From 4f0a7213abb8849ba8c301d8b86ae7e637853d5d Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 13:08:42 -0500 Subject: [PATCH 1/2] Add reciprocal native responses and verified low-displacement companions --- .../ANNEX-INDEPENDENT-CHECKS-OPTIMIZED.json | 480 + .../ANNEX-INDEPENDENT-CHECKS.json | 480 + .../ANNEX-REPLAY.json | 158 + .../reciprocal-native-responses/COMMANDS.json | 108 + .../FROZEN-INPUT-CHECKS.json | 656 + .../IMPORT-BOUNDARY.json | 48 + .../INDEPENDENT-CHECKS-OPTIMIZED.json | 498 + .../INDEPENDENT-CHECKS.json | 498 + .../reciprocal-native-responses/REPLAY.json | 307 + .../reciprocal-native-responses/REVIEW.json | 720 + .../reciprocal-native-responses/REVIEW.md | 280 + .../annex-replay-logs/normal-cross-gram.log | 1 + .../normal-extension-matrices.log | 2 + .../annex-replay-logs/normal-native.log | 1 + .../annex-replay-logs/normal-paired-line.log | 1 + .../normal-rank30-matrix.log | 2 + 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"d2e66195f1e9190f846d1383fcf4378c7421e06426c3e968c68463b8e4fc07b0", + "replay-logs/optimized-rank-two-review.log": "d9319d6c1741520cb3f46269b219fe491dd9c6b7a7f093ae012de308ab0cd401", + "replay-logs/optimized-rank-two.log": "46d00b713f1035d362cda9d5f0b1097d39c551c7d4a2320c867091916b44bcc2" + }, + "reviewer_issue_resolved": "Initial import audit compared resolved Homebrew files to an unresolved prefix. Corrected to the resolved Python runtime; no package change.", + "scope": "Reciprocal matrix proof, direct and dual native words, metric wrappers, coalescing, conditional caller algebra, and the rank-30/rank-16 supporting supplement with coded exits and scoped obstructions.", + "status": "PASS_INDEPENDENT_PUBLICATION_REVIEW" +} diff --git a/research/publication-reviews/reciprocal-native-responses/REVIEW.md b/research/publication-reviews/reciprocal-native-responses/REVIEW.md new file mode 100644 index 0000000000..3dcd750547 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/REVIEW.md @@ -0,0 +1,280 @@ +# Independent publication review: reciprocal native responses + +The package passes this bounded review. No blocking mathematical, native, +cost, restoration, or replay defect was found. This verdict applies to the +local response construction, the conditional caller algebra, and the +supporting low-displacement supplement. It does not admit the construction +to a recursive supplier or improve kappa. + +The reviewer read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. +The reviewer also read the complete PR body template and found no claim +defect. The final PR body, commit-pinned package links, GitHub rendering, +and published readback remain the coordinator's publication checks. This +review did not commit, push, create a PR, merge, or change a selected file. + +## Proof review + +The integer family is correct for every `n>=3`. The identity `ell u=-2` +proves `R^2=I`. The two explicit coordinate maps prove both zero +diagonals. The displayed factors of `E-I` have full rank two. The +rank-one inverse argument rules out rank one over a field of +characteristic zero. This proves sharpness for `rank(A-I)` in the stated +class. It does not prove a native-cost lower bound or a lower bound of +32 for a coupled 112-port response. + +The rational symmetric six-mode argument is also valid. The two diagonal +conditions force equal squared eigenvector coordinates `1/6`. Rationality +then forces the two sign-vector projectors to agree, which conflicts with +orthogonality. The rational-entry restriction is necessary. + +For `n>=5`, the last column norm gives equal last two metric entries. The +other column norms force all first `n-2` entries to agree and force the +ratio `-1/(n-4)`. The displayed metric proves sufficiency. Its entries are +dyadic units up to scale exactly when `n-4` is a power of two. The stated +dimension limits and the absence of a positive diagonal metric in this +range are correct. Finite checks support, but do not replace, these +quantified arguments. + +The separate checker reconstructs the actual pair code from its 24 pair +records and reconstructs each block from the formula. It verifies eight +six-mode blocks and eight eight-mode blocks. The physical matrices have +`rank(E-P)=16`, `rank(E-I)=32`, and both zero diagonals. Physical `P` has +160 nonzero entries, including signed halves. It is not a field +permutation. The metric has 80 entries equal to one, 16 equal to `-1/2`, +and 16 equal to `-1/4`. The pair-code normalization gives the exact centre +Gram `diag(4 I8,2 I8)`. Similarity alone would not prove the metric claim; +the package correctly supplies the sectorwise pair-code scale. + +## Native words and coalescing + +The reviewer used separate sparse rational arithmetic and an independent +frame ledger. No producer interpreter was imported. All twelve original +words and all twelve coalesced words pass on all 640 arbitrary content +columns. All scalar reads and writes have the required ordered frame. +Each data field advances by eight ranks. The 416 outside fields retain +their content and frame. + +The coalescing review projects each complete word onto each field. Scalar +uses form barriers. Each maximal native chain between two barriers has +the same old frame, final frame, total rank, and source-event indices in +the new word. Every scalar instruction and its global order are equal. +This check uses a different method from the producer's pending-map +algorithm. It establishes the disjoint-field commutations and the exact +telescoping map. It does not infer an operator from an unordered subspace. + +| Quantity per word | Original | Coalesced | +| --- | ---: | ---: | +| Native children | 1632 | 1292 | +| Native rank mass | 1792 | 1792 | +| Direct real scalar primitives | 6440 | 6440 | +| Metric-wrapper real scalar primitives | 7080 | 7080 | +| Endpoint maps | 224 | 224 | +| Native side-map upper bound | 3264 | 2584 | + +The coalesced profile is +`971 H1 + 237 H2 + 46 H3 + 12 H4 + 5 H5 + 11 H6 + 10 H7`. +The direct prefix one-norm bounds are `46,16,30,30`; the metric-wrapper +bounds are `60,30`. The denominator heights are one except for the +backward metric wrapper, which has height two. These match the package +table. They concern top-level content prefixes, not recursive interiors. + +The reviewer checked all 206 fresh recipe records in both Python modes +with the pinned compiler-independent Pauli and exact reference-column +engine. The engine was read and reused; this is not a second spatial +interpreter. Eighteen Pauli images fix the unitary up to scalar, and the +exact reference column fixes that scalar. A changed global phase fails. +The 1071 remaining recipe records equal the original records. All words +use this same checked recipe table. A changed scalar-frame cut also fails. + +The original 1561 recipe records and 224 endpoint records retain the +accepted predecessor phase evidence. The advertised independent native +review was rerun and checks exact predecessor occurrence and record +equality. The older predecessor's full spatial replay was not rerun. +The coalesced companion now has a separate content, schedule, price, and +phase-inheritance review in this directory. Its historical freeze still +correctly says that this review did not exist at that time. + +The inverse-adjoint chronology and both-bank metric wrappers are valid. +A unitary gate is unchanged by inverse adjoint, while each real scalar +gate changes as stated. The wrapper scales commute with the spatial map +of the same physical field. Both input banks and both output banks are +needed to restore arbitrary baselines. A one-bank price of 320 is not the +native-shear wrapper price of 640. + +## Caller scope and remaining obligations + +The two `P` wrapper positions give the displayed `D(P)L_R` and +`D(P)U_-R` maps. The three-stage transport keeps the order of all factors. +The square-zero factorization proves a residual rank at most 48 arrays. +The three inverse shears must run in the stated order. The middle query +must be retained before either write changes a source. The record +`c1=L1(P0 t)` retains its transport; replacing it by `L1 t` is invalid. + +The clean-reflection hidden-output formulas follow by reversing the +three local maps. The final `R2` cancels because its reconstructed input +is zero. In the selected-conjugate variant, the two remaining query +families give hidden rank at most 32 arrays. The ordinary hidden +observation remains. The exact regressions attain 48 and 32, but their +signed conjugations are not actual D25 routes and give no routed lower +bound. + +No native cleanR32 service is emitted. The package says this explicitly. +The 64 selected endpoint lines, 32 optional formation lines, six endpoint +`P` words with scalar subtotal 4368, and native subtotal 5440 are +conditional subtotals. They do not price record capture, later frame +progress, ordinary-hole access, the remaining `Q` scatter, record +restoration, or the terminal residual. The six stage-wrapper `P` words +are also separate from the six endpoint-removal words. No complete scalar +or supplier total is claimed. + +The current selected snapshot is PR #4470 at main commit +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. The historical source contracts +in this package are not automatically admitted to that selected source. +The