, or a +complete supplier improvement. + +## The exact forward contract + +Let P be the stored set of 24 selected ports and let R be its +88-port complement. Let C be the frozen actual unitary code: + +```text +C* C = C C* = I, +C^-* = C, +(C E)_R = C_R. +``` + +All ordinary mode diagonals of C vanish. The selected set is closed +under each physical pair code. The selected small ports contain the +eight nonzero diagonals of C. + +The input is X=Qx. The target has Y_P=z for I entry and Y_P=Q_P z +for Q entry; its ordinary part is Y_R=v. All these contents and +all helper contents are arbitrary. + +Put w=Cx. The forward content map is + +```text +X_P = -z, X_R = w_R, +Y_P = w_P, Y_R = v+w_R. +``` + +All X fields and selected Y fields end in F9. Each ordinary Y field +ends in F9 q_p. Thus the selected code coordinates have no borrowed +target contribution. The old selected target values are retained, +with a minus sign, on selected X. + +The original sixteen centre readers are recovered from w_P by the +frozen decoder V C*. The map also retains all contrast information. +It does not overwrite or discard independent input coordinates. + +## The complete forward word + +Start with the pinned rank-sixteen native provider. Remove every +event whose target is a selected Y field. This removes 380 events, +including 192 H1 calls. No retained event reads a selected Y field. +The retained X paths are complete and unchanged. + +Retune each retained transfer slot to the corresponding ordinary +mode coefficient of C. A zero coefficient removes that scalar +transfer. Every nonzero coefficient stays in its original six-mode +vertex or small clique, so it uses an existing equal-frame transfer +slot. The ledger records the old event index, exact source and target +mode, and new Gaussian coefficient. + +The resulting ordinary response is C_R x. Advance each selected Y +baseline directly to FULL. For I entry this is the existing exact +H9 kernel with identity wrappers. For Q entry it is the exact +canonical line-to-FULL H8 operator. + +After the retained sweep and selected progress, all 112 X fields +are at the same FULL frame. Apply the complete scalar word for C +to X. Then, for each selected port, execute + +```text +Y_p += X_p; +X_p -= Y_p; +Y_p += X_p. +``` + +These three complex unit ADDs map (X_p,Y_p) to (-Y_p,X_p). +They cost 24 real scalar primitives per port. + +The complete scalar bill is + +```text +retained and retuned core 7,392 +complete source code C 8,052 +24 signed exchanges 576 +total 16,020. +``` + +The I-entry word has 112 explicit input views, 88 explicit ordinary +output views, and at most 2,880 native side maps. Its 24 direct FULL +children have identity wrappers. Each Q-entry word has 136 input +views, 88 output views, and at most 2,928 native side maps. +These are complete local map counts; they do not make map or helper +hosting cost zero. + +## Complex scalar macros + +For a Gaussian coefficient a+ib, one transfer is the contiguous +real-component word + +```text +target.real += a source.real +target.real -= b source.imag +target.imag += b source.real +target.imag += a source.imag. +``` + +Zero terms are omitted. Source and target are distinct fields. +The checker verifies the complete real matrix of this word against +the stated complex ADD, on every real input component. + +An individual component ADD need not commute with a complex native +frame. Therefore the payload stores the complete Gaussian transfer +as one macro. It stores the complete source code C as a second type +of contiguous macro. No native event or address map can occur inside +either macro. The common complex frame is checked only at macro +entry and exit. + +Each completed macro is complex-linear and commutes with the common +complex frame on its fields. Its implementation uses the stated +real scalar instructions; no complex multiply primitive is hidden. +The full C macro is checked on all 224 active real coordinates. + +The receipt gives two different local bounds. At complete macro +endpoints, the largest content coefficient component one-norm is +10 for the forward word and 5 for the dual words. Within one macro, +the largest component one-norm relative to that macro's physical +input fields is 16 for the forward word and 7 for the dual words. +These quantities are not a complete recursive rounding bound. + +## The literal inverse-adjoint + +For a chronological word M=G_n ... G_1, + +```text +M^-* = G_n^-* ... G_1^-*. +``` + +Thus the chronological order stays the same. Each native operator +and each monomial view is unitary, so its inverse-adjoint is the +same physical operator. + +For a real scalar ADD, transpose its source and target and negate +its coefficient. For a real scale, use its reciprocal. For each +complete component macro, apply those rules to its component +instructions in the same order. The macro boundary is preserved. +The complete Gaussian ADD then has coefficient -conjugate(a+ib) +on the transposed source-target pair. + +The complete C macro has inverse-adjoint C. The checker verifies +this at the real-component instruction level; it does not merely +replace its descriptor by the matrix identity. + +The resulting inverse-adjoint content is + +```text +w = Cx, +X_P = -z, X_R = w_R-v, +Y_P = w_P, Y_R = v. +``` + +Now conjugate the whole Q-entry word by the selected-bank +permutation S. At each selected port, both input fields have Q_p +and both output fields have FULL. Therefore the permutation is an +exact wire relabeling. Every event target, component index, input +view, and endpoint frame is rebound. No unpriced physical swap is +inserted. + +With x=(a,u), the selected-conjugate map is + +```text +w = C(z,u), +X_P = w_P, X_R = w_R-v, +Y_P = -a, Y_R = v. +``` + +This is the complete Bswap contract. It is not the earlier +triangular-reader formula. The unitary code now acts on the mixed +cohort consisting of selected Y and ordinary X. + +## Phase checks and inherited operators + +All retained native recipes, ordered frame bases, source input +views, and ordinary output views are exact records from the pinned +reviewed provider and direct-formation packet. The 88 ordinary +output records are a subset of the accepted 96-record table. + +The direct H9 recipe is inherited from the accepted identity-wrapper +refinement. Sixteen Q-to-FULL checks are fresh: eight new selected +large ports in each provider. Each check compares the exact Pauli +action and an exact Gaussian-dyadic reference state, which fixes the +global phase. The other selected H8 recipes are exact copies of the +accepted line-entry records. + +No physical phase is inferred from the scalar response. The +inverse-adjoint keeps every native phase record unchanged and +checks its rebound target and ordered entry/exit frames. + +The one-alphabet native identities lift by tensor products. The +complete scalar codes apply entrywise with fixed scalar +coefficients at each field width. This does not replace a tensor +native operator by a one-bit scalar polynomial or an O(f) sequence +of field scans. + +## Validation and remaining work + +The producer checks both providers and all four word types. Each +complete complex-linear map has all 640 independent complex +columns, equivalently all 1,280 real columns. Each component macro +is checked independently as a real matrix before it is applied to +the complete content state. + +Both inverse orders of the forward and selected-conjugate maps +pass. All final frames and all 416 helper outputs pass. The complete +serialized words are replayed. A wrong atomic component ADD is +rejected in every word. + +Run in new directories: + +```text +python3 emit_unitary_clean.py --out +python3 -O emit_unitary_clean.py --out +``` + +Normal and optimized payloads and receipts are byte-identical. +Independent native review is separate. The code and its scalar +word have an independent review; that review alone does not +certify this new native service. + +The root lane proposed the unitary completion target and the +coordinate lower bound. This lane constructed the actual 24-field +completion and the complete native words. The existing cyclic +providers supplied the transfer geometry and phases. The native +review lane identified the need for explicit complete component +macro boundaries. The controller and cover lanes study routed +caller composition. AI assistance was used throughout. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/emit_unitary_clean.py b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/emit_unitary_clean.py new file mode 100644 index 0000000000..e0dc6ac1b5 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/emit_unitary_clean.py @@ -0,0 +1,471 @@ +#!/usr/bin/env python3 +"""Emit a clean 24-coordinate unitary centre interface.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +PARENT = HERE.parent +LANES = PARENT.parents[1] +PINS = { + "code_helper": (PARENT / "metric-completion-20261020/check_twenty_four.py", + "5eb67764619b90a4dc2dbcf80466823dfe0a81f7872a0a334193f101249018ee"), + "code": (PARENT / "metric-completion-20261020/twenty-four-v2-normal/UNITARY-24.json.gz", + "9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c"), + "code_freeze": (PARENT / "metric-completion-20261020/TWENTY-FOUR-FREEZE.json", + "3fda436c0390fb8ef2ee72b4d9fe6ccbfc0ea994208f4d962bb9f43960af7a82"), + "native_helper": (PARENT / "emit_native.py", + "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745"), + "native": (PARENT / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"), + "formation": (PARENT / "row-only-capture-20261020/direct-normal/DIRECT-FULL-CAPTURE.json.gz", + "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c"), + "line_prefix": (PARENT / "fixed-reader-reuse-20261020/prefix-normal/CARRIER-PREFIX.json.gz", + "54c561cfc49ad3fe1258ba5a8760eeadaa11784272cf458e2a6e54403a0e655e"), + "native_review": (LANES / "new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json", + "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c"), + "formation_review": (LANES / "new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json", + "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"), + "line_review": (LANES / "new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"), +} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def read(name): + path, pin = PINS[name] + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Pinned input " + name) + return raw + + +def module(name, key): + read(key) + spec = importlib.util.spec_from_file_location(name, PINS[key][0]) + result = importlib.util.module_from_spec(spec) + sys.modules[name] = result + spec.loader.exec_module(result) + return result + + +c = module("clean_unitary_code", "code_helper") +n = module("clean_unitary_native", "native_helper") +g = c.g +ZERO, ONE = g.ZERO, g.ONE +MACRO_CACHE = {} + + +def component_adjoint(word, permutation): + result = [] + for op, target, source, coefficient in word: + value = F(coefficient) + def remap(component): + return 2 * permutation[component // 2] + component % 2 + if op == "add": + result.append([op, remap(source), remap(target), str(-value)]) + else: + need(op == "scale" and value, "An invertible component scale") + result.append([op, remap(target), None, str(1 / value)]) + return result + + +def gaussian_add(target, source, coefficient, frame): + a, b = coefficient + components = [] + for t, s, value in ((2 * target, 2 * source, a), + (2 * target, 2 * source + 1, -b), + (2 * target + 1, 2 * source, b), + (2 * target + 1, 2 * source + 1, a)): + if value: + components.append(["add", t, s, str(value)]) + return ["gaussian_add", target, source, [str(a), str(b)], frame, components] + + +def check_component_block(fields, instructions, expected): + positions = {p: i for i, p in enumerate(fields)} + local = [] + for op, target, source, coefficient in instructions: + need(target // 2 in positions and (source is None or source // 2 in positions), + "Every component stays inside its complete macro") + local.append([op, 2 * positions[target // 2] + target % 2, + None if source is None else 2 * positions[source // 2] + source % 2, + coefficient]) + key = json.dumps([local, g.serialize(expected)], separators=(",", ":")) + if key not in MACRO_CACHE: + actual, report = c.b.replay(local, 2 * len(fields)) + need(actual == c.u.realify(expected, len(fields)), "The complete component macro is complex-linear") + need(report["scalar"] % 2 == 0, "The real component tariff is integral") + report["scalar"] //= 2 + MACRO_CACHE[key] = report + return MACRO_CACHE[key] + + +def event_price(event): + if event[0] == "native": + return 0 + if event[0] == "scalar": + return n.r.price([event[1]]) + instructions = event[5] if event[0] == "gaussian_add" else event[2] + cost = n.r.price(instructions) + need(cost % 2 == 0, "An integral real scalar invoice") + return cost // 2 + + +def verify(word, expected): + current = list(word["start"]) + state = g.eye(640) + maximum = F(1) + macro_maximum = F(1) + for event in word["events"]: + kind = event[0] + if kind == "native": + _, field, old, new, rank, key = event + need(current[field] == old, "The native input frame") + need(len(n.basis(word["frames"][old] + word["frames"][new])) + == len(word["frames"][new]), "The native frame inclusion") + need(rank == len(word["frames"][new]) - len(word["frames"][old]) + == word["native_recipes"][key]["rank"], "The exact native rank") + current[field] = new + continue + if kind == "scalar": + op, target, source, coefficient = event[1] + frame = event[2] + need(current[target] == frame, "The real-complex scalar target frame") + value = g.real(coefficient) + if op == "add": + need(target != source and current[source] == frame, "The real-complex scalar source frame") + for j, x in state[source].items(): + g.put(state[target], j, g.times(value, x)) + else: + need(op == "scale", "The scalar grammar") + state[target] = {j: g.times(value, x) for j, x in state[target].items()} + changed = [target] + elif kind == "gaussian_add": + _, target, source, raw, frame, components = event + need(target != source and current[target] == current[source] == frame, + "The complete Gaussian macro has one common complex frame") + value = F(raw[0]), F(raw[1]) + report = check_component_block([target, source], components, + [{0: ONE, 1: value}, {1: ONE}]) + macro_maximum = max(macro_maximum, F(report["prefix_row_one_norm"])) + for j, x in state[source].items(): + g.put(state[target], j, g.times(value, x)) + changed = [target] + else: + need(kind == "component_code", "The complete event grammar") + _, fields, components, raw_matrix, frame = event + need(len(fields) == len(set(fields)) and all(current[p] == frame for p in fields), + "The complete code macro has one common complex frame") + matrix = c.rows(raw_matrix) + report = check_component_block(fields, components, matrix) + macro_maximum = max(macro_maximum, F(report["prefix_row_one_norm"])) + result = g.multiply(matrix, [state[p] for p in fields]) + for p, row in zip(fields, result): + state[p] = row + changed = fields + for p in changed: + maximum = max(maximum, sum(abs(a) + abs(b) for a, b in state[p].values())) + need(current == word["final"], "All640 final frames") + need(state == expected, "All640 independent complex input columns") + need(state[224:] == g.eye(640)[224:], "All416 arbitrary helper fields") + profile = Counter(e[4] for e in word["events"] if e[0] == "native") + full = sum(e[0] == "native" and e[5] == "direct-full" for e in word["events"]) + return { + "all_complex_input_columns": 640, "all_real_input_columns": 1280, + "unchanged_arbitrary_helpers": 416, "owned_fields": 0, "private_fields": 0, + "native_profile": dict(sorted(profile.items())), "native_mass": sum(k * v for k, v in profile.items()), + "native_children": sum(profile.values()), + "native_side_map_upper_bound": 2 * (sum(profile.values()) - full), + "direct_full_identity_wrapper_children": full, + "explicit_input_views": len(word["input_views"]), "explicit_output_views": len(word["output_views"]), + "scalar": sum(event_price(e) for e in word["events"]), + "scalar_stage_prices": {name: sum(event_price(e) for e in word["events"][start:end]) + for name, (start, end) in word["stage_ranges"].items()}, + "complete_macro_content_component_l1": str(maximum), + "local_macro_prefix_component_l1": str(macro_maximum), + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "odd_divisions": 0, + } + + +def maps(code, selected): + direct = g.eye(224) + for p in range(112): + if p in selected: + direct[p] = {112 + p: g.real(-1)} + direct[112 + p] = dict(code[p]) + else: + direct[p] = dict(code[p]) + direct[112 + p] = dict(code[p]) + g.put(direct[112 + p], 112 + p, ONE) + w = [{112 + p if p in selected else p: ONE} for p in range(112)] + inverse = g.multiply(g.adjoint(code, 112), w) + for p in range(112): + inverse.append({p: g.real(-1)} if p in selected else + {112 + p: ONE, p: g.real(-1)}) + need(g.multiply(direct, inverse) == g.multiply(inverse, direct) == g.eye(224), + "Both forward content inverse orders") + return direct, inverse + + +def conjugate(matrix, permutation): + result = [{} for _ in matrix] + for p, row in enumerate(matrix): + result[permutation[p]] = {permutation[j]: value for j, value in row.items()} + return result + + +def lower_dual(original, permutation): + word = deepcopy(original) + events = [] + for event in original["events"]: + kind = event[0] + if kind == "native": + changed = deepcopy(event) + changed[1] = permutation[event[1]] + elif kind == "scalar": + op, target, source, coefficient = event[1] + value = F(coefficient) + gate = ([op, permutation[source], permutation[target], str(-value)] if op == "add" else + [op, permutation[target], None, str(1 / value)]) + changed = ["scalar", gate, event[2]] + elif kind == "gaussian_add": + _, target, source, raw, frame, components = event + value = g.neg(g.conjugate((F(raw[0]), F(raw[1])))) + changed = ["gaussian_add", permutation[source], permutation[target], + [str(x) for x in value], frame, component_adjoint(components, permutation)] + else: + need(kind == "component_code", "The dual macro grammar") + _, fields, components, matrix, frame = event + unitary = c.rows(matrix) + need(g.multiply(unitary, g.adjoint(unitary, len(fields))) == g.eye(len(fields)), + "The complete source code is unitary") + changed = ["component_code", [permutation[p] for p in fields], + component_adjoint(components, permutation), deepcopy(matrix), frame] + events.append(changed) + word["events"] = events + for key in ("start", "final"): + word[key] = [original[key][permutation[p]] for p in range(640)] + need(word[key] == original[key], "The selected endpoint types are symmetric") + for view in word["input_views"]: + view["field"] = permutation[view["field"]] + word["input_views"].sort(key=lambda v: v["field"]) + old = {v["field"]: v for v in original["input_views"]} + for view in word["input_views"]: + need(all(view[k] == old[view["field"]][k] for k in ("port", "frame", "left", "right", "rank")), + "The full same-port input monomial is invariant") + need(all(permutation[112 + view["port"]] == 112 + view["port"] for view in word["output_views"]), + "All ordinary output views keep their field") + word["wire_permutation"] = {str(p): q for p, q in enumerate(permutation) if p != q} + return word + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + for name in PINS: + read(name) + code_source = json.loads(read("code")) + native = json.loads(read("native")) + formation = json.loads(read("formation")) + prefix = json.loads(read("line_prefix")) + cyclic = json.loads(c.b.read("cyclic")) + code = c.rows(code_source["code"]) + mode = c.rows(code_source["mode_code"]) + old_mode = n.rows(native["model"]["mode_response"]) + old_physical = n.rows(native["model"]["response"]) + selected = set(code_source["selected_full_ports"]) + selected_fields = {112 + p for p in selected} + parameters = {x["id"]: x for x in cyclic["parameters"]} + forward, inverse = maps(code, selected) + dual = g.adjoint(inverse, 224) + dual_inverse = g.adjoint(forward, 224) + permutation = list(range(640)) + for p in selected: + permutation[p], permutation[112 + p] = 112 + p, p + swap = conjugate(dual, permutation[:224]) + swap_inverse = conjugate(dual_inverse, permutation[:224]) + need(g.multiply(swap, swap_inverse) == g.multiply(swap_inverse, swap) == g.eye(224), + "Both selected-conjugate content inverse orders") + formula = g.eye(224) + for p in range(112): + formula[p] = {112 + j if j in selected else j: z for j, z in code[p].items()} + if p in selected: + formula[112 + p] = {p: g.real(-1)} + else: + g.put(formula[p], 112 + p, g.real(-1)) + need(formula == swap, "The direct unitary Bswap formula") + providers, reports, fresh_phases = {}, {}, [] + for provider, source_directions in native["providers"].items(): + original = source_directions["forward"] + old_formation = formation["providers"][provider] + old_prefix = prefix["providers"][provider] + transfers = {x["event"]: x for x in original["transfer_records"]} + kept, retained, retunings = [], [], [] + for index, event in enumerate(original["events"]): + target = event[1] if event[0] == "native" else event[1][1] + if target in selected_fields: + continue + if event[0] == "scalar" and event[1][0] == "add": + need(event[1][2] not in selected_fields, "No retained read of a removed target") + retained.append(index) + if index not in transfers: + kept.append(deepcopy(event)) + continue + record = transfers[index] + if record["part"] == "large48": + parameter = parameters[record["parameter"]] + ports = cyclic["cyclic_carriers"][parameter["vertex"]] + p, j = ports[parameter["row"]], ports[parameter["column"]] + old_coefficient = old_mode[p][j] + else: + p, j = record["target_port"], record["source_port"] + old_coefficient = old_physical[p][j] + op, target, source, coefficient = event[1] + need(op == "add" and p not in selected, "An ordinary transfer slot") + ratio = F(coefficient) / old_coefficient + value = tuple(ratio * z for z in mode[p].get(j, ZERO)) + retunings.append({"original_event": index, "mode_target": p, "mode_source": j, + "coefficient": [str(x) for x in value]}) + if value != ZERO: + kept.append(gaussian_add(target, source, value, event[2])) + used = {e[5] for e in kept if e[0] == "native"} + recipes = {k: deepcopy(original["native_recipes"][k]) for k in used} + source_views = {v["port"]: v for v in old_formation["input_views"]} + output_views = [deepcopy(v) for v in old_formation["output_views"] if v["port"] not in selected] + need(len(output_views) == 88, "All ordinary output views are inherited") + providers[provider], reports[provider] = {}, {} + for entry in ("I", "Q"): + word = { + "frames": deepcopy(original["frames"]), "start": list(original["start"]), + "final": list(original["final"]), "events": deepcopy(kept), + "native_recipes": deepcopy(recipes), + "input_views": [{**deepcopy(v), "field": p} for p, v in sorted(source_views.items())], + "output_views": deepcopy(output_views), + "retained_original_event_indices": retained, "transfer_retunings": retunings, + "stage_ranges": {"retained_retuned_core": [0, len(kept)]}, + } + begin = len(word["events"]) + for p in sorted(selected): + if entry == "I": + key, old, rank = "direct-full", 0, 9 + word["native_recipes"][key] = deepcopy(old_formation["native_recipes"]["capture-full"]) + else: + key, old, rank = "unitary-line:" + str(p), original["start"][p], 8 + word["start"][112 + p] = old + old_key = "capture-line:" + str(p) + if old_key in old_prefix["native_recipes"]: + recipe = deepcopy(old_prefix["native_recipes"][old_key]) + else: + before = n.compiler.canonical_frame(9, tuple(word["frames"][old])) + after = n.compiler.canonical_frame(9, tuple(word["frames"][1])) + recipe, _ = n.compiler.lower_child(before.adjoint().then(after)) + circuit = n.phase.adjoint(n.phase.frame(word["frames"][old], 9)) + n.phase.frame(word["frames"][1], 9) + n.phase.equal(n.phase.recipe(recipe), circuit, "Fresh selected Q-to-FULL child") + fresh_phases.append({"provider": provider, "port": p, "recipe": recipe, "circuit": circuit}) + need(recipe["rank"] == 8, "The exact selected line progress") + word["native_recipes"][key] = recipe + word["input_views"].append({**deepcopy(source_views[p]), "field": 112 + p, + "role": "selected_target", "source_entry_port": p}) + word["events"].append(["native", 112 + p, old, 1, rank, key]) + word["final"][112 + p] = 1 + word["stage_ranges"]["selected_progress"] = [begin, len(word["events"])] + begin = len(word["events"]) + word["events"].append(["component_code", list(range(112)), + deepcopy(code_source["component_words"]["code"]), + deepcopy(code_source["code"]), 1]) + word["stage_ranges"]["source_unitary_code"] = [begin, len(word["events"])] + begin = len(word["events"]) + for p in sorted(selected): + word["events"].extend([ + ["scalar", ["add", 112 + p, p, "1"], 1], + ["scalar", ["add", p, 112 + p, "-1"], 1], + ["scalar", ["add", 112 + p, p, "1"], 1], + ]) + word["stage_ranges"]["signed_selected_exchanges"] = [begin, len(word["events"])] + word["input_views"].sort(key=lambda v: v["field"]) + report = verify(word, forward + g.eye(640)[224:]) + need(report["native_profile"] == {1: 1328, 2: 64, 3: 48, 9 if entry == "I" else 8: 24}, + "The complete24-coordinate native profile") + need(report["scalar_stage_prices"]["source_unitary_code"] == 8052 + and report["scalar_stage_prices"]["signed_selected_exchanges"] == 576, + "The complete paid code and exchanges") + providers[provider]["forward_" + entry] = word + reports[provider]["forward_" + entry] = report + for name, perm, expected in ( + ("inverse_adjoint_Q", list(range(640)), dual), + ("selected_conjugate_Q", permutation, swap)): + word = lower_dual(providers[provider]["forward_Q"], perm) + providers[provider][name] = word + reports[provider][name] = verify(word, expected + g.eye(640)[224:]) + print(json.dumps({"provider": provider, "reports": reports[provider]}), flush=True) + content_maps = {"forward_I": forward, "forward_Q": forward, + "inverse_adjoint_Q": dual, "selected_conjugate_Q": swap} + inverse_maps = {"forward_I": inverse, "forward_Q": inverse, + "inverse_adjoint_Q": dual_inverse, "selected_conjugate_Q": swap_inverse} + payload = { + "schema": "clean-unitary-24-centre-native-v1", + "source_pins": {name: {"path": str(path), "sha256": pin} for name, (path, pin) in PINS.items()}, + "ports": native["model"]["ports"], "selected_ports": sorted(selected), + "code": code_source["code"], "inverse_and_adjoint_code": code_source["inverse_and_adjoint"], + "content_maps": {name: g.serialize(value) for name, value in content_maps.items()}, + "inverse_content_maps": {name: g.serialize(value) for name, value in inverse_maps.items()}, + "providers": providers, "fresh_phase_records": fresh_phases, + "component_contract": "Component operations occur only inside a complete contiguous complex-linear macro. There is no native or map interleaving. Only the macro endpoints have the common complex frame.", + "physical_contract": { + "input_I": "X=Q x; Y_P=z; Y_R=v.", + "input_Q": "X=Q x; Y_P=Q_P z; Y_R=v.", + "forward_content": "Put w=Cx. X_P=-z; X_R=w_R; Y_P=w_P; Y_R=v+w_R.", + "conjugate_content": "Put w=C(z,u), where x=(a,u). X_P=w_P; X_R=w_R-v; Y_P=-a; Y_R=v.", + "output_frames": "All X and selectedY have F9. OrdinaryY has F9 q_R.", + "scope": "Complete local native clean unitary interface and its literal inverse-adjoint. Routed composition, recursive hosting, precision and complete supplier cost remain separate.", + }, + } + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + saved = json.loads(raw) + for provider, words in saved["providers"].items(): + for name, word in words.items(): + expected = c.rows(saved["content_maps"][name]) + g.eye(640)[224:] + need(verify(word, expected) == reports[provider][name], "The complete serialized word") + bad = deepcopy(word) + macro = next(e for e in bad["events"] if e[0] == "gaussian_add" and F(e[3][1])) + macro[5][0][3] = str(-F(macro[5][0][3])) + try: + verify(bad, expected) + except ValueError: + pass + else: + raise ValueError("A wrong complex component ADD was accepted") + (args.out / "UNITARY-CLEAN.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + receipt = { + "status": "PASS_COMPLETE_UNITARY_24_CLEAN_NATIVE_WORDS", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), "reports": reports, + "fresh_phase_checks": len(fresh_phases), "all_content_inverse_orders": True, + "negative_control": "A wrong atomic component ADD is rejected in every complete word.", + "scope": payload["physical_contract"]["scope"], + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(json.dumps({"status": receipt["status"], "payload": receipt["payload_decompressed_sha256"], + "fresh_phase_checks": len(fresh_phases)}), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/run-v2-normal/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/run-v2-normal/CHECKS.json new file mode 100644 index 0000000000..4fdc9b60b0 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/run-v2-normal/CHECKS.json @@ -0,0 +1,255 @@ +{ + "all_content_inverse_orders": true, + "fresh_phase_checks": 16, + "negative_control": "A wrong atomic component ADD is rejected in every complete word.", + "payload_decompressed_sha256": "472935ba574b78c6ec1fd6f02fc1c0c29d37b53f73ec55b8583904bd5d5af245", + "producer_sha256": "b903cbade7b907e9ce82e1e3266f3267bc524ce53ee6ef1aeaed3c5c443e898b", + "reports": { + "base": { + "forward_I": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "10", + "direct_full_identity_wrapper_children": 24, + "explicit_input_views": 112, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "16", + "native_children": 1464, + "native_mass": 1816, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "9": 24 + }, + "native_side_map_upper_bound": 2880, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + }, + "forward_Q": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "10", + "direct_full_identity_wrapper_children": 0, + "explicit_input_views": 136, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "16", + "native_children": 1464, + "native_mass": 1792, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "8": 24 + }, + "native_side_map_upper_bound": 2928, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + }, + "inverse_adjoint_Q": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "5", + "direct_full_identity_wrapper_children": 0, + "explicit_input_views": 136, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "7", + "native_children": 1464, + "native_mass": 1792, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "8": 24 + }, + "native_side_map_upper_bound": 2928, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + }, + "selected_conjugate_Q": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "5", + "direct_full_identity_wrapper_children": 0, + "explicit_input_views": 136, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "7", + "native_children": 1464, + "native_mass": 1792, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "8": 24 + }, + "native_side_map_upper_bound": 2928, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + } + }, + "extra": { + "forward_I": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "10", + "direct_full_identity_wrapper_children": 24, + "explicit_input_views": 112, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "16", + "native_children": 1464, + "native_mass": 1816, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "9": 24 + }, + "native_side_map_upper_bound": 2880, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + }, + "forward_Q": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "10", + "direct_full_identity_wrapper_children": 0, + "explicit_input_views": 136, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "16", + "native_children": 1464, + "native_mass": 1792, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "8": 24 + }, + "native_side_map_upper_bound": 2928, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + }, + "inverse_adjoint_Q": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "5", + "direct_full_identity_wrapper_children": 0, + "explicit_input_views": 136, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "7", + "native_children": 1464, + "native_mass": 1792, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "8": 24 + }, + "native_side_map_upper_bound": 2928, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + }, + "selected_conjugate_Q": { + "all_complex_input_columns": 640, + "all_real_input_columns": 1280, + "complete_macro_content_component_l1": "5", + "direct_full_identity_wrapper_children": 0, + "explicit_input_views": 136, + "explicit_output_views": 88, + "local_macro_prefix_component_l1": "7", + "native_children": 1464, + "native_mass": 1792, + "native_profile": { + "1": 1328, + "2": 64, + "3": 48, + "8": 24 + }, + "native_side_map_upper_bound": 2928, + "odd_divisions": 0, + "owned_fields": 0, + "prefix_scope": "Macro endpoints have the complex frame. Atomic component bounds refer only to that macro's physical input fields.", + "private_fields": 0, + "scalar": 16020, + "scalar_stage_prices": { + "retained_retuned_core": 7392, + "selected_progress": 0, + "signed_selected_exchanges": 576, + "source_unitary_code": 8052 + }, + "unchanged_arbitrary_helpers": 416 + } + } + }, + "scope": "Complete local native clean unitary interface and its literal inverse-adjoint. 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b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/isotropic-pair-review-20261018/check.py @@ -0,0 +1,593 @@ +#!/usr/bin/env python3 +"""Check the common port gauge with exact sparse Gaussian columns.""" +from collections import Counter +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / 'coherent-port/isotropic-pair-gauge-20261018' +H6 = LANES / 'oblique-native-20261017/radical-centre-carry' +PINS = { + 'GAUGE.md': '17f7fcb6d67499f2d0280d1c49b0c0d01076ec839b620d0a82b8ce6de3e3395b', + 'check_isotropic_gauge.py': 'fdab75d06215e6dc1215d8aaf6737443be0c5b4fe3ad8088ff95c5d9221c730d', + 'GAUGE-PROGRAMS.json': '20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701', + 'CHECKS.json': '4ef0a622416d46a2ccab39d6f87a2e67be82fdbbe0e6d7cc0e0e0bac5e0ad0c3', +} +INPUTS = {} + + +def need(value, label): + if not value: + raise ValueError(label) + + +def read(path, expected=None, compressed=False): + raw = path.read_bytes() + digest = sha256(raw).hexdigest() + content = gzip.decompress(raw) if compressed else raw + need(expected is None or sha256(content).hexdigest() == expected, 'Input pin: '+str(path)) + INPUTS[str(path.relative_to(LANES))] = {'sha256': digest} + if compressed: + INPUTS[str(path.relative_to(LANES))]['decompressed_sha256'] = sha256(content).hexdigest() + return content + + +def frozen(path, pin): + record = json.loads(read(path/'FREEZE.json', pin)) + for name, digest in record['files'].items(): + read(path/name, digest) + return record + + +def rotate(r, i, power): + return ((r, i), (-i, r), (-r, -i), (i, -r))[power % 4] + + +def phase_at(rows, linear, x): + exponent = sum(value for j, value in enumerate(linear) if x & (1 << j)) + for j, row in enumerate(rows): + if x & (1 << j): + exponent += 2*((row & x) >> (j+1)).bit_count() + return exponent % 4 + + +def compile_circuit(circuit, n=9): + """Combine adjacent address and phase tables, without a Clifford tableau.""" + size = 1 << n + mapping, phases = list(range(size)), [0]*size + output = [] + + def flush(): + nonlocal mapping, phases + if mapping != list(range(size)) or any(phases): + output.append(('M', tuple(mapping), tuple(phases))) + mapping, phases = list(range(size)), [0]*size + + for event in circuit: + kind = event[0] + if kind == 'C': + flush() + need(0 <= event[1] < size and event[2] in (-1, 1), 'Literal C gate') + output.append(tuple(event)) + continue + if kind == 'P': + rows = event[1] + need(len(rows) == n and all(0 <= r < size for r in rows), 'Address matrix') + image = [sum(((r & x).bit_count() % 2) << j for j, r in enumerate(rows)) + for x in range(size)] + need(sorted(image) == list(range(size)), 'Address matrix is a permutation') + mapping = [image[x] for x in mapping] + elif kind == 'X': + mapping = [x ^ event[1] for x in mapping] + elif kind in ('D', 'phase'): + powers = ([event[1] % 4]*size if kind == 'phase' else + [phase_at(event[1], event[2], x) for x in range(size)]) + phases = [(p+powers[x]) % 4 for p, x in zip(phases, mapping)] + else: + raise ValueError(event) + flush() + return output + + +def inverse(compiled): + result = [] + for event in reversed(compiled): + if event[0] == 'C': + result.append(('C', event[1], -event[2])) + else: + image, phase = event[1:] + back, powers = [0]*len(image), [0]*len(image) + for x, y in enumerate(image): + back[y], powers[y] = x, -phase[x] % 4 + result.append(('M', tuple(back), tuple(powers))) + return result + + +def normalized(state, denominator): + state = {x: value for x, value in state.items() if value != (0, 0)} + if not state: + return {}, 0 + bits = 0 + for real, imag in state.values(): + bits |= abs(real) | abs(imag) + shift = min(denominator, (bits & -bits).bit_length()-1) + return ({x: (real >> shift, imag >> shift) for x, (real, imag) in state.items()}, + denominator-shift) + + +def run(compiled, column): + state, denominator = {column: (1, 0)}, 0 + for event in compiled: + if event[0] == 'M': + image, phases = event[1:] + state = {image[x]: rotate(real, imag, phases[x]) + for x, (real, imag) in state.items()} + else: + _, v, sign = event + moved = {} + for x, (real, imag) in state.items(): + for y, value in ((x, (real-sign*imag, imag+sign*real)), + (x ^ v, (real+sign*imag, imag-sign*real))): + old = moved.get(y, (0, 0)) + moved[y] = (old[0]+value[0], old[1]+value[1]) + state = {x: value for x, value in moved.items() if value != (0, 0)} + denominator += 1 + return normalized(state, denominator) + + +def monomial(record): + need(set(record) == {'matrix_rows', 'quadratic_rows', 'linear_Z4', 'offset', 'phase'}, + 'Complete monomial record') + return [['D', record['quadratic_rows'], record['linear_Z4']], + ['P', record['matrix_rows']], ['X', record['offset']], ['phase', record['phase']]] + + +def recipe(record): + rank = record['rank'] + need(0 <= rank <= 9, 'Native rank') + before = [] if record['right'] is None else monomial(record['right']) + return compile_circuit(before + [['C', 1 << j, 1] for j in range(rank)] + + monomial(record['left'])) + + +def compare(left, right, label, support=None): + digest = sha256() + coefficients = 0 + for x in range(512): + actual, expected = run(left, x), run(right, x) + need(actual == expected, label+' column '+str(x)) + if support is not None: + need(len(actual[0]) == support, label+' support') + coefficients += len(actual[0]) + digest.update(json.dumps([x, actual[1], sorted(actual[0].items())], separators=(',', ':')).encode()) + return {'spatial_columns': 512, 'nonzero_coefficients': coefficients, 'digest': digest.hexdigest()} + + +def gauge(n, a, b): + size = 1 << n + phase = ('M', tuple(range(size)), tuple((b & x).bit_count() % 2 for x in range(size))) + return [phase, ('C', a, 1), phase] + + +def span(vectors): + values = {0} + for vector in vectors: + values |= {x ^ vector for x in values} + return values + + +def canonical(vectors, n=9): + """Build the declared chart from a truth-table inverse of its address map.""" + rank, size = len(vectors), 1 << n + need(len(span(vectors)) == 1 << rank, 'Independent declared frame basis') + if rank == n: + return [('C', 1 << j, 1) for j in range(n)] + if not rank: + return [] + columns = list(vectors) + for vector in (1 << j for j in range(n)): + if vector not in span(columns): + columns.append(vector) + need(len(columns) == n, 'Complete chart basis') + image = [] + for x in range(size): + y = 0 + for j, column in enumerate(columns): + if x & (1 << j): + y ^= column + image.append(y) + back = [0]*size + for x, y in enumerate(image): + back[y] = x + inverse_columns = [back[1 << j] for j in range(n)] + quadratic = [(1 << j) ^ sum(((v & w).bit_count() % 2) << k + for k, w in enumerate(inverse_columns)) + for j, v in enumerate(inverse_columns)] + linear = [(row >> j) & 1 for j, row in enumerate(quadratic)] + K = [('M', tuple(image), tuple(phase_at(quadratic, linear, y) for y in image))] + return inverse(K)+[('C', 1 << j, 1) for j in range(rank)]+K + + +def formula(n, a, b, q, x): + t, u = (b & q).bit_count() % 2, (b & x).bit_count() % 2 + q0 = q ^ (a if t else 0) + return {x ^ (q0 if u else 0): rotate(1, 0, (2*t-1)*u)}, 0 + + +def general_checks(): + counts = {} + for n in range(1, 5): + total = 0 + for a in range(1, 1 << n): + for b in range(1, 1 << n): + if (a & b).bit_count() % 2 != 1: + continue + w = gauge(n, a, b) + for q in range(1 << n): + circuit = inverse(w)+[('C', q ^ a, -1), ('C', q, 1)]+w + for x in range(1 << n): + need(run(circuit, x) == formula(n, a, b, q, x), 'General pair formula') + total += 1 + counts[n] = total + w = gauge(9, 45, 1) + for q in range(512): + circuit = inverse(w)+[('C', q ^ 45, -1), ('C', q, 1)]+w + for x in range(512): + need(run(circuit, x) == formula(9, 45, 1, q, x), 'Every local direction') + for x in range(512): + need(run(w+w, x) == ({x: (0, 1)}, 0), 'Exact square phase') + for v in range(512): + need((run(w+[('C', v, 1)], 0) == run([('C', v, 1)]+w, 0)) == (v & 1 == 0), + 'Exact pure-C continuation criterion') + # This shear is not orthogonal. Covectors use the inverse transpose. + chart = compile_circuit([['P', [3, 2]]], 2) + transported = inverse(chart)+gauge(2, 1, 1)+chart + dual_action = gauge(2, 1, 3) + for x in range(4): + need(run(transported, x) == run(dual_action, x), 'General chart dual action') + need(any(run(transported, x) != run(gauge(2, 1, 1), x) for x in range(4)), + 'Naive covector action rejects for a non-orthogonal chart') + # Two two-bit columns check the tensor phase separately. + for q in range(4): + tensor = [] + wg = [] + for shift in (0, 2): + local = gauge(4, 3 << shift, 1 << shift) + tensor += inverse(local)+[('C', (q ^ 3) << shift, -1), ('C', q << shift, 1)]+local + wg += local + for x in range(16): + y, phase = 0, 0 + for shift in (0, 2): + value = (x >> shift) & 3 + t, u = q & 1, value & 1 + y |= (value ^ ((q ^ (3 if t else 0)) if u else 0)) << shift + phase += (2*t-1)*u + need(run(tensor, x) == ({y: rotate(1, 0, phase)}, 0), 'Tensor pair phase') + need(run(wg+wg, x) == ({x: (-1, 0)}, 0), 'Tensor square phase i squared') + print('general formula and tensor phases PASS', flush=True) + return {'all_parameters_dimensions_1_to_4': counts, 'all_nine_bit_q_columns': 512*512, + 'tensor_width_two_columns': 64, 'pure_C_continuation_directions': 512, + 'nonorthogonal_chart_columns': 4} + + +def transition_checks(): + counts = {} + for n in range(1, 5): + parameters = [(a, b) for a in range(1, 1 << n) for b in range(1, 1 << n) + if (a & b).bit_count() % 2] + gauges = {(a, b): gauge(n, a, b) for a, b in parameters} + total = 0 + for a1, b1 in parameters: + for a2, b2 in parameters: + op = inverse(gauges[a1, b1])+gauges[a2, b2] + for x in (range(1 << n) if n <= 3 else (0,)): + u1, u2 = (b1 & x).bit_count() % 2, (b2 & x).bit_count() % 2 + if a1 == a2: + delta = u1 ^ u2 + expected = ({x ^ (a1 if delta else 0): ((-1)**(u1*delta), 0)}, 0) + else: + cross = (b2 & a1).bit_count() % 2 + expected = ({x: ((-1)**(u1+u2), 0), + x ^ a2: ((-1)**u1, 0), + x ^ a1: ((-1)**(u2+cross), 0), + x ^ a1 ^ a2: (1, 0)}, 1) + need(run(op, x) == expected, 'Exact transition formula and global phase') + need(len(expected[0]) == (1 if a1 == a2 else 4), 'Transition support criterion') + total += 1 + counts[n] = total + print('general transition formula and rank obstruction PASS', flush=True) + return {'dimensions_1_to_3_all_columns_and_dimension_4_zero_column': counts, + 'same_radical_rank': 0, 'distinct_radicals_rank': 2} + + +def source_binding(packet, h6, signed, core, geometry): + labels = next(iter(core['providers'].values()))['canonical']['ports'] + need(all(p['canonical']['ports'] == labels for p in core['providers'].values()), 'Provider labels') + large = signed['large_ports'] + need(sorted(row['port'] for row in packet['monomials']) == sorted(large), 'All actual centre ports') + need([p for p, q in enumerate(labels) if (q & 45).bit_count() % 2 == 0] == sorted(large), + 'Exactly the actual radical-perpendicular ports') + need(sorted(tuple(row['ports']) for row in packet['left_coded_pair_plane_tails']) == + sorted(tuple(row['ports']) for row in geometry['pair_edges']), 'Actual pair planes') + source_rows = packet['left_coded_source_tails'] + target_rows = {row['port']: row for row in packet['left_coded_tails']} + routes = {} + for provider, record in h6['providers'].items(): + for direction, word in record.items(): + need(word['frames'][word['carry_frame']] == [45], 'Actual canonical carry frame') + need(len(word['centre_frames']) == 8, 'Eight source frames') + for j, frame in enumerate(word['centre_frames']): + need(span(word['frames'][frame]) == span(source_rows[j]['frame_basis']), + 'Actual centre subspace binding') + flags = [False]*640 + changed = Counter() + endpoint = {(r['role'], r['port']): r for r in word['endpoint_adapters']} + checks = [] + for event in word['events']: + if event[0] == 'native': + _, field, before, after, rank, key = event + need(not flags[field], 'No later native call on a coded source') + if field in large and after == 1: + j = word['centre_frames'].index(before) + need(rank == 2, 'Old source exit rank') + flags[field] = True + changed['source_2_to_1'] += 1 + elif 112 <= field < 224 and field-112 in large and before == word['carry_frame']: + p = field-112 + need(after == endpoint['target', p]['frame'] and rank == 7, + 'Old target exit and endpoint adapter') + flags[field] = True + changed['target_7_to_6'] += 1 + checks.append((p, word['native_recipes'][key], endpoint['target', p])) + elif event[0] == 'scalar': + op = event[1] + if op[0] in ('add', 'copy'): + need(flags[op[1]] == flags[op[2]], 'Common W commutes with remaining scalar graph') + elif op[0] == 'clear': + need(not flags[op[1]], 'No coded field is cleared') + else: + need(op[0] == 'scale', 'Known scalar operation') + elif event[0] == 'set_empty_frame': + need(not flags[event[1]], 'No coded frame reset') + else: + raise ValueError(event) + need(changed == {'source_2_to_1': 48, 'target_7_to_6': 48}, 'All changed exits') + need({i for i, flag in enumerate(flags) if flag} == set(large) | {112+p for p in large}, + 'Exactly two coded centre banks, with helpers unchanged') + routes[provider+'/'+direction] = {'changed_exits': dict(changed), 'coded_fields': 96, + 'coded_borrowed_fields': 0, + 'literal_source_basis_equal': [word['frames'][f] == source_rows[j]['frame_basis'] + for j, f in enumerate(word['centre_frames'])]} + if provider == 'base' and direction == 'forward': + routes['_target_checks'] = checks + routes['_carry_recipe'] = word['native_recipes']['0:'+str(word['carry_frame'])] + routes['_source_old'] = [word['native_recipes'][str(frame)+':1'] + for frame in word['centre_frames']] + return labels, routes + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('output', type=Path) + args = parser.parse_args() + args.output.mkdir(parents=True, exist_ok=False) + for name, pin in PINS.items(): + read(SOURCE/name, pin) + read(SOURCE/'FREEZE.json', '3c1669513029238abf181d4137b7a25efd4113c951ac78301a9da2c7e9df6ec1') + packet = json.loads(read(SOURCE/'GAUGE-PROGRAMS.json', PINS['GAUGE-PROGRAMS.json'])) + receipt = json.loads(read(SOURCE/'CHECKS.json', PINS['CHECKS.json'])) + need(receipt['program_sha256'] == PINS['GAUGE-PROGRAMS.json'], 'Receipt packet binding') + dependencies = {} + for name, (kind, pin) in packet['pins'].items(): + raw = read(LANES/name, pin, kind == 'gzip') + if name.endswith(('.json', '.gz')): + dependencies[name] = json.loads(raw) + frozen(H6, 'a1b0ec7bbead298e1484199b15896e2b5b688d53b3f2f5d9e0d73c29bea04a80') + h6 = json.loads(read(H6/'RADICAL-CENTRE-PROGRAM.json.gz', + '25ddd47640a98e61b5edf5f36e2aad9867eab00e072545322bb36e4d63c561ea', True)) + h6_binding_pins = { + 'H6-SOURCE-PROGRAMS.json': '4eb739a9191aaba6b8c15a2c10868ceba80c4596000eca50c8f68f29c527e569', + 'bind_h6_sources.py': '150453ca6e3bd75bdfab1805def824c44c34e83037b6996ff355d493de26686b', + 'H6-SOURCE-CHECKS.json': 'cb5a9d3b4f83b4718ec70bdd5473d55cc25d3c3078d696f6f6504862c6443e7e', + 'H6-SOURCE-BINDING.md': '7a3a9313f6c8b01dc5a2dc2aa156abb109ad624d25cf92f9aa0dc0b57d11d783', + } + for name, pin in h6_binding_pins.items(): + read(SOURCE/name, pin) + actual_sources = json.loads(read(SOURCE/'H6-SOURCE-PROGRAMS.json', h6_binding_pins['H6-SOURCE-PROGRAMS.json'])) + read(SOURCE/'H6-SOURCE-FREEZE.json', 'cf436b1016f7d9c5b933eb818098ff0339436fec20d0ed497045fc992e6ee0b5') + matching_freeze = json.loads(read(SOURCE/'MATCHING-EXITS-FREEZE.json', + '9d5e63259b861bf69ac5e00b2ec9ad3158aec3edac4ce54e08fcf33249f137be')) + for name, pin in matching_freeze['pins'].items(): + read(SOURCE/name, pin) + matching = json.loads(read(SOURCE/'MATCHING-EXITS-PROGRAMS.json', + '89ce6c4b426498e2fb9e7dfce9a4a192e3183644fef457c5b357baf63b9c6276')) + signed = dependencies['controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz'] + core = dependencies['new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz'] + geometry = dependencies['controller-followthrough-20261017/partial-orthogonal/SYMMETRIC-FAMILY.json'] + labels, routes = source_binding(packet, h6, signed, core, geometry) + results = {'general': general_checks(), 'transitions': transition_checks()} + W, Z = compile_circuit(packet['W']['circuit']), compile_circuit(packet['canonical_Z']) + need(Z == canonical([45]), 'Independent construction of the exact canonical Z') + FULL = [('C', 1 << j, 1) for j in range(9)] + need(packet['n'] == 9 and packet['a'] == 45 and packet['b'] == 1, 'Actual gauge parameters') + results['W'] = compare(W, gauge(9, 45, 1), 'Literal W', 2) + need(packet['W']['native_recipe']['rank'] == 1, 'Native W rank') + results['W_recipe'] = compare(recipe(packet['W']['native_recipe']), W, 'W native recipe', 2) + results['canonical_carry_binding'] = compare(recipe(routes.pop('_carry_recipe')), Z, 'Actual canonical Z', 2) + results['alignments'] = {} + for name, intended in [('W_Z_inverse', inverse(Z)+W), ('Z_inverse_W', W+inverse(Z))]: + row = packet['alignments'][name] + actual = compile_circuit(monomial(row['record'])) + need(actual == compile_circuit(row['circuit']), 'Serialized alignment circuit') + results['alignments'][name] = compare(actual, intended, name, 1) + results['pairs'] = [] + for row in packet['monomials']: + p, q = row['port'], row['q'] + need(q == labels[p] and row['q_partner'] == q ^ 45, 'Actual pair labels') + t, q0 = q & 1, q ^ (45 if q & 1 else 0) + need(row['q0'] == q0 and row['phase_coefficient'] == 2*t-1, 'Formula fields') + need(row['matrix_rows'] == [(1 << j) ^ (1 if q0 >> j & 1 else 0) for j in range(9)], + 'Formula address matrix') + canonical_pair = inverse(Z)+[('C', q ^ 45, -1), ('C', q, 1)]+Z + results['pairs'].append({'port': p, **compare(compile_circuit(monomial(row['canonical_record'])), + canonical_pair, 'Canonical pair '+str(p), 1)}) + print('canonical gauge and all actual pairs PASS', flush=True) + results['target_tails'] = [] + old_targets = {p: (old, adapter) for p, old, adapter in routes.pop('_target_checks')} + for row in packet['left_coded_tails']: + p, q = row['port'], row['q'] + need(q == labels[p] and row['recipe']['rank'] == row['left_coded_rank'] == 6 and + row['right_coded_rank'] == 8, 'Target rank declarations') + expected = inverse(Z)+[('C', q, -1)]+FULL+W + actual = recipe(row['recipe']) + need(actual == compile_circuit(row['circuit']), 'Native target serialization') + entry = {'port': p, **compare(actual, expected, 'Left target '+str(p), 64)} + right = inverse(Z)+W+[('C', q, -1)]+FULL + for x in range(512): + need(len(run(right, x)[0]) == 256, 'Right-coded rank eight on every column') + old, adapter = old_targets[p] + intended_old = inverse(Z)+[('C', q, -1)]+FULL + entry['old_endpoint_binding'] = compare(recipe(old)+inverse(recipe(adapter)), intended_old, + 'Actual old target exit '+str(p), 128) + need(run(actual, 0) != run(right, 0), 'Wrong W order rejects') + need(run(actual+[('M', tuple(range(512)), (2,)*512)], 0) != run(expected, 0), + 'Wrong global sign rejects') + results['target_tails'].append(entry) + if len(results['target_tails']) % 8 == 0: + print('target tails', len(results['target_tails']), 'PASS', flush=True) + results['source_tails'] = [] + old_sources = routes.pop('_source_old') + for row, old in zip(packet['left_coded_source_tails'], old_sources): + source = compile_circuit(row['source_frame']) + need(source == canonical(row['frame_basis']), 'Source frame and exact ordered basis') + need(row['recipe']['rank'] == row['new_rank'] == 1 and row['old_rank'] == 2, + 'Source rank declarations') + need(recipe(row['recipe']) == compile_circuit(row['circuit']), 'Native source serialization') + entry = {'vertex': row['vertex'], **compare(recipe(row['recipe']), inverse(source)+FULL+W, + 'Source tail '+str(row['vertex']), 2)} + actual_old, claimed_old = recipe(old), inverse(source)+FULL + mismatches = [] + for x in range(512): + if run(actual_old, x) != run(claimed_old, x): + mismatches.append(x) + need(len(run(actual_old+W, x)[0]) == 2, 'Actual coded H6 source rank one') + entry['h6_operator_binding'] = {'equal_columns': 512-len(mismatches), + 'first_mismatch': next(iter(mismatches), None), + 'actual_W_completed_support': 2} + results['source_tails'].append(entry) + results['pair_plane_tails'] = [] + for row in packet['left_coded_pair_plane_tails']: + p, r = row['ports'] + need(labels[p] ^ labels[r] == 45 and row['recipe']['rank'] == row['new_rank'] == 6 and + row['old_rank'] == 7, 'Actual pair plane and ranks') + source = compile_circuit(row['source_frame']) + need(source == canonical(row['frame_basis']), 'Pair plane and exact ordered basis') + need(recipe(row['recipe']) == compile_circuit(row['circuit']), 'Native plane serialization') + entry = {'ports': [p, r], **compare(recipe(row['recipe']), inverse(source)+FULL+W, + 'Pair plane '+str(p), 64)} + for x in range(512): + need(len(run(inverse(source)+FULL, x)[0]) == 128, 'Old pair-plane rank seven') + results['pair_plane_tails'].append(entry) + print('source tails and pair planes PASS', flush=True) + results['actual_h6_sources'] = [] + need(len(actual_sources['recipes']) == 16, 'Both actual providers and eight source vertices') + seen = set() + for row in actual_sources['recipes']: + provider, j = row['provider'], row['vertex'] + need((provider, j) not in seen, 'Unique actual source recipe') + seen.add((provider, j)) + word = h6['providers'][provider]['forward'] + frame = word['centre_frames'][j] + need(row['frame_id'] == frame and row['frame_basis'] == word['frames'][frame], + 'Exact actual H6 frame') + need(compile_circuit(row['frame_circuit']) == canonical(row['frame_basis']), + 'Independent actual source canonical frame') + need(row['recipe']['rank'] == 1 and recipe(row['recipe']) == compile_circuit(row['circuit']), + 'Actual one-child source recipe') + for direction in ('forward', 'backward'): + other = h6['providers'][provider][direction] + need(other['frames'][other['centre_frames'][j]] == row['frame_basis'] and + other['native_recipes'][str(frame)+':1'] == word['native_recipes'][str(frame)+':1'], + 'Both orientation source records are identical') + old = recipe(word['native_recipes'][str(frame)+':1']) + results['actual_h6_sources'].append({'provider': provider, 'vertex': j, + **compare(recipe(row['recipe']), old+W, 'Actual source binding', 2)}) + print('actual H6 source binding PASS', flush=True) + need(matching['gauge_freeze_sha256'] == '3c1669513029238abf181d4137b7a25efd4113c951ac78301a9da2c7e9df6ec1', + 'Matching gauge dependency') + need(matching['source_pins'] == packet['pins'], 'Same matching source pins') + results['matching_targets'] = [] + need(len(matching['target_exits']) == 48, 'All matching target exits') + for row in matching['target_exits']: + p, pair = row['port'], row['pair'] + need(p in pair and tuple(pair) in {tuple(e['ports']) for e in geometry['pair_edges']}, + 'Actual matching pair and target') + perpendicular = {x for x in range(512) if all((x & labels[z]).bit_count() % 2 == 0 for z in pair)} + need(span(row['input_frame_basis']) == perpendicular and len(row['input_frame_basis']) == 7, + 'Exact pair-perpendicular subspace') + source = compile_circuit(row['input_frame']) + need(source == canonical(row['input_frame_basis']), 'Literal matching input frame') + expected = inverse(source)+[('C', labels[p], -1)]+FULL+W + actual = compile_circuit(monomial(row['record'])) + need(actual == compile_circuit(row['circuit']) and row['new_rank'] == 0 and row['old_rank'] == 1, + 'Matching monomial record') + results['matching_targets'].append({'port': p, **compare(actual, expected, 'Matching target', 1)}) + need(len(run(expected+inverse(W), 0)[0]) == 2, 'Old matching target rank one') + orders = [[] for _ in range(8)] + for edge in geometry['pair_edges']: + for vertex, port in zip(edge['vertices'], edge['ports']): + orders[vertex].append(port) + need(all(len(order) == 6 for order in orders), 'Actual six-carrier cyclic orders') + results['cyclic_sources'] = [] + need(len(matching['cyclic_source_exits']) == 48, 'All cyclic source exits') + for row in matching['cyclic_source_exits']: + vertex, p = row['vertex'], row['carrier'] + order = orders[vertex] + index = order.index(p) + five = [order[(index+j) % 6] for j in range(5)] + need(row['cyclic_order'] == order and row['five_ports'] == five, 'Exact cyclic source order') + need(span(row['input_frame_basis']) == span([45]+[labels[q] for q in five]) and + len(row['input_frame_basis']) == 6, 'Actual cyclic source subspace') + source = compile_circuit(row['input_frame']) + need(source == canonical(row['input_frame_basis']), 'Literal cyclic input frame') + actual = recipe(row['recipe']) + need(actual == compile_circuit(row['circuit']) and row['new_rank'] == row['recipe']['rank'] == 2 and + row['old_rank'] == 3, 'Cyclic native record') + results['cyclic_sources'].append({'vertex': vertex, 'carrier': p, + **compare(actual, inverse(source)+FULL+W, 'Cyclic source', 4)}) + need(len(run(inverse(source)+FULL, 0)[0]) == 8, 'Old cyclic source rank three') + print('matching and cyclic exit phases PASS', flush=True) + control = receipt['width_two_control'] + q, chars = control['q'], control['characters'] + need(len(chars) == 2 and all((45 & x).bit_count() % 2 == 1 for x in chars), 'Width-two characters') + exponent = sum(((q & x).bit_count() % 2)-(((q ^ 45) & x).bit_count() % 2) for x in chars) % 4 + need(exponent == 2 and sum((45 & x).bit_count() % 2 for x in chars) % 2 == 0, + 'Simultaneous translation shortcut rejects') + old_profile = Counter() + for event in h6['providers']['base']['forward']['events']: + if event[0] == 'native': + old_profile[event[4]] += 1 + new_profile = old_profile.copy() + new_profile[2] -= 48; new_profile[1] += 48 + new_profile[7] -= 48; new_profile[6] += 48 + results.update(status='PASS', routes=routes, source_pins=PINS, + h6_route_delta={'old_profile': dict(sorted(old_profile.items())), + 'new_profile': {k:v for k,v in sorted(new_profile.items()) if v}, + 'old_mass': sum(k*v for k,v in old_profile.items()), + 'new_mass': sum(k*v for k,v in new_profile.items()), + 'children': sum(new_profile.values()), 'scalar_graph_delta': 0, + 'scope': 'The target replacement and corrected source recipes are bound to H6. Replace each selected target native exit together with its inverse endpoint adapter. The structural replacement gives W on 96 centre-bank outputs. Native side-map execution and complete supplier costs remain open.'}, + negative_controls={'wrong_W_order':48, 'wrong_global_sign':48, + 'tensor_simultaneous_translation':1}, + phase_method='Sparse exact Gaussian columns; no producer or Clifford compiler import.') + for name, value in [('REVIEW.json', results), ('INPUTS.json', INPUTS)]: + (args.output/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n') + print('PASS_ISOTROPIC_PAIR_INDEPENDENT_REVIEW', flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json new file mode 100644 index 0000000000..786ab73ff4 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "REPRODUCTION.json": "5fe7900ca1791738790a663c882ea411d8e3f41cdb9f9b7f5d23f06deffbf939", + "REVIEW.md": "f6ddd5a2581319ac5b07d402384c4847bce88f10505cca926c9287e838e1760f", + "check.py": "c2a8f93e2c1cf23f8fc279e6dc87d6bd923e60c438531fe1770b0992d1dfdb7d", + "normal/INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5", + "normal/REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f", + "optimized/INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5", + "optimized/REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f" + }, + "publication": "No PR, push, commit, or publication.", + "scope": "Both local arbitrary-record provider words, exact phases, same-reader restriction, and complete local invoice. No routed past-reader query or complete supplier claim.", + "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..e94c51f785 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REPRODUCTION.json @@ -0,0 +1,8 @@ +{ + "normal_optimized_byte_identical": { + "INPUTS.json": "7dd502092b351949a4312d9b94d78b4554474c140715a31d6b1ae849c1ecc7c5", + "REVIEW.json": "28b3fb22941c24fd208864c501f7992b887932d6186a6553abb1c46ef0a08d4f" + }, + "source_files_rechecked": 35, + "status": "PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md new file mode 100644 index 0000000000..5a1315e905 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/REVIEW.md @@ -0,0 +1,199 @@ +# Independent review of the local line-entry reuse interface + +The frozen word accepts sixteen arbitrary independent records in +positive line frames and preserves them as additive baselines. +Both providers pass the complete local map, frame, phase, and +invoice checks. No material defect was found. + +This is local reuse with the same reader. It is separate from the +query for a reader kept from an earlier routed stage. + +## Frozen inputs and method + +The producer +[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/LINE-ENTRY-REUSE-FREEZE.json) +has SHA256 +`a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60`. +The decompressed payload SHA256 is +`efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110`. + +The accepted formation +[review](../row-capture-native-review-20261020/FREEZE.json) +has SHA256 +`488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532`. +Its exact source payload has decompressed SHA256 +`7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2`. + +The checker imports only the pinned independent review helper and +its integer Gaussian phase interpreter. It imports no producer +code. It checks the new word by reverse output-column propagation +and a separate forward prefix-row pass. It compares exact spatial +columns for every new native recipe. + +## Exact arbitrary-record contract + +Keep the fixed selected set P and the actual response E from the +formation packet. Put \(W=V_P^{-1}V\), and let C have rows W on P +and identity rows elsewhere. For independent inputs x, ordinary +target values \(y_R\), and selected records \(z_P\), the physical +input is + +\[ +X_p=Q_px_p,\qquad +Y_p=y_p\quad(p\in R),\qquad +Y_p=Q_pz_p\quad(p\in P). +\] + +The physical output is + +\[ +X'_p=F_9x_p,\qquad +Y'_p=F_9q_p(y+Ex)_p\quad(p\in R),\qquad +Y'_p=F_9[z_p+(CEx)_p]\quad(p\in P). +\] + +The ordinary formula uses only \(y_R\); no selected baseline y is +needed there. All sixteen z records are independent of each other, +of x, and of every other field. The word does not form or decode z. + +## Literal order and field checks + +The word contains no row precode. Its event list is exactly: + +1. The 2390 retained core events from the accepted formation word. +2. Sixteen selected line-to-FULL native calls. +3. The 248 events in the accepted late-query word. + +Every retained event has its original bytes and order. No retained +event reads or writes a selected target. The selected records +therefore remain unchanged until their line-to-FULL calls. + +The new input frame on each selected target is exactly the source +line frame for that port. Its input adapter is the accepted source +adapter for that same port, with an explicit binding to the target +field. All 128 input view fields are distinct. + +Every source and selected target is FULL before the late query. +Every scalar addition has the same actual source and target frame. +The final declarations are identical to those of the formation +word. A selected input declared as I is rejected. + +Both providers pass all 640 arbitrary input columns. The column +for each selected record is exactly the unit column for that +record's output. All 416 fields outside the two data banks retain +their arbitrary values. No event accesses those fields, and no +new or owned field is introduced. + +The forward row pass agrees with the reverse-column result. An +omitted late query is rejected. + +## Exact phases + +All 1447 retained native recipes are byte equal to the accepted +formation records. The 112 source input adapters and the 96 +outgoing ordinary adapters are also exact inherited records. +The sixteen additional input adapters use the accepted source +records with their explicit new field bindings. + +For each selected port p, the new recipe must satisfy + +\[ +N_p\Gamma_{\mathrm{line}(p)}=F_9. +\] + +The independent interpreter checks this exact identity on all +512 spatial input columns. There are sixteen new recipes, hence +8192 complete spatial columns and 4194304 nonzero coefficients. +The checks include global phase. A wrong global phase is rejected. + +Combining this identity with the accepted input-adapter identity +gives the physical operation \(Q_pz_p\mapsto F_9z_p\). +No Q operator is moved through the reader or the response. +The exact spatial identities tensor to all widths admitted by +the retained native primitive contract. + +These H8 recipes retain their two generic monomial maps. The +identity-map refinement for a complete F9 call does not apply here. + +## Local invoice and precision scope + +Each provider has the exact profile + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H8. +``` + +The complete local counts are: + +| Item | Count | +| --- | ---: | +| Native children | 1520 | +| Native mass | 1792 | +| Old real scalar units | 9880 | +| Retained-core scalar units | 6456 | +| Late-query scalar units | 3424 | +| Input monomial views | 128 | +| Output monomial views | 96 | +| Native side-map upper bound | 3040 | +| New or private fields | 0 | +| Odd-arithmetic scans | 0 | + +The exact content row one-norm at emitted operation boundaries +is at most 112. The additional content binary denominator height +is one. These bounds include the full retained word and query. +They do not bound primitive internals, recursive-child numerical +guards, or accumulated roundoff. + +The sixteen calls remain rank-eight calls. Their exact recursive +sizes, the owner-view work, and the complete caller must be priced +before any complete supplier cost can be claimed. + +## The reader condition is necessary + +If z stores \(Wy\), the selected output stores \(W(y+Ex)\). +Thus the local update preserves that same reader. + +For a different stored reader L, the required update is \(LEx\). +The emitted update \(WEx\) is equal to it on all source inputs if +and only if + +\[ +(L-W)E=0. +\] + +The checker verifies both exact inverse orders for this actual E. +Therefore that condition is equivalent to \(L=W\). More generally, +the same implication holds for ordered operators when E has an +inverse. It does not require any commutation of L, W, or E. + +Consequently, a reader from an earlier routed stage needs its +actual ordered query \(L_sE_t\), unless equality of the transported +reader with the current local reader has been proved. The separate +bridge-access construction supplies such queries under its own +premises and invoice. The 9880 local figure is not that invoice. + +This review proves the local line-entry interface. It does not +prove a complete routed reuse, a final decoder, a recursive host, +a complete supplier, or a kappa improvement. + +## Reproduction and credit + +Run from the workspace root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/optimized +``` + +The required final line is +`PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE`. +The reproduction receipt records the final byte comparison and +source hash checks. +Both runs completed with the required result. Their result and +input receipts are byte identical. All 35 consumed source files +were rechecked and are unchanged. + +The producer proof retains the controller, cyclic-family, and +formation-work credit. AI assistance was used. No PR, push, commit, +or publication is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py new file mode 100644 index 0000000000..0419f9c41f --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py @@ -0,0 +1,200 @@ +#!/usr/bin/env python3 +"""Check the exact local interface for arbitrary line-encoded records.""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PREVIOUS = HERE.parent/'row-capture-native-review-20261020' +HELPER = PREVIOUS/'check.py' +HELPER_PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84' +if sha256(HELPER.read_bytes()).hexdigest() != HELPER_PIN: + raise ValueError('Independent review helper pin') +spec = importlib.util.spec_from_file_location('independent_row_review', HELPER) +review = importlib.util.module_from_spec(spec) +spec.loader.exec_module(review) +review.read(HELPER, HELPER_PIN) +need, read, frozen = review.need, review.read, review.frozen +P = review.P +SOURCE = review.NATIVE + + +def trace(word): + current = list(word['start']) + profile, used = Counter(), set() + for i, event in enumerate(word['events']): + if i == word['stage_ranges']['late_query'][0]: + need(all(current[p] == 1 for p in range(112)) and + all(current[112+p] == 1 for p in P), 'Complete common-FULL query cut') + if event[0] == 'native': + _, field, before, after, rank, key = event + need(0 <= field < 224 and current[field] == before, 'Native field and input frame') + need(word['native_recipes'][key]['rank'] == rank, 'Native occurrence rank') + current[field] = after + profile[rank] += 1 + used.add(key) + else: + need(event[0] == 'scalar', 'Event opcode') + _, scalar, frame = event + op, target, origin, _ = scalar + need(0 <= target < 224 and current[target] == frame, 'Scalar target frame') + if op == 'add': + need(0 <= origin < 224 and current[origin] == frame and target != origin, + 'Scalar source frame') + else: + need(op == 'scale' and origin is None, 'Scale grammar') + need(current == word['final'], 'Exact complete final frames') + need(used == set(word['native_recipes']), 'Every stored native recipe is used') + return profile + + +def check_word(word, old, e, ce): + need(word['frames'] == old['frames'] and word['final'] == old['final'], + 'Exact inherited frame geometry and output declarations') + expected_start = list(old['start']) + for p in P: + expected_start[112+p] = old['start'][p] + need(len(word['frames'][expected_start[112+p]]) == 1, + 'Selected canonical line frame') + need(word['start'] == expected_start, 'Only selected input frames change') + start, end = old['stage_ranges']['retained_core'] + kept = old['events'][start:end] + start, end = old['stage_ranges']['late_query'] + query = old['events'][start:end] + progress = [['native', 112+p, old['start'][p], 1, 8, 'capture-line:'+str(p)] for p in P] + need(word['events'] == kept+progress+query, 'Exact complete local reuse order') + need(word['retained_original_event_indices'] == old['retained_original_event_indices'], + 'Same retained raw events') + need(word['stage_ranges'] == { + 'precode': [0, 0], 'retained_core': [0, 2390], + 'selected_line_progress': [2390, 2406], 'late_query': [2406, 2654]}, + 'Exact reuse stage boundaries') + selected = {112+p for p in P} + for event in kept: + if event[0] == 'scalar': + need(event[1][1] not in selected and + (event[1][0] != 'add' or event[1][2] not in selected), + 'Retained core does not access selected records') + else: + need(event[1] not in selected, 'Retained native core does not access selected records') + inherited = set(old['native_recipes'])-{'capture-full'} + fresh = {'capture-line:'+str(p) for p in P} + need(set(word['native_recipes']) == inherited|fresh, 'Exact native recipe set') + for key in inherited: + need(word['native_recipes'][key] == old['native_recipes'][key], + 'Byte-equal inherited native recipe') + need(word['output_views'] == old['output_views'], 'All96 exact outgoing views') + source_views = {r['port']: r for r in old['input_views']} + inputs = [{**r, 'field': r['port']} for r in old['input_views']] + inputs += [{**source_views[p], 'role': 'selected_target', 'field': 112+p, + 'source_entry_port': p} for p in P] + need(word['input_views'] == inputs, 'Copied source adapters bound to actual target fields') + need(len({r['field'] for r in inputs}) == 128, 'Distinct charged input view fields') + count = trace(word) + need(count == {1: 1392, 2: 64, 3: 48, 8: 16}, 'Complete reuse native profile') + scalars = [event[1] for event in word['events'] if event[0] == 'scalar'] + expected = review.unit(640) + for p in range(112): + review.add(expected[112+p], ce[p] if p in P else e[p]) + columns = review.reverse(scalars, 640) + need(columns == review.transpose(expected, 640), 'All640 arbitrary input columns') + for p in P: + need(columns[112+p] == {112+p: F(1)}, 'Independent selected record preserved exactly') + actual, bound = review.prefix(scalars, 640) + need(actual == expected and actual[224:] == review.unit(640)[224:], + 'Separate forward map and arbitrary outside fields') + need(bound == {'row_one_norm': '112', 'binary_height': 1}, 'Complete local content bounds') + need(review.price(scalars) == 9880, 'Complete reuse scalar invoice') + need(review.price([e[1] for e in kept if e[0] == 'scalar']) == 6456 and + review.price([e[1] for e in query if e[0] == 'scalar']) == 3424, 'Both scalar stages') + bad = dict(word) + bad['start'] = list(word['start']) + bad['start'][112+P[0]] = 0 + try: + trace(bad) + except ValueError: + pass + else: + raise ValueError('Wrong selected I-frame control') + need(review.reverse([e[1] for e in kept if e[0] == 'scalar'], 640) != columns, + 'Omitted late-query control') + return { + 'input_columns': 640, 'arbitrary_selected_records': 16, 'unchanged_arbitrary_roles': 416, + 'events': len(word['events']), 'native_profile': dict(sorted(count.items())), + 'native_children': sum(count.values()), 'native_mass': sum(k*v for k, v in count.items()), + 'real_scalar_primitives': 9880, 'retained_scalar_primitives': 6456, + 'late_query_scalar_primitives': 3424, 'input_views': 128, 'output_views': 96, + 'native_side_maps_upper_bound': 3040, 'new_fields': 0, 'private_fields': 0, + 'odd_scans': 0, 'growth': bound, 'inherited_distinct_recipes': len(inherited), + 'fresh_distinct_recipes': len(fresh), + } + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', required=True, type=Path) + args = parser.parse_args() + frozen(PREVIOUS, 'FREEZE.json', + '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532') + frozen(SOURCE, 'LINE-ENTRY-REUSE-FREEZE.json', + 'a8e212f9cd3cc7ac4a020737ba4889c04a7ae6124877cf770b9555f6f3e54f60') + original = json.loads(read(SOURCE/'run-normal/PRODUCTIVE-CAPTURE.json.gz', + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', True)) + payload = json.loads(read(SOURCE/'reuse-normal/LINE-ENTRY-REUSE.json.gz', + 'efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110', True)) + need(payload['source_decompressed_sha256'] == + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', + 'Exact formation source') + need(payload['schema'] == 'productive-sixteen-line-entry-reuse-v1', 'Reuse schema') + need(payload['selected_ports'] == P and payload['ports'] == original['ports'] and + payload['ordinary_ports'] == original['ordinary_ports'], 'Actual ordered ports') + need(payload['response'] == original['response'] and + payload['selected_query_response'] == original['captured_response'], + 'Same local reader response') + need(set(payload['providers']) == {'base', 'extra'} and + payload['providers']['base'] == payload['providers']['extra'], 'Both exact providers') + e, ce = review.rows(payload['response']), review.rows(payload['selected_query_response']) + reports = {name: check_word(word, original['providers'][name], e, ce) + for name, word in payload['providers'].items()} + phase = review.inherit() + word = payload['providers']['base'] + full = [('C', 1 << j, 1) for j in range(9)] + checks = [] + for p in P: + frame = word['start'][112+p] + native = phase.recipe(word['native_recipes']['capture-line:'+str(p)]) + result = phase.compare(phase.canonical(word['frames'][frame])+native, + full, 'Exact selected line progress '+str(p), 512) + checks.append({'port': p, 'frame': frame, **result}) + first = P[0] + frame = word['start'][112+first] + bad = phase.canonical(word['frames'][frame])+phase.recipe( + word['native_recipes']['capture-line:'+str(first)])+phase.compile_circuit([['phase', 1]]) + need(phase.run(bad, 0) != phase.run(full, 0), 'Wrong global phase control') + raw = json.loads(read(review.RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz', + 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True)) + inverse = review.rows(raw['model']['response_inverse']) + need(review.mul(e, inverse) == review.unit(112) and + review.mul(inverse, e) == review.unit(112), 'Actual invertible response') + report = { + 'status': 'PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE', + 'literal_words': reports, 'fresh_phase_checks': checks, + 'exact_response_inverse_orders': True, + 'negative_controls': ['wrong selected I input frame', 'omitted late query', 'wrong global phase'], + 'reader_scope': 'The required update for a stored reader L is L E. Since E is invertible, equality with W E on all inputs requires L=W. No routed reader change is priced here.', + 'scope': 'Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.', + } + args.out.mkdir(parents=True, exist_ok=True) + for name, value in [('REVIEW.json', report), ('INPUTS.json', review.INPUTS)]: + (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n') + print(report['status'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json new file mode 100644 index 0000000000..668725b9d5 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/normal/INPUTS.json @@ -0,0 +1,110 @@ +{ + "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz": { + "decompressed_sha256": 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Since E is invertible, equality with W E on all inputs requires L=W. No routed reader change is priced here.", + "scope": "Complete local arbitrary-record reuse with the same reader, exact physical phases, and local invoice. No routed past-reader query, full caller, recursive host, or supplier claim.", + "status": "PASS_INDEPENDENT_LOCAL_LINE_ENTRY_REUSE" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json new file mode 100644 index 0000000000..1781475f6e --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json @@ -0,0 +1,8 @@ +{ + "normal_optimized_byte_identical": { + "EXTENSIONS-INPUTS.json": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3", + "EXTENSIONS-REVIEW.json": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3" + }, + "source_files_rechecked": 23, + "status": "PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json new file mode 100644 index 0000000000..8cfb592501 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json @@ -0,0 +1,15 @@ +{ + "base_review_freeze": "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976", + "files": { + "EXTENSIONS-REPRODUCTION.json": "5991ca1da15d3ffd7778e1de6be870c71f8811c867da6155e963e8bad1570aee", + "EXTENSIONS-REVIEW.md": "67efc6a9b0a04be1b9f2454db4ff5746d1bb389c2e80e0cff7f73e2481e4e798", + "check_extensions.py": "d6fcc9f2279bdd2e6b466dd42552f8add9a8fb05bef3f7f39030a582d729dd8f", + "extensions-normal/EXTENSIONS-INPUTS.json": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3", + "extensions-normal/EXTENSIONS-REVIEW.json": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3", + "extensions-optimized/EXTENSIONS-INPUTS.json": "819b8ee862d941367ed676b16e93a120a307b4edbb189d299c4a8d5d9832bed3", + "extensions-optimized/EXTENSIONS-REVIEW.json": "98f274b060b3118ce790e1386a895acd133c9e02f7ea08481f8ea8cbbddb05f3" + }, + "publication": "No PR, push, commit, or publication.", + "scope": "Exact local native reciprocal-large and rank16 data words. Odd-grid inverse implementation, productive helper progress, recursive host, terminal, and complete supplier remain separate.", + "status": "FROZEN_INDEPENDENT_NATIVE_EXTENSIONS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md new file mode 100644 index 0000000000..8a7aaff05c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md @@ -0,0 +1,177 @@ +# Independent native review of the two response extensions + +The reciprocal-large and rank-sixteen words pass the independent native +checks. Each complete word implements its declared response on all 640 +input roles in both directions. The two actual providers have identical +words and port directions. + +The reciprocal-large word uses the exact rank-thirty native sequence. +The rank-sixteen word uses 685 exact inherited ordered frame pairs and +876 new edges. All 876 new recipes pass all 512 spatial columns, including +global phase. The 224 endpoint adapters are unchanged. + +## Frozen inputs + +The consumed +[extension freeze](../../new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json) +has SHA256 +`aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689`. +Only its final v2 payloads are used: + +| Variant | Decompressed SHA256 | +| --- | --- | +| reciprocal-large | `e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416` | +| odd-grid-rank16 | `d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4` | + +The accepted base phase dependency is +[NATIVE-REVIEW-FREEZE.json](NATIVE-REVIEW-FREEZE.json), at SHA256 +`cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976`. +Its complete input and result receipts are pinned in the extension +checker. The extension does not repeat an inherited phase calculation. + +The separate +[matrix extension review](../../independent-review-20261017/response-extensions-review-20261020/FREEZE.json) +has SHA256 +`1c20e6736b1109ce10746472d3e00d464d5ea2629fe30c37a9d51bd5b74feedc`. +It owns the reciprocal identities, correction rank, principal inverses, +and clique geometry. This review checks that the literal native streams +implement those final matrices. The complete inputs are in +`extensions-normal/EXTENSIONS-INPUTS.json`. + +## Inherited and fresh physical operators + +A phase recipe is inherited only when both ordered frame bases and the +complete recipe are exactly equal to an accepted base entry. Equal +subspaces, equal native ranks, or equal frame names are not sufficient. + +For the reciprocal-large variant, the entire native occurrence sequence, +frame table, and recipe table are equal to the base word. There are 1141 +inherited edges and no fresh edge. Scalar coefficient changes and +omitted zero-coefficient ADDs do not change this native sequence. + +For the rank-sixteen variant, all 685 inherited entries pass that exact +comparison. Each of the other 876 entries is checked as + +\[ + R T_{\mathrm{old}}=T_{\mathrm{new}} +\] + +on all 512 spatial basis vectors. The independent sparse Gaussian +interpreter is the same as in the base review. It imports no producer, +Clifford compiler, or producer phase checker. The fresh checks cover +448512 complete columns and 41619456 exact nonzero coefficients. + +All entry and final frame IDs retain their exact ordered bases from the +base word. The 224 stored endpoint adapters are equal to the accepted +records. Their previously checked physical phases therefore apply +without a new endpoint sweep. + +## Complete data maps and legal access + +For either variant, let \(A\) be the response in that variant's final +model. The literal maps are + +\[ + F_A:(x,y,h)\longmapsto(x,y+Ax,h),\qquad + B_A:(x,y,h)\longmapsto(x-A^{\mathsf T}y,y,h). +\] + +The physical input is \(X=Qx,\ Y=y\). The physical output is +\(X=F_9x'\), \(Y=F_9Q^{-1}y'\). No response matrix is moved through \(Q\). +In particular, the backward map does not use \(A^{-1}\). + +The frame ledger verifies each native entry, each strictly nested exit, +each rank difference, each equal-frame scalar ADD, and every final +frame. It also checks that transfer metadata selects the actual ADD. +The complete reverse coefficient propagation checks every one of the +640 input columns in each direction. An omitted nonzero transfer is +rejected for both variants and both directions. + +Every operation is confined to the 224 data roles. All 416 other live +roles retain their arbitrary values and frames. There are no owned +fields, private fields, CLEAR operations, or hidden source accesses. +As in the base word, this supplies no productive progress on those roles. + +For the reciprocal-large variant, the separate matrix review proves + +\[ + A=E_{48}^{-\mathsf T}\oplus C. +\] + +Thus the backward map supplies the old large-sector inverse +\(-E_{48}^{-1}\). The small sector still supplies \(-C^{\mathsf T}\), +not \(-C^{-1}\). The native review preserves this exact scope. + +## Local invoices + +| Variant | Native profile | Children | Mass | Real scalar primitives | +| --- | --- | ---: | ---: | ---: | +| reciprocal-large | 1036 H1 + 48 H3 + 55 H4 + 55 H5 + 9 H6 + 9 H7 | 1212 | 1792 | 5288 | +| odd-grid-rank16 | 1520 H1 + 64 H2 + 48 H3 | 1632 | 1792 | 7384 | + +Both directions have the stated profile and scalar bill. Each word has +224 external endpoint maps. The native side-map upper bounds are 2424 +and 3264, respectively. These maps are not treated as free. + +The native mass still telescopes to eight per data role. The number and +sizes of the children change. Equal mass alone therefore does not prove +equal recursive cost. + +The exact top-level array norm bounds are 30 forward and 46 backward +for the reciprocal-large variant. The rank-sixteen bound is 22 in either +direction. These are bounds at the literal event boundaries, not on +recursive or scalar primitive internals. + +The scalar price check admits only nonzero dyadic ADD coefficients and +dyadic unit scales. Every native phase recipe has Gaussian-dyadic +entries. No odd division occurs in either emitted native word. + +## What the rank-sixteen word does not implement + +The separate matrix review proves that the rank-sixteen response is an +integer matrix whose correction has rank sixteen. Its inverse uses +denominators five and seven. The selected ordinary normalization also +uses prime 31. + +Those inverse matrices are metadata and later code requirements. They +are not native instructions in the word checked here. This review does +not turn division by five, seven, or 31 into a dyadic scalar primitive. +It does not prove the retained-grid conversion, a denominator-height +bound, legal access for the inverse queries and scatters, or the final +conversion. + +The rank-sixteen opportunity changes two restrictions. It uses an inverse +with a nonzero diagonal as a later scalar code, and it permits the odd +denominators needed by that code. Odd denominators alone do not defeat +the earlier reciprocal zero-diagonal rank-two obstruction. + +Recursive child hosting, productive helper progress, the full precision +bound, stage access, terminal removal, and the complete supplier remain +open. The selected frontier and the complete kappa calculation do not +change as a result of this local review. + +## Reproduction + +First reproduce the base native review. Then run, from the workspace +root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-optimized +``` + +The expected final line is: + +```text +PASS_INDEPENDENT_NATIVE_EXTENSIONS +``` + +Both final runs passed, with byte-identical result and input receipts. +The extension review freeze records that comparison and the final input +hash check. All producer and base-review bytes are +preserved. The source packets retain credit for the response, cyclic +flags, pair factors, and phase construction. AI assistance was used. + +No PR, push, commit, or publication is authorized. Before any future PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json new file mode 100644 index 0000000000..f19774d033 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json @@ -0,0 +1,8 @@ +{ + "normal_optimized_byte_identical": { + "INPUTS.json": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90", + "REVIEW.json": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6" + }, + "source_files_rechecked": 20, + "status": "PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json new file mode 100644 index 0000000000..05fc30b335 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "NATIVE-REPRODUCTION.json": "57e3b9367f31183f95a66c9ff8c41350dbbe5d771f97a69b71654e42ce045b0c", + "REVIEW.md": "2ef8464d4f8b4867dfacdc7515285d690eb84adc299b7d7ebd1ce46ede1c7b29", + "check_native.py": "e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56", + "normal/INPUTS.json": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90", + "normal/REVIEW.json": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6", + "optimized/INPUTS.json": "8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90", + "optimized/REVIEW.json": "ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6" + }, + "publication": "No PR, push, commit, or publication.", + "scope": "Exact local native data word and phases. No productive helper progress, recursive host, routed inverse code, terminal, or complete supplier claim.", + "status": "FROZEN_INDEPENDENT_NATIVE_RANK30" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md new file mode 100644 index 0000000000..affe6325a2 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md @@ -0,0 +1,193 @@ +# Independent native review of the rank-thirty data word + +The literal native word passes the independent physical checks. It +implements the declared local response on all 640 input roles. Every one +of its 1141 distinct native edges and 224 endpoint adapters passes an +exact check on all 512 spatial input columns, including global phase. +The local invoice is 1792 native mass, 1212 native children, and 5288 real +scalar primitives in each direction. + +This is a local data operation. It does not provide productive progress +for the 416 other live roles, a recursive host, a routed inverse code, a +terminal construction, or a complete supplier bound. + +## Sources and separate review + +The consumed +[native freeze](../../new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json) +has SHA256 +`efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24`. +The decompressed payload hash is +`e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558`. +The reviewer uses only the final `native-normal-v2` payload. It does not +use an earlier draft. + +The +[matrix and common-frame scalar review](../../independent-review-20261017/rank-thirty-review-20261020/FREEZE.json) +has SHA256 +`15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189`. +It owns the matrix factorization, correction rank, inverses, clique +census, and common-frame scalar codes. This review binds the literal +native program to that exact response. It does not repeat those matrix +proofs. In particular, its scalar invoice is the complete native word's +invoice, not the separate common-frame code invoice. + +The physical interpreter is the +[independent sparse Gaussian interpreter](../isotropic-pair-review-20261018/check.py), +at SHA256 +`e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18`. +The reviewer does not import the producer, its Clifford compiler, or its +Pauli/state checker. All consumed source hashes are in +`normal/INPUTS.json`. + +## Exact edge theorem and phase check + +Let \(T_f\) denote the canonical operator built from the literal ordered +basis of frame \(f\). Let \(R\) denote an emitted recipe for a declared +edge \(a\longrightarrow b\). The reviewer checks + +\[ + R T_a=T_b +\] + +on all 512 spatial basis vectors. Since \(T_a\) is unitary, this is +equivalent to \(R=T_bT_a^{-1}\). The check does not replace an ordered +basis by another basis of the same space. It also does not infer the +phase from a rank or from a symplectic matrix. + +The interpreter uses integer real and imaginary coefficients with +powers of two as denominators. It applies the literal affine maps, +quadratic phases, fourth-root phases, and coordinate C gates. It compares +the complete output coefficient dictionaries. This fixes global phase. +The output support is also checked against \(2^{\dim b}\) in the displayed +identity. + +For a source endpoint with physical convention \(Q_p=C_{q_p}\), the +adapter check is + +\[ + A_p Q_p=T_{\mathrm{line}(q_p)}. +\] + +For a target endpoint, it is + +\[ + A_p F_9Q_p^{-1}=T_{\mathrm{hole}(q_p)}. +\] + +Thus the target uses the inverse of its stored adapter at exit. All 224 +adapters are rank zero, each with one explicit monomial map. + +The 1365 checks cover 698880 spatial columns and 69706752 exact nonzero +coefficients. A wrong fourth-root global phase is rejected. The check +uses no floating-point arithmetic and no sampled input vectors. + +Under the inherited columnwise tensor model, the complete one-column +identity extends to every field width. Constant phases must tensor with +the operator; a phase \(i^c\) in each of \(f\) columns gives \(i^{cf}\). +The local test does not replace that factor by a width-independent phase. +All primitive C kernels and monomial maps have Gaussian-dyadic entries. +This fact does not supply a recursive implementation or its workspace. + +## Complete literal word + +The physical input is \(X_p=Q_px_p,\ Y_p=y_p\). The physical output is + +\[ + X_p=F_9x'_p,\qquad Y_p=F_9Q_p^{-1}y'_p. +\] + +The two logical maps are + +\[ + F:(x,y,h)\longmapsto(x,y+Ex,h),\qquad + B:(x,y,h)\longmapsto(x-E^{\mathsf T}y,y,h). +\] + +The backward response uses the transpose, not the inverse. +No scalar response is moved through \(Q\). + +The reviewer tracks each role's actual frame at every event. Each +native edge is strictly nested, and its positive rank equals the +difference in the two frame dimensions. Each scalar ADD has exactly +equal source and target frame IDs. All declared frame bases are +independent. Each source starts at its actual line, and each target ends +at its actual perpendicular hole. + +These checks give a direct induction. If a physical role is \(T_av\), +the checked edge changes it to \(T_bv\). An equal-frame scalar ADD changes +the logical contents by the same scalar ADD. The endpoint checks give +the displayed physical conventions. + +A separate reverse propagation computes the complete scalar map. +For \(t\leftarrow t+cs\), an output coefficient at \(t\) contributes \(c\) +times that coefficient at \(s\). This proves all 640 columns at once. +The two providers' complete serialized words are equal, and their +actual port directions agree. Both directions are checked. These +checks therefore cover all four provider/direction uses. + +Every operation reads or writes only the 224 data roles. The 416 +remaining roles are arbitrary and unchanged, with their input frames +retained. There is no owned field, private field, CLEAR, or hidden source. +The actual transfer metadata selects the claimed ADD event. Removing a +nonzero transfer changes the complete response and is rejected. + +## Invoice and scope + +| Rank | Child count | +| --- | ---: | +| 1 | 1036 | +| 3 | 48 | +| 4 | 55 | +| 5 | 55 | +| 6 | 9 | +| 7 | 9 | + +There are 1212 children and native mass 1792. Each X role advances from +dimension one to dimension nine, and each Y role advances from dimension +zero to dimension eight. Since all edges are nested, the rank sums +telescope to eight per role. This explains the total mass but does not +make different child profiles have the same recursive price. + +There are 224 external endpoint maps and at most 2424 native side maps. +The complete scalar bill is 5288 real primitives. The reviewer sums the +accepted cost of every literal dyadic ADD and unit scale. + +At top-level operation boundaries, each forward array has norm at most +46 times the maximum input-array norm. The backward bound is 30. +The reviewer computes the exact prefix row absolute sums. These bounds +do not cover scalar primitive internals or recursive child internals. + +At the level of the literal word, there is no borrowed-state restoration +debt because those roles are never accessed. The word also makes no +productive progress on them. +That distinction is required before this word can replace an actual +supplier component. Recursive child hosting, complete precision, +routed controller access, and terminal work remain separate obligations. +The selected frontier and the complete kappa calculation do not change +as a result of this review. + +## Reproduction + +From the workspace root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-review-20261020/optimized +``` + +The expected final line is: + +```text +PASS_INDEPENDENT_FULL_NATIVE_RANK30 +``` + +Both final runs passed. Their review and input receipts are byte-identical. +The native review freeze records the two-mode comparison and the final +input hash check. All source files remain unchanged. AI assistance was used. +The response, cyclic flag, pair-code, and native phase predecessors keep +the credit given in their pinned source packets. + +No PR, push, commit, or publication is authorized. Before any future PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py new file mode 100644 index 0000000000..33c667c847 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py @@ -0,0 +1,158 @@ +#!/usr/bin/env python3 +"""Check exact path reuse and the fresh native edges in the frozen extensions.""" +from hashlib import sha256 +from pathlib import Path +from fractions import Fraction as F +import argparse +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES/'new-core-transfer-20261017/low-displacement-20261020' + + +def load(name, path, pin): + if sha256(path.read_bytes()).hexdigest() != pin: + raise ValueError('Independent interpreter pin: '+str(path)) + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + return module + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=True) + review = load('rank30_native_review', HERE/'check_native.py', + 'e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56') + need = review.need + review.read(HERE/'check_native.py', + 'e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56') + review.frozen(HERE, 'NATIVE-REVIEW-FREEZE.json', + 'cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976') + review.frozen(LANES/'independent-review-20261017/response-extensions-review-20261020', + 'FREEZE.json', '1c20e6736b1109ce10746472d3e00d464d5ea2629fe30c37a9d51bd5b74feedc') + base_receipts = { + 'REVIEW.json': 'ea1674fbd0549cbf9161f1754a9dc0cb76d9c257ef295b391da9271df91a1aa6', + 'INPUTS.json': '8729c993a8eac3ed60b96c414160a4be8be33fb013905942ca9bdf61df728d90', + } + for name, digest in base_receipts.items(): + a = (HERE/'normal'/name).read_bytes() + b = (HERE/'optimized'/name).read_bytes() + need(a == b, 'Completed independent base runs agree') + review.read(HERE/'normal'/name, digest) + review.read(HERE/'optimized'/name, digest) + checked = json.loads((HERE/'normal/REVIEW.json').read_text()) + need(checked['status'] == 'PASS_INDEPENDENT_FULL_NATIVE_RANK30' + and len(checked['native_phase_checks']) == 1141 + and len(checked['endpoint_phase_checks']) == 224, 'Complete base phase dependency') + review.frozen(SOURCE, 'EXTENSIONS-FREEZE.json', + 'aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689') + raw = json.loads(review.read(SOURCE/'native-normal-v2/NATIVE-PROGRAM.json.gz', + 'e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558', True)) + base = raw['providers']['base']['forward'] + known = {} + for key, record in base['native_recipes'].items(): + before, after = map(int, key.split(':')) + pair = tuple(base['frames'][before]), tuple(base['frames'][after]) + need(pair not in known or known[pair] == record, 'Unambiguous base physical edge') + known[pair] = record + phase_path = HERE.parent/'isotropic-pair-review-20261018/check.py' + phase_pin = 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18' + review.read(phase_path, phase_pin) + phase = load('full_spatial_extension_review', phase_path, phase_pin) + pins = { + 'reciprocal-large': ('reciprocal-normal-v2', 'e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416'), + 'odd-grid-rank16': ('odd16-normal-v2', 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4'), + } + reports = {} + for kind, (directory, digest) in pins.items(): + data = json.loads(review.read(SOURCE/directory/'EXTENSION-PROGRAM.json.gz', digest, True)) + need(data['kind'] == kind and set(data['providers']) == {'base', 'extra'}, 'Exact extension family') + need(data['providers']['base'] == data['providers']['extra'], 'Both provider words are byte-equal') + words = data['providers']['base'] + need(set(words) == {'forward', 'backward'}, 'Both extension directions') + word = words['forward'] + ports = data['model']['ports'] + frames = word['frames'] + response = [{int(k): F(v) for k, v in row.items()} for row in data['model']['response']] + need(data['model']['selected_ports'] == raw['selected_ports'], 'Actual selected partition') + per_word, used = {}, set() + for direction, current in words.items(): + need(current['frames'] == frames and current['native_recipes'] == word['native_recipes'], + 'Directions share exact native phase geometry') + need(current['start'] == base['start'] and current['final'] == base['final'] + and current['endpoint_adapters'] == base['endpoint_adapters'], + 'Exact retained endpoint arrays and adapters') + for index in set(current['start']+current['final']): + need(frames[index] == base['frames'][index], 'Exact ordered endpoint frame basis') + report, edges = review.ledger(current, ports, response, direction) + want = ({1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9} + if kind == 'reciprocal-large' else {1: 1520, 2: 64, 3: 48}) + need(report['native_profile'] == want and report['native_mass'] == 1792, + 'Complete extension native invoice') + need(report['real_scalar_primitives'] == (5288 if kind == 'reciprocal-large' else 7384), + 'Complete extension scalar invoice') + wanted_bound = ('30' if direction == 'forward' else '46') if kind == 'reciprocal-large' else '22' + need(report['top_level_array_norm_bound'] == wanted_bound, 'Complete extension prefix bound') + if kind == 'reciprocal-large': + old = raw['providers']['base'][direction] + need(current['frames'] == old['frames'] + and current['native_recipes'] == old['native_recipes'], + 'Reciprocal geometry and recipes are byte-equal') + need([e for e in current['events'] if e[0] == 'native'] == + [e for e in old['events'] if e[0] == 'native'], + 'Reciprocal native occurrence sequence is byte-equal') + per_word[direction] = report + used |= edges + need(used == set(word['native_recipes']), 'All and only the emitted extension recipes are checked') + inherited, fresh = [], [] + frame_cache = {} + + def frame(index): + if index not in frame_cache: + frame_cache[index] = phase.canonical(frames[index]) + return frame_cache[index] + + for key, record in word['native_recipes'].items(): + before, after = map(int, key.split(':')) + pair = tuple(frames[before]), tuple(frames[after]) + if pair in known: + need(record == known[pair], 'Exact inherited recipe at the same ordered frame pair') + inherited.append(key) + continue + result = phase.compare(frame(before)+phase.recipe(record), frame(after), + kind+' native '+key, 1 << len(frames[after])) + fresh.append({'edge': key, 'rank': record['rank'], **result}) + if len(fresh) % 40 == 0: + print('Independent fresh extension edges', kind, len(fresh), flush=True) + need((len(inherited), len(fresh)) == ((1141, 0) if kind == 'reciprocal-large' else (685, 876)), + 'Exact inherited and fresh phase counts') + for direction, current in words.items(): + missing = list(current['events']) + del missing[current['transfer_records'][0]['event']] + need(review.reverse(missing) != review.response_columns(response, direction), + 'An omitted transfer changes the full extension response') + reports[kind] = { + 'literal_words': per_word, 'both_providers': ['base', 'extra'], + 'exact_inherited_frame_pairs': inherited, 'fresh_native_phase_checks': fresh, + 'inherited_endpoints': 224, 'owned_fields': 0, 'private_fields': 0, + 'untouched_arbitrary_roles': 416, + 'inverse_grid_implementation': 'Not supplied or priced by this native review.', + } + print('Literal extension', kind, 'PASS', flush=True) + output = { + 'status': 'PASS_INDEPENDENT_NATIVE_EXTENSIONS', + 'extensions': reports, 'spatial_columns_per_fresh_edge': 512, + 'scope': 'Complete local native data responses and physical phases. Matrix and inverse-code claims require their separate reviews. No odd-grid implementation, productive helper progress, recursive host, stage or terminal construction, or full supplier claim.', + } + for name, value in (('EXTENSIONS-REVIEW.json', output), ('EXTENSIONS-INPUTS.json', review.INPUTS)): + (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n') + print(output['status'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py new file mode 100644 index 0000000000..d8a4b0dd76 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py @@ -0,0 +1,268 @@ +#!/usr/bin/env python3 +"""Check all native edges, endpoint phases, and complete literal data words.""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES/'new-core-transfer-20261017/low-displacement-20261020' +PEER = LANES/'independent-review-20261017/rank-thirty-review-20261020' +INPUTS = {} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(path, pin=None, compressed=False): + data = path.read_bytes() + digest = sha256(data).hexdigest() + content = gzip.decompress(data) if compressed else data + need(pin is None or sha256(content).hexdigest() == pin, 'Input pin: '+str(path)) + INPUTS[str(path.relative_to(LANES))] = {'sha256': digest} + if compressed: + INPUTS[str(path.relative_to(LANES))]['decompressed_sha256'] = sha256(content).hexdigest() + return content + + +def frozen(path, name, pin): + record = json.loads(read(path/name, pin)) + for file, digest in record['files'].items(): + read(path/file, digest) + return record + + +def add(target, source, coefficient): + for key, value in source.items(): + result = target.get(key, F(0))+coefficient*value + if result: + target[key] = result + else: + target.pop(key, None) + + +def span(vectors): + result = {0} + for vector in vectors: + result |= {x ^ vector for x in result} + return result + + +def reverse(events): + """Return the full map by reverse propagation of output coefficients.""" + columns = [{i: F(1)} for i in range(640)] + for event in reversed(events): + if event[0] != 'scalar': + continue + op, target, origin, coefficient = event[1] + c = F(coefficient) + if op == 'scale': + columns[target] = {j: c*v for j, v in columns[target].items()} + else: + need(op == 'add' and target != origin, 'Scalar grammar') + add(columns[origin], columns[target], c) + return columns + + +def response_columns(response, direction): + columns = [{i: F(1)} for i in range(640)] + for target, row in enumerate(response): + for origin, coefficient in row.items(): + if direction == 'forward': + add(columns[origin], {112+target: coefficient}, F(1)) + else: + add(columns[112+target], {origin: -coefficient}, F(1)) + return columns + + +def scalar_price(events): + count = 0 + for event in events: + if event[0] != 'scalar': + continue + op, _, _, value = event[1] + c = F(value) + n, d = abs(c.numerator), c.denominator + need(n > 0 and d & (d-1) == 0, 'Nonzero dyadic scalar coefficient') + if op == 'scale': + need(n & (n-1) == 0, 'Dyadic unit scale') + count += 2*(abs(n.bit_length()-d.bit_length())+(c < 0)) + else: + count += 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) + return count + + +def ledger(word, ports, response, direction): + current = list(word['start']) + frames = word['frames'] + spaces = [span(basis) for basis in frames] + need(len(current) == len(word['final']) == 640, 'Exactly 640 live roles') + need(all(len(s) == 1 << len(b) and all(0 <= x < 512 for x in s) + for s, b in zip(spaces, frames)), 'Independent literal frame bases') + for p, q in enumerate(ports): + need(spaces[current[p]] == {0, q} and spaces[current[112+p]] == {0}, + 'Actual physical source line and target I') + need(len(spaces[word['final'][p]]) == 512, 'Final X is FULL') + need(spaces[word['final'][112+p]] == + {x for x in range(512) if (x & q).bit_count() % 2 == 0}, + 'Final Y is the actual q hole') + used = set() + prefix_rows = [{i: F(1)} for i in range(224)] + maximum = F(1) + for event in word['events']: + if event[0] == 'native': + _, target, before, after, rank, key = event + need(0 <= target < 224 and current[target] == before, 'Actual native source role and frame') + need(spaces[before] < spaces[after], 'Strictly nested native frame') + need(rank == len(frames[after])-len(frames[before]) + == word['native_recipes'][key]['rank'], 'Native rank and dimension difference') + need(key == str(before)+':'+str(after), 'Native occurrence has the exact edge key') + current[target] = after + used.add(key) + else: + need(event[0] == 'scalar', 'No hidden operation') + gate, frame = event[1:] + op, target, origin, coefficient = gate + need(0 <= target < 224 and current[target] == frame, 'Scalar target has the declared frame') + c = F(coefficient) + if op == 'scale': + need(origin is None, 'Scale has no hidden source') + prefix_rows[target] = {j: c*v for j, v in prefix_rows[target].items()} + else: + need(op == 'add' and 0 <= origin < 224 and origin != target + and current[origin] == frame, 'Scalar source has the same actual frame') + add(prefix_rows[target], prefix_rows[origin], c) + maximum = max(maximum, sum(abs(v) for v in prefix_rows[target].values())) + need(current == word['final'], 'Every final frame') + need(current[224:] == word['start'][224:], 'All 416 other roles remain in their input frame') + need(reverse(word['events']) == response_columns(response, direction), 'All 640 reverse columns') + profile = Counter(e[4] for e in word['events'] if e[0] == 'native') + for transfer in word['transfer_records']: + event = word['events'][transfer['event']] + need(event[0] == 'scalar' and event[1][0] == 'add' + and event[1][-1] == transfer['coefficient'], 'Transfer metadata selects the actual ADD') + return { + 'all_input_columns': 640, 'untouched_arbitrary_roles': 416, + 'owned_fields': 0, 'private_fields': 0, 'used_native_edges': len(used), + 'native_profile': dict(sorted(profile.items())), + 'native_mass': sum(rank*count for rank, count in profile.items()), + 'native_children': sum(profile.values()), 'real_scalar_primitives': scalar_price(word['events']), + 'top_level_array_norm_bound': str(maximum), + }, used + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=True) + frozen(SOURCE, 'NATIVE-FREEZE.json', + 'efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24') + frozen(SOURCE, 'RESPONSE-FREEZE.json', + '59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9') + frozen(PEER, 'FREEZE.json', + '15c54c0f0d0f33bdcf420a4c7610d55fff6104fe22d2c4ade8ae9255a3ff8189') + payload = json.loads(read(SOURCE/'native-normal-v2/NATIVE-PROGRAM.json.gz', + 'e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558', True)) + for relative, (mode, pin) in payload['source_pins'].items(): + read(LANES/relative, pin, mode == 'decompressed') + cyclic = json.loads(read(LANES/'independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json', + '3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585')) + core = json.loads(read(LANES/'new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz', + 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa', True)) + model = json.loads(read(SOURCE/'run-normal/RESPONSE-PROGRAM.json', + '5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c')) + need(payload['response'] == model['response'], 'Exact matrix-layer response') + ports = cyclic['ports'] + need(all(p['canonical']['ports'] == ports for p in core['providers'].values()), + 'Both actual providers have the same port labels') + interpreter = HERE.parent/'isotropic-pair-review-20261018/check.py' + read(interpreter, 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18') + spec = importlib.util.spec_from_file_location('spatial_native_review', interpreter) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + need(set(payload['providers']) == {'base', 'extra'}, 'Both providers') + need(payload['providers']['base'] == payload['providers']['extra'], 'Byte-equal provider words') + words = payload['providers']['base'] + need(set(words) == {'forward', 'backward'}, 'Both directions') + first = words['forward'] + for word in words.values(): + need(word['frames'] == first['frames'] and word['native_recipes'] == first['native_recipes'] + and word['endpoint_adapters'] == first['endpoint_adapters'], 'One exact native geometry') + need(word['start'] == cyclic['start'] and word['final'] == cyclic['final'], + 'Exact inherited input and output frame declarations') + frame_cache = {} + + def frame(index): + if index not in frame_cache: + frame_cache[index] = phase.canonical(first['frames'][index]) + return frame_cache[index] + + response = [{int(k): F(v) for k, v in row.items()} for row in payload['response']] + reports, union = {}, set() + for direction, word in words.items(): + report, used = ledger(word, ports, response, direction) + need(report['native_profile'] == {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}, + 'Complete declared native profile') + need(report['native_mass'] == 1792 and report['native_children'] == 1212 + and report['real_scalar_primitives'] == 5288, 'Complete local invoice') + need(report['top_level_array_norm_bound'] == ('46' if direction == 'forward' else '30'), + 'Exact top-level prefix bound') + reports[direction] = report + union |= used + need(union == set(first['native_recipes']) and len(union) == 1141, + 'Every fresh recipe is used and every used edge is checked') + phases = [] + for i, (key, record) in enumerate(first['native_recipes'].items(), 1): + before, after = map(int, key.split(':')) + result = phase.compare(frame(before)+phase.recipe(record), frame(after), + 'Native '+key, 1 << len(first['frames'][after])) + phases.append({'edge': key, 'rank': record['rank'], **result}) + if i % 40 == 0: + print('Independent full native columns', i, '/ 1141', flush=True) + endpoints = first['endpoint_adapters'] + need(len(endpoints) == 224 and {(r['port'], r['role']) for r in endpoints} == + {(p, role) for p in range(112) for role in ('source', 'target')}, 'All 224 endpoints') + endpoint_checks = [] + full = [('C', 1 << j, 1) for j in range(9)] + for i, record in enumerate(endpoints, 1): + p, role = record['port'], record['role'] + target_frame = first['start'][p] if role == 'source' else first['final'][112+p] + need(record['rank'] == 0 and record['right'] is None and record['frame'] == target_frame, + 'One explicit endpoint monomial with the actual endpoint frame') + conventional = [('C', ports[p], 1)] if role == 'source' else [('C', ports[p], -1)]+full + result = phase.compare(conventional+phase.recipe(record), frame(target_frame), + 'Endpoint '+role+' '+str(p), 1 << len(first['frames'][target_frame])) + endpoint_checks.append({'port': p, 'role': role, **result}) + if i % 32 == 0: + print('Independent full endpoint columns', i, '/ 224', flush=True) + key = next(iter(first['native_recipes'])) + before, after = map(int, key.split(':')) + bad = frame(before)+phase.recipe(first['native_recipes'][key])+phase.compile_circuit([['phase', 1]]) + need(phase.run(bad, 0) != phase.run(frame(after), 0), 'Wrong global phase control') + missing = list(first['events']) + del missing[first['transfer_records'][0]['event']] + need(reverse(missing) != response_columns(response, 'forward'), 'Missing transfer control') + result = { + 'status': 'PASS_INDEPENDENT_FULL_NATIVE_RANK30', + 'literal_words': reports, 'providers_share_exact_words': ['base', 'extra'], + 'native_phase_checks': phases, 'endpoint_phase_checks': endpoint_checks, + 'native_edges': 1141, 'endpoint_maps': 224, 'spatial_columns_per_check': 512, + 'negative_controls': ['wrong global phase', 'one omitted nonzero transfer'], + 'matrix_layer_review': 'independent-review-20261017/rank-thirty-review-20261020/FREEZE.json', + 'scope': 'Complete local data maps and physical phases. No productive helper progress, recursive host, routed inverse code, terminal decoder, or complete supplier claim.', + } + for name, value in (('REVIEW.json', result), ('INPUTS.json', INPUTS)): + (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+'\n') + print(result['status'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json new file mode 100644 index 0000000000..8e38cab0a9 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json @@ -0,0 +1,74 @@ +{ + "independent-review-20261017/response-extensions-review-20261020/CHECKS.json": { + "sha256": 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"providers_share_exact_words": [ + "base", + "extra" + ], + "scope": "Complete local data maps and physical phases. No productive helper progress, recursive host, routed inverse code, terminal decoder, or complete supplier claim.", + "spatial_columns_per_check": 512, + "status": "PASS_INDEPENDENT_FULL_NATIVE_RANK30" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/FREEZE.json new file mode 100644 index 0000000000..3fb72bc88d --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/FREEZE.json @@ -0,0 +1,18 @@ +{ + "actual_code_source_decompressed_sha256": "b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32", + "files": { + "REPRODUCTION.json": "0388d961a4b372085f7e9c009be044b01b1a79d37dfd8395bd2ea1f22720d369", + "REVIEW.md": "79fb1c1ce1a35bbd9242a0164cf48032b1e42b0ca8e3bb2f093f7218a22ac258", + "check.py": "ddf0d1bb13cdd7ad1bd536f4e2387eee2e6a70721f2cadd8061c4db4c1235303", + "normal-final/INPUTS.json": "5231e3f636b2e35456af9fb020950f3570f45daec9db9cd3fc88c2cb2ce8be23", + "normal-final/REVIEW.json": "d929f05a9ad601007b046602ecd52ba4b2709fe8315e325475817eb9ece1c6d7", + "optimized-final/INPUTS.json": "5231e3f636b2e35456af9fb020950f3570f45daec9db9cd3fc88c2cb2ce8be23", + "optimized-final/REVIEW.json": "d929f05a9ad601007b046602ecd52ba4b2709fe8315e325475817eb9ece1c6d7" + }, + "normal_optimized_bytes_equal": true, + "producer_freeze_sha256": "2db9b1d5425dea76345ecbfde9a601e47a620693fc5e58350d311db292fc5fdc", + "publication": "No PR, commit, push or publication. Before any future PR description read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.", + "schema": "independent-rational-unitary-packing-grid-review-freeze-v1", + "scope": "Paid scalar words at one common complex frame, exact divisibility domains, fixed-odd scans and conditional root-grid admission. No native response, mixed-hole access, unmatched recursive child or complete supplier is admitted.", + "status": "PASS_INDEPENDENT_REVIEW" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..44b8ae3b1b --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/REPRODUCTION.json @@ -0,0 +1,17 @@ +{ + "all_claimed_scalar_invoices_and_prefix_bounds_match": true, + "checked_local_links": [ + "bridge-access-20261017/rational-unitary-packing-20261020/FREEZE.json", + "new-native-recipes-20261017/rational-packing-grid-review-20261020/check.py", + "new-native-recipes-20261017/rational-packing-grid-review-20261020/normal-final/INPUTS.json", + "new-native-recipes-20261017/rational-packing-grid-review-20261020/normal-final/REVIEW.json" + ], + "checker_sha256": "ddf0d1bb13cdd7ad1bd536f4e2387eee2e6a70721f2cadd8061c4db4c1235303", + "normal_optimized_bytes_equal": { + "INPUTS.json": "5231e3f636b2e35456af9fb020950f3570f45daec9db9cd3fc88c2cb2ce8be23", + "REVIEW.json": "d929f05a9ad601007b046602ecd52ba4b2709fe8315e325475817eb9ece1c6d7" + }, + "publication": "No PR, commit, push or publication.", + "status": "PASS_REPRODUCTION_AND_SOURCE_AUDIT", + "unchanged_input_files": 36 +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/REVIEW.md new file mode 100644 index 0000000000..7416ef8b0f --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/REVIEW.md @@ -0,0 +1,248 @@ +# Independent review of the paid rational packing and grid + +The frozen scalar packet passes. Both complete code words agree with +the actual 112-port C16 matrix and its adjoint on all 1,280 real input +columns. The 528 outside complex fields remain arbitrary and unchanged. +The exact scalar invoices, divisibility domains, and stated local +prefix bounds also pass. No material error was found. + +The [producer freeze](../../bridge-access-20261017/rational-unitary-packing-20261020/FREEZE.json) +has SHA256 +`2db9b1d5425dea76345ecbfde9a601e47a620693fc5e58350d311db292fc5fdc`. +Its actual matrix source has decompressed SHA256 +`b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32`. +This is the first C16 packing of the actual reader. It is not a +modification of the later native-compatible C24. + +The [checker](check.py) uses a pinned independent rational-arithmetic +helper. It imports no producer interpreter. A reverse column pass +checks each literal word. A separate forward pass checks every +instruction boundary. All input hashes are in +[INPUTS.json](normal-final/INPUTS.json), and the finite results are in +[REVIEW.json](normal-final/REVIEW.json). + +## Literal word and cost + +The review reconstructs A, B, the paid middle permutation, and + +```text +R = (1/3) diag(A*,A*) P diag(B,B) +``` + +directly. It checks both norm-three identities, the exact R matrix, +and both unitary orders. It verifies the four actual disjoint port +quartets and the complete preliminary-code joins. + +The full code adjoint word is the literal reverse inverse of the +full code word. Both complete inverse products pass. The review +also checks C16's actual reader decoder: its support has sixteen +complex coordinates and its product with C16 is the original +sixteen-row reader. The reader is bound to the accepted actual +source matrix. + +| Word | Old real scalar units | Real ×3 scans | Real /3 scans | Instructions | Prefix row one-norm | Binary height | Odd height | +| --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | +| Four R blocks | 840 | 16 | 16 | 256 | 7 | 1 | 1 | +| Four R* blocks | 840 | 16 | 16 | 256 | 6 | 1 | 1 | +| Complete C16 | 5702 | 16 | 16 | 2110 | 17 | 2 | 1 | +| Complete C16* | 5702 | 16 | 16 | 2110 | 28/3 | 2 | 1 | + +There is no scratch field or native child. The old scalar tariff is +computed only from the dyadic component instructions. Multiplication +and division by three remain separate scan opcodes. + +The words act at a proved common complex frame. Their complete real +matrices are complex-linear. Individual real-component instructions +need not commute with that complex frame. The complete word must +remain contiguous, with no native operation, map, or partial-field +use inserted inside it. The displayed prefix bounds refer to the +physical input components at that common cut. They do not include +primitive ADD interiors or recursive child arithmetic. + +## Exact division domain + +Put `R0=Z[i,1/2]` and `N=3R`. The review performs elimination directly +over `F9=F3[i]`. It obtains Gaussian rank one for N, and separately +obtains real rank two for its real matrix. + +The first row, normalized by its first nonzero entry, is + +```text +(1, (1-i)/2, -(1+i), -1) modulo 3. +``` + +Consequently, for `x in R0^4`, + +```text +Rx is in R0^4 +if and only if +x0 + ((1-i)/2)x1 - (1+i)x2 - x3 = 0 modulo 3. +``` + +The independent check enumerates all 6,561 residue inputs in each +direction. Exactly 729 inputs satisfy the literal division contract. +For both R and R*, that contract is exactly the condition that the +complete output is dyadic. For R it also agrees with the displayed +Gaussian congruence. + +This finite test proves the full R0 domain. Every tested condition +depends only on the residue modulo three. The prefix matrices have +at most one factor three in their denominators; changing an input +by an element of `3R0^4` changes every relevant postdivision value +by a dyadic value. + +Cpre is a dyadic unit. Thus it does not impose this congruence on +arbitrary input. The full code check rejects the contract with only +a binary root guard. It proves every actual division on every +column after the one required ternary level is supplied. + +For the four R blocks, a local numerator factor `2×3` suffices. +For a complete code word, `4×3` suffices relative to integral input +numerators. These factors describe the local binary and ternary +guard. They are not a complete recursive grid or an uncharged +representation change. + +## Independent proof of exact power growth + +The review recomputes the trace of the actual complete C16: + +```text +trace(C16) = (11+7i)/6, +h3(C16) = h3(C16*) = 1. +``` + +There is a finite-field proof of the all-power claim. It does not +need an eigenvalue calculation. + +Let `A=3C16`. Its entries belong to R0. Reduce A modulo three to +obtain `Abar` over F9. The exact trace is + +```text +trace(Abar) = (11+7i)/2 modulo 3 = 1+2i != 0. +``` + +A nilpotent matrix over a field has trace zero. For example, a +basis adapted to its kernel filtration makes it strictly triangular. +Therefore Abar is not nilpotent. In particular, `Abar^m` is nonzero +for every positive integer m. + +But `A^m=3^m C16^m`. Its nonzero residue means that at least one +entry is not divisible by three. Hence `h3(C16^m)>=m`. +Multiplication of the original coefficients gives the reverse +bound `h3(C16^m)<=m`. Therefore + +```text +h3(C16^m) = m, for all integers m >= 1. +``` + +For the adjoint the residue trace is `1+i`, also nonzero, and the +same proof applies. The full residues of `3C16` and `3C16*` each +have rank four. The rank-one statement belongs to one quartet's +numerator N; it is not a rank-one claim about the complete code. +The first four exact powers in each direction are separate finite +controls for this proof. + +The theorem is unchanged by a fixed dyadic-unit change of basis. +If G and its inverse have no factor three in their denominators, +then + +```text +h3(G^-1 M G) <= h3(M) +``` + +and the reverse inequality follows by conjugating back. Thus a +fixed legal dyadic stage view cannot remove this power growth. +The same conclusion holds after tensoring with an identity. +No claim about products of different stage codes follows from +this statement. + +A full bounded three-adic lattice that is stable under C16 would +bound all its powers in the coordinate norm. The exact growth +excludes such a lattice. In particular, no such lattice can be +stable under both the actual Cpre and the complete packing Rall. + +R alone is different. Its order is exactly four. A finite invariant +lattice is obtained by summing the four images of the coordinate +lattice. The independent check also confirms the producer's signed +interleaving example: `3RS` has nonzero residue trace `-2+2i`. +It therefore has the same unbounded unmatched power growth. + +## Paid grid and matching types + +The scan review checks all finite-control transitions and 16,380 +signed division or multiplication cases through width twelve. +It uses modular inversion to compute the expected quotient, +separately from the producer's scan interpreter. The signed tests +reject nonmultiples and multiplication overflow. + +The source-backed scan bound remains `4(w_g+1)` arithmetic-head +steps per real record. Descriptor work is separate. Thus one +complete code direction adds at most `128 n(w_g+1)` arithmetic-head +steps for the 32 odd scans when each field has n records. + +The retained root-grid theorem applies if each completed recursive +child has a proved Gaussian-dyadic endpoint on all roles. If a +finite parent has local odd height at most M and recursive edge +depth at most D, the common exponent is `K=M(D+1)`. Every numeric +root stream must be converted, including arbitrary borrowed +values. Addresses and tags are excluded. + +The two outer conversions cost at most +`8 N_real K(w_g+1)` arithmetic-head steps. The added width is at +most `2K` bits. A full binary guard and descriptor costs remain +separate. The final physical endpoint must be dyadic on every role +before exact outer unscaling. + +C16 itself is not such a completed dyadic child. Its unitarity does +not change that fact. Matching rational boundary types are allowed: +the exact products `C_out A C_in^-1` cancel adjacent types in order +when A is dyadic on the complete semantic state. The caller must +prove all whole-state types, decoded child-entry types, and local +prefix bounds. A code on 112 fields does not supply a type for a +recursive call on one field. + +A useful bounded case is already proved by the literal words here. +The matched pair C16 followed by C16* has prefix odd height one: +the inverse word retraces the first word's intermediate states. +This does not imply a height-one bound for unmatched C16 calls or +for an unproved recursive caller. + +The 224-view common-FULL access count remains a separate conditional +access statement from the pinned general-stage proof. It does not +admit mixed holes or make view execution free. All 96 ordinary +diagonals of this particular C16 are nonzero, so this scalar packing +does not inherit the current off-diagonal native realization. + +## Reproduction and scope + +Run the checker under both modes into new directories: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/check.py --out +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/check.py --out +``` + +Expected output: + +```text +PASS_INDEPENDENT_RATIONAL_PACKING_GRID +``` + +The reproduction record compares the receipts and input manifests +byte for byte and checks every consumed source hash again. +The missing-instruction control rejects a damaged packing word. + +This review establishes the paid scalar words, their exact grid +requirements, and the stated reuse limit. It does not establish a +changed native response, mixed-hole access, a complete recursive +child, a new helper host, or an improvement to the full supplier. + +The original packing and preliminary code came from the +independent-review lane. The bridge-access lane supplied the paid +packing and grid packet. This review supplies a distinct replay, +an exhaustive domain check, and the finite-field power proof. +AI assistance was used. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/check.py b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/check.py new file mode 100644 index 0000000000..15da83f282 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/check.py @@ -0,0 +1,407 @@ +#!/usr/bin/env python3 +"""Check the paid rational packing and its exact input domains.""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from itertools import product +from pathlib import Path +import argparse +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +HELPER = HERE.parent/'row-capture-native-review-20261020/check.py' +PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84' +if sha256(HELPER.read_bytes()).hexdigest() != PIN: + raise ValueError('Independent arithmetic helper pin') +spec = importlib.util.spec_from_file_location('independent_real_rows', HELPER) +q = importlib.util.module_from_spec(spec) +spec.loader.exec_module(q) +q.read(HELPER, PIN) +need = q.need +SOURCE = q.LANES/'bridge-access-20261017/rational-unitary-packing-20261020' +MATRIX = q.LANES/'independent-review-20261017/odd-unitary-packing-20261020' +ZERO, ONE = (0, 0), (1, 0) + + +def realify(matrix, ncols): + result = [{} for _ in range(2*len(matrix))] + for i, row in enumerate(matrix): + for key, pair in row.items(): + j, (a, b) = int(key), tuple(map(F, pair)) + need(0 <= j < ncols, 'Complex column') + for target, source, value in ((2*i, 2*j, a), (2*i, 2*j+1, -b), + (2*i+1, 2*j, b), (2*i+1, 2*j+1, a)): + if value: + result[target][source] = value + return result + + +def scale(rows, value): + return [{j: value*x for j, x in row.items() if value*x} for row in rows] + + +def heights(rows): + h2, h3 = 0, 0 + for row in rows: + for value in row.values(): + d, a, b = value.denominator, 0, 0 + while d % 2 == 0: + d, a = d//2, a+1 + while d % 3 == 0: + d, b = d//3, b+1 + need(d == 1, 'Only the stated denominator primes') + h2, h3 = max(h2, a), max(h3, b) + return h2, h3 + + +def inverse_word(word): + return [[op, t, s, str(-F(value) if op == 'add' else 1/F(value))] + for op, t, s, value in reversed(word)] + + +def ordinary(word): + result = [] + for op, t, s, value in word: + need(op in ('add', 'scale', 'odd'), 'Literal component grammar') + if op == 'odd': + need(s is None and F(value) in (F(3), F(1, 3)), 'Fixed odd scan') + result.append(['scale' if op == 'odd' else op, t, s, value]) + return result + + +def check_word(word, expected, active, target_bill): + gates = ordinary(word) + need(q.reverse(gates, 1280) == q.transpose(expected, 1280), 'All1280 reverse input columns') + state = q.unit(1280) + peak, h2, h3 = F(1), 0, 0 + scans = Counter() + before_division, after_division = [], [] + for (op, t, s, value), gate in zip(word, gates): + value = F(value) + need(0 <= t < active and (s is None or 0 <= s < active), 'Declared active real fields') + if op == 'odd': + scans[str(value)] += 1 + if op == 'odd' and value == F(1, 3): + before_division.append(dict(state[t])) + if op == 'add': + need(s != t, 'Distinct ADD components') + q.add(state[t], state[s], value) + else: + need(s is None, 'Scale has no source') + state[t] = {j: value*x for j, x in state[t].items()} + if op == 'odd' and value == F(1, 3): + after_division.append(dict(state[t])) + peak = max(peak, sum(map(abs, state[t].values()), F(0))) + a, b = heights([state[t]]) + h2, h3 = max(h2, a), max(h3, b) + need(state == expected, 'Separate forward prefix replay') + need(state[active:] == q.unit(1280)[active:], 'Every outside field remains arbitrary') + binary_gates = [gate for gate, old in zip(gates, word) if old[0] != 'odd'] + cost = q.price(binary_gates)//2 + need(cost == target_bill and scans == {'3': 16, '1/3': 16}, 'Separate binary and odd invoices') + guard = 2**h2 * 3**h3 + for row in before_division: + need(all((guard*x).denominator == 1 and int(guard*x) % 3 == 0 for x in row.values()), + 'Every division input is a multiple of three on the paid grid') + need(all((guard*x).denominator == 1 for row in after_division for x in row.values()), + 'All postdivision columns are integral on the same grid') + no_odd = 2**h2 + need(any((no_odd*x).denominator % 3 == 0 for row in after_division for x in row.values()), + 'The arbitrary unscaled dyadic-grid contract fails') + return { + 'real_columns': 1280, 'untouched_complex_fields': (1280-active)//2, + 'old_real_scalar_units': cost, 'odd_scans': dict(scans), 'instructions': len(word), + 'prefix_real_row_one_norm': str(peak), 'binary_height': h2, 'odd_height': h3, + 'local_root_numerator_factor': guard, 'new_fields': 0, 'native_children': 0, + 'exact_division_on_all_scaled_columns': True, + }, after_division + + +def fadd(a, b): + return ((a[0]+b[0]) % 3, (a[1]+b[1]) % 3) + + +def fneg(a): + return (-a[0] % 3, -a[1] % 3) + + +def fmul(a, b): + return ((a[0]*b[0]-a[1]*b[1]) % 3, (a[0]*b[1]+a[1]*b[0]) % 3) + + +def finv(a): + norm = (a[0]*a[0]+a[1]*a[1]) % 3 + need(norm, 'A nonzero F9 element has nonzero norm') + factor = pow(norm, -1, 3) + return (a[0]*factor % 3, -a[1]*factor % 3) + + +def mod3(value): + value = F(value) + need(value.denominator % 3, 'A residue requires a denominator prime to three') + return value.numerator*pow(value.denominator, -1, 3) % 3 + + +def residue(matrix, multiplier=F(1)): + return [{int(j): (mod3(multiplier*F(pair[0])), mod3(multiplier*F(pair[1]))) + for j, pair in row.items() + if (mod3(multiplier*F(pair[0])), mod3(multiplier*F(pair[1]))) != ZERO} + for row in matrix] + + +def frank(rows): + pivots = {} + for raw in rows: + row = dict(raw) + while row: + j = min(row) + if j not in pivots: + inv = finv(row[j]) + pivots[j] = {k: fmul(v, inv) for k, v in row.items()} + break + factor = row[j] + for k, value in pivots[j].items(): + entry = fadd(row.get(k, ZERO), fneg(fmul(factor, value))) + if entry == ZERO: + row.pop(k, None) + else: + row[k] = entry + return len(pivots) + + +def ftrace(rows): + value = ZERO + for i, row in enumerate(rows): + value = fadd(value, row.get(i, ZERO)) + return value + + +def block_domain(packing, numerator, word, inverse): + mod = residue(packing, F(3)) + need(frank(mod) == 1, 'Packing numerator has Gaussian rank one modulo three') + inv = finv(mod[0][0]) + normalized = [fmul(mod[0].get(j, ZERO), inv) for j in range(4)] + need(normalized == [(1, 0), (2, 1), (2, 2), (2, 0)], 'Exact published Gaussian syndrome') + # The first quartet in each word is complete; the other three are disjoint. + first = [g for g in word if g[1] < 8] + first_inverse = [g for g in inverse if g[1] < 8] + outcomes = {} + for name, gates, endpoint in [('R', first, realify(packing, 4)), + ('Rstar', first_inverse, q.transpose(realify(packing, 4), 8))]: + state = q.unit(8) + rows = [] + for op, t, s, value in gates: + value = F(value) + if op == 'add': + q.add(state[t], state[s], value) + else: + state[t] = {j: value*x for j, x in state[t].items()} + if op == 'odd' and value == F(1, 3): + rows.append(dict(state[t])) + need(state == endpoint and len(rows) == 4, 'Complete literal quartet and four real divisions') + accepted = 0 + for x in product(range(3), repeat=8): + literal = all(sum((v*x[j] for j, v in row.items()), F(0)).denominator % 3 + for row in rows) + final = all(sum((v*x[j] for j, v in row.items()), F(0)).denominator % 3 + for row in endpoint) + need(literal == final, 'Literal division domain equals the exact dyadic endpoint domain') + if name == 'R': + syndrome = ZERO + for j, coefficient in enumerate(normalized): + syndrome = fadd(syndrome, fmul(coefficient, (x[2*j], x[2*j+1]))) + need(literal == (syndrome == ZERO), 'Literal divisions equal the stated Gaussian congruence') + accepted += literal + need(accepted == 729, 'One Gaussian condition in four Gaussian variables') + outcomes[name] = {'residue_inputs': 6561, 'accepted_residues': accepted, + 'literal_division_domain_equals_dyadic_endpoint': True} + real_rank = frank([{j: (mod3(value), 0) for j, value in row.items() if mod3(value)} + for row in numerator]) + need(real_rank == 2, 'Independent real residue rank') + return {'gaussian_rank': 1, 'real_rank': real_rank, + 'normalized_syndrome_F9': normalized, 'exhaustive_domains': outcomes} + + +def scan_checks(): + transitions = 0 + for carry in range(3): + for bit in range(2): + out = (bit-carry) % 2 + next_carry = (carry+3*out-bit)//2 + need(0 <= next_carry < 3 and 2*next_carry == carry+3*out-bit, + 'Division finite-control invariant') + out, next_carry = (3*bit+carry) % 2, (3*bit+carry)//2 + need(0 <= next_carry < 3 and 3*bit+carry == out+2*next_carry, + 'Multiplication finite-control invariant') + transitions += 2 + cases = 0 + for width in range(1, 13): + modulus = 2**width + for n in range(-modulus//2, modulus//2): + unsigned = n % modulus + quotient = unsigned*pow(3, -1, modulus) % modulus + carry = (3*quotient-unsigned)//modulus + sign_in, sign_out = int(n < 0), int(quotient >= modulus//2) + valid = carry == 3*sign_out-sign_in + need(valid == (n % 3 == 0), 'Independent modular-inverse quotient domain') + if valid: + need(quotient-sign_out*modulus == n//3, 'Exact signed quotient') + product_unsigned = 3*unsigned % modulus + carry = (3*unsigned-product_unsigned)//modulus + sign_out = int(product_unsigned >= modulus//2) + valid = carry == 3*sign_in-sign_out + fits = -modulus//2 <= 3*n < modulus//2 + need(valid == fits, 'Independent multiplication overflow domain') + if valid: + need(product_unsigned-sign_out*modulus == 3*n, 'Exact signed product') + cases += 2 + return {'finite_control_transitions': transitions, 'signed_cases': cases, 'max_width': 12} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + freeze = q.frozen(SOURCE, 'FREEZE.json', + '2db9b1d5425dea76345ecbfde9a601e47a620693fc5e58350d311db292fc5fdc') + for path, digest in freeze['sources'].items(): + q.read(q.LANES/path, digest) + q.frozen(MATRIX, 'FREEZE.json', '22769396f123964addb9024b2fda452148388c67868714b4121a8fe3bfb9d410') + q.frozen(q.LANES/'bridge-review-20261017/odd-grid-a8-review-20261017', 'FREEZE.json', + '81ebbea971c0902a80479f9af4c82e72c660093c9f712b537690293aaaf21d60') + source = json.loads(q.read(MATRIX/'run-normal/PACKING.json.gz', + 'b460c1b4603f4b75da5ca4bf1da4a642f2cc4d970599f9c1068832e7b230ac32', True)) + prior = json.loads(q.read(q.RAW/'metric-completion-20261020/twenty-four-v2-normal/UNITARY-24.json.gz', + '9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c', True)) + q.frozen(q.LANES/'independent-review-20261017/unitary-footprint-review-20261020', 'FREEZE.json', + 'c537f75e6b76397e8fa390cd03a01e8021b7e0e55ff6c8932c3cc439613d0a61') + need(source['original_readers'] == prior['original_centre_readers'], + 'The reader is the accepted actual sixteen-row reader') + packet = json.loads(q.read(SOURCE/'actual-normal/PACKING.json', + '1076d6e7b1c9d0fe1cf6c4d04130236ed8bed052b2f811c48f7e08b3ad7c11f5')) + a = realify([{'0': ['1', '0'], '1': ['1', '1']}, + {'0': ['-1', '1'], '1': ['1', '0']}], 2) + b = realify([{'0': ['1', '-1'], '1': ['0', '-1']}, + {'0': ['0', '-1'], '1': ['1', '1']}], 2) + need(q.mul(q.transpose(a, 4), a) == scale(q.unit(4), F(3)) and + q.mul(q.transpose(b, 4), b) == scale(q.unit(4), F(3)), 'Both norm-three identities') + aa = q.transpose(a, 4)+[{j+4: x for j, x in row.items()} for row in q.transpose(a, 4)] + bb = b+[{j+4: x for j, x in row.items()} for row in b] + permutation = [0, 1, 4, 5, 2, 3, 6, 7] + middle = [{j: F(1)} for j in permutation] + numerator = q.mul(q.mul(aa, middle), bb) + r = scale(numerator, F(1, 3)) + need(q.rows(packet['A_real']) == a and q.rows(packet['B_real']) == b and + q.rows(packet['numerator_real']) == numerator and q.rows(packet['R_real']) == r, + 'Independent exact packing factors') + need(realify(source['packing'], 4) == r and q.mul(q.transpose(r, 8), r) == q.unit(8) + and q.mul(r, q.transpose(r, 8)) == q.unit(8), 'Actual packing and both unitary orders') + words = packet['words'] + need(set(words) == {'packing', 'inverse'} and words['inverse'] == inverse_word(words['packing']), + 'Literal reverse inverse, including every odd opcode') + rr = [{j+8*k: x for j, x in row.items()} for k in range(4) for row in r]+q.unit(1280)[32:] + reports = {} + reports['packing'], _ = check_word(words['packing'], rr, 32, 840) + reports['inverse'], _ = check_word(words['inverse'], q.transpose(rr, 1280), 32, 840) + need(reports['packing']['prefix_real_row_one_norm'] == '7' and + reports['inverse']['prefix_real_row_one_norm'] == '6', 'Exact packing prefix norms') + domains = block_domain(source['packing'], numerator, words['packing'], words['inverse']) + cp, cpstar = (realify(source[key], 112) for key in ('precode', 'precode_adjoint')) + c, cstar = (realify(source[key], 112) for key in ('code', 'code_adjoint')) + need(cpstar == q.transpose(cp, 224) and cstar == q.transpose(c, 224), 'Both exact adjoints') + need(q.mul(cp, cpstar) == q.unit(224) and q.mul(cpstar, cp) == q.unit(224), + 'The preliminary code is a dyadic unit') + need(q.mul(c, cstar) == q.unit(224) and q.mul(cstar, c) == q.unit(224), + 'Both actual full unitary orders') + ports = sum(source['packing_ports'], []) + need(len(ports) == len(set(ports)) == 16 and + packet['actual_code']['packing_ports'] == source['packing_ports'], 'Actual disjoint quartets') + + def placed(word): + return [[op, 2*ports[t//2]+t % 2, None if s is None else 2*ports[s//2]+s % 2, value] + for op, t, s, value in word] + + need(packet['actual_code']['words']['code'] == + source['precode_words']['precode']+placed(words['packing']), 'Complete forward join') + need(packet['actual_code']['words']['adjoint'] == + placed(words['inverse'])+source['precode_words']['precode_adjoint'], 'Complete adjoint join') + need(source['precode_words']['precode_adjoint'] == inverse_word(source['precode_words']['precode']) and + packet['actual_code']['words']['adjoint'] == inverse_word(packet['actual_code']['words']['code']), + 'The complete adjoint word is the literal inverse word') + for name, expected in [('code', c), ('adjoint', cstar)]: + reports[name], _ = check_word(packet['actual_code']['words'][name], + expected+q.unit(1280)[224:], 224, 5702) + need((reports[name]['binary_height'], reports[name]['odd_height']) == (2, 1), + 'The complete local coefficient guard') + need(reports['code']['prefix_real_row_one_norm'] == '17' and + reports['adjoint']['prefix_real_row_one_norm'] == '28/3', 'Exact joined prefix norms') + need(q.reverse(ordinary(packet['actual_code']['words']['code']+ + packet['actual_code']['words']['adjoint']), 1280) == q.unit(1280) and + q.reverse(ordinary(packet['actual_code']['words']['adjoint']+ + packet['actual_code']['words']['code']), 1280) == q.unit(1280), + 'Both literal complete inverse orders') + decoder = realify(source['decoder'], 112) + readers = realify(source['original_readers'], 112) + need(q.mul(decoder, c) == readers and q.mul(readers, cstar) == decoder, 'Actual full reader recovery') + support = {j//2 for row in decoder for j in row} + need(support == set(source['selected_ports']) and len(support) == 16, 'Sixteen actual output fields') + need(q.rank(readers) == 32, 'The sixteen Gaussian reader rows are independent') + response = realify(prior['response'], 112) + coded = q.mul(c, response) + need(coded == realify(source['coded_response'], 112), 'Actual coded response') + rest = set(range(112))-support + need(rest == set(source['ordinary_ports']) and len(rest) == 96, 'Actual ordinary coordinates') + need(all(coded[2*p+b] == c[2*p+b] for p in rest for b in (0, 1)), + 'Every ordinary coded-response row equals the code row') + need(all(source['code'][p].get(str(p), ['0', '0']) != ['0', '0'] for p in rest), + 'Every ordinary diagonal needs a changed native construction') + trace = tuple(sum((F(row.get(str(i), ['0', '0'])[part]) + for i, row in enumerate(source['code'])), F(0)) for part in (0, 1)) + need(trace == (F(11, 6), F(7, 6)), 'Trace of the complete actual C') + mod_c, mod_star = residue(source['code'], F(3)), residue(source['code_adjoint'], F(3)) + need(ftrace(mod_c) == (1, 2) and ftrace(mod_star) == (1, 1), 'Nonzero residue traces exclude nilpotence') + need(heights(c)[1] == heights(cstar)[1] == 1, 'Exact first odd height') + powers = {} + for name, base in [('C', c), ('Cstar', cstar)]: + current, values = q.unit(224), [] + for m in range(1, 5): + current = q.mul(base, current) + need(heights(current)[1] == m, 'Finite control for the all-power theorem') + values.append(m) + powers[name] = values + r2 = q.mul(r, r) + need(q.mul(r2, r2) == q.unit(8) and r2 != q.unit(8), 'Packing has order exactly four') + sign = q.unit(8) + sign[0], sign[1] = {0: F(-1)}, {1: F(-1)} + signed = q.mul(numerator, sign) + signed_trace = (sum((signed[2*j].get(2*j, F(0)) for j in range(4)), F(0)), + sum((signed[2*j+1].get(2*j, F(0)) for j in range(4)), F(0))) + need(signed_trace == (F(-2), F(2)) and tuple(map(mod3, signed_trace)) != ZERO, + 'Signed dyadic interleaving also has a nonnilpotent residue') + damaged = list(words['packing'][1:]) + need(q.reverse(ordinary(damaged), 1280) != q.transpose(rr, 1280), 'Missing paid component control') + result = { + 'status': 'PASS_INDEPENDENT_RATIONAL_PACKING_GRID', + 'words': reports, 'packing_divisibility_domain': domains, + 'signed_scans': scan_checks(), 'actual_trace': list(map(str, trace)), + 'residue_trace_C': ftrace(mod_c), 'residue_trace_Cstar': ftrace(mod_star), + 'actual_residue_rank_C': frank(mod_c), 'actual_residue_rank_Cstar': frank(mod_star), + 'power_controls': powers, + 'all_positive_power_proof': '3C and 3C* have nonzero trace over F9. Neither residue is nilpotent. Every positive power is nonzero modulo 3, so the exact odd height is m.', + 'packing_order': 4, 'signed_interleaving_trace': list(map(str, signed_trace)), + 'full_reader_output_coordinates': 16, 'new_fields': 0, 'native_children': 0, + 'actual_reader_real_rank': 32, 'ordinary_rows_CE_equal_C': 96, + 'nonzero_ordinary_diagonal_entries': 96, + 'matched_C_then_Cstar_pair_prefix_odd_height': 1, + 'matched_pair_proof': 'The second complete word is the literal reverse inverse. Its prefix states retrace the first word.', + 'scope': 'Paid scalar words at one common complex frame, exact divisibility domains, fixed-odd scans and conditional root-grid admission. No native response, mixed-hole access, unmatched recursive child or complete supplier is admitted.', + } + args.out.mkdir(parents=True, exist_ok=False) + for name, obj in [('REVIEW.json', result), ('INPUTS.json', q.INPUTS)]: + (args.out/name).write_text(json.dumps(obj, sort_keys=True, indent=2)+'\n') + print(result['status'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/normal-final/INPUTS.