selected supplier verifier, recursive host, complete precision and +tape calculation, and integer-multiplication theorem were not run here. + +## Replay, imports, and source credit + +The advertised command ran in a fresh directory: + +```sh +python3 -I -B work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/reciprocal-native-responses/replay.py --out /tmp/reciprocal-publication-independent-20261022-a +``` + +All nine checks passed in normal Python and with `-O`. Each child ran +sequentially in one process. The final line was +`PASS_RECIPROCAL_NATIVE_RESPONSES`. The copied receipt is `REPLAY.json`; +the complete child logs are in `replay-logs/`. Regenerated plain receipts +match exact bytes, and gzip artifacts match decompressed bytes. All 70 +frozen inputs retain their manifest hashes. + +The separate reviewer checker passes in both modes. Its result files +are equal after elapsed time is removed. `COMMANDS.json` gives its exact +commands. `IMPORT-BOUNDARY.json` records the top-level import closure of +all nine tasks: no import read escapes the package or resolved Python +runtime, and no subprocess or network event occurs during those imports. +The old helpers contain unused entry points that require older sources; +the package does not claim those entry points are standalone. No runtime +adapter, path rewrite, source edit, or monkey patch is present. + +The source notice matches the retained native notice and distinguishes +the coordinating, oblique-native, new-core-transfer, independent-review, +cover-algebra, and bridge-access contributions. Historical PR #3133, +PR #3148, and PR #2588 pins remain unchanged. The external source worker's +GitHub readbacks verify the compiler blob, provider words, Apache-2.0 +license, and retained notices. This reviewer checked the package files +against those receipt hashes; it did not make a second GitHub request. +No individual author is inferred from a submitter account. Substantial +AI assistance is disclosed. + +The first reviewer import audit compared resolved paths with an unresolved +Homebrew runtime path. That reviewer error was corrected by resolving the +runtime prefix. The rerun passed. No package change was needed. No fragile +workaround was introduced. + +## Supporting low-displacement annex + +The added annex preserves 59 further frozen files and refers to 14 core +files. It does not change the core input tree, source manifest, or replay +program. Its new prose states the change of response class and the native +and representation limits correctly. + +The rank-30 construction has a rank-16 large part and a rank-14 small +part. The selected block is `L` in both inverse directions. The full and +ordinary determinants are `2^25` and `2^21`. The fourteen-block optimum +is restricted to the stated disjoint dyadic rank-one clique model. The +no-nine-clique argument is valid: nine orthonormal odd vectors would +express the isotropic vector `z` as their sum and give `z dot z=1`. +This contradicts its actual zero norm. The cardinality argument then +excludes thirteen or fewer blocks of allowed sizes 2, 3, and 5. + +The rank-16 construction is symmetric with determinant `35^8`. Its +large inverse follows from `(K^T K)^2=12 K^T K`. It does not contradict +the reciprocal rank-two minimum: its inverse has a nonzero diagonal, +and the later scalar inverse uses primes 5 and 7. The selected ordinary +inverse also uses prime 31. The fresh review finds exactly 512 nonzero +entries with denominator 7, 568 with denominator 31, and 640 with +denominator 62. No odd-grid admission or conversion invoice follows. + +The separate annex checker verifies all three response matrices, both +inverse orders, correction ranks, complete determinants, ordinary +inverses, and the retained common-frame scalar words. It checks all +twelve raw native words on 640 arbitrary columns with their frames and +prices. The rank-30 and reciprocal-large words cost 5288 scalar +primitives and have 1212 children of mass 1792. Rank 16 costs 7384 and +has 1632 children of the same mass. + +The sixteen coded words also pass. The checker binds the literal code +`S_e0 C_45 S_e0`, the exact coded port set, every retained endpoint +record, the unchanged scalar gates, every unchanged native occurrence, +and each changed final exit. It checks the exact final circuits +`W F9` and `W F9 Q_p^-1`. Scalar pair decoding after a changed source +exit uses the common completed coded frame. Such a frame change is +permitted only at that declared final view. It is not an arbitrary +frame rewrite. + +All four coded profiles, side-map counts, inline monomial counts, +external endpoint counts, scalar prices, and prefix bounds match the +annex table. All 416 outside fields keep their values and frames. All +352 distinct changed-exit recipes pass the exact Pauli and +reference-column comparison. This includes the 48 previously inherited +changed exits. The checker imports the reviewer's rational arithmetic +and the existing compiler-independent phase engine, but no producer. +It does not rerun the historical full-column raw spatial reviews. + +The cross-Gram obstruction is valid for the specified section-swap +mechanism. Independent sparse elimination gives the full rank census +`{0:32,4:96,8:12,14:256,16:116}`. Minimal scalar factor changes conjugate +this Gram matrix and preserve its singularity. If a factorization +through more coordinates had an invertible cross-Gram, its two factors +would be injective and surjective, which would force their coordinate +count to equal the correction rank. Thus that change does not remove +this obstruction. Different encodings remain outside the proof. + +The paired-line proof is valid. Each scalar ADD can at most double the +maximum input support of a row; monomial views do not increase it. +The `2^f` terms of the tensor line operator therefore require at least +`f` ADDs in the no-native-call class. The determinant proof excludes +one native line call only in the narrower translation-view class. +Translations form a commutative group algebra, so that determinant +argument is valid there. It is not a lower bound for general native +views. The historical producer-only status remains unchanged; this +paragraph is a new, separate proof review. + +## Final supplement replay and source check + +The advertised supplement command passed in a second fresh directory: + +```sh +python3 -I -B work/centre-encoding-campaign-20261014/publication-wrap-20261022/packages/reciprocal-native-responses/replay_annex.py --out /tmp/reciprocal-annex-publication-replay-20261022-a +``` + +All five checks passed in normal Python and with `-O`. The final line was +`PASS_LOW_DISPLACEMENT_RESPONSE_ANNEX`. Eight frozen receipts match exact +bytes. The two new native receipts match the accepted independent receipt +after removal of only Python version and elapsed time. The runner retains +the hashes of the complete raw receipts. The copied runner receipt is +`ANNEX-REPLAY.json`; all ten child logs are in `annex-replay-logs/`. +The checks ran sequentially, with one CPU per child. + +The supplement contains 59 additional frozen files and refers to 14 +unchanged core files. All 129 distinct frozen files match both their +manifests and the original campaign files. The 14 shared records match +the core manifest. The two publication checker copies and the accepted +receipt match their review source bytes. The separate normal and optimized +review results are equal after elapsed time is removed. These checks are +recorded in `FROZEN-INPUT-CHECKS.json`. + +The final source notice retains both earlier PR #2226 notices from the +pinned PR #2588 tree. Those notices identify the unchanged compiler's +vendor531 lineage. Their scope is source credit; this package does not +import the dirty-borrowing replay. The local copies match the supplied +GitHub readback hashes. This reviewer did not make a second remote request. + +The final package snapshot has 152 files and 10,099,109 bytes. The core +runner and all frozen inputs are unchanged. `REVIEW.json` binds that +snapshot and the completed review receipts. No mathematical or replay +blocker remains within this review's stated scope. Current selected +supplier replay, recursive admission, complete precision and tape checks, +and the final GitHub publication checks remain outside this review. diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-cross-gram.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-cross-gram.log new file mode 100644 index 0000000000..0b7e08aa4d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-cross-gram.log @@ -0,0 +1 @@ +PASS_EVEN_CLIQUE_CROSS_GRAM_OBSTRUCTION {0: 32, 4: 96, 8: 12, 14: 256, 16: 116} {'character': 2, 'clique_index': 0, 'ports': [1, 5, 19, 54, 64, 73, 82, 83], 'directions': [19, 259, 273, 196, 200, 224, 446, 382], 'signs': [-1, -1, 1, 1, 1, 1, -1, -1], 'cross_gram_column': 8} diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-extension-matrices.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-extension-matrices.log new file mode 100644 index 0000000000..1e4d6e4028 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-extension-matrices.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_RESPONSE_EXTENSIONS +receipt_sha256=e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-native.