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/normal-final/INPUTS.json new file mode 100644 index 0000000000..6ff6f92052 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/normal-final/INPUTS.json @@ -0,0 +1,112 @@ +{ + "bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md": { + "sha256": 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"actual_reader_real_rank": 32, + "actual_residue_rank_C": 4, + "actual_residue_rank_Cstar": 4, + "actual_trace": [ + "11/6", + "7/6" + ], + "all_positive_power_proof": "3C and 3C* have nonzero trace over F9. Neither residue is nilpotent. Every positive power is nonzero modulo 3, so the exact odd height is m.", + "full_reader_output_coordinates": 16, + "matched_C_then_Cstar_pair_prefix_odd_height": 1, + "matched_pair_proof": "The second complete word is the literal reverse inverse. Its prefix states retrace the first word.", + "native_children": 0, + "new_fields": 0, + "nonzero_ordinary_diagonal_entries": 96, + "ordinary_rows_CE_equal_C": 96, + "packing_divisibility_domain": { + "exhaustive_domains": { + "R": { + "accepted_residues": 729, + "literal_division_domain_equals_dyadic_endpoint": true, + "residue_inputs": 6561 + }, + "Rstar": { + "accepted_residues": 729, + "literal_division_domain_equals_dyadic_endpoint": true, + "residue_inputs": 6561 + } + }, + "gaussian_rank": 1, + "normalized_syndrome_F9": [ + [ + 1, + 0 + ], + [ + 2, + 1 + ], + [ + 2, + 2 + ], + [ + 2, + 0 + ] + ], + "real_rank": 2 + }, + "packing_order": 4, + "power_controls": { + "C": [ + 1, + 2, + 3, + 4 + ], + "Cstar": [ + 1, + 2, + 3, + 4 + ] + }, + "residue_trace_C": [ + 1, + 2 + ], + "residue_trace_Cstar": [ + 1, + 1 + ], + "scope": "Paid scalar words at one common complex frame, exact divisibility domains, fixed-odd scans and conditional root-grid admission. No native response, mixed-hole access, unmatched recursive child or complete supplier is admitted.", + "signed_interleaving_trace": [ + "-2", + "2" + ], + "signed_scans": { + "finite_control_transitions": 12, + "max_width": 12, + "signed_cases": 16380 + }, + "status": "PASS_INDEPENDENT_RATIONAL_PACKING_GRID", + "words": { + "adjoint": { + "binary_height": 2, + "exact_division_on_all_scaled_columns": true, + "instructions": 2110, + "local_root_numerator_factor": 12, + "native_children": 0, + "new_fields": 0, + "odd_height": 1, + "odd_scans": { + "1/3": 16, + "3": 16 + }, + "old_real_scalar_units": 5702, + "prefix_real_row_one_norm": "28/3", + "real_columns": 1280, + "untouched_complex_fields": 528 + }, + "code": { + "binary_height": 2, + "exact_division_on_all_scaled_columns": true, + "instructions": 2110, + "local_root_numerator_factor": 12, + "native_children": 0, + "new_fields": 0, + "odd_height": 1, + "odd_scans": { + "1/3": 16, + "3": 16 + }, + "old_real_scalar_units": 5702, + 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a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/optimized-final/REVIEW.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/optimized-final/REVIEW.json new file mode 100644 index 0000000000..32f9ee5091 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/optimized-final/REVIEW.json @@ -0,0 +1,155 @@ +{ + "actual_reader_real_rank": 32, + "actual_residue_rank_C": 4, + "actual_residue_rank_Cstar": 4, + "actual_trace": [ + "11/6", + "7/6" + ], + "all_positive_power_proof": "3C and 3C* have nonzero trace over F9. Neither residue is nilpotent. Every positive power is nonzero modulo 3, so the exact odd height is m.", + "full_reader_output_coordinates": 16, + "matched_C_then_Cstar_pair_prefix_odd_height": 1, + "matched_pair_proof": "The second complete word is the literal reverse inverse. Its prefix states retrace the first word.", + "native_children": 0, + "new_fields": 0, + "nonzero_ordinary_diagonal_entries": 96, + "ordinary_rows_CE_equal_C": 96, + "packing_divisibility_domain": { + "exhaustive_domains": { + "R": { + "accepted_residues": 729, + "literal_division_domain_equals_dyadic_endpoint": true, + "residue_inputs": 6561 + }, + "Rstar": { + "accepted_residues": 729, + "literal_division_domain_equals_dyadic_endpoint": true, + "residue_inputs": 6561 + } + }, + "gaussian_rank": 1, + "normalized_syndrome_F9": [ + [ + 1, + 0 + ], + [ + 2, + 1 + ], + [ + 2, + 2 + ], + [ + 2, + 0 + ] + ], + "real_rank": 2 + }, + "packing_order": 4, + "power_controls": { + "C": [ + 1, + 2, + 3, + 4 + ], + "Cstar": [ + 1, + 2, + 3, + 4 + ] + }, + "residue_trace_C": [ + 1, + 2 + ], + "residue_trace_Cstar": [ + 1, + 1 + ], + "scope": "Paid scalar words at one common complex frame, exact divisibility domains, fixed-odd scans and conditional root-grid admission. No native response, mixed-hole access, unmatched recursive child or complete supplier is admitted.", + "signed_interleaving_trace": [ + "-2", + "2" + ], + "signed_scans": { + "finite_control_transitions": 12, + "max_width": 12, + "signed_cases": 16380 + }, + "status": "PASS_INDEPENDENT_RATIONAL_PACKING_GRID", + "words": { + "adjoint": { + "binary_height": 2, + "exact_division_on_all_scaled_columns": true, + "instructions": 2110, + "local_root_numerator_factor": 12, + "native_children": 0, + "new_fields": 0, + "odd_height": 1, + "odd_scans": { + "1/3": 16, + "3": 16 + }, + "old_real_scalar_units": 5702, + "prefix_real_row_one_norm": "28/3", + "real_columns": 1280, + "untouched_complex_fields": 528 + }, + "code": { + "binary_height": 2, + "exact_division_on_all_scaled_columns": true, + "instructions": 2110, + "local_root_numerator_factor": 12, + "native_children": 0, + "new_fields": 0, + "odd_height": 1, + "odd_scans": { + "1/3": 16, + "3": 16 + }, + "old_real_scalar_units": 5702, + "prefix_real_row_one_norm": "17", + "real_columns": 1280, + "untouched_complex_fields": 528 + }, + "inverse": { + "binary_height": 1, + "exact_division_on_all_scaled_columns": true, + "instructions": 256, + "local_root_numerator_factor": 6, + "native_children": 0, + "new_fields": 0, + "odd_height": 1, + "odd_scans": { + "1/3": 16, + "3": 16 + }, + "old_real_scalar_units": 840, + "prefix_real_row_one_norm": "6", + "real_columns": 1280, + "untouched_complex_fields": 624 + }, + "packing": { + "binary_height": 1, + "exact_division_on_all_scaled_columns": true, + "instructions": 256, + "local_root_numerator_factor": 6, + "native_children": 0, + "new_fields": 0, + "odd_height": 1, + "odd_scans": { + "1/3": 16, + "3": 16 + }, + "old_real_scalar_units": 840, + "prefix_real_row_one_norm": "7", + "real_columns": 1280, + "untouched_complex_fields": 624 + } + } +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md new file mode 100644 index 0000000000..64df4c61d3 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/DERIVATION.md @@ -0,0 +1,98 @@ +# Independent derivation of the selected-row service + +This derivation precedes the review of the emitted word. It gives the +map that the word must implement. It does not certify that word. + +Let V have r independent rows. Let P be an ordered set of r ports, +and let V_P be the square submatrix on those columns. Assume V_P is +invertible. Put W=V_P^{-1}V. Then W_P=I. + +Define C to have rows W on P and identity rows on the other ports. +If B=W-pi_P, where pi_P selects P, then + +\[ +C=I+\iota_P B,\qquad B\iota_P=0,\qquad +C^{-1}=I-\iota_P B. +\] + +Here iota_P inserts r coordinates at P. Thus C is a shear. Its +determinant is one. If W is dyadic, both C and its inverse are dyadic. +Every addition uses an unchanged coordinate outside P. No extra field +or zero-input assumption is needed. Reversing the literal additions +gives the inverse. + +The row code is independent of the basis used for the row space of V. +Replacing V by A V, for any invertible A, leaves W unchanged. + +For the present response E, direct normalization of the pinned V gives +eight rows of support 21 and eight rows of support 8. The first rows +have pivot coefficient 1 and twenty coefficients of magnitude 1/2. +The other rows have pivot coefficient 1 and seven coefficients 1. +The precode therefore has 216 complex additions, at 2048 old real +scalar units under the retained scalar invoice. + +These rows are left eigenvectors: + +\[ +WE=\Lambda W,\qquad +\Lambda=\operatorname{diag}(-5I_8,-7I_8). +\] + +Therefore the selected rows of CE are exactly Lambda W. Their direct +late additions cost 3696 old real scalar units. These are separate +costs; they do not include the retained core or the new native children. + +## Physical operation + +Use Q for the diagonal family of positive input line operators, +q=Q^{-1}, and F for the common full operator. The raw forward word has +physical contract + +\[ +(Qx,y)\longmapsto(Fx,Fq(y+Ex)). +\] + +Suppose the exact event list permits all operations on the selected +target fields to be removed. Every retained operation must have no +read from those fields. The source subsystem and the other targets +must retain their original event lists. + +Apply C to current input Y while all target fields have the I frame. +Apply F to each selected target. Run the retained source and ordinary +target operations. After all source fields have reached F, add +the selected rows of CE from those source fields to the selected +targets. The physical result is + +\[ +X'=Fx,\qquad +Y'_P=F[C(y+Ex)]_P,\qquad +Y'_R=F[q(y+Ex)]_R. +\] + +Scalar coefficients commute with the common F in the final query. +No step commutes C or E through Q. In particular, the precode acts +on the physical current-I target values. It does not act on a +changed logical frame. + +Write T for the output operator that is F on P and Fq on R. +Then the full target contract is T C(y+Ex), since C is identity +on the rows in R. This is an invertible output representation. +Its entry into a later word, inverse, final decode, and recursive +hosting require their own implementation and cost. + +## Required literal checks + +The review must check the selected set and every removed event. +It must reject a retained read of a removed target. It must check +the exact full-frame recipe, including its global phase, and all +inherited native records. It must check that every source has +reached the same F frame before the final query. + +The complete word must pass every arbitrary input column. The +unchanged helper fields must retain their arbitrary values. +The native and scalar invoice must include the precode, all retained +events, the sixteen full children, and the late query. + +No PR, push, commit, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json new file mode 100644 index 0000000000..60530966a8 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/FREEZE.json @@ -0,0 +1,15 @@ +{ + "files": { + "DERIVATION.md": "74bfa14362b8a704d409cb3995fe645173e99205653528bcf6b47f62de7455a1", + "REPRODUCTION.json": "9525e5e1871d60a01c8acd222944abe6edab71f9d5448410265859dcece6901f", + "REVIEW.md": "39cb0df65e81f92854d0238d9023eaa092205bdce8e3b81724c2e4d19a3ef4f1", + "check.py": "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84", + "normal/INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1", + "normal/REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56", + "optimized/INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1", + "optimized/REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56" + }, + "publication": "No PR, push, commit, or publication.", + "scope": "Both complete local providers, direct-FULL refinement, exact physical phases, arbitrary inputs, and local invoice. No recursive hosting, later-stage conversion, full decoder, supplier, or kappa claim.", + "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..b8d020d7f9 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REPRODUCTION.json @@ -0,0 +1,8 @@ +{ + "normal_optimized_byte_identical": { + "INPUTS.json": "d79a37765cffb8a31650c0b0bc4b57570004d9d5182c68f65915b1def3ac4af1", + "REVIEW.json": "e473e90dfb6fa588121f126b0d3f884ac1695ab58cebde8b768d494ba70d4e56" + }, + "source_files_rechecked": 44, + "status": "PASS" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md new file mode 100644 index 0000000000..8bdaaa327e --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/REVIEW.md @@ -0,0 +1,255 @@ +# Independent review of the selected-row native service + +The frozen word forms the sixteen centre rows of the actual rank16 +response in sixteen existing target fields. It preserves arbitrary +target baselines and all 416 fields outside the two data banks. +It uses no new field, private field, or odd-arithmetic scan. + +The local service and its direct-FULL refinement pass the independent +checks below. No material defect was found. The output representation +has changed. Its use by a complete recursive caller remains open. + +## Inputs and independent method + +The main producer +[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/FREEZE.json) +has SHA256 +`5321a8ff856042c5ca30ce6b29b90a51ccd4dcf02317820243bfffbb433c84d8`. +Its decompressed payload SHA256 is +`7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2`. + +The separate direct-FULL +[freeze](../../new-core-transfer-20261017/low-displacement-20261020/row-only-capture-20261020/DIRECT-FULL-FREEZE.json) +has SHA256 +`f0d3b0d7c8d93e391089a2d28066dd02b4a9b28e306dea5f4e7cb5fc895b054e`. +Its decompressed payload SHA256 is +`fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c`. + +The actual source word is the rank16 extension at decompressed SHA256 +`d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4`. +The controller's scalar +[freeze](../../controller-followthrough-20261017/row-capture-20261020/FREEZE.json) +has SHA256 +`0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf`. + +The checker imports no producer code. It constructs the pivot inverse +from the exact signed Hadamard Gram matrix. It then constructs C, +its inverse, CE, and the encoded response independently. It checks +the scalar words by reverse output-column propagation. A separate +forward row pass checks the complete map and every scalar prefix. + +The physical phase interpreter is the pinned independent integer +Gaussian interpreter from the isotropic-pair review. It uses literal +address maps and exact Gaussian coefficients. It does not import +the producer's Clifford compiler or phase checker. + +## Exact code and physical contract + +The independent derivation is in [DERIVATION.md](DERIVATION.md). +Let \(E=I+UV\), and let P be the ordered set + +```text +0,27,36,111,20,7,57,46,1,3,6,8,17,18,24,23. +``` + +Put \(W=V_P^{-1}V\). The actual pivot Gram matrix is +\(\operatorname{diag}(2I_8,I_8)\). This gives a direct exact inverse +for \(V_P\), with both inverse orders checked. + +Define C to have rows W on P and identity rows elsewhere. The +correction \(C-I\) has square zero and rank sixteen. Thus + +\[ +C=I+\iota_P(W-\pi_P),\qquad +C^{-1}=I-\iota_P(W-\pi_P). +\] + +The checker verifies both matrix inverse orders and both literal +scalar inverse orders. The code and inverse are dyadic and each +cost 1760 old real scalar units. They need no extra field. + +The actual rows satisfy + +\[ +WE=\operatorname{diag}(-5I_8,-7I_8)W. +\] + +The selected rows of CE are therefore those same sixteen queries +with multipliers -5 or -7. The scalar late-query word adds these +rows to an arbitrary existing target value. It costs 3424 units. +It does not divide by five or seven. + +Write \(q=Q^{-1}\). For physical input \((Qx,y)\), the exact output is + +\[ +X'=F_9x,\qquad +Y'_P=F_9[C(y+Ex)]_P,\qquad +Y'_R=F_9[q(y+Ex)]_R. +\] + +The selected values include the arbitrary baseline \(Wy\). No +baseline is set to zero or removed from the output contract. +Equivalently, \(Y'=TC(y+Ex)\), where T is \(F_9\) on P and +\(F_9q\) on R. This is an invertible output representation. +No step commutes C or E through Q. + +## Complete operation order + +The checker derives the deletion from the original literal word. +It removes all events whose target is selected Y. For each provider, +this is exactly 128 H1 calls and 122 scalar events. Those scalar +events cost 928 units. + +Every retained event is inspected. No retained scalar event reads a +selected target. All retained events appear in their original order +and with their exact original bytes. Removing only one member of a +selected large pair fails the retained-read check. + +The new complete word has four stages: + +| Stage | Event interval, end excluded | Real scalar units | +| --- | --- | ---: | +| Current-I precode C | 0 to 232 | 1760 | +| Retained original word | 232 to 2622 | 6456 | +| Sixteen I-to-FULL children | 2622 to 2638 | 0 | +| Late common-FULL query | 2638 to 2886 | 3424 | + +Every source and selected target has frame FULL before the late +query. Every scalar addition has the same actual source and target +frame. All final frame declarations are checked. The 96 ordinary +target declarations are unchanged. The selected targets end in FULL. + +Both providers pass all 640 independent input columns. A separate +forward pass gives the same complete map. Every field numbered +224 through 639 retains its arbitrary input. No operation addresses +these fields. There is no CLEAR, hidden zero field, or new owned state. +Deleting the precode or late query is rejected by the full-column test. + +## Physical phases + +There are 1447 distinct retained native recipes. Each is byte equal +to the exact ordered frame pair in the already accepted rank16 word. +The inherited phase proof is pinned by +[the independent extension freeze](../low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json), +at SHA256 +`c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c`, +and its base native review. This review does not repeat that full +phase sweep. + +The new rank-nine recipe occurs sixteen times. The independent +interpreter checks all 512 spatial input columns against the exact +nine positive coordinate kernels. Every column has 512 exact +nonzero coefficients. The comparison includes the global phase. +A wrong global phase is rejected. + +All 112 source entry adapters are exact inherited records. The +96 ordinary outgoing adapters are new explicit inverse monomials. +For each, the checker composes it with the accepted incoming +target adapter in both orders. Every one of the 512 input columns +is exactly the identity in both orders. This proves the outgoing +map to \(F_9q_p\), including phase. + +No outgoing hole adapter is present on a selected target. Its +canonical FULL frame is exactly \(F_9\). These exact spatial +identities tensor to every width admitted by the retained primitive +contract. They are exact equalities, not equalities up to phase. + +The checker verifies the executed recipes. The producer's +descriptive compiler circuits are not executed by this review. +Their intended endpoint functions are checked through the exact +inverse-adapter identities above. + +## Direct-FULL refinement + +The accepted native recipe convention uses +\(C_{e_0}\cdots C_{e_{r-1}}\) between its two monomial maps. +At rank nine, this is already the required \(F_9\). Identity +left and right maps therefore suffice. + +The checker verifies that direct recipe on every spatial column. +It then compares both complete refined provider words with the +main packet. All events, frames, endpoint views, and matrices are +byte equal. Only the shared rank-nine recipe changes. Thus the +complete-word correctness proof transfers by exact substitution. +There is no need for a new logical-column replay of an unchanged +event list. + +The refinement removes the two nontrivial side maps from each of +the sixteen new calls. It does not change their sizes or number. +The native side-map upper bound drops from 3040 to 3008. + +## Complete local invoice and precision scope + +Each provider has the profile + +```text +1392 H1 + 64 H2 + 48 H3 + 16 H9. +``` + +This is 1520 recursive calls and native mass 1808. The complete +old scalar invoice is 11640. The direct refinement has 112 input +monomial views, 96 output monomial views, and at most 3008 native +side maps. It uses no odd-arithmetic scan or new field. + +The high-rank calls remain sixteen rank-nine calls. A complete +recurrence must use their exact sizes. Replacing their costs by +native mass alone is not a complete cost calculation. + +The exact content row one-norm over the entire emitted word is at +most 132. The additional content binary denominator height is one. +Both bounds include the precode and the late scaled queries. +Under the unitary native charts, the first bound also applies to +the per-field Hilbert norm at operation boundaries. + +These are local content bounds. They do not price primitive +internals, recursive-child guards, rounding error, outer owner +views, or the full numerical precision requirement. + +## Reuse and remaining scope + +The row-replacement argument is structural. If a forward word has +independent source progress, an isolated selected target set, and +an invertible row code that can be formed at the common input +frame, replace those target paths by frame advances and a late +coded response query. The output retains every arbitrary target +baseline. The present word verifies all these premises. + +The separate +[access packet](../../bridge-access-20261017/row-capture-access-20261020/FREEZE.json), +at SHA256 +`9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11`, +binds the construction to its literal D25 owner views. This review +pins that packet but does not rerun its phase census. + +That packet gives the next current-entry type as Q on selected +carriers and I elsewhere. This is not the old all-I target type. +A later caller must consume that type or implement its conversion. +No such conversion, final decoder, full controller, or recursive +host is included in the local invoice. + +This review establishes local centre formation in existing output +fields. It does not establish a complete supplier or a kappa +improvement. + +## Reproduction and credit + +Run from the workspace root: + +```text +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal +OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 MKL_NUM_THREADS=1 python3 -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/optimized +``` + +The required final line is `PASS_INDEPENDENT_ROW_CAPTURE_NATIVE`. +`REPRODUCTION.json` records the byte comparison and final source +hash checks. +Both runs completed with that result. Their result and input +receipts are byte identical. All 44 consumed source files were +rechecked and are unchanged. + +The producer proof records the source, cyclic, controller, and +bridge-access contributions. The independent review supplied the +direct-FULL identity-map deduction. AI assistance was used. +No PR, push, commit, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py new file mode 100644 index 0000000000..6fa689d442 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py @@ -0,0 +1,450 @@ +#!/usr/bin/env python3 +"""Check the selected-row code and its complete native service.""" +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +INPUTS = {} +P = [0, 27, 36, 111, 20, 7, 57, 46, 1, 3, 6, 8, 17, 18, 24, 23] +RAW = LANES/'new-core-transfer-20261017/low-displacement-20261020' +ALG = LANES/'controller-followthrough-20261017/row-capture-20261020' +NATIVE = RAW/'row-only-capture-20261020' +ACCEPTED = LANES/'new-native-recipes-20261017/low-displacement-review-20261020' + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(path, pin=None, compressed=False): + data = path.read_bytes() + content = gzip.decompress(data) if compressed else data + need(pin is None or sha256(content).hexdigest() == pin, + 'Input pin: '+str(path)) + INPUTS[str(path.relative_to(LANES))] = {'sha256': sha256(data).hexdigest()} + if compressed: + INPUTS[str(path.relative_to(LANES))]['decompressed_sha256'] = sha256(content).hexdigest() + return content + + +def frozen(path, name, pin): + obj = json.loads(read(path/name, pin)) + for name, digest in obj['files'].items(): + read(path/name, digest) + return obj + + +def rows(value): + return [{int(k): F(v) for k, v in row.items() if F(v)} for row in value] + + +def unit(n): + return [{i: F(1)} for i in range(n)] + + +def add(target, source, coefficient=F(1)): + for key, value in source.items(): + x = target.get(key, F(0))+coefficient*value + if x: + target[key] = x + else: + target.pop(key, None) + + +def mul(a, b): + out = [] + for row in a: + result = {} + for k, v in row.items(): + add(result, b[k], v) + out.append(result) + return out + + +def rank(a): + pivots = {} + for original in a: + row = dict(original) + while row: + j = min(row) + if j not in pivots: + value = row[j] + pivots[j] = {k: v/value for k, v in row.items()} + break + add(row, pivots[j], -row[j]) + return len(pivots) + + +def transpose(a, n): + out = [{} for _ in range(n)] + for i, row in enumerate(a): + for j, v in row.items(): + out[j][i] = v + return out + + +def price(events): + total = 0 + for op, _, _, value in events: + c = F(value) + n, d = abs(c.numerator), c.denominator + need(n > 0 and d & (d-1) == 0, 'Nonzero dyadic coefficient') + if op == 'scale': + need(n & (n-1) == 0, 'Dyadic unit scale') + total += 2*(abs(n.bit_length()-d.bit_length())+(c < 0)) + else: + need(op == 'add', 'Scalar opcode') + total += 2*(3+n.bit_length()-1+n.bit_count()+d.bit_length()-1) + return total + + +def reverse(events, n): + """Propagate output columns through the scalar word in reverse order.""" + columns = unit(n) + for op, target, origin, value in reversed(events): + c = F(value) + if op == 'scale': + columns[target] = {k: c*v for k, v in columns[target].items()} + else: + need(op == 'add' and target != origin, 'Distinct ADD fields') + add(columns[origin], columns[target], c) + return columns + + +def prefix(events, n): + """Compute exact prefix rows, separately from the reverse pass.""" + state = unit(n) + norm, height = F(1), 0 + for op, target, origin, value in events: + c = F(value) + if op == 'scale': + state[target] = {k: c*v for k, v in state[target].items()} + else: + add(state[target], state[origin], c) + norm = max(norm, sum(map(abs, state[target].values()), F(0))) + for x in state[target].values(): + d = x.denominator + need(d & (d-1) == 0, 'Dyadic prefix coefficient') + height = max(height, d.bit_length()-1) + return state, {'row_one_norm': str(norm), 'binary_height': height} + + +def algebra(raw, code): + model = raw['model'] + e, u, v = (rows(model[name]) for name in ('response', 'correction_U', 'correction_V')) + uv = mul(u, v) + expected_e = unit(112) + for row, correction in zip(expected_e, uv): + add(row, correction) + need(e == expected_e, 'Actual response factorization') + vp = [{j: row[p] for j, p in enumerate(P) if p in row} for row in v] + # The actual pivot blocks are signed two-coordinate Hadamards and units. + vp_t = transpose(vp, 16) + gram = [{i: F(2 if i < 8 else 1)} for i in range(16)] + need(mul(vp, vp_t) == gram, 'Actual pivot Gram matrix') + vi = [{j: x/(2 if j < 8 else 1) for j, x in row.items()} for row in vp_t] + need(mul(vi, vp) == unit(16) and mul(vp, vi) == unit(16), 'Pivot inverse orders') + w = mul(vi, v) + c, ci, b = unit(112), unit(112), [] + for i, p in enumerate(P): + need({j: w[i].get(q, F(0)) for j, q in enumerate(P)} == + {j: F(i == j) for j in range(16)}, 'Normalized pivot columns') + c[p] = dict(w[i]) + correction = dict(w[i]) + add(correction, {p: F(1)}, F(-1)) + b.append(correction) + add(ci[p], correction, F(-1)) + need(mul(c, ci) == unit(112) and mul(ci, c) == unit(112), 'Shear inverse orders') + need(rank(b) == 16, 'Exact shear displacement rank') + lamb = [{i: F(-5 if i < 8 else -7)} for i in range(16)] + need(mul(w, e) == mul(lamb, w), 'Selected left eigenvectors') + ce = mul(c, e) + encoded = mul(ce, ci) + need(all(set(row)-{i} <= set(P) for i, row in enumerate(encoded)), + 'Encoded response changes only pivot columns') + for name, value in [('pivot_minor', vp), ('pivot_minor_inverse', vi), + ('centre_reader', w), ('code', c), ('code_inverse', ci), + ('response', e), ('selected_capture_response', ce), + ('encoded_response', encoded)]: + need(rows(code[name]) == value, 'Independent algebra: '+name) + need(code['pivots'] == P, 'Exact selected ports') + for name, matrix in [('scalar_word', c), ('inverse_scalar_word', ci)]: + events = code[name] + need(reverse(events, 112) == transpose(matrix, 112), 'Reverse code: '+name) + need(price(events) == 1760, 'Code scalar price') + for op, target, origin, _ in events: + need(target in P and (op == 'scale' or origin not in P), 'Unchanged shear source') + word = code['scalar_word']+code['inverse_scalar_word'] + need(reverse(word, 112) == unit(112), 'Literal inverse order') + need(reverse(code['inverse_scalar_word']+code['scalar_word'], 112) == unit(112), + 'Other literal inverse order') + query = unit(224) + for p in P: + add(query[p], {112+j: x for j, x in ce[p].items()}) + need(reverse(code['final_query_word'], 224) == transpose(query, 224), + 'Arbitrary-baseline late query') + need(price(code['final_query_word']) == 3424, 'Late query scalar price') + a, pre_bound = prefix(code['scalar_word'], 112) + need(a == c, 'Separate forward code') + a, query_bound = prefix(code['final_query_word'], 224) + need(a == query, 'Separate forward late query') + return e, c, ce, { + 'code_price': 1760, 'query_price': 3424, + 'code_prefix': pre_bound, 'query_prefix_on_independent_inputs': query_bound, + 'displacement_rank': 16, 'extra_fields': 0, 'odd_scans': 0, + } + + +def inherit(): + frozen(ACCEPTED, 'NATIVE-REVIEW-FREEZE.json', + 'cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976') + frozen(ACCEPTED, 'EXTENSIONS-REVIEW-FREEZE.json', + 'c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c') + phase_path = LANES/'new-native-recipes-20261017/isotropic-pair-review-20261018/check.py' + read(phase_path, 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18') + spec = importlib.util.spec_from_file_location('independent_spatial_phase', phase_path) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + return phase + + +def select_raw(raw_word, selected): + indices, removed = [], [] + for i, event in enumerate(raw_word['events']): + need(event[0] in ('native', 'scalar'), 'Raw event grammar') + target = event[1] if event[0] == 'native' else event[1][1] + (removed if target in selected else indices).append(i) + for i in indices: + event = raw_word['events'][i] + if event[0] == 'scalar' and event[1][0] == 'add': + need(event[1][2] not in selected, 'Retained read of removed target') + return indices, removed + + +def check_word(word, old, code, e, c, ce): + need(word['frames'] == old['frames'] and word['start'] == old['start'], + 'Unchanged exact input geometry') + selected = {112+p for p in P} + indices, removed = select_raw(old, selected) + need(word['retained_original_event_indices'] == indices, 'Exact removal indices') + kept = [old['events'][i] for i in indices] + cut = [old['events'][i] for i in removed] + need(Counter(x[0] for x in cut) == {'native': 128, 'scalar': 122}, + 'Complete removed inventory') + need(Counter(x[4] for x in cut if x[0] == 'native') == {1: 128}, + 'Only the selected rank-one children are removed') + need(price([x[1] for x in cut if x[0] == 'scalar']) == 928, 'Removed scalar price') + pre = [['scalar', [op, 112+t, None if s is None else 112+s, v], 0] + for op, t, s, v in code['scalar_word']] + progress = [['native', 112+p, 0, 1, 9, 'capture-full'] for p in P] + late = [['scalar', [op, 112+t, None if s is None else s-112, v], 1] + for op, t, s, v in code['final_query_word']] + need(word['events'] == pre+kept+progress+late, 'Exact complete operation order') + stages = [('precode', pre), ('retained_core', kept), + ('selected_full_progress', progress), ('late_query', late)] + cursor, expected_ranges = 0, {} + for name, events in stages: + expected_ranges[name] = [cursor, cursor+len(events)] + cursor += len(events) + need(word['stage_ranges'] == expected_ranges, 'Exact stage boundaries') + need(cursor == 2886, 'Complete event count') + final = list(old['final']) + for field in selected: + final[field] = 1 + need(word['final'] == final, 'Exact changed output frames') + need(old['frames'][0] == [] and len(old['frames'][1]) == 9, 'I and FULL declarations') + current = list(word['start']) + count, used = Counter(), set() + for i, event in enumerate(word['events']): + if i == expected_ranges['late_query'][0]: + need(all(current[p] == 1 for p in range(112)) and + all(current[p] == 1 for p in selected), 'Late common-FULL cut') + if event[0] == 'native': + _, field, before, after, r, key = event + need(0 <= field < 224 and current[field] == before, 'Native field and old frame') + need(word['native_recipes'][key]['rank'] == r, 'Native rank binding') + if key == 'capture-full': + need(field in selected and (before, after, r) == (0, 1, 9), + 'Only selected complete FULL replacements') + else: + need(word['native_recipes'][key] == old['native_recipes'][key], + 'Exact inherited phase record') + need(key == str(before)+':'+str(after), 'Ordered inherited frame pair') + current[field] = after + count[r] += 1 + used.add(key) + else: + _, scalar, frame = event + op, target, origin, _ = scalar + need(0 <= target < 224 and current[target] == frame, 'Scalar target frame') + if op == 'add': + need(0 <= origin < 224 and current[origin] == frame, 'Scalar source frame') + else: + need(op == 'scale' and origin is None, 'Scale grammar') + need(current == final, 'Complete final frame ledger') + need(used == set(word['native_recipes']), 'Every stored recipe is used') + need(count == {1: 1392, 2: 64, 3: 48, 9: 16}, 'Complete native profile') + scalars = [event[1] for event in word['events'] if event[0] == 'scalar'] + expected = unit(640) + for p in range(112): + target = 112+p + expected[target] = {112+j: v for j, v in c[p].items()} + add(expected[target], ce[p] if p in P else e[p]) + need(reverse(scalars, 640) == transpose(expected, 640), 'All640 reverse input columns') + actual, growth = prefix(scalars, 640) + need(actual == expected and actual[224:] == unit(640)[224:], 'Separate forward row check') + need(growth == {'row_one_norm': '132', 'binary_height': 1}, + 'Complete operation-boundary content bounds') + need(price(scalars) == 11640, 'Complete scalar invoice') + stage_prices = {name: price([e[1] for e in events if e[0] == 'scalar']) + for name, events in stages} + need(stage_prices == {'precode': 1760, 'retained_core': 6456, + 'selected_full_progress': 0, 'late_query': 3424}, + 'All four scalar stage bills') + input_views = [r for r in old['endpoint_adapters'] if r['role'] == 'source'] + need(word['input_views'] == input_views, 'All112 exact input phase adapters') + outputs = word['output_views'] + need(len(outputs) == 96 and {r['port'] for r in outputs} == set(range(112))-set(P), + 'Exactly the96 ordinary output adapters') + for r in outputs: + need(r['frame'] == final[112+r['port']] and r['recipe']['rank'] == 0 and + r['recipe']['right'] is None, 'One output monomial in the actual ordinary frame') + full = [['C', 1 << j, 1] for j in range(9)] + need(word['new_full_recipe_circuit'] == full, 'Declared complete positive FULL kernel') + need(reverse([x[1] for x in kept+progress+late if x[0] == 'scalar'], 640) != + transpose(expected, 640), 'Missing precode control') + need(reverse([x[1] for x in pre+kept+progress if x[0] == 'scalar'], 640) != + transpose(expected, 640), 'Missing late query control') + try: + select_raw(old, selected-{112+27}) + except ValueError: + pass + else: + raise ValueError('Incomplete selected-pair control') + return { + 'input_columns': 640, 'unchanged_arbitrary_roles': 416, 'events': cursor, + 'removed_events': len(removed), 'removed_scalar_price': 928, + 'native_profile': dict(sorted(count.items())), + 'native_children': sum(count.values()), 'native_mass': sum(r*n for r, n in count.items()), + 'real_scalar_primitives': price(scalars), 'scalar_stage_prices': stage_prices, + 'input_views': 112, 'output_views': 96, + 'native_side_maps_upper_bound': 2*sum(count.values()), + 'inherited_distinct_native_recipes': len(used)-1, + 'new_distinct_native_recipes': 1, 'growth': growth, + 'private_fields': 0, 'new_fields': 0, 'odd_scans': 0, + } + + +def phases(word, old, phase): + full = [('C', 1 << j, 1) for j in range(9)] + record = word['native_recipes']['capture-full'] + result = {'full': phase.compare(phase.recipe(record), full, 'New complete F9', 512)} + old_target = {r['port']: r for r in old['endpoint_adapters'] if r['role'] == 'target'} + inverse_checks = [] + for view in word['output_views']: + p = view['port'] + inherited = phase.recipe(old_target[p]) + new = phase.recipe(view['recipe']) + left = phase.compare(inherited+new, [], 'Output inverse '+str(p), 1) + right = phase.compare(new+inherited, [], 'Output inverse other order '+str(p), 1) + inverse_checks.append({'port': p, 'orders': [left, right]}) + result['output_inverse_monomials'] = inverse_checks + identity = {'matrix_rows': [1 << j for j in range(9)], + 'quadratic_rows': [0]*9, 'linear_Z4': [0]*9, 'offset': 0, 'phase': 0} + direct = {'rank': 9, 'left': identity, 'right': identity} + result['identity_wrapper_corollary'] = phase.compare( + phase.recipe(direct), full, 'Direct identity-wrapper F9', 512) + bad = phase.recipe(record)+phase.compile_circuit([['phase', 1]]) + need(phase.run(bad, 0) != phase.run(full, 0), 'Wrong global phase control') + result['scope'] = 'Exact executed recipes; descriptive compiler circuits are not executed.' + return result + + +def direct_refinement(payload): + frozen(NATIVE, 'DIRECT-FULL-FREEZE.json', + 'f0d3b0d7c8d93e391089a2d28066dd02b4a9b28e306dea5f4e7cb5fc895b054e') + direct = json.loads(read(NATIVE/'direct-normal/DIRECT-FULL-CAPTURE.json.gz', + 'fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c', True)) + need(direct['refinement_source_decompressed_sha256'] == + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', + 'Exact refinement source') + need(set(direct) == set(payload)|{'refinement_source_decompressed_sha256'}, + 'No additional refinement state') + for key in set(payload)-{'providers', 'schema'}: + need(direct[key] == payload[key], 'Unchanged refinement metadata: '+key) + identity = {'matrix_rows': [1 << j for j in range(9)], + 'quadratic_rows': [0]*9, 'linear_Z4': [0]*9, 'offset': 0, 'phase': 0} + expected = {'rank': 9, 'left': identity, 'right': identity} + for name, word in payload['providers'].items(): + changed = direct['providers'][name] + need(set(changed) == set(word), 'Unchanged word schema') + for key in set(word)-{'native_recipes'}: + need(changed[key] == word[key], 'Exact unchanged complete word: '+key) + need(set(changed['native_recipes']) == set(word['native_recipes']), + 'No additional native recipe') + for key, record in word['native_recipes'].items(): + need(changed['native_recipes'][key] == (expected if key == 'capture-full' else record), + 'Only the direct FULL recipe changes') + return {'providers': ['base', 'extra'], 'changed_occurrences_per_word': 16, + 'all_events_and_boundary_views_byte_equal': True, + 'real_scalar_primitives': 11640, 'native_children': 1520, 'native_mass': 1808, + 'native_side_maps_upper_bound': 3008, + 'proof': 'Exact complete-word substitution using the independently checked identity-wrapper kernel.'} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + frozen(ALG, 'FREEZE.json', '0810ec37cb70d819a1d40f817476a41dd1151535309972af1b5b1db2bcb42baf') + raw = json.loads(read(RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz', + 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True)) + code = json.loads(read(ALG/'run-normal/ROW-CAPTURE.json', + '4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7')) + e, c, ce, algebra_report = algebra(raw, code) + frozen(NATIVE, 'FREEZE.json', + '5321a8ff856042c5ca30ce6b29b90a51ccd4dcf02317820243bfffbb433c84d8') + frozen(LANES/'bridge-access-20261017/row-capture-access-20261020', 'FREEZE.json', + '9d4eda12aa32eb11d97f6a9a88c691152a0c9580ea678cceaacae3d9b06c5b11') + payload = json.loads(read(NATIVE/'run-normal/PRODUCTIVE-CAPTURE.json.gz', + '7c3b8343ec04c65f98b7170c7f37c9f80605e28c95df00bcf2a189908461c8b2', True)) + need(payload['schema'] == 'productive-sixteen-full-capture-v1', 'Native schema') + need(payload['selected_ports'] == P and payload['ports'] == raw['model']['ports'], + 'Exact physical selected ports and line directions') + need(payload['ordinary_ports'] == sorted(set(range(112))-set(P)) and + payload['inverse_code'] == code['code_inverse'], 'Complete inverse and ordinary metadata') + for key, expected in [('response', e), ('code', c), ('captured_response', ce)]: + need(rows(payload[key]) == expected, 'Native matrix contract: '+key) + need(set(payload['providers']) == {'base', 'extra'}, 'Both providers') + need(payload['providers']['base'] == payload['providers']['extra'], + 'Byte-equal provider payloads') + word_reports = {} + for provider, word in payload['providers'].items(): + word_reports[provider] = check_word(word, raw['providers'][provider]['forward'], code, e, c, ce) + phase = inherit() + phase_report = phases(payload['providers']['base'], raw['providers']['base']['forward'], phase) + refinement_report = direct_refinement(payload) + report = { + 'status': 'PASS_INDEPENDENT_ROW_CAPTURE_NATIVE', + 'algebra': algebra_report, 'literal_words': word_reports, + 'phases': phase_report, 'direct_full_refinement': refinement_report, + 'negative_controls': ['missing precode', 'missing late query', + 'incomplete selected pair', 'wrong global phase'], + 'scope': 'Complete local forward native service with changed output representation. No free later-stage conversion, global decoder, recursive host, or complete supplier claim.', + } + args.out.mkdir(parents=True, exist_ok=True) + (args.out/'REVIEW.json').write_text(json.dumps(report, indent=2, sort_keys=True)+'\n') + (args.out/'INPUTS.json').write_text(json.dumps(INPUTS, indent=2, sort_keys=True)+'\n') + print(report['status']) + + +if __name__ == '__main__': + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json new file mode 100644 index 0000000000..7ef7d475fc --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/normal/INPUTS.json @@ -0,0 +1,137 @@ +{ + "bridge-access-20261017/row-capture-access-20261020/ACCESS.md": { + "sha256": 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No free later-stage conversion, global decoder, recursive host, or complete supplier claim.", + "status": "PASS_INDEPENDENT_ROW_CAPTURE_NATIVE" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/FREEZE.json new file mode 100644 index 0000000000..75b6cce7cb --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/FREEZE.json @@ -0,0 +1,20 @@ +{ + "complete_words": 30, + "files": { + "REPRODUCTION.json": "b6e95290f995e433a17632749fcff13f8d7299d9bba51f5dcb84d62f253d8d0f", + "REVIEW.md": "31c0e10b2694d31443460937e13283c130a102da86fc09e874e063be8aa8d40a", + "check.py": "ac1e9f827d06a86262b3814b7e75588b19bfcf23b3a741ffbafa38dd83a0ecf4", + "normal-final/INPUTS.json": "fa827c1a46d2f72325099cf1111a1a0d0aa65746baaee41b24588fa789a98797", + "normal-final/REVIEW.json": "367b51faa030b534e2c547587a09d1ef30b8cc3cd05e5fd6283c62954b1a85c7", + "optimized-final/INPUTS.json": "fa827c1a46d2f72325099cf1111a1a0d0aa65746baaee41b24588fa789a98797", + "optimized-final/REVIEW.json": "367b51faa030b534e2c547587a09d1ef30b8cc3cd05e5fd6283c62954b1a85c7" + }, + "normal_optimized_bytes_equal": true, + "payload_decompressed_sha256": "aa5c064837350c50928c984e03a3d7dffb5ab37da4510dc75607ced6166be797", + "producer_freeze_sha256": "d0d88ff73aa4762e53bce289544a1635c711e4bfeef5f499489199f506509df2", + "publication": "No PR, push, commit or publication. Before any future PR description read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.", + "schema": "independent-signed-sixteen-native-review-freeze-v1", + "scope": "Thirty complete local physical words and exact invoices. No routed caller, saved-record restoration, recursive hosting, finite map implementation, rounding bound or full supplier claim.", + "status": "PASS_INDEPENDENT_REVIEW", + "unchanged_inputs": 65 +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..5ffa324815 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/REPRODUCTION.json @@ -0,0 +1,22 @@ +{ + "local_markdown_links_checked": [ + "../../new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/FREEZE.json", + "../../new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/run-normal/SIGNED-CLEAN.json.gz", + "../../new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/SIGNED-CLEAN.md", + "../../bridge-review-20261017/signed-metric-review-20261020/REVIEW.md", + "check.py", + "../row-capture-native-review-20261020/FREEZE.json", + "../line-entry-reuse-review-20261020/FREEZE.json", + "../low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json", + "REPRODUCTION.json" + ], + "normal_command": "python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py --out ", + "normal_optimized_byte_equal": [ + "REVIEW.json", + "INPUTS.json" + ], + "optimized_command": "python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py --out ", + "python": "3.14.7", + "status": "PASS_REPRODUCTION_AND_SOURCE_PRESERVATION", + "unchanged_consumed_inputs": 65 +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/REVIEW.md new file mode 100644 index 0000000000..8b98d8c4b0 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/REVIEW.md @@ -0,0 +1,252 @@ +# Independent review of the complete signed16 native services + +All thirty local words pass the independent exact replay. The three +codes form sixteen selected centre outputs and preserve arbitrary +target baselines. Every word acts on 640 independent complex fields. +The 416 other fields are untouched. + +The result includes the literal inverse-adjoint, the selected-bank +conjugate, and its paid metric conversion. There is no new native +phase operator. The review binds each native occurrence and endpoint +adapter to exact accepted records. It does not certify a routed +caller, a recursive host, or a complete supplier improvement. + +## Sources and method + +The reviewed [producer freeze](../../new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/FREEZE.json) +has SHA256 +`d0d88ff73aa4762e53bce289544a1635c711e4bfeef5f499489199f506509df2`. +The decompressed [native payload](../../new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/run-normal/SIGNED-CLEAN.json.gz) +has SHA256 +`aa5c064837350c50928c984e03a3d7dffb5ab37da4510dc75607ced6166be797`. +The [producer proof](../../new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/SIGNED-CLEAN.md) +states the full local contract and invoice. + +The separate [matrix and scalar review](../../bridge-review-20261017/signed-metric-review-20261020/REVIEW.md) +has freeze +`b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762`. +It derives the original code \(C\), the pair-closed code \(\bar C\), +their metrics, and the actual support of \(\bar C^T\). The original +\(C^T\) has 32 ordinary mode rows outside the admitted support. This +packet does not emit that code. + +[check.py](check.py) imports only the pinned exact arithmetic helper +from this lane's [row-capture review](../row-capture-native-review-20261020/FREEZE.json). +It imports no producer module or Clifford compiler. It propagates +covectors in reverse order through each full scalar word. A separate +forward row pass checks the endpoints and all prefix bounds. Exact +fractions are used in both passes. + +The checker reads the frozen matrices, proves both code inverse +orders and the metric identity again, and derives every two-bank +endpoint from those matrices. It then checks the actual native +chronology, adapter targets, transfer coefficients, stage cuts, and +all helper roles. It compares each derived invoice and prefix bound +with the frozen producer receipt. + +## The general local interface + +Let \(P\) be the coordinate projection onto the sixteen selected +fields, and let \(R=I-P\). Let \(A\) be an invertible code. The forward +content map is + +\[ + F_A= + \begin{pmatrix}RA&-P\\A&R\end{pmatrix}. +\] + +For \(x=(a,u)\) and \(y=(z,v)\), put \(w=Ax\). Then + +\[ + X'=(-z,w_R),\qquad Y'=(w_P,v+w_R). +\] + +Both banks are arbitrary. In particular, the word preserves \(z\) as +\(-z\). It uses no zero work field. + +To invert the map, first recover +\(w=RX'+PY'\). Then +\(x=A^{-1}w\) and \(y=-X'+RY'\). Thus + +\[ + F_A^{-1}= + \begin{pmatrix}A^{-1}R&A^{-1}P\\-I&R\end{pmatrix}, + \qquad + F_A^{-T}= + \begin{pmatrix}RA^{-T}&-I\\PA^{-T}&R\end{pmatrix}. +\] + +Let \(S\) exchange the two banks on the selected ports. The map +\(S F_A^{-T}S\) sends + +\[ + (a,u;z,v)\longmapsto + \bigl((A^{-T}(z,u))_P,\, + (A^{-T}(z,u))_R-v;\,-a,v\bigr). +\] + +The checker derives this formula directly and compares it with the +complete literal word. It also checks both inverse orders. + +For \(A=\bar C^T\), the mixed-source code in this raw selected dual is +exactly \(\bar C^{-1}\). This is an admitted local interface. It does +not imply that codes from different routed stages cancel. + +## The full metric conversion + +Suppose \(K,G\) are invertible diagonal real matrices and + +\[ + AKA^T=G,\qquad J=K^{-1}. +\] + +Then \(A^{-T}=G^{-1}AK\). Since \(G\) commutes with \(P\) and \(R\), + +\[ + \operatorname{diag}(G,G)F_A^{-T} + \operatorname{diag}(J,G^{-1}) + = + \begin{pmatrix}RA&-I\\PA&R\end{pmatrix}. +\] + +Conjugation by \(S\) gives the preceding selected-dual formula with +\(A\) in place of \(A^{-T}\). No commutation of \(A\) with \(P\) is +used. No positivity assumption on \(K\) or \(G\) is used. + +The actual metrics are signed powers of two. Each scale acts on one +field, so it commutes with that field's complex spatial frame. This +remains true when the two banks have different frames. The checker +binds every scale to the field after the selected-bank relabeling. + +Both input banks require a metric. Removing the input scales on the +target bank changes the full map. The negative control confirms this +on arbitrary inputs. The conversion is not a one-bank code identity +with target baselines suppressed. + +For the transpose family, the code identity is +\(\bar C^T\bar G^{-1}\bar C=K^{-1}\). The input and output metrics +are therefore exchanged in the precise order given by this identity. +The checker does not reuse the original code's scales for that family. + +## The native construction and phase binding + +For each provider, the checker reconstructs the exact selected-target +removal from the accepted dense source. It removes 250 events: +128 H1 children and 122 scalar events. No retained event reads a +removed target. + +There are 592 retained ordinary transfer slots. The original event +index, actual source and target fields, mode parameter, old coefficient, +and new coefficient are checked for every slot. The individual and +paired codes keep 280 nonzero transfers. The transpose family keeps +312. Every other event is an exact source event. + +The code emits the ordinary response rows of \(A\) directly. It does +not identify the old response with a new code by an unpriced physical +permutation. A separate matrix fact about \(E=PR\) is not used to +replace the actual native response. + +All source fields then have FULL. The complete paid \(A\) word acts +there. Each selected target also reaches FULL. Three unit ADDs perform +each signed exchange: +\((w_P,z)\mapsto(-z,w_P)\). The source code and all exchanges have +one common frame at each scalar operation. + +The I-entry variant uses the accepted direct F9 record with identity +side maps. The Q-entry variant uses the exact sixteen H8 records from +the [line-entry review](../line-entry-reuse-review-20261020/FREEZE.json), +freeze +`cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c`. +Its selected input adapters are exact same-port copies of the source +adapters. The ordered frame basis is checked with each record. + +The remaining native recipes and their ordered frames bind to the +accepted [dense-provider extension review](../low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json), +freeze +`c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c`. +The endpoint records also bind to the accepted direct FULL formation. +These source reviews include global phase. This review does not run +a second spatial interpreter on unchanged records. + +For any unitary physical operation \(U\), \(U^{-*}=U\). Therefore the +inverse-adjoint retains every native and map operation in the same +chronological position. A real ADD transposes its fields and negates +its coefficient; a scale becomes its reciprocal. The checker compares +every literal dual event with this rule and verifies its actual frame. + +The selected conjugate is a complete field relabeling. It adds no +runtime swaps. Both selected input fields have the same exact Q +operator, and both selected outputs have FULL. Every input adapter is +rebound to its actual field. Ordinary output adapters remain fixed. + +All changed scalar coefficients are real. They commute with the common +complex spatial frame. The physical identities extend by tensor +products of the complete native operators. No one-bit polynomial is +substituted for a child operator. + +## Exact local invoices + +The prices include both complex components. + +| Code | Retuned core | Source code | Rotations | Forward or raw dual | Metric-selected dual | +| --- | ---: | ---: | ---: | ---: | ---: | +| \(C\) | 4040 | 5564 | 384 | 9988 | 11252 | +| \(\bar C\) | 4040 | 5644 | 384 | 10068 | 11284 | +| \(\bar C^T\) | 4296 | 5644 | 384 | 10324 | 11156 | + +The metric input/output prices are 528/736, 512/704, and 512/320, +respectively. No scale fusion is assumed. + +| Entry | Profile | Children | Mass | Input views | Output views | Side-map upper bound | +| --- | --- | ---: | ---: | ---: | ---: | ---: | +| I | 1392 H1 + 64 H2 + 48 H3 + 16 H9 | 1520 | 1808 | 112 | 96 | 3008 | +| Q and every dual | 1392 H1 + 64 H2 + 48 H3 + 16 H8 | 1520 | 1792 | 128 | 96 | 3040 | + +The side-map count is an upper bound. It is not a price for finite +map execution. No word adds a field, private buffer, odd scan, or +CLEAR. No event touches the 416 auxiliary fields. + +The exact event-boundary content bounds are: + +| Code | Forward norm / binary height | Raw dual norm / height | Metric dual norm / height | +| --- | --- | --- | --- | +| \(C\) | 26 / 3 | 8 / 3 | 13 / 5 | +| \(\bar C\) | 26 / 3 | 8 / 3 | 13 / 5 | +| \(\bar C^T\) | 18 / 3 | 22 / 3 | 40 / 2 | + +These are row one-norms of exact content matrices. They exclude child +internals, scalar scan internals, and roundoff propagation. + +## Reproduction and limits + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py --out +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py --out +``` + +The expected status is `PASS_INDEPENDENT_SIGNED_SIXTEEN_NATIVE`. +The controls reject an omitted target metric, a wrong metric sign, +reversed dual chronology, and a changed native global phase. + +Both commands passed. The final normal and optimized receipts and +input manifests are byte identical. All 65 consumed inputs remain +unchanged. All nine local Markdown links resolve. These checks are +recorded in [REPRODUCTION.json](REPRODUCTION.json). + +This result supplies complete local signed-metric interfaces. It +does not prove that their fields satisfy a routed old-reader contract. +It does not provide saved-record restoration, a new helper host, +a finite map implementation, or a complete precision bound. It makes +no change to the selected frontier or the complete kappa calculation. + +The root, oblique, cover, bridge-access, and native lanes supplied +the constructions and prior records. The bridge-review lane supplied +the separate matrix proof. This review supplies the independent full +native binding, reverse replay, and exact local invoice. AI assistance +was used. + +No PR, push, commit, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py new file mode 100644 index 0000000000..a87611f98a --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/check.py @@ -0,0 +1,440 @@ +#!/usr/bin/env python3 +"""Check complete signed-metric words and their physical field types.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +HELPER = HERE.parent / "row-capture-native-review-20261020/check.py" +PIN = "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84" +if sha256(HELPER.read_bytes()).hexdigest() != PIN: + raise ValueError("Independent arithmetic helper pin") +spec = importlib.util.spec_from_file_location("independent_signed_arithmetic", HELPER) +q = importlib.util.module_from_spec(spec) +spec.loader.exec_module(q) +q.read(HELPER, PIN) +need = q.need +SOURCE = q.RAW / "signed-clean-native-20261020" +CODE = q.RAW / "signed-sixteen-20261020" +FREEZE = "d0d88ff73aa4762e53bce289544a1635c711e4bfeef5f499489199f506509df2" +PAYLOAD = "aa5c064837350c50928c984e03a3d7dffb5ab37da4510dc75607ced6166be797" + + +def forward(code, selected): + matrix = q.unit(640) + for p in range(112): + matrix[p] = {112+p: F(-1)} if p in selected else dict(code[p]) + matrix[112+p] = dict(code[p]) + if p not in selected: + q.add(matrix[112+p], {112+p: F(1)}) + return matrix + + +def inverse(code_inverse, selected): + z = [{112+p if p in selected else p: F(1)} for p in range(112)] + matrix = q.unit(640) + matrix[:112] = q.mul(code_inverse, z) + for p in range(112): + matrix[112+p] = {p: F(-1)} + if p not in selected: + q.add(matrix[112+p], {112+p: F(1)}) + return matrix + + +def conjugate(matrix, permutation): + return [{permutation[j]: v for j, v in matrix[permutation[p]].items()} + for p in range(len(matrix))] + + +def selected_dual(code, selected): + z = [{112+p if p in selected else p: F(1)} for p in range(112)] + matrix = q.unit(640) + matrix[:112] = q.mul(code, z) + for p in range(112): + if p in selected: + matrix[112+p] = {p: F(-1)} + else: + q.add(matrix[p], {112+p: F(-1)}) + return matrix + + +def diagonal_word(matrix, offset=0): + result = [] + for p, row in enumerate(matrix): + need(set(row) == {p} and row[p], "A nonzero diagonal metric") + c = row[p] + need(abs(c.numerator) & (abs(c.numerator)-1) == 0 and + c.denominator & (c.denominator-1) == 0, "A signed power-of-two metric") + if c != 1: + result.append(["scale", offset+p, None, str(c)]) + return result + + +def scalar_events(word): + return [e[1] for e in word["events"] if e[0] == "scalar"] + + +def family_matrices(family, source, payload, selected, permutation): + raw_c, raw_ci, raw_mode, tape, raw_j, raw_g = source + for key, value in (("code", raw_c), ("inverse", raw_ci), ("native_code", raw_mode), + ("metric_input_inverse", raw_j), ("metric_output", raw_g)): + need(payload[key] == value, "Exact source matrix: "+family+":"+key) + c, ci, j, g = map(q.rows, (raw_c, raw_ci, raw_j, raw_g)) + need(q.mul(c, ci) == q.unit(112) and q.mul(ci, c) == q.unit(112), + "Both actual code inverse orders") + gi = [{p: 1/row[p]} for p, row in enumerate(g)] + k = [{p: 1/row[p]} for p, row in enumerate(j)] + need(q.mul(q.mul(c, k), q.transpose(c, 112)) == g, "Actual signed metric") + need(q.transpose(ci, 112) == q.mul(q.mul(gi, c), k), + "Independent inverse-transpose metric formula") + pre = diagonal_word(j) + diagonal_word(gi, 112) + post = diagonal_word(g) + diagonal_word(g, 112) + need(payload["metric_pre_word"] == pre and payload["metric_post_word"] == post, + "Both banks have the exact input and output metric scales") + need(q.reverse(tape, 112) == q.transpose(c, 112), "Independent reverse source code") + f, fi = forward(c, selected), inverse(ci, selected) + d, di = q.transpose(fi, 640), q.transpose(f, 640) + b, bi = conjugate(d, permutation), conjugate(di, permutation) + need(b == selected_dual(q.transpose(ci, 112), selected), + "Independent arbitrary-baseline raw selected-dual formula") + pre_matrix = q.transpose(q.reverse(pre, 640), 640) + post_matrix = q.transpose(q.reverse(post, 640), 640) + converted = conjugate(q.mul(q.mul(post_matrix, d), pre_matrix), permutation) + need(converted == selected_dual(c, selected), "Independent complete metric conversion") + pre_inverse = [{p: 1/row[p]} for p, row in enumerate(pre_matrix)] + post_inverse = [{p: 1/row[p]} for p, row in enumerate(post_matrix)] + converted_inverse = conjugate(q.mul(q.mul(pre_inverse, di), post_inverse), permutation) + maps = {"forward_I": f, "forward_Q": f, "inverse_adjoint_Q": d, + "selected_conjugate_Q": b, "metric_selected_conjugate_Q": converted} + inverses = {"forward_I": fi, "forward_Q": fi, "inverse_adjoint_Q": di, + "selected_conjugate_Q": bi, + "metric_selected_conjugate_Q": converted_inverse} + need(set(payload["content_maps"]) == set(maps), "All five serialized endpoint maps") + for name, matrix in maps.items(): + need(q.rows(payload["content_maps"][name]) == matrix[:224], + "Independently derived complete endpoint: "+name) + need(q.mul(matrix[:224], inverses[name][:224]) == q.unit(224) and + q.mul(inverses[name][:224], matrix[:224]) == q.unit(224), + "Both complete content inverse orders: "+name) + return maps, pre, post + + +def forward_binding(word, old, model, formation, reuse, source, cyclic, selected, entry): + need(word["frames"] == old["frames"], "Exact ordered source frame table") + kept, removed = q.select_raw(old, {112+p for p in selected}) + need(word["retained_original_event_indices"] == kept and + word["removed_original_event_indices"] == removed, "Exact retained and removed event indices") + need(len(removed) == 250 and + Counter(old["events"][i][0] for i in removed) == {"native": 128, "scalar": 122} and + Counter(old["events"][i][4] for i in removed + if old["events"][i][0] == "native") == {1: 128}, + "Complete selected-target removal census") + transfers = {r["event"]: r for r in old["transfer_records"]} + need(len(transfers) == len(old["transfer_records"]), "Unique source transfer indices") + parameters = {p["id"]: p for p in cyclic["parameters"]} + mode = q.rows(source[2]) + core, retunings, active = [], [], 0 + for index in kept: + event = old["events"][index] + if index not in transfers: + core.append(event) + continue + record = transfers[index] + if record["part"] == "large48": + par = parameters[record["parameter"]] + ports = cyclic["cyclic_carriers"][par["vertex"]] + p, j = ports[par["row"]], ports[par["column"]] + original_value = F(model["mode_response"][p][str(j)]) + else: + need(record["part"] == "small64", "Actual transfer sector") + p, j = record["target_port"], record["source_port"] + original_value = F(model["response"][p][str(j)]) + op, target, origin, raw = event[1] + need(event[0] == "scalar" and op == "add" and target == 112+p and origin == j and + p not in selected and F(record["coefficient"]) == F(raw), + "Actual mode coefficient and physical transfer fields") + value = mode[p].get(j, F(0))*F(raw)/original_value + retunings.append({"original_event": index, "mode_target": p, "mode_source": j, + "coefficient": str(value)}) + if value: + core.append(["scalar", ["add", target, origin, str(value)], event[2]]) + active += 1 + need(word["transfer_retunings"] == retunings, "Every ordinary coefficient is explicitly bound") + sources = {v["port"]: v for v in formation["input_views"]} + need(set(sources) == set(range(112)), "Every actual source adapter") + inputs = [{**v, "field": p} for p, v in sorted(sources.items())] + start, final = list(old["start"]), list(old["final"]) + progress, recipes = [], {} + for event in core: + if event[0] == "native": + recipes[event[5]] = old["native_recipes"][event[5]] + for p in sorted(selected): + if entry == "I": + key, before, rank = "direct-full", 0, 9 + recipes[key] = formation["native_recipes"]["capture-full"] + else: + key, before, rank = "capture-line:"+str(p), old["start"][p], 8 + need(reuse["frames"][reuse["start"][112+p]] == old["frames"][before], + "Accepted exact ordered line frame") + recipes[key] = reuse["native_recipes"][key] + inputs.append({**sources[p], "field": 112+p, "role": "selected_target"}) + start[112+p] = before + final[112+p] = 1 + progress.append(["native", 112+p, before, 1, rank, key]) + code = [["scalar", gate, 1] for gate in source[3]] + rotations = [] + for p in sorted(selected): + rotations += [["scalar", ["add", 112+p, p, "1"], 1], + ["scalar", ["add", p, 112+p, "-1"], 1], + ["scalar", ["add", 112+p, p, "1"], 1]] + need(word["events"] == core+progress+code+rotations, "Complete literal forward word") + need(word["native_recipes"] == recipes, "Every exact phase recipe is inherited") + need(word["start"] == start and word["final"] == final, "Complete endpoint frame declarations") + need(word["input_views"] == sorted(inputs, key=lambda v: v["field"]), + "Every exact input adapter has its physical field") + need(word["output_views"] == [v for v in formation["output_views"] if v["port"] not in selected], + "Every ordinary inverse target adapter is inherited") + at, ranges = 0, {} + for name, events in (("retained_retuned_core", core), ("selected_progress", progress), + ("source_code", code), ("signed_selected_exchanges", rotations)): + ranges[name] = [at, at+len(events)] + at += len(events) + need(word["stage_ranges"] == ranges, "Exact forward stage chronology") + return {"removed_events": 250, "removed_H1_children": 128, + "ordinary_transfer_slots": len(retunings), "nonzero_retuned_ADDs": active} + + +def dual_binding(word, source, permutation): + for name in ("frames", "start", "final", "native_recipes", "output_views", "stage_ranges"): + need(word[name] == source[name], "Exact dual record: "+name) + need(word["wire_permutation"] == {str(p): j for p, j in enumerate(permutation) if p != j}, + "Exact full physical-field permutation") + need(all(source[k][p] == source[k][permutation[p]] + for k in ("start", "final") for p in range(640)), "Selected endpoint frame symmetry") + source_views = {v["field"]: v for v in source["input_views"]} + expected_views = deepcopy(source["input_views"]) + for v in expected_views: + v["field"] = permutation[v["field"]] + need(word["input_views"] == sorted(expected_views, key=lambda v: v["field"]), + "Every dual adapter is rebound to its physical field") + for v in word["input_views"]: + need(all(v[k] == source_views[v["field"]][k] + for k in ("port", "frame", "rank", "left", "right")), + "Same-port Q/Q input phase equality") + expected = [] + for old in source["events"]: + if old[0] == "native": + e = list(old) + e[1] = permutation[e[1]] + else: + op, p, j, raw = old[1] + value = F(raw) + gate = (["add", permutation[j], permutation[p], str(-value)] if op == "add" + else ["scale", permutation[p], None, str(1/value)]) + e = ["scalar", gate, old[2]] + expected.append(e) + need(word["events"] == expected, "Literal same-order inverse-adjoint and field rebind") + + +def metric_binding(word, source, pre, post, permutation): + for key in ("frames", "start", "final", "native_recipes", "input_views", "output_views", + "wire_permutation"): + need(word[key] == source[key], "Unchanged metric-wrapper physical record: "+key) + def bind(tape, frames): + return [["scalar", [op, permutation[p], None, c], frames[permutation[p]]] + for op, p, _, c in tape] + prefix, suffix = bind(pre, source["start"]), bind(post, source["final"]) + need(word["events"] == prefix+source["events"]+suffix, "Complete two-bank metric word") + ranges = {"metric_input": [0, len(prefix)]} + ranges.update({name: [start+len(prefix), end+len(prefix)] + for name, (start, end) in source["stage_ranges"].items()}) + at = len(prefix)+len(source["events"]) + ranges["metric_output"] = [at, at+len(suffix)] + need(word["stage_ranges"] == ranges, "Exact metric-wrapper placement") + + +def trace(word, expected, entry): + current = list(word["start"]) + count, used = Counter(), set() + for event in word["events"]: + if event[0] == "native": + _, p, before, after, rank, key = event + need(0 <= p < 224 and current[p] == before, "Actual native source frame") + need(word["native_recipes"][key]["rank"] == rank, "Actual inherited native rank") + current[p] = after + count[rank] += 1 + used.add(key) + else: + need(event[0] == "scalar", "Only native and real dyadic scalar events") + _, (op, p, j, value), frame = event + need(0 <= p < 224 and current[p] == frame, "Actual scalar target frame") + if op == "add": + need(0 <= j < 224 and j != p and current[j] == frame, "Actual common scalar frame") + else: + need(op == "scale" and j is None and F(value), "Invertible scalar scale") + need(len(current) == 640 and current == word["final"], "All actual final frames") + need(current[224:] == word["start"][224:] and used == set(word["native_recipes"]), + "Complete helper and phase-recipe ledger") + need(count == {1: 1392, 2: 64, 3: 48, 9 if entry == "I" else 8: 16}, + "Complete child profile") + gates = scalar_events(word) + need(q.reverse(gates, 640) == q.transpose(expected, 640), + "Independent reverse replay on all640 complex input columns") + rows, bound = q.prefix(gates, 640) + need(rows == expected and rows[224:] == q.unit(640)[224:], + "Separate forward rows and416 arbitrary helper outputs") + at, prices = 0, {} + for name, (start, end) in sorted(word["stage_ranges"].items(), key=lambda x: x[1][0]): + need(start == at and end >= start, "Complete disjoint scalar stage ledger") + prices[name] = q.price([e[1] for e in word["events"][start:end] if e[0] == "scalar"]) + at = end + need(at == len(word["events"]) and q.price(gates) == sum(prices.values()), + "The invoice covers every operation") + return {"complex_input_columns": 640, "unchanged_arbitrary_complex_helpers": 416, + "native_profile": dict(sorted(count.items())), "native_children": sum(count.values()), + "native_mass": sum(k*v for k, v in count.items()), + "scalar_price": sum(prices.values()), "scalar_stage_prices": prices, + "input_views": len(word["input_views"]), "output_views": len(word["output_views"]), + "native_side_map_upper_bound": 2*(sum(count.values())-(16 if entry == "I" else 0)), + "content_prefix_bound": bound, "new_fields": 0, "private_fields": 0, + "odd_scans": 0, "runtime_boundary_swaps": 0} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + for path, name, pin in ( + (SOURCE, "FREEZE.json", FREEZE), + (CODE, "FREEZE.json", "8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2"), + (CODE, "PAIRED-FREEZE.json", "810508791ea43aecaaf894c3cb50a8170d3e6f1f8e52684e274cda16c2c2db57"), + (q.LANES/"bridge-review-20261017/signed-metric-review-20261020", "FREEZE.json", + "b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762"), + (HERE.parent/"row-capture-native-review-20261020", "FREEZE.json", + "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"), + (HERE.parent/"line-entry-reuse-review-20261020", "FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"), + (q.ACCEPTED, "NATIVE-REVIEW-FREEZE.json", + "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976"), + (q.ACCEPTED, "EXTENSIONS-REVIEW-FREEZE.json", + "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c")): + q.frozen(path, name, pin) + payload = json.loads(q.read(SOURCE/"run-normal/SIGNED-CLEAN.json.gz", PAYLOAD, True)) + need(len(payload["source_pins"]) == 12, "All twelve declared source pins") + for record in payload["source_pins"].values(): + path = Path(record["path"]) + q.read(path, record["sha256"], path.suffix == ".gz") + producer_receipt = json.loads(q.read(SOURCE/"run-normal/CHECKS.json", + "21e5ae1b7757429dac8ecc4c4238f7e7f1296bf3f6cb3b3c67b09166c22a79ca")) + first = json.loads(q.read(CODE/"run-v2-normal/SIGNED-SIXTEEN.json.gz", + "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c", True)) + paired = json.loads(q.read(CODE/"paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz", + "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1", True)) + raw = json.loads(q.read(q.RAW/"odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", True)) + formation = json.loads(q.read(q.NATIVE/"direct-normal/DIRECT-FULL-CAPTURE.json.gz", + "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c", True)) + reuse = json.loads(q.read(q.NATIVE/"reuse-normal/LINE-ENTRY-REUSE.json.gz", + "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110", True)) + cyclic = json.loads(q.read(q.LANES/"independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585")) + selected = set(first["centre_ports"]) + need(len(selected) == 16 and selected == set(q.P) == set(paired["centre_ports"]) and + payload["selected_ports"] == sorted(selected), "Exact16 selected physical ports") + need(payload["ports"] == raw["model"]["ports"], "Exact source port labels") + sources = { + "individual": (first["code"], first["inverse"], first["native_code"], + first["scalar_words"]["code"], first["input_metric_inverse"], first["output_metric"]), + "paired": (paired["code"], paired["inverse"], paired["native_codes"]["code"], + paired["scalar_words"]["code"], paired["input_metric_inverse"], paired["output_metric"]), + "paired_transpose": (paired["transpose"], paired["inverse_transpose"], paired["native_codes"]["transpose"], + paired["scalar_words"]["transpose"], paired["output_metric"], paired["input_metric_inverse"])} + need(set(payload["families"]) == set(sources) == set(payload["providers"]), "All three code families") + identity = list(range(640)) + swap = [112+p if p in selected else p-112 if p-112 in selected else p for p in range(640)] + reports, total = {}, 0 + for family, source in sources.items(): + maps, pre, post = family_matrices(family, source, payload["families"][family], selected, swap) + need(set(payload["providers"][family]) == {"base", "extra"}, "Both actual provider words") + reports[family] = {} + for provider, words in payload["providers"][family].items(): + need(set(words) == set(maps), "Every local variant is present") + reports[family][provider] = {} + for name, word in words.items(): + entry = "I" if name == "forward_I" else "Q" + binding = {} + if name.startswith("forward_"): + binding = forward_binding(word, raw["providers"][provider]["forward"], raw["model"], + formation["providers"][provider], reuse["providers"][provider], + source, cyclic, selected, entry) + elif name == "metric_selected_conjugate_Q": + metric_binding(word, words["selected_conjugate_Q"], pre, post, swap) + else: + dual_binding(word, words["forward_Q"], identity if name == "inverse_adjoint_Q" else swap) + report = {**trace(word, maps[name], entry), **binding} + recorded = producer_receipt["reports"][family][provider][name] + for a, b in (("scalar_price", "scalar"), ("scalar_stage_prices", "scalar_stages"), + ("native_profile", "native_profile"), ("native_children", "native_children"), + ("native_mass", "native_mass"), ("input_views", "input_views"), + ("output_views", "output_views"), + ("native_side_map_upper_bound", "native_side_map_upper_bound")): + value = report[a] + if a == "native_profile": + value = {str(k): v for k, v in value.items()} + need(value == recorded[b], "Independent invoice agrees with frozen receipt: "+a) + need(report["content_prefix_bound"] == + {"row_one_norm": recorded["content_row_one_norm"], + "binary_height": recorded["binary_height"]}, + "Independent prefix bound agrees with frozen receipt") + reports[family][provider][name] = report + total += 1 + print("PASS", family, provider, flush=True) + sample = payload["providers"]["individual"]["base"] + word = sample["metric_selected_conjugate_Q"] + start, end = word["stage_ranges"]["metric_input"] + omitted_target_scales = [e[1] for i, e in enumerate(word["events"]) if e[0] == "scalar" and + not (start <= i < end and swap[e[1][1]] >= 112)] + target = q.transpose(q.rows(payload["families"]["individual"]["content_maps"]["metric_selected_conjugate_Q"]) + + q.unit(640)[224:], 640) + need(q.reverse(omitted_target_scales, 640) != target, "Omitting target-bank metric scales is rejected") + gates = scalar_events(word) + bad = deepcopy(gates) + bad[0][3] = str(-F(bad[0][3])) + need(q.reverse(bad, 640) != target, "A wrong metric sign is rejected") + need(q.reverse(list(reversed(scalar_events(sample["inverse_adjoint_Q"]))), 640) != + q.transpose(q.rows(payload["families"]["individual"]["content_maps"]["inverse_adjoint_Q"]) + + q.unit(640)[224:], 640), "Wrong inverse-adjoint chronology is rejected") + bad_phase = dict(sample["forward_Q"]) + bad_phase["native_recipes"] = deepcopy(bad_phase["native_recipes"]) + record = next(iter(bad_phase["native_recipes"].values())) + record["left"]["phase"] = (record["left"]["phase"]+1) % 4 + try: + forward_binding(bad_phase, raw["providers"]["base"]["forward"], raw["model"], + formation["providers"]["base"], reuse["providers"]["base"], + sources["individual"], cyclic, selected, "Q") + except ValueError as error: + need(str(error) == "Every exact phase recipe is inherited", "The phase control fails at its exact test") + else: + raise ValueError("A changed native global phase was accepted") + result = { + "status": "PASS_INDEPENDENT_SIGNED_SIXTEEN_NATIVE", + "producer_freeze_sha256": FREEZE, "payload_decompressed_sha256": PAYLOAD, + "complete_words": total, "reports": reports, "fresh_native_phase_shapes": 0, + "phase_scope": "Each ordered native frame, exact recipe and physical endpoint adapter is bound to an accepted source. All changed gates are real scalar operations at a common complex frame.", + "both_complete_content_inverse_orders": True, + "negative_controls": ["omitted target-bank metric", "wrong metric sign", + "wrong dual chronology", "wrong native global phase"], + "scope": "Thirty complete local physical words. No routed caller, saved-record restoration, recursive host, finite map cost, rounding bound or complete supplier cost is claimed."} + args.out.mkdir(parents=True, exist_ok=False) + for name, value in (("REVIEW.json", result), ("INPUTS.json", q.INPUTS)): + (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+"\n") + print(result["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/normal-final/INPUTS.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/normal-final/INPUTS.json new file mode 100644 index 0000000000..4f8a08bf8c --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020/normal-final/INPUTS.json @@ -0,0 +1,204 @@ +{ + "bridge-review-20261017/signed-metric-review-20261020/FREEZE.json": { + "sha256": "b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762" + }, + "bridge-review-20261017/signed-metric-review-20261020/REVIEW.md": { + "sha256": "79ffc65f3037d00a03fbfa99e0a24ab3c889412602be21a022399ad59f8599f1" + }, + "bridge-review-20261017/signed-metric-review-20261020/check_review.py": { + "sha256": "415a45c0475f0d6499d77e0b41b695596ddb99536c60e5ec9859fd564f8edf0f" + }, + "bridge-review-20261017/signed-metric-review-20261020/normal/REVIEW-CHECKS.json": { + "sha256": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b" + }, + "bridge-review-20261017/signed-metric-review-20261020/optimized/REVIEW-CHECKS.json": { + "sha256": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b" + }, + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": { + "sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + }, + "new-core-transfer-20261017/low-displacement-20261020/emit_native.py": { + "sha256": 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1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "new_fields": 0, + "odd_scans": 0, + "output_views": 96, + "private_fields": 0, + "runtime_boundary_swaps": 0, + "scalar_price": 10324, + "scalar_stage_prices": { + "retained_retuned_core": 4296, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_code": 5644 + }, + "unchanged_arbitrary_complex_helpers": 416 + }, + "metric_selected_conjugate_Q": { + "complex_input_columns": 640, + "content_prefix_bound": { + "binary_height": 2, + "row_one_norm": "40" + }, + "input_views": 128, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "new_fields": 0, + "odd_scans": 0, + "output_views": 96, + "private_fields": 0, + "runtime_boundary_swaps": 0, + "scalar_price": 11156, + "scalar_stage_prices": { + "metric_input": 512, + "metric_output": 320, + "retained_retuned_core": 4296, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_code": 5644 + }, + "unchanged_arbitrary_complex_helpers": 416 + }, + "selected_conjugate_Q": { + "complex_input_columns": 640, + "content_prefix_bound": { + "binary_height": 3, + "row_one_norm": "22" + }, + "input_views": 128, + "native_children": 1520, + "native_mass": 1792, + "native_profile": { + "1": 1392, + "2": 64, + "3": 48, + "8": 16 + }, + "native_side_map_upper_bound": 3040, + "new_fields": 0, + "odd_scans": 0, + "output_views": 96, + "private_fields": 0, + "runtime_boundary_swaps": 0, + "scalar_price": 10324, + "scalar_stage_prices": { + "retained_retuned_core": 4296, + "selected_progress": 0, + "signed_selected_exchanges": 384, + "source_code": 5644 + }, + "unchanged_arbitrary_complex_helpers": 416 + } + } + } + }, + "scope": "Thirty complete local physical words. No routed caller, saved-record restoration, recursive host, finite map cost, rounding bound or complete supplier cost is claimed.", + "status": "PASS_INDEPENDENT_SIGNED_SIXTEEN_NATIVE" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/BLOCK-DERIVATION.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/BLOCK-DERIVATION.md new file mode 100644 index 0000000000..203dd8b425 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/BLOCK-DERIVATION.md @@ -0,0 +1,134 @@ +# Complex component blocks and the clean unitary map + +This note gives the algebra used by the independent native review. +The review receipt must bind the actual word before this note can +support a claim about that word. + +Let a complex field have real components `(r,i)`. For a Gaussian +dyadic matrix `M`, let `R(M)` be its real matrix in the interleaved +component order. The identities are + +```text +R(MN) = R(M) R(N), +R(M*) = R(M)^T. +``` + +These identities hold for rectangular matrices of compatible sizes. +They follow by expansion of complex multiplication. + +## A complete Gaussian ADD + +For distinct fields `t` and `s`, the operation `t += (a+ib)s` has +the following real instructions. Omit an instruction with coefficient +zero. + +```text +r_t += a r_s +r_t -= b i_s +i_t += b r_s +i_t += a i_s +``` + +The source field is unchanged. Thus the complete block has the stated +Gaussian ADD matrix. This argument does not apply to a same-field +complex scale. Such a scale needs its own invertible real word. + +Let `T` be the common complex frame on all fields in one block. +A complex matrix on the field index commutes with `T` on the spatial +index. Thus a complete real word for `R(M)` can be used between two +common-frame boundaries. This holds at every spatial width and for +every complex input. + +An individual real instruction need not commute with `T`. The word +must keep all instructions of the block contiguous. No native child, +map, or frame change can occur inside the block. Only its two +boundaries have the stated complex frame. + +The cost is the sum of the real instructions. For the Gaussian ADD, +it is twice the real ADD cost of `a` plus twice the real ADD cost of +`b`. Zero terms have zero cost. A prefix bound inside the block +refers to its physical input components. It is not a claim that +each prefix has the common complex frame. + +## The chronological inverse-adjoint + +For a real ADD `t += c s`, the inverse-transpose instruction is +`s -= c t`. For a nonzero real scale `t *= c`, it is `t /= c`. +Apply these rules in the original chronological order. + +For the complete Gaussian ADD above, the four resulting instructions +give `s -= conjugate(a+ib)t`. Therefore the real inverse-transpose +is the complex inverse-adjoint at the block boundaries. + +For a complete unitary code `C`, the same rule gives `C^{-*}=C`. +The new real word need not be equal to the old real word. Its +complete matrix is equal. The field list and the component labels +must both be changed if the caller renames fields. + +Each native frame change is unitary. Its inverse-adjoint is the +same exact operator, including its scalar phase. Hence its recipe +and its chronological position stay the same in the dual word. + +## The clean local map + +Let `P` be the selected-coordinate projection and let `R=I-P`. +Let `S` exchange the two banks on the selected coordinates only. +Set `D=I-2P`. If the native ordinary response is `RC`, the source +code is `C`, and the selected rotations are `(x,y) -> (-y,x)`, +then the complete content map is + +```text +F_C = S N_C, + +N_C = [ C 0 ] + [ RC D ]. +``` + +Equivalently, + +```text +X' = R C x - P y, +Y' = C x + R y. +``` + +This formula retains every arbitrary selected input in `-P y`. +It uses no zero field. + +When `C` is unitary, + +```text +N_C^-1 = [ C* 0 ] + [ -R D ], + +N_C^{-*} = [ C -R ] + [ 0 D ]. +``` + +Both formulas follow by block multiplication, using `D R=R` +and `D^2=I`. No commutation of `C` with `P` or `R` is used. +The selected-bank conjugate of the inverse-adjoint is + +```text +B_C = S F_C^{-*} S = N_C^{-*} S. +``` + +If `x=(a,u)` and `y=(z,v)` in selected and ordinary coordinates, +put `w=C(z,u)`. Then + +```text +X'_P=w_P, X'_R=w_R-v, +Y'_P=-a, Y'_R=v. +``` + +This is the map that the full native replay must check. The forward +and backward maps act as the identity on the other 416 complex +fields. + +The physical boundary adds the stated source line, FULL, and ordinary +hole frames. The review must bind those frames and all endpoint +adapters separately. These equations do not admit a routed caller, +recursive child host, or terminal decoder by themselves. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/FREEZE.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/FREEZE.json new file mode 100644 index 0000000000..702541100d --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/FREEZE.json @@ -0,0 +1,19 @@ +{ + "files": { + "BLOCK-DERIVATION.md": "453c79e549e8510cfa8156510dae279561711274b0e9764db0639ca98302b6d3", + "REPRODUCTION.json": "32c2738460c55fd2d44b104473a19997e05ff1b3f0794b4905f3e269ad5c9e77", + "REVIEW.md": "5dd730d448a0bd5ac9790a9f5d3c1571366dcfa051a26461a10238849a6102d7", + "check.py": "5c1a1eaa1ac9140a5edb122fb6f02d654a7d1b7eec8f2d0a7eb31fb86245c61f", + "normal-final/INPUTS.json": "2462a323f974b2417108a47aebc93974a8f2c94511252d67e47cb0debf0f6c11", + "normal-final/REVIEW.json": "67fff6260e4ba02fc12322b31e3325de98f25ac52d35d29a6f53806677bca3bd", + "optimized-final/INPUTS.json": "2462a323f974b2417108a47aebc93974a8f2c94511252d67e47cb0debf0f6c11", + "optimized-final/REVIEW.json": "67fff6260e4ba02fc12322b31e3325de98f25ac52d35d29a6f53806677bca3bd" + }, + "normal_optimized_bytes_equal": true, + "payload_decompressed_sha256": "472935ba574b78c6ec1fd6f02fc1c0c29d37b53f73ec55b8583904bd5d5af245", + "producer_freeze_sha256": "95fa9e61ddf860f3305fff398996077b6ecc164c011d37b60f6db0e459719fc5", + "publication": "No PR, commit, push or publication. Before a future PR description read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md.", + "schema": "independent-unitary-24-clean-native-review-freeze-v1", + "scope": "Eight complete local physical words on640 arbitrary complex fields. Every real component block closes before any native or map event. No routed caller, recursive hosting, rounding bound or complete supplier cost is claimed.", + "status": "PASS_INDEPENDENT_NATIVE_REVIEW" +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/REPRODUCTION.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..ddcb839c7b --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/REPRODUCTION.json @@ -0,0 +1,19 @@ +{ + "all_eight_producer_invoices_and_stated_local_norms_match": true, + "checked_local_links": [ + "new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/FREEZE.json", + "new-native-recipes-20261017/unitary-clean-24-review-20261020/normal-final/INPUTS.json", + "new-native-recipes-20261017/unitary-clean-24-review-20261020/normal-final/REVIEW.json", + "new-native-recipes-20261017/unitary-clean-24-review-20261020/check.py", + "new-native-recipes-20261017/unitary-clean-24-review-20261020/BLOCK-DERIVATION.md", + "independent-review-20261017/unitary-footprint-review-20261020/REVIEW.md" + ], + "checker_sha256": "5c1a1eaa1ac9140a5edb122fb6f02d654a7d1b7eec8f2d0a7eb31fb86245c61f", + "normal_optimized_byte_equal": { + "INPUTS.json": "2462a323f974b2417108a47aebc93974a8f2c94511252d67e47cb0debf0f6c11", + "REVIEW.json": "67fff6260e4ba02fc12322b31e3325de98f25ac52d35d29a6f53806677bca3bd" + }, + "publication": "No PR, commit, push or publication.", + "status": "PASS_REPRODUCTION_AND_FINAL_INPUT_AUDIT", + "unchanged_input_files": 58 +} diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/REVIEW.md b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/REVIEW.md new file mode 100644 index 0000000000..5fb382e291 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/REVIEW.md @@ -0,0 +1,185 @@ +# Independent review of the clean 24-coordinate native interface + +The eight frozen local words pass. The review checks both providers, +both forward entry types, the inverse-adjoint, and the selected-bank +conjugate. Each word has the stated map on all 640 independent complex +input fields. The other 416 complex fields remain unchanged. No +material error was found in the frozen packet. + +The [producer freeze](../../new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/FREEZE.json) is +`95fa9e61ddf860f3305fff398996077b6ecc164c011d37b60f6db0e459719fc5`. +The decompressed native payload is +`472935ba574b78c6ec1fd6f02fc1c0c29d37b53f73ec55b8583904bd5d5af245`. +The exact inputs and their hashes are in [INPUTS.json](normal-final/INPUTS.json). +The results are in [REVIEW.json](normal-final/REVIEW.json). + +## Scope and method + +The [checker](check.py) imports only the pinned arithmetic helper from +an earlier independent review and the pinned independent spatial +interpreter. It does not import the producer's native emitter, +Gaussian helper, Clifford compiler, or scalar checker. + +The main replay is a reverse propagation of 1,280 real input columns. +The checker expands the literal component instructions, including +the complete source-code block. A separate forward row trace checks +the same endpoint and measures the bounds at complete block ends. +Both real and imaginary input components are independent. + +The [block derivation](BLOCK-DERIVATION.md) proves why the real +component words are valid at a common complex frame. An individual +component instruction need not preserve that frame. Each complete +Gaussian ADD and the complete source code are contiguous blocks. +The checker proves their real matrices, checks their fields at the +two block boundaries, and excludes native or map instructions inside +the block. + +The code matrix and the separate paid code words have the +[independent code review](../../independent-review-20261017/unitary-footprint-review-20261020/REVIEW.md) +with freeze +`c537f75e6b76397e8fa390cd03a01e8021b7e0e55ff6c8932c3cc439613d0a61`. +That review supplies the actual 24-coordinate centre recovery, +unitarity, ordinary-row identities, and mode support. This review +checks their use in the complete native word. It also checks both +unitary orders again through the real matrix of C. + +## Complete local maps + +Let P be the actual 24-coordinate projection and let R=I-P. +For the forward word, put `w=Cx`. The exact content map is + +```text +X'_P=-z, X'_R=w_R, +Y'_P=w_P, Y'_R=v+w_R. +``` + +The I-entry contract has `X=Qx`, `Y_P=z`, and `Y_R=v`. +The Q-entry contract has `X=Qx`, `Y_P=Q_P z`, and `Y_R=v`. +All X outputs and all selected Y outputs have FULL. The ordinary +Y outputs have the stated `F9 q_p` frames. + +For the selected conjugate, write `x=(a,u)` and `y=(z,v)`. +Put `w=C(z,u)`. Its content map is + +```text +X'_P=w_P, X'_R=w_R-v, +Y'_P=-a, Y'_R=v. +``` + +The arbitrary selected baseline is retained with its sign. The +construction uses no zero field. The checker also checks the +unpermuted inverse-adjoint and both inverse orders of every content +map. + +The dual uses the chronological real inverse-transpose of each +complete block. This gives the complex inverse-adjoint. It conjugates +each Gaussian coefficient and preserves the complete C block +boundary. Unitarity gives `C^{-*}=C`; no commutation of C with P or R +is used. + +The selected-bank conjugation changes every native target, +component index, and input-adapter target. Both selected entry +fields have the same Q phase and both selected exit fields have +FULL. The checker verifies these exact phase records. There is no +runtime boundary swap. + +## Native paths, phases, and fields + +For each provider, the checker reconstructs the deletion of 380 +events, including 192 H1 calls. It proves that no retained event +reads or writes a removed selected target. It binds all 552 retained +transfer slots to their original event indices and actual mode +coordinates. There are 328 nonzero Gaussian transfers. + +Every retained native recipe and ordered frame record is byte-equal +to the accepted source. Every source input adapter and ordinary +output adapter is bound to its actual field. The 88 ordinary output +adapters are an exact subset of the accepted table. + +The sixteen old selected H8 kernels per provider are exact copies +of the independently reviewed line-entry kernels. The eight new +distinct H8 kernels pass all 512 spatial input columns in a separate +Gaussian-integer interpreter. This checks 4,096 distinct columns, +including their full global phase. The results bind both providers. +The direct H9 identity-wrapper kernel is inherited by exact equality. + +The inverse-adjoint preserves each exact unitary native operator +and its phase. Its field binding is checked again after the selected +permutation. The native identities lift by tensor products. The +scalar blocks act on the field index and commute with the common +complex spatial frame. No one-bit polynomial substitution is used. + +All top-level instructions stay in the 224 data fields. The other +416 arbitrary complex fields are the identity in the full replay. +There is no private field, CLEAR operation, or extra field. +Recursive child hosting is a separate obligation. + +## Exact local invoice and bounds + +All eight words cost 16,020 real scalar primitives: + +| Part | Real scalar primitives | +| --- | ---: | +| Retained and retuned core | 7,392 | +| Complete source code | 8,052 | +| 24 signed rotations | 576 | +| Total | 16,020 | + +The real component word has 4,154 instructions. Its tariff is +computed from those instructions. It does not assume a complex +multiply primitive. + +| Entry or word | Native profile | Children | Rank mass | Input views | Output views | Native side maps, upper bound | +| --- | --- | ---: | ---: | ---: | ---: | ---: | +| I forward | 1328 H1 + 64 H2 + 48 H3 + 24 H9 | 1464 | 1816 | 112 | 88 | 2880 | +| Q forward or either dual | 1328 H1 + 64 H2 + 48 H3 + 24 H8 | 1464 | 1792 | 136 | 88 | 2928 | + +At complete block ends, the content component row one-norm is at +most 10 for the forward words and 5 for the dual words. The binary +height at these ends is at most 2. Within one complete block, the +largest component row one-norm is 16 for the forward words and 7 +for the dual words. The respective local binary heights are 3 and +4. These internal bounds use that block's physical input components. + +In particular, the dual's literal code word has height 4. The +height 2 bound for the separately emitted C* word cannot be used +for this different word. None of these bounds includes a recursive +child's internal arithmetic or rounding error. + +## Reproduction and limits + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/check.py --source-freeze 95fa9e61ddf860f3305fff398996077b6ecc164c011d37b60f6db0e459719fc5 --payload-sha256 472935ba574b78c6ec1fd6f02fc1c0c29d37b53f73ec55b8583904bd5d5af245 --out +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/check.py --source-freeze 95fa9e61ddf860f3305fff398996077b6ecc164c011d37b60f6db0e459719fc5 --payload-sha256 472935ba574b78c6ec1fd6f02fc1c0c29d37b53f73ec55b8583904bd5d5af245 --out +``` + +Expected output: + +```text +PASS_INDEPENDENT_UNITARY_24_CLEAN_NATIVE +``` + +The negative controls reject a wrong Gaussian component sign, +reversed scalar chronology, and a wrong native global phase. +Normal and optimized review receipts and input manifests must +match byte for byte. The separate reproduction record reports +that comparison and the final source-byte check. + +This review establishes the local native interfaces and the stated +local invoice. It does not establish routed composition, a terminal +decoder, recursive helper hosting, finite-precision correctness, +map implementation cost, or a complete supplier improvement. In +particular, the 24 stored coordinates do not make a later +hole-to-data conversion free. + +The producer lane supplied the native word. The matrix review lane +checked the code and its footprint. The native review lane supplied +the complete component-block requirement and this independent +physical replay. The source providers and earlier phase reviews +supply the unchanged native geometry. AI assistance was used. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/check.py b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/check.py new file mode 100644 index 0000000000..4897c1abde --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/check.py @@ -0,0 +1,499 @@ +#!/usr/bin/env python3 +"""Check complete complex blocks and their native field types.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import importlib.util +import json + +HERE = Path(__file__).resolve().parent +HELPER = HERE.parent/'row-capture-native-review-20261020/check.py' +PIN = '5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84' +if sha256(HELPER.read_bytes()).hexdigest() != PIN: + raise ValueError('Independent helper pin') +spec = importlib.util.spec_from_file_location('independent_real_arithmetic', HELPER) +q = importlib.util.module_from_spec(spec) +spec.loader.exec_module(q) +q.read(HELPER, PIN) +need = q.need +SOURCE = q.RAW/'unitary-clean-24-20261020' +CODE = q.RAW/'metric-completion-20261020' + + +def realify(matrix, size): + result = [{} for _ in range(2*size)] + need(len(matrix) == size, 'Square complex matrix') + for p, row in enumerate(matrix): + for raw_j, (raw_a, raw_b) in row.items(): + j, a, b = int(raw_j), F(raw_a), F(raw_b) + need(0 <= j < size, 'Complex matrix column') + for t, s, value in ((2*p, 2*j, a), (2*p, 2*j+1, -b), + (2*p+1, 2*j, b), (2*p+1, 2*j+1, a)): + if value: + result[t][s] = value + return result + + +def component_real(gate): + op, target, source, value = gate + return [[op, 2*target+c, None if source is None else 2*source+c, value] + for c in (0, 1)] + + +def component_dual(gates, permutation): + def p(k): + return 2*permutation[k//2]+k % 2 + result = [] + for op, target, source, value in gates: + value = F(value) + if op == 'add': + result.append(['add', p(source), p(target), str(-value)]) + else: + need(op == 'scale' and source is None and value, 'Invertible component scale') + result.append(['scale', p(target), None, str(1/value)]) + return result + + +def flatten(events): + result = [] + for event in events: + if event[0] == 'native': + continue + if event[0] == 'scalar': + result += component_real(event[1]) + elif event[0] == 'gaussian_add': + result += event[5] + else: + need(event[0] == 'component_code', 'Complete event grammar') + result += event[2] + return result + + +def endpoint(code, selected): + c = realify(code, 112) + result = q.unit(1280) + for p in range(112): + for b in (0, 1): + x, y = 2*p+b, 224+2*p+b + result[x] = {y: F(-1)} if p in selected else dict(c[x]) + result[y] = dict(c[x]) + if p not in selected: + q.add(result[y], {y: F(1)}) + return result + + +def inverse_endpoint(code, selected): + c = realify(code, 112) + z = [{224+j if j//2 in selected else j: F(1)} for j in range(224)] + x = q.mul(q.transpose(c, 224), z) + result = q.unit(1280) + result[:224] = x + for p in range(112): + for b in (0, 1): + j = 2*p+b + result[224+j] = {j: F(-1)} if p in selected else {224+j: F(1), j: F(-1)} + return result + + +def conjugate(matrix, permutation): + cp = [2*permutation[j//2]+j % 2 for j in range(1280)] + return [{cp[j]: value for j, value in matrix[cp[i]].items()} for i in range(1280)] + + +def swap_formula(code, selected): + c = realify(code, 112) + source = [224+j if j//2 in selected else j for j in range(224)] + result = q.unit(1280) + for p in range(112): + for b in (0, 1): + j = 2*p+b + result[j] = {source[k]: value for k, value in c[j].items()} + if p in selected: + result[224+j] = {j: F(-1)} + else: + q.add(result[j], {224+j: F(-1)}) + return result + + +def local_block(fields, gates, expected): + need(len(fields) == len(set(fields)), 'Distinct fields in a complete block') + index = {p: i for i, p in enumerate(fields)} + local = [] + for op, t, s, value in gates: + need(t//2 in index and (s is None or s//2 in index), 'No field outside its block') + need(op in ('add', 'scale') and (op != 'add' or t != s), 'Component opcode') + local.append([op, 2*index[t//2]+t % 2, + None if s is None else 2*index[s//2]+s % 2, value]) + need(q.reverse(local, 2*len(fields)) == q.transpose(expected, 2*len(fields)), + 'Complete block real matrix, including complex linearity') + rows, bound = q.prefix(local, 2*len(fields)) + need(rows == expected, 'Separate block forward replay') + return bound + + +def trace(word, selected, entry, expected, block_cache): + current = list(word['start']) + profile, used = Counter(), set() + maximum_local, maximum_height = F(1), 0 + for event in word['events']: + kind = event[0] + if kind == 'native': + _, field, before, after, rank, key = event + need(0 <= field < 224 and current[field] == before, 'Actual native input field and frame') + need(word['native_recipes'][key]['rank'] == rank, 'Actual native child rank') + current[field] = after + profile[rank] += 1 + used.add(key) + continue + if kind == 'scalar': + _, gate, frame = event + op, target, origin, _ = gate + need(0 <= target < 224 and current[target] == frame, 'Complex-real scalar target') + if op == 'add': + need(0 <= origin < 224 and origin != target and current[origin] == frame, + 'Complex-real scalar source') + else: + need(op == 'scale' and origin is None, 'Complex-real scale grammar') + continue + if kind == 'gaussian_add': + _, target, origin, value, frame, gates = event + need(target != origin, 'Gaussian ADD needs distinct fields') + fields = [target, origin] + a, b = map(F, value) + need(a or b, 'A nonzero Gaussian transfer') + matrix = [{0: F(1)}, {1: F(1)}, {2: F(1)}, {3: F(1)}] + q.add(matrix[0], {2: a, 3: -b}) + q.add(matrix[1], {2: b, 3: a}) + matrix = [{j: v for j, v in row.items() if v} for row in matrix] + else: + need(kind == 'component_code', 'Only complete component blocks are admitted') + _, fields, gates, matrix_raw, frame = event + matrix = realify(matrix_raw, len(fields)) + need(all(0 <= field < 224 and current[field] == frame for field in fields), + 'One common complex frame at both block boundaries') + key = json.dumps([fields, gates, matrix], sort_keys=True, default=str) + if key not in block_cache: + block_cache[key] = local_block(fields, gates, matrix) + bound = block_cache[key] + maximum_local = max(maximum_local, F(bound['row_one_norm'])) + maximum_height = max(maximum_height, bound['binary_height']) + need(current == word['final'] and len(current) == 640, 'All640 final frames') + need(used == set(word['native_recipes']), 'Every stored recipe has an occurrence') + rank = 9 if entry == 'I' else 8 + need(profile == {1: 1328, 2: 64, 3: 48, rank: 24}, 'Complete native profile') + need(current[224:] == word['start'][224:], 'Unchanged helper frames') + gates = flatten(word['events']) + columns = q.reverse(gates, 1280) + need(columns == q.transpose(expected, 1280), 'All1280 independent reverse input columns') + need(all(t < 448 and (s is None or s < 448) for _, t, s, _ in gates), + 'No component instruction touches an arbitrary helper') + costs = {} + cursor = 0 + for name, (start, end) in sorted(word['stage_ranges'].items(), key=lambda item: item[1][0]): + need(start == cursor and start <= end, 'Complete ordered stage cuts') + cursor = end + cost = q.price(flatten(word['events'][start:end])) + need(cost % 2 == 0, 'Integral real-component cost') + costs[name] = cost//2 + need(cursor == len(word['events']), 'Stage ledger covers the complete word') + need(costs['source_unitary_code'] == 8052 and costs['signed_selected_exchanges'] == 576, + 'Paid code and all24 rotations') + total = q.price(gates)//2 + need(total == sum(costs.values()), 'Complete scalar invoice') + need(costs == {'retained_retuned_core': 7392, 'selected_progress': 0, + 'source_unitary_code': 8052, 'signed_selected_exchanges': 576} + and total == 16020, 'All exact stage invoices') + state = q.unit(1280) + endpoint_norm, endpoint_height = F(1), 0 + for event in word['events']: + changed = set() + for op, target, origin, value in flatten([event]): + value = F(value) + if op == 'scale': + state[target] = {j: value*x for j, x in state[target].items()} + else: + q.add(state[target], state[origin], value) + changed.add(target) + for target in changed: + endpoint_norm = max(endpoint_norm, sum(map(abs, state[target].values()), F(0))) + for value in state[target].values(): + denominator = value.denominator + need(denominator & (denominator-1) == 0, 'Dyadic macro endpoint') + endpoint_height = max(endpoint_height, denominator.bit_length()-1) + need(state == expected and state[448:] == q.unit(1280)[448:], + 'Separate forward trace and all416 arbitrary complex helper outputs') + return { + 'real_input_columns': 1280, 'complex_input_columns': 640, + 'unchanged_arbitrary_complex_fields': 416, + 'native_profile': dict(sorted(profile.items())), + 'native_children': sum(profile.values()), + 'native_mass': sum(k*v for k, v in profile.items()), + 'native_side_maps_upper_bound': 2*(sum(profile.values())-(24 if entry == 'I' else 0)), + 'input_views': len(word['input_views']), 'output_views': len(word['output_views']), + 'scalar_stage_prices': costs, 'real_scalar_primitives': total, + 'component_instructions': len(gates), 'new_fields': 0, 'private_fields': 0, + 'odd_divisions': 0, 'maximum_local_block_component_row_norm': str(maximum_local), + 'maximum_local_block_binary_height': maximum_height, + 'maximum_macro_endpoint_content_component_norm': str(endpoint_norm), + 'maximum_macro_endpoint_content_binary_height': endpoint_height, + 'bound_scope': 'Each complete block has a complex frame. Its internal component bound uses its physical input components.', + } + + +def forward_source(word, old, model, formation, code, cyclic, selected, entry): + need(word['frames'] == old['frames'], 'Unchanged literal frame table') + selected_fields = {112+p for p in selected} + kept_indices, removed = q.select_raw(old, selected_fields) + need(word['retained_original_event_indices'] == kept_indices, 'Exact removal index ledger') + need(len(removed) == 380 and + Counter(old['events'][i][4] for i in removed if old['events'][i][0] == 'native') == {1: 192}, + 'Exact380-event and192-H1 removal census') + need(all(not (e[0] == 'native' and e[1] in selected_fields) and + not (e[0] == 'scalar' and (e[1][1] in selected_fields or + e[1][0] == 'add' and e[1][2] in selected_fields)) + for e in [old['events'][i] for i in kept_indices]), + 'No retained access to a removed selected target') + records = {r['event']: r for r in old['transfer_records']} + need(len(records) == len(old['transfer_records']), 'Unique original transfer sites') + params = {r['id']: r for r in cyclic['parameters']} + mode = code['mode_code'] + start, end = word['stage_ranges']['retained_retuned_core'] + need(start == 0, 'The core is first') + core = word['events'][start:end] + cursor, retunings = 0, [] + for i in kept_indices: + old_event = old['events'][i] + if i not in records: + need(core[cursor] == old_event, 'Every nontransfer core event is byte-equal') + cursor += 1 + continue + record = records[i] + if record['part'] == 'large48': + par = params[record['parameter']] + ports = cyclic['cyclic_carriers'][par['vertex']] + p, j = ports[par['row']], ports[par['column']] + old_coefficient = F(model['mode_response'][p][str(j)]) + else: + need(record['part'] == 'small64', 'Transfer source part') + p, j = record['target_port'], record['source_port'] + old_coefficient = F(model['response'][p][str(j)]) + op, target, origin, old_value = old_event[1] + need(op == 'add' and target == 112+p and origin == j and p not in selected, + 'Actual ordinary transfer fields') + need(F(record['coefficient']) == F(old_value), 'Accepted scalar transfer coefficient') + a, b = map(F, mode[p].get(str(j), ['0', '0'])) + ratio = F(old_value)/old_coefficient + a, b = ratio*a, ratio*b + retunings.append({'original_event': i, 'mode_target': p, 'mode_source': j, + 'coefficient': [str(a), str(b)]}) + if not (a or b): + continue + expected = ['gaussian_add', target, origin, [str(a), str(b)], old_event[2]] + need(core[cursor][:5] == expected, 'Actual retuned transfer and common frame') + cursor += 1 + need(cursor == len(core) and word['transfer_retunings'] == retunings, + 'Complete retuned transfer census') + input_views = [{**v, 'field': v['port']} for v in formation['input_views']] + source_views = {v['port']: v for v in formation['input_views']} + before = list(old['start']) + progress = [] + for p in sorted(selected): + if entry == 'I': + key, old_frame, rank = 'direct-full', 0, 9 + need(word['native_recipes'][key] == formation['native_recipes']['capture-full'], + 'Exact accepted direct F9 recipe') + else: + key, old_frame, rank = 'unitary-line:'+str(p), old['start'][p], 8 + before[112+p] = old_frame + input_views.append({**source_views[p], 'field': 112+p, + 'role': 'selected_target', 'source_entry_port': p}) + progress.append(['native', 112+p, old_frame, 1, rank, key]) + after = list(old['final']) + for p in selected: + after[112+p] = 1 + need(word['start'] == before and word['final'] == after, 'All actual endpoint frame declarations') + need(word['input_views'] == sorted(input_views, key=lambda v: v['field']), + 'Every input adapter is bound to its actual complex field') + need(word['output_views'] == [v for v in formation['output_views'] if v['port'] not in selected], + 'Every ordinary inverse target adapter is inherited') + code_block = [['component_code', list(range(112)), code['component_words']['code'], code['code'], 1]] + rotations = [] + for p in sorted(selected): + rotations += [['scalar', ['add', 112+p, p, '1'], 1], + ['scalar', ['add', p, 112+p, '-1'], 1], + ['scalar', ['add', 112+p, p, '1'], 1]] + need(word['events'] == core+progress+code_block+rotations, 'Complete forward chronology') + stages = [('retained_retuned_core', core), ('selected_progress', progress), + ('source_unitary_code', code_block), ('signed_selected_exchanges', rotations)] + expected_ranges, at = {}, 0 + for name, events in stages: + expected_ranges[name] = [at, at+len(events)] + at += len(events) + need(word['stage_ranges'] == expected_ranges, 'Exact complete stage boundaries') + for event in core: + if event[0] == 'native': + need(word['native_recipes'][event[5]] == old['native_recipes'][event[5]], + 'Byte-equal retained exact-phase recipe') + return {'removed_events': len(removed), 'removed_H1_children': 192, + 'retained_transfer_slots': len(retunings), + 'nonzero_gaussian_transfers': sum(e[0] == 'gaussian_add' for e in core)} + + +def dual_source(word, original, permutation): + need(word['stage_ranges'] == original['stage_ranges'], 'Dual preserves macro chronology') + need(word['wire_permutation'] == {str(p): t for p, t in enumerate(permutation) if p != t}, + 'Exact field permutation') + for key in ('frames', 'start', 'final', 'native_recipes', 'output_views'): + need(word[key] == original[key], 'Exact dual physical record: '+key) + need(all(original[key][p] == original[key][permutation[p]] + for key in ('start', 'final') for p in range(640)), 'Selected endpoint symmetry') + expected_views = deepcopy(original['input_views']) + for view in expected_views: + view['field'] = permutation[view['field']] + need(word['input_views'] == sorted(expected_views, key=lambda v: v['field']), + 'Every dual input adapter is explicitly rebound') + original_views = {v['field']: v for v in original['input_views']} + for view in word['input_views']: + need(all(view[k] == original_views[view['field']][k] + for k in ('port', 'frame', 'rank', 'left', 'right')), + 'Same-port Q/Q phase identity at each input field') + need(len(word['events']) == len(original['events']), 'No hidden runtime exchanges') + for event, old in zip(word['events'], original['events']): + kind = old[0] + if kind == 'native': + expected = deepcopy(old) + expected[1] = permutation[old[1]] + elif kind == 'scalar': + op, target, source, value = old[1] + value = F(value) + gate = (['add', permutation[source], permutation[target], str(-value)] if op == 'add' + else ['scale', permutation[target], None, str(1/value)]) + expected = ['scalar', gate, old[2]] + elif kind == 'gaussian_add': + _, target, source, value, frame, components = old + a, b = map(F, value) + expected = ['gaussian_add', permutation[source], permutation[target], + [str(-a), str(b)], frame, component_dual(components, permutation)] + else: + need(kind == 'component_code', 'Dual block grammar') + _, fields, components, matrix, frame = old + expected = ['component_code', [permutation[p] for p in fields], + component_dual(components, permutation), matrix, frame] + need(event == expected, 'Literal chronological real inverse-transpose and field rebind') + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--source-freeze', required=True) + parser.add_argument('--payload-sha256', required=True) + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + q.frozen(SOURCE, 'FREEZE.json', args.source_freeze) + q.frozen(CODE, 'TWENTY-FOUR-FREEZE.json', + '3fda436c0390fb8ef2ee72b4d9fe6ccbfc0ea994208f4d962bb9f43960af7a82') + q.frozen(q.LANES/'independent-review-20261017/unitary-footprint-review-20261020', 'FREEZE.json', + 'c537f75e6b76397e8fa390cd03a01e8021b7e0e55ff6c8932c3cc439613d0a61') + q.frozen(HERE.parent/'row-capture-native-review-20261020', 'FREEZE.json', + '488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532') + q.frozen(HERE.parent/'line-entry-reuse-review-20261020', 'FREEZE.json', + 'cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c') + phase = q.inherit() + payload = json.loads(q.read(SOURCE/'run-v2-normal/UNITARY-CLEAN.json.gz', args.payload_sha256, True)) + code = json.loads(q.read(CODE/'twenty-four-v2-normal/UNITARY-24.json.gz', + '9be7deb70acfc20d98408c84d59a24dbd6e2eddaea408958ec64b6003eb75f8c', True)) + raw = json.loads(q.read(q.RAW/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz', + 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True)) + formation = json.loads(q.read(q.NATIVE/'direct-normal/DIRECT-FULL-CAPTURE.json.gz', + 'fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c', True)) + reuse = json.loads(q.read(q.NATIVE/'reuse-normal/LINE-ENTRY-REUSE.json.gz', + 'efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110', True)) + cyclic = json.loads(q.read(q.LANES/'independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json', + '3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585')) + selected = set(code['selected_full_ports']) + need(len(selected) == 24 and payload['selected_ports'] == sorted(selected), 'Actual24 selected ports') + need(payload['ports'] == raw['model']['ports'] and payload['code'] == code['code'] and + payload['inverse_and_adjoint_code'] == code['inverse_and_adjoint'], 'Exact matrix and port sources') + c = realify(code['code'], 112) + need(q.mul(c, q.transpose(c, 224)) == q.unit(224) and + q.mul(q.transpose(c, 224), c) == q.unit(224), 'Both real unitary orders') + f, fi = endpoint(code['code'], selected), inverse_endpoint(code['code'], selected) + identity = list(range(640)) + swap = [112+p if p in selected else p-112 if p-112 in selected else p for p in range(640)] + d, di = q.transpose(fi, 1280), q.transpose(f, 1280) + b, bi = conjugate(d, swap), conjugate(di, swap) + need(b == swap_formula(code['code'], selected), 'Separate unitary Bswap block formula') + maps = {'forward_I': f, 'forward_Q': f, 'inverse_adjoint_Q': d, 'selected_conjugate_Q': b} + inverses = {'forward_I': fi, 'forward_Q': fi, 'inverse_adjoint_Q': di, 'selected_conjugate_Q': bi} + for name in maps: + need(realify(payload['content_maps'][name], 224) == maps[name][:448], + 'Exact serialized content map: '+name) + need(realify(payload['inverse_content_maps'][name], 224) == inverses[name][:448], + 'Exact serialized inverse map: '+name) + need(q.mul(maps[name][:448], inverses[name][:448]) == q.unit(448) and + q.mul(inverses[name][:448], maps[name][:448]) == q.unit(448), 'Both complete inverse orders') + need(set(payload['providers']) == {'base', 'extra'}, 'Both actual providers') + reports, phase_reports, cache = {}, {}, {} + phase_seen = {} + for provider, words in payload['providers'].items(): + need(set(words) == set(maps), 'All four complete local variants') + reports[provider] = {} + for name, word in words.items(): + entry = 'I' if name == 'forward_I' else 'Q' + if name.startswith('forward'): + source_report = forward_source(word, raw['providers'][provider]['forward'], + raw['model'], formation['providers'][provider], + code, cyclic, selected, entry) + else: + dual_source(word, words['forward_Q'], identity if name == 'inverse_adjoint_Q' else swap) + source_report = {'chronological_inverse_adjoint': True, 'runtime_boundary_swaps': 0} + reports[provider][name] = {**trace(word, selected, entry, maps[name], cache), **source_report} + line_word = words['forward_Q'] + for p in sorted(selected): + before = line_word['start'][112+p] + record = line_word['native_recipes']['unitary-line:'+str(p)] + if p in q.P: + accepted = reuse['providers'][provider] + need(record == accepted['native_recipes']['capture-line:'+str(p)] and + line_word['frames'][before] == accepted['frames'][accepted['start'][112+p]], + 'Exact accepted line-to-FULL phase and ordered input basis') + phase_reports[provider+':'+str(p)] = {'inherited_review': 'cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c'} + continue + signature = json.dumps([line_word['frames'][before], record], sort_keys=True) + if signature not in phase_seen: + native = phase.recipe(record) + full = [('C', 1 << j, 1) for j in range(9)] + phase_seen[signature] = phase.compare(phase.canonical(line_word['frames'][before])+native, + full, 'Actual selected line '+str(p), 512) + phase_reports[provider+':'+str(p)] = phase_seen[signature] + # The controls use executed component instructions and exact physical phase. + gates = flatten(payload['providers']['base']['forward_Q']['events']) + first_complex = next(e for e in payload['providers']['base']['forward_Q']['events'] + if e[0] == 'gaussian_add' and F(e[3][1])) + bad_macro = deepcopy(first_complex[5]) + bad_macro[0][3] = str(-F(bad_macro[0][3])) + need(q.reverse(bad_macro, 1280) != q.reverse(first_complex[5], 1280), 'Wrong complex sign control') + need(q.reverse(list(reversed(gates)), 1280) != q.transpose(f, 1280), + 'Wrong chronological order control') + record = payload['providers']['base']['forward_Q']['native_recipes']['unitary-line:'+str(min(selected))] + bad = phase.recipe(record)+phase.compile_circuit([['phase', 1]]) + need(phase.run(bad, 0) != phase.run(phase.recipe(record), 0), 'Wrong global phase control') + result = { + 'status': 'PASS_INDEPENDENT_UNITARY_24_CLEAN_NATIVE', + 'producer_freeze_sha256': args.source_freeze, 'payload_decompressed_sha256': args.payload_sha256, + 'words': reports, 'selected_line_full_phase_checks': phase_reports, + 'distinct_selected_line_recipes_checked': len(phase_seen), + 'complex_block_cache_entries': len(cache), 'both_content_inverse_orders': True, + 'negative_controls': ['wrong Gaussian component sign', 'wrong scalar chronology', 'wrong native global phase'], + 'scope': 'Eight complete local physical words on640 arbitrary complex fields. Every real component block closes before any native or map event. No routed caller, recursive hosting, rounding bound or complete supplier cost is claimed.', + } + args.out.mkdir(parents=True, exist_ok=False) + for name, obj in [('REVIEW.json', result), ('INPUTS.json', q.INPUTS)]: + (args.out/name).write_text(json.dumps(obj, sort_keys=True, indent=2)+'\n') + print(result['status'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/normal-final/INPUTS.json b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/normal-final/INPUTS.json new file mode 100644 index 0000000000..684d32202e --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/normal-final/INPUTS.json @@ -0,0 +1,181 @@ +{ + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": { + "sha256": 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723, + "distinct_selected_line_recipes_checked": 8, + "negative_controls": [ + "wrong Gaussian component sign", + "wrong scalar chronology", + "wrong native global phase" + ], + "payload_decompressed_sha256": "472935ba574b78c6ec1fd6f02fc1c0c29d37b53f73ec55b8583904bd5d5af245", + "producer_freeze_sha256": "95fa9e61ddf860f3305fff398996077b6ecc164c011d37b60f6db0e459719fc5", + "scope": "Eight complete local physical words on640 arbitrary complex fields. 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Put m=n-4 and k=n-2. Over the real +numbers, or over a characteristic-zero subfield, define + +```text +u=(1^k,m,0)^T, ell=(-1^k,1,0), +R=I+u ell, P=diag(I_k, swap), +E=P R. +``` + +Then R^2=I, E^-1=R P, and both E and E^-1 have zero diagonal. +The displacement E-P has rank 1. The displacement E-I has rank 2. +These facts follow directly from ell u=-2 and the displayed coordinate +formulas in `MODEL.md`. + +This family gives one centre per block relative to the simple map P. +It gives two displacement directions per block relative to identity. +The distinction is needed in a controller: P must still be implemented +or carried. + +## Classification of diagonal metrics + +Every diagonal real matrix D with E^T D E=D is a scalar multiple of + +```text +J=diag(1^k,-1/m,-1/m). +``` + +To prove this, write D=diag(d_0,...,d_(k-1),e,f). The last column of E +has its only nonzero entry, equal to 1, in row b. Its norm equation gives +e=f. The norm equation for column a_i is + +```text +sum_j d_j + m^2 f = 2 d_i. +``` + +Thus all d_i have the same value d. Since k=m+2, this equation reduces +to m(d+m f)=0. The field has characteristic zero and m is nonzero, so +f=e=-d/m. These are necessary equations. The identity in `MODEL.md` +proves that they are sufficient. + +Consequently, a nonsingular diagonal metric exists, but it is +indefinite. It has inertia (n-2,2) or (2,n-2), according to the sign +of its nonzero scale. No positive diagonal metric is possible. + +Over the dyadic ring Z[1/2], a diagonal metric whose entries are all +units exists if and only if m is a power of 2. Indeed, the units are +the signed powers of 2. If d and -d/m are units, their ratio m is a +unit. Conversely, if m is a power of 2, J and J^-1 are diagonal +matrices of dyadic units. + +Thus the permitted block sizes in this family are + +```text +n=4+2^h, h>=0. +``` + +The actual native geometry supplies sizes 6 and 8. The larger abstract +family does not assert that the repository has a native geometry for +every listed size. + +## A unit centre norm + +Let K=J^-1. Then + +```text +K ell^T=-u, ell K ell^T=2, +R=I-K ell^T ell. +``` + +The centre has signed norm 2 for every n. This removes the odd norm +factor n-1 that occurs with the unsigned all-ones centre. In the actual +physical pair basis, the large-block centre norm is 4 and the small-block +norm is 2. Both are dyadic units. This permits a metric-compatible +one-centre completion in principle. A complete code still needs its +physical basis, native access, and paid implementation. + +## Minimum displacement in the reciprocal zero-diagonal grammar + +Let A be an invertible n-by-n matrix over a characteristic-zero field, +where n>=3. Suppose that both A and A^-1 have zero diagonal. Then + +```text +rank(A-I) >= 2. +``` + +Rank 0 is impossible. If rank(A-I)=1, write A=I+v w^T. +Zero diagonal gives v_i w_i=-1 for every i, and hence w^T v=-n. +The rank-one inverse formula is + +```text +A^-1 = I + v w^T/(n-1). +``` + +Every diagonal entry of A^-1 is then (n-2)/(n-1), which is nonzero. +This contradicts the hypothesis. + +The family E attains the lower bound 2 in every block. Therefore the +actual rank 32 is minimum among direct sums of sixteen independent +blocks of sizes 6 and 8 for which both the response and its reciprocal +must have zero diagonal. This is not a rank 32 lower bound for arbitrary +112-by112 responses, coupled blocks, a changed native grammar, or a +different baseline P. + +The assumptions have concrete boundary cases. At n=2, a coordinate +swap has zero diagonal in both directions and rank(A-I)=1. At n=3, +this family becomes a coordinate 3-cycle and has a positive diagonal +metric. At n=4, every diagonal invariant metric in this family is +singular: it has zero ordinary weights and equal final two weights. +The diagonal-metric classification above is therefore stated for n>=5. + +## Checks and provenance + +The formal arguments above apply to all stated n. The companion checker +also verifies the exact matrices, ranks, metric equations, and the +dimension of the diagonal-metric solution space for n=5,...,24. It +checks the boundary cases and the rank-one inverse counterexample +directly. These finite checks support the proof; they do not replace +its quantified argument. + +The actual 112 matrices and native words remain pinned in the model +and native freezes. This theorem adds the metric classification and the +sharp blockwise displacement bound. It does not close the global +caller or terminal. + +The coordinating agent supplied the E=P R family and its candidate +metric. This lane supplied the classification, boundary cases, and +blockwise lower bound. AI assistance was used. + +No PR, push, commit, or publication is authorized. Before any future PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json new file mode 100644 index 0000000000..7126204dcc --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json @@ -0,0 +1,26 @@ +{ + "files": { + "MODEL.md": { + "sha256": "e2ecd052675336ffc78a53262d8b86be038535fc497a8732560acedea0b5c335" + }, + "check_model.py": { + "sha256": "9d7052a27139990fe9eb4e397b672d2ae7069de75636e3b068f172760cf173fb" + }, + "model-normal-v2/CHECKS.json": { + "sha256": "1cbfb5ccb96b3b2e4bd9b14bf5fc557dc11da14cde5577cb22853982554b0d05" + }, + "model-normal-v2/RESPONSE.json.gz": { + "decompressed_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "sha256": "cf29241b788142811a1e5c7051c96f143ce5ab866cb2c38028e5d933e9272194" + }, + "model-optimized/CHECKS.json": { + "sha256": "1cbfb5ccb96b3b2e4bd9b14bf5fc557dc11da14cde5577cb22853982554b0d05" + }, + "model-optimized/RESPONSE.json.gz": { + "decompressed_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "sha256": "cf29241b788142811a1e5c7051c96f143ce5ab866cb2c38028e5d933e9272194" + } + }, + "normal_optimized_bytes_equal": true, + "status": "FROZEN_MODEL" +} diff --git a/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL.md b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL.md new file mode 100644 index 0000000000..cd2fd125cc --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL.md @@ -0,0 +1,130 @@ +# A dyadic signed metric on the actual112 ports + +This packet gives a reciprocal response with a diagonal physical metric. +It uses eight6-mode blocks and eight8-mode blocks. The common-frame code +uses dyadic operations. It does not use an odd division. + +For n in {6,8}, put m=n-4 and use coordinates (a_0,...,a_(n-3),b,c). +Define + +```text +u = (1,...,1,m,0)^T, ell = (-1,...,-1,1,0), +R = I + u ell, P(a,b,c) = (a,c,b), +E = P R, +J = diag(1,...,1,-1/m,-1/m). +``` + +The product ell u is -2. Thus R^2=I and E^-1=R P. Also Ju=-ell^T +and ell J^-1 ell^T=2. Expansion gives R^T J R=J. The two last metric +entries agree, so P^T J P=J. Consequently + +```text +E^T J E = J, E^-T = J E J^-1. +``` + +Both E and E^-1 have zero diagonal. In full coordinates they are + +```text +E: a' = a - sum(a) + b, b' = c, + c' = -m sum(a) + (m+1)b; +E^-1: a' = a - sum(a) + c, b' = -m sum(a)+(m+1)c, + c' = b. +``` + +These formulas also show that E-P has rank1 and E-I has rank2 in +each block. In the latter case, the two nonzero factors are independent. +The exact112-column check gives ranks16 and32 for the full response. + +## Actual physical placement + +The source placement is the frozen signed-probe packet from the +new-core-transfer lane. In each large block, use the roles in this order: + +```text +centre, pair_difference_a, pair_difference_b, negative_difference, +contrast, negative. +``` + +Use the stored port order for each small8-clique. The final two modes +are b and c. No sign vector from an earlier response is used. + +Let H be the actual24 physical pair codes, with identity on the small64 +ports. The physical matrices are H^-1 E H, H^-1 P H, H^-1 R H, and +H^-1 J H. The notation E,P,R,J below refers to those physical matrices. +The b modes and c modes each use a complete matching of physical pairs. +The physical metric therefore remains diagonal. Its entries are + +```text +80 entries 1, 16 entries -1/2, 16 entries -1/4. +``` + +All pair blocks of H have H^T H=2I. This scale is constant on each +large component and commutes with the mode response. Therefore the +metric identity survives the physical change of coordinates. + +Both E and E^-1 have zero diagonal in physical coordinates. No response +entry joins the two modes of the same physical pair: those modes +belong to different large blocks. Each nonzero physical response entry +joins orthogonal actual port labels. The checker verifies these facts +from the complete112 matrices and the pinned labels. + +P is identity on80 physical fields and maps the other32 fields into +themselves. It is not a physical permutation. It has160 nonzero entries; +the large16-field part includes signed half entries. + +The physical reflection factor is R-I=U L, where U=H^-1 u and L=ell H +block by block. Its centre Gram matrix is + +```text +L J^-1 L^T = diag(4 I8, 2 I8). +``` + +The factor4 on the large centres comes from the physical pair code. +These entries are dyadic units. A later centre-code construction must +retain this normalization. + +## Complete common-frame scalar words + +The checker emits a paid pair code, the local reflection word, and the +inverse pair code. In each block the reflection word first subtracts +all a fields from b, adds that b value to each a field, negates b, and +adds all updated a fields to b. A paid signed swap then gives E. + +Every word is replayed on all640 arbitrary input fields. It leaves all +528 fields outside the112-field code unchanged. The invoice is: + +| Word | Real scalar primitives | +| --- | ---: | +| E, E^-1, E^-T | 3308 each | +| R | 2892 | +| P, supported on32 fields | 728 | +| J E J^-1 | 3628 | + +The diagonal conversion adds320 primitives to a common-frame E code. +This is a one-bank code cost. It is not the cost to conjugate a two-bank +native shear. That cost must include both unchanged baseline banks. + +No word uses an extra field or an odd denominator. Every prefix has +binary denominator height at most1 in the supplied words. + +## Verification and scope + +Run `python3 -I -B check_model.py --out `. Repeat with +`-O` and compare the decompressed response and receipt bytes. +The checks use exact fractions for all matrices, inverses, ranks, +support tests, scalar words, and costs. + +This packet does not claim a native caller, a terminal decoder, helper +progress, a recursive host, or a change to the selected bound. A separate +native packet will bind this response to the actual transfer word. + +The coordinating agent supplied the signed-metric E=P R identity. +The new-core-transfer lane supplied the actual pair-closed role placement. +The independent-review and controller lanes supplied the physical pair +geometry and cyclic native grammar. This lane binds these parts and +checks the complete physical response and paid scalar words. AI +assistance was used. + +No PR, push, commit, or publication is authorized. Before any future PR +description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_family.py b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_family.py new file mode 100644 index 0000000000..383fdb5bcd --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_family.py @@ -0,0 +1,109 @@ +#!/usr/bin/env python3 +"""Check the reciprocal family and the diagonal-metric equations.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +MODEL_PIN = "9d7052a27139990fe9eb4e397b672d2ae7069de75636e3b068f172760cf173fb" +need_path = HERE / "check_model.py" +if sha256(need_path.read_bytes()).hexdigest() != MODEL_PIN: + raise ValueError("Frozen model checker pin") +spec = importlib.util.spec_from_file_location("reciprocal_family_model", need_path) +model = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = model +spec.loader.exec_module(model) +r, need = model.r, model.need + + +def metric_constraints(E): + n = len(E) + result = [] + for i in range(n): + for j in range(i, n): + row = {k: E[k].get(i, F(0)) * E[k].get(j, F(0)) for k in range(n) + if E[k].get(i, 0) * E[k].get(j, 0)} + if i == j: + r.add(row, {i: F(-1)}) + if row: + result.append(row) + return result + + +def unit(c): + a, b = abs(c.numerator), c.denominator + return bool(a) and not a & (a - 1) and not b & (b - 1) + + +def reflection_response(n): + m, k = n - 4, n - 2 + u, ell = [F(1)] * k + [F(m), F(0)], [F(-1)] * k + [F(1), F(0)] + R = r.identity(n) + for i in range(n): + r.add(R[i], {j: c for j, c in enumerate(ell) if c}, u[i]) + P = r.identity(n) + P[-2], P[-1] = P[-1], P[-2] + return r.product(P, R), r.product(R, P) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + reports = [] + for n in range(5, 25): + E, Ei, R, P, J, Ji, u, ell = model.block(n) + constraints = metric_constraints(E) + need(r.rank(constraints, n) == n - 1, "Exact diagonal-metric nullity one") + need(all(sum(c * J[i][i] for i, c in row.items()) == 0 for row in constraints), + "The stated metric spans the kernel") + m = n - 4 + need(all(unit(row[i]) for i, row in enumerate(J)) == (not m & (m - 1)), + "The exact dyadic-unit condition") + need(r.rank(model.difference(E, P), n) == 1 + and r.rank(model.difference(E, r.identity(n)), n) == 2, + "The two exact displacement ranks") + A = [{j: F(int(i == j) - 1) for j in range(n) if i != j} for i in range(n)] + Ai = [{j: F(int(i == j)) - F(1, n - 1) for j in range(n)} for i in range(n)] + need(r.product(A, Ai) == r.product(Ai, A) == r.identity(n), + "Both rank-one comparison inverse orders") + need(all(Ai[i][i] == F(n - 2, n - 1) for i in range(n)), + "The nonzero reciprocal diagonal obstruction") + reports.append({"n": n, "metric_equation_rank": n - 1, + "dyadic_unit_metric": all(unit(row[i]) for i, row in enumerate(J)), + "rank_E_minus_I": 2, "rank_E_minus_P": 1, + "centre_signed_norm": "2"}) + swap = [{1: F(1)}, {0: F(1)}] + need(r.product(swap, swap) == r.identity(2) + and r.rank(model.difference(swap, r.identity(2)), 2) == 1, + "The n=2 lower-bound exception") + E3, Ei3 = reflection_response(3) + need(r.product(r.transpose(E3, 3), E3) == r.identity(3) + and all(not row.get(i) for i, row in enumerate(Ei3)), + "The positive n=3 exception") + E4, Ei4 = reflection_response(4) + constraints4 = metric_constraints(E4) + need(r.rank(constraints4, 4) == 3 + and all(sum(row.get(i, F(0)) for i in (2, 3)) == 0 for row in constraints4), + "The singular n=4 metric kernel") + checks = { + "status": "PASS_RECIPROCAL_FAMILY", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "model_checker_sha256": MODEL_PIN, "reports": reports, + "boundary_controls": {"n2_rank_one_swap": True, "n3_positive_metric": True, + "n4_only_singular_diagonal_metrics": True}, + "scope": "Finite exact checks support the quantified algebraic proof in FAMILY.md. No global native or supplier lower bound is inferred.", + } + (args.out / "CHECKS.json").write_text(json.dumps(checks, sort_keys=True, indent=2) + "\n") + print(json.dumps(checks, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_model.py b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_model.py new file mode 100644 index 0000000000..e361d331b3 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_model.py @@ -0,0 +1,283 @@ +#!/usr/bin/env python3 +"""Bind the signed metric and reciprocal response to the actual ports.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "placement": ( + "new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/METRIC-COMPLETION.json.gz", + "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e"), + "cyclic": ( + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"), + "arithmetic": ( + "new-core-transfer-20261017/low-displacement-20261020/check_response.py", + "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(name): + relative, pin = PINS[name] + path = LANES / relative + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, "Source pin " + name) + return raw + + +read("arithmetic") +spec = importlib.util.spec_from_file_location("signed_metric_arithmetic", LANES / PINS["arithmetic"][0]) +r = importlib.util.module_from_spec(spec) +sys.modules[spec.name] = r +spec.loader.exec_module(r) + + +def rows(value): + return [{int(p): F(c) for p, c in row.items() if F(c)} for row in value] + + +def difference(a, b): + out = [dict(row) for row in a] + for left, right in zip(out, b): + r.add(left, right, -1) + return out + + +def diag(values): + return [{i: F(c)} for i, c in enumerate(values)] + + +def substitute(local, ports, matrix): + for i, p in enumerate(ports): + matrix[p] = {ports[j]: c for j, c in local[i].items() if c} + + +def block(n): + m = n - 4 + u = [F(1)] * (n - 2) + [F(m), F(0)] + ell = [F(-1)] * (n - 2) + [F(1), F(0)] + reflection = r.identity(n) + for i in range(n): + r.add(reflection[i], {j: c for j, c in enumerate(ell) if c}, u[i]) + permutation = r.identity(n) + permutation[-2], permutation[-1] = permutation[-1], permutation[-2] + metric = diag([F(1)] * (n - 2) + [F(-1, m), F(-1, m)]) + metric_inverse = diag([1 / row[i] for i, row in enumerate(metric)]) + response = r.product(permutation, reflection) + inverse = r.product(reflection, permutation) + need(r.product(reflection, reflection) == r.identity(n), "Local reflection square") + need(r.product(response, inverse) == r.product(inverse, response) == r.identity(n), + "Both local inverse orders") + need(r.product(r.product(r.transpose(response, n), metric), response) == metric, + "Local signed metric") + need(sum(ell[i] * metric_inverse[i][i] * ell[i] for i in range(n)) == 2, + "The centre has signed norm two") + need(all(not response[i].get(i) and not inverse[i].get(i) for i in range(n)), + "Both local native diagonals vanish") + return response, inverse, reflection, permutation, metric, metric_inverse, u, ell + + +def swap_word(b, c): + return [["add", b, c, "1"], ["add", c, b, "-1"], + ["add", b, c, "1"], ["scale", c, None, "-1"]] + + +def reflection_word(ports): + a, b = ports[:-2], ports[-2] + return ([["add", b, p, "-1"] for p in a] + + [["add", p, b, "1"] for p in a] + + [["scale", b, None, "-1"]] + + [["add", b, p, "1"] for p in a]) + + +def pair_word(pairs): + word = [] + for pair in pairs: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + if aa != 1: + word.append(["scale", a, None, str(aa)]) + word.