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-native.log new file mode 100644 index 0000000000..068531799d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-native.log @@ -0,0 +1 @@ +PASS_SUPPORTING_LOW_DISPLACEMENT_REVIEW diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-paired-line.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-paired-line.log new file mode 100644 index 0000000000..19fe2214be --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-paired-line.log @@ -0,0 +1 @@ +{"checks": [{"inverse": true, "line_support": 2, "paired_identity": true, "shortcut_rejected": false, "tensor_width": 1}, {"inverse": true, "line_support": 4, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 2}, {"inverse": true, "line_support": 8, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 3}, {"inverse": true, "line_support": 16, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 4}, {"inverse": true, "line_support": 32, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 5}, {"inverse": true, "line_support": 64, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 6}], "producer_sha256": "f8ee8d5734a9840b47914882821cc4ce9dac4639c8a344a94e65251e5d0a7d3d", "scope": "Exact finite examples support the algebraic proof. The general support and translation-only determinant arguments are in PAIRED-LINE-TENSOR-SCOPE.md.", "status": "PASS_PAIRED_LINE_SCOPE"} diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-rank30-matrix.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-rank30-matrix.log new file mode 100644 index 0000000000..8ea29c681a --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/normal-rank30-matrix.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_RANK_THIRTY_RESPONSE +receipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97 diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-cross-gram.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-cross-gram.log new file mode 100644 index 0000000000..0b7e08aa4d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-cross-gram.log @@ -0,0 +1 @@ +PASS_EVEN_CLIQUE_CROSS_GRAM_OBSTRUCTION {0: 32, 4: 96, 8: 12, 14: 256, 16: 116} {'character': 2, 'clique_index': 0, 'ports': [1, 5, 19, 54, 64, 73, 82, 83], 'directions': [19, 259, 273, 196, 200, 224, 446, 382], 'signs': [-1, -1, 1, 1, 1, 1, -1, -1], 'cross_gram_column': 8} diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-extension-matrices.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-extension-matrices.log new file mode 100644 index 0000000000..1e4d6e4028 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-extension-matrices.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_RESPONSE_EXTENSIONS +receipt_sha256=e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-native.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-native.log new file mode 100644 index 0000000000..068531799d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-native.log @@ -0,0 +1 @@ +PASS_SUPPORTING_LOW_DISPLACEMENT_REVIEW diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-paired-line.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-paired-line.log new file mode 100644 index 0000000000..19fe2214be --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-paired-line.log @@ -0,0 +1 @@ +{"checks": [{"inverse": true, "line_support": 2, "paired_identity": true, "shortcut_rejected": false, "tensor_width": 1}, {"inverse": true, "line_support": 4, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 2}, {"inverse": true, "line_support": 8, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 3}, {"inverse": true, "line_support": 16, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 4}, {"inverse": true, "line_support": 32, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 5}, {"inverse": true, "line_support": 64, "paired_identity": true, "shortcut_rejected": true, "tensor_width": 6}], "producer_sha256": "f8ee8d5734a9840b47914882821cc4ce9dac4639c8a344a94e65251e5d0a7d3d", "scope": "Exact finite examples support the algebraic proof. The general support and translation-only determinant arguments are in PAIRED-LINE-TENSOR-SCOPE.md.", "status": "PASS_PAIRED_LINE_SCOPE"} diff --git a/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-rank30-matrix.log b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-rank30-matrix.log new file mode 100644 index 0000000000..8ea29c681a --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/annex-replay-logs/optimized-rank30-matrix.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_RANK_THIRTY_RESPONSE +receipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97 diff --git a/research/publication-reviews/reciprocal-native-responses/check_import_boundary.py b/research/publication-reviews/reciprocal-native-responses/check_import_boundary.py new file mode 100644 index 0000000000..636ce27b0a --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/check_import_boundary.py @@ -0,0 +1,55 @@ +#!/usr/bin/env python3 +"""Record the local import boundary of the nine replay tasks.""" + +import argparse +import importlib.util +import json +from pathlib import Path +import runpy +import sys + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--package", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + package = args.package.resolve() + runtime = Path(sys.base_prefix).resolve() + spec = importlib.util.spec_from_file_location("review_runner", package/"replay.py") + runner = importlib.util.module_from_spec(spec) + spec.loader.exec_module(runner) + opened, forbidden = [], [] + + def audit(event, values): + if event == "open" and isinstance(values[0], str): + opened.append(Path(values[0]).resolve()) + if event in ("subprocess.Popen", "socket.connect", "os.system"): + forbidden.append(event) + raise RuntimeError("Unexpected external action during import: " + event) + + sys.addaudithook(audit) + checks = [] + for name, script, _, _ in runner.tasks(): + runpy.run_path(str(package/"frozen"/script), run_name="publication_import_review") + checks.append(name) + outside = [str(p) for p in set(opened) if not p.is_relative_to(package) and not p.is_relative_to(runtime)] + if outside or forbidden: + raise ValueError({"unexpected_paths": outside, "external_actions": forbidden}) + modules = sorted({str(Path(module.__file__).resolve()) for module in sys.modules.values() + if getattr(module, "__file__", None) and + Path(module.__file__).resolve().is_relative_to(package)}) + result = { + "status": "PASS_IMPORT_BOUNDARY", "scripts": checks, + "python_runtime": str(runtime), "package_modules": modules, + "source_reads": sorted(str(p) for p in set(opened) if p.is_relative_to(package)), + "external_process_or_network_events": forbidden, + "reads_outside_package_and_python_runtime": outside, + "scope": "Top-level import closure of all nine replay tasks. The separate fresh replay ran each main path in its copied frozen tree.", + } + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/publication-reviews/reciprocal-native-responses/check_low_displacement_annex.py b/research/publication-reviews/reciprocal-native-responses/check_low_displacement_annex.py new file mode 100644 index 0000000000..51df3e6644 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/check_low_displacement_annex.py @@ -0,0 +1,235 @@ +#!/usr/bin/env python3 +"""Review the frozen supporting responses and changed exits.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys +import time + + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location("publication_arithmetic", HERE/"check_publication_review.py") +a = importlib.util.module_from_spec(spec) +spec.loader.exec_module(a) +PINS = { + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c", + "native-normal-v2/NATIVE-PROGRAM.json.gz": "aca3b3364b73e3c2115ede3082088e7566d789273711031381e44406c0ae793c", + "reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz": "825f27e5b3705dace14c75ae53aa21ea94b9dc69284bbdbd3377591fbcce7439", + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b", + "coded-normal/CODED-EXITS-PROGRAM.json.gz": "aad4decc178d7b9ac19ef4b97d3b77d56854c26714f063e1ff6fa762cf2b6b08", +} + + +def determinant(matrix): + work = [dict(row) for row in matrix] + result = F(1) + for column in range(len(work)): + pivot = next((i for i in range(column, len(work)) if work[i].get(column)), None) + if pivot is None: + return F(0) + if pivot != column: + work[column], work[pivot] = work[pivot], work[column] + result = -result + value = work[column][column] + result *= value + for i in range(column+1, len(work)): + scale = work[i].get(column, 0)/value + if scale: + for j, entry in work[column].items(): + a.put(work[i], j, -scale*entry) + return result + + +def restrict(matrix, indices): + return [{j: matrix[p][q] for j, q in enumerate(indices) if q in matrix[p]} for p in indices] + + +def expected_map(response, backward): + result = a.eye(640) + for i, row in enumerate(response): + for j, value in row.items(): + a.put(result[j if backward else 112+i], 112+i if backward else j, -value if backward else value) + return result + + +def physical_model(model, correction_rank): + e, ei = a.rows(model["response"]), a.rows(model["response_inverse"]) + a.need(a.mul(e, ei) == a.mul(ei, e) == a.eye(112), "Supporting inverse orders") + delta = a.plus(e, a.eye(112), -1) + a.need(a.rank(delta) == correction_rank, "Supporting