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + return word + + +def full_replay(word): + state = r.identity(640) + peak, height = F(1), 0 + for op, target, source, coefficient in word: + c = F(coefficient) + if op == "add": + need(target != source, "Distinct scalar fields") + r.add(state[target], state[source], c) + else: + need(op == "scale", "Scalar grammar") + state[target] = {p: c * v for p, v in state[target].items() if c * v} + peak = max(peak, sum(abs(v) for v in state[target].values())) + for value in state[target].values(): + denominator = value.denominator + need(not denominator & (denominator - 1), "No odd denominator") + height = max(height, denominator.bit_length() - 1) + need(state[112:] == r.identity(640)[112:], "All outside fields are unchanged") + return state[:112], { + "real_scalar_primitives": r.price(word), "instructions": len(word), + "prefix_row_l1_bound": str(peak), "binary_height": height, + "all_input_columns": 640, "untouched_arbitrary_fields": 528, + } + + +def make_model(): + placement, cyclic = json.loads(read("placement")), json.loads(read("cyclic")) + H, Hi = rows(placement["pair_code"]), rows(placement["pair_code_inverse"]) + need(r.product(H, Hi) == r.product(Hi, H) == r.identity(112), "Actual pair code inverse") + names = ("E", "inverse_E", "R", "P", "J", "inverse_J") + modes = {name: r.identity(112) for name in names} + blocks, special, centres = [], [], [] + mode_u, mode_l = [{} for _ in range(112)], [] + eword, pword, rword = [], [], [] + for record in placement["mode_blocks"]: + if record["kind"] == "large6": + roles = record["roles"] + ports = [roles[label] for label in ( + "centre", "pair_difference_a", "pair_difference_b", + "negative_difference", "contrast", "negative")] + need(set(ports) == set(cyclic["cyclic_carriers"][record["vertex"]]), + "The six carriers use the actual vertex") + else: + need(record["kind"] == "small8", "Known block kind") + ports = record["ports"] + need(all((placement["ports"][p] & placement["ports"][q]).bit_count() % 2 + == int(p == q) for p in ports for q in ports), + "An actual orthonormal eight-clique") + local = block(len(ports)) + for name, matrix in zip(names, local[:6]): + substitute(matrix, ports, modes[name]) + index = len(blocks) + for p, value in zip(ports, local[6]): + if value: + mode_u[p] = {index: value} + mode_l.append({p: value for p, value in zip(ports, local[7]) if value}) + special.extend(ports[-2:]) + centres.append(ports[0]) + rw, pw = reflection_word(ports), swap_word(*ports[-2:]) + eword += rw + pw + rword += rw + pword += pw + blocks.append({"kind": record["kind"], "index": index, "ports": ports, + "centre": ports[0], "b": ports[-2], "c": ports[-1], + "u": [str(c) for c in local[6]], + "ell": [str(c) for c in local[7]], + **({"vertex": record["vertex"]} if record["kind"] == "large6" else {})}) + need(sorted(p for b in blocks for p in b["ports"]) == list(range(112)), + "The sixteen blocks partition all112 ports") + need(len(set(special)) == 32, "Thirty-two special physical fields") + special_set = set(special) + need(all(not special_set.intersection(pair["ports"]) + or set(pair["ports"]) <= special_set for pair in cyclic["pair_codes"]), + "The special large modes are complete physical pairs") + physical = {name: r.product(Hi, r.product(matrix, H)) for name, matrix in modes.items()} + I = r.identity(112) + E, Ei, R, P, J, Ji = (physical[name] for name in names) + for name in ("J", "inverse_J"): + need(all(set(row) == {p} for p, row in enumerate(physical[name])), + "The physical metric is diagonal") + need(Counter(row[p] for p, row in enumerate(J)) == {F(1): 80, F(-1, 2): 16, F(-1, 4): 16}, + "Actual metric weights") + need(r.product(E, Ei) == r.product(Ei, E) == I and r.product(P, R) == E + and r.product(P, P) == r.product(R, R) == I, "Full112 reciprocal and reflection identities") + need(r.product(r.product(r.transpose(E, 112), J), E) == J, "Full112 signed metric") + dual = r.transpose(Ei, 112) + need(dual == r.product(J, r.product(E, Ji)), "Exact inverse-adjoint diagonal conversion") + need(all(not matrix[p].get(p) for p in range(112) + for matrix in (E, Ei, dual, modes["E"], modes["inverse_E"])), + "Both required physical and mode diagonals vanish") + support = sorted(p for p in range(112) if P[p] != I[p]) + need(support == sorted(special) and all(P[p] == I[p] for p in range(112) if p not in special_set), + "The physical P changes exactly32 fields") + need(all(set(P[p]) <= special_set for p in special_set), "P is closed on its32 fields") + U, L = r.product(Hi, mode_u), r.product(mode_l, H) + need(r.product(U, L) == difference(R, I), "The physical rank16 reflection factor") + need(r.rank(difference(E, P), 112) == r.rank(difference(R, I), 112) == 16 + and r.rank(difference(E, I), 112) == 32, "Both complete displacement ranks") + need(r.product(L, r.product(Ji, r.transpose(L, 112))) + == diag([4] * 8 + [2] * 8), "The physical centre Gram includes the pair-code normalization") + need(all((cyclic["ports"][p] & cyclic["ports"][q]).bit_count() % 2 == 0 + for p, row in enumerate(E) for q in row), "Actual response support is orthogonal") + hw = pair_word(cyclic["pair_codes"]) + need(r.replay(hw)[0] == H, "The paid physical pair code") + words = {"E": hw + eword + r.inverse_word(hw), + "R": hw + rword + r.inverse_word(hw)} + selected_pairs = [pair for pair in cyclic["pair_codes"] if set(pair["ports"]) <= special_set] + ph = pair_word(selected_pairs) + words["P"] = ph + pword + r.inverse_word(ph) + words["inverse_E"] = r.inverse_word(words["E"]) + words["inverse_adjoint_E"] = r.transpose_word(words["inverse_E"]) + jword = [["scale", p, None, str(J[p][p])] for p in special] + jiword = r.inverse_word(jword) + words["metric_inverse_adjoint_E"] = jiword + words["E"] + jword + expected = dict(physical, inverse_adjoint_E=dual, metric_inverse_adjoint_E=dual) + reports = {} + for name, word in words.items(): + actual, reports[name] = full_replay(word) + need(actual == expected[name], "Complete common-frame scalar map " + name) + need(r.determinant(E) == 1 and r.determinant(R) == r.determinant(P) == 1, + "Exact full determinants") + payload = { + "schema": "actual112-signed-metric-reciprocal-v1", "source_pins": PINS, + "ports": cyclic["ports"], "blocks": blocks, "special_ports": sorted(special), + "centre_ports": centres, "large_ports": sorted(cyclic["affected_ports"]), + "small_ports": sorted(set(range(112)) - set(cyclic["affected_ports"])), + "pair_codes": cyclic["pair_codes"], "pair_code": r.encoded(H), "pair_code_inverse": r.encoded(Hi), + "mode": {name: r.encoded(matrix) for name, matrix in modes.items()}, + "physical": {**{name: r.encoded(matrix) for name, matrix in physical.items()}, + "inverse_adjoint_E": r.encoded(dual)}, + "reflection_U": r.encoded(U), "reflection_L": r.encoded(L), + "scalar_words": words, "metric_scale_word": jword, + "metric_inverse_scale_word": jiword, + "scope": "Exact112 response and common-frame scalar words. Native access and a complete caller require separate proofs.", + } + reports["summary"] = { + "rank_E_minus_I": 32, "rank_E_minus_P": 16, "special_physical_fields": 32, + "physical_metric_counts": {str(k): v for k, v in Counter(row[p] for p, row in enumerate(J)).items()}, + "metric_conversion_extra_scalar": r.price(jword) + r.price(jiword), + "odd_divisions": 0, "nonzero_E": sum(map(len, E)), "nonzero_inverse_E": sum(map(len, Ei)), + "nonzero_P": sum(map(len, P)), "determinant_E": "1", + } + return payload, reports + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + payload, reports = make_model() + raw = (json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n").encode() + (args.out / "RESPONSE.json.gz").write_bytes(gzip.compress(raw, mtime=0)) + checks = {"status": "PASS_SIGNED_METRIC_ACTUAL112", "source_pins": PINS, + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(raw).hexdigest(), "reports": reports} + (args.out / "CHECKS.json").write_text(json.dumps(checks, sort_keys=True, indent=2) + "\n") + print(json.dumps(checks, sort_keys=True), flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/family-normal/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/family-normal/CHECKS.json new file mode 100644 index 0000000000..eeb63ec2b2 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/family-normal/CHECKS.json @@ -0,0 +1,173 @@ +{ + "boundary_controls": { + "n2_rank_one_swap": true, + "n3_positive_metric": true, + "n4_only_singular_diagonal_metrics": true + }, + "model_checker_sha256": "9d7052a27139990fe9eb4e397b672d2ae7069de75636e3b068f172760cf173fb", + "producer_sha256": "4b3769563f024e3a3a3728c5f640f44697ec418a64dc53bff9ae1320167eabed", + "reports": [ + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 4, + "n": 5, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 5, + "n": 6, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 6, + "n": 7, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 7, + "n": 8, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 8, + "n": 9, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 9, + "n": 10, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 10, + "n": 11, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 11, + "n": 12, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 12, + "n": 13, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 13, + "n": 14, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 14, + "n": 15, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 15, + "n": 16, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 16, + "n": 17, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 17, + "n": 18, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 18, + "n": 19, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 19, + "n": 20, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 20, + "n": 21, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 21, + "n": 22, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 22, + "n": 23, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 23, + "n": 24, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + } + ], + "scope": "Finite exact checks support the quantified algebraic proof in FAMILY.md. No global native or supplier lower bound is inferred.", + "status": "PASS_RECIPROCAL_FAMILY" +} diff --git a/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/family-optimized/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/family-optimized/CHECKS.json new file mode 100644 index 0000000000..eeb63ec2b2 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/family-optimized/CHECKS.json @@ -0,0 +1,173 @@ +{ + "boundary_controls": { + "n2_rank_one_swap": true, + "n3_positive_metric": true, + "n4_only_singular_diagonal_metrics": true + }, + "model_checker_sha256": "9d7052a27139990fe9eb4e397b672d2ae7069de75636e3b068f172760cf173fb", + "producer_sha256": "4b3769563f024e3a3a3728c5f640f44697ec418a64dc53bff9ae1320167eabed", + "reports": [ + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 4, + "n": 5, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 5, + "n": 6, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 6, + "n": 7, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 7, + "n": 8, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 8, + "n": 9, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 9, + "n": 10, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 10, + "n": 11, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 11, + "n": 12, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 12, + "n": 13, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 13, + "n": 14, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 14, + "n": 15, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 15, + "n": 16, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 16, + "n": 17, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 17, + "n": 18, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 18, + "n": 19, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": true, + "metric_equation_rank": 19, + "n": 20, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 20, + "n": 21, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 21, + "n": 22, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 22, + "n": 23, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + }, + { + "centre_signed_norm": "2", + "dyadic_unit_metric": false, + "metric_equation_rank": 23, + "n": 24, + "rank_E_minus_I": 2, + "rank_E_minus_P": 1 + } + ], + "scope": "Finite exact checks support the quantified algebraic proof in FAMILY.md. No global native or supplier lower bound is inferred.", + "status": "PASS_RECIPROCAL_FAMILY" +} diff --git a/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/CHECKS.json b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/CHECKS.json new file mode 100644 index 0000000000..e740999096 --- /dev/null +++ b/research/centre-metric-encoders/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/CHECKS.json @@ -0,0 +1,85 @@ +{ + "payload_decompressed_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "producer_sha256": "9d7052a27139990fe9eb4e397b672d2ae7069de75636e3b068f172760cf173fb", + "reports": { + "E": { + "all_input_columns": 640, + "binary_height": 1, + "instructions": 480, + "prefix_row_l1_bound": "44", + "real_scalar_primitives": 3308, + "untouched_arbitrary_fields": 528 + }, + "P": { + 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z`NQX5js5;)tGxU4{PN}V&G$c80ohs3JQ@d;%k6>H9)Oe{&#B6c#&WAW z>$8Dxw5^`);G^C3Y`YtV$&zq6?VJy({rSsYv}x{4Ty{zQXb1HC^UM9|-KWQoc0hl> zxqEs1@&`NTkN0+XHy=-bA@|QOC-UXx?&IeVrx(I{rtHh~?bGvL$iw63PfvIEr=LzA zzf4b9e``PG{h!{=-{V)G{${7`UOgCQH}FYtAqT2XgQALmQ1|rVbjQSp_Yda1I+^#B z^A8^$*r~r)LOtByQGI{c_jiL`KR5S(yMMZn_4x7O^yy^(&vyHA`tzfu($RIPMLyj< zzK{=3cfbEUKN@a-{eOS`+kg2r`5(Xi@Bj0E|LTvQpFdi{c+bU&K78Ox_aBrv$@kja zNqQ%^e9)%nANc!|zCV4S{eyZh26Z>Qe-ICX_4j5la*!ioZVpyY*|f-~b@*tPu6s0X z1G@s>pKky4H~;w`b_Bov_kaD}Z-4Wj|MKtub{@vBe*a%~B*SoLK4|&jZqV=P9h1X@ zokDryz0rfbr+0U!d;0#QxZw{%og{sK-`@#kPKtf#%}Jha&in9_-Dh`xfuAKkJ!=~5 ttQKFu1nTT(w!+IwBe(>uz)6;%G07?v7q{KC3jgun{y(|tI+)%H0ss_K=2, +_K=_K=0, +_K=_K=0, +_K=-k. +``` + +Therefore + +```text +C K C^T = G + = diag(-2k, k^(k-1), 2, 2, 2k, -k). +``` + +Every entry of G is a dyadic unit. This proves that C is invertible +over the dyadic rationals, with + +```text +C^-1 = K C^T G^-1, +C^-T = G^-1 C K. +``` + +Every ordinary row annihilates u. The designated centre sends u +to -2. Hence + +```text +C R = Z C, +Z = diag(1,...,1,-1,1,1,1), +``` + +where the only negative entry is at output k. In particular, +C R C^-1=Z. The determinant has the exact square + +```text +det(C)^2 = det(G)/det(K) = 16 k^k. +``` + +These equations prove the result for all r. A finite replay is +not used to infer the general statement. + +## Complete in-place word + +The butterfly on two fields a,b is + +```text +a += b +b *= -2 +b += a +``` + +It produces (old a+old b, old a-old b). Apply the usual r +Walsh stages to the first k fields. Apply one butterfly to x,y. +At this point the named physical fields hold S,T,d,b,c. + +Apply these six instructions: + +```text +S -= b +T += S +T *= -1 +b += (k/2) T +b += ((k+2)/4) S +b *= -1 +``` + +The S,T,b fields now hold v,l,w', respectively. One final +butterfly on S,b gives the stated C output order. The c field +is unchanged. Every input can have arbitrary content. + +Reverse the word and invert each instruction to obtain C^-1. +All scales are signed powers of two. Every ADD coefficient is +dyadic. No pivot, zero target, or scratch field is assumed. + +## Exact scalar cost and prefix bounds + +For a nonzero dyadic coefficient a/b in lowest terms, the +inherited complex-field ADD tariff is + +```text +2*(1+bit_length(|a|)+popcount(|a|)+bit_length(b)). +``` + +A signed power-of-two scale costs twice its absolute binary +exponent, plus2 if its sign is negative. The factor2 accounts +for the two real components. These are the same primitive costs +used by the actual supplier's scalar words. + +A butterfly costs20. The Walsh part costs10kr. The two other +butterflies cost40. The six-instruction block costs20 plus the +two nonunit ADD prices. Thus the complete forward and inverse +prices are equal and are exactly + +```text +86 if r=0, +96 if r=1, +10kr+76+4r if r>=2. +``` + +The instruction count is 3kr/2+12. In particular, n=6 costs96 +and n=8 costs164, before a physical pair code or output +reassignment. This count is for this basis only. + +The prefix row one-norm is at most4(k+1)max(k,2) forward and +2(k+5) in reverse. To see these bounds, first separate the +Walsh and x,y blocks, whose forward prefix norms are at most +max(k,2). In the three-field block, the S and T rows have +norm at most2 and3. The b row has norm at most2k+2 after the +two ADDs. The final butterfly has prefix norm at most4k+4. +In reverse order, the three-field prefix norm is at mostk+5. +The remaining inverse butterflies have prefix norm at most2; +their completed row one-norm is1. They act on disjoint blocks. + +Forward binary denominator height is at most2. The inverse +three-field block has height at most3. The remaining inverse +Walsh and x,y words add at most max(r,1). Thus inverse height +is at most max(r,1)+3. These bounds cover the literal scalar +word. They do not cover recursive children or rounding. + +## Verification and scope + +`check_signed_metric_family.py` imports no producer code. It +constructs C directly from its displayed row coefficients and +compares it with the literal word. It checks both inverse +orders, the full Gram identity, the reader, response +diagonalization, determinant, price, and prefix bounds for +k=1,2,4,8,16,32,64. Four extra arbitrary fields are included +and remain unchanged. A deleted first instruction must fail. + +Normal and optimized Python produced identical receipts with +SHA256 + +```text +3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37 +``` + +Reproduce into two new output files: + +```sh +python3 check_signed_metric_family.py --out new-normal.json +python3 -O check_signed_metric_family.py --out new-optimized.json +``` + +Independent proof review is pending. This theorem provides a +general dyadic scalar completion. It does not prove a native +supplier or an improvement to the complete kappa calculation. + +Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. +No publication is authorized. diff --git a/research/centre-metric-encoders/frozen/root/UNITARY-ARRAY-ADDENDUM-FREEZE-20261020.json b/research/centre-metric-encoders/frozen/root/UNITARY-ARRAY-ADDENDUM-FREEZE-20261020.json new file mode 100644 index 0000000000..7bc05e8306 --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/UNITARY-ARRAY-ADDENDUM-FREEZE-20261020.json @@ -0,0 +1,12 @@ +{ + "addendum": { + "path": "UNITARY-FOOTPRINT-ARRAY-ADDENDUM-20261020.md", + "sha256": "fd3028f070d18291694d4faf629ea6165adaaf72ac6e6721e653473348ec548f" + }, + "base_freeze_sha256": "9ec2cb0f38210cf95246991f9637c036c7e5489cfc9ad78b7075213d9ca3ba75", + "independent_review": { + "path": "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/unitary-footprint-review-20261020/FREEZE.json", + "sha256": "c537f75e6b76397e8fa390cd03a01e8021b7e0e55ff6c8932c3cc439613d0a61" + }, + "scope": "Unitary array coordinate lower bound, including arbitrary borrowed entries and stated frame units. No native-cost lower bound." +} diff --git a/research/centre-metric-encoders/frozen/root/UNITARY-CENTRE-FOOTPRINT-20261020.md b/research/centre-metric-encoders/frozen/root/UNITARY-CENTRE-FOOTPRINT-20261020.md new file mode 100644 index 0000000000..39bc3c94fa --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/UNITARY-CENTRE-FOOTPRINT-20261020.md @@ -0,0 +1,192 @@ +# A sharp coordinate bound for unitary centre codes + +The actual sixteen centre readers need at least 24 complex output +coordinates in any Gaussian dyadic unitary code. The code can mix all +112 ports and can act on additional arbitrary borrowed fields. The +lower bound does not require the code to preserve the old blocks. + +The bound is attained by an explicit unitary matrix. A separate new +native-support construction in the core lane also reaches 24. The +matrix bound does not give a lower bound for native cost. It does not +exclude a nonunitary code, odd denominators, or a different output +interface. + +## A finite-field bound + +Let A be an r by n matrix over Z[1/2]. Let p be an odd prime. Suppose +the reduction of A modulo p has row rank r. Let the reduction of +A A^T have rank s. + +Suppose an orthogonal matrix U over Z[1/2] encodes the n real inputs. +Additional arbitrary borrowed inputs are permitted: append zero +columns to A and include those columns in U. Suppose all rows of A +can be recovered exactly from m coordinates of Ux, for every input x. +Then + +```text +m >= 2r-s. +``` + +To prove this, write T=A U^T. Exact recovery from those m coordinates +means that T is supported on those coordinates. This follows even +if the proposed recovery coefficients are not declared dyadic: +the recovery matrix is unique because U is invertible, and it is T. + +Reduce all entries modulo p. Orthogonality makes U invertible after +reduction. Thus the row space W of T has dimension r and + +```text +T T^T = A A^T. +``` + +The radical R=W intersect W^perp of the restricted bilinear form +therefore has dimension r-s. The ambient form on F_p^m is +nondegenerate. It follows that R^perp has dimension m-(r-s). +Every vector in W is orthogonal to R. Hence + +```text +r = dim(W) <= dim(R^perp) = m-r+s. +``` + +This proves the bound. The argument does not assume that the +restricted form on W is nondegenerate. That defect gives the +additional coordinates. + +For a Gaussian dyadic unitary matrix, replace each complex entry +a+ib by its real two-by-two matrix. The result is a real dyadic +orthogonal matrix. This gives the same bound for complex fields +after the real coordinate count is divided by two. + +## Application to the actual supplier + +Let V contain the sixteen original centre readers. The pinned +physical matrix satisfies + +```text +V V* = diag(12 I8, 8 I8). +``` + +The first eight rows are the signed six-mode readers after the +actual pair matrix H. The pair matrices satisfy H*H=2I. Thus each +of these rows has squared norm 12. The last eight rows are the +eight disjoint eight-port sums and have squared norm 8. + +The reduction of V modulo 3 has row rank sixteen. Before the +invertible pair change, its sixteen nonzero rows have disjoint +block supports. The pair matrices have determinants that are +units modulo 3. The exact checker also verifies the rank directly. + +In real coordinates, A has 32 rows. Its rank modulo 3 is 32, while +the rank of A A^T modulo 3 is 16. The theorem gives + +```text +real output coordinates >= 2*32-16 = 48, +complex output fields >= 24. +``` + +The argument still applies when U mixes the large and small port +sets. It also applies when U acts on any number of additional +arbitrary borrowed fields and the readers ignore those inputs. +The initial contents of these fields must remain arbitrary for +this extension of the statement. No claim about a promise of zero +initial contents is needed. + +There is an equivalent Hermitian proof over F9. The sixteen +complex rows have an eight-dimensional radical after reduction +modulo 3. Their containing coordinate space therefore needs +dimension at least sixteen plus eight. + +## Exact attainment and native access + +The independently checked 32-coordinate code uses sixteen +selected physical outputs on the large sector and sixteen on the +small sector. Keep its large 48-by-48 unitary block unchanged. +On each small eight-port clique, use + +```text +C8 = ((1+i)/4) H8, +``` + +where H8 is the real Walsh matrix. Since H8 H8^T=8I, this matrix +is Gaussian dyadic and unitary. Its first output is +((1+i)/4) times the clique sum. The other seven outputs have +zero sum. All sixteen original readers are therefore available +from sixteen large outputs and eight small outputs. + +The exact checker constructs this physical 112-by-112 matrix, +verifies both unitary product orders, and verifies the full +24-coordinate centre decoder. This proves that the matrix bound +is sharp. + +This direct Walsh attainment has nonzero diagonal entries on +56 ordinary small outputs. It is not an admitted ordinary native +response. The core lane found a different completion that removes +these diagonal entries. It keeps one selected centre per small +clique, modifies the Haar basis with a dyadic reflection that +fixes the sum, and permutes the seven ordinary output rows. +That extension needs its own pinned scalar and native-support +review. It is not inferred from the Walsh construction. + +## Why this changes the construction target + +A unitary code C satisfies C^-*=C. Thus a native forward service +and its chronological inverse-adjoint can use the same code. +The prior one-coordinate normalized centre shear does not have +this property. A unitary completion can remove that algebraic +code mismatch. + +The bound identifies the cheapest possible coordinate target +within this class. Twenty-four fields are necessary; thirty-two +are not forced by the required centre information. The current +native follow-through is to form the 24-coordinate code, use its +ordinary rows in the existing native transfer paths, and test +the full forward/backward caller. + +The remaining obligations are the actual frame types, all +native transfers and phases, source access, arbitrary borrowed +state, the final decoder, recursive composition, and complete +cost. Neither unitarity nor the coordinate bound resolves these +obligations by itself. No supplier exponent or kappa improvement +is claimed here. + +## Independent checks and credit + +The root checker imports no producer arithmetic or replay code. +It uses sparse real matrices over Fraction. It checks the pinned +112-port unitary code, both adjoint products, all sixteen readers, +all ordinary-row equations, and both literal scalar words on +1280 arbitrary real columns. The words each cost 5460 real scalar +primitives. The 1056 outside real components are unchanged. +The largest component prefix one-norms are 16 and 28; the binary +denominator height is two. + +It rejects one deleted ADD in each scalar word and one changed +adjoint entry. It also checks the modulo-3 ranks and the explicit +24-coordinate Walsh attainment. It does not replay a changed +native word or a routed caller. + +The consumed code payload has decompressed SHA256 +fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428. +The producer is +../lanes/new-core-transfer-20261017/low-displacement-20261020/ +metric-completion-20261020/UNITARY-FREEZE.json, with SHA256 +f48111c62d3da6541739419111411f939f8929a6864a71afc8a0251ae9adb8f6. + +Run from the workspace: + +```text +python3 work/centre-encoding-campaign-20261014/root/check_unitary_completion_review.py --out +python3 -O work/centre-encoding-campaign-20261014/root/check_unitary_completion_review.py --out +``` + +The root lane supplied the distributed unitary normalization, +the finite-field coordinate bound, and this independent matrix +engine. The core lane supplied the actual matching placement, +physical pair binding, native row support, and complete scalar +code. The controller and earlier native packets supplied the +actual centre readers and their supports. AI assistance was used +throughout. + +No PR or publication is authorized. Before a future PR description, +read /Users/aliromman/Projects/IntegerMultiplicationBounds/ +PR-DESCRIPTION-STANDARD.md. diff --git a/research/centre-metric-encoders/frozen/root/UNITARY-COMPLETION-REVIEW-NORMAL.json b/research/centre-metric-encoders/frozen/root/UNITARY-COMPLETION-REVIEW-NORMAL.json new file mode 100644 index 0000000000..07805e5227 --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/UNITARY-COMPLETION-REVIEW-NORMAL.json @@ -0,0 +1,124 @@ +{ + "arbitrary_real_columns_per_component_word": 1280, + "centre_readers": 16, + "component_words": { + "code": { + "binary_height": 2, + "prefix_one_norm": "16", + "price": 5460 + }, + "inverse_and_adjoint": { + "binary_height": 2, + "prefix_one_norm": "28", + "price": 5460 + } + }, + "direct_source_pins_checked": { + "arithmetic": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "cyclic": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "native": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "reader": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7" + }, + "independent_engine": "Real sparse matrices over Fraction; no producer code imports.", + "negative_controls": [ + "one deleted ADD in each word", + "one wrong adjoint entry" + ], + "ordinary_ports": 80, + "physical_complex_columns": 112, + "scope": "Scalar code and response algebra only. No native service or routed caller.", + "selected_full_ports": 32, + "source_sha256_decompressed": "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428", + "unchanged_real_columns_per_component_word": 1056, + "unitary_coordinate_bound": { + "abstract_attainment_failed_ordinary_native_diagonals": [ + 4, + 5, + 12, + 19, + 22, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 38, + 39, + 40, + 45, + 48, + 49, + 50, + 54, + 55, + 56, + 58, + 59, + 60, + 64, + 65, + 66, + 67, + 68, + 69, + 73, + 74, + 75, + 77, + 80, + 82, + 83, + 84, + 85, + 86, + 88, + 93, + 95, + 96, + 97, + 98, + 100, + 101, + 102, + 103, + 107, + 108, + 109 + ], + "abstract_attainment_ports": [ + 0, + 1, + 2, + 3, + 6, + 7, + 8, + 11, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 27, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "minimum_complex_coordinates": 24, + "minimum_real_coordinates": 48, + "prime": 3, + "real_gram_rank": 16, + "real_reader_rank": 32 + } +} diff --git a/research/centre-metric-encoders/frozen/root/UNITARY-COMPLETION-REVIEW-OPTIMIZED.json b/research/centre-metric-encoders/frozen/root/UNITARY-COMPLETION-REVIEW-OPTIMIZED.json new file mode 100644 index 0000000000..07805e5227 --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/UNITARY-COMPLETION-REVIEW-OPTIMIZED.json @@ -0,0 +1,124 @@ +{ + "arbitrary_real_columns_per_component_word": 1280, + "centre_readers": 16, + "component_words": { + "code": { + "binary_height": 2, + "prefix_one_norm": "16", + "price": 5460 + }, + "inverse_and_adjoint": { + "binary_height": 2, + "prefix_one_norm": "28", + "price": 5460 + } + }, + "direct_source_pins_checked": { + "arithmetic": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "cyclic": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "native": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "reader": "4c98af5d7a1437a03f53e84f0f2cbc7cd2ac47d4c6d4ee1523c16bf469692eb7" + }, + "independent_engine": "Real sparse matrices over Fraction; no producer code imports.", + "negative_controls": [ + "one deleted ADD in each word", + "one wrong adjoint entry" + ], + "ordinary_ports": 80, + "physical_complex_columns": 112, + "scope": "Scalar code and response algebra only. No native service or routed caller.", + "selected_full_ports": 32, + "source_sha256_decompressed": "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428", + "unchanged_real_columns_per_component_word": 1056, + "unitary_coordinate_bound": { + "abstract_attainment_failed_ordinary_native_diagonals": [ + 4, + 5, + 12, + 19, + 22, + 26, + 28, + 29, + 30, + 31, + 32, + 33, + 34, + 35, + 38, + 39, + 40, + 45, + 48, + 49, + 50, + 54, + 55, + 56, + 58, + 59, + 60, + 64, + 65, + 66, + 67, + 68, + 69, + 73, + 74, + 75, + 77, + 80, + 82, + 83, + 84, + 85, + 86, + 88, + 93, + 95, + 96, + 97, + 98, + 100, + 101, + 102, + 103, + 107, + 108, + 109 + ], + "abstract_attainment_ports": [ + 0, + 1, + 2, + 3, + 6, + 7, + 8, + 11, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 27, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "minimum_complex_coordinates": 24, + "minimum_real_coordinates": 48, + "prime": 3, + "real_gram_rank": 16, + "real_reader_rank": 32 + } +} diff --git a/research/centre-metric-encoders/frozen/root/UNITARY-FOOTPRINT-ARRAY-ADDENDUM-20261020.md b/research/centre-metric-encoders/frozen/root/UNITARY-FOOTPRINT-ARRAY-ADDENDUM-20261020.md new file mode 100644 index 0000000000..f04998c7bc --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/UNITARY-FOOTPRINT-ARRAY-ADDENDUM-20261020.md @@ -0,0 +1,74 @@ +# The coordinate bound also covers array encodings + +This note extends UNITARY-CENTRE-FOOTPRINT-20261020.md. It does not +change that frozen proof or its scalar-code checks. + +Let each of the 112 port fields have N complex entries. The entries +can include the owner and payload indices. Let V be the pinned +sixteen-row centre matrix. The corresponding full reader is +V tensor I_N. + +In real coordinates, its rank modulo 3 is 32N and the rank of its +Gram matrix modulo 3 is 16N. The same radical argument therefore +requires at least + +```text +48N real output coordinates, or 24N complex output coordinates. +``` + +Consequently, at least 24 output arrays of size N are required. +This conclusion permits an arbitrary Gaussian dyadic unitary +encoder that mixes ports, spatial entries, and owner indices. +It is not limited to a scalar 112-by-112 port matrix. Additional +arbitrary borrowed entries do not change the bound. + +The statement counts coordinates. If output arrays have different +sizes, the lower bound applies to their total size; it is not a +lower bound of 24 names or registers of unrestricted size. + +## Change of physical frame + +Let A be the real form of V tensor I_N. Let U be any dyadic +orthogonal input-frame map. Let L be any dyadic output-frame map +whose inverse is also dyadic. For the transformed reader + +```text +A_physical = L A U, +``` + +the rank of A_physical modulo 3 remains 32N. Its Gram matrix is + +```text +A_physical A_physical^T = L (A A^T) L^T. +``` + +Its Gram rank modulo 3 therefore remains 16N. The same coordinate +bound applies. In complex form the corresponding hypothesis is a +Gaussian dyadic unitary input map. The output map and its inverse +must both be Gaussian dyadic. + +In particular, a routed unitary phase or a monomial owner view on +the input does not remove the coordinate obstruction. This +statement applies to the actual physical centre reader whenever +its pinned frame maps satisfy these hypotheses. It is not a +claim that every change of encoding or representation must be +unitary or dyadic. + +## Proof for arbitrary recovery + +The bound does not require the recovery routine to be declared +linear. Let the unitary code be C and let y=Cx. Every y is a +possible output because all inputs, including borrowed inputs, +are arbitrary. The required centre values are A C* y. +If those values depend only on a selected coordinate set, every +column of A C* outside that set must be zero. Otherwise changing +only that output coordinate would change a required centre. +Thus exact recovery already gives the row-support premise used +in the finite-field proof. + +All steps are finite-dimensional identities. The result applies +separately at every finite N. It gives no native-gate, map-call, +rounding, or total supplier-cost lower bound. The implemented +24-coordinate port code attains this information bound +entrywise; a legal complete native supplier still needs its +separate phase, access, restoration, and recursion proofs. diff --git a/research/centre-metric-encoders/frozen/root/UNITARY-FOOTPRINT-FREEZE-20261020.json b/research/centre-metric-encoders/frozen/root/UNITARY-FOOTPRINT-FREEZE-20261020.json new file mode 100644 index 0000000000..8e67227309 --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/UNITARY-FOOTPRINT-FREEZE-20261020.json @@ -0,0 +1,10 @@ +{ + "files": { + "UNITARY-CENTRE-FOOTPRINT-20261020.md": "464628f0966138a9f95c34d26abeed214ab38720916fb1214820dd62e998f0a0", + "UNITARY-COMPLETION-REVIEW-NORMAL.json": "34f22e5e44090cc80bb4476b5daa5df0223a4f3e92720d8bb0140c830740986e", + "UNITARY-COMPLETION-REVIEW-OPTIMIZED.json": "34f22e5e44090cc80bb4476b5daa5df0223a4f3e92720d8bb0140c830740986e", + "check_unitary_completion_review.py": "b7b81142cb1780fc83c035f5f60e352ffcf080dd6c56527c2d5f29ed5bff40be" + }, + "publication": "No PR, push, or publication authorized.", + "scope": "Root independent32 code review, finite-field bound, and abstract24 matrix attainment. Changed24 native-support extension and all callers are separate." +} diff --git a/research/centre-metric-encoders/frozen/root/check_signed_metric_family.py b/research/centre-metric-encoders/frozen/root/check_signed_metric_family.py new file mode 100644 index 0000000000..16158005ca --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/check_signed_metric_family.py @@ -0,0 +1,173 @@ +#!/usr/bin/env python3 +"""Check a dyadic centre code and its complete scalar word.""" + +import argparse +from fractions import Fraction as F +import hashlib +import json +from pathlib import Path + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def identity(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def product(a, b): + bt = list(zip(*b)) + return [[sum(x * y for x, y in zip(row, column)) + for column in bt] for row in a] + + +def determinant(a): + a = [row[:] for row in a] + answer = F(1) + for j in range(len(a)): + p = next(i for i in range(j, len(a)) if a[i][j]) + if p != j: + a[j], a[p] = a[p], a[j] + answer = -answer + pivot = a[j][j] + answer *= pivot + for i in range(j + 1, len(a)): + multiple = a[i][j] / pivot + a[i] = [x - multiple * y for x, y in zip(a[i], a[j])] + return answer + + +def butterfly(word, a, b): + word.extend((("add", a, b, F(1)), + ("scale", b, None, F(-2)), + ("add", b, a, F(1)))) + + +def make_word(k): + word = [] + stride = 1 + while stride < k: + for start in range(0, k, 2 * stride): + for offset in range(stride): + butterfly(word, start + offset, start + offset + stride) + stride *= 2 + s, t, d, b = 0, k, k + 1, k + 2 + butterfly(word, t, d) + word.extend((("add", s, b, F(-1)), + ("add", t, s, F(1)), + ("scale", t, None, F(-1)), + ("add", b, t, F(k, 2)), + ("add", b, s, F(k + 2, 4)), + ("scale", b, None, F(-1)))) + butterfly(word, s, b) + return word + + +def inverse_word(word): + return [(op, target, source, -c if op == "add" else 1 / c) + for op, target, source, c in reversed(word)] + + +def replay(word, n): + a = identity(n) + price, height, peak = 0, 0, F(1) + for op, target, source, c in word: + numerator, denominator = abs(c.numerator), c.denominator + require(numerator and not denominator & (denominator - 1), + "A coefficient is not nonzero dyadic.") + if op == "add": + require(source != target, "An ADD uses the same field twice.") + a[target] = [x + c * y for x, y in zip(a[target], a[source])] + price += 2 * (1 + numerator.bit_length() + + numerator.bit_count() + denominator.bit_length()) + else: + require(op == "scale" and not numerator & (numerator - 1), + "A scale is not a signed power of two.") + a[target] = [c * x for x in a[target]] + price += 2 * (abs(numerator.bit_length() - denominator.bit_length()) + + (c < 0)) + peak = max(peak, sum(map(abs, a[target]))) + for value in a[target]: + denominator = value.denominator + require(not denominator & (denominator - 1), + "An intermediate coefficient is not dyadic.") + height = max(height, denominator.bit_length() - 1) + return a, {"scalar_price": price, "instructions": len(word), + "prefix_row_one_norm": str(peak), "binary_height": height} + + +def closed_matrix(k): + n = k + 4 + a = [[F(0) for _ in range(n)] for _ in range(n)] + for i in range(1, k): + for j in range(k): + a[i][j] = F((-1) ** ((i & j).bit_count())) + for j in range(k): + a[0][j], a[k][j], a[k + 2][j] = F(k + 2, 4), F(-1), F(6 - k, 4) + for j in (k, k + 1): + a[0][j], a[k][j], a[k + 2][j] = F(k, 2), F(-1), F(-k, 2) + a[0][k + 2] = F(-k - 6, 4) + a[k][k + 2] = F(1) + a[k + 1][k], a[k + 1][k + 1] = F(1), F(-1) + a[k + 2][k + 2] = F(k - 2, 4) + a[k + 3][k + 3] = F(1) + return a + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + results = [] + for r in range(7): + k, n = 2 ** r, 2 ** r + 4 + word = make_word(k) + forward, forward_bill = replay(word, n + 4) + backward, backward_bill = replay(inverse_word(word), n + 4) + code = closed_matrix(k) + extended = [row + [F(0)] * 4 for row in code] + identity(n + 4)[n:] + require(forward == extended, "The literal word differs from the closed matrix.") + eye = identity(n + 4) + require(product(forward, backward) == product(backward, forward) == eye, + "A complete inverse order fails.") + metric = [F(1)] * (k + 2) + [F(-k)] * 2 + wanted_gram = [F(-2 * k)] + [F(k)] * (k - 1) + [F(2), F(2), F(2 * k), F(-k)] + gram = product([[x * metric[j] for j, x in enumerate(row)] for row in code], + list(zip(*code))) + require(gram == [[wanted_gram[i] if i == j else F(0) for j in range(n)] + for i in range(n)], "The diagonal metric law fails.") + u = [F(1)] * (k + 2) + [F(k), F(0)] + ell = [F(-1)] * (k + 2) + [F(1), F(0)] + reflection = [[F(i == j) + u[i] * ell[j] for j in range(n)] for i in range(n)] + require(product(reflection, reflection) == identity(n), "The response is not an involution.") + diagonalized = [row[:] for row in code] + diagonalized[k] = [-x for x in diagonalized[k]] + require(code[k] == ell and product(code, reflection) == diagonalized, + "The selected centre or ordinary invariant rows differ.") + require(determinant(code) ** 2 == 16 * k ** k, "The determinant formula fails.") + expected_price = 86 if r == 0 else 96 if r == 1 else 10 * k * r + 76 + 4 * r + require(forward_bill["scalar_price"] == backward_bill["scalar_price"] == expected_price, + "The complete scalar price differs from the formula.") + require(F(forward_bill["prefix_row_one_norm"]) <= 4 * (k + 1) * max(k, 2) + and F(backward_bill["prefix_row_one_norm"]) <= 2 * (k + 5), + "A prefix norm exceeds the proved bound.") + require(forward_bill["binary_height"] <= 2 + and backward_bill["binary_height"] <= max(r, 1) + 3, + "A binary height exceeds the proved bound.") + require(replay(word[1:], n + 4)[0] != extended, "The missing-gate control did not fail.") + results.append({"k": k, "n": n, "arbitrary_complex_columns": n + 4, + "unchanged_borrowed_columns": 4, + "determinant": str(determinant(code)), + "forward": forward_bill, "inverse": backward_bill}) + output = {"status": "PASS_SIGNED_METRIC_DYADIC_FAMILY", + "engine": "Independent Fraction matrices; no producer imports.", + "checker_sha256": hashlib.sha256(Path(__file__).read_bytes()).hexdigest(), + "checks": results, + "scope": "Common-frame scalar completion. Native layout and recursive hosting are separate."} + args.out.write_text(json.dumps(output, indent=2, sort_keys=True) + "\n", encoding="utf-8") + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/root/check_unitary_completion_review.py b/research/centre-metric-encoders/frozen/root/check_unitary_completion_review.py new file mode 100644 index 0000000000..3f3acaca3e --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/check_unitary_completion_review.py @@ -0,0 +1,234 @@ +#!/usr/bin/env python3 +"""Check the unitary centre code with an independent real matrix engine.""" + +import argparse +from fractions import Fraction +import gzip +import hashlib +import json +from pathlib import Path + + +ROOT = Path(__file__).resolve().parents[1] +SOURCE = ROOT / ( + "lanes/new-core-transfer-20261017/low-displacement-20261020/" + "metric-completion-20261020/unitary-v2-normal/UNITARY-COMPLETION.json.gz" +) +SOURCE_PIN = "fd3b442caa13104cef4b7c046e1c2781f2ffa216d8d098b4e2a4e51e6063f428" + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def identity(size): + return [{j: Fraction(1)} for j in range(size)] + + +def product(left, right): + result = [] + for row in left: + out = {} + for j, a in row.items(): + for k, b in right[j].items(): + out[k] = out.get(k, Fraction(0)) + a * b + result.append({k: v for k, v in out.items() if v}) + return result + + +def transpose(matrix, columns): + result = [{} for _ in range(columns)] + for j, row in enumerate(matrix): + for k, value in row.items(): + result[k][j] = value + return result + + +def real_matrix(rows): + result = [{} for _ in range(2 * len(rows))] + for p, row in enumerate(rows): + for raw_q, pair in row.items(): + q = int(raw_q) + a, b = map(Fraction, pair) + for i, j, v in ((2*p, 2*q, a), (2*p, 2*q+1, -b), + (2*p+1, 2*q, b), (2*p+1, 2*q+1, a)): + if v: + result[i][j] = v + return result + + +def rank_mod_three(matrix): + pivots = {} + for row in matrix: + current = {j: (v.numerator * pow(v.denominator, -1, 3)) % 3 + for j, v in row.items()} + current = {j: v for j, v in current.items() if v} + while current: + j = min(current) + if j not in pivots: + inverse = pow(current[j], -1, 3) + pivots[j] = {k: v * inverse % 3 for k, v in current.items()} + break + multiple = current[j] + for k, value in pivots[j].items(): + current[k] = (current.get(k, 0) - multiple * value) % 3 + if not current[k]: + del current[k] + return len(pivots) + + +def replay(word): + state = identity(1280) + maximum, height, price = Fraction(1), 0, 0 + for operation, target, source, raw in word: + coefficient = Fraction(raw) + require(0 <= target < 224, "A component instruction leaves the code.") + if operation == "add": + require(0 <= source < 224 and source != target, + "An ADD source is invalid.") + for j, value in state[source].items(): + state[target][j] = state[target].get(j, Fraction(0)) + coefficient * value + state[target] = {j: value for j, value in state[target].items() if value} + a, b = abs(coefficient.numerator), coefficient.denominator + price += 1 + a.bit_length() + a.bit_count() + b.bit_length() + else: + require(operation == "scale" and coefficient, "A SCALE is invalid.") + numerator, denominator = abs(coefficient.numerator), coefficient.denominator + require(numerator & (numerator-1) == denominator & (denominator-1) == 0, + "A SCALE is not a signed power of two.") + state[target] = {j: coefficient * value for j, value in state[target].items()} + price += abs(numerator.bit_length() - denominator.bit_length()) + (coefficient < 0) + maximum = max(maximum, sum(map(abs, state[target].values()))) + for value in state[target].values(): + d = value.denominator + require(d & (d-1) == 0, "A component value is not dyadic.") + height = max(height, d.bit_length()-1) + return state, {"price": price, "prefix_one_norm": str(maximum), "binary_height": height} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + raw = gzip.decompress(SOURCE.read_bytes()) + require(hashlib.sha256(raw).hexdigest() == SOURCE_PIN, "The code source pin differs.") + data = json.loads(raw) + checked_pins = {} + native = None + for name, pin in data["source_pins"].items(): + if not isinstance(pin, dict): + continue + path = Path(pin["path"]) + content = path.read_bytes() + if path.suffix == ".gz": + content = gzip.decompress(content) + digest = hashlib.sha256(content).hexdigest() + require(digest == pin["sha256"], "A direct source pin differs: " + name) + checked_pins[name] = digest + if name == "native": + native = json.loads(content)["model"] + code = real_matrix(data["code"]) + inverse = real_matrix(data["inverse_and_adjoint"]) + response = real_matrix(data["response"]) + coded_response = real_matrix(data["coded_response"]) + mode = real_matrix(data["mode_code"]) + mode_response = real_matrix(data["mode_response"]) + mode_coded = real_matrix(data["mode_coded_response"]) + readers = real_matrix(data["original_centre_readers"]) + decoder = real_matrix(data["full_carrier_centre_decoder"]) + eye = identity(224) + require(inverse == transpose(code, 224), "The code inverse is not its real adjoint.") + require(product(code, inverse) == product(inverse, code) == eye, + "A unitary product differs from the identity.") + require(product(mode, transpose(mode, 224)) == eye, "The mode code is not unitary.") + require(product(code, response) == coded_response, "The physical response differs.") + require(product(mode, mode_response) == mode_coded, "The mode response differs.") + require(all(j not in row and (j ^ 1) not in row for j, row in enumerate(code)), + "A physical complex diagonal is nonzero.") + require(all(j not in row and (j ^ 1) not in row for j, row in enumerate(mode)), + "A mode complex diagonal is nonzero.") + selected = set(data["selected_full_ports"]) + ordinary = set(data["ordinary_ports"]) + require(len(selected) == 32 and len(ordinary) == 80 + and selected.isdisjoint(ordinary) and selected | ordinary == set(range(112)), + "The selected partition differs.") + require(all(coded_response[2*p+i] == code[2*p+i] + for p in ordinary for i in (0, 1)), "An ordinary row changed.") + require(all(j // 2 in selected for row in decoder for j in row), + "A centre reader uses an ordinary output.") + require(product(decoder, code) == readers, "The centre decoder is incorrect.") + gram = product(readers, transpose(readers, 224)) + require(gram == [{j: Fraction(12 if j < 16 else 8)} for j in range(32)], + "The exact real centre Gram matrix differs.") + reader_rank = rank_mod_three(readers) + gram_rank = rank_mod_three(gram) + require(reader_rank == 32 and gram_rank == 16, "A finite-field rank differs.") + minimum_real_coordinates = 2 * reader_rank - gram_rank + code24 = [dict(row) for row in code] + require(native is not None, "The native model is absent.") + for clique in native["small_cliques"]: + require(len(clique) == 8, "An eight-port clique is absent.") + for i, p in enumerate(clique): + code24[2*p], code24[2*p+1] = {}, {} + for j, q in enumerate(clique): + coefficient = Fraction((-1) ** ((i & j).bit_count()), 4) + code24[2*p][2*q] = code24[2*p+1][2*q+1] = coefficient + code24[2*p][2*q+1] = -coefficient + code24[2*p+1][2*q] = coefficient + inverse24 = transpose(code24, 224) + require(product(code24, inverse24) == product(inverse24, code24) == eye, + "The abstract 24-coordinate code is not unitary.") + decoder24 = product(readers, inverse24) + support24 = sorted({j // 2 for row in decoder24 for j in row}) + require(len(support24) == 24 and product(decoder24, code24) == readers, + "The abstract 24-coordinate code does not attain the bound.") + bad_ordinary_diagonals = [ + p for p in range(112) if p not in support24 + and any(2*p+i in code24[2*p] for i in (0, 1)) + ] + require(len(bad_ordinary_diagonals) == 56, + "The abstract code native-support limit differs.") + checks = {} + for name, wanted in (("code", code), ("inverse_and_adjoint", inverse)): + actual, receipt = replay(data["component_words"][name]) + require(actual == wanted + identity(1280)[224:], + "The complete real component word is incorrect: " + name) + require(receipt["price"] == 5460, "The literal component price differs.") + changed = list(data["component_words"][name]) + deletion = next(i for i, gate in enumerate(changed) if gate[0] == "add") + del changed[deletion] + require(replay(changed)[0] != actual, "The missing ADD control was not rejected.") + checks[name] = receipt + wrong_adjoint = [dict(row) for row in inverse] + p = next(p for p, row in enumerate(wrong_adjoint) if row) + j = next(iter(wrong_adjoint[p])) + wrong_adjoint[p][j] *= -1 + require(product(code, wrong_adjoint) != eye, "The wrong adjoint control was not rejected.") + output = { + "source_sha256_decompressed": SOURCE_PIN, + "direct_source_pins_checked": checked_pins, + "independent_engine": "Real sparse matrices over Fraction; no producer code imports.", + "physical_complex_columns": 112, + "arbitrary_real_columns_per_component_word": 1280, + "unchanged_real_columns_per_component_word": 1056, + "centre_readers": 16, + "selected_full_ports": 32, + "ordinary_ports": 80, + "component_words": checks, + "unitary_coordinate_bound": { + "prime": 3, "real_reader_rank": reader_rank, "real_gram_rank": gram_rank, + "minimum_real_coordinates": minimum_real_coordinates, + "minimum_complex_coordinates": minimum_real_coordinates // 2, + "abstract_attainment_ports": support24, + "abstract_attainment_failed_ordinary_native_diagonals": bad_ordinary_diagonals, + }, + "negative_controls": ["one deleted ADD in each word", "one wrong adjoint entry"], + "scope": "Scalar code and response algebra only. No native service or routed caller.", + } + args.out.write_text(json.dumps(output, indent=2, sort_keys=True) + "\n") + print(json.dumps({"pass": True, "source": SOURCE_PIN, "output": str(args.out)})) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/frozen/root/signed-metric-family-normal.json b/research/centre-metric-encoders/frozen/root/signed-metric-family-normal.json new file mode 100644 index 0000000000..cb99293063 --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/signed-metric-family-normal.json @@ -0,0 +1,141 @@ +{ + "checker_sha256": "9daacf3e3f5683477235824a18afb92b09aad42c5ac297862aa1d2c7c5dea9fa", + "checks": [ + { + "arbitrary_complex_columns": 9, + "determinant": "4", + "forward": { + "binary_height": 2, + "instructions": 12, + "prefix_row_one_norm": "4", + "scalar_price": 86 + }, + "inverse": { + "binary_height": 3, + "instructions": 12, + "prefix_row_one_norm": "3", + "scalar_price": 86 + }, + "k": 1, + "n": 5, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 10, + "determinant": "-8", + "forward": { + "binary_height": 0, + "instructions": 15, + "prefix_row_one_norm": "6", + "scalar_price": 96 + }, + "inverse": { + "binary_height": 2, + "instructions": 15, + "prefix_row_one_norm": "3", + "scalar_price": 96 + }, + "k": 2, + "n": 6, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 12, + "determinant": "64", + "forward": { + "binary_height": 1, + "instructions": 24, + "prefix_row_one_norm": "15", + "scalar_price": 164 + }, + "inverse": { + "binary_height": 4, + "instructions": 24, + "prefix_row_one_norm": "4", + "scalar_price": 164 + }, + "k": 4, + "n": 8, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 16, + "determinant": "16384", + "forward": { + "binary_height": 1, + "instructions": 48, + "prefix_row_one_norm": "45", + "scalar_price": 328 + }, + "inverse": { + "binary_height": 5, + "instructions": 48, + "prefix_row_one_norm": "13/2", + "scalar_price": 328 + }, + "k": 8, + "n": 12, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 24, + "determinant": "17179869184", + "forward": { + "binary_height": 1, + "instructions": 108, + "prefix_row_one_norm": "153", + "scalar_price": 732 + }, + "inverse": { + "binary_height": 6, + "instructions": 108, + "prefix_row_one_norm": "25/2", + "scalar_price": 732 + }, + "k": 16, + "n": 20, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 40, + "determinant": "4835703278458516698824704", + "forward": { + "binary_height": 1, + "instructions": 252, + "prefix_row_one_norm": "561", + "scalar_price": 1696 + }, + "inverse": { + "binary_height": 7, + "instructions": 252, + "prefix_row_one_norm": "49/2", + "scalar_price": 1696 + }, + "k": 32, + "n": 36, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 72, + "determinant": "25108406941546723055343157692830665664409421777856138051584", + "forward": { + "binary_height": 1, + "instructions": 588, + "prefix_row_one_norm": "2145", + "scalar_price": 3940 + }, + "inverse": { + "binary_height": 8, + "instructions": 588, + "prefix_row_one_norm": "97/2", + "scalar_price": 3940 + }, + "k": 64, + "n": 68, + "unchanged_borrowed_columns": 4 + } + ], + "engine": "Independent Fraction matrices; no producer imports.", + "scope": "Common-frame scalar completion. Native layout and recursive hosting are separate.", + "status": "PASS_SIGNED_METRIC_DYADIC_FAMILY" +} diff --git a/research/centre-metric-encoders/frozen/root/signed-metric-family-optimized.json b/research/centre-metric-encoders/frozen/root/signed-metric-family-optimized.json new file mode 100644 index 0000000000..cb99293063 --- /dev/null +++ b/research/centre-metric-encoders/frozen/root/signed-metric-family-optimized.json @@ -0,0 +1,141 @@ +{ + "checker_sha256": "9daacf3e3f5683477235824a18afb92b09aad42c5ac297862aa1d2c7c5dea9fa", + "checks": [ + { + "arbitrary_complex_columns": 9, + "determinant": "4", + "forward": { + "binary_height": 2, + "instructions": 12, + "prefix_row_one_norm": "4", + "scalar_price": 86 + }, + "inverse": { + "binary_height": 3, + "instructions": 12, + "prefix_row_one_norm": "3", + "scalar_price": 86 + }, + "k": 1, + "n": 5, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 10, + "determinant": "-8", + "forward": { + "binary_height": 0, + "instructions": 15, + "prefix_row_one_norm": "6", + "scalar_price": 96 + }, + "inverse": { + "binary_height": 2, + "instructions": 15, + "prefix_row_one_norm": "3", + "scalar_price": 96 + }, + "k": 2, + "n": 6, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 12, + "determinant": "64", + "forward": { + "binary_height": 1, + "instructions": 24, + "prefix_row_one_norm": "15", + "scalar_price": 164 + }, + "inverse": { + "binary_height": 4, + "instructions": 24, + "prefix_row_one_norm": "4", + "scalar_price": 164 + }, + "k": 4, + "n": 8, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 16, + "determinant": "16384", + "forward": { + "binary_height": 1, + "instructions": 48, + "prefix_row_one_norm": "45", + "scalar_price": 328 + }, + "inverse": { + "binary_height": 5, + "instructions": 48, + "prefix_row_one_norm": "13/2", + "scalar_price": 328 + }, + "k": 8, + "n": 12, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 24, + "determinant": "17179869184", + "forward": { + "binary_height": 1, + "instructions": 108, + "prefix_row_one_norm": "153", + "scalar_price": 732 + }, + "inverse": { + "binary_height": 6, + "instructions": 108, + "prefix_row_one_norm": "25/2", + "scalar_price": 732 + }, + "k": 16, + "n": 20, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 40, + "determinant": "4835703278458516698824704", + "forward": { + "binary_height": 1, + "instructions": 252, + "prefix_row_one_norm": "561", + "scalar_price": 1696 + }, + "inverse": { + "binary_height": 7, + "instructions": 252, + "prefix_row_one_norm": "49/2", + "scalar_price": 1696 + }, + "k": 32, + "n": 36, + "unchanged_borrowed_columns": 4 + }, + { + "arbitrary_complex_columns": 72, + "determinant": "25108406941546723055343157692830665664409421777856138051584", + "forward": { + "binary_height": 1, + "instructions": 588, + "prefix_row_one_norm": "2145", + "scalar_price": 3940 + }, + "inverse": { + "binary_height": 8, + "instructions": 588, + "prefix_row_one_norm": "97/2", + "scalar_price": 3940 + }, + "k": 64, + "n": 68, + "unchanged_borrowed_columns": 4 + } + ], + "engine": "Independent Fraction matrices; no producer imports.", + "scope": "Common-frame scalar completion. Native layout and recursive hosting are separate.", + "status": "PASS_SIGNED_METRIC_DYADIC_FAMILY" +} diff --git a/research/centre-metric-encoders/notices/LICENSE b/research/centre-metric-encoders/notices/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/centre-metric-encoders/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. Definitions. + + "License" shall mean the terms and conditions for use, reproduction, + and distribution as defined by Sections 1 through 9 of this document. + + "Licensor" shall mean the copyright owner or entity authorized by + the copyright owner that is granting the License. + + "Legal Entity" shall mean the union of the acting entity and all + other entities that control, are controlled by, or are under common + control with that entity. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/centre-metric-encoders/notices/ODD-GRID-SOURCE-PINS.json b/research/centre-metric-encoders/notices/ODD-GRID-SOURCE-PINS.json new file mode 100644 index 0000000000..c249721e5e --- /dev/null +++ b/research/centre-metric-encoders/notices/ODD-GRID-SOURCE-PINS.json @@ -0,0 +1,65 @@ +{ + "base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f", + "files": { + "notes/bulk-complex-guard.tex": { + "git_blob": "a37613f05f8301156dca00e202e275e4bb42ddcf", + "sha256": "2e5f923dfdb38aba99262e08fa265a75f2f15934d31a9bacec0830b47bf72c37" + }, + "notes/finite-alphabet-transfer.tex": { + "git_blob": "bc9540b3c576cf0e3fee949030d2a7faaa2879cb", + "sha256": "0e3b0e98581dbd54fef2f6f7aee79a9b190a60a3f0d2726aefecdb3528131ce5" + }, + "notes/partial-gauge-assembly.tex": { + "git_blob": "4a09f324a3fe8a3c2397f34244b5cedebeb95a7c", + "sha256": "ef27afc3a70656d3139bf3661ac0b2088622f37221141cc386d41324b7c563d0" + }, + "notes/stopped-product-complex.tex": { + "git_blob": "4a9037137cd3158dbeca6d9e3b1881a599ebfcb5", + "sha256": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a" + }, + "notes/three-stage-cover-assembly.tex": { + "git_blob": "983ffb6ac8fb9117360cd0797c00c05dfa071c9d", + "sha256": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d" + }, + "research/community-frontier1094-audit/SELECTED-SOURCE.json": { + "git_blob": "6a75493790b4eff9c4a98051ef8b01d6aad0d5a8", + "sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b" + }, + "research/complex-sw4-frame8/local/hpe_audit_and_transport.py": { + "git_blob": "d5d3509d90c01fd91dd00b78743287614b532e48", + "sha256": "c9a05ff291016b870b4fc925b317abd9c3a604c73ffc8920dfdbbeb475e20aa3" + }, + "research/complex-sw4-frame8/local/hpe_emit_local.py": { + "git_blob": "534fdc71f7641c704575efc038363d7eb206b2df", + "sha256": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805" + }, + "research/gauge44-slots-t16/CONSTRUCTION.md": { + "git_blob": "fa156763668d1c761968b6dfaecbb55199904415", + "sha256": "7d96eb958a6b4274ea4c4c539b585f8ae2e89363b76aef930f90d2d513e164ea" + }, + "research/gauge44-slots-t16/code/assembly_controls.py": { + "git_blob": "096ba9cdfe9b5188b54768b845161014c5fb9a76", + "sha256": "da7e981ae1b9f099d4e1524cb4f3ba1116011936ebe378692889b5dbfa99029d" + }, + "research/gauge44-slots-t16/code/invoice_allcold.py": { + "git_blob": "d1dd2212917ad1e7f099287a141f741fd52bdcf6", + "sha256": "71eb57514e28ced97251e0507105f654f59885ec4d40486a780bf166098858a8" + }, + "upstream/build/sections/02-streams.tex": { + "git_blob": "088fceea1867abc76271d7efe7532b779fee9039", + "sha256": "606c80db61cad13aa0c3b6060dc4b88dbbe7ac60cdd831aa93f28d908fd09dab" + }, + "upstream/build/sections/05-layers.tex": { + "git_blob": "5ce8b3c83c455f221bb84858a97230b0285644aa", + "sha256": "20cfc8d12099d4e4ed9e3e7eeb6162edd9b6e0e076f24693364cd24377252594" + } + }, + "selected_archive": { + "members": { + "candidate/strict/global/audit/GLOBAL-PREFIX.json": "8d6bc4f2c747d07bb0cd19fce1c94e0f589dba0b401a5f67cd5676ef7346c201", + "candidate/strict/global/audit/OWNERS-AND-PROFILE.json": "30bafff060afcfb3644e951214d66cfaffe58242881c652e28003958b42127cc", + "candidate/strict/global/audit/PREFIX-AND-INVOICE.json": "212cf4ee3b16081bf66f300fa18b4070d25c17210c21c78c2967892c91870d12" + }, + "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6" + } +} diff --git a/research/centre-metric-encoders/notices/PR2588-NOTICE b/research/centre-metric-encoders/notices/PR2588-NOTICE new file mode 100644 index 0000000000..46411b80b2 --- /dev/null +++ b/research/centre-metric-encoders/notices/PR2588-NOTICE @@ -0,0 +1,10 @@ +Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls. + +New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained. +Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance. + +T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance. + +PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged. + +Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance. diff --git a/research/centre-metric-encoders/notices/PR3133-CREDITS.md b/research/centre-metric-encoders/notices/PR3133-CREDITS.md new file mode 100644 index 0000000000..24f00912d4 --- /dev/null +++ b/research/centre-metric-encoders/notices/PR3133-CREDITS.md @@ -0,0 +1,19 @@ +# Credits + +- **PR #2908, Jeremy Diviney**: the paired input/output extraction, its compensation rule `C*S`, the exact two-sided certificate (`structure.py`, vendored unchanged) and the closed-adapter admission chain. +- **PR #2917, Mason Hale**: the nine paired extractions and 82-endpoint words under PR2942, the refit/compose producer model that stage 2 follows, the T74 chronology (ORDER/DISPATCH), the allocation checker, moment auditor, extension stage and adapter derivation reused here. +- **PR #2957 / #2948 / #2966, Jeremy Kothe (jeremykothe2)**: the fourteen declared exactness-preserving gate rewrites in five classes (R-retime, A3779-cut-start-read, PM-carrier-lender-entry, B-carrier-retime, A-commuting-swap) and their pure applier (`vendor/declared_rewrites.py`, vendored unchanged); stage 3 composes exactly these rewrites onto this package's stage-2 word (`data/REWRITES-2957.json`, re-addressed with exact preimages). PR2966 composed the same rewrites onto our PR2942 words. +- **PR #2969, Dugongue**: the PR2942 + PR2957 composition at T370 and its cap-level headline nomination, this package's comparator and moment baseline (`allocation/baseline/`). Our stage 3 composes the same fourteen rewrites, here onto the stage-2 word. +- **PR #2918 (research/helper408-rank7-pairing), RossRichardson**: the fixed-cut rank-seven obstruction for helper408; this package's census of fresh rank-7 extractions reproduces it exactly and is consistent with it. +- **PR #2894 / #2833, Jeremy Kothe**: the preload re-synthesis supplier, the frame accounting and inverse-reverse cleanup (`vendor/preload_move.py`), the source materializer and the inherited supplier lineage. +- **PR #2857 / #2848, Yiyang Lu (Lyy-iiis)**: the shared-kernel words, the staged native/overlay tooling and the chronological flow model and realization (edge colouring) used to construct the allocation; PR2843 (Marius-Paul Dumitrean) is that flow model's starting point. +- **PR #2863 / #2839, Dugongue**: the packing lineage and the PR2839 owner engine. +- **Tekalign**: the independent owner/chronology checker (`allocation/vendor/independent_owners.py`) and admission tooling. +- **icekylinx**: the exact free-operator auditor retained as `vendor/audit_local.py` (PR2833). +- **themilkman216**: the observation that a cap-level allocation of these inventories needs a T whose basic counts are integral, which the allocation's degenerate-face step builds on. +- **Gareth Davidson (bitplane), PR #1995 / #2013**: the fixed-word terminal-subspace bounds that frame stage 1's scope; earlier rank-seven helper ends on other words are in `research/complex-rank7-end-pair`, `research/k8-rank7-composition` and the PR1090/PR1104 lineage (credited there). +- **PR #2930 / #2942, Marius-Paul Dumitrean**: the cap allocation of PR2917's words, the four normal-45 extractions under these words, the relaxation tools and the overlay/producer conventions reused here. +- **PR #2979, Marius-Paul Dumitrean (with substantial AI assistance from Anthropic Claude via Claude Code)**: the codimension-2 census on paired-extraction words, the joint end-frame lowering of 22 restored helpers in five groups (stage 1), the five further extractions it makes profitable (stage 2), the exact composition with PR2957's rewrites (stage 3), the producer and local verification for all three stages, the overlay stage `rank7-joint-endframes` with its rebuild guards, the adapter generalization to six width classes, the literal T74 allocation of the changed inventory, its relaxation certificates and recorded gap, and the complete fresh replay. +- **PR #3015, Jeremy Kothe (jeremykothe2)**: the declared literal edit stage (`edits/`, `tools/build_edits.py`) with its independent review (`edits/edits_review.py`), and edit R1 on PR #2979's restore section (carrier 61 for register 63). +- **PR #3042, dcharb78 (with AI assistance)**: the six restore carrier/pivot skips (`R1_E42` at `restore[162:188]`, `26 -> 33` gates skipping `{22, 40, 54, 63}`, and `R2_E7` at `restore[190:203]`, `13 -> 15` gates skipping `{5, 73}`) on PR #2979's words that serve as the direct starting words for `B_586_438` and `B_588_440`. +- **New here (dcharb78, with AI assistance)**: the two coupled `B` + `restore` dying-helper carrier folds (`B_586_438` and `B_588_440`, `6` hunks / `6 -> 5` gates each) and `helper_final` lowerings on entering helpers `586` ($E_{30} \to V_{30,76,82}$) and `588` ($E_{30} \to V_{30,97,127}$) shifting the 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}` (`+665` net profit per helper, `+1,330` joint), the literal `T74_optimal_idle39` allocation (`allocation/FILL.json.gz`), the 21-control per-word edit review (`edits/edits_review.py`) and 100-control four-stage replay (`verify.py`), and the re-derived paid profile, cap certificate (`certificates/RELAX-CAP.json`), and complete fresh-native admission and release receipts. PR #2979 (mdumitrean), PR #3015 (jeremykothe2), and PR #3042 (dcharb78) are credited first. diff --git a/research/centre-metric-encoders/notices/PR3133-NOTICE b/research/centre-metric-encoders/notices/PR3133-NOTICE new file mode 100644 index 0000000000..89c20926ea --- /dev/null +++ b/research/centre-metric-encoders/notices/PR3133-NOTICE @@ -0,0 +1,28 @@ +research/rank7-joint-endframes +Copyright 2026 Marius-Paul Dumitrean. Licensed under the Apache License, Version 2.0. +Prepared with substantial AI assistance (Anthropic Claude, via Claude Code). + +This package retains, byte-identical, Apache-2.0 files from: PR #2942 (Marius-Paul Dumitrean, head +a027b0f6fdb0ab2b42ba10fc31b53960166bf2bf, research/paired-extension-normal45): data/PARENT-base.json.gz and +data/PARENT-extra.json.gz (its data/WORD-*.json.gz), comparators/PR2942-CLAIM.json and tools/wordedit.py; PR #2917 +(Mason Hale, head 224bd5e56041c40078ff6b5fa7393733a215de5c, research/paired-helper-extension): structure.py (Jeremy +Diviney's PR2908 two-sided certificate checker), vendor/audit_local.py (PR2833's independent exact auditor, icekylinx +attribution), vendor/preload_move.py (Jeremy Kothe's PR2894 frame accounting and cleanup), allocation/ORDER.json, +allocation/DISPATCH.json and allocation/vendor/ (independent_owners.py: Tekalign's independent owner checker as vendored +by PR2839/PR2917; PLAN.json.gz, TEMPLATE.json.gz); PR #2957 (Jeremy Kothe, head b74b25f3ccc84c16e1a801d73b2f47e5ea764c78, +research/paired-extension-cap-fill-swaps): vendor/declared_rewrites.py (the pure applier of the fourteen declared +rewrites) and comparators/PR2957-CLAIM.json; PR #2966 (Jeremy Kothe, head e62d3eb9005117d82a9babcfa937ecc53237c490, +research/paired-extension-normal45-rewrites): comparators/PR2966-CLAIM.json; PR #2969 (Dugongue, head +e2ca469b08385d3d5e29a918d66dbefaf889e9f3, research/paired-swap-normal45): allocation/baseline/ (its CLAIM.json and its +allocation ORDER.json and PROFILE.json); and PR #2930 (head 81f3b5d12977eba09e06fbff729167d59faabe90): tools/relax.py, +tools/root.py, tools/relax_exact.py. +data/REWRITES-2957.json is Jeremy Kothe's PR2957 rewrite list, re-addressed to this package's stage-2 word with exact +preimages (every entry keeps a credit field). producer.py follows PR2917's producer.py (Mason Hale) for its paired steps; +verify.py, check_allocation.py, check_cap.py, run_registered.py and reproduce.py adapt our PR2942 versions of PR2917's and +PR2930's; tools/audit_allocation_moment.py is PR2917's exact moment auditor with only its authenticated baseline changed (to +the PR2969 headline); tools/derive_adapters.py generalizes PR2917's adapter derivation (PR2908, Jeremy Diviney); +tools/build_overlay.py follows the overlay conventions of PR2908's and PR2917's builders. construction/allocation/ retains +the flow model of PR2857/PR2843 (Yiyang Lu, Marius-Paul Dumitrean) as adapted for this allocation. All original notices of +the exported predecessor packages remain in force. + +Derived work (Apache-2.0): this package (`research/rank7-restore-carrier-skips`) builds on PR #2979 (Marius-Paul Dumitrean, head be191346, research/rank7-joint-endframes) and PR #3015 (Jeremy Kothe, jeremykothe2, research/rank7-joint-endframes-restore-edit), retained byte-identical except for the files named in README.md, plus two declared restore edit blocks (`R1_E42` and `R2_E7` in `edits/EDITS.json` and `edits/FINAL-WORD-*.json.gz`) and their re-derived certificates and complete fresh-native admission and release receipts by dcharb78, with AI assistance. PR #2979's own evidence is kept under evidence/pr2979/. diff --git a/research/centre-metric-encoders/notices/UPSTREAM-NOTICE b/research/centre-metric-encoders/notices/UPSTREAM-NOTICE new file mode 100644 index 0000000000..59d8e0cf31 --- /dev/null +++ b/research/centre-metric-encoders/notices/UPSTREAM-NOTICE @@ -0,0 +1,415 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. + +Partial-gauge extension, 9 October 2026 +Copyright 2026 icekylinx + +The pair-first cube assembly, compatible backward frame enlargement, +partial source-gauge schedule and stopped whole-projector composition are +contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834. + +The physical deferred bit word, reflected event accounting, fan-order +clarification and signed two-stage endpoint are adopted from Zhihao Chen +(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with +Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen +witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38, +with the original Claude disclosure retained. Cyclic interval and core-aware +pair primitives build on Avi Eisenberg (ikeboy), PR #62, +ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance. +Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and +precision credits remain in force. Imported source notices and licenses +are preserved under references/partial-gauge/; see SOURCES.json. + +Three-stage cover extension, 9 October 2026 +Copyright 2026 icekylinx + +The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry, +weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring +fallback, uniform batching, internal row borrowing and exact composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This +repository integration uses Codex assistance and extends +PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86. + +The selected local complex DAG and support/label replay are adopted from +Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf, +with its original Apache-2.0 terms and Claude assistance disclosure. +The unchanged bit physical word retains Zhihao Chen (jacklightChen), +PR #97, and Swapnil Jain's underlying witness and assistance notices. +The prior opposite-bank, stopped ordinary-leaf, copied-center, topology, +semantic/bulk, precision and analytic credits remain applicable. +Original source notices and license bytes are preserved in +references/three-stage-cover/pr117/ and references/partial-gauge/. + +Paired-cube and shared-core extension, 9 October 2026 +Copyright 2026 icekylinx + +The paired-coordinate triple-cube identity, signed overlap channels, +original-source involution, coordinate-star centers, concrete frame/carrier +compiler, chronological source gauges, PR97 gauge-subset selection, +orthogonal cross-stage routing and exact supplier/assembly integration +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. +Repository integration uses Codex assistance and extends PR #130 at +6a9970a530119174507904e23592fd59ede19a5d. + +The substantial completed-core workspace-sharing principle is credited to +an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported +OpenAI Codex assistance. No source code, partition or serialized witness +from that PR is imported. The new routing and paired-motif integration +are described separately and claim no exclusive priority for broad sharing, +paired-coordinate, Fourier or carrier-matching ideas. + +Selected coarse queries restrict the retained eumemic PR #117 positive DAG; +its original Apache-2.0 and Claude assistance notices remain unchanged. +The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil +Jain's frozen witness, notices and historical assistance disclosures. +Earlier generalized Clifford, three-stage, uniform weighted recursion, +ordinary-leaf, semantic/bulk, precision and analytic credits remain in force. +Source-specific license bytes are preserved under references/. + +October 9 recycled-bit integration: +DaysSky (#150), William Porter/hpst3r (#147), Thomas Marchand/Th0rgal (#146), +Rohan Gupta/gupt1156 (#148), James Chang/jamesyc (#124), SovereignSteak (#122). +The original notices and assistance disclosures are retained under research/, +including research/recycled-bit-integration/NOTICE. Andrew Barnes/Bortlesboat +(#101) repairs shared verifiers using rfu08's #64 counterexample. rfu08's +scoped finite and formal-transfer packages are included separately; they do +not establish the full multiplication theorem. Earlier and parallel credits +remain applicable. Douglas Colkitt integrated these with OpenAI Codex assistance. + +SovereignSteak PR151 independently supplies the matching gauge/recycling +composition and the selected 473/10^6 atom refinement; its original package +and assistance disclosure are retained under research/gauge-recycling/. + +October 9 coordinated-frame and completed-entrance-bank integration: +Dugongue PR186, 166a34d75e853e933855f0f7e940fe77c4bb6b8d, builds on +Chafik Boukhalfa/chafreaky's PR181, 7fb2194801e3a10f54772c7f0d5505035a4fc0ad, +and eumemic's PR168 v4, 4a3c769e5c5430e7114c4d3e099ff34664677f17. +The frozen package and prerequisite archive preserve all author, source-license +and assistance notices, including PR175's compiler optimization. DaysSky's +carrier closure, James Chang's terminal substitution and balanced assembly, +geckods' stopping refinements and all preceding framework credits remain. +Rohan Arun's PR185 bootstrap and chafreaky's PR182 bit refinement are reviewed +parallel contributions; their gains are not added to the selected witness. +Douglas Colkitt integrated the package and supplied the bank scheduling +supplement with OpenAI Codex assistance, under Apache-2.0. The all-size +interfaces remain conditional; finite verification is not full formalization. diff --git a/research/centre-metric-encoders/portable/check_signed_clean.py b/research/centre-metric-encoders/portable/check_signed_clean.py new file mode 100644 index 0000000000..0e67311343 --- /dev/null +++ b/research/centre-metric-encoders/portable/check_signed_clean.py @@ -0,0 +1,445 @@ +#!/usr/bin/env python3 +"""Check complete signed-metric words and their physical field types.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import argparse +import importlib.util +import json + +HERE = Path(__file__).resolve().parents[1] / "frozen/lanes/new-native-recipes-20261017/signed-clean-native-review-20261020" +HELPER = HERE.parent / "row-capture-native-review-20261020/check.py" +PIN = "5b8f2839db4fd4b0e4b24d5b8f8938c74a15497ae0e58f324896cf431d3ecb84" +if sha256(HELPER.read_bytes()).hexdigest() != PIN: + raise ValueError("Independent arithmetic helper pin") +spec = importlib.util.spec_from_file_location("independent_signed_arithmetic", HELPER) +q = importlib.util.module_from_spec(spec) +spec.loader.exec_module(q) +q.read(HELPER, PIN) +need = q.need +SOURCE = q.RAW / "signed-clean-native-20261020" +CODE = q.RAW / "signed-sixteen-20261020" +FREEZE = "d0d88ff73aa4762e53bce289544a1635c711e4bfeef5f499489199f506509df2" +PAYLOAD = "aa5c064837350c50928c984e03a3d7dffb5ab37da4510dc75607ced6166be797" + + +def forward(code, selected): + matrix = q.unit(640) + for p in range(112): + matrix[p] = {112+p: F(-1)} if p in selected else dict(code[p]) + matrix[112+p] = dict(code[p]) + if p not in selected: + q.add(matrix[112+p], {112+p: F(1)}) + return matrix + + +def inverse(code_inverse, selected): + z = [{112+p if p in selected else p: F(1)} for p in range(112)] + matrix = q.unit(640) + matrix[:112] = q.mul(code_inverse, z) + for p in range(112): + matrix[112+p] = {p: F(-1)} + if p not in selected: + q.add(matrix[112+p], {112+p: F(1)}) + return matrix + + +def conjugate(matrix, permutation): + return [{permutation[j]: v for j, v in matrix[permutation[p]].items()} + for p in range(len(matrix))] + + +def selected_dual(code, selected): + z = [{112+p if p in selected else p: F(1)} for p in range(112)] + matrix = q.unit(640) + matrix[:112] = q.mul(code, z) + for p in range(112): + if p in selected: + matrix[112+p] = {p: F(-1)} + else: + q.add(matrix[p], {112+p: F(-1)}) + return matrix + + +def diagonal_word(matrix, offset=0): + result = [] + for p, row in enumerate(matrix): + need(set(row) == {p} and row[p], "A nonzero diagonal metric") + c = row[p] + need(abs(c.numerator) & (abs(c.numerator)-1) == 0 and + c.denominator & (c.denominator-1) == 0, "A signed power-of-two metric") + if c != 1: + result.append(["scale", offset+p, None, str(c)]) + return result + + +def scalar_events(word): + return [e[1] for e in word["events"] if e[0] == "scalar"] + + +def family_matrices(family, source, payload, selected, permutation): + raw_c, raw_ci, raw_mode, tape, raw_j, raw_g = source + for key, value in (("code", raw_c), ("inverse", raw_ci), ("native_code", raw_mode), + ("metric_input_inverse", raw_j), ("metric_output", raw_g)): + need(payload[key] == value, "Exact source matrix: "+family+":"+key) + c, ci, j, g = map(q.rows, (raw_c, raw_ci, raw_j, raw_g)) + need(q.mul(c, ci) == q.unit(112) and q.mul(ci, c) == q.unit(112), + "Both actual code inverse orders") + gi = [{p: 1/row[p]} for p, row in enumerate(g)] + k = [{p: 1/row[p]} for p, row in enumerate(j)] + need(q.mul(q.mul(c, k), q.transpose(c, 112)) == g, "Actual signed metric") + need(q.transpose(ci, 112) == q.mul(q.mul(gi, c), k), + "Independent inverse-transpose metric formula") + pre = diagonal_word(j) + diagonal_word(gi, 112) + post = diagonal_word(g) + diagonal_word(g, 112) + need(payload["metric_pre_word"] == pre and payload["metric_post_word"] == post, + "Both banks have the exact input and output metric scales") + need(q.reverse(tape, 112) == q.transpose(c, 112), "Independent reverse source code") + f, fi = forward(c, selected), inverse(ci, selected) + d, di = q.transpose(fi, 640), q.transpose(f, 640) + b, bi = conjugate(d, permutation), conjugate(di, permutation) + need(b == selected_dual(q.transpose(ci, 112), selected), + "Independent arbitrary-baseline raw selected-dual formula") + pre_matrix = q.transpose(q.reverse(pre, 640), 640) + post_matrix = q.transpose(q.reverse(post, 640), 640) + converted = conjugate(q.mul(q.mul(post_matrix, d), pre_matrix), permutation) + need(converted == selected_dual(c, selected), "Independent complete metric conversion") + pre_inverse = [{p: 1/row[p]} for p, row in enumerate(pre_matrix)] + post_inverse = [{p: 1/row[p]} for p, row in enumerate(post_matrix)] + converted_inverse = conjugate(q.mul(q.mul(pre_inverse, di), post_inverse), permutation) + maps = {"forward_I": f, "forward_Q": f, "inverse_adjoint_Q": d, + "selected_conjugate_Q": b, "metric_selected_conjugate_Q": converted} + inverses = {"forward_I": fi, "forward_Q": fi, "inverse_adjoint_Q": di, + "selected_conjugate_Q": bi, + "metric_selected_conjugate_Q": converted_inverse} + need(set(payload["content_maps"]) == set(maps), "All five serialized endpoint maps") + for name, matrix in maps.items(): + need(q.rows(payload["content_maps"][name]) == matrix[:224], + "Independently derived complete endpoint: "+name) + need(q.mul(matrix[:224], inverses[name][:224]) == q.unit(224) and + q.mul(inverses[name][:224], matrix[:224]) == q.unit(224), + "Both complete content inverse orders: "+name) + return maps, pre, post + + +def forward_binding(word, old, model, formation, reuse, source, cyclic, selected, entry): + need(word["frames"] == old["frames"], "Exact ordered source frame table") + kept, removed = q.select_raw(old, {112+p for p in selected}) + need(word["retained_original_event_indices"] == kept and + word["removed_original_event_indices"] == removed, "Exact retained and removed event indices") + need(len(removed) == 250 and + Counter(old["events"][i][0] for i in removed) == {"native": 128, "scalar": 122} and + Counter(old["events"][i][4] for i in removed + if old["events"][i][0] == "native") == {1: 128}, + "Complete selected-target removal census") + transfers = {r["event"]: r for r in old["transfer_records"]} + need(len(transfers) == len(old["transfer_records"]), "Unique source transfer indices") + parameters = {p["id"]: p for p in cyclic["parameters"]} + mode = q.rows(source[2]) + core, retunings, active = [], [], 0 + for index in kept: + event = old["events"][index] + if index not in transfers: + core.append(event) + continue + record = transfers[index] + if record["part"] == "large48": + par = parameters[record["parameter"]] + ports = cyclic["cyclic_carriers"][par["vertex"]] + p, j = ports[par["row"]], ports[par["column"]] + original_value = F(model["mode_response"][p][str(j)]) + else: + need(record["part"] == "small64", "Actual transfer sector") + p, j = record["target_port"], record["source_port"] + original_value = F(model["response"][p][str(j)]) + op, target, origin, raw = event[1] + need(event[0] == "scalar" and op == "add" and target == 112+p and origin == j and + p not in selected and F(record["coefficient"]) == F(raw), + "Actual mode coefficient and physical transfer fields") + value = mode[p].get(j, F(0))*F(raw)/original_value + retunings.append({"original_event": index, "mode_target": p, "mode_source": j, + "coefficient": str(value)}) + if value: + core.append(["scalar", ["add", target, origin, str(value)], event[2]]) + active += 1 + need(word["transfer_retunings"] == retunings, "Every ordinary coefficient is explicitly bound") + sources = {v["port"]: v for v in formation["input_views"]} + need(set(sources) == set(range(112)), "Every actual source adapter") + inputs = [{**v, "field": p} for p, v in sorted(sources.items())] + start, final = list(old["start"]), list(old["final"]) + progress, recipes = [], {} + for event in core: + if event[0] == "native": + recipes[event[5]] = old["native_recipes"][event[5]] + for p in sorted(selected): + if entry == "I": + key, before, rank = "direct-full", 0, 9 + recipes[key] = formation["native_recipes"]["capture-full"] + else: + key, before, rank = "capture-line:"+str(p), old["start"][p], 8 + need(reuse["frames"][reuse["start"][112+p]] == old["frames"][before], + "Accepted exact ordered line frame") + recipes[key] = reuse["native_recipes"][key] + inputs.append({**sources[p], "field": 112+p, "role": "selected_target"}) + start[112+p] = before + final[112+p] = 1 + progress.append(["native", 112+p, before, 1, rank, key]) + code = [["scalar", gate, 1] for gate in source[3]] + rotations = [] + for p in sorted(selected): + rotations += [["scalar", ["add", 112+p, p, "1"], 1], + ["scalar", ["add", p, 112+p, "-1"], 1], + ["scalar", ["add", 112+p, p, "1"], 1]] + need(word["events"] == core+progress+code+rotations, "Complete literal forward word") + need(word["native_recipes"] == recipes, "Every exact phase recipe is inherited") + need(word["start"] == start and word["final"] == final, "Complete endpoint frame declarations") + need(word["input_views"] == sorted(inputs, key=lambda v: v["field"]), + "Every exact input adapter has its physical field") + need(word["output_views"] == [v for v in formation["output_views"] if v["port"] not in selected], + "Every ordinary inverse target adapter is inherited") + at, ranges = 0, {} + for name, events in (("retained_retuned_core", core), ("selected_progress", progress), + ("source_code", code), ("signed_selected_exchanges", rotations)): + ranges[name] = [at, at+len(events)] + at += len(events) + need(word["stage_ranges"] == ranges, "Exact forward stage chronology") + return {"removed_events": 250, "removed_H1_children": 128, + "ordinary_transfer_slots": len(retunings), "nonzero_retuned_ADDs": active} + + +def dual_binding(word, source, permutation): + for name in ("frames", "start", "final", "native_recipes", "output_views", "stage_ranges"): + need(word[name] == source[name], "Exact dual record: "+name) + need(word["wire_permutation"] == {str(p): j for p, j in enumerate(permutation) if p != j}, + "Exact full physical-field permutation") + need(all(source[k][p] == source[k][permutation[p]] + for k in ("start", "final") for p in range(640)), "Selected endpoint frame symmetry") + source_views = {v["field"]: v for v in source["input_views"]} + expected_views = deepcopy(source["input_views"]) + for v in expected_views: + v["field"] = permutation[v["field"]] + need(word["input_views"] == sorted(expected_views, key=lambda v: v["field"]), + "Every dual adapter is rebound to its physical field") + for v in word["input_views"]: + need(all(v[k] == source_views[v["field"]][k] + for k in ("port", "frame", "rank", "left", "right")), + "Same-port Q/Q input phase equality") + expected = [] + for old in source["events"]: + if old[0] == "native": + e = list(old) + e[1] = permutation[e[1]] + else: + op, p, j, raw = old[1] + value = F(raw) + gate = (["add", permutation[j], permutation[p], str(-value)] if op == "add" + else ["scale", permutation[p], None, str(1/value)]) + e = ["scalar", gate, old[2]] + expected.append(e) + need(word["events"] == expected, "Literal same-order inverse-adjoint and field rebind") + + +def metric_binding(word, source, pre, post, permutation): + for key in ("frames", "start", "final", "native_recipes", "input_views", "output_views", + "wire_permutation"): + need(word[key] == source[key], "Unchanged metric-wrapper physical record: "+key) + def bind(tape, frames): + return [["scalar", [op, permutation[p], None, c], frames[permutation[p]]] + for op, p, _, c in tape] + prefix, suffix = bind(pre, source["start"]), bind(post, source["final"]) + need(word["events"] == prefix+source["events"]+suffix, "Complete two-bank metric word") + ranges = {"metric_input": [0, len(prefix)]} + ranges.update({name: [start+len(prefix), end+len(prefix)] + for name, (start, end) in source["stage_ranges"].items()}) + at = len(prefix)+len(source["events"]) + ranges["metric_output"] = [at, at+len(suffix)] + need(word["stage_ranges"] == ranges, "Exact metric-wrapper placement") + + +def trace(word, expected, entry): + current = list(word["start"]) + count, used = Counter(), set() + for event in word["events"]: + if event[0] == "native": + _, p, before, after, rank, key = event + need(0 <= p < 224 and current[p] == before, "Actual native source frame") + need(word["native_recipes"][key]["rank"] == rank, "Actual inherited native rank") + current[p] = after + count[rank] += 1 + used.add(key) + else: + need(event[0] == "scalar", "Only native and real dyadic scalar events") + _, (op, p, j, value), frame = event + need(0 <= p < 224 and current[p] == frame, "Actual scalar target frame") + if op == "add": + need(0 <= j < 224 and j != p and current[j] == frame, "Actual common scalar frame") + else: + need(op == "scale" and j is None and F(value), "Invertible scalar scale") + need(len(current) == 640 and current == word["final"], "All actual final frames") + need(current[224:] == word["start"][224:] and used == set(word["native_recipes"]), + "Complete helper and phase-recipe ledger") + need(count == {1: 1392, 2: 64, 3: 48, 9 if entry == "I" else 8: 16}, + "Complete child profile") + gates = scalar_events(word) + need(q.reverse(gates, 640) == q.transpose(expected, 640), + "Independent reverse replay on all640 complex input columns") + rows, bound = q.prefix(gates, 640) + need(rows == expected and rows[224:] == q.unit(640)[224:], + "Separate forward rows and416 arbitrary helper outputs") + at, prices = 0, {} + for name, (start, end) in sorted(word["stage_ranges"].items(), key=lambda x: x[1][0]): + need(start == at and end >= start, "Complete disjoint scalar stage ledger") + prices[name] = q.price([e[1] for e in word["events"][start:end] if e[0] == "scalar"]) + at = end + need(at == len(word["events"]) and q.price(gates) == sum(prices.values()), + "The invoice covers every operation") + return {"complex_input_columns": 640, "unchanged_arbitrary_complex_helpers": 416, + "native_profile": dict(sorted(count.items())), "native_children": sum(count.values()), + "native_mass": sum(k*v for k, v in count.items()), + "scalar_price": sum(prices.values()), "scalar_stage_prices": prices, + "input_views": len(word["input_views"]), "output_views": len(word["output_views"]), + "native_side_map_upper_bound": 2*(sum(count.values())-(16 if entry == "I" else 0)), + "content_prefix_bound": bound, "new_fields": 0, "private_fields": 0, + "odd_scans": 0, "runtime_boundary_swaps": 0} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + for path, name, pin in ( + (SOURCE, "FREEZE.json", FREEZE), + (CODE, "FREEZE.json", "8739b5dbba6a5422c9b68035683876931fbf8f6599a43375d10e73eee55b2de2"), + (CODE, "PAIRED-FREEZE.json", "810508791ea43aecaaf894c3cb50a8170d3e6f1f8e52684e274cda16c2c2db57"), + (q.LANES/"bridge-review-20261017/signed-metric-review-20261020", "FREEZE.json", + "b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762"), + (HERE.parent/"row-capture-native-review-20261020", "FREEZE.json", + "488dc693d6e7d48e8024455c9c3f2f899f94a8e9058aef28ad38f7c46c7d8532"), + (HERE.parent/"line-entry-reuse-review-20261020", "FREEZE.json", + "cc5ed3b0ecc6eb5cec48f8baead43ec813042c3e83cd68104b7745366c13c55c"), + (q.ACCEPTED, "NATIVE-REVIEW-FREEZE.json", + "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976"), + (q.ACCEPTED, "EXTENSIONS-REVIEW-FREEZE.json", + "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c")): + q.frozen(path, name, pin) + payload = json.loads(q.read(SOURCE/"run-normal/SIGNED-CLEAN.json.gz", PAYLOAD, True)) + need(len(payload["source_pins"]) == 12, "All twelve declared source pins") + for record in payload["source_pins"].values(): + original_path = Path(record["path"]) + anchor = "centre-encoding-campaign-20261014" + need(original_path.parts.count(anchor) == 1, "Unique source campaign path") + relative = original_path.parts[original_path.parts.index(anchor)+1:] + need(relative and relative[0] == "lanes", "Source stays in the lane archive") + path = q.LANES.parent.joinpath(*relative) + q.read(path, record["sha256"], path.suffix == ".gz") + producer_receipt = json.loads(q.read(SOURCE/"run-normal/CHECKS.json", + "21e5ae1b7757429dac8ecc4c4238f7e7f1296bf3f6cb3b3c67b09166c22a79ca")) + first = json.loads(q.read(CODE/"run-v2-normal/SIGNED-SIXTEEN.json.gz", + "5ba0e042c6f27aa24e230e27a4eca5e1da573d3e39d22dab93886b207f14016c", True)) + paired = json.loads(q.read(CODE/"paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz", + "99fad6bbc9e4a463a576fe33c8d2093739e5c696851412b1e9115c78d88daec1", True)) + raw = json.loads(q.read(q.RAW/"odd16-normal-v2/EXTENSION-PROGRAM.json.gz", + "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", True)) + formation = json.loads(q.read(q.NATIVE/"direct-normal/DIRECT-FULL-CAPTURE.json.gz", + "fa3342f8b4ddf286f6f67922f4184486ec0162610e4de6a457de3eed0750504c", True)) + reuse = json.loads(q.read(q.NATIVE/"reuse-normal/LINE-ENTRY-REUSE.json.gz", + "efe67a962752f2c36513d84094d215fd0909a5360707938ff99d62743dc72110", True)) + cyclic = json.loads(q.read(q.LANES/"independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585")) + selected = set(first["centre_ports"]) + need(len(selected) == 16 and selected == set(q.P) == set(paired["centre_ports"]) and + payload["selected_ports"] == sorted(selected), "Exact16 selected physical ports") + need(payload["ports"] == raw["model"]["ports"], "Exact source port labels") + sources = { + "individual": (first["code"], first["inverse"], first["native_code"], + first["scalar_words"]["code"], first["input_metric_inverse"], first["output_metric"]), + "paired": (paired["code"], paired["inverse"], paired["native_codes"]["code"], + paired["scalar_words"]["code"], paired["input_metric_inverse"], paired["output_metric"]), + "paired_transpose": (paired["transpose"], paired["inverse_transpose"], paired["native_codes"]["transpose"], + paired["scalar_words"]["transpose"], paired["output_metric"], paired["input_metric_inverse"])} + need(set(payload["families"]) == set(sources) == set(payload["providers"]), "All three code families") + identity = list(range(640)) + swap = [112+p if p in selected else p-112 if p-112 in selected else p for p in range(640)] + reports, total = {}, 0 + for family, source in sources.items(): + maps, pre, post = family_matrices(family, source, payload["families"][family], selected, swap) + need(set(payload["providers"][family]) == {"base", "extra"}, "Both actual provider words") + reports[family] = {} + for provider, words in payload["providers"][family].items(): + need(set(words) == set(maps), "Every local variant is present") + reports[family][provider] = {} + for name, word in words.items(): + entry = "I" if name == "forward_I" else "Q" + binding = {} + if name.startswith("forward_"): + binding = forward_binding(word, raw["providers"][provider]["forward"], raw["model"], + formation["providers"][provider], reuse["providers"][provider], + source, cyclic, selected, entry) + elif name == "metric_selected_conjugate_Q": + metric_binding(word, words["selected_conjugate_Q"], pre, post, swap) + else: + dual_binding(word, words["forward_Q"], identity if name == "inverse_adjoint_Q" else swap) + report = {**trace(word, maps[name], entry), **binding} + recorded = producer_receipt["reports"][family][provider][name] + for a, b in (("scalar_price", "scalar"), ("scalar_stage_prices", "scalar_stages"), + ("native_profile", "native_profile"), ("native_children", "native_children"), + ("native_mass", "native_mass"), ("input_views", "input_views"), + ("output_views", "output_views"), + ("native_side_map_upper_bound", "native_side_map_upper_bound")): + value = report[a] + if a == "native_profile": + value = {str(k): v for k, v in value.items()} + need(value == recorded[b], "Independent invoice agrees with frozen receipt: "+a) + need(report["content_prefix_bound"] == + {"row_one_norm": recorded["content_row_one_norm"], + "binary_height": recorded["binary_height"]}, + "Independent prefix bound agrees with frozen receipt") + reports[family][provider][name] = report + total += 1 + print("PASS", family, provider, flush=True) + sample = payload["providers"]["individual"]["base"] + word = sample["metric_selected_conjugate_Q"] + start, end = word["stage_ranges"]["metric_input"] + omitted_target_scales = [e[1] for i, e in enumerate(word["events"]) if e[0] == "scalar" and + not (start <= i < end and swap[e[1][1]] >= 112)] + target = q.transpose(q.rows(payload["families"]["individual"]["content_maps"]["metric_selected_conjugate_Q"]) + + q.unit(640)[224:], 640) + need(q.reverse(omitted_target_scales, 640) != target, "Omitting target-bank metric scales is rejected") + gates = scalar_events(word) + bad = deepcopy(gates) + bad[0][3] = str(-F(bad[0][3])) + need(q.reverse(bad, 640) != target, "A wrong metric sign is rejected") + need(q.reverse(list(reversed(scalar_events(sample["inverse_adjoint_Q"]))), 640) != + q.transpose(q.rows(payload["families"]["individual"]["content_maps"]["inverse_adjoint_Q"]) + + q.unit(640)[224:], 640), "Wrong inverse-adjoint chronology is rejected") + bad_phase = dict(sample["forward_Q"]) + bad_phase["native_recipes"] = deepcopy(bad_phase["native_recipes"]) + record = next(iter(bad_phase["native_recipes"].values())) + record["left"]["phase"] = (record["left"]["phase"]+1) % 4 + try: + forward_binding(bad_phase, raw["providers"]["base"]["forward"], raw["model"], + formation["providers"]["base"], reuse["providers"]["base"], + sources["individual"], cyclic, selected, "Q") + except ValueError as error: + need(str(error) == "Every exact phase recipe is inherited", "The phase control fails at its exact test") + else: + raise ValueError("A changed native global phase was accepted") + result = { + "status": "PASS_INDEPENDENT_SIGNED_SIXTEEN_NATIVE", + "producer_freeze_sha256": FREEZE, "payload_decompressed_sha256": PAYLOAD, + "complete_words": total, "reports": reports, "fresh_native_phase_shapes": 0, + "phase_scope": "Each ordered native frame, exact recipe and physical endpoint adapter is bound to an accepted source. All changed gates are real scalar operations at a common complex frame.", + "both_complete_content_inverse_orders": True, + "negative_controls": ["omitted target-bank metric", "wrong metric sign", + "wrong dual chronology", "wrong native global phase"], + "scope": "Thirty complete local physical words. No routed caller, saved-record restoration, recursive host, finite map cost, rounding bound or complete supplier cost is claimed."} + args.out.mkdir(parents=True, exist_ok=False) + for name, value in (("REVIEW.json", result), ("INPUTS.json", q.INPUTS)): + (args.out/name).write_text(json.dumps(value, indent=2, sort_keys=True)+"\n") + print(result["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/replay.py b/research/centre-metric-encoders/replay.py new file mode 100644 index 0000000000..ccee9cc823 --- /dev/null +++ b/research/centre-metric-encoders/replay.py @@ -0,0 +1,131 @@ +#!/usr/bin/env python3 +"""Run the exact package checks in sequence. Keep all source files unchanged.""" +import argparse +import gzip +import hashlib +import json +import os +from pathlib import Path +import platform +import runpy +import shutil +import subprocess +import sys +import time + +ROOT = Path(__file__).resolve().parent +FROZEN = ROOT / "frozen" +NATIVE = "lanes/new-native-recipes-20261017/" +BRIDGE = "lanes/bridge-review-20261017/" + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def digest(data): + return hashlib.sha256(data).hexdigest() + + +def verify_sources(): + entries = json.loads((ROOT / "SOURCE-MANIFEST.json").read_bytes())["immutable_inputs"] + for entry in entries: + data = (ROOT / entry["path"]).read_bytes() + require(digest(data) == entry["sha256"], "Source changed: " + entry["path"]) + if "decompressed_sha256" in entry: + require(digest(gzip.decompress(data)) == entry["decompressed_sha256"], + "Payload changed: " + entry["path"]) + return len(entries) + + +def worker(): + script, output, *arguments = sys.argv[2:] + allowed = (ROOT, Path(output).resolve(), Path(sys.base_prefix).resolve()) + opened = set() + def audit(event, arguments): + if event != "open" or not isinstance(arguments[0], (str, bytes, os.PathLike)): + return + path = Path(os.fsdecode(arguments[0])).resolve() + require(path == Path(os.devnull) or any(path.is_relative_to(base) for base in allowed), + "File access outside the package, output, or Python runtime: " + str(path)) + if path.is_relative_to(ROOT): + opened.add(path.relative_to(ROOT).as_posix()) + sys.addaudithook(audit) + sys.argv = [script, *arguments] + runpy.run_path(script, run_name="__main__") + (Path(output) / "FILE-ACCESS.json").write_text(json.dumps(sorted(opened), indent=2) + "\n") + + +def jobs(): + return [ + ("unitary_footprint", FROZEN / "lanes/independent-review-20261017/unitary-footprint-review-20261020/check_review.py", "--out", "result.json", [], + {"result.json": "lanes/independent-review-20261017/unitary-footprint-review-20261020/REVIEW-NORMAL.json"}), + ("unitary_native", FROZEN / (NATIVE + "unitary-clean-24-review-20261020/check.py"), "--out", "result", [ + "--source-freeze", "95fa9e61ddf860f3305fff398996077b6ecc164c011d37b60f6db0e459719fc5", + "--payload-sha256", "472935ba574b78c6ec1fd6f02fc1c0c29d37b53f73ec55b8583904bd5d5af245"], + {"result/REVIEW.json": NATIVE + "unitary-clean-24-review-20261020/normal-final/REVIEW.json", + "result/INPUTS.json": NATIVE + "unitary-clean-24-review-20261020/normal-final/INPUTS.json"}), + ("signed_metric", FROZEN / (BRIDGE + "signed-metric-review-20261020/check_review.py"), "--output", "result", [], + {"result/REVIEW-CHECKS.json": BRIDGE + "signed-metric-review-20261020/normal/REVIEW-CHECKS.json"}), + ("signed_native", ROOT / "portable/check_signed_clean.py", "--out", "result", [], + {"result/REVIEW.json": NATIVE + "signed-clean-native-review-20261020/normal-final/REVIEW.json", + "result/INPUTS.json": NATIVE + "signed-clean-native-review-20261020/normal-final/INPUTS.json"}), + ("signed_family", FROZEN / "root/check_signed_metric_family.py", "--out", "result.json", [], + {"result.json": "root/signed-metric-family-normal.json"}), + ("signed_family_review", FROZEN / (BRIDGE + "signed-family-review-20261020/check_family_review.py"), "--output", "result.json", [], + {"result.json": BRIDGE + "signed-family-review-20261020/normal.json"}), + ("rational_grid", FROZEN / (NATIVE + "rational-packing-grid-review-20261020/check.py"), "--out", "result", [], + {"result/REVIEW.json": NATIVE + "rational-packing-grid-review-20261020/normal-final/REVIEW.json", + "result/INPUTS.json": NATIVE + "rational-packing-grid-review-20261020/normal-final/INPUTS.json"}), + ] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + output = args.output.resolve() + require(not output.exists(), "Use a new output directory") + require(shutil.disk_usage(ROOT).free >= 3 * 1024**3, "At least 3 GiB of free disk space is required") + count = verify_sources() + output.mkdir(parents=True) + reports = [] + for name, script, flag, result, extra, expected in jobs(): + for mode in ("normal", "optimized"): + directory = output / name / mode + directory.mkdir(parents=True) + command = [sys.executable, "-I", "-B"] + (["-O"] if mode == "optimized" else []) + command += [str(ROOT / "replay.py"), "--worker", str(script), str(directory), flag, str(directory / result), *extra] + print("RUN", name, mode, flush=True) + started = time.monotonic() + with (directory / "stdout.log").open("w") as log: + completed = subprocess.run(command, cwd=ROOT, stdout=log, stderr=subprocess.STDOUT) + require(completed.returncode == 0, "Check failed. Read " + str(directory / "stdout.log")) + matches = {} + for relative, frozen in expected.items(): + actual = (directory / relative).read_bytes() + require(actual == (FROZEN / frozen).read_bytes(), "Frozen receipt mismatch: " + name + "/" + relative) + if mode == "optimized": + require(actual == (output / name / "normal" / relative).read_bytes(), "Normal and optimized receipts differ") + matches[relative] = digest(actual) + reports.append({"check": name, "mode": mode, "seconds": round(time.monotonic()-started, 3), + "receipts_equal_frozen": matches, "file_access_confined": True}) + print("PASS", name, mode, flush=True) + require(verify_sources() == count, "Source count changed") + receipt = {"status": "PASS_CENTRE_METRIC_ENCODERS", "immutable_inputs": count, + "checks": reports, "normal_optimized_equal": True, "frozen_sources_unchanged": True, + "python": platform.python_version(), "platform": platform.platform(), + "replay_sha256": digest(Path(__file__).read_bytes()), + "portable_signed_checker_sha256": digest((ROOT / "portable/check_signed_clean.py").read_bytes()), + "source_manifest_sha256": digest((ROOT / "SOURCE-MANIFEST.json").read_bytes()), + "scope": "Exact local proofs, matrices, scalar words, native words, phases, invoices, and grid checks. No recursive supplier or kappa claim."} + (output / "REPLAY.json").write_text(json.dumps(receipt, indent=2, sort_keys=True)+"\n") + print(receipt["status"], flush=True) + + +if __name__ == "__main__": + if len(sys.argv) > 1 and sys.argv[1] == "--worker": + worker() + else: + main() diff --git a/research/publication-reviews/centre-metric-encoders/COMMANDS.sh b/research/publication-reviews/centre-metric-encoders/COMMANDS.sh new file mode 100644 index 0000000000..c0feb1acf6 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/COMMANDS.sh @@ -0,0 +1,5 @@ +#!/bin/sh +set -eu +env OMP_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 MKL_NUM_THREADS=1 VECLIB_MAXIMUM_THREADS=1 NUMEXPR_NUM_THREADS=1 python3 -I -B /Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/cold/package/replay.py --output /Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/cold/replay +python3 -I -B /Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/direct_check.py --package /Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/cold/package --output /Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/DIRECT-CHECKS.json +python3 -I -B /Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/check_package.py diff --git a/research/publication-reviews/centre-metric-encoders/DIRECT-CHECKS.json b/research/publication-reviews/centre-metric-encoders/DIRECT-CHECKS.json new file mode 100644 index 0000000000..e205119631 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/DIRECT-CHECKS.json @@ -0,0 +1,101 @@ +{ + "C16_nonzero_ordinary_diagonals": 96, + "C16_residue_real_rank_mod3": 8, + "C16_scaled_trace_mod3": [ + 1, + 2 + ], + "C16_selected_support": 16, + "C16_trace": [ + "11/6", + "7/6" + ], + "C24_selected_support": 24, + "Cbar_L_decoder_support": 16, + "Cbar_transpose_L_decoder_support": 96, + "input_sha256": { + "lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal/PACKING.json.gz": "dd9f9f053f929df31cf9ffbe8404256f9b34fdbd031162bd4b7873f7aaf70544", + "lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/twenty-four-v2-normal/UNITARY-24.json.gz": "d6f7bc4d89c0ae552e2bb7eb9c5e441ff099bc87a9cfec78935055a667539c9d", + "lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz": "d31ddebdde5225c8dbae7f1a2899bb7d6bd598f1a6f8b59c3e05933cee17092e", + "lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz": "cf29241b788142811a1e5c7051c96f143ce5ab866cb2c38028e5d933e9272194" + }, + "original_complex_bound": 24, + "original_gram": [ + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 12, + 8, + 8, + 8, + 8, + 8, + 8, + 8, + 8 + ], + "original_real_ranks_mod3": [ + 32, + 16 + ], + "physical_P_changed_ports": 32, + "physical_P_nonzero_entries": 160, + "producer_imports": 0, + "reciprocal_complex_bound_mod5_or_mod7": 24, + "reciprocal_gram": [ + 10, + 10, + 10, + 10, + 10, + 10, + 10, + 10, + 7, + 7, + 7, + 7, + 7, + 7, + 7, + 7 + ], + "reciprocal_real_ranks": { + "3": [ + 32, + 32 + ], + "5": [ + 32, + 16 + ], + "7": [ + 32, + 16 + ] + }, + "reciprocal_weighted_gram": [ + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 4, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 2 + ], + "scope": "Independent exact matrix checks. The proof of all-power height uses the nonzero residue trace. No native or recursive theorem is inferred from these calculations.", + "status": "PASS_DIRECT_ENCODER_MATRIX_CHECKS" +} diff --git a/research/publication-reviews/centre-metric-encoders/PACKAGE-CHECKS.json b/research/publication-reviews/centre-metric-encoders/PACKAGE-CHECKS.json new file mode 100644 index 0000000000..ece7436f6f --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/PACKAGE-CHECKS.json @@ -0,0 +1,96 @@ +{ + "cold_code_equal_final": true, + "current_selected_record_equal": true, + "failure_controls": [ + { + "control": "false_requirement", + "exit_code": 1, + "mode": "normal", + "rejected_at_expected_check": true + }, + { + "control": "outside_read", + "exit_code": 1, + "mode": "normal", + "rejected_at_expected_check": true + }, + { + "control": "false_requirement", + "exit_code": 1, + "mode": "optimized", + "rejected_at_expected_check": true + }, + { + "control": "outside_read", + "exit_code": 1, + "mode": "optimized", + "rejected_at_expected_check": true + } + ], + "immutable_sources_equal_original": 185, + "native_credit_source_checks": [ + { + "label": "PR3133-README", + "sha256": "7cbc11533925ba93f87d6f9e8a3059df328b0dc50c35a9d09b382782beb40810", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/51eb9c4ee9e4722010d308aa3309e039d3940cc2/research/rank7-coupled-586-588-carrier-fold/README.md" + }, + { + "label": "PR3148-README", + "sha256": "1442d0a676e2f7528c5eea000d9abdbddf4649ee8e7a85f03f903f96eaad18a5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/README.md" + }, + { + "label": "PR2588-README", + "sha256": "6252142912118a7c4dcc30ec0a9b0cba30672135c88ce7d34a8423126abf16f1", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/README.md" + } + ], + "package_files": 253, + "package_manifest_sha256": "f7aa100a7389e94518b980fe93e91773602f53b5d782a7c677612be4c9790866", + "python_files_read_assertion_counts": { + "frozen/lanes/bridge-access-20261017/rational-unitary-packing-20261020/check_packing.py": 0, + "frozen/lanes/bridge-review-20261017/fixed-reader-reuse-review-20261020/check_review.py": 0, + "frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/check_review.py": 0, + "frozen/lanes/bridge-review-20261017/signed-family-review-20261020/check_family_review.py": 0, + "frozen/lanes/bridge-review-20261017/signed-metric-review-20261020/check_review.py": 0, + "frozen/lanes/independent-review-20261017/odd-unitary-packing-20261020/check_packing.py": 0, + "frozen/lanes/independent-review-20261017/unitary-footprint-review-20261020/check_review.py": 0, + "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py": 0, + "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py": 0, + "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/check_twenty_four.py": 0, + "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-clean-native-20261020/emit_signed_clean.py": 0, + "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_paired_companion.py": 0, + "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/check_signed_sixteen.py": 0, + "frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/unitary-clean-24-20261020/emit_unitary_clean.py": 0, + "frozen/lanes/new-native-recipes-20261017/isotropic-pair-review-20261018/check.py": 0, + "frozen/lanes/new-native-recipes-20261017/line-entry-reuse-review-20261020/check.py": 0, + "frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py": 0, + "frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py": 0, + "frozen/lanes/new-native-recipes-20261017/rational-packing-grid-review-20261020/check.py": 0, + "frozen/lanes/new-native-recipes-20261017/row-capture-native-review-20261020/check.py": 0, + "frozen/lanes/new-native-recipes-20261017/unitary-clean-24-review-20261020/check.py": 0, + "frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_family.py": 0, + "frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_model.py": 0, + "frozen/root/check_signed_metric_family.py": 0, + "portable/check_signed_clean.py": 0 + }, + "retained_git_sources": [ + { + "equal": true, + "sha256": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "source_path": "notes/stopped-product-complex.tex" + }, + { + "equal": true, + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "source_path": "LICENSE" + }, + { + "equal": true, + "sha256": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd", + "source_path": "NOTICE" + } + ], + "scope": "The file list includes hash reads, not only executed imports. The file-access hook is a reproducibility check, not a security sandbox.", + "status": "PASS_ENCODER_PACKAGE_CHECKS" +} diff --git a/research/publication-reviews/centre-metric-encoders/REVIEW.json b/research/publication-reviews/centre-metric-encoders/REVIEW.json new file mode 100644 index 0000000000..70c55a986a --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/REVIEW.json @@ -0,0 +1,145 @@ +{ + "Cbar_transpose_scope": { + "L_decoder_support_Cbar": 16, + "L_decoder_support_Cbar_transpose": 96, + "sixteen_selected_outputs_decode_L_for_transpose": false + }, + "artifacts": { + "COMMANDS.sh": "f718dd77c783f1b3a0067400053b2d71aea4e752ee4f767ca022620025dbf3a3", + "DIRECT-CHECKS.json": "0c334499b41ab91e192e484da50db820a65439d37318db03d4b256ca474a19bb", + "PACKAGE-CHECKS.json": "ab24fee2f10928a14c99444cdf555cd3ac4c7a6e54b71a647872daa7649a2b4d", + "REVIEW.md": "1aad258ca380ec9812f3e3f80117771ad49189b9288c8230737cad24479d1143", + "check_package.py": "1a5fff442f2c496fa0b8d815ab53f5fe1e8dea87998fc288a071879f3581ced6", + "direct_check.py": "85d9054966514c1119c427a82c039e45e0697b4ed322d5f1a5cfc72be84e2980" + }, + "claim_scope": "Exact coordinate theorem, matrix constructions, local scalar/native interfaces and grid limits. No routed caller, restoration proof, recursive host, finite map price, full precision bound or kappa improvement.", + "cold_replay": { + "checks": 14, + "normal_optimized_equal": true, + "numerical_thread_limits": 1, + "portable_signed_checker_sha256": "ec0fc10da3570981191420255c1bb30c2f26bfdb638137ae7077006f123f02ca", + "process_concurrency": 1, + "python": "3.14.7", + "replay_sha256": "b75eb0f615c31b93130f0dcd986b794137ee3d9ded8cb9e8f6d237340ee87bb6", + "seconds_sum": 74.053, + "source_manifest_sha256": "71c42b6191c8f2fc6afdc3c79357352372a3d1911b79ef8a41130c0ef7a25b9e", + "status": "PASS_CENTRE_METRIC_ENCODERS" + }, + "date": "2026-10-22", + "direct_matrix_check_status": "PASS_DIRECT_ENCODER_MATRIX_CHECKS", + "failure_controls": [ + { + "control": "false_requirement", + "exit_code": 1, + "mode": "normal", + "rejected_at_expected_check": true + }, + { + "control": "outside_read", + "exit_code": 1, + "mode": "normal", + "rejected_at_expected_check": true + }, + { + "control": "false_requirement", + "exit_code": 1, + "mode": "optimized", + "rejected_at_expected_check": true + }, + { + "control": "outside_read", + "exit_code": 1, + "mode": "optimized", + "rejected_at_expected_check": true + } + ], + "frozen_sources_changed": false, + "immutable_inputs_equal_original": 185, + "native_words": { + "C24": 8, + "arbitrary_complex_input_fields": 640, + "signed_or_transpose_interface": 30, + "total": 38, + "unchanged_auxiliary_fields": 416 + }, + "open_blocking_findings": [], + "package": "centre-metric-encoders", + "package_files": 253, + "remaining_coordinator_gates": [ + "Use exact published commit links", + "Verify each final PR link target", + "Inspect GitHub rendered Markdown", + "Read back published body and rendered HTML" + ], + "resolved_findings": [ + { + "evidence": "DIRECT-CHECKS.json", + "finding": "Cbar transpose is a native companion interface; its sixteen selected outputs do not decode the same reciprocal L. The unique decoder uses96 outputs.", + "id": "ENC-1", + "resolution": "README opening, exact scope sentence, and table labels now distinguish C and Cbar from the transpose interface. Frozen source text is unchanged.", + "type": "claim_scope" + }, + { + "evidence": "PACKAGE-CHECKS.json", + "finding": "The retained odd-grid method and native provider inputs need explicit source credit.", + "id": "ENC-2", + "resolution": "NOTICE.md names the source contributions; original notices, exact source pins, and immutable GitHub readback receipts are retained.", + "type": "attribution" + }, + { + "evidence": "evidence/SELECTED-CONTEXT.json in the package", + "finding": "The local source constructions must not be read as changes to the current selected supplier.", + "id": "ENC-3", + "resolution": "PROVENANCE.md states refreshed main b58ad9ef, selected PR4470, and non-application of these words to the selected construction.", + "type": "historical_applicability" + } + ], + "reviewed_package_manifest_sha256": "f7aa100a7389e94518b980fe93e91773602f53b5d782a7c677612be4c9790866", + "skipped_checks": [ + "Archived producer emitters", + "All old predecessor suites", + "Selected-frontier replay", + "Complete recursive supplier", + "Lean formalization", + "Fresh spatial replay of unchanged signed native recipes", + "Final PR publication and rendered GitHub readback" + ], + "source_credit_review": { + "authorship_inferred_from_submitter": false, + "native_credit_sources": [ + { + "label": "PR3133-README", + "sha256": "7cbc11533925ba93f87d6f9e8a3059df328b0dc50c35a9d09b382782beb40810", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/51eb9c4ee9e4722010d308aa3309e039d3940cc2/research/rank7-coupled-586-588-carrier-fold/README.md" + }, + { + "label": "PR3148-README", + "sha256": "1442d0a676e2f7528c5eea000d9abdbddf4649ee8e7a85f03f903f96eaad18a5", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/README.md" + }, + { + "label": "PR2588-README", + "sha256": "6252142912118a7c4dcc30ec0a9b0cba30672135c88ce7d34a8423126abf16f1", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/README.md" + } + ], + "retained_git_sources": [ + { + "equal": true, + "sha256": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "source_path": "notes/stopped-product-complex.tex" + }, + { + "equal": true, + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "source_path": "LICENSE" + }, + { + "equal": true, + "sha256": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd", + "source_path": "NOTICE" + } + ] + }, + "status": "PASS_LOCAL_PUBLICATION_REVIEW" +} diff --git a/research/publication-reviews/centre-metric-encoders/REVIEW.md b/research/publication-reviews/centre-metric-encoders/REVIEW.md new file mode 100644 index 0000000000..5da057fa96 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/REVIEW.md @@ -0,0 +1,184 @@ +# Independent publication review: centre metric encoders + +The package passes this local publication review. No open mathematical or +replay defect was found in the stated scope. One claim limit needed a +correction: the transpose companion is a native interface, but its selected +sixteen outputs do not decode the original reciprocal reader L. The final +README now states this limit. + +The reviewed package manifest SHA256 is +`f7aa100a7389e94518b980fe93e91773602f53b5d782a7c677612be4c9790866`. +The manifest covers 253 files. The 185 immutable inputs, the runner, and +the portable signed checker are unchanged from the cold replay. The proof +and result files were not edited. The coordinator must still check the +final PR description, commit links, GitHub rendering, and publication +readback. This review did not create a commit, push, PR, or frontier change. + +## Reproduction and evidence + +The reviewer copied the package to `cold/package` in this review directory. +The replay output is in `cold/replay`. The command ran one check process at +a time with the numerical thread limits set to one. The checkers use Python +exact arithmetic and the standard library. The measured run used Python +3.14.7 on macOS arm64. The sum of the fourteen check times was 74.053 seconds. + +All seven selected checks passed in normal Python and in optimized Python. +Every computed result receipt matched its frozen receipt byte for byte. +The two Python modes also matched. The replay checked all 185 immutable +source hashes before and after execution. Compressed payload hashes also +matched. See [the cold receipt](cold/replay/REPLAY.json). + +The checks include eight complete C24 native words and thirty signed-code +or transpose-interface native words. Each full word was checked on 640 +arbitrary complex input fields. The 416 auxiliary fields remain unchanged +at this local interface. The C24 check also checks eight distinct new H8 +operators on all 512 spatial columns. The signed words reuse exact pinned +phase records; they add no new spatial operator. + +The review used a separate small exact engine for the main matrix claims. +It imports no package code. Its receipt is [DIRECT-CHECKS.json](DIRECT-CHECKS.json), +and its source is [direct_check.py](direct_check.py). The package and source +checks are in [PACKAGE-CHECKS.json](PACKAGE-CHECKS.json) and +[check_package.py](check_package.py). The exact commands are in +[COMMANDS.sh](COMMANDS.sh). + +## Mathematical checks + +The original-reader theorem has the required scope. For a row space of +dimension r with Gram rank s over an odd finite field, its radical has +dimension r-s. A containing nondegenerate coordinate space therefore has +dimension at least 2r-s. Orthogonal encoding preserves the row rank and +Gram. Exact recovery from selected coordinates forces zero coefficients +outside those coordinates. This last step also holds for nonlinear +recovery because all encoded output coordinates can vary independently. +Arbitrary borrowed inputs, tensor products with identity, and the stated +dyadic input and output frame changes preserve these premises. + +The direct check obtains `V V*=diag(12 I8,8 I8)`. Realification gives row +rank 32 and Gram rank 16 modulo three. The lower bound is thus 24 complex +coordinates, or 24N complex coordinates for arrays of length N. It counts +capacity. It does not apply to unrestricted register names, promised zero +inputs, approximate recovery, or general nonunitary codes. The actual C24 +matrix is unitary in both product orders. Its exact decoder has support +24 and recovers V. The proof of its native support uses the stated Haar +normalization, dyadic reflection, and output assignment. + +The reciprocal reader is a different matrix. The direct check obtains +`L L^T=diag(10 I8,7 I8)` and `L K L^T=diag(4 I8,2 I8)`. Its real row rank +is 32 modulo three, five, and seven. Its real Gram rank is 32 modulo three +and 16 modulo five or seven. The 24-coordinate Euclidean-unitary bound +therefore uses five or seven for L. The old modulo-three instance cannot +be substituted. The signed code avoids the Euclidean-unitary premise. +It captures `E-P`, of rank sixteen, rather than `E-I`, of rank thirty-two. +Physical P changes 32 ports and has 160 nonzero entries. Its paid scalar +word costs 728 real primitives before view costs. + +The signed dual algebra includes both input banks. From `A K A^T=G`, +one gets `A^-T=G^-1 A K`. The complete two-bank correction is +`diag(G,G) F_A^-T diag(K^-1,G^-1)`. The ordinary target baseline is +arbitrary, so its input metric cannot be omitted. The complete replay +rejects that omission. It also checks the signs, selected-bank relabeling, +actual endpoint adapters, and chronological inverse-adjoint. The original +C transpose has 32 ordinary support violations. The paid 80-primitive +selected-pair suffix produces Cbar and repairs this support defect. + +The review found a scope ambiguity in the summary of the three code +families. The unique decoder `L Cbar^-1` uses the sixteen selected outputs. +In contrast, `L Cbar^-T`, which decodes L after Cbar transpose, uses 96 +outputs. This does not refute the transpose native word. It shows that its +sixteen selected outputs are a different interface. The final README +separates these claims and retains the paid recovery of individual L +readers from Cbar. No frozen proof was changed. + +The C24 component proof requires complete complex-linear blocks at a +common complex frame. Individual real-component ADDs need not preserve +that frame. The native checker checks block matrices and boundaries and +excludes native or map events inside them. The signed words have real +scalar coefficients at their required common frames. The inverse-adjoint +keeps each exact unitary native operator in its chronological position. +The checks bind its global phase, field, and adapters. + +The general signed-family proof works for every `k=2^r`, including k=1. +The displayed Walsh contrasts and the three remaining rows give the +diagonal Gram with dyadic-unit entries. The literal six-instruction middle +word gives the stated basis. The two extra butterflies give the prices +86, 96, and `10kr+76+4r` in the three stated cases. The finite checks through +k=64 are controls for this proof, not its all-size justification. The +package correctly says that the bridge review supplied the basis and then +checked the root's word and price. It does not call that a second +independent proof of the same basis. General native row placement remains +open. + +The rational comparison uses the first actual C16 packing. Its separate +odd scans stay in the invoice. The complete words cost 5702 dyadic real +primitives plus sixteen multiplication-by-three and sixteen +division-by-three real scans in each direction. The exhaustive quartet +test accepts 729 of 6561 residue inputs in each direction. The prefix +conditions depend only on these residues, which justifies the exact +Gaussian-dyadic division domain. + +The direct matrix calculation gives `trace(C16)=(11+7i)/6`. The trace of +`3C16` modulo three is `1+2i`, which is nonzero. Thus its residue is not +nilpotent, and every positive power has a nonzero residue. Together with +the entrywise upper bound, this proves `h3(C16^m)=m`. The adjoint proof is +the conjugate argument. The complete residue has Gaussian rank four, not +one. Rank one applies to a single quartet numerator. The matched inverse +word retraces the forward word, so the matched pair has prefix odd height +one. This does not bound unmatched repeated calls. The root-grid method +still requires a dyadic endpoint on every completed recursive child's +roles. All 96 ordinary C16 diagonals are nonzero, so this scalar packing +does not have the current C24 native realization. + +## Costs and unresolved composition work + +The replay derives the local invoices from the literal words. C24 costs +16020 real scalar primitives. The signed C, Cbar, and transpose-interface +raw words cost 9988, 10068, and 10324. Their metric-selected duals cost +11252, 11284, and 11156. The Q-entry native rank mass is 1792. The I-entry +mass is 1816 for C24 and 1808 for each signed or transpose interface. The +side-map counts are upper bounds, not finite map execution prices. + +The package supplies no complete routed caller, saved-record restoration, +terminal decoder, recursive helper host, complete precision bound, or +complete supplier cost. The local auxiliary identity is not a recursive +hosting proof. No complete kappa improvement follows. The refreshed +selected record at main `b58ad9ef4d4e861b0eaa5dba41742bdc072dca51` names +PR #4470 and `60403/20000000`. The final provenance file explicitly marks +the reviewed words as historical local constructions and does not apply +them to that selected construction. + +## Portability, controls, and credit + +The signed-checker adaptation changes only its source-directory binding +and its absolute source-path resolution. The reviewed diff preserves all +arithmetic, original payload pins, endpoint checks, phase checks, invoices, +and negative controls. The cold run's file-access records stay within the +copied package, check output, or Python runtime. The control that tries to +read outside those paths fails at the stated check in both modes. The +explicit false-requirement control also fails in both modes. No Python +file read by the checks contains an `assert` statement that optimization +could remove. Some files are read only to verify their hashes; this is not +a claim that every read file was imported. The audit hook is a +reproducibility check, not a security sandbox. + +The reviewer checked all 185 immutable inputs against their original +campaign bytes. The retained odd-grid source, Apache license, and upstream +NOTICE match the pinned local Git objects at `bce54fb3`. The source notice +credits icekylinx for the stopped product-ring and grid work. The final +package states that credit next to the retained source. + +The refreshed PR #3133 README and retained credit record name dcharb78 for +the coupled folds. The PR #3148 README names Jeremy Diviney for its +packing exchange, integration, and verification. The PR #2588 notice +separates Cinna Davis's dirty-borrowing method, Rohan Arun's new package +work, Jeremy Kothe's retained methods, and the earlier lineage. The review +checked those refreshed source hashes against the retained immutable +GitHub readback records. It did not infer authorship from a PR submitter +account or attribute every inherited compiler file to one person. + +The review did not rerun the archived producer emitters, all historical +predecessor suites, the selected frontier, a complete recursive supplier, +or a Lean formalization. It did not repeat the old spatial interpreter for +unchanged signed phase records. Final GitHub link and rendering checks +remain with the publication coordinator. 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No kappa claim." +} diff --git a/research/publication-reviews/centre-metric-encoders/REVIEWED-README.md b/research/publication-reviews/centre-metric-encoders/REVIEWED-README.md new file mode 100644 index 0000000000..464c33db9e --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/REVIEWED-README.md @@ -0,0 +1,158 @@ +# Centre codes with unitary, signed, and rational metrics + +This package proves a sharp 24-coordinate bound for the original sixteen +readers in the Gaussian-dyadic unitary model. It gives an actual code and +complete local native words that attain 24. A different reciprocal reader +has a signed-metric code with sixteen coordinates. Thirty complete local +native words implement this code, its paid pair companion, and a separate +transpose interface. A general dyadic scalar construction and a rational-unitary +sixteen-coordinate comparison explain the representation limits. + +These results do not improve the complete kappa calculation. No complete +routed caller, terminal decoder, recursive host, finite map cost, or full +precision bound is supplied. Native rank mass is a local invoice. It is not +a multiplication exponent. + +Read the [proof and review index](PROOFS.md), the [source record](PROVENANCE.md), +and the [fresh replay receipt](evidence/REPLAY.json). + +## The two reader families + +| Reader | Euclidean Gram | Representation result | +| --- | --- | --- | +| Original sixteen rows V | diag(12 I8, 8 I8) | A Gaussian-dyadic unitary code needs at least 24 complex coordinates. The actual C24 attains 24. | +| Reciprocal sixteen rows L | diag(10 I8, 7 I8) | A Euclidean-unitary code also needs at least 24 coordinates, by reduction modulo five or seven. A signed-metric code uses sixteen. | + +For L, the signed Gram is diag(4 I8, 2 I8). The signed code stores the +rank-sixteen difference E-P. The difference E-I has rank thirty-two. +The physical P is a code on 32 ports, with 160 nonzero entries. It costs +728 real scalar primitives before address-view costs. + +The original-reader bound also covers arbitrary borrowed inputs, +nonlinear recovery, and unitary mixing of spatial and owner coordinates. +For arrays of N complex entries, the bound is 24N complex coordinates. +It counts capacity, not names of registers with unrestricted size. +A dyadic-unit output frame and a dyadic orthogonal input frame preserve +the bound. Promised zero inputs, approximate recovery, and general +nonunitary encodings are outside this theorem. + +## Exact local words and costs + +The standalone C24 code and its adjoint each cost 8052 real scalar +primitives. All eight complete native C24 services cost 16020. A complete +real-component block is treated as one complex-linear frame operation. +An individual component ADD need not preserve that frame. + +For the reciprocal readers, C K C^T=G and C^-T=G^-1 C K. The complete +dual conversion includes metric scales on both arbitrary input banks. +The original C transpose violates 32 ordinary support rows. A paid +80-scalar suffix gives the companion Cbar and repairs that support. +Cbar changes the selected coordinates. Recovery of the individual L rows +requires the paid selected-pair code. Only C and Cbar carry L in the sixteen +selected coordinates. Cbar transpose supplies a companion native interface; +its sixteen selected outputs do not decode L. +The raw selected dual of the Cbar-transpose service uses Cbar inverse. +Its metric-converted dual uses Cbar transpose. + +| Code | Forward or raw dual scalar cost | Metric-selected dual scalar cost | +| --- | ---: | ---: | +| C24 | 16020 | Not needed | +| Signed C | 9988 | 11252 | +| Signed Cbar | 10068 | 11284 | +| Cbar transpose interface | 10324 | 11156 | + +| Service | Q-entry profile | Q-entry mass | I-entry change | I-entry mass | +| --- | --- | ---: | --- | ---: | +| C24 | 1328 H1 + 64 H2 + 48 H3 + 24 H8 | 1792 | Replace 24 H8 by 24 H9 | 1816 | +| Signed code or transpose interface | 1392 H1 + 64 H2 + 48 H3 + 16 H8 | 1792 | Replace 16 H8 by 16 H9 | 1808 | + +All duals use the Q-entry profile. Each word acts on 640 arbitrary complex +inputs and preserves the 416 auxiliary roles. The words add no field, +private buffer, CLEAR, or odd division. The signed words have no new +spatial operator; every inherited phase and adapter is bound to its source. +The C24 check also replays eight distinct fresh H8 operators on all 512 +spatial columns. Neither result supplies a recursive helper host. + +## General signed family + +For every k=2^r and n=k+4, the scalar construction gives one centre output +and its metric-orthogonal complement. Its metric and inverse are dyadic. +The exact price in either direction is 86 for r=0, 96 for r=1, and +10kr+76+4r for r at least two. The instruction count is 3kr/2+12. + +The proof applies to all r. The checks for k=1,2,4,8,16,32,64 are exact +finite controls. The basis was supplied by the bridge-review lane and +checked by the root lane. The later bridge review checks the root's +word and cost. It is not a second independent proof of its own basis. +No general native row placement is claimed. + +## Rational sixteen-coordinate comparison + +The first rational unitary C16 packs the original V into sixteen +coordinates. Each complete scalar direction costs 5702 dyadic scalar +primitives, plus sixteen real multiplication-by-three scans and sixteen +real division-by-three scans. Odd scans remain separately priced. +One direction needs ternary height one and local binary height two. +Its complete word must remain contiguous at a common complex frame. + +For every positive integer m, h3(C16^m)=h3((C16*)^m)=m. This is a proved +all-power result. The nonzero trace of 3C16 modulo three prevents its +residue matrix from being nilpotent. A fixed dyadic-unit change of basis +or tensoring with an identity preserves the growth. A matched C16 then +C16* pair has prefix odd height one because the inverse word retraces +the first word. This does not give a uniform guard for unmatched calls. + +The exact quartet division domain is a congruence modulo three. The +check enumerates all 6561 residue inputs in each direction and accepts +729. The retained root-grid theorem requires a dyadic endpoint on every +role for each completed recursive child. C16 itself has no such endpoint. +All 96 ordinary diagonals of this C16 are nonzero, so this scalar packing +does not have the native realization used by C24. The later supported +packing extension is outside this package. + +## Reproduction + +Use Python 3.11 or later. No third-party library or network access is needed. +Run from this directory with a new output directory: + +```sh +python3 -I -B replay.py --output /tmp/centre-metric-encoders-replay +``` + +Expected final output: + +```text +PASS_CENTRE_METRIC_ENCODERS +``` + +The runner executes seven checks in normal and optimized Python, in +sequence. It compares each result with the frozen receipt and compares +both Python modes. It checks every immutable source hash before and +after the run. For compressed inputs it checks the decompressed payload +as well as the retained source bytes. It confines each check's file +access to this package, its output directory, and the Python runtime. +The command does not run the archived producer emitters or regenerate +their compressed containers. + +The negative controls reject damaged scalar words, wrong metric signs, +omitted target-bank metric scales, wrong dual chronology, wrong global +phases, and an insufficient rational division domain. The review files +state which controls belong to each result. No selected-frontier replay, +Lean formalization, or full recursive supplier check was run. + +## Open next questions + +A complete signed-code caller must supply route access, saved-record +restoration, and a paid terminal. Start with the explicit local input and +output maps in the signed native review. A count of selected coordinates +does not provide those operations. + +A recursive rational boundary type must control whole-state prefixes and +prove decoded child-entry types. Start with the matched C16/C16* case. +The all-power theorem blocks a constant ternary guard for unmatched +repetitions of this fixed C16. It makes no claim about products of +different stage codes. + +A general signed-family native construction needs physical row placement +and admissible support for every n=4+2^r. Start with the actual n=6 and n=8 +codes. 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"34f22e5e44090cc80bb4476b5daa5df0223a4f3e92720d8bb0140c830740986e", + "frozen/root/UNITARY-FOOTPRINT-ARRAY-ADDENDUM-20261020.md": "fd3028f070d18291694d4faf629ea6165adaaf72ac6e6721e653473348ec548f", + "frozen/root/UNITARY-FOOTPRINT-FREEZE-20261020.json": "9ec2cb0f38210cf95246991f9637c036c7e5489cfc9ad78b7075213d9ca3ba75", + "frozen/root/check_signed_metric_family.py": "9daacf3e3f5683477235824a18afb92b09aad42c5ac297862aa1d2c7c5dea9fa", + "frozen/root/check_unitary_completion_review.py": "b7b81142cb1780fc83c035f5f60e352ffcf080dd6c56527c2d5f29ed5bff40be", + "frozen/root/signed-metric-family-normal.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37", + "frozen/root/signed-metric-family-optimized.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37", + "notices/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "notices/ODD-GRID-SOURCE-PINS.json": "48886903f9d95d403dec50143b329d1bbcd48f44528bbaaa561bb82fc96e09f5", + "portable/check_signed_clean.py": "ec0fc10da3570981191420255c1bb30c2f26bfdb638137ae7077006f123f02ca", + "replay.py": "b75eb0f615c31b93130f0dcd986b794137ee3d9ded8cb9e8f6d237340ee87bb6" +} diff --git a/research/publication-reviews/centre-metric-encoders/check_package.py b/research/publication-reviews/centre-metric-encoders/check_package.py new file mode 100644 index 0000000000..1be2e6aa44 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/check_package.py @@ -0,0 +1,108 @@ +"""Check package bytes, retained sources, and replay failure controls.""" + +import ast +import hashlib +import json +from pathlib import Path +import subprocess +import sys + + +HERE = Path(__file__).resolve().parent +BASE = HERE.parents[1] +PACKAGE = BASE / "packages/centre-metric-encoders" +CAMPAIGN = BASE.parent + + +def need(value, message): + if not value: + raise ValueError(message) + + +def digest(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def main(): + manifest = json.loads((PACKAGE / "PACKAGE-MANIFEST.json").read_text()) + for item in manifest["files"]: + path = PACKAGE / item["path"] + need(path.stat().st_size == item["bytes"] and digest(path) == item["sha256"], + "Package manifest: " + item["path"]) + source_manifest = json.loads((PACKAGE / "SOURCE-MANIFEST.json").read_text()) + for item in source_manifest["immutable_inputs"]: + source = CAMPAIGN / item["source_campaign_path"] + target = PACKAGE / item["path"] + need(source.read_bytes() == target.read_bytes(), "Original source: " + item["path"]) + cold = HERE / "cold/package" + for relative in ("replay.py", "portable/check_signed_clean.py", "SOURCE-MANIFEST.json"): + need((cold / relative).read_bytes() == (PACKAGE / relative).read_bytes(), + "Cold checked code is final: " + relative) + read_paths = set() + for path in (HERE / "cold/replay").glob("*/*/FILE-ACCESS.json"): + read_paths.update(json.loads(path.read_text())) + assertions = {} + for relative in sorted(read_paths): + if relative.endswith(".py"): + tree = ast.parse((cold / relative).read_text()) + assertions[relative] = sum(isinstance(node, ast.Assert) for node in ast.walk(tree)) + need(not any(assertions.values()), "No checked Python file loses assertions under optimization") + + source_checks = [] + for item in json.loads((PACKAGE / "evidence/SOURCE-LICENSE-CHECK.json").read_text())["checks"]: + raw = subprocess.check_output(["git", "show", item["source_commit"] + ":" + item["source_path"]], cwd=CAMPAIGN) + need(raw == (PACKAGE / item["retained_path"]).read_bytes(), "Pinned Git source: " + item["source_path"]) + source_checks.append({"source_path": item["source_path"], "sha256": hashlib.sha256(raw).hexdigest(), "equal": True}) + native_sources = json.loads((PACKAGE / "evidence/NATIVE-SOURCE-VERIFICATION.json").read_text()) + native_credit_checks = [] + for label in ("PR3133-README", "PR3148-README", "PR2588-README"): + item = next(record for record in native_sources["files"] if record["label"] == label) + path = BASE / "refresh" / (label + ".md") + need(digest(path) == item["sha256"], "Refreshed credit source: " + label) + native_credit_checks.append({"label": label, "sha256": digest(path), "url": item["url"]}) + for name, expected in (("PR3133-NOTICE", "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661"), + ("PR3133-CREDITS.md", "1d9d8f56d8899f55878e4cb2c4e052b22506444016a51c2e678773505f5189e6"), + ("PR2588-NOTICE", "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b")): + need(digest(PACKAGE / "notices" / name) == expected, "Retained native notice: " + name) + + context = json.loads((PACKAGE / "evidence/SELECTED-CONTEXT.json").read_text()) + selected = BASE / "refresh/main/certificates/selected-result.json" + need(digest(selected) == context["selected_record_sha256"], "Current selected record pin") + need(json.loads(selected.read_text()) == context["selected_record"], "Current selected record bytes") + + controls = [] + directory = HERE / "failure-controls" + directory.mkdir(exist_ok=True) + forbidden = directory / "outside.txt" + forbidden.write_text("This file is outside each worker output directory.\n") + for mode in ("normal", "optimized"): + for control in ("false_requirement", "outside_read"): + target = directory / (mode + "-" + control) + target.mkdir(exist_ok=True) + probe = target / "probe.py" + if control == "false_requirement": + probe.write_text("import runpy\nmodule = runpy.run_path(" + repr(str(cold / "replay.py")) + ")\nmodule['require'](False, 'EXPECTED_FALSE_REQUIREMENT_REJECTION')\n") + expected = "EXPECTED_FALSE_REQUIREMENT_REJECTION" + else: + probe.write_text("from pathlib import Path\nPath(" + repr(str(forbidden)) + ").read_bytes()\n") + expected = "File access outside the package, output, or Python runtime: " + str(forbidden) + command = [sys.executable, "-I", "-B"] + (["-O"] if mode == "optimized" else []) + command += [str(cold / "replay.py"), "--worker", str(probe), str(target)] + result = subprocess.run(command, capture_output=True, text=True) + (target / "output.log").write_text(result.stdout + result.stderr) + need(result.returncode != 0 and expected in result.stderr, "Failure control: " + control + "/" + mode) + controls.append({"mode": mode, "control": control, "exit_code": result.returncode, "rejected_at_expected_check": True}) + + report = {"status": "PASS_ENCODER_PACKAGE_CHECKS", "package_manifest_sha256": digest(PACKAGE / "PACKAGE-MANIFEST.json"), + "package_files": len(manifest["files"]), "immutable_sources_equal_original": len(source_manifest["immutable_inputs"]), + "cold_code_equal_final": True, "retained_git_sources": source_checks, + "native_credit_source_checks": native_credit_checks, + "current_selected_record_equal": True, "python_files_read_assertion_counts": assertions, + "failure_controls": controls, + "scope": "The file list includes hash reads, not only executed imports. The file-access hook is a reproducibility check, not a security sandbox."} + (HERE / "PACKAGE-CHECKS.