correction rank") + if "correction_U" in model: + u, v = a.rows(model["correction_U"]), a.rows(model["correction_V"]) + a.need(a.mul(u, v) == delta and a.rank(u) == a.rank(v) == correction_rank, "Supporting correction factor") + ordinary = model["ordinary_ports"] + principal = restrict(e, ordinary) + inverse = a.rows(model["ordinary_inverse"]) + a.need(a.mul(principal, inverse) == a.mul(inverse, principal) == a.eye(104), "Ordinary inverse orders") + selected = model["selected_ports"] + l = a.rows(model["selected_block"]) + a.need(restrict(e, selected) == l and a.mul(l, l) == [{i: F(1, 2)} for i in range(8)], "Selected block") + expected_det = 2**25 if correction_rank == 30 else 35**8 + expected_ordinary = F(2**21) if correction_rank == 30 else F(7**8*31**4, 16) + a.need(determinant(e) == expected_det and determinant(principal) == expected_ordinary, "Supporting determinants") + if correction_rank == 16: + inverse_selected = a.plus([{i: F(4, 5)} for i in range(8)], l, F(1, 5)) + a.need(restrict(ei, selected) == inverse_selected, "Changed selected inverse") + denominators = Counter(value.denominator for row in inverse for value in row.values()) + a.need(denominators == {7: 512, 31: 568, 62: 640}, "Prime 31 in ordinary inverse") + a.need(a.transpose(e, 112) == e, "Rank16 symmetry") + else: + a.need(restrict(ei, selected) == l, "Rank30 inverse selected block") + return {"rank": correction_rank, "determinant": str(expected_det), "ordinary_determinant": str(expected_ordinary)} + + +def as_tuple(value): + return tuple(map(as_tuple, value)) if isinstance(value, list) else value + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--source-root", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + start = time.monotonic() + source_dir = args.source_root/"lanes/new-core-transfer-20261017/low-displacement-20261020" + for name, digest in PINS.items(): + a.need(sha256((source_dir/name).read_bytes()).hexdigest() == digest, "Supporting input " + name) + base = a.read(source_dir/"run-normal/RESPONSE-PROGRAM.json") + raw = a.read(source_dir/"native-normal-v2/NATIVE-PROGRAM.json.gz") + reciprocal = a.read(source_dir/"reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz") + odd = a.read(source_dir/"odd16-normal-v2/EXTENSION-PROGRAM.json.gz") + coded = a.read(source_dir/"coded-normal/CODED-EXITS-PROGRAM.json.gz") + reports = {"rank30": physical_model(base, 30), "reciprocal_large": physical_model(reciprocal["model"], 30), + "rank16": physical_model(odd["model"], 16)} + raw_reports = {} + for name, model, packet, scalar, profile in ( + ("rank30", base, raw, 5288, {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}), + ("reciprocal_large", reciprocal["model"], reciprocal, 5288, {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}), + ("rank16", odd["model"], odd, 7384, {1: 1520, 2: 64, 3: 48}), + ): + for provider, directions in packet["providers"].items(): + for direction, word in directions.items(): + expected = expected_map(a.rows(model["response"]), direction == "backward") + raw_reports[name+"/"+provider+"/"+direction] = a.word_check(word, expected, profile, scalar) + for word_name, gates in model.get("common_frame_words", {}).items(): + state, cost, _, _ = a.scalar_replay(gates, 112) + expected = a.rows(model["response_inverse"] if "inverse" in word_name else model["response"]) + if "transpose" in word_name: + expected = a.transpose(expected, 112) + a.need(state == expected and cost == 3210, "Supporting common-frame scalar code") + + model = odd["model"] + u, v, q = a.rows(model["correction_U"]), a.rows(model["correction_V"]), model["ports"] + histogram = Counter() + for character in range(512): + moved = [{j: value*(-1 if (q[p] & character).bit_count() % 2 else 1) for j, value in row.items()} for p, row in enumerate(u)] + histogram[a.rank(a.mul(v, moved))] += 1 + a.need(histogram == {0: 32, 4: 96, 8: 12, 14: 256, 16: 116}, "Independent cross-Gram rank census") + + phase_path = args.source_root/"lanes/interface-proof/verify_native_lift.py" + phase_spec = importlib.util.spec_from_file_location("supporting_phase_engine", phase_path) + phase = importlib.util.module_from_spec(phase_spec) + phase_spec.loader.exec_module(phase) + changed = {} + coded_reports = {} + raw_packets = {"rank30": raw, "rank16": odd} + a.need(base["ports"] == odd["model"]["ports"], "Same physical directions") + fourier = [["C", 1 << i, 1] for i in range(9)] + s0 = ["D", [1]+[0]*8, [1]+[0]*8] + gauge = [s0, ["C", 45, 1], s0] + profiles = { + ("rank30", "W48_I64"): {1: 988, 2: 48, 4: 55, 5: 55, 6: 9, 7: 9}, + ("rank30", "W112"): {1: 988, 2: 48, 5: 55, 6: 55, 7: 9, 8: 9}, + ("rank16", "W48_I64"): {1: 1472, 2: 112}, + ("rank16", "W112"): {1: 1408, 2: 112, 3: 64}, + } + for name, codes in coded["providers_by_response_and_code"].items(): + for code, providers in codes.items(): + for provider, directions in providers.items(): + for direction, word in directions.items(): + raw_word = raw_packets[name]["providers"][provider][direction] + coded_ports = set(range(112)) if code == "W112" else set(base["large_ports"]) + a.need(set(word["left_W_ports"]) == coded_ports and set(word["raw_output_ports"]) == set(range(112))-coded_ports, "Exact coded port set") + a.need(word["gauge_circuit"] == gauge, "Literal S_e0 C_45 S_e0 code") + a.need(word["start"] == raw_word["start"], "Unchanged input frame ids") + a.need(word["frames"][:len(raw_word["frames"])] == [{"kind": "canonical", "basis": f} for f in raw_word["frames"]], "Unchanged ordered canonical frames") + endpoints = [record for record in raw_word["endpoint_adapters"] if record["role"] == "source" or record["port"] not in coded_ports] + a.need(word["endpoint_adapters"] == endpoints, "Exact retained endpoint records") + for p in range(112): + if p in coded_ports: + for field, circuit in ((p, fourier+gauge), (112+p, [["C", base["ports"][p], -1]]+fourier+gauge)): + frame = word["frames"][word["final"][field]] + a.need(frame["kind"] == "literal" and frame["circuit"] == circuit, "Literal W F9 Q inverse output order") + else: + a.need(word["final"][p] == raw_word["final"][p] and word["final"][112+p] == raw_word["final"][112+p], "Unchanged uncoded exits") + current, census, monomials, gates = list(word["start"]), Counter(), 0, [] + a.need(len(word["events"]) == len(raw_word["events"]), "One event per original position") + for event, raw_event in zip(word["events"], raw_word["events"]): + if event[0] == "scalar": + gate, frame = event[1:] + if gate[0] == "add": + _, target, source, num, den = gate + a.need(current[source] == frame and 0 <= source < 224, "Coded source access") + else: + _, target, num, den = gate + source = None + a.need(current[target] == frame and 0 <= target < 224, "Coded target access") + gates.append([gate[0], target, source, str(F(num, den))]) + a.need(raw_event[:2] == ["scalar", gates[-1]], "Scalar operation and coefficient unchanged") + if raw_event[2] != frame: + fields = [target] if source is None else [target, source] + a.need(all(raw_event[2] == raw_word["final"][p] and frame == word["final"][p] + and p % 112 in coded_ports for p in fields), "Scalar access changes only to its completed coded output frame") + continue + field, old, new, key = event[1], event[2], event[3], event[-1] + a.need(0 <= field < 224 and current[field] == old, "Coded transformation entry") + current[field] = new + record = word["native_recipes"][key] + if event[0] == "native": + a.need(event[4] == record["rank"] > 0, "Coded native rank") + census[event[4]] += 1 + else: + a.need(event[0] == "monomial" and record["rank"] == 0, "Explicit rank-zero map") + monomials += 1 + if key.startswith("coded:"): + a.need(raw_event[0] == "native" and raw_event[1:3] == event[1:3] and raw_event[3] == raw_word["final"][field], "Only the final physical exit changes") + objects = [word["frames"][old], word["frames"][new], record] + changed[json.dumps(objects, sort_keys=True)] = objects + else: + a.need(event == raw_event and record == raw_word["native_recipes"][key], "Exact inherited native occurrence and recipe") + state, scalar, peak, height = a.scalar_replay(gates, 640) + a.need(state == expected_map(a.rows(coded["responses"][name]), direction == "backward"), "Coded 640-column content") + a.need(current == word["final"] and current[224:] == word["start"][224:], "Coded final frames and outside restoration") + a.need(census == profiles[name, code] and monomials == 48, "Coded profile and monomial count") + a.need(scalar == (5288 if name == "rank30" else 7384), "Coded scalar invoice") + a.need(len(word["endpoint_adapters"]) == (112 if code == "W112" else 176), "Coded endpoint census") + coded_reports[name+"/"+code+"/"+provider+"/"+direction] = { + "profile": dict(census), "children": sum(census.values()), "mass": sum(k*v for k, v in census.items()), + "scalar": scalar, "inline_monomials": monomials, "endpoints": len(word["endpoint_adapters"]), + "prefix_one_norm": str(peak), "binary_height": height, + } + a.need(len(changed) == 352, "Changed exit recipe count") + for old, new, record in changed.values(): + def frame(value): + return phase.frame(value["basis"], 9) if value["kind"] == "canonical" else as_tuple(value["circuit"]) + phase.equal(phase.recipe(record), phase.adjoint(frame(old))+frame(new), "Supporting changed exit") + for name, digest in PINS.items(): + a.need(sha256((source_dir/name).read_bytes()).hexdigest() == digest, "Supporting input unchanged") + result = {"status": "PASS_SUPPORTING_LOW_DISPLACEMENT_REVIEW", "python": sys.version, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), "input_sha256": PINS, + "response_models": reports, "raw_native_words": raw_reports, "cross_gram_rank_census": dict(histogram), + "coded_words": coded_reports, "changed_exit_exact_phase_checks": len(changed), + "phase_engine_sha256": sha256(phase_path.read_bytes()).hexdigest(), + "scope": "Independent rational maps, scalar prices, typed frame ledger, and 352 changed-exit phases with the existing compiler-independent engine. Inherited raw phases and physical endpoints retain the pinned predecessor reviews. No odd-grid admission or supplier replay.", + "elapsed_seconds": round(time.monotonic()-start, 3)} + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/publication-reviews/reciprocal-native-responses/check_publication_review.py b/research/publication-reviews/reciprocal-native-responses/check_publication_review.py new file mode 100644 index 0000000000..7df119e9d4 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/check_publication_review.py @@ -0,0 +1,366 @@ +#!