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + print(report["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/publication-reviews/centre-metric-encoders/cold/replay/REPLAY.json b/research/publication-reviews/centre-metric-encoders/cold/replay/REPLAY.json new file mode 100644 index 0000000000..663683d5bc --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/cold/replay/REPLAY.json @@ -0,0 +1,146 @@ +{ + "checks": [ + { + "check": "unitary_footprint", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result.json": "28db16426c29a8c5268bedfdde0e207c98db429d463b3e8a00ca1f8fdc5dfe08" + }, + "seconds": 6.945 + }, + { + "check": "unitary_footprint", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result.json": "28db16426c29a8c5268bedfdde0e207c98db429d463b3e8a00ca1f8fdc5dfe08" + }, + "seconds": 5.368 + }, + { + "check": "unitary_native", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/INPUTS.json": "2462a323f974b2417108a47aebc93974a8f2c94511252d67e47cb0debf0f6c11", + "result/REVIEW.json": "67fff6260e4ba02fc12322b31e3325de98f25ac52d35d29a6f53806677bca3bd" + }, + "seconds": 11.598 + }, + { + "check": "unitary_native", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/INPUTS.json": "2462a323f974b2417108a47aebc93974a8f2c94511252d67e47cb0debf0f6c11", + "result/REVIEW.json": "67fff6260e4ba02fc12322b31e3325de98f25ac52d35d29a6f53806677bca3bd" + }, + "seconds": 9.506 + }, + { + "check": "signed_metric", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/REVIEW-CHECKS.json": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b" + }, + "seconds": 4.068 + }, + { + "check": "signed_metric", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/REVIEW-CHECKS.json": "04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b" + }, + "seconds": 3.821 + }, + { + "check": "signed_native", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/INPUTS.json": "fa827c1a46d2f72325099cf1111a1a0d0aa65746baaee41b24588fa789a98797", + "result/REVIEW.json": "367b51faa030b534e2c547587a09d1ef30b8cc3cd05e5fd6283c62954b1a85c7" + }, + "seconds": 3.454 + }, + { + "check": "signed_native", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/INPUTS.json": "fa827c1a46d2f72325099cf1111a1a0d0aa65746baaee41b24588fa789a98797", + "result/REVIEW.json": "367b51faa030b534e2c547587a09d1ef30b8cc3cd05e5fd6283c62954b1a85c7" + }, + "seconds": 7.218 + }, + { + "check": "signed_family", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37" + }, + "seconds": 3.865 + }, + { + "check": "signed_family", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result.json": "3a4e4e27835be8431a68051e9c58a64cb22ec53e89beaac6f58fba4a945a0d37" + }, + "seconds": 3.699 + }, + { + "check": "signed_family_review", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result.json": "bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba" + }, + "seconds": 3.376 + }, + { + "check": "signed_family_review", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result.json": "bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba" + }, + "seconds": 4.305 + }, + { + "check": "rational_grid", + "file_access_confined": true, + "mode": "normal", + "receipts_equal_frozen": { + "result/INPUTS.json": "5231e3f636b2e35456af9fb020950f3570f45daec9db9cd3fc88c2cb2ce8be23", + "result/REVIEW.json": "d929f05a9ad601007b046602ecd52ba4b2709fe8315e325475817eb9ece1c6d7" + }, + "seconds": 3.54 + }, + { + "check": "rational_grid", + "file_access_confined": true, + "mode": "optimized", + "receipts_equal_frozen": { + "result/INPUTS.json": "5231e3f636b2e35456af9fb020950f3570f45daec9db9cd3fc88c2cb2ce8be23", + "result/REVIEW.json": "d929f05a9ad601007b046602ecd52ba4b2709fe8315e325475817eb9ece1c6d7" + }, + "seconds": 3.29 + } + ], + "frozen_sources_unchanged": true, + "immutable_inputs": 185, + "normal_optimized_equal": true, + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "portable_signed_checker_sha256": "ec0fc10da3570981191420255c1bb30c2f26bfdb638137ae7077006f123f02ca", + "python": "3.14.7", + "replay_sha256": "b75eb0f615c31b93130f0dcd986b794137ee3d9ded8cb9e8f6d237340ee87bb6", + "scope": "Exact local proofs, matrices, scalar words, native words, phases, invoices, and grid checks. No recursive supplier or kappa claim.", + "source_manifest_sha256": "71c42b6191c8f2fc6afdc3c79357352372a3d1911b79ef8a41130c0ef7a25b9e", + "status": "PASS_CENTRE_METRIC_ENCODERS" +} diff --git a/research/publication-reviews/centre-metric-encoders/direct_check.py b/research/publication-reviews/centre-metric-encoders/direct_check.py new file mode 100644 index 0000000000..1f2a6b9794 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/direct_check.py @@ -0,0 +1,180 @@ +"""Check the main matrix claims with a separate exact engine.""" + +import argparse +from fractions import Fraction as F +import gzip +import hashlib +import json +from pathlib import Path + + +def need(value, message): + if not value: + raise ValueError(message) + + +def add(a, b): + return a[0] + b[0], a[1] + b[1] + + +def mul(a, b): + return a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0] + + +ZERO = (F(0), F(0)) +ONE = (F(1), F(0)) + + +def rows(raw): + return [{int(j): tuple(map(F, value)) if isinstance(value, list) else (F(value), F(0)) + for j, value in row.items()} for row in raw] + + +def star(a, size): + out = [{} for _ in range(size)] + for i, row in enumerate(a): + for j, (x, y) in row.items(): + out[j][i] = (x, -y) + return out + + +def product(a, b): + out = [] + for row in a: + result = {} + for j, x in row.items(): + for k, y in b[j].items(): + value = add(result.get(k, ZERO), mul(x, y)) + if value == ZERO: + result.pop(k, None) + else: + result[k] = value + out.append(result) + return out + + +def realify(a): + out = [{} for _ in range(2 * len(a))] + for i, row in enumerate(a): + for j, (x, y) in row.items(): + for target, source, value in ((2*i, 2*j, x), (2*i, 2*j+1, -y), + (2*i+1, 2*j, y), (2*i+1, 2*j+1, x)): + if value: + out[target][source] = value + return out + + +def rank_mod(a, prime): + pivots = {} + for raw in a: + row = {j: value.numerator * pow(value.denominator, -1, prime) % prime + for j, value in raw.items()} + row = {j: value for j, value in row.items() if value} + while row: + j = min(row) + value = row[j] + if j not in pivots: + inverse = pow(value, -1, prime) + pivots[j] = {k: v * inverse % prime for k, v in row.items()} + break + for k, v in pivots[j].items(): + new = (row.get(k, 0) - value*v) % prime + if new: + row[k] = new + else: + row.pop(k, None) + return len(pivots) + + +def diagonal(values): + return [{i: (F(value), F(0))} for i, value in enumerate(values)] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--package", type=Path, required=True) + parser.add_argument("--output", type=Path, required=True) + args = parser.parse_args() + frozen = args.package / "frozen" + pins = {} + + def read(relative): + raw = (frozen / relative).read_bytes() + pins[relative] = hashlib.sha256(raw).hexdigest() + return json.loads(gzip.decompress(raw)) + + c24 = read("lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/twenty-four-v2-normal/UNITARY-24.json.gz") + response = read("lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz") + rational = read("lanes/independent-review-20261017/odd-unitary-packing-20261020/run-normal/PACKING.json.gz") + companion = read("lanes/new-core-transfer-20261017/low-displacement-20261020/signed-sixteen-20261020/paired-normal/PAIRED-SIGNED-SIXTEEN.json.gz") + v = rows(c24["original_centre_readers"]) + vg = product(v, star(v, 112)) + need(vg == diagonal([12]*8 + [8]*8), "Original reader Gram") + need((rank_mod(realify(v), 3), rank_mod(realify(vg), 3)) == (32, 16), + "Original reader and Gram ranks") + code = rows(c24["code"]) + cs = star(code, 112) + need(product(code, cs) == product(cs, code) == diagonal([1]*112), "C24 is unitary") + decoder = product(v, cs) + need(len({j for row in decoder for j in row}) == 24, "C24 uses 24 coordinates") + need(product(decoder, code) == v, "C24 recovers the original reader") + + ell = rows(response["reflection_L"]) + lg = product(ell, star(ell, 112)) + need(lg == diagonal([10]*8 + [7]*8), "Reciprocal reader Euclidean Gram") + modular = {str(p): [rank_mod(realify(ell), p), rank_mod(realify(lg), p)] for p in (3, 5, 7)} + need(modular == {"3": [32, 32], "5": [32, 16], "7": [32, 16]}, "Reciprocal modular ranks") + k = rows(response["physical"]["inverse_J"]) + need(product(product(ell, k), star(ell, 112)) == diagonal([4]*8 + [2]*8), + "Reciprocal weighted Gram") + physical_p = rows(response["physical"]["P"]) + need(sum(len(row) for row in physical_p) == 160, "Physical P has 160 nonzero entries") + need(sum(row != {i: ONE} for i, row in enumerate(physical_p)) == 32, + "Physical P changes 32 ports") + companion_decoder = product(ell, rows(companion["inverse"])) + transpose_decoder = product(ell, rows(companion["inverse_transpose"])) + companion_support = {j for row in companion_decoder for j in row} + transpose_support = {j for row in transpose_decoder for j in row} + need(companion_support == set(companion["centre_ports"]), "Cbar recovers L from its 16 selected outputs") + need(len(transpose_support) == 96 and not transpose_support <= set(companion["centre_ports"]), + "Cbar transpose is a companion interface, not a 16-coordinate L code") + need(product(transpose_decoder, rows(companion["transpose"])) == ell, + "The full transpose decoder is the unique exact L decoder") + + c16 = rows(rational["code"]) + c16star = star(c16, 112) + need(product(c16, c16star) == product(c16star, c16) == diagonal([1]*112), "C16 is unitary") + trace = ZERO + for i, row in enumerate(c16): + trace = add(trace, row.get(i, ZERO)) + need(trace == (F(11, 6), F(7, 6)), "Complete C16 trace") + trace_residue = [(3*x).numerator * pow((3*x).denominator, -1, 3) % 3 for x in trace] + need(trace_residue == [1, 2], "Nonzero residue trace proves non-nilpotence") + residue = [{j: (3*a, 3*b) for j, (a, b) in row.items()} for row in c16] + need(rank_mod(realify(residue), 3) == 8, "Complete residue has Gaussian rank four") + decoder16 = product(v, c16star) + need(len({j for row in decoder16 for j in row}) == 16, "Rational C16 uses 16 coordinates") + need(product(decoder16, c16) == v, "C16 recovers the original reader") + ordinary = rational["ordinary_ports"] + need(len(ordinary) == 96 and all(c16[i].get(i, ZERO) != ZERO for i in ordinary), + "All 96 ordinary C16 diagonals are nonzero") + + result = {"status": "PASS_DIRECT_ENCODER_MATRIX_CHECKS", "producer_imports": 0, + "original_real_ranks_mod3": [32, 16], "original_complex_bound": 24, + "reciprocal_real_ranks": modular, "reciprocal_complex_bound_mod5_or_mod7": 24, + "original_gram": [12]*8 + [8]*8, "reciprocal_gram": [10]*8 + [7]*8, + "reciprocal_weighted_gram": [4]*8 + [2]*8, + "physical_P_changed_ports": 32, "physical_P_nonzero_entries": 160, + "Cbar_L_decoder_support": len(companion_support), + "Cbar_transpose_L_decoder_support": len(transpose_support), + "C24_selected_support": 24, "C16_selected_support": 16, + "C16_trace": list(map(str, trace)), "C16_scaled_trace_mod3": trace_residue, + "C16_residue_real_rank_mod3": 8, "C16_nonzero_ordinary_diagonals": 96, + "input_sha256": pins, + "scope": "Independent exact matrix checks. The proof of all-power height uses the nonzero residue trace. No native or recursive theorem is inferred from these calculations."} + args.output.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/publication-reviews/centre-metric-encoders/failure-controls/normal-false_requirement/probe.py b/research/publication-reviews/centre-metric-encoders/failure-controls/normal-false_requirement/probe.py new file mode 100644 index 0000000000..37caf8298f --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/failure-controls/normal-false_requirement/probe.py @@ -0,0 +1,3 @@ +import runpy +module = runpy.run_path('/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/cold/package/replay.py') +module['require'](False, 'EXPECTED_FALSE_REQUIREMENT_REJECTION') diff --git a/research/publication-reviews/centre-metric-encoders/failure-controls/normal-outside_read/probe.py b/research/publication-reviews/centre-metric-encoders/failure-controls/normal-outside_read/probe.py new file mode 100644 index 0000000000..9beadb9631 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/failure-controls/normal-outside_read/probe.py @@ -0,0 +1,2 @@ +from pathlib import Path +Path('/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/failure-controls/outside.txt').read_bytes() diff --git a/research/publication-reviews/centre-metric-encoders/failure-controls/optimized-false_requirement/probe.py b/research/publication-reviews/centre-metric-encoders/failure-controls/optimized-false_requirement/probe.py new file mode 100644 index 0000000000..37caf8298f --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/failure-controls/optimized-false_requirement/probe.py @@ -0,0 +1,3 @@ +import runpy +module = runpy.run_path('/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/cold/package/replay.py') +module['require'](False, 'EXPECTED_FALSE_REQUIREMENT_REJECTION') diff --git a/research/publication-reviews/centre-metric-encoders/failure-controls/optimized-outside_read/probe.py b/research/publication-reviews/centre-metric-encoders/failure-controls/optimized-outside_read/probe.py new file mode 100644 index 0000000000..9beadb9631 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/failure-controls/optimized-outside_read/probe.py @@ -0,0 +1,2 @@ +from pathlib import Path +Path('/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/publication-wrap-20261022/reviews/centre-metric-encoders/failure-controls/outside.txt').read_bytes() diff --git a/research/publication-reviews/centre-metric-encoders/failure-controls/outside.txt b/research/publication-reviews/centre-metric-encoders/failure-controls/outside.txt new file mode 100644 index 0000000000..f8e4d65ff5 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/failure-controls/outside.txt @@ -0,0 +1 @@ +This file is outside each worker output directory. From b051312d7dbd9093b7e8d82e1f009a4764fd61a7 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 12:56:05 -0500 Subject: [PATCH 2/3] Include retained replay logs and complete source credit context --- .../replay/rational_grid/normal/stdout.log | 1 + .../replay/rational_grid/optimized/stdout.log | 1 + .../replay/signed_family/normal/stdout.log | 0 .../replay/signed_family/optimized/stdout.log | 0 .../signed_family_review/normal/stdout.log | 2 + .../signed_family_review/optimized/stdout.log | 2 + .../replay/signed_metric/normal/stdout.log | 2 + .../replay/signed_metric/optimized/stdout.log | 2 + .../replay/signed_native/normal/stdout.log | 7 +++ .../replay/signed_native/optimized/stdout.log | 7 +++ .../unitary_footprint/normal/stdout.log | 1 + .../unitary_footprint/optimized/stdout.log | 1 + .../replay/unitary_native/normal/stdout.log | 1 + .../unitary_native/optimized/stdout.log | 1 + .../additional-notices/CREDIT-ADDENDUM.md | 25 ++++++++ .../additional-notices/GITHUB-READBACK.json | 63 +++++++++++++++++++ .../additional-notices/NOTICE-PR2226.md | 21 +++++++ .../additional-notices/PR2226-NOTICE.md | 22 +++++++ 18 files changed, 159 insertions(+) create mode 100644 research/centre-metric-encoders/evidence/replay/rational_grid/normal/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/rational_grid/optimized/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_family/normal/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_family/optimized/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_family_review/normal/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_family_review/optimized/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_metric/normal/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_metric/optimized/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_native/normal/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/signed_native/optimized/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/unitary_footprint/normal/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/unitary_footprint/optimized/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/unitary_native/normal/stdout.log create mode 100644 research/centre-metric-encoders/evidence/replay/unitary_native/optimized/stdout.log create mode 100644 research/publication-reviews/centre-metric-encoders/additional-notices/CREDIT-ADDENDUM.md create mode 100644 research/publication-reviews/centre-metric-encoders/additional-notices/GITHUB-READBACK.json create mode 100644 research/publication-reviews/centre-metric-encoders/additional-notices/NOTICE-PR2226.md create mode 100644 research/publication-reviews/centre-metric-encoders/additional-notices/PR2226-NOTICE.md diff --git a/research/centre-metric-encoders/evidence/replay/rational_grid/normal/stdout.log b/research/centre-metric-encoders/evidence/replay/rational_grid/normal/stdout.log new file mode 100644 index 0000000000..d05136917e --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/rational_grid/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_RATIONAL_PACKING_GRID diff --git a/research/centre-metric-encoders/evidence/replay/rational_grid/optimized/stdout.log b/research/centre-metric-encoders/evidence/replay/rational_grid/optimized/stdout.log new file mode 100644 index 0000000000..d05136917e --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/rational_grid/optimized/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_RATIONAL_PACKING_GRID diff --git a/research/centre-metric-encoders/evidence/replay/signed_family/normal/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_family/normal/stdout.log new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/centre-metric-encoders/evidence/replay/signed_family/optimized/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_family/optimized/stdout.log new file mode 100644 index 0000000000..e69de29bb2 diff --git a/research/centre-metric-encoders/evidence/replay/signed_family_review/normal/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_family_review/normal/stdout.log new file mode 100644 index 0000000000..68f684dc94 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/signed_family_review/normal/stdout.log @@ -0,0 +1,2 @@ +PASS_SIGNED_FAMILY_WORD_AND_METRIC_CLASSIFICATION +bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba diff --git a/research/centre-metric-encoders/evidence/replay/signed_family_review/optimized/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_family_review/optimized/stdout.log new file mode 100644 index 0000000000..68f684dc94 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/signed_family_review/optimized/stdout.log @@ -0,0 +1,2 @@ +PASS_SIGNED_FAMILY_WORD_AND_METRIC_CLASSIFICATION +bc4d9ba03b351b375a314660569eaf659cd761cbf67ac5089d7bc720308c5eba diff --git a/research/centre-metric-encoders/evidence/replay/signed_metric/normal/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_metric/normal/stdout.log new file mode 100644 index 0000000000..673fa5f6b1 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/signed_metric/normal/stdout.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_SIGNED_METRIC_AND_SIXTEEN_CENTRES +04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b diff --git a/research/centre-metric-encoders/evidence/replay/signed_metric/optimized/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_metric/optimized/stdout.log new file mode 100644 index 0000000000..673fa5f6b1 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/signed_metric/optimized/stdout.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_SIGNED_METRIC_AND_SIXTEEN_CENTRES +04ceefeca93516dd77fec30ac2b4324b33c3ba531da5c1e9397515175738466b diff --git a/research/centre-metric-encoders/evidence/replay/signed_native/normal/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_native/normal/stdout.log new file mode 100644 index 0000000000..7c811da534 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/signed_native/normal/stdout.log @@ -0,0 +1,7 @@ +PASS individual base +PASS individual extra +PASS paired base +PASS paired extra +PASS paired_transpose base +PASS paired_transpose extra +PASS_INDEPENDENT_SIGNED_SIXTEEN_NATIVE diff --git a/research/centre-metric-encoders/evidence/replay/signed_native/optimized/stdout.log b/research/centre-metric-encoders/evidence/replay/signed_native/optimized/stdout.log new file mode 100644 index 0000000000..7c811da534 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/signed_native/optimized/stdout.log @@ -0,0 +1,7 @@ +PASS individual base +PASS individual extra +PASS paired base +PASS paired extra +PASS paired_transpose base +PASS paired_transpose extra +PASS_INDEPENDENT_SIGNED_SIXTEEN_NATIVE diff --git a/research/centre-metric-encoders/evidence/replay/unitary_footprint/normal/stdout.log b/research/centre-metric-encoders/evidence/replay/unitary_footprint/normal/stdout.log new file mode 100644 index 0000000000..fb02ea58b0 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/unitary_footprint/normal/stdout.log @@ -0,0 +1 @@ +PASS_UNITARY_FOOTPRINT_AND_24_CODE_REVIEW diff --git a/research/centre-metric-encoders/evidence/replay/unitary_footprint/optimized/stdout.log b/research/centre-metric-encoders/evidence/replay/unitary_footprint/optimized/stdout.log new file mode 100644 index 0000000000..fb02ea58b0 --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/unitary_footprint/optimized/stdout.log @@ -0,0 +1 @@ +PASS_UNITARY_FOOTPRINT_AND_24_CODE_REVIEW diff --git a/research/centre-metric-encoders/evidence/replay/unitary_native/normal/stdout.log b/research/centre-metric-encoders/evidence/replay/unitary_native/normal/stdout.log new file mode 100644 index 0000000000..93266a965d --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/unitary_native/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_UNITARY_24_CLEAN_NATIVE diff --git a/research/centre-metric-encoders/evidence/replay/unitary_native/optimized/stdout.log b/research/centre-metric-encoders/evidence/replay/unitary_native/optimized/stdout.log new file mode 100644 index 0000000000..93266a965d --- /dev/null +++ b/research/centre-metric-encoders/evidence/replay/unitary_native/optimized/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_UNITARY_24_CLEAN_NATIVE diff --git a/research/publication-reviews/centre-metric-encoders/additional-notices/CREDIT-ADDENDUM.md b/research/publication-reviews/centre-metric-encoders/additional-notices/CREDIT-ADDENDUM.md new file mode 100644 index 0000000000..f03700f4e3 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/additional-notices/CREDIT-ADDENDUM.md @@ -0,0 +1,25 @@ +# Additional source credit for centre metric encoders + +These two unchanged notices complete the source credit chain named in +the encoder package's retained PR #2588 notice. They are source context. +The encoder package retains generated native words and source proof +ancestry. It does not copy the PR #2226 borrowing implementation. + +The [PR #2588 source notice](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/NOTICE) +points to [NOTICE-PR2226.md](NOTICE-PR2226.md). That file records the +borrowing lineage and identifies the unchanged compiler. It also points +to the retained [vendor notice](PR2226-NOTICE.md), which gives the earlier +contributor and license record. Preserve both notices without changes. + +Both files come from commit +`8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb` of +`CrocSwap/integer-mult-bounds`. Their [readback receipt](GITHUB-READBACK.json) +contains the exact GitHub requests, base64 responses, Git blob identities, +and SHA-256 hashes. The decoded bytes match the files in this directory. + +This addendum does not change the accepted encoder package, its frozen +inputs, or its manifest with SHA-256 +`f7aa100a7389e94518b980fe93e91773602f53b5d782a7c677612be4c9790866`. +It changes no proof, construction, validation result, or kappa claim. +No mathematical replay was repeated. Substantial OpenAI Codex assistance +was used to prepare this source readback and addendum. diff --git a/research/publication-reviews/centre-metric-encoders/additional-notices/GITHUB-READBACK.json b/research/publication-reviews/centre-metric-encoders/additional-notices/GITHUB-READBACK.json new file mode 100644 index 0000000000..edb7e42aef --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/additional-notices/GITHUB-READBACK.json @@ -0,0 +1,63 @@ +{ + "accepted_encoder_manifest_sha256": "f7aa100a7389e94518b980fe93e91773602f53b5d782a7c677612be4c9790866", + "accepted_encoder_package_modified": false, + "addendum_sha256": "28f68f9dbed7613c362b8ce281d1adc6a587abdb801e3a170a812c992a022dc6", + "files": [ + { + "bytes": 1754, + "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "computed_git_blob_sha": "a14b299ef55c5581166988aa78baba329cebde04", + "git_blob_matches": true, + "immutable_url": 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No claim that the encoder package copies the PR2226 implementation.", + "source_tool": "github.fetch_file at the exact commit with base64 encoding", + "status": "PASS_EXACT_NOTICE_READBACK", + "verified_utc": "2026-10-22T17:55:17.870781+00:00" +} diff --git a/research/publication-reviews/centre-metric-encoders/additional-notices/NOTICE-PR2226.md b/research/publication-reviews/centre-metric-encoders/additional-notices/NOTICE-PR2226.md new file mode 100644 index 0000000000..a14b299ef5 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/additional-notices/NOTICE-PR2226.md @@ -0,0 +1,21 @@ +# Credit: anticipatory dirty borrowing (PR2226) + +The construction realised by this native chain is **PR2226, "anticipatory dirty borrowing"**, by Cinna Davis +(@1337isnot1337), prepared with substantial OpenAI Codex assistance (Apache-2.0): the logical reference change +K_G of a lender register (a monomial Clifford: a permutation of the 512 columns with phase mod 4), the initial +compensation terms c K_G z, the early cold tail, the exact cold restoration and the private zero buffers of the +FULL-frame cleanup. `vendor/pr2226_operators.py`, `vendor/pr2226_replay.py` and `vendor/PR2226-NOTICE.md` are byte copies +of PR2226's `operators.py`, `replay.py` and `NOTICE.md`. `bw_gauss.py` is a port of `operators.py` (change, monomial, +apply_mono, coord, frame, check) and adds a decoder from a serialized `clifford_exact` monomial to its exact 512 x 512 +Gaussian matrix. + +What this chain adds (the P3 native realisation, with the borrowing work's explicit chronological BORROW-WORD as input): +warp events and zero buffers in `LOCAL-PROGRAMS`, warp recipes in `CLIFFORD-RECIPES.json` (lowered with the unchanged +`lower_child`, rank zero, then compared with the exact numpy column product), logical K_G recipes in +`RESIDUAL-ADAPTERS.json`, an independent local replay in both orientations that checks every warp product on all 512 +columns, and the negative controls listed in `INDEPENDENT-LOCAL-REPLAY.json`, `WRAPPER-CHECKS.json`, `WARP-RECIPE-CHECKS.json` +and `bw_tamper.py`. + +Lineage retained: icekylinx (PR425/433/514, scalar and wrapper machinery), DreamingOfClouds (PR458/484/593 hyperplane/cold-HPE +extensions), the clifford_exact compiler (vendor531), and the owners named in the package README. `vendor/clifford/clifford_exact.py` +is a byte copy. diff --git a/research/publication-reviews/centre-metric-encoders/additional-notices/PR2226-NOTICE.md b/research/publication-reviews/centre-metric-encoders/additional-notices/PR2226-NOTICE.md new file mode 100644 index 0000000000..5ea70357a0 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/additional-notices/PR2226-NOTICE.md @@ -0,0 +1,22 @@ +# Attribution and license + +New construction, proof text and checkers: Cinna Davis (@1337isnot1337), with +substantial OpenAI Codex assistance, Apache-2.0. + +The selected complex canonical word is the PR1042 ancestry retained in PR1094. +Jeremy Kothe, Rohan Arun, Hao Yan, Chafik Boukhalfa, icekylinx, Jonathan Capalbo +and the source package's full provider/frame/controller lineage retain credit. +Ali Romman supplied the source-bound fixed-block theorem and certificate; +Thomas DiFiore supplied the earlier block discovery. The borrowing construction +does not attribute its changed interface to those predecessor results. + +`price_engine.py` is an unchanged copy of the incorporated +`research/complex-local-word-ceiling/ceiling.py`: Douglas Colkitt, with Claude +(Anthropic) assistance; original SPDX/license context and docstring retained. +General Clifford frame and exact Gaussian normal forms are inherited from +`notes/general-clifford-frames.tex` and the repository's credited phase/compiler +lineage. The package independently checks its actual local Gaussian products. + +Source hashes, base commits and the copied engine's Git blob are in SOURCES.json. +No full native supplier, all-size compiler, precision theorem or new kappa is +claimed. No independent human review is claimed. From 6c6ff8b48ef238a7adebe2391c3c2912ae90f0c4 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 13:56:19 -0500 Subject: [PATCH 3/3] Add sign-metric centre capture and exact reader limits --- .../sign-metric-capture/ANNEX-MANIFEST.json | 296 + .../annexes/sign-metric-capture/NOTICE.md | 28 + .../annexes/sign-metric-capture/README.md | 176 + .../annexes/sign-metric-capture/SOURCES.json | 163 + .../evidence/DOCUMENT-LINKS.json | 77 + .../sign-metric-capture/evidence/REPLAY.json | 142 + .../evidence/replay/REPLAY.json | 142 + .../replay/capture32/normal/CHECKS.json | 13 + .../replay/capture32/normal/RESPONSE.json | 12558 +++++++ .../replay/capture32/normal/stdout.log | 1 + .../replay/capture32/optimized/CHECKS.json | 13 + .../replay/capture32/optimized/RESPONSE.json | 12558 +++++++ .../replay/capture32/optimized/stdout.log | 1 + .../replay/reader24/normal/READER-CHECKS.json | 81 + .../replay/reader24/normal/stdout.log | 1 + 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.../READER-CHECKS.json | 81 + .../READER-FREEZE.json | 9 + .../sign-metric-review-20261020/REVIEW.md | 165 + .../check_reader_addendum.py | 52 + .../check_review.py | 235 + .../run-normal/CHECKS.json | 144 + .../run-optimized/CHECKS.json | 144 + .../FREEZE.json | 13 + .../REVIEW.md | 145 + .../check_review.py | 135 + .../run-normal/CHECKS.json | 109 + .../run-optimized/CHECKS.json | 109 + .../root/SIGN-METRIC-FREEZE-20261020.json | 11 + .../root/SIGN-METRIC-INVOLUTIONS-20261020.md | 146 + .../root/SIGN-METRIC-UNIT-CAPTURE-20261020.md | 99 + .../SIGN-METRIC-UNIT-FREEZE-20261020.json | 11 + .../check_sign_metric_involutions_20261020.py | 223 + ...check_sign_metric_unit_capture_20261020.py | 137 + .../sign-metric-normal-20261020/CHECKS.json | 17 + .../sign-metric-normal-20261020/RESPONSE.json | 17953 ++++++++++ .../CHECKS.json | 13 + .../RESPONSE.json | 12558 +++++++ .../sign-metric-capture/notices/LICENSE | 201 + .../annexes/sign-metric-capture/replay.py | 100 + 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The accepted parent files and its historical manifest are unchanged." +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/NOTICE.md b/research/centre-metric-encoders/annexes/sign-metric-capture/NOTICE.md new file mode 100644 index 0000000000..6fda70d6ab --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/NOTICE.md @@ -0,0 +1,28 @@ +# Notice + +The new annex files and campaign contributions use the repository's +Apache-2.0 license. A copy is in [notices/LICENSE](notices/LICENSE). +All files under `frozen/` are unchanged campaign sources. Their exact +paths and hashes are in [SOURCES.json](SOURCES.json). + +Frozen statements that publication was not authorized record the original +source stage. They are retained as historical text. + +The root lane supplied the sign-metric reflection and unit-capture +constructions. The oblique-native independent review supplied the +integer reconstruction, physical support checks, scope counterexamples, +whole-reader norm-five obstruction, code-metric rejection, and the +unchanged-response option with an expanded read set. The original proof +and review files retain those contributions separately. + +The controller-followthrough row-involution packet supplied the actual +signed blocks, original response, and centre pivots. The independent +cyclic-pair packet supplied the actual physical pair matrices. These are +pinned matrix inputs; this annex does not replay their earlier native +or owner-history claims. The [parent notice](../../NOTICE.md) retains +the broader source lineage and contributor notices. This annex does not +claim the inherited data or methods as new work. + +Substantial OpenAI Codex assistance was used for the original work, +independent agent checks, and this publication package. The checks are +not a formal verification of the complete multiplication theorem. diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/README.md b/research/centre-metric-encoders/annexes/sign-metric-capture/README.md new file mode 100644 index 0000000000..84b98cea91 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/README.md @@ -0,0 +1,176 @@ +# Sign-metric responses and unit centre capture + +This annex retains two exact 112-port matrix constructions and a scoped +lower bound. The first response has 24 diagonal exceptions and a diagonal +sign metric. Its selected reader has no right inverse over the Gaussian +dyadic ring. A second response uses 32 FULL fields and gives a dyadic unit +row code with 16 centre fields. The prior independent review also gives +an option that keeps the first response and expands its read set to 32 +fields. These are algebraic results. No native word, complete invoice, or +complete kappa improvement follows. + +The two original proofs are [the sign-metric reflection](frozen/root/SIGN-METRIC-INVOLUTIONS-20261020.md) +and [unit centre capture](frozen/root/SIGN-METRIC-UNIT-CAPTURE-20261020.md). +The retained independent reviews cover [the response and its exact scope](frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/REVIEW.md), +[the whole selected-reader obstruction](frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-ADDENDUM.md), +and [the unit code, minimum, and unchanged-response option](frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/REVIEW.md). +[SOURCES.json](SOURCES.json) binds all 26 original files. + +## The 24-exception response + +Let `R = Z[i,1/2]`. For a diagonal sign matrix `D` and a column `w` +with `w* D w = 2`, set `S = I - w w* D`. Here `*` is the conjugate +transpose. Direct multiplication gives + +```text +S^2 = I, S* = D S D, S* D S = D. +``` + +Each block has correction rank one. In each of the eight six-mode +blocks, two coordinates have negative metric sign and all entries of +`w` have norm one. In each of the eight eight-mode blocks, one coordinate +has negative metric sign and its entry of `w` is a sign times `1+2i`. +The latter norm is five, so its metric norm is `7-5=2`. No division by +five occurs in this response construction. + +The selected ports are closed under the actual physical pair code `H`. +Thus `H` commutes with `D`. Its Gram matrix is `2I` on the large component +and `I` on the small component; the response does not mix the components. +The physical matrix `A = H^-1 S H` therefore satisfies + +```text +A^2 = I, A* = D A D, A* D A = D. +``` + +Its correction rank is 16, determinant is one, and trace is 80. Its +diagonal has sixteen entries equal to two, eight equal to six, and 88 +zeros. Each ordinary physical row keeps its old support. The ordinary +principal block is unchanged, but all 24 selected columns change within +the ordinary rows. This construction is not a selected-row replacement. + +For a diagonal unitary field operator `Z` that commutes with `D`, +`D (Z A)* D = (Z A)^-1`. The order is fixed; it does not require `A Z = Z A`. +For two-bank shears the signs act on both banks. Each sign still has a +cost, and all intervening progress must commute with `D` or have a proved +conjugated implementation. The identity removes neither stage dependence +nor a final phase. + +## The reader obstruction and its two escapes + +Write `A = I + U V`. In the 24 selected columns, each of the eight +small-block rows of `V` has one entry, a sign times `1-2i`. The ring map +`R -> F5` with `i -> 3` and `1/2 -> 3` sends all eight restricted rows +to zero. Thus the entire selected reader has no right inverse over `R`. +This rules out arbitrary Gaussian-dyadic normalization on those columns, +not only one square minor. It does not exclude proved division on a code +image, other source columns, or a different representation. + +The unit-capture construction selects two coordinates in each eight-mode +block and uses entries `(1+i)d` there. Its metric norm is `6-2-2=2`. +The selected reader entries are signs times `1-i`, whose inverse is +`(1+i)/2` up to sign. The six-mode blocks stay fixed. There are 32 FULL +fields, with diagonal entries two on 16 fields and three on 16 fields. +The original 16 centre pivots form a Gaussian-dyadic unit minor after +the actual pair code. Both the FULL set and the centre set are pair-closed. + +For the physical reader, let `P` be those 16 pivots and set + +```text +L = V_P^-1 V, L_P = I, L A = -L. +C_P = L, C_R = I_R. +(C-I)^2 = 0, C^-1 = 2I-C. +``` + +Both `C` and its inverse are Gaussian dyadic on arbitrary input arrays. +Only 16 rows carry centre values. The other 16 FULL fields can retain +response values. No zero-target or code-image promise is used. + +The sign metric does not pass through this row code. The actual matrices +satisfy `C* D C != D` and `(C A)* != D (C A)^-1 D`. A caller must therefore +distinguish `Z A` from `Z C A`. The sign-only adjoint conversion for the +first matrix does not apply to the second matrix by inheritance. + +There is a separate escape with the unchanged 24-exception response. +Add the eight ordinary small ports `5,4,35,12,29,32,26,31` to its FULL +read set. Use those ports as the small centre pivots. Their reader entries +are `-1`; the large minor is unchanged. The resulting 32-field read set +has a unit 16-column minor. This option keeps the response and metric, +but uses different small centre slots. Its native access remains open. + +## Exact scope of the minimum + +In an independent rank-one reflection over the Gaussian rationals with +a diagonal sign metric, one exceptional diagonal coordinate in a block +of size `k > 3` requires a rational Gaussian norm `k-3`. A six-mode block +would require norm three. Reduction modulo three and descent exclude +that norm. Zero exceptions also contradict the trace `k-2`. Two +exceptions are therefore necessary in each six-mode block. One exception +is possible in an eight-mode block, where norm five is available. + +For arbitrary blockwise reader normalization over `R`, require every +diagonal exception and every reader pivot to lie in the FULL selected +fields. One FULL field in an eight-mode block then has the norm-five +unit obstruction. These hypotheses require at least two FULL fields per +block, hence 32 in total. The construction attains that count with 16 +centre fields. The actual pair-closed representation preserves this split. + +This minimum does not cover coupled blocks, higher correction rank, +non-diagonal metrics, a mixed representation that is not pair-closed, +normalization from other frames, code-image division, extra carriers, +or a different transfer grammar. It is not a general native lower bound. +The parent package's sharp unitary C24 coordinate bound and its signed +reciprocal C16 code concern different matrices and reader maps. + +## Reproduction + +Use Python 3.11 or later, the standard library, at least 3 GiB free space, +and a new output directory outside the annex. No network or external +package is required. +From this annex directory, run: + +```sh +python3 -I -B replay.py --out /tmp/sign-metric-capture-annex +``` + +The final line must be: + +```text +PASS_SIGN_METRIC_CAPTURE_ANNEX +``` + +[The fresh receipt](evidence/REPLAY.json) records ten sequential runs: +the two producers and the three independent checks, each with normal +and optimized Python. All receipts and both full response payloads match +the frozen bytes. The independent response checks use integer real +matrices; they do not import the Gaussian-pair producers. The reader +check uses the full selected reader and its finite-field obstruction. + +The checks cover all 112 ports, both physical metric identities, the +rank contraction, pair closure, both minor inverse orders, both code +inverse orders, and `L A = -L`. Controls reject a bilinear transpose, +missing metric signs, a broken pair, a one-exception real-sign attempt, +and metric inheritance through `C`. They retain examples outside the +lower-bound class. The symbolic minimum is a written proof; finite +checks do not replace its hypotheses. + +The runner copies the frozen tree to its new output directory before it +runs any script. It preserves all source bytes and uses their original +relative layout. No import adaptation is needed. It does not run or +change the main encoder suite. [ANNEX-MANIFEST.json](ANNEX-MANIFEST.json) +is separate from the accepted parent manifest. + +## Costs and open next questions + +No Gaussian scalar lowering, native response word, centre-access word, +or recursive invoice is supplied. The old real-1760 scalar tariff and +old 16-carrier native profile do not apply to these changed columns and +32 target paths. A complete caller must supply those paths, track the +actual coded response, check intervening progress, and price all boundary +codes, signs, phases, storage, and precision. No claim of applicability +to the current selected supplier follows from this historical packet. + +The next questions are a literal complex scalar lowering, native access +for each stated centre choice, and a complete forward/backward caller +with its cost and precision proof. They remain open. This annex adds no +new research or proposed repair. [NOTICE.md](NOTICE.md) records the source +contributions, license, and AI assistance. diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/SOURCES.json b/research/centre-metric-encoders/annexes/sign-metric-capture/SOURCES.json new file mode 100644 index 0000000000..d044db8069 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/SOURCES.json @@ -0,0 +1,163 @@ +{ + "files": [ + { + "bytes": 401187, + "campaign_path": "lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json", + "path": "frozen/lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json", + "sha256": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b" + }, + { + "bytes": 316632, + "campaign_path": "lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "path": "frozen/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", + "sha256": 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b/research/centre-metric-encoders/annexes/sign-metric-capture/evidence/replay/capture32/optimized/stdout.log @@ -0,0 +1 @@ +{"centre_minor_is_gaussian_dyadic_unit": true, "centre_ports": 16, "code_displacement_square_is_zero": true, "correction_rank": 16, "data_ports": 112, "full_caller_closed": false, "full_ports": 32, "native_word_emitted": false, "payload_sha256": "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a", "scalar_invoice_established": false, "status": "PASS_EXACT_SIGN_METRIC_UNIT_CAPTURE"} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/evidence/replay/reader24/normal/READER-CHECKS.json b/research/centre-metric-encoders/annexes/sign-metric-capture/evidence/replay/reader24/normal/READER-CHECKS.json new file mode 100644 index 0000000000..5b5f7ac650 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/evidence/replay/reader24/normal/READER-CHECKS.json @@ -0,0 +1,81 @@ +{ + "certificate": "Apply the ring map 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No native word or complete supplier.", + "status": "PASS_INDEPENDENT_SIGN_METRIC_REVIEW" +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-ADDENDUM.md b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-ADDENDUM.md new file mode 100644 index 0000000000..c663bdcf19 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-ADDENDUM.md @@ -0,0 +1,38 @@ +# Selected reader normalization is a separate obligation + +This addendum does not change the frozen matrix review. The response, +sign metric, involution, rank, and support conclusions remain valid. +The root identified a further interface condition after that freeze. + +Let R=Z[i,1/2], and restrict the physical reader V in the frozen +factorization A=I+UV to the 24 selected columns. Each small-block +reader row has exactly one nonzero entry in those columns. That +entry is a sign times 1-2i. Its norm is 5, so it is not a unit of R. + +This is not only a failure of one chosen square minor. There is a +ring map R -> F5 that sends i to 3 and 1/2 to 3. It sends 1-2i to +zero. Under this map, eight rows of the entire selected reader +V_P become zero. Thus no matrix X over R can satisfy V_P X=I16. + +The old normalized selected-row centre interface therefore cannot +be inherited as an arbitrary Gaussian dyadic right inverse of V_P. +One must supply a different representation, more source columns, +or a proved division on the actual code image. Division on that +image is not excluded by this argument. The argument does not +prove a native obstruction for the 24-port response. + +For comparison, a size-eight block with two negative metric entries, +each of whose w entries is 1+i, has metric norm 6-2-2=2. +Its selected reader entries 1-i are Gaussian dyadic units, with +inverse (1+i)/2. This explains the root's proposed 32-selected-port +variant. This addendum does not bind that variant to the actual +pair geometry or give it a native word. + +`check_reader_addendum.py` checks the eight actual restricted rows +and the finite-field certificate from the preserved payload. +It does not import the response producer. + +The root supplied this interface finding. This independent +addendum strengthens it from a square-minor issue to failure of +a right inverse on all 24 selected columns. AI assistance was +used. No PR or publication is authorized. diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-CHECKS.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-CHECKS.json new file mode 100644 index 0000000000..5b5f7ac650 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-CHECKS.json @@ -0,0 +1,81 @@ +{ + "certificate": "Apply the ring map Z[i,1/2] -> F5 with i -> 3. Eight rows of V_P vanish; a right inverse would give an identity row.", + "scope": "No arbitrary selected-reader normalization over the Gaussian dyadic ring. Code-image divisions and other source columns are not excluded.", + "selected_column_count": 24, + "selected_reader_has_Gaussian_dyadic_right_inverse": false, + "small_selected_rows": [ + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 8, + "selected_port": 1 + }, + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 9, + "selected_port": 3 + }, + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 10, + "selected_port": 6 + }, + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 11, + "selected_port": 8 + }, + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 12, + "selected_port": 17 + }, + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 13, + "selected_port": 18 + }, + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 14, + "selected_port": 24 + }, + { + "coefficient": [ + "1", + "-2" + ], + "norm": "5", + "row": 15, + "selected_port": 23 + } + ], + "source_sha256": "9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c" +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-FREEZE.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-FREEZE.json new file mode 100644 index 0000000000..7e08d479e9 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-FREEZE.json @@ -0,0 +1,9 @@ +{ + "files": { + "READER-ADDENDUM.md": "2ce6c21c11974f2dfa1809e1660a1f74df4f231907da3bd5703b45d7ec7584dd", + "READER-CHECKS.json": "f7ce27efaa097b8214a16b56fe060028ae5f94b9ed2aacd0f150667f02e382b8", + "check_reader_addendum.py": "acf61958fb4b4f724bf69b48af6e61b1c11ec60ba27f52a940ca337fdc385dd9" + }, + "normal_optimized_byte_identical": true, + "original_review_freeze": "2d6877192147549f3f86d6df5426b9d95db5d7ef49f1a8e8bd5a77c0aefeb6bf" +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/REVIEW.md b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/REVIEW.md new file mode 100644 index 0000000000..a366e80301 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/REVIEW.md @@ -0,0 +1,165 @@ +# Independent review of the sign-metric response + +The frozen response passes this review. There is no material finding. +The result is a matrix construction. It is not a native word or a +complete supplier. + +## General reflection + +Let D be a diagonal sign matrix, and let w be a Gaussian rational +column with w*Dw=2. Set S=I-ww*D. Then + +```text +S^2 = I-2ww*D+w(w*Dw)w*D = I; +S* = I-Dww* = DSD; +S*DS = D. +``` + +The range of S-I is the line spanned by w. S acts as -1 on that line +and as +1 on the kernel of w*D. Thus its correction rank is one, +its determinant is -1, and its trace is k-2 in a block of size k. +These claims use characteristic zero. + +In each actual six-mode block, w has sign entries. Two negative +metric entries and four positive entries give w*Dw=2. The two +selected diagonal entries of S are 2. All other diagonal entries +are zero. + +In each actual eight-mode block, one selected entry of w is changed +from d to (1+2i)d. Its norm is 5. The other seven norms are one. +One negative metric entry gives 7-5=2. The selected diagonal entry +is 6. No division by 5 or by 1+2i is used. + +The sixteen blocks have disjoint mode coordinates. Their correction +rank is therefore 16, their determinant is 1, and their trace is +8 times 4 plus 8 times 6, which is 80. + +## Actual physical pair code + +The independent checker reads the pinned pair matrices and the old +mode blocks. It does not import either producer. The selected large +ports are exactly these complete pairs: + +```text +(0,27), (2,25), (7,57), (11,63), +(13,51), (20,46), (36,111), (42,105). +``` + +There are eight further selected small ports. The actual code H +therefore commutes with the physical diagonal D. Also, H*H is 2I +on the large component and I on the small component. S does not +mix those two components. It follows that + +```text +A = H^-1 S H; +A^2 = I; +A* = D A D. +``` + +The checker uses integer realification: a complex matrix X+iY is +represented by the real integer block matrix [[X,-Y],[Y,X]], after +an explicit common factor of 2 when needed. This is distinct from +the producer's pairs of rational Gaussian coefficients. + +It reconstructs every entry of A from the old block signs, the +selected ports, and the actual pair matrices. It verifies the +serialized response and adjoint, both physical identities, the +metric identity, and the correction factors. The contraction +VU=-2I proves exact complex rank 16; it is not a modular rank +estimate. + +The physical diagonal has 16 entries equal to 2 and 8 entries equal +to 6. It is zero at all 88 ordinary ports. A stronger support check +also passes: every ordinary physical row has its old support, and +the entire ordinary physical principal block is unchanged. Every +selected column changes in the ordinary rows. Thus the result is +not a selected-row replacement. + +## Ordered phase conversion + +For any diagonal unitary field operator Z that commutes with D, + +```text +(ZA)^-1 = A Z^-1; +(ZA)* = A* Z^-1 = D A Z^-1 D; +D (ZA)* D = (ZA)^-1. +``` + +No commutation of A and Z is used. The checker uses an explicit +noncommuting diagonal phase as a control. It also rejects the +bilinear transpose in place of the adjoint, omission of D, and +changing the metric sign on only one member of a physical pair. + +The corresponding two-bank conjugation uses diag(D,D). It costs +field signs. Any progress between these signs must commute with +D, or its conjugated implementation must be supplied. The +identities do not remove stage changes, boundary code costs, +spatial phases, or a final decoder. + +## Scope of the one-exception bound + +The bound can be stated for every nontrivial rank-one reflection +S over the Gaussian rationals that is self-adjoint in a diagonal +sign metric. Write S=I-u v* with v*u=2. The identity S*D=DS forces +v=cDu for a nonzero real rational c. A zero ordinary diagonal +entry gives c d_j |u_j|^2=1. + +Normalize by one such coordinate u_j. After an overall sign change +of D, all ordinary metric signs are positive and all ordinary +norms are one. If there is exactly one exceptional coordinate in +a block of size k>3, the metric norm equation becomes + +```text +(k-1) - |w_p|^2 = 2. +``` + +The exceptional metric sign must be negative, and its Gaussian +rational norm must be k-3. For k=6, this requires a^2+b^2=3 over +the rationals. Clear denominators in lowest terms. Reduction +modulo 3 forces both numerators to be divisible by 3; the original +equation then forces the denominator to be divisible by 3. This +is a contradiction. For k=8, 1+2i has the required norm 5. + +Zero exceptions are also impossible in these rank-one blocks, +since their trace is k-2, which is nonzero. Thus two exceptions +for each six-mode block and one for each eight-mode block are +minimal in this family. + +Two counterexamples show why the hypotheses matter: + +- A direct sum of three ordinary swaps on six coordinates is an + involution with no diagonal exceptions. Its correction rank is + three, not one. +- The real integral matrix I-u v^T with + u=(1,1,1,1,1,1)^T and v=(1,1,1,1,1,-3)^T is a rank-one + involution with one exception. Its diagonal is (0,0,0,0,0,4). + Its diagonal symmetrizer has an unequal magnitude 3; it cannot + use a diagonal sign metric. + +The bound does not cover coupled blocks, higher correction rank, +non-diagonal metrics, or arbitrary native circuits. + +## Reproduction and limits + +Run from this directory: + +```text +python3 -I -B check_review.py --out run-normal +python3 -I -O -B check_review.py --out run-optimized +``` + +Both runs must produce the same `CHECKS.json` bytes. The source +freeze is checked before either run. Every input file is pinned. +No producer code is imported. + +The review does not price Gaussian scalar gates, emit a native +word, or prove recursive hosting or a complete caller. Those +obligations remain separate. The root supplied the sign-metric +construction; the pinned controller and cyclic packets supplied +the actual mode blocks and pair code. This review adds an +independent exact reconstruction, the physical support check, +and the stated scope controls. AI assistance was used. + +No PR, push, commit, or publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/check_reader_addendum.py b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/check_reader_addendum.py new file mode 100644 index 0000000000..bc0e95b746 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/check_reader_addendum.py @@ -0,0 +1,52 @@ +#!/usr/bin/env python3 +"""Check the selected reader obstruction in the frozen response.""" +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +HERE=Path(__file__).resolve().parent +SOURCE=HERE.parents[2]/'root/sign-metric-normal-20261020/RESPONSE.json' +PIN='9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c' + + +def need(condition,label): + if not condition: + raise ValueError(label) + + +def residue_mod5(value): + value=Q(value) + return value.numerator*pow(value.denominator,-1,5)%5 + + +def main(): + raw=SOURCE.read_bytes() + need(sha256(raw).hexdigest()==PIN,'Frozen response') + packet=json.loads(raw) + selected=set(packet['selected']) + rows=[] + for k,block in enumerate(packet['blocks']): + if len(block['ports'])!=8: + continue + restricted={int(j):[Q(x),Q(y)] for j,(x,y) in packet['correction_V'][k].items() if int(j) in selected} + need(len(restricted)==1,'One selected reader entry in each small row') + port,(a,b)=next(iter(restricted.items())) + need(a*a+b*b==5,'Selected reader norm5') + need(a!=0 and b==-2*a,'Selected reader is a sign times1-2i') + # The map i -> 3 in F5 sends i^2+1 and 1-2i to zero. + need((3*3+1)%5==0 and (residue_mod5(a)+3*residue_mod5(b))%5==0, + 'Proper ideal obstruction over the Gaussian dyadic ring') + rows.append({'row':k,'selected_port':port,'coefficient':[str(a),str(b)],'norm':'5'}) + need(len(rows)==8,'Eight small-block obstructions') + result={'source_sha256':PIN,'small_selected_rows':rows, + 'selected_column_count':24, + 'selected_reader_has_Gaussian_dyadic_right_inverse':False, + 'certificate':'Apply the ring map Z[i,1/2] -> F5 with i -> 3. Eight rows of V_P vanish; a right inverse would give an identity row.', + 'scope':'No arbitrary selected-reader normalization over the Gaussian dyadic ring. Code-image divisions and other source columns are not excluded.'} + (HERE/'READER-CHECKS.json').write_text(json.dumps(result,sort_keys=True,indent=2)+'\n') + print(json.dumps(result,sort_keys=True)) + + +if __name__=='__main__': + main() diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/check_review.py b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/check_review.py new file mode 100644 index 0000000000..8ac370dccd --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/check_review.py @@ -0,0 +1,235 @@ +#!/usr/bin/env python3 +"""Check the sign-metric response with integer real matrices.""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + +HERE=Path(__file__).resolve().parent +CAMPAIGN=HERE.parents[2] +PINS={ + 'root/SIGN-METRIC-FREEZE-20261020.json':'33c920f59ef3e2c644ba5c798a81bda257863e5e3a9cef68fba46968332471b1', + 'root/sign-metric-normal-20261020/RESPONSE.json':'9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c', + 'lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json': + 'a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b', + 'lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json': + '3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585', +} + + +def need(condition,label): + if not condition: + raise ValueError(label) + + +def load(path): + raw=(CAMPAIGN/path).read_bytes() + need(sha256(raw).hexdigest()==PINS[path],'Source pin '+path) + return json.loads(raw) + + +def eye(n,scale=1): + return [{i:scale} for i in range(n)] + + +def scale(a,c): + return [{j:c*v for j,v in row.items() if c*v} for row in a] + + +def plus(a,b): + result=[] + for x,y in zip(a,b): + row=dict(x) + for j,c in y.items(): + row[j]=row.get(j,0)+c + if not row[j]: + del row[j] + result.append(row) + return result + + +def times(a,b): + out=[] + for source in a: + row={} + for j,x in source.items(): + for k,y in b[j].items(): + row[k]=row.get(k,0)+x*y + out.append({j:c for j,c in row.items() if c}) + return out + + +def transpose(a,width): + out=[{} for _ in range(width)] + for i,row in enumerate(a): + for j,v in row.items(): + out[j][i]=v + return out + + +def realify(rows,width,denominator=1): + n=len(rows) + out=[{} for _ in range(2*n)] + for i,row in enumerate(rows): + for key,value in row.items(): + j=int(key) + a,b=[Q(v)*denominator for v in value] + need(a.denominator==b.denominator==1,'Integer realification') + a,b=int(a),int(b) + if a: + out[i][j]=a;out[n+i][width+j]=a + if b: + out[i][width+j]=-b;out[n+i][j]=b + return out + + +def real_rows(rows): + return [{str(j):[str(v),'0'] for j,v in row.items()} for row in rows] + + +def block_support(a,i,n=112): + return {j for j in range(n) if a[i].get(j,0) or a[n+i].get(j,0)} + + +def main(): + parser=argparse.ArgumentParser() + parser.add_argument('--out',type=Path,default=HERE/'run-normal') + args=parser.parse_args() + freeze=load('root/SIGN-METRIC-FREEZE-20261020.json') + for name,pin in freeze['files'].items(): + need(sha256((CAMPAIGN/'root'/name).read_bytes()).hexdigest()==pin,'Frozen root file '+name) + packet=load('root/sign-metric-normal-20261020/RESPONSE.json') + prior=load('lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json') + pairs=load('lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json') + selected=set(prior['pivots'])|{2,25,13,51,11,63,42,105} + need(sorted(selected)==packet['selected'] and len(selected)==24,'Actual24 selected ports') + h=eye(112) + large=set() + closed_pairs=[] + for pair in pairs['pair_codes']: + p,q=pair['ports'] + need((p in selected)==(q in selected),'Every physical pair is closed') + large.update((p,q)) + if p in selected: + closed_pairs.append([p,q]) + for row,target in zip(pair['matrix'],(p,q)): + h[target]={j:int(v) for j,v in zip((p,q),row) if v} + ht=transpose(h,112) + gram=times(ht,h) + need(gram==[{i:2 if i in large else 1} for i in range(112)],'Actual H*H block scales') + hi2=[{j:(1 if i in large else 2)*c for j,c in ht[i].items()} for i in range(112)] + need(times(hi2,h)==times(h,hi2)==eye(112,2),'Actual pair inverse without division') + H=realify(real_rows(h),112) + R=realify(real_rows(hi2),112) + D=realify(real_rows([{i:-1 if i in selected else 1} for i in range(112)]),112) + need(D==realify(packet['metric'],112),'Actual sign metric') + need(times(D,H)==times(H,D),'Metric and physical pair code commute') + w=[{} for _ in range(112)] + occupied=[] + kinds=Counter() + for k,block in enumerate(prior['blocks']): + ports=block['ports'] + occupied.extend(ports) + picks=sorted(selected.intersection(ports)) + need(len(picks)==(2 if len(ports)==6 else 1),'Actual block exceptions') + values={} + for p,d in zip(ports,block['signs']): + values[str(p)]=[str(Q(d)),str(2*Q(d) if len(ports)==8 and p in selected else 0)] + w[p][str(k)]=values[str(p)] + need(packet['blocks'][k]=={'ports':ports,'selected':picks,'w':values},'Independent block reconstruction') + kinds[len(ports)]+=1 + need(sorted(occupied)==list(range(112)) and kinds=={6:8,8:8},'Sixteen disjoint complete blocks') + W=realify(w,16) + V=scale(times(transpose(W,32),D),-1) + need(times(V,W)==eye(32,-2),'Sixteen independent reflection contractions') + S=plus(eye(224),times(W,V)) + A2=times(times(R,S),H) + A2_saved=realify(packet['response'],112,2) + need(A2==A2_saved,'All112 complex columns from independent integer reconstruction') + need(S==realify(packet['mode_response'],112),'Mode response') + need(times(A2,A2)==eye(224,4),'Physical involution') + need(transpose(A2,224)==times(times(D,A2),D),'Physical adjoint and sign metric') + need(times(times(transpose(A2,224),D),A2)==scale(D,4),'Metric preservation') + need(transpose(A2,224)==realify(packet['response_adjoint'],112,2),'Serialized physical adjoint') + U2=times(R,W) + VP=times(V,H) + need(U2==realify(packet['correction_U'],16,2),'Serialized physical correction U') + need(VP==realify(packet['correction_V'],112),'Serialized physical correction V') + need(times(VP,U2)==eye(32,-4),'Exact correction rank16') + need(A2==plus(eye(224,2),times(U2,VP)),'Physical displacement factorization') + diagonal={i:A2[i].get(i,0)//2 for i in range(112) if A2[i].get(i,0)} + need(set(diagonal)==selected and Counter(diagonal.values())=={2:16,6:8},'Exact physical diagonal exceptions') + need(sum(diagonal.values())==80,'Trace80') + old2=realify([{j:[c,'0'] for j,c in row.items()} for row in prior['original_response']],112,2) + ordinary=set(range(112))-selected + for i in ordinary: + need(block_support(A2,i)==block_support(old2,i),'Ordinary physical row support') + for j in ordinary: + need(A2[i].get(j,0)==old2[i].get(j,0) and A2[112+i].get(j,0)==old2[112+i].get(j,0), + 'Ordinary physical principal block') + changed_columns=[] + for j in selected: + if any(A2[i].get(j,0)!=old2[i].get(j,0) or A2[112+i].get(j,0)!=old2[112+i].get(j,0) for i in ordinary): + changed_columns.append(j) + need(set(changed_columns)==selected,'Every selected column changes in ordinary rows') + # Use a noncommuting diagonal unitary to check the exact mixed-phase order. + zrows=[{i:['0','1'] if i==1 else ['1','0']} for i in range(112)] + Z=realify(zrows,112);Zi=transpose(Z,224) + E2=times(Z,A2) + Einv2=times(A2,Zi) + need(times(E2,Einv2)==times(Einv2,E2)==eye(224,4),'Mixed-phase inverse') + need(times(times(D,transpose(E2,224)),D)==Einv2,'Mixed-phase adjoint conversion') + need(times(A2,Z)!=times(Z,A2),'Noncommuting phase witness') + complex_conjugation=[{i:1 if i<112 else -1} for i in range(224)] + bilinear=times(times(complex_conjugation,transpose(A2,224)),complex_conjugation) + need(bilinear!=transpose(A2,224) and times(times(D,bilinear),D)!=A2,'Transpose mutation rejected') + need(transpose(A2,224)!=A2,'Omitting metric signs fails') + # Moving only one member of a pair breaks the physical diagonal metric. + wrongD=[dict(row) for row in D] + p=closed_pairs[0][0] + wrongD[p][p]*=-1;wrongD[112+p][112+p]*=-1 + need(times(wrongD,H)!=times(H,wrongD),'Pair-closure mutation rejected') + need(times(times(wrongD,A2),wrongD)!=transpose(A2,224),'Wrong physical metric rejected') + # A size-six rank-one sign reflection with one exception has norm4, not2. + bad=[{j:(1 if i==j else 0)-(1 if j<5 else -1) for j in range(6)} for i in range(6)] + bad=[{j:v for j,v in row.items() if v} for row in bad] + need(times(bad,bad)!=eye(6),'One-exception real-sign mutation rejected') + need([(a,b) for a in range(3) for b in range(3) if (a*a+b*b)%3==0]==[(0,0)],'Norm3 rational descent residue') + swaps=[{i^1:1} for i in range(6)] + need(times(swaps,swaps)==eye(6) and all(i not in row for i,row in enumerate(swaps)), + 'Higher-rank zero-exception counterexample') + uneven=[{j:(1 if i==j else 0)-(1 if j<5 else -3) for j in range(6)} for i in range(6)] + uneven=[{j:v for j,v in row.items() if v} for row in uneven] + need(times(uneven,uneven)==eye(6) and [row.get(i,0) for i,row in enumerate(uneven)]==[0,0,0,0,0,4], + 'Unequal-metric one-exception counterexample') + for mask in range(64): + signs=[{i:-1 if (mask>>i)&1 else 1} for i in range(6)] + need(times(times(signs,uneven),signs)!=transpose(uneven,6),'No diagonal sign metric for counterexample') + receipt={ + 'status':'PASS_INDEPENDENT_SIGN_METRIC_REVIEW', + 'source_pins':PINS, + 'engine':'Integer realification; no producer code or Gaussian pair arithmetic imported', + 'complex_ports':112,'real_integer_matrix_rows':224, + 'correction_rank_over_Gaussian_rationals':16, + 'selected_ports':sorted(selected),'closed_selected_pairs':closed_pairs, + 'diagonal_values':diagonal,'trace':80,'determinant':1, + 'determinant_reason':'Sixteen disjoint rank-one reflections each have determinant minus one', + 'ordinary_physical_support_preserved':True, + 'ordinary_physical_principal_block_preserved':True, + 'selected_columns_changed_in_ordinary_rows':sorted(changed_columns), + 'mutation_checks':['bilinear transpose','missing sign metric','broken physical pair closure','one-exception real signs'], + 'mixed_phase_noncommutation_witness':True, + 'outside_scope_counterexamples':['rank3 zero-exception involution','rank1 one-exception involution with unequal metric magnitudes'], + 'one_exception_bound_scope':'Rank-one reflection with a diagonal sign metric over Gaussian rationals; independent six/eight coordinate blocks', + 'native_word_or_invoice_reviewed':False, + 'producer_sha256':sha256(Path(__file__).read_bytes()).hexdigest(), + } + args.out.mkdir(parents=True,exist_ok=True) + (args.out/'CHECKS.json').write_text(json.dumps(receipt,sort_keys=True,indent=2)+'\n') + print(json.dumps({k:v for k,v in receipt.items() if k not in ('source_pins','diagonal_values')},sort_keys=True)) + + +if __name__=='__main__': + main() diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/run-normal/CHECKS.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..4b17824956 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/run-normal/CHECKS.json @@ -0,0 +1,144 @@ +{ + "closed_selected_pairs": [ + [ + 0, + 27 + ], + [ + 2, + 25 + ], + [ + 7, + 57 + ], + [ + 11, + 63 + ], + [ + 13, + 51 + ], + [ + 20, + 46 + ], + [ + 36, + 111 + ], + [ + 42, + 105 + ] + ], + "complex_ports": 112, + "correction_rank_over_Gaussian_rationals": 16, + "determinant": 1, + "determinant_reason": "Sixteen disjoint rank-one reflections each have determinant minus one", + "diagonal_values": { + "0": 2, + "1": 6, + "2": 2, + "3": 6, + "6": 6, + "7": 2, + "8": 6, + "11": 2, + "13": 2, + "17": 6, + "18": 6, + "20": 2, + "23": 6, + "24": 6, + "25": 2, + "27": 2, + "36": 2, + "42": 2, + "46": 2, + "51": 2, + "57": 2, + "63": 2, + "105": 2, + "111": 2 + }, + "engine": "Integer realification; no producer code or Gaussian pair arithmetic imported", + "mixed_phase_noncommutation_witness": true, + "mutation_checks": [ + "bilinear transpose", + "missing sign metric", + "broken physical pair closure", + "one-exception real signs" + ], + "native_word_or_invoice_reviewed": false, + "one_exception_bound_scope": "Rank-one reflection with a diagonal sign metric over Gaussian rationals; independent six/eight coordinate blocks", + "ordinary_physical_principal_block_preserved": true, + "ordinary_physical_support_preserved": true, + "outside_scope_counterexamples": [ + "rank3 zero-exception involution", + "rank1 one-exception involution with unequal metric magnitudes" + ], + "producer_sha256": "2dc96dc39b42c85885859c3b7c09700bda447ffe223f3d9aa03b5ffd1df68867", + "real_integer_matrix_rows": 224, + "selected_columns_changed_in_ordinary_rows": [ + 0, + 1, + 2, + 3, + 6, + 7, + 8, + 11, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 27, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "selected_ports": [ + 0, + 1, + 2, + 3, + 6, + 7, + 8, + 11, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 27, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "source_pins": { + "lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b", + "lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "root/SIGN-METRIC-FREEZE-20261020.json": "33c920f59ef3e2c644ba5c798a81bda257863e5e3a9cef68fba46968332471b1", + "root/sign-metric-normal-20261020/RESPONSE.json": "9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c" + }, + "status": "PASS_INDEPENDENT_SIGN_METRIC_REVIEW", + "trace": 80 +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/run-optimized/CHECKS.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/run-optimized/CHECKS.json new file mode 100644 index 0000000000..4b17824956 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/run-optimized/CHECKS.json @@ -0,0 +1,144 @@ +{ + "closed_selected_pairs": [ + [ + 0, + 27 + ], + [ + 2, + 25 + ], + [ + 7, + 57 + ], + [ + 11, + 63 + ], + [ + 13, + 51 + ], + [ + 20, + 46 + ], + [ + 36, + 111 + ], + [ + 42, + 105 + ] + ], + "complex_ports": 112, + "correction_rank_over_Gaussian_rationals": 16, + "determinant": 1, + "determinant_reason": "Sixteen disjoint rank-one reflections each have determinant minus one", + "diagonal_values": { + "0": 2, + "1": 6, + "2": 2, + "3": 6, + "6": 6, + "7": 2, + "8": 6, + "11": 2, + "13": 2, + "17": 6, + "18": 6, + "20": 2, + "23": 6, + "24": 6, + "25": 2, + "27": 2, + "36": 2, + "42": 2, + "46": 2, + "51": 2, + "57": 2, + "63": 2, + "105": 2, + "111": 2 + }, + "engine": "Integer realification; no producer code or Gaussian pair arithmetic imported", + "mixed_phase_noncommutation_witness": true, + "mutation_checks": [ + "bilinear transpose", + "missing sign metric", + "broken physical pair closure", + "one-exception real signs" + ], + "native_word_or_invoice_reviewed": false, + "one_exception_bound_scope": "Rank-one reflection with a diagonal sign metric over Gaussian rationals; independent six/eight coordinate blocks", + "ordinary_physical_principal_block_preserved": true, + "ordinary_physical_support_preserved": true, + "outside_scope_counterexamples": [ + "rank3 zero-exception involution", + "rank1 one-exception involution with unequal metric magnitudes" + ], + "producer_sha256": "2dc96dc39b42c85885859c3b7c09700bda447ffe223f3d9aa03b5ffd1df68867", + "real_integer_matrix_rows": 224, + "selected_columns_changed_in_ordinary_rows": [ + 0, + 1, + 2, + 3, + 6, + 7, + 8, + 11, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 27, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "selected_ports": [ + 0, + 1, + 2, + 3, + 6, + 7, + 8, + 11, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 27, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "source_pins": { + "lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json": "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b", + "lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "root/SIGN-METRIC-FREEZE-20261020.json": "33c920f59ef3e2c644ba5c798a81bda257863e5e3a9cef68fba46968332471b1", + "root/sign-metric-normal-20261020/RESPONSE.json": "9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c" + }, + "status": "PASS_INDEPENDENT_SIGN_METRIC_REVIEW", + "trace": 80 +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/FREEZE.