/usr/bin/env python3 +"""Check the extracted response and native words with separate arithmetic.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from functools import lru_cache +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys +import time + + +def need(value, label): + if not value: + raise ValueError(label) + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == ".gz" else data) + + +def rows(value): + return [{int(j): F(v) for j, v in row.items() if F(v)} for row in value] + + +def eye(n): + return [{i: F(1)} for i in range(n)] + + +def put(row, j, v): + value = row.get(j, F(0)) + v + if value: + row[j] = value + else: + row.pop(j, None) + + +def plus(a, b, c=1): + out = deepcopy(a) + for row, extra in zip(out, b): + for j, v in extra.items(): + put(row, j, c*v) + return out + + +def mul(a, b): + out = [] + for row in a: + result = {} + for j, v in row.items(): + for k, w in b[j].items(): + put(result, k, v*w) + out.append(result) + return out + + +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 rank(a): + basis = {} + for original in a: + row = dict(original) + while row: + j = min(row) + v = row[j] + if j not in basis: + basis[j] = {k: w/v for k, w in row.items()} + break + for k, w in basis[j].items(): + put(row, k, -v*w) + return len(basis) + + +def family(n): + u = [F(1)]*(n-2) + [F(n-4), F(0)] + ell = [F(-1)]*(n-2) + [F(1), F(0)] + r = plus(eye(n), [{j: a*b for j, b in enumerate(ell) if a*b} for a in u]) + p = eye(n) + p[-2], p[-1] = p[-1], p[-2] + return mul(p, r), mul(r, p), p, r + + +def check_model(model): + generic = [] + for n in range(3, 25): + e, ei, p, r = family(n) + need(mul(e, ei) == mul(ei, e) == eye(n), "Family inverse orders") + need(all(i not in a[i] for a in (e, ei) for i in range(n)), "Family zero diagonals") + need(rank(plus(e, eye(n), -1)) == 2, "Family correction rank") + if n >= 5: + metric = [{i: F(1) if i < n-2 else F(-1, n-4)} for i in range(n)] + need(mul(transpose(e, n), mul(metric, e)) == metric, "Family metric identity") + equations = [] + for i in range(n): + for j in range(i, n): + row = {k: e[k].get(i, 0)*e[k].get(j, 0) for k in range(n)} + if i == j: + put(row, i, -1) + equations.append({k: v for k, v in row.items() if v}) + need(rank(equations) == n-1, "One-dimensional invariant diagonal metric space") + generic.append(n) + + h, hi = eye(112), eye(112) + for pair in model["pair_codes"]: + a, b = pair["ports"] + local = [[F(x) for x in row] for row in pair["matrix"]] + for i, target in enumerate((a, b)): + h[target] = {origin: local[i][j] for j, origin in enumerate((a, b)) if local[i][j]} + hi[target] = {origin: local[j][i]/2 for j, origin in enumerate((a, b)) if local[j][i]} + need(mul(h, hi) == eye(112), "Pair inverse from pair records") + need(h == rows(model["pair_code"]) and hi == rows(model["pair_code_inverse"]), "Serialized pair code") + mode = {name: eye(112) for name in ("E", "inverse_E", "P", "R", "J")} + sizes = Counter() + for block in model["blocks"]: + ports = block["ports"] + n = len(ports) + sizes[n] += 1 + matrices = family(n) + ([{i: F(1) if i < n-2 else F(-1, n-4)} for i in range(n)],) + for name, matrix in zip(mode, matrices): + for i, p in enumerate(ports): + mode[name][p] = {ports[j]: v for j, v in matrix[i].items()} + need(sizes == {6: 8, 8: 8}, "Actual block census") + physical = {name: mul(hi, mul(matrix, h)) for name, matrix in mode.items()} + for name, value in physical.items(): + need(value == rows(model["physical"][name]), "Independent physical reconstruction " + name) + e, ei, p, r, j = (physical[name] for name in mode) + need(mul(e, ei) == mul(ei, e) == eye(112), "Physical inverse orders") + need(mul(p, r) == e and mul(p, p) == mul(r, r) == eye(112), "Physical factors") + need(rank(plus(e, p, -1)) == 16 and rank(plus(e, eye(112), -1)) == 32, "Physical displacement ranks") + need(all(i not in a[i] for a in (e, ei) for i in range(112)), "Physical zero diagonals") + need(mul(transpose(e, 112), mul(j, e)) == j, "Physical metric after pair normalization") + need(Counter(j[i][i] for i in range(112)) == {F(1): 80, F(-1, 2): 16, F(-1, 4): 16}, "Metric weights") + need(sum(map(len, p)) == 160 and any(len(row) > 1 for row in p), "P is not a permutation") + u, ell = rows(model["reflection_U"]), rows(model["reflection_L"]) + ji = [{i: 1/j[i][i]} for i in range(112)] + need(mul(u, ell) == plus(r, eye(112), -1), "Reflection rank factor") + need(mul(ell, mul(ji, transpose(ell, 112))) == [{i: F(4 if i < 8 else 2)} for i in range(16)], "Centre Gram normalization") + for name, word in model["scalar_words"].items(): + state, cost, _, _ = scalar_replay(word, 640) + wanted = rows(model["physical"][name]) if name in model["physical"] else transpose(ei, 112) + need(state[:112] == wanted and state[112:] == eye(640)[112:], "Common-frame map and restoration " + name) + expected = {"P": 728, "R": 2892, "metric_inverse_adjoint_E": 3628}.get(name, 3308) + need(cost == expected, "Common-frame price " + name) + return {"family_dimensions": generic, "invariant_diagonal_space_dimensions": list(range(5, 25)), + "actual_blocks": dict(sizes), "rank_E_minus_P": 16, "rank_E_minus_I": 32, + "physical_P_nonzeros": 160, "physical_Gram": [4]*8 + [2]*8} + + +def tariff(gate): + op, _, _, raw = gate + c = F(raw) + a, b = abs(c.numerator), c.denominator + need(a > 0 and b & (b-1) == 0, "Dyadic coefficient") + if op == "scale": + need(a & (a-1) == 0, "Unit scale") + return 2*(abs(a.bit_length()-b.bit_length()) + (c < 0)) + need(op == "add", "Scalar grammar") + return 2*(1+a.bit_length()+a.bit_count()+b.bit_length()) + + +def scalar_replay(gates, n): + state, cost, peak, height = eye(n), 0, F(1), 0 + for gate in gates: + op, target, origin, raw = gate + c = F(raw) + if op == "add": + need(target != origin, "Distinct fields") + for j, v in state[origin].items(): + put(state[target], j, c*v) + else: + need(op == "scale" and origin is None, "Scale grammar") + state[target] = {j: c*v for j, v in state[target].items() if c*v} + cost += tariff(gate) + peak = max(peak, sum(map(abs, state[target].values()), F(0))) + for v in state[target].values(): + need(v.denominator & (v.denominator-1) == 0, "Dyadic prefix") + height = max(height, v.denominator.bit_length()-1) + return state, cost, peak, height + + +@lru_cache(None) +def span(vectors): + values = {0} + for v in vectors: + values |= {x ^ v for x in values} + return frozenset(values) + + +def word_check(word, expected, profile, scalar): + current = list(word["start"]) + progress, census, gates = Counter(), Counter(), [] + for event in word["events"]: + if event[0] == "native": + _, field, old, new, dimension, key = event + need(0 <= field < 224 and current[field] == old, "Native entry") + need(span(tuple(word["frames"][old])) < span(tuple(word["frames"][new])), "Strict nested advance") + need(dimension == len(word["frames"][new])-len(word["frames"][old]) == word["native_recipes"][key]["rank"], "Native rank") + need(key == str(old)+":"+str(new), "Ordered recipe") + current[field] = new + progress[field] += dimension + census[dimension] += 1 + else: + need(event[0] == "scalar", "Event grammar") + _, gate, frame = event + _, target, origin, _ = gate + need(0 <= target < 224 and current[target] == frame, "Scalar target access") + if origin is not None: + need(0 <= origin < 224 and current[origin] == frame, "Scalar source access") + gates.append(gate) + need(current == word["final"] and census == profile, "Final frames and native census") + need(all(progress[p] == 8 for p in range(224)), "Data advance mass") + state, cost, peak, height = scalar_replay(gates, 640) + need(state == expected, "All 640 arbitrary columns") + need(state[224:] == eye(640)[224:] and current[224:] == word["start"][224:], "Outside values and frames restored") + need(cost == scalar, "Native scalar price") + return {"scalar_real": cost, "prefix_one_norm": str(peak), "binary_height": height, + "native_profile": dict(census), "native_mass": sum(k*v for k, v in census.items()), + "native_children": sum(census.values()), "columns": 640, "outside_fields": 416} + + +def field_projection(word, combine): + projected = [[] for _ in range(224)] + scalar_index = 0 + for index, event in enumerate(word["events"]): + if event[0] == "native": + _, field, old, new, dimension, _ = event + seq = projected[field] + if combine and seq and seq[-1][0] == "native": + need(seq[-1][2] == old, "Original chain joins") + seq[-1][2] = new + seq[-1][3] += dimension + seq[-1][4].append(index) + else: + seq.append(["native", old, new, dimension, [index]]) + else: + for field in (event[1][1], event[1][2]): + if field is not None: + projected[field].append(["scalar", scalar_index]) + scalar_index += 1 + return projected + + +def coalescing_check(original, result): + old_scalars = [e for e in original["events"] if e[0] == "scalar"] + new_scalars = [e for e in result["events"] if e[0] == "scalar"] + need(old_scalars == new_scalars, "Every scalar gate and its global order") + old, new = field_projection(original, True), field_projection(result, False) + chains = {row["event"]: row for row in result["coalesced_native_chains"]} + need(len(chains) == sum(e[0] == "native" for e in result["events"]), "One chain record per new native event") + for field, (a, b) in enumerate(zip(old, new)): + need(len(a) == len(b), "Same per-field scalar barriers") + for source, target in zip(a, b): + if source[0] == "scalar": + need(source == target, "Same scalar use cut") + continue + need(source[:4] == target[:4], "Same total frame map between scalar uses") + chain = chains[target[4][0]] + need(chain["source_events"] == source[4], "Independent source-event chain") + need((chain["field"], chain["old"], chain["new"], chain["rank"]) == (field, *source[1:4]), "Chain metadata") + for key in ("frames", "start", "final", "endpoint_adapters"): + need(original[key] == result[key], "Same physical boundary " + key) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--package", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + start = time.monotonic() + package = args.package.resolve() + frozen = package / "frozen" + manifest = read(package / "SOURCES.json") + for name, entry in manifest["frozen_files"].items(): + need(sha256((frozen/name).read_bytes()).hexdigest() == entry["sha256"], "Frozen input pin " + name) + directory = frozen / "lanes/oblique-native-20261017/signed-metric-reciprocal-20261020" + original = read(directory / "native-normal/NATIVE.json.gz") + coalesced = read(directory / "coalesced-normal/NATIVE.json.gz") + model = read(directory / "model-normal-v2/RESPONSE.json.gz") + need(original["model"] == coalesced["model"] == model, "Same model in all payloads") + model_report = check_model(model) + word_reports = {} + for provider in ("base", "extra"): + for name, old in original["providers"][provider].items(): + response = rows(model["physical"]["E" if name in ("forward_E", "backward_transpose_E") else "inverse_adjoint_E"]) + expected = eye(640) + for i, row in enumerate(response): + for j, value in row.items(): + put(expected[j if name.startswith("backward") else 112+i], 112+i if name.startswith("backward") else j, + -value if name.startswith("backward") else value) + scalar = 7080 if name.endswith("by_metric") else 6440 + old_report = word_check(old, expected, {1: 1520, 2: 64, 3: 48}, scalar) + new = coalesced["providers"][provider][name] + new_report = word_check(new, expected, {1: 971, 2: 237, 3: 46, 4: 12, 5: 5, 6: 11, 7: 10}, scalar) + coalescing_check(old, new) + need((old_report["prefix_one_norm"], old_report["binary_height"]) == + (new_report["prefix_one_norm"], new_report["binary_height"]), "Unchanged prefix bounds") + word_reports[provider+"/"+name] = {"original": old_report, "coalesced": new_report} + + phase_path = frozen / "lanes/interface-proof/verify_native_lift.py" + spec = importlib.util.spec_from_file_location("frozen_exact_phase", phase_path) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + first = coalesced["providers"]["base"]["forward_E"] + inherited = original["providers"]["base"]["forward_E"]["native_recipes"] + fresh = [] + for key, record in first["native_recipes"].items(): + if key in inherited: + need(record == inherited[key], "Inherited phase record") + continue + a, b = map(int, key.split(":")) + actual = phase.recipe(record) + target = phase.adjoint(phase.frame(first["frames"][a], 9)) + phase.frame(first["frames"][b], 9) + phase.equal(actual, target, "Fresh recipe " + key) + fresh.append(key) + need(len(fresh) == 206, "Fresh phase census") + for provider in coalesced["providers"].values(): + for word in provider.values(): + need(word["native_recipes"] == first["native_recipes"], "All words use the checked recipes") + + bad = deepcopy(first["native_recipes"][fresh[0]]) + bad["left"]["phase"] = (bad["left"]["phase"]+1) % 4 + a, b = map(int, fresh[0].split(":")) + try: + phase.equal(phase.recipe(bad), phase.adjoint(phase.frame(first["frames"][a], 9)) + phase.frame(first["frames"][b], 9), "Changed phase") + except ValueError: + phase_rejected = True + else: + raise ValueError("Changed phase accepted") + bad = deepcopy(first) + scalar_event = next(e for e in bad["events"] if e[0] == "scalar") + scalar_event[2] = (scalar_event[2]+1) % len(bad["frames"]) + try: + coalescing_check(original["providers"]["base"]["forward_E"], bad) + except ValueError: + scalar_rejected = True + else: + raise ValueError("Changed scalar cut accepted") + + for name, entry in manifest["frozen_files"].items(): + need(sha256((frozen/name).read_bytes()).hexdigest() == entry["sha256"], "Input unchanged " + name) + result = {"status": "PASS_INDEPENDENT_PUBLICATION_REVIEW", "python": sys.version, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_manifest_sha256": sha256((package/"SOURCES.json").read_bytes()).hexdigest(), + "model": model_report, "words": word_reports, "fresh_phase_checks": len(fresh), + "phase_engine_sha256": sha256(phase_path.read_bytes()).hexdigest(), + "phase_engine_scope": "Reused pinned compiler-independent exact Pauli and reference-column engine. No producer interpreter was imported.", + "negative_controls": {"changed_global_phase_rejected": phase_rejected, "changed_scalar_cut_rejected": scalar_rejected}, + "frozen_inputs_unchanged": len(manifest["frozen_files"]), "elapsed_seconds": round(time.monotonic()-start, 3)} + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(result["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-coalesced.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-coalesced.log new file mode 100644 index 0000000000..496dcd4a96 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-coalesced.log @@ -0,0 +1,9 @@ +Fresh exact phase checks 25 +Fresh exact phase checks 50 +Fresh exact phase checks 75 +Fresh exact phase checks 100 +Fresh exact phase checks 125 +Fresh exact phase checks 150 +Fresh exact phase checks 175 +Fresh exact phase checks 200 +{"fresh_exact_native_phase_checks": 206, "inherited_native_records": 1071, "payload_decompressed_sha256": "308044e47b3456e0fdb80325e3aa26327e5d71e61176d6db9c2d658241d5d255", "phase_method": "Exact18 Pauli images and the exact reference column fix the full Clifford operator and global phase.", "producer_sha256": "3b3c1e1a3c33a5391c27d89d3484c0802c63d6ec02c9ac041fde6a4c6b844efb", "reports": {"base": {"backward_inverse_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "backward_inverse_by_metric": {"all_input_columns": 640, "binary_height": 2, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 7080, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "backward_transpose_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "16", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "forward_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "46", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_by_metric": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "60", "private_fields": 0, "real_scalar_primitives": 7080, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}}, "extra": {"backward_inverse_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "backward_inverse_by_metric": {"all_input_columns": 640, "binary_height": 2, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 7080, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "backward_transpose_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "16", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "forward_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "46", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 6440, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_by_metric": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "60", "private_fields": 0, "real_scalar_primitives": 7080, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}}}, "scope": "Complete local data words. All scalar events and endpoints are unchanged. The caller, terminal, helper progress and recursive host remain separate.", "source_pins": {"freeze": ["NATIVE-FREEZE.json", "ced70c0c6fe961b1a840819ee5e8cce2756a229d4eee7ec3b5a6f8e4bac6c6eb"], "producer": ["emit_native.py", "b6db27a1a7e990ac297972f0306efa624bfa317d70bcb18615a38a4b8d2aac03"], "source": ["native-normal/NATIVE.json.gz", "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e"]}, "status": "PASS_COALESCED_SIGNED_METRIC_NATIVE", "unchanged_endpoint_phase_records": 224} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-conditional-clean-reflection.