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/FREEZE.json new file mode 100644 index 0000000000..78c70de935 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/FREEZE.json @@ -0,0 +1,13 @@ +{ + "files": { + "REVIEW.md": "7ffeb455714a19b347dabd78a48fa5ff30f10286733fd9acac6ef2157418d048", + "check_review.py": "0d45392237eb117fbc45ad108a64f923be573578633df5fb056fbb5da71388f1", + "run-normal/CHECKS.json": "47fa3c6eda467849775da7aedb0b250db4cf95782de550cd32296d11d56fd089", + "run-optimized/CHECKS.json": "47fa3c6eda467849775da7aedb0b250db4cf95782de550cd32296d11d56fd089" + }, + "normal_optimized_byte_equal": true, + "scope": "Exact response, actual pair closure, Gaussian dyadic reader and row code, scoped blockwise minimum. No native word or invoice.", + "source_freeze_sha256": "0deadea1883d80a603a2819200697e60d518a580ed1d7bb04ffe60e6991bb82c", + "source_payload_sha256": "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a", + "status": "PASS_INDEPENDENT_SIGN_METRIC_UNIT_CAPTURE_REVIEW" +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/REVIEW.md b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/REVIEW.md new file mode 100644 index 0000000000..0d55352853 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/REVIEW.md @@ -0,0 +1,145 @@ +# Independent review of the 32-field unit centre code + +The frozen algebraic construction passes this review. There is no +material finding. It removes the selected-reader unit obstruction +of the 24-exception response. It does not give a native word or +inherit the response metric through the row code. + +## Response and actual physical ports + +In each eight-mode block, two selected entries have w_j=(1+i)d_j +and negative metric sign. The six other entries have norm one and +positive sign. Thus w*Dw=6-2-2=2. The matrix S=I-ww*D is a +rank-one reflection, and S*=DSD. The selected diagonal entries +are 3. + +The six-mode blocks retain two selected norm-one entries. Their +selected diagonal entries are 2. All sixteen blocks remain +disjoint before the physical pair code. The full correction rank +is 16, the determinant is 1, and the trace is 80. + +The independent checker reconstructs the full 112-port matrix +from the old pinned block signs and physical pair matrices. It +uses the preserved integer-realification engine from the earlier +independent review. No root producer or Gaussian arithmetic +helper is imported. + +Both the 32 FULL ports and the original 16 centre pivots are +closed under the actual physical pair code. The checker verifies +this directly. It checks every response and correction entry, +the exact rank contraction, A^2=I, and A*=DAD. The physical +diagonal is zero outside the 32 FULL ports. It has 16 entries +equal to 2 and 16 entries equal to 3. + +## Normalized reader and row code + +Let P be the ordered original 16 centre pivots. The large part of +V_P is a signed pair-code matrix with a dyadic inverse. Each small +part is the scalar 1-i. Its inverse is (1+i)/2. The checker verifies +both inverse orders of the actual physical minor. + +Set L=V_P^-1 V. The stored reader satisfies + +```text +L_P = I16; +L A = -L. +``` + +The second identity follows from VA=-V, since VU=-2I. Both +identities are also checked on the complete actual matrices. + +Replace rows P of the identity by L to obtain C. If N=C-I, +then N has nonzero rows only in P and nonzero columns only +outside P. Hence N^2=0, and C^-1=I-N=2I-C. The checker verifies +both inverse orders and every serialized coefficient. All +response, reader, and code coefficients are Gaussian dyadic. + +This is a unit on arbitrary arrays. It does not use a promise +that a field is zero or belongs to a proper code image. + +The response metric does not pass through C. This is an actual +failure, not only an unproved assertion: the checker verifies + +```text +C* D C != D; +(C A)* != D (C A)^-1 D. +``` + +Thus a caller must distinguish ZA from ZCA. The sign-only +adjoint conversion for A cannot be assigned to the coded +response without another proof. + +## Meaning of the 32-field minimum + +The minimum applies to independent rank-one sign-metric blocks +with blockwise normalization. It assumes that every diagonal +exception and every pivot for an arbitrary normalized reader is +in the FULL selected coordinates. The actual pair-closed code +preserves this coordinate split. + +A six-mode block needs at least two diagonal exceptions by the +rational norm-three obstruction. An eight-mode block can have +one exception, but its single selected reader coefficient has +norm five and is not a Gaussian dyadic unit. If only that field +is FULL, the reader has no right inverse there. A second FULL +field is therefore required in each eight-mode block. + +These conditions give at least 8 times 2 plus 8 times 2 FULL +coordinates. The present construction reaches 32. It uses +only 16 of them as centre carriers. + +This is not a general native lower bound. It does not cover +coupled blocks, a non-pair-closed mixed representation, +normalization from other frames, code-image division, +additional carriers, or a different diagonal-transfer grammar. + +## An alternative with the unchanged 24-exception matrix + +The checker also verifies a distinct option. Keep the entire +earlier 24-exception response and its metric unchanged. Add the +same eight small ordinary ports to the FULL read set. Use these +16 centre pivots: + +```text +0,27,36,111,20,7,57,46,5,4,35,12,29,32,26,31. +``` + +The first eight give the same dyadic large minor. Each new small +pivot has reader coefficient -1. Both inverse orders of this +minor pass exactly. Thus the unchanged 24-exception response +also has a Gaussian dyadic normalized reader once 32 fields +are available for reading. It uses different small centre +slots. A native access word and its price remain separate. + +This option does not contradict the earlier obstruction: +that obstruction restricted the reader to the original 24 +selected columns. + +## Reproduction and scope + +Run from this directory: + +```text +python3 -I -B check_review.py --out run-normal +python3 -I -O -B check_review.py --out run-optimized +``` + +The receipts must be byte-identical. The checker pins the root +freeze, the actual matrix inputs, and the independent integer +engine. The root's frozen files are unchanged. + +The accepted result is the 32-FULL/16-centre algebraic response +and dyadic row code, with the stated blockwise minimum. Complex +scalar lowering, all 32 target paths, the actual centre access, +native and recursive invoices, and a complete caller remain open. + +The root supplied the 32-field construction. It follows the +norm-five reader obstruction found during the preceding review. +The campaign's controller and cyclic packets supplied the actual +mode and pair data. This review adds an independent exact check, +the coded-metric rejection, and the unchanged-response option. +AI assistance was used. + +No PR, push, commit, or publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/check_review.py b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/check_review.py new file mode 100644 index 0000000000..9d1bfc5f15 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/check_review.py @@ -0,0 +1,135 @@ +#!/usr/bin/env python3 +"""Check the 32-port unit reader with independent integer realification.""" +import argparse +from collections import Counter +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys + +HERE=Path(__file__).resolve().parent +CAMPAIGN=HERE.parents[2] +ENGINE=HERE.parent/'sign-metric-review-20261020/check_review.py' +ENGINE_PIN='2dc96dc39b42c85885859c3b7c09700bda447ffe223f3d9aa03b5ffd1df68867' +FREEZE='root/SIGN-METRIC-UNIT-FREEZE-20261020.json' +FREEZE_PIN='0deadea1883d80a603a2819200697e60d518a580ed1d7bb04ffe60e6991bb82c' +PAYLOAD='root/sign-metric-unit-normal-20261020/RESPONSE.json' +PAYLOAD_PIN='1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a' +if sha256(ENGINE.read_bytes()).hexdigest()!=ENGINE_PIN: + raise ValueError('Independent integer engine pin') +spec=importlib.util.spec_from_file_location('unit_reader_integer_review',ENGINE) +r=importlib.util.module_from_spec(spec);sys.modules[spec.name]=r;spec.loader.exec_module(r) +need=r.need + + +def restrict_columns(a,ports,total): + columns=list(ports)+[total+p for p in ports] + return [{j:row[p] for j,p in enumerate(columns) if p in row} for row in a] + + +def divide(a,d): + need(all(c%d==0 for row in a for c in row.values()),'Exact integer division') + return [{j:c//d for j,c in row.items()} for row in a] + + +def main(): + parser=argparse.ArgumentParser() + parser.add_argument('--out',type=Path,default=HERE/'run-normal') + args=parser.parse_args() + raw=(CAMPAIGN/FREEZE).read_bytes() + need(sha256(raw).hexdigest()==FREEZE_PIN,'Root unit reader freeze') + freeze=json.loads(raw) + for name,pin in freeze['files'].items(): + need(sha256((CAMPAIGN/'root'/name).read_bytes()).hexdigest()==pin,'Root frozen file '+name) + raw=(CAMPAIGN/PAYLOAD).read_bytes() + need(sha256(raw).hexdigest()==PAYLOAD_PIN,'Root unit reader payload') + packet=json.loads(raw) + prior=r.load('lanes/controller-followthrough-20261017/row-involution-20261020/run-normal/ROW-INVOLUTION.json') + pairs=r.load('lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json') + old=r.load('root/sign-metric-normal-20261020/RESPONSE.json') + extra={5,4,35,12,29,32,26,31} + full=set(old['selected'])|extra + centre=prior['pivots'] + need(len(full)==32 and packet['full_ports']==sorted(full),'Actual32 FULL ports') + need(packet['centre_ports']==centre and len(centre)==16,'Actual16 centre ports') + h=r.eye(112);large=set() + for pair in pairs['pair_codes']: + p,q=pair['ports'];large.update((p,q)) + need((p in full)==(q in full) and (p in centre)==(q in centre),'Both physical pair closures') + for i,row in zip((p,q),pair['matrix']): + h[i]={j:int(c) for j,c in zip((p,q),row) if c} + ht=r.transpose(h,112) + hi2=[{j:(1 if i in large else 2)*v for j,v in row.items()} for i,row in enumerate(ht)] + need(r.times(h,hi2)==r.times(hi2,h)==r.eye(112,2),'Pair inverse') + H=r.realify(r.real_rows(h),112);R=r.realify(r.real_rows(hi2),112) + D=r.realify(r.real_rows([{i:-1 if i in full else 1} for i in range(112)]),112) + need(D==r.realify(packet['metric'],112) and r.times(D,H)==r.times(H,D),'Actual sign metric') + w=[{} for _ in range(112)] + for k,block in enumerate(prior['blocks']): + need(len(set(block['ports'])&full)==2,'Two FULL ports per block') + for p,d in zip(block['ports'],block['signs']): + w[p][k]=[d,d if len(block['ports'])==8 and p in full else '0'] + W=r.realify(w,16) + Vmode=r.scale(r.times(r.transpose(W,32),D),-1) + need(r.times(Vmode,W)==r.eye(32,-2),'Sixteen rank-one reflection contractions') + S=r.plus(r.eye(224),r.times(W,Vmode)) + A2=r.times(r.times(R,S),H) + U2=r.times(R,W);V=r.times(Vmode,H) + need(A2==r.realify(packet['response'],112,2),'Independent actual112 response') + need(U2==r.realify(packet['correction_U'],16,2) and V==r.realify(packet['correction_V'],112), + 'Independent actual correction factors') + need(r.times(V,U2)==r.eye(32,-4),'Exact correction rank16') + need(r.times(A2,A2)==r.eye(224,4),'Actual involution') + need(r.transpose(A2,224)==r.times(r.times(D,A2),D),'Actual sign-metric adjoint') + diagonal={i:A2[i].get(i,0)//2 for i in range(112) if A2[i].get(i,0)} + need(set(diagonal)==full and Counter(diagonal.values())=={2:16,3:16},'Actual32 diagonal exceptions') + need(sum(diagonal.values())==80,'Trace80') + M=restrict_columns(V,centre,112) + need(M==r.realify(packet['centre_minor'],16),'Actual centre minor') + Mi2=r.realify(packet['centre_minor_inverse'],16,2) + need(r.times(M,Mi2)==r.times(Mi2,M)==r.eye(32,2),'Both exact Gaussian dyadic minor inverses') + L2=r.times(Mi2,V) + need(L2==r.realify(packet['centre_reader'],112,2),'Actual normalized reader') + need(restrict_columns(L2,centre,112)==r.eye(32,2),'Reader centre block identity') + need(r.times(L2,A2)==r.scale(L2,-2),'Actual centre action LA=-L') + C2=r.eye(224,2) + for k,p in enumerate(centre): + C2[p]=L2[k];C2[112+p]=L2[16+k] + Ci2=r.plus(r.eye(224,4),r.scale(C2,-1)) + need(C2==r.realify(packet['row_code'],112,2) and Ci2==r.realify(packet['row_code_inverse'],112,2), + 'Unit row code and its exact inverse') + need(r.times(C2,Ci2)==r.times(Ci2,C2)==r.eye(224,4),'Both code inverse orders') + N2=r.plus(C2,r.eye(224,-2)) + need(r.times(N2,N2)==[{} for _ in range(224)],'Square-zero code difference') + CA2=divide(r.times(C2,A2),2) + CAinv2=divide(r.times(A2,Ci2),2) + need(r.times(CA2,CAinv2)==r.times(CAinv2,CA2)==r.eye(224,4),'Actual coded inverse') + need(r.transpose(CA2,224)!=r.times(r.times(D,CAinv2),D),'The response metric does not pass through C') + need(r.times(r.times(r.transpose(C2,224),D),C2)!=r.scale(D,4),'C does not preserve the sign metric') + # An alternative uses the unchanged24-exception response with the same32 read ports. + alt_centres=centre[:8]+[next(p for p in b['ports'] if p in extra) for b in prior['blocks'][8:]] + oldV=r.realify(old['correction_V'],112) + altM=restrict_columns(oldV,alt_centres,112) + altMi2=[{j:c*(2 if i%16>=8 else 1) for j,c in row.items()} for i,row in enumerate(r.transpose(altM,32))] + need(r.times(altM,altMi2)==r.times(altMi2,altM)==r.eye(32,2),'Unchanged24 response with32 read-port unit minor') + altL2=r.times(altMi2,oldV) + need(restrict_columns(altL2,alt_centres,112)==r.eye(32,2),'Alternative normalized centre coordinates') + receipt={'status':'PASS_INDEPENDENT_SIGN_METRIC_UNIT_CAPTURE_REVIEW', + 'root_freeze_sha256':FREEZE_PIN,'payload_sha256':PAYLOAD_PIN,'independent_engine_sha256':ENGINE_PIN, + 'data_ports':112,'full_ports':32,'centre_ports':16,'correction_rank':16, + 'diagonal_values':diagonal,'trace':80,'determinant':1, + 'both_minor_inverse_orders':True,'both_row_code_inverse_orders':True,'centre_action_LA_equals_minus_L':True, + 'row_code_metric_inheritance_rejected':True, + 'alternative_unchanged24_response':{'full_read_ports':sorted(full),'unit_centre_pivots':alt_centres, + 'both_minor_inverse_orders':True,'scope':'Algebra only; different centre slots and actual access need a separate word.'}, + 'blockwise32_minimality_scope':'Independent rank-one sign-metric blocks; all diagonal exceptions and arbitrary normalized reader pivots must be in FULL selected fields.', + 'native_word_or_invoice_reviewed':False, + 'producer_sha256':sha256(Path(__file__).read_bytes()).hexdigest()} + args.out.mkdir(parents=True,exist_ok=True) + (args.out/'CHECKS.json').write_text(json.dumps(receipt,sort_keys=True,indent=2)+'\n') + print(json.dumps({k:v for k,v in receipt.items() if k!='diagonal_values'},sort_keys=True)) + + +if __name__=='__main__': + main() diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/run-normal/CHECKS.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/run-normal/CHECKS.json new file mode 100644 index 0000000000..0fe5cc3a29 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/run-normal/CHECKS.json @@ -0,0 +1,109 @@ +{ + "alternative_unchanged24_response": { + "both_minor_inverse_orders": true, + "full_read_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 11, + 12, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 26, + 27, + 29, + 31, + 32, + 35, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "scope": "Algebra only; different centre slots and actual access need a separate word.", + "unit_centre_pivots": [ + 0, + 27, + 36, + 111, + 20, + 7, + 57, + 46, + 5, + 4, + 35, + 12, + 29, + 32, + 26, + 31 + ] + }, + "blockwise32_minimality_scope": "Independent rank-one sign-metric blocks; all diagonal exceptions and arbitrary normalized reader pivots must be in FULL selected fields.", + "both_minor_inverse_orders": true, + "both_row_code_inverse_orders": true, + "centre_action_LA_equals_minus_L": true, + "centre_ports": 16, + "correction_rank": 16, + "data_ports": 112, + "determinant": 1, + "diagonal_values": { + "0": 2, + "1": 3, + "2": 2, + "3": 3, + "4": 3, + "5": 3, + "6": 3, + "7": 2, + "8": 3, + "11": 2, + "12": 3, + "13": 2, + "17": 3, + "18": 3, + "20": 2, + "23": 3, + "24": 3, + "25": 2, + "26": 3, + "27": 2, + "29": 3, + "31": 3, + "32": 3, + "35": 3, + "36": 2, + "42": 2, + "46": 2, + "51": 2, + "57": 2, + "63": 2, + "105": 2, + "111": 2 + }, + "full_ports": 32, + "independent_engine_sha256": "2dc96dc39b42c85885859c3b7c09700bda447ffe223f3d9aa03b5ffd1df68867", + "native_word_or_invoice_reviewed": false, + "payload_sha256": "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a", + "producer_sha256": "0d45392237eb117fbc45ad108a64f923be573578633df5fb056fbb5da71388f1", + "root_freeze_sha256": "0deadea1883d80a603a2819200697e60d518a580ed1d7bb04ffe60e6991bb82c", + "row_code_metric_inheritance_rejected": true, + "status": "PASS_INDEPENDENT_SIGN_METRIC_UNIT_CAPTURE_REVIEW", + "trace": 80 +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/run-optimized/CHECKS.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/run-optimized/CHECKS.json new file mode 100644 index 0000000000..0fe5cc3a29 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/run-optimized/CHECKS.json @@ -0,0 +1,109 @@ +{ + "alternative_unchanged24_response": { + "both_minor_inverse_orders": true, + "full_read_ports": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 11, + 12, + 13, + 17, + 18, + 20, + 23, + 24, + 25, + 26, + 27, + 29, + 31, + 32, + 35, + 36, + 42, + 46, + 51, + 57, + 63, + 105, + 111 + ], + "scope": "Algebra only; different centre slots and actual access need a separate word.", + "unit_centre_pivots": [ + 0, + 27, + 36, + 111, + 20, + 7, + 57, + 46, + 5, + 4, + 35, + 12, + 29, + 32, + 26, + 31 + ] + }, + "blockwise32_minimality_scope": "Independent rank-one sign-metric blocks; all diagonal exceptions and arbitrary normalized reader pivots must be in FULL selected fields.", + "both_minor_inverse_orders": true, + "both_row_code_inverse_orders": true, + "centre_action_LA_equals_minus_L": true, + "centre_ports": 16, + "correction_rank": 16, + "data_ports": 112, + "determinant": 1, + "diagonal_values": { + "0": 2, + "1": 3, + "2": 2, + "3": 3, + "4": 3, + "5": 3, + "6": 3, + "7": 2, + "8": 3, + "11": 2, + "12": 3, + "13": 2, + "17": 3, + "18": 3, + "20": 2, + "23": 3, + "24": 3, + "25": 2, + "26": 3, + "27": 2, + "29": 3, + "31": 3, + "32": 3, + "35": 3, + "36": 2, + "42": 2, + "46": 2, + "51": 2, + "57": 2, + "63": 2, + "105": 2, + "111": 2 + }, + "full_ports": 32, + "independent_engine_sha256": "2dc96dc39b42c85885859c3b7c09700bda447ffe223f3d9aa03b5ffd1df68867", + "native_word_or_invoice_reviewed": false, + "payload_sha256": "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a", + "producer_sha256": "0d45392237eb117fbc45ad108a64f923be573578633df5fb056fbb5da71388f1", + "root_freeze_sha256": "0deadea1883d80a603a2819200697e60d518a580ed1d7bb04ffe60e6991bb82c", + "row_code_metric_inheritance_rejected": true, + "status": "PASS_INDEPENDENT_SIGN_METRIC_UNIT_CAPTURE_REVIEW", + "trace": 80 +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-FREEZE-20261020.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-FREEZE-20261020.json new file mode 100644 index 0000000000..849c0d19d4 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-FREEZE-20261020.json @@ -0,0 +1,11 @@ +{ + "files": { + "SIGN-METRIC-INVOLUTIONS-20261020.md": "6e734a7f471dbb8be9e2bdc0216fb034905e9b9e90ec3fa554e165fabe7dde1f", + "check_sign_metric_involutions_20261020.py": "4c053a9fbc5da82ec1ef39c6740256f3fc0f6d5784df630130b1110a7efae863", + "sign-metric-normal-20261020/CHECKS.json": "065750a71244c5032e433b00bd17d167c14b3d9945ffb0d49094b53e0a05b0c9", + "sign-metric-normal-20261020/RESPONSE.json": "9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c" + }, + "normal_optimized_byte_identical": true, + "schema": "sign-metric-response-freeze-v1", + "scope": "Exact response and sign-metric theorem; native emission and caller remain open." +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-INVOLUTIONS-20261020.md b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-INVOLUTIONS-20261020.md new file mode 100644 index 0000000000..0ad014646b --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-INVOLUTIONS-20261020.md @@ -0,0 +1,146 @@ +# Involutions with a diagonal sign metric + +The actual sixteen-block response admits a Gaussian dyadic replacement +with correction rank sixteen and twenty-four diagonal exceptions. +Its inverse equals itself. Its adjoint equals its conjugate by a diagonal +sign matrix. This removes the odd diagonal scales from the adjoint-to- +inverse conversion at the matrix level. + +This packet gives the exact actual response and its factorization. It +does not give a native word, a complete caller, or a recursive invoice. +In particular, the new complex transfer coefficients need literal scalar +programs and costs. + +## Construction + +Let D be a diagonal matrix with entries in {1,-1}. Choose a column w +over the Gaussian dyadic ring such that w* D w=2, where * is the +conjugate transpose. Then + +```text +S = I - w w* D +S^2 = I +S* = D S D +S* D S = D. +``` + +These identities follow by direct multiplication. No division occurs. +The correction has rank one. Its -1 eigenspace is spanned by w. + +For each signed six-mode block, select two coordinates. Set w=d, +where d is the old sign vector. Give the two selected coordinates sign +-1 in D, and give the other four sign +1. Then w* D w=4-2=2. +The diagonal of S is two at the selected coordinates and zero elsewhere. +All coefficients are real integers. + +For each eight-mode block, select one coordinate p. Set w_j=d_j on +the other seven coordinates, and set w_p=(1+2i)d_p. Give p sign -1 +in D and give the other coordinates sign +1. Then + +```text +w* D w = 7 - |1+2i|^2 = 7-5 = 2. +``` + +The selected diagonal entry of S is six; the other diagonal entries +are zero. Its coefficients are Gaussian integers. The identity uses +the norm of 1+2i. It does not divide by 1+2i or by five. + +Take the direct sum over the eight blocks of each size. The result has +correction rank sixteen, determinant one, and trace eighty. + +## Actual physical ports + +Start with the sixteen pivots from the row-capture construction. Add + +```text +2,25,13,51,11,63,42,105. +``` + +The new large pivots form four complete pair-code blocks: + +```text +(2,25), (13,51), (11,63), (42,105). +``` + +Together with the four old selected pairs, they give exactly two +selected coordinates in each six-mode block. The eight small pivots +remain unchanged. Thus the selected set has twenty-four ports and is +closed under every physical pair code. + +Let H be the actual pair code. It commutes with D. On the large +component H*H=2I; on the small component H=I. The two components do +not mix. Therefore the physical response + +```text +A = H^-1 S H +``` + +satisfies A^2=I and A*=D A D with the same physical diagonal D. +Its diagonal support is exactly the twenty-four selected ports. +The ordinary mode rows keep the old off-diagonal support. Their +coefficients between two ordinary coordinates also remain unchanged. +Their selected-column coefficients change and must be retuned. + +This last point differs from the sixteen-row completion. The present +construction changes selected columns in ordinary rows. The sixteen- +row lower bound for row replacement does not apply to it. + +## Why a sign metric helps the mixed phase + +Let Z be any diagonal unitary field operator that commutes with D. +The line-entry interface has Z=diag(Q_P,I_R). Put E_eff=Z A. Then + +```text +E_eff* = A* Z^-1 + = D A Z^-1 D + = D E_eff^-1 D. +``` + +Thus conjugating the dual cross response by D converts its adjoint +to its inverse. The conversion uses only field signs. It introduces +no odd denominator and no new spatial transform. + +For a literal upper shear B(E*) with cross term -E*, pre- and +post-conjugation by diag(D,D) gives B(E^-1). Each D scale must still +appear in the scalar ledger. All other progress must commute with D; +this condition holds for fieldwise diagonal progress. It must be +checked for any coupled code or bank reset in a complete caller. +This identity does not remove stage dependence or a final phase. + +## A limit of one exception in the six-mode block + +Within a rank-one sign-metric reflection, suppose all but one diagonal +entries are zero. Normalize one ordinary coordinate to one. The zero +diagonal equations give norm one and the same metric sign on all +ordinary coordinates. After an overall sign change of the metric, +the selected coordinate must have Gaussian rational norm k-3. + +For k=6 this would require a^2+b^2=3 for rational a,b. This is +impossible. Write a=A/C and b=B/C in lowest common integer terms. +Modulo three, A^2+B^2=3C^2 forces both A and B to be divisible by +three. The equation then forces C to be divisible by three, a +contradiction. + +For k=8 the required norm is five, and 1+2i supplies it. Thus the +construction uses the minimum number of diagonal exceptions in +each independent rank-one sign-metric block: two for size six and +one for size eight. This is not a bound for coupled blocks, higher +correction rank, non-diagonal metrics, or general native circuits. + +## Validation and scope + +The checker uses exact pairs of rational numbers for Gaussian values. +It checks the pinned actual pair codes, the selected pair closure, +both physical identities, the complete 112-column matrices, and the +rank-sixteen contraction VU=-2I. It also checks ordinary support and +all dyadic denominators. + +Run the checker normally and with optimized Python into separate +directories. The payloads and receipts must be byte-identical. +Independent proof review and a native emission are separate steps. + +This result builds on the campaign's actual signed-clique response, +row-replacement mechanism, normalized pivots, and mixed-phase dual. +AI assistance was used. No publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-CAPTURE-20261020.md b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-CAPTURE-20261020.md new file mode 100644 index 0000000000..66b49b72ff --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-CAPTURE-20261020.md @@ -0,0 +1,99 @@ +# A sign metric with a dyadic centre code + +The twenty-four-exception response has a useful sign metric, but its +selected centre minor is not a unit over the Gaussian dyadic ring. +In each eight-mode block, its reader has coefficient 1-2i at the +only selected field. That coefficient has norm five. This prevents +an arbitrary normalized reader in those selected fields. It does +not invalidate the response or its sign-metric identity. + +A thirty-two-field variant removes this centre-code obstruction. +It retains correction rank sixteen. All response coefficients, the +normalized centre reader, and its row code are Gaussian dyadic. +This is an algebraic construction. A native word and its full invoice +remain separate obligations. + +## Change to the eight-mode blocks + +Retain the two selected fields in each six-mode block from the +previous construction. In each eight-mode block select two fields. +Set + +```text +D_j = -1 on both selected fields, +1 elsewhere; +w_j = (1+i)d_j on both selected fields, d_j elsewhere; +S = I - w w* D. +``` + +Then w* D w=6-2-2=2. Thus S^2=I and S*=D S D. The two selected +diagonal entries are three; the other diagonal entries are zero. +The selected reader coefficient is 1-i up to sign. Its inverse +(1+i)/2 lies in the same Gaussian dyadic ring. + +In each six-mode block the old reader coefficient at a selected +field is a signed unit. Hence one selected field per block supplies +a unit sixteen-by-sixteen minor before the physical pair code. +The original sixteen pivots are closed under that code, so the +physical minor is a unit as well. + +The additional small ports are + +```text +5,4,35,12,29,32,26,31. +``` + +Together with the twenty-four-field set they give thirty-two FULL +fields. Only the original sixteen fields need carry centre rows. +The other sixteen can retain ordinary response values. + +## Unit row code + +Let V be the physical rank-sixteen reader and P the original sixteen +pivots. Set L=V_P^-1 V. Then + +```text +L_P = I, L A = -L. +``` + +Define C by C_P=L and C_R=I_R. The difference C-I has square zero, +so C^-1=2I-C. Every entry of both codes is Gaussian dyadic. +Thus the capture is a unit on arbitrary data. It needs no promise +that a target is zero or already in a special image. + +The source word still requires a literal complex scalar lowering. +The changed selected-column coefficients and all thirty-two +selected target paths must be included. It is not valid to import +the old real1760 scalar tariff or the old sixteen-carrier native +profile. + +The response sign metric does not automatically pass through the +new code C. In particular, the coded effective response Z C A +must not be identified with Z A. A complete forward/backward caller +must track this difference. + +## Scope of the tradeoff + +For independent blocks, the six-mode sign-metric rank-one family +needs at least two diagonal exceptions. The previous proof gives +this rational norm obstruction. In an eight-mode block, one +exception is possible, but its selected reader has norm five and +cannot form a unit minor. A second FULL field is therefore needed +if the centre must be normalized entirely in FULL selected fields. +The present construction reaches these blockwise counts. + +This is not a lower bound for coupled blocks, code-image division, +additional fields, or a general native algorithm. + +The exact checker binds the earlier Gaussian arithmetic helper and +actual matrix/pair sources. It verifies both minor inverse orders, +both code inverse orders, the centre action, actual pair closure, +the full response identities, and every coefficient denominator. +It emits the actual112-port response and the code. Normal and +optimized runs must produce identical files. + +This extension follows the independent review's norm-five reader +obstruction for the twenty-four-field response. It builds on the +campaign's row-capture mechanism and actual signed blocks. +AI assistance was used. No publication is authorized. Before any +future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-FREEZE-20261020.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-FREEZE-20261020.json new file mode 100644 index 0000000000..13f18be5d1 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-FREEZE-20261020.json @@ -0,0 +1,11 @@ +{ + "files": { + "SIGN-METRIC-UNIT-CAPTURE-20261020.md": "c8a582706326c3fcc34a6c350733c6d031d02c6b53bd2df6c91efecd60c329b5", + "check_sign_metric_unit_capture_20261020.py": "54224d9e17085e162d016b7d129d551a71772ce363dddda8bb5db2031f7b9c8e", + "sign-metric-unit-normal-20261020/CHECKS.json": "ef8ed183b6a9917ec24581ac2849b8dfb9b760f14cca3a4ed4d5ba9f391b63f7", + "sign-metric-unit-normal-20261020/RESPONSE.json": "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a" + }, + "normal_optimized_byte_identical": true, + "schema": "sign-metric-unit-capture-freeze-v1", + "scope": "Exact32FULL/16centre response and dyadic unit row code; native word and caller open." +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/check_sign_metric_involutions_20261020.py b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/check_sign_metric_involutions_20261020.py new file mode 100644 index 0000000000..52a191cfb3 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/check_sign_metric_involutions_20261020.py @@ -0,0 +1,223 @@ +#!/usr/bin/env python3 +"""Check a Gaussian dyadic response with a diagonal sign metric.""" + +from fractions import Fraction as F +from pathlib import Path +import argparse +import hashlib +import json + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent / "lanes" +N = 112 +PINS = { + "rows": ( + "controller-followthrough-20261017/row-involution-20261020/" + "run-normal/ROW-INVOLUTION.json", + "a25551b3b99b82477fde561a742fabe1114acbfe6c67cd14284747aaac3dd95b", + ), + "pairs": ( + "independent-review-20261017/cyclic-pair-flags-20261018/" + "CYCLIC-FLAGS.json", + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + ), +} +ZERO = (F(0), F(0)) +ONE = (F(1), F(0)) + + +def need(condition, text): + if not condition: + raise ValueError(text) + + +def add(a, b): + return a[0] + b[0], a[1] + b[1] + + +def neg(a): + return -a[0], -a[1] + + +def times(a, b): + return a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0] + + +def conjugate(a): + return a[0], -a[1] + + +def real(x): + return F(x), F(0) + + +def eye(n): + return [{j: ONE} for j in range(n)] + + +def put(row, j, value): + value = add(row.get(j, ZERO), value) + if value == ZERO: + row.pop(j, None) + else: + row[j] = value + + +def multiply(a, b): + result = [] + for row in a: + out = {} + for j, x in row.items(): + for k, y in b[j].items(): + put(out, k, times(x, y)) + result.append(out) + return result + + +def adjoint(a, width): + out = [{} for _ in range(width)] + for i, row in enumerate(a): + for j, value in row.items(): + out[j][i] = conjugate(value) + return out + + +def serialize(a): + return [{str(j): [str(x), str(y)] for j, (x, y) in sorted(row.items())} + for row in a] + + +def encoded(x): + return (json.dumps(x, sort_keys=True, indent=2) + "\n").encode() + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, + default=HERE / "sign-metric-normal-20261020") + args = parser.parse_args() + sources = {} + for key, (path, pin) in PINS.items(): + raw = (LANES / path).read_bytes() + need(hashlib.sha256(raw).hexdigest() == pin, "source pin: " + key) + sources[key] = json.loads(raw) + rows, pairs = sources["rows"], sources["pairs"] + blocks = rows["blocks"] + old_p = set(rows["pivots"]) + extra = {2, 25, 13, 51, 11, 63, 42, 105} + selected = old_p | extra + need(len(selected) == 24, "selected count") + h, hi = eye(N), eye(N) + for record in pairs["pair_codes"]: + p, q = record["ports"] + need((p in selected) == (q in selected), "selected physical pair closure") + m = [[F(v) for v in row] for row in record["matrix"]] + determinant = m[0][0] * m[1][1] - m[0][1] * m[1][0] + inverse = [[m[1][1] / determinant, -m[0][1] / determinant], + [-m[1][0] / determinant, m[0][0] / determinant]] + for port, row, inverse_row in zip((p, q), m, inverse): + h[port] = {j: real(v) for j, v in zip((p, q), row) if v} + hi[port] = {j: real(v) for j, v in zip((p, q), inverse_row) if v} + need(multiply(h, hi) == multiply(hi, h) == eye(N), "physical pair inverses") + metric = [{p: real(-1 if p in selected else 1)} for p in range(N)] + need(multiply(h, metric) == multiply(metric, h), "metric and pair code commute") + mode = eye(N) + u = [{} for _ in range(N)] + v = [] + records = [] + for index, block in enumerate(blocks): + ports = block["ports"] + d = {p: F(x) for p, x in zip(ports, block["signs"])} + pivots = sorted(set(ports) & selected) + need(len(pivots) == (2 if len(ports) == 6 else 1), "block pivot count") + w = {p: real(d[p]) for p in ports} + if len(ports) == 8: + p = pivots[0] + w[p] = (d[p], 2 * d[p]) + contraction = ZERO + reader = {} + for p in ports: + sigma = -1 if p in selected else 1 + term = times(conjugate(w[p]), real(sigma)) + contraction = add(contraction, times(term, w[p])) + reader[p] = neg(term) + u[p][index] = w[p] + need(contraction == real(2), "block metric norm") + v.append(reader) + for p in ports: + for q in ports: + put(mode[p], q, times(w[p], reader[q])) + records.append({"ports": ports, "selected": pivots, + "w": {str(p): [str(a), str(b)] for p, (a, b) in w.items()}}) + need(multiply(v, u) == [{i: real(-2)} for i in range(16)], + "rank-sixteen contraction") + physical = multiply(multiply(hi, mode), h) + up = multiply(hi, u) + vp = multiply(v, h) + displacement = multiply(up, vp) + expected = eye(N) + for i, row in enumerate(displacement): + for j, value in row.items(): + put(expected[i], j, value) + need(expected == physical, "physical displacement factorization") + need(multiply(physical, physical) == eye(N), "physical involution") + star = adjoint(physical, N) + need(star == multiply(multiply(metric, physical), metric), "sign-metric adjoint") + need(multiply(multiply(star, metric), physical) == metric, "metric preservation") + need({p for p in range(N) if physical[p].get(p, ZERO) != ZERO} == selected, + "physical diagonal support") + need(sum(physical[p].get(p, ZERO)[0] for p in range(N)) == 80, "trace") + old = [{int(j): real(x) for j, x in row.items()} + for row in rows["original_response"]] + old_mode = multiply(multiply(h, old), hi) + ordinary = set(range(N)) - selected + for p in ordinary: + need(set(mode[p]) == set(old_mode[p]), "ordinary mode support") + for q in ordinary: + need(mode[p].get(q, ZERO) == old_mode[p].get(q, ZERO), + "ordinary-to-ordinary coefficients") + for row in physical: + for value in row.values(): + for component in value: + den = component.denominator + need(den & (den - 1) == 0, "Gaussian dyadic coefficient") + payload = { + "schema": "sign-metric-rank16-response-v1", + "source_pins": {name: pin for name, (_, pin) in PINS.items()}, + "selected": sorted(selected), + "extra_selected": sorted(extra), + "blocks": records, + "mode_response": serialize(mode), + "response": serialize(physical), + "response_adjoint": serialize(star), + "metric": serialize(metric), + "correction_U": serialize(up), + "correction_V": serialize(vp), + } + raw = encoded(payload) + args.output.mkdir(parents=True, exist_ok=True) + (args.output / "RESPONSE.json").write_bytes(raw) + receipt = { + "status": "PASS_EXACT_SIGN_METRIC_RESPONSE", + "payload_sha256": hashlib.sha256(raw).hexdigest(), + "data_ports": N, + "selected_ports": 24, + "correction_rank": 16, + "trace": 80, + "determinant": 1, + "large_blocks": 8, + "small_blocks": 8, + "all_coefficients_gaussian_dyadic": True, + "metric_diagonal_signs_only": True, + "ordinary_mode_support_unchanged": True, + "native_word_emitted": False, + "native_invoice_established": False, + "complete_caller_closed": False, + } + (args.output / "CHECKS.json").write_bytes(encoded(receipt)) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/check_sign_metric_unit_capture_20261020.py b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/check_sign_metric_unit_capture_20261020.py new file mode 100644 index 0000000000..b3376616c9 --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/check_sign_metric_unit_capture_20261020.py @@ -0,0 +1,137 @@ +#!/usr/bin/env python3 +"""Check the dyadic centre minor of the thirty-two-carrier variant.""" + +from pathlib import Path +import argparse +import hashlib +import importlib.util +import json + + +HERE = Path(__file__).resolve().parent +HELPER = HERE / "check_sign_metric_involutions_20261020.py" +HELPER_SHA = "4c053a9fbc5da82ec1ef39c6740256f3fc0f6d5784df630130b1110a7efae863" + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--output", type=Path, + default=HERE / "sign-metric-unit-normal-20261020") + args = parser.parse_args() + if hashlib.sha256(HELPER.read_bytes()).hexdigest() != HELPER_SHA: + raise ValueError("helper pin") + spec = importlib.util.spec_from_file_location("frozen_gaussian_helpers", HELPER) + g = importlib.util.module_from_spec(spec) + spec.loader.exec_module(g) + sources = {} + for key, (path, pin) in g.PINS.items(): + raw = (g.LANES / path).read_bytes() + g.need(hashlib.sha256(raw).hexdigest() == pin, "source pin: " + key) + sources[key] = json.loads(raw) + blocks = sources["rows"]["blocks"] + pivots = sources["rows"]["pivots"] + selected = set(pivots) | {2, 25, 13, 51, 11, 63, 42, 105} + for block in blocks: + if block["size"] == 8: + selected.add(next(p for p in block["ports"] if p != block["pivot"])) + g.need(len(selected) == 32, "thirty-two selected fields") + h, hi = g.eye(112), g.eye(112) + for record in sources["pairs"]["pair_codes"]: + p, q = record["ports"] + g.need((p in selected) == (q in selected), "full pair closure") + g.need((p in pivots) == (q in pivots), "centre pair closure") + m = [[g.F(x) for x in row] for row in record["matrix"]] + determinant = m[0][0] * m[1][1] - m[0][1] * m[1][0] + inv = [[m[1][1] / determinant, -m[0][1] / determinant], + [-m[1][0] / determinant, m[0][0] / determinant]] + for port, row, inverse in zip((p, q), m, inv): + h[port] = {j: g.real(x) for j, x in zip((p, q), row) if x} + hi[port] = {j: g.real(x) for j, x in zip((p, q), inverse) if x} + metric = [{p: g.real(-1 if p in selected else 1)} for p in range(112)] + u, v, section = [{} for _ in range(112)], [], [{} for _ in range(112)] + for index, block in enumerate(blocks): + d = {p: g.F(s) for p, s in zip(block["ports"], block["signs"])} + sel = selected & set(block["ports"]) + g.need(len(sel) == 2, "two selected ports per block") + w = {p: (d[p], d[p] if block["size"] == 8 and p in sel else g.F(0)) + for p in block["ports"]} + reader = {} + for p in block["ports"]: + u[p][index] = w[p] + reader[p] = g.times(g.conjugate(w[p]), g.real(1 if p in selected else -1)) + v.append(reader) + a, b = reader[block["pivot"]] + norm = a * a + b * b + section[block["pivot"]][index] = (a / norm, -b / norm) + g.need(g.multiply(v, u) == [{i: g.real(-2)} for i in range(16)], + "metric contraction") + g.need(g.multiply(v, section) == g.eye(16), "mode dyadic section") + up, vp = g.multiply(hi, u), g.multiply(v, h) + jp = g.multiply(hi, section) + g.need(g.multiply(vp, jp) == g.eye(16), "physical dyadic section") + g.need(all(not row for p, row in enumerate(jp) if p not in pivots), + "section supported on sixteen centre carriers") + response = g.eye(112) + for i, row in enumerate(g.multiply(up, vp)): + for j, value in row.items(): + g.put(response[i], j, value) + inverse_minor = [jp[p] for p in pivots] + minor = [{j: row[p] for j, p in enumerate(pivots) if p in row} for row in vp] + g.need(g.multiply(minor, inverse_minor) == g.eye(16), "minor right inverse") + g.need(g.multiply(inverse_minor, minor) == g.eye(16), "minor left inverse") + reader = g.multiply(inverse_minor, vp) + g.need([{j: row[p] for j, p in enumerate(pivots) if p in row} + for row in reader] == g.eye(16), "normalized centre reader") + code, inverse_code = g.eye(112), g.eye(112) + for p, row in zip(pivots, reader): + code[p] = dict(row) + inverse_code[p] = {j: (value if j == p else g.neg(value)) + for j, value in row.items()} + g.need(g.multiply(code, inverse_code) == g.multiply(inverse_code, code) == g.eye(112), + "both centre code inverse orders") + g.need(g.multiply(reader, response) == + [{j: g.neg(value) for j, value in row.items()} for row in reader], + "centre action is minus identity") + g.need(g.multiply(response, response) == g.eye(112), "response involution") + g.need(g.adjoint(response, 112) == g.multiply(g.multiply(metric, response), metric), + "sign-metric adjoint") + g.need({p for p in range(112) if response[p].get(p, g.ZERO) != g.ZERO} == selected, + "exact diagonal support") + for matrix in (response, inverse_minor, reader, code, inverse_code): + for row in matrix: + for value in row.values(): + for x in value: + g.need(x.denominator & (x.denominator - 1) == 0, "Gaussian dyadic entry") + payload = { + "schema": "sign-metric-rank16-unit-centre-v1", + "source_pins": {"helper": HELPER_SHA, **{k: p for k, (_, p) in g.PINS.items()}}, + "full_ports": sorted(selected), + "centre_ports": pivots, + "response": g.serialize(response), + "metric": g.serialize(metric), + "correction_U": g.serialize(up), + "correction_V": g.serialize(vp), + "centre_minor": g.serialize(minor), + "centre_minor_inverse": g.serialize(inverse_minor), + "centre_reader": g.serialize(reader), + "row_code": g.serialize(code), + "row_code_inverse": g.serialize(inverse_code), + } + raw = g.encoded(payload) + args.output.mkdir(parents=True, exist_ok=True) + (args.output / "RESPONSE.json").write_bytes(raw) + receipt = { + "status": "PASS_EXACT_SIGN_METRIC_UNIT_CAPTURE", + "payload_sha256": hashlib.sha256(raw).hexdigest(), + "data_ports": 112, "full_ports": 32, "centre_ports": 16, + "correction_rank": 16, "centre_minor_is_gaussian_dyadic_unit": True, + "code_displacement_square_is_zero": True, + "native_word_emitted": False, "scalar_invoice_established": False, + "full_caller_closed": False, + } + (args.output / "CHECKS.json").write_bytes(g.encoded(receipt)) + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/sign-metric-normal-20261020/CHECKS.json b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/sign-metric-normal-20261020/CHECKS.json new file mode 100644 index 0000000000..21351feb8c --- /dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/sign-metric-normal-20261020/CHECKS.json @@ -0,0 +1,17 @@ +{ + "all_coefficients_gaussian_dyadic": true, + "complete_caller_closed": false, + "correction_rank": 16, + "data_ports": 112, + "determinant": 1, + "large_blocks": 8, + "metric_diagonal_signs_only": true, + "native_invoice_established": false, + "native_word_emitted": false, + "ordinary_mode_support_unchanged": true, + "payload_sha256": "9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c", + "selected_ports": 24, + "small_blocks": 8, + "status": "PASS_EXACT_SIGN_METRIC_RESPONSE", + "trace": 80 +} diff --git a/research/centre-metric-encoders/annexes/sign-metric-capture/frozen/root/sign-metric-normal-20261020/RESPONSE.json 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/dev/null +++ b/research/centre-metric-encoders/annexes/sign-metric-capture/replay.py @@ -0,0 +1,100 @@ +#!/usr/bin/env python3 +"""Replay the frozen sign-metric checks in a new output directory.""" + +import argparse +import hashlib +import json +from pathlib import Path +import shutil +import subprocess +import sys + + +HERE = Path(__file__).resolve().parent +REVIEW = "lanes/oblique-native-20261017/sign-metric-review-20261020" +UNIT_REVIEW = "lanes/oblique-native-20261017/sign-metric-unit-review-20261020" +CASES = [ + ("response24", "root/check_sign_metric_involutions_20261020.py", "--output", + "root/sign-metric-normal-20261020", ("CHECKS.json", "RESPONSE.json")), + ("review24", REVIEW + "/check_review.py", "--out", + REVIEW + "/run-normal", ("CHECKS.json",)), + ("reader24", REVIEW + "/check_reader_addendum.py", None, + REVIEW, ("READER-CHECKS.json",)), + ("capture32", "root/check_sign_metric_unit_capture_20261020.py", "--output", + "root/sign-metric-unit-normal-20261020", ("CHECKS.json", "RESPONSE.json")), + ("review32", UNIT_REVIEW + "/check_review.py", "--out", + UNIT_REVIEW + "/run-normal", ("CHECKS.json",)), +] + + +def digest(path): + return hashlib.sha256(path.read_bytes()).hexdigest() + + +def check_sources(manifest): + for entry in manifest["files"]: + path = HERE / entry["path"] + if path.stat().st_size != entry["bytes"] or digest(path) != entry["sha256"]: + raise ValueError("Source changed: " + entry["path"]) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + output = args.out.resolve() + if output.is_relative_to(HERE): + raise ValueError("The output directory must be outside the annex") + if output.exists(): + raise ValueError("The output directory must be new") + if shutil.disk_usage(HERE).free < 3 * 1024**3: + raise ValueError("At least 3 GiB free space is required") + manifest = json.loads((HERE / "SOURCES.json").read_text()) + check_sources(manifest) + output.mkdir(parents=True) + results = [] + for mode, flags in (("normal", []), ("optimized", ["-O"])): + scratch = output / ("source-" + mode) + shutil.copytree(HERE / "frozen", scratch) + for name, script, option, expected_dir, names in CASES: + target = output / name / mode + target.mkdir(parents=True) + command = [sys.executable, "-I", *flags, "-B", str(scratch / script)] + if option: + command.extend((option, str(target))) + result = subprocess.run(command, cwd=scratch, stdout=subprocess.PIPE, + stderr=subprocess.STDOUT, text=True, check=False) + (target / "stdout.log").write_text(result.stdout) + if result.returncode: + raise RuntimeError(name + " failed; read " + str(target / "stdout.log")) + files = [] + for filename in names: + actual = target / filename if option else scratch / expected_dir / filename + expected = HERE / "frozen" / expected_dir / filename + if actual.read_bytes() != expected.read_bytes(): + raise ValueError(name + " differs from the frozen " + filename) + if not option: + shutil.copyfile(actual, target / filename) + files.append({"name": filename, "sha256": digest(actual), + "matches_frozen_bytes": True}) + results.append({"check": name, "mode": mode, "files": files}) + print("PASS " + name + " " + mode, flush=True) + shutil.rmtree(scratch) + check_sources(manifest) + receipt = { + "status": "PASS_SIGN_METRIC_CAPTURE_ANNEX", + "checks": results, + "source_files_checked": len(manifest["files"]), + "sources_sha256": digest(HERE / "SOURCES.json"), + "runner_sha256": digest(Path(__file__)), + "source_files_unchanged": True, + "original_scripts_unchanged": True, + "native_word_or_invoice_checked": False, + "main_encoder_suite_run": False, + } + (output / "REPLAY.json").write_text(json.dumps(receipt, sort_keys=True, indent=2) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/publication-reviews/centre-metric-encoders/sign-metric-review/ANNEX-LINKS.json b/research/publication-reviews/centre-metric-encoders/sign-metric-review/ANNEX-LINKS.json new file mode 100644 index 0000000000..b50f01f641 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/sign-metric-review/ANNEX-LINKS.json @@ -0,0 +1,54 @@ +{ + "links": [ + [ + "README.md", + "frozen/root/SIGN-METRIC-INVOLUTIONS-20261020.md" + ], + [ + "README.md", + "frozen/root/SIGN-METRIC-UNIT-CAPTURE-20261020.md" + ], + [ + "README.md", + "frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/REVIEW.md" + ], + [ + "README.md", + "frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-ADDENDUM.md" + ], + [ + "README.md", + "frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/REVIEW.md" + ], + [ + "README.md", + "SOURCES.json" + ], + [ + "README.md", + "evidence/REPLAY.json" + ], + [ + "README.md", + "ANNEX-MANIFEST.json" + ], + [ + "README.md", + "NOTICE.md" + ], + [ + "NOTICE.md", + "notices/LICENSE" + ], + [ + "NOTICE.md", + "SOURCES.json" + ], + [ + "NOTICE.md", + "../../NOTICE.md" + ] + ], + "remote_links_not_verified": true, + "status": "PASS_NEW_SIGN_METRIC_ANNEX_LINKS" +} diff --git a/research/publication-reviews/centre-metric-encoders/sign-metric-review/BODY-CLAIM-CHECK.json b/research/publication-reviews/centre-metric-encoders/sign-metric-review/BODY-CLAIM-CHECK.json new file mode 100644 index 0000000000..f75c050817 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/sign-metric-review/BODY-CLAIM-CHECK.json @@ -0,0 +1,27 @@ +{ + "accepted_review_sha256": "c46845f56ac987a180aac699cae8854ca29e0c3a13fd46eda81fc408fc6adab1", + "annex_manifest_sha256": "c19c4c25c1d2b20c89e674537a5afbbb19869e7a7bd354f8e26df4d19130cf6d", + "body_sha256": "e687dce3b6481ca0e20f6ca27e0526fc4303d121ea1efc5c0d2927ed9c1adb49", + "claim_checks": [ + "24-exception response and ordered sign-metric conversion retain their hypotheses", + "Whole24-column reader obstruction is arbitrary Gaussian-dyadic normalization only", + "32-FULL/16-centre minimum is limited to the stated blockwise class", + "The failure of C to preserve D and the changed centre slots of the alternative remain explicit", + "Ten-run evidence, command, prerequisites, exact byte comparisons and omitted main/native/global checks agree with the annex", + "No native invoice or complete kappa improvement is claimed" + ], + "not_performed": [ + "Final COMMIT substitution and remote file-object verification", + "GitHub rendering or published-body readback", + "Any package pointer creation or accepted README edit" + ], + "pointer_proposal_sha256": "dd44004ffd460b4f168b40461b26745f3afce1953714aa3c035bc8ac95fd7819", + "required_claim_edits": [], + "resolved_publication_findings": [ + "Opening now states correction rank16; A itself is a rank112 unit", + "Pointer proposal no longer asks to change the accepted README while claiming preservation", + "Fresh independent publication review has the required nested public link" + ], + "status": 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+ } + ], + "mode": "normal" + }, + { + "check": "reader24", + "files": [ + { + "matches_frozen_bytes": true, + "name": "READER-CHECKS.json", + "sha256": "f7ce27efaa097b8214a16b56fe060028ae5f94b9ed2aacd0f150667f02e382b8" + } + ], + "mode": "normal" + }, + { + "check": "capture32", + "files": [ + { + "matches_frozen_bytes": true, + "name": "CHECKS.json", + "sha256": "ef8ed183b6a9917ec24581ac2849b8dfb9b760f14cca3a4ed4d5ba9f391b63f7" + }, + { + "matches_frozen_bytes": true, + "name": "RESPONSE.json", + "sha256": "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a" + } + ], + "mode": "normal" + }, + { + "check": "review32", + "files": [ + { + "matches_frozen_bytes": true, + "name": "CHECKS.json", + "sha256": "47fa3c6eda467849775da7aedb0b250db4cf95782de550cd32296d11d56fd089" + } + ], + "mode": "normal" + }, + { + "check": "response24", + "files": [ + { + "matches_frozen_bytes": true, + "name": "CHECKS.json", + "sha256": "065750a71244c5032e433b00bd17d167c14b3d9945ffb0d49094b53e0a05b0c9" + }, + { + "matches_frozen_bytes": true, + "name": "RESPONSE.json", + "sha256": "9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c" + } + ], + "mode": "optimized" + }, + { + "check": "review24", + "files": [ + { + "matches_frozen_bytes": true, + "name": "CHECKS.json", + "sha256": "35bd3020f2d93efc4e972e1713982e240e88473b84e72eb86efc248a6460a162" + } + ], + "mode": "optimized" + }, + { + "check": "reader24", + "files": [ + { + "matches_frozen_bytes": true, + "name": "READER-CHECKS.json", + "sha256": "f7ce27efaa097b8214a16b56fe060028ae5f94b9ed2aacd0f150667f02e382b8" + } + ], + "mode": "optimized" + }, + { + "check": "capture32", + "files": [ + { + "matches_frozen_bytes": true, + "name": "CHECKS.json", + "sha256": "ef8ed183b6a9917ec24581ac2849b8dfb9b760f14cca3a4ed4d5ba9f391b63f7" + }, + { + "matches_frozen_bytes": true, + "name": "RESPONSE.json", + "sha256": "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a" + } + ], + "mode": "optimized" + }, + { + "check": "review32", + "files": [ + { + "matches_frozen_bytes": true, + "name": "CHECKS.json", + "sha256": "47fa3c6eda467849775da7aedb0b250db4cf95782de550cd32296d11d56fd089" + } + ], + "mode": "optimized" + } + ], + "main_encoder_suite_run": false, + "native_word_or_invoice_checked": false, + "original_scripts_unchanged": true, + "runner_sha256": "bb7ced02ce61e902ea61d6520d0edd7b2bd65398c887dd5ac2c9c9711338dd3b", + "source_files_checked": 26, + "source_files_unchanged": true, + "sources_sha256": "935e7716b4c69387a5e5818fe41ab64e6ba9bf141128a788e4f54efbca2de515", + "status": "PASS_SIGN_METRIC_CAPTURE_ANNEX" +} diff --git a/research/publication-reviews/centre-metric-encoders/sign-metric-review/REVIEW.json b/research/publication-reviews/centre-metric-encoders/sign-metric-review/REVIEW.json new file mode 100644 index 0000000000..3a190fc434 --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/sign-metric-review/REVIEW.json @@ -0,0 +1,78 @@ +{ + "accepted_claims": [ + "Actual 24-exception Gaussian-dyadic response is an involution with diagonal sign metric and correction rank 16", + "The entire old 24-column reader has no Gaussian-dyadic right inverse", + "Actual 32-FULL/16-centre response has an exact Gaussian-dyadic normalized reader and unit row code on arbitrary arrays", + "32 FULL fields are minimal only in the stated independent rank-one sign-metric blockwise normalization class", + "An expanded 32-field read set gives an exact unit minor for the unchanged 24-exception response with different small centre slots", + "The response sign metric does not pass through the new row code" + ], + "annex_manifest_sha256": "c19c4c25c1d2b20c89e674537a5afbbb19869e7a7bd354f8e26df4d19130cf6d", + "artifacts": { + "ANNEX-LINKS.json": "77cad084e33c66117aacf9d812296357eedbc04fbea24f68669e1e7f923ec56f", + "COLD-REPLAY.json": "362135dc06233b3a4930817a845a47d53875b641ba9c36a1d5c094cb580a6f21", + "INDEPENDENT-READER-AUDIT.json": "1940d67e39d3b2fac96bf295c7233858beafc40b15dcaa7d6fe53cae91efad1d", + "INPUT-HASHES.json": "18d097a6768009c85fc55f6644f6dd40b831042a3898eb2f9e0fcd7934035b71", + "REPLAY.json": "236a2d33084c98dbb3119f1d712fc1b184a1d4c79da6c3464d6559ce25f2c38f", + "REVIEW.md": "ec9a6c591b8ee77d7d448ca9ee45f097ada048182a683979d0af891d371c8951", + "SOURCE-CLOSURE.json": "2f7d7795d1feb26fbc8df17bd6756f9e5bf83c3ec5539b5b2bd820202c0e4634", + "independent_reader_audit.py": "2b6294f63bdd9600f79058c0bd4fc5c7e64e770742a4da12840fe2fa17d9b3e6" + }, + "checks_not_run": [ + "Main encoder suite", + "Native complex scalar lowering, centre access or native invoice", + "Complete coupled caller, recursive hosting, storage or finite precision", + "Current selected-supplier admission", + "Complete kappa calculation", + "Git or network operations", + "Final remote objects, GitHub rendering or published readback" + ], + "checks_run": [ + "All 26 frozen files match original campaign bytes", + "Fresh relocated cold replay runs both producers and three independent checks in normal and optimized Python", + "All receipts and both full response payloads equal frozen bytes", + "Complete cold replay receipt equals writer receipt byte for byte", + "Direct selected-reader ranks in both F5 sectors and an imaginary-coefficient mutation control", + "Both exact minor and code inverse orders; Gaussian-dyadic denominator checks", + "Concrete C*DC off-diagonal entry differs from D", + "Output-inside-annex and same-size changed-source rejection controls", + "Original 254 main files and ten prior review files unchanged; twelve new local links checked" + ], + "independent_human_review": false, + "kappa_improvement": false, + "local_review_links_checked": [ + "../../../centre-metric-encoders/annexes/sign-metric-capture/README.md", + "../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-INVOLUTIONS-20261020.md", + "../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-ADDENDUM.md", + "../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-CAPTURE-20261020.md", + "../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/REVIEW.md", + "SOURCE-CLOSURE.json", + "../../../centre-metric-encoders/annexes/sign-metric-capture/NOTICE.md", + "COLD-REPLAY.json", + "REPLAY.json", + "INDEPENDENT-READER-AUDIT.json" + ], + "original_main_files_including_manifest_unchanged": 254, + "prior_main_review_files_unchanged": 10, + "proof_qualifications": [ + "The response itself has rank 112; its correction has rank 16", + "All exceptions and arbitrary-reader pivots must lie in the FULL fields for the blockwise minimum", + "No native impossibility conclusion from the norm-five selected-reader obstruction", + "ZA and ZCA require separate caller treatment", + "No inherited real-1760 tariff or 16-carrier native profile" + ], + "public_review_layout": "research/publication-reviews/centre-metric-encoders/sign-metric-review", + "resolved_findings": [ + { + "finding": "New runner accepted output inside its frozen source tree, which could recurse during copy", + "fix": "Resolved-path outside-annex guard before output creation", + "verification": "Rejected a fresh path inside frozen without creating it" + } + ], + "review_type": "Independent OpenAI Codex agent proof review, cold replay, and reader audit", + "runner_sha256": "bb7ced02ce61e902ea61d6520d0edd7b2bd65398c887dd5ac2c9c9711338dd3b", + "schema": 1, + "sources_sha256": "935e7716b4c69387a5e5818fe41ab64e6ba9bf141128a788e4f54efbca2de515", + "status": "PASS_SCOPED_SIGN_METRIC_CAPTURE_ANNEX_REVIEW", + "unresolved_material_findings": [] +} diff --git a/research/publication-reviews/centre-metric-encoders/sign-metric-review/REVIEW.md b/research/publication-reviews/centre-metric-encoders/sign-metric-review/REVIEW.md new file mode 100644 index 0000000000..0444f149fe --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/sign-metric-review/REVIEW.md @@ -0,0 +1,121 @@ +# Independent review of the sign-metric capture annex + +The annex passes for its stated matrix and reader claims. It gives a +24-exception response with correction rank 16, a whole selected-reader +obstruction, and a 32-FULL/16-centre Gaussian-dyadic unit construction. +The minimum of 32 applies only to the stated blockwise class. A separate +option retains the first response and expands the read set to 32 fields. +No native word, complete invoice, or complete kappa improvement follows. + +This is a fresh review by a separate OpenAI Codex agent. It does not +claim independent human review or a formal-kernel proof. The accepted +main encoder package and its earlier review remain unchanged. + +The [annex README](../../../centre-metric-encoders/annexes/sign-metric-capture/README.md) +states the adopted claims. The +[first proof](../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-INVOLUTIONS-20261020.md) +uses S=I-ww*D with w*Dw=2. Direct multiplication proves the involution +and sign-metric identities. Its correction has rank one in each of the +sixteen disjoint mode blocks. The exact physical pair code commutes +with D, and its Gram matrix has constant scale on each invariant size +component. This proves the corresponding identities for A=H^-1 S H. +The full response A is a unit of rank 112. Its correction A-I has +rank 16, its determinant is one, and its trace is 80. + +The 24 exceptional diagonal coordinates have the stated pair closure. +The ordinary physical principal block and row support are preserved. +All 24 selected columns change within ordinary rows. The construction +therefore cannot inherit a theorem restricted to selected-row changes. +For diagonal unitary Z commuting with D, the ordered identity is +D(ZA)*D=(ZA)^-1. This proof does not commute A past Z. Intervening +progress, code boundaries, signs, and final phases remain obligations. + +The [reader addendum](../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-review-20261020/READER-ADDENDUM.md) +proves a whole-reader obstruction, not only a failed square minor. +Each of eight small rows has a single selected coefficient with norm +five. The ring map to F5 with i mapped to three kills those rows. +A right inverse over Z[i,1/2] would reduce to an impossible right +inverse of that rank-deficient matrix. The claim concerns arbitrary +normalization from those 24 columns. It does not exclude code-image +division, other columns, or a different representation. + +The [unit-capture proof](../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/root/SIGN-METRIC-UNIT-CAPTURE-20261020.md) +uses two selected entries of norm two in each small block. Their reader +coefficients are Gaussian-dyadic units. The actual original centre +pivots give a unit minor after the pair code. Thus L=V_P^-1 V satisfies +L_P=I and LA=-L. The row code C has C_P=L and identity ordinary rows. +Its difference from the identity has only centre rows and noncentre +columns, so its square is zero. Both inverse orders hold on arbitrary +arrays, with no clean-input promise. + +The actual C fails C*DC=D. The sign-only adjoint conversion for ZA +therefore does not pass to ZCA. The complete caller must use the actual +coded response. The unchanged-response option in the +[unit review](../../../centre-metric-encoders/annexes/sign-metric-capture/frozen/lanes/oblique-native-20261017/sign-metric-unit-review-20261020/REVIEW.md) +has a different small centre set. Its exact unit minor requires the +expanded 32-field read set; it does not remove the original obstruction. + +The blockwise minimum is valid with all stated hypotheses. A rank-one +sign-metric reflection with one exceptional diagonal coordinate in a +k-mode block requires Gaussian rational norm k-3. The norm-three +descent excludes one exception for a six-mode block. Zero exceptions +contradict its trace. An eight-mode block can use one exception, but +its sole FULL reader coefficient then has norm five and is not a unit. +For arbitrary blockwise normalization, a second FULL field is required. +The two fields per block give 32 in total, and the construction attains +this count. The argument requires independent rank-one blocks, a +diagonal sign metric, and every exception and reader pivot in the FULL +set. The actual pair-closed representation preserves that split. +Coupled blocks, higher rank, other frames, other representations, +code-image division, and general native algorithms are outside it. + +The [source closure check](SOURCE-CLOSURE.json) verifies all 26 original +files byte for byte, including the reader addendum and its freeze. +The annex contains 59 files, including its separate manifest. All 253 +main-manifest members and that historical manifest remain unchanged. +All ten files in the prior main publication review also remain +unchanged. The new README and notice have twelve valid local links. +The [notice](../../../centre-metric-encoders/annexes/sign-metric-capture/NOTICE.md) +retains source roles, the parent lineage, license, AI credit, and the +historical status of the frozen authorization text. + +The [cold replay](COLD-REPLAY.json) used a copy outside the workspace: + +```sh +python3 -I -B /private/tmp/sign-metric-capture-review-20261022/annex/replay.py --out /private/tmp/sign-metric-capture-review-20261022/output +``` + +All ten runs passed: two producers and three independent checks, each +in normal and optimized Python. All receipts and both complete response +payloads equal the frozen bytes. The complete new [replay receipt](REPLAY.json) +also equals the writer's receipt byte for byte. The independent full +response checks use integer realification and import no Gaussian-pair +producer. The checks include actual pair closure, all 112 columns, +rank contractions, both inverse orders, mixed-phase ordering, and +the stated mathematical negative controls. + +The separate [reader audit](INDEPENDENT-READER-AUDIT.json) imports no +source program. The old selected reader has rank eight under i mapped +to three in F5, while the full reader and expanded read set have rank +16. The other Gaussian residue sector has rank 16 even on the old +selected set. This distinguishes the ring obstruction from one +favourable residue check. Discarding imaginary coefficients also loses +the obstruction. The audit checks both exact minor inverse orders and +both exact row-code inverse orders over Gaussian rationals, with dyadic +denominators. At row zero, column 13, C*DC is -1/2 while D is zero. +This is a concrete rejection of metric inheritance through C. + +Review found one new-runner defect: output inside the frozen subtree +could make the copy include its own output. The writer added a resolved +path guard before creation. A negative control confirms rejection +without creating the path. A changed source of the same byte length +is also rejected before output creation. No frozen source needed a +change. The first admission stopped when a notice-only update changed +the candidate manifest; the final manifest is bound in this review. + +The main encoder suite was not run. No native scalar lowering, native +centre access, coupled caller, recursive invoice, storage or precision +proof, or complete kappa calculation ran. The old real-1760 tariff and +16-carrier native profile do not price this changed response family. +No Git operation or network access was used. Final remote objects, +rendering, and published-body readback remain with the publisher. diff --git a/research/publication-reviews/centre-metric-encoders/sign-metric-review/SOURCE-CLOSURE.json b/research/publication-reviews/centre-metric-encoders/sign-metric-review/SOURCE-CLOSURE.json new file mode 100644 index 0000000000..6328efa4dc --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/sign-metric-review/SOURCE-CLOSURE.json @@ -0,0 +1,24 @@ +{ + "admission_note": "The first admission used the earlier manifest and stopped after the writer changed only the historical-status notice. The final notice and manifest are bound here. No mathematical replay ran on the earlier candidate.", + "annex_files_including_manifest": 59, + "annex_manifest_sha256": "c19c4c25c1d2b20c89e674537a5afbbb19869e7a7bd354f8e26df4d19130cf6d", + "frozen_sources_modified": false, + "git_or_network_used": false, + "main_manifest_entries_unchanged": 253, + "main_manifest_sha256": "f7aa100a7389e94518b980fe93e91773602f53b5d782a7c677612be4c9790866", + "prior_review_file_hashes": { + "COMMANDS.sh": "f718dd77c783f1b3a0067400053b2d71aea4e752ee4f767ca022620025dbf3a3", + "DIRECT-CHECKS.json": "0c334499b41ab91e192e484da50db820a65439d37318db03d4b256ca474a19bb", + "PACKAGE-CHECKS.json": "ab24fee2f10928a14c99444cdf555cd3ac4c7a6e54b71a647872daa7649a2b4d", + "REVIEW.json": "2694ef4027489696b7713e1e8399ea702322abca4e73e4c444708d083302c44d", + "REVIEW.md": "1aad258ca380ec9812f3e3f80117771ad49189b9288c8230737cad24479d1143", + "REVIEWED-PACKAGE-MANIFEST.json": "f7aa100a7389e94518b980fe93e91773602f53b5d782a7c677612be4c9790866", + "REVIEWED-README.md": "564e2f1624003818c06ed156d0a2b6e04f1fa465fce730485850c734137f0a2d", + "SOURCE-SNAPSHOT.json": "a77150c7677d932253c50a92ddabad3c8fa50c8fc26ff5317c1be8346ccfc5ad", + "check_package.py": "1a5fff442f2c496fa0b8d815ab53f5fe1e8dea87998fc288a071879f3581ced6", + "direct_check.py": "85d9054966514c1119c427a82c039e45e0697b4ed322d5f1a5cfc72be84e2980" + }, + "source_files_byte_exact": 26, + "source_manifest_sha256": "935e7716b4c69387a5e5818fe41ab64e6ba9bf141128a788e4f54efbca2de515", + "status": "PASS_SIGN_METRIC_ANNEX_SOURCE_CLOSURE" +} diff --git a/research/publication-reviews/centre-metric-encoders/sign-metric-review/independent_reader_audit.py b/research/publication-reviews/centre-metric-encoders/sign-metric-review/independent_reader_audit.py new file mode 100644 index 0000000000..896b141f9b --- /dev/null +++ b/research/publication-reviews/centre-metric-encoders/sign-metric-review/independent_reader_audit.py @@ -0,0 +1,165 @@ +#!/usr/bin/env python3 +"""Check the selected readers without importing a source program.""" + +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path + + +ZERO, ONE = (Q(0), Q(0)), (Q(1), Q(0)) + + +def need(condition, label): + if not condition: + raise ValueError(label) + + +def add(a, b): + return a[0]+b[0], a[1]+b[1] + + +def mul(a, b): + return a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0] + + +def conjugate(a): + return a[0], -a[1] + + +def decode(rows): + return [{int(j): tuple(Q(x) for x in z) for j, z in row.items()} for row in rows] + + +def eye(n): + return [{i: ONE} for i in range(n)] + + +def product(a, b): + result = [] + for row in a: + target = {} + for k, value in row.items(): + for j, other in b[k].items(): + target[j] = add(target.get(j, ZERO), mul(value, other)) + result.append({j: z for j, z in target.items() if z != ZERO}) + return result + + +def restrict(rows, columns): + return [{j: row[p] for j, p in enumerate(columns) if p in row} for row in rows] + + +def residue(q): + return q.numerator*pow(q.denominator, -1, 5) % 5 + + +def residue_rank(rows, columns, image_i): + a = [[(residue(row.get(j, ZERO)[0])+image_i*residue(row.get(j, ZERO)[1])) % 5 + for j in columns] for row in rows] + pivot = 0 + for j in range(len(columns)): + found = next((i for i in range(pivot, len(a)) if a[i][j]), None) + if found is None: + continue + a[pivot], a[found] = a[found], a[pivot] + scale = pow(a[pivot][j], -1, 5) + a[pivot] = [x*scale % 5 for x in a[pivot]] + for i in range(pivot+1, len(a)): + scale = a[i][j] + a[i] = [(x-scale*y) % 5 for x, y in zip(a[i], a[pivot])] + pivot += 1 + if pivot == len(a): + break + return pivot + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--annex", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + need(not args.out.exists(), "Use a new output file") + root = args.annex / "frozen/root" + pins = {"sign-metric-normal-20261020/RESPONSE.json": + "9ae1c4bf391f8ac082d2137e686f7de474005002399648bff5d443c3bc215c9c", + "sign-metric-unit-normal-20261020/RESPONSE.json": + "1fe13e786e70ef7408fb5fbd121d08fb40d8ce0e117fe096aaee9f4243140d6a"} + packets = [] + for name, expected in pins.items(): + raw = (root/name).read_bytes() + need(sha256(raw).hexdigest() == expected, "Frozen payload pin") + packets.append(json.loads(raw)) + old, new = packets + old_v, new_v = decode(old["correction_V"]), decode(new["correction_V"]) + selected, full, centres = old["selected"], new["full_ports"], new["centre_ports"] + need(len(selected) == 24 and len(full) == 32 and len(centres) == 16, "Actual field counts") + ranks = {} + for image_i in (2, 3): + need((image_i*image_i+1) % 5 == 0, "Gaussian residue map") + ranks[str(image_i)] = { + "old_selected24": residue_rank(old_v, selected, image_i), + "old_full112": residue_rank(old_v, list(range(112)), image_i), + "old_expanded32": residue_rank(old_v, full, image_i), + "new_centres16": residue_rank(new_v, centres, image_i), + } + need(ranks["3"] == {"old_selected24": 8, "old_full112": 16, + "old_expanded32": 16, "new_centres16": 16}, "Actual F5 obstruction and release") + need(ranks["2"] == {"old_selected24": 16, "old_full112": 16, + "old_expanded32": 16, "new_centres16": 16}, "Other Gaussian residue sector") + real_only = [{j: (value[0], Q(0)) for j, value in row.items()} for row in old_v] + need(residue_rank(real_only, selected, 3) == 16, "Discarding imaginary coefficients loses the obstruction") + vanished = [i for i, row in enumerate(old_v) + if all((residue(row.get(j, ZERO)[0])+3*residue(row.get(j, ZERO)[1])) % 5 == 0 + for j in selected)] + need(vanished == list(range(8, 16)), "Exactly the eight small reader rows vanish") + + minor, inverse = decode(new["centre_minor"]), decode(new["centre_minor_inverse"]) + need(minor == restrict(new_v, centres), "Actual selected minor") + need(product(minor, inverse) == product(inverse, minor) == eye(16), "Both exact minor inverse orders") + reader = decode(new["centre_reader"]) + need(product(inverse, new_v) == reader and restrict(reader, centres) == eye(16), "Actual normalized reader") + code, code_inverse = decode(new["row_code"]), decode(new["row_code_inverse"]) + expected = eye(112) + for row, p in zip(reader, centres): + expected[p] = row + need(code == expected, "Actual row code") + need(product(code, code_inverse) == product(code_inverse, code) == eye(112), "Both exact code inverse orders") + need(all(q.denominator & (q.denominator-1) == 0 + for rows in (minor, inverse, reader, code, code_inverse) + for row in rows for value in row.values() for q in value), "All reader and code coefficients are dyadic") + + # A concrete off-diagonal entry of C*DC differs from the diagonal metric. + p, j = next((p, j) for p in centres for j, value in code[p].items() + if j not in centres and value != ZERO) + metric = decode(new["metric"]) + entry = ZERO + for k in range(112): + entry = add(entry, mul(mul(conjugate(code[k].get(p, ZERO)), metric[k][k]), + code[k].get(j, ZERO))) + need(entry != ZERO and metric[p].get(j, ZERO) == ZERO, "C does not preserve D") + need(mul((Q(1), Q(-1)), (Q(1, 2), Q(1, 2))) == ONE, "Norm-two reader unit") + need([(a, b) for a in range(3) for b in range(3) if (a*a+b*b) % 3 == 0] == [(0, 0)], + "Norm-three descent residue") + result = { + "status": "PASS_INDEPENDENT_SIGN_METRIC_READER_AUDIT", + "method": "Direct Gaussian-rational arithmetic and both F5 residue sectors; no source program import", + "payload_pins": pins, + "residue_ranks": ranks, + "vanishing_selected_reader_rows_at_i3": vanished, + "real_only_mutation_rank": 16, + "exact_minor_inverse_orders": 2, + "exact_code_inverse_orders": 2, + "reader_and_code_gaussian_dyadic": True, + "coded_metric_rejection_witness": {"row": p, "column": j, + "C_star_D_C": [str(x) for x in entry], "D": ["0", "0"]}, + "scope": "Selected-reader obstruction and unit-code release; modular full ranks alone are not a unit proof", + "checks_not_run": ["Native lowering or cost", "Complete caller or recursive invoice", "Kappa calculation"], + } + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n", encoding="utf-8") + print(result["status"]) + + +if __name__ == "__main__": + main()

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