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-conditional-clean-reflection.log new file mode 100644 index 0000000000..3b9541a385 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-conditional-clean-reflection.log @@ -0,0 +1 @@ +{"status": "PASS", "sha256": "2cad019620b5cffe1596c066fc15a8dc36eedb0afab9e8bf2dce01d26504e3a5"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-family.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-family.log new file mode 100644 index 0000000000..8ba30ec276 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-family.log @@ -0,0 +1 @@ +{"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/publication-reviews/reciprocal-native-responses/replay-logs/normal-model.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-model.log new file mode 100644 index 0000000000..6cfdc5951d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-model.log @@ -0,0 +1 @@ +{"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": {"all_input_columns": 640, "binary_height": 1, "instructions": 116, "prefix_row_l1_bound": "4", "real_scalar_primitives": 728, "untouched_arbitrary_fields": 528}, "R": {"all_input_columns": 640, "binary_height": 1, "instructions": 416, "prefix_row_l1_bound": "38", "real_scalar_primitives": 2892, "untouched_arbitrary_fields": 528}, "inverse_E": {"all_input_columns": 640, "binary_height": 1, "instructions": 480, "prefix_row_l1_bound": "44", "real_scalar_primitives": 3308, "untouched_arbitrary_fields": 528}, "inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "instructions": 480, "prefix_row_l1_bound": "14", "real_scalar_primitives": 3308, "untouched_arbitrary_fields": 528}, "metric_inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "instructions": 544, "prefix_row_l1_bound": "56", "real_scalar_primitives": 3628, "untouched_arbitrary_fields": 528}, "summary": {"determinant_E": "1", "metric_conversion_extra_scalar": 320, "nonzero_E": 1056, "nonzero_P": 160, "nonzero_inverse_E": 1056, "odd_divisions": 0, "physical_metric_counts": {"-1/2": 16, "-1/4": 16, "1": 80}, "rank_E_minus_I": 32, "rank_E_minus_P": 16, "special_physical_fields": 32}}, "source_pins": {"arithmetic": ["new-core-transfer-20261017/low-displacement-20261020/check_response.py", "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"], "cyclic": ["independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"], "placement": ["new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/METRIC-COMPLETION.json.gz", "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e"]}, "status": "PASS_SIGNED_METRIC_ACTUAL112"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-native-review.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-native-review.log new file mode 100644 index 0000000000..c58e30242f --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-native-review.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_SIGNED_METRIC_NATIVE diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-native.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-native.log new file mode 100644 index 0000000000..b496974033 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-native.log @@ -0,0 +1 @@ +{"native_phase_scope": "All inherited native records, ordered frames and endpoint adapters are byte-equal. No new spatial phase recipe is used or claimed.", "negative_controls": "One nonzero transfer is deleted and rejected in each principal direction and provider.", "payload_decompressed_sha256": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e", "producer_sha256": "b6db27a1a7e990ac297972f0306efa624bfa317d70bcb18615a38a4b8d2aac03", "reports": {"base": {"backward_inverse_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "inherited_native_recipe_count": 1561, "native_children": 1632, "native_mass": 1792, "native_profile": {"1": 1520, "2": 64, "3": 48}, "native_sequence_byte_equal": true, "native_side_map_bound": 3264, "new_native_recipe_count": 0, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 6440, "untouched_arbitrary_fields": 416}, "backward_inverse_by_metric": {"all_input_columns": 640, "binary_height": 2, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, 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224, "explicit_endpoint_monomials": 224, "inherited_native_recipe_count": 1561, "native_children": 1632, "native_mass": 1792, "native_profile": {"1": 1520, "2": 64, "3": 48}, "native_sequence_byte_equal": true, "native_side_map_bound": 3264, "new_native_recipe_count": 0, "owned_fields": 0, "prefix_row_l1_bound": "46", "private_fields": 0, "real_scalar_primitives": 6440, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "inherited_native_recipe_count": 1561, "native_children": 1632, "native_mass": 1792, "native_profile": {"1": 1520, "2": 64, "3": 48}, "native_sequence_byte_equal": true, "native_side_map_bound": 3264, "new_native_recipe_count": 0, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 6440, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_by_metric": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "inherited_native_recipe_count": 1561, "native_children": 1632, "native_mass": 1792, "native_profile": {"1": 1520, "2": 64, "3": 48}, "native_sequence_byte_equal": true, "native_side_map_bound": 3264, "new_native_recipe_count": 0, "owned_fields": 0, "prefix_row_l1_bound": "60", "private_fields": 0, "real_scalar_primitives": 7080, "untouched_arbitrary_fields": 416}}}, "scope": "Complete local native data service. Productive helper progress, global routing, centre retention, terminal decoding and recursive hosting remain separate.", "source_pins": {"cyclic": {"path": "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", "sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"}, "model": {"path": "oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz", "sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0"}, "model_freeze": {"path": "oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json", "sha256": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7"}, "native": {"path": "new-core-transfer-20261017/low-displacement-20261020/emit_native.py", "sha256": "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745"}, "source": {"path": "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz", "sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"}}, "status": "PASS_SIGNED_METRIC_NATIVE"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-ordered-caller.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-ordered-caller.log new file mode 100644 index 0000000000..8bf228daff --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-ordered-caller.log @@ -0,0 +1 @@ +{"status": "PASS", "sha256": "c418cfbbf92f423cd2e5bcd8639c7d5b523376dad4a1d09c9a531157fed06fee"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-rank-two-review.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-rank-two-review.log new file mode 100644 index 0000000000..227630c4eb --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-rank-two-review.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_RECIPROCAL_RANK_TWO +receipt_sha256=6c24c5a9ae096409998da667f1d237231c82aba43383853e2e1b96565cb7e978 diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-rank-two.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-rank-two.log new file mode 100644 index 0000000000..9915b77b5f --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/normal-rank-two.log @@ -0,0 +1,2 @@ +PASS_RECIPROCAL_RANK_TWO +receipt_sha256=971df2cc46160babf79b668c5677ab03e48ae86551d727db05c6f4118fc6658e diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-coalesced.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-coalesced.log new file mode 100644 index 0000000000..496dcd4a96 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-coalesced.log @@ -0,0 +1,9 @@ +Fresh exact phase checks 25 +Fresh exact phase checks 50 +Fresh exact phase checks 75 +Fresh exact phase checks 100 +Fresh exact phase checks 125 +Fresh exact phase checks 150 +Fresh exact phase checks 175 +Fresh exact phase checks 200 +{"fresh_exact_native_phase_checks": 206, "inherited_native_records": 1071, "payload_decompressed_sha256": "308044e47b3456e0fdb80325e3aa26327e5d71e61176d6db9c2d658241d5d255", "phase_method": "Exact18 Pauli images and the exact reference column fix the full Clifford operator and global phase.", "producer_sha256": "3b3c1e1a3c33a5391c27d89d3484c0802c63d6ec02c9ac041fde6a4c6b844efb", "reports": {"base": {"backward_inverse_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, 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true, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_by_metric": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "merged_chain_count": 1292, "native_children": 1292, "native_mass": 1792, "native_profile": {"1": 971, "2": 237, "3": 46, "4": 12, "5": 5, "6": 11, "7": 10}, "native_side_map_bound": 2584, "owned_fields": 0, "prefix_row_l1_bound": "60", "private_fields": 0, "real_scalar_primitives": 7080, "scalar_events_byte_equal": true, "untouched_arbitrary_fields": 416}}}, "scope": "Complete local data words. All scalar events and endpoints are unchanged. The caller, terminal, helper progress and recursive host remain separate.", "source_pins": {"freeze": ["NATIVE-FREEZE.json", "ced70c0c6fe961b1a840819ee5e8cce2756a229d4eee7ec3b5a6f8e4bac6c6eb"], "producer": ["emit_native.py", "b6db27a1a7e990ac297972f0306efa624bfa317d70bcb18615a38a4b8d2aac03"], "source": ["native-normal/NATIVE.json.gz", "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e"]}, "status": "PASS_COALESCED_SIGNED_METRIC_NATIVE", "unchanged_endpoint_phase_records": 224} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-conditional-clean-reflection.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-conditional-clean-reflection.log new file mode 100644 index 0000000000..3b9541a385 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-conditional-clean-reflection.log @@ -0,0 +1 @@ +{"status": "PASS", "sha256": "2cad019620b5cffe1596c066fc15a8dc36eedb0afab9e8bf2dce01d26504e3a5"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-family.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-family.log new file mode 100644 index 0000000000..8ba30ec276 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-family.log @@ -0,0 +1 @@ +{"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/publication-reviews/reciprocal-native-responses/replay-logs/optimized-model.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-model.log new file mode 100644 index 0000000000..6cfdc5951d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-model.log @@ -0,0 +1 @@ +{"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": {"all_input_columns": 640, "binary_height": 1, "instructions": 116, "prefix_row_l1_bound": "4", "real_scalar_primitives": 728, "untouched_arbitrary_fields": 528}, "R": {"all_input_columns": 640, "binary_height": 1, "instructions": 416, "prefix_row_l1_bound": "38", "real_scalar_primitives": 2892, "untouched_arbitrary_fields": 528}, "inverse_E": {"all_input_columns": 640, "binary_height": 1, "instructions": 480, "prefix_row_l1_bound": "44", "real_scalar_primitives": 3308, "untouched_arbitrary_fields": 528}, "inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "instructions": 480, "prefix_row_l1_bound": "14", "real_scalar_primitives": 3308, "untouched_arbitrary_fields": 528}, "metric_inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "instructions": 544, "prefix_row_l1_bound": "56", "real_scalar_primitives": 3628, "untouched_arbitrary_fields": 528}, "summary": {"determinant_E": "1", "metric_conversion_extra_scalar": 320, "nonzero_E": 1056, "nonzero_P": 160, "nonzero_inverse_E": 1056, "odd_divisions": 0, "physical_metric_counts": {"-1/2": 16, "-1/4": 16, "1": 80}, "rank_E_minus_I": 32, "rank_E_minus_P": 16, "special_physical_fields": 32}}, "source_pins": {"arithmetic": ["new-core-transfer-20261017/low-displacement-20261020/check_response.py", "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8"], "cyclic": ["independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"], "placement": ["new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/METRIC-COMPLETION.json.gz", "88a9f75fa87b1a258d6465e309785c1aaec1be6393d46e51bc0a469e62f09e5e"]}, "status": "PASS_SIGNED_METRIC_ACTUAL112"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-native-review.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-native-review.log new file mode 100644 index 0000000000..c58e30242f --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-native-review.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_SIGNED_METRIC_NATIVE diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-native.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-native.log new file mode 100644 index 0000000000..b496974033 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-native.log @@ -0,0 +1 @@ +{"native_phase_scope": "All inherited native records, ordered frames and endpoint adapters are byte-equal. 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224, "explicit_endpoint_monomials": 224, "inherited_native_recipe_count": 1561, "native_children": 1632, "native_mass": 1792, "native_profile": {"1": 1520, "2": 64, "3": 48}, "native_sequence_byte_equal": true, "native_side_map_bound": 3264, "new_native_recipe_count": 0, "owned_fields": 0, "prefix_row_l1_bound": "46", "private_fields": 0, "real_scalar_primitives": 6440, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_E": {"all_input_columns": 640, "binary_height": 1, "endpoint_maps": 224, "explicit_endpoint_monomials": 224, "inherited_native_recipe_count": 1561, "native_children": 1632, "native_mass": 1792, "native_profile": {"1": 1520, "2": 64, "3": 48}, "native_sequence_byte_equal": true, "native_side_map_bound": 3264, "new_native_recipe_count": 0, "owned_fields": 0, "prefix_row_l1_bound": "30", "private_fields": 0, "real_scalar_primitives": 6440, "untouched_arbitrary_fields": 416}, "forward_inverse_adjoint_by_metric": {"all_input_columns": 640, "binary_height": 1, 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Productive helper progress, global routing, centre retention, terminal decoding and recursive hosting remain separate.", "source_pins": {"cyclic": {"path": "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json", "sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585"}, "model": {"path": "oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz", "sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0"}, "model_freeze": {"path": "oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json", "sha256": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7"}, "native": {"path": "new-core-transfer-20261017/low-displacement-20261020/emit_native.py", "sha256": "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745"}, "source": {"path": "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz", "sha256": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4"}}, "status": "PASS_SIGNED_METRIC_NATIVE"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-ordered-caller.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-ordered-caller.log new file mode 100644 index 0000000000..8bf228daff --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-ordered-caller.log @@ -0,0 +1 @@ +{"status": "PASS", "sha256": "c418cfbbf92f423cd2e5bcd8639c7d5b523376dad4a1d09c9a531157fed06fee"} diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-rank-two-review.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-rank-two-review.log new file mode 100644 index 0000000000..227630c4eb --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-rank-two-review.log @@ -0,0 +1,2 @@ +PASS_INDEPENDENT_RECIPROCAL_RANK_TWO +receipt_sha256=6c24c5a9ae096409998da667f1d237231c82aba43383853e2e1b96565cb7e978 diff --git a/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-rank-two.log b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-rank-two.log new file mode 100644 index 0000000000..9915b77b5f --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/replay-logs/optimized-rank-two.log @@ -0,0 +1,2 @@ +PASS_RECIPROCAL_RANK_TWO +receipt_sha256=971df2cc46160babf79b668c5677ab03e48ae86551d727db05c6f4118fc6658e diff --git a/research/reciprocal-native-responses/APPLICATION.md b/research/reciprocal-native-responses/APPLICATION.md new file mode 100644 index 0000000000..43a765fe30 --- /dev/null +++ b/research/reciprocal-native-responses/APPLICATION.md @@ -0,0 +1,207 @@ +# Ordered three-call response and conditional cleanup + +This application uses the actual `E=P R` response, with `P^2=R^2=I` +and `R-I=U L` of rank 16. Its identities keep all stage orders. +The exact matrix regression uses three distinct signed conjugations +of the actual 112-port matrices. Those conjugations test order; they +are not a replay of the actual D25 routes. + +## Wrapped local responses + +Write `D(A)=diag(A,A)` and + +```text +L_A=[[I,0],[A,I]], U_A=[[I,A],[0,I]]. +``` + +For a raw forward response `E`, apply `P` on the current-I Y input +and on the completed-FULL X output. For a raw backward response +`E^-1`, use the same wrapper positions. The resulting content maps are + +```text +F^P=[[P,0],[E,P]]=D(P)L_R, +B^P=[[P,-P R],[0,P]]=D(P)U_-R. +``` + +These wrapper positions use the pinned +[stage-view premise](frozen/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md). +No port-mixing wrapper is granted on a retired ordinary Y hole. +The common-frame `P` word costs 728 real primitives. Its address +views are separate costs. + +## Three distinct stages + +Set + +```text +H=P1 P0, Ptot=P2 P1 P0, +Rhat0=R0, +Rhat1=P0^-1 R1 P0, +Rhat2=H^-1 R2 H. +``` + +Then + +```text +F2^P B1^P F0^P=D(Ptot)L_Rhat2 U_-Rhat1 L_Rhat0. +``` + +Let `K_i=Rhat_i-I` and `W=L_I U_-I L_I=[[0,-I],[I,0]]`. The +normalized defect is + +```text +T=W^-1 L_Rhat2 U_-Rhat1 L_Rhat0=A2 A1 A0, + +A0=[[I,0],[K0,I]], +A1=[[I-K1,-K1],[K1,I+K1]], +A2=[[I,-K2],[0,I]]. +``` + +Each `A_i-I` has square zero and rank at most 16 in array units. +For the middle term, use + +```text +A1-I=[-I;I]K1[I,I], [I,I][-I;I]=0. +``` + +Thus `rank(T-I)<=48` in array units, or at most `48d` over a payload +field of dimension `d`. The exact inverse is the following ordered +sequence: + +```text +X += K2 Y +q = K1(X+Y); X += q; Y -= q +Y -= K0 X. +``` + +The middle sum remains unchanged by the two writes. A serial +implementation must retain its complete query before either write +changes a required source. + +## Source records and literal read cuts + +Let `Uhat_i,Lhat_i` be the transported factors of `K_i`. In particular, + +```text +Uhat0=U0, Lhat0=L0, +Uhat1=P0^-1 U1, Lhat1=L1 P0, +Uhat2=H^-1 U2, Lhat2=L2 H. +``` + +For initial logical data `x,y`, put + +```text +c0=L0 x, +t=y+R0 x, c1=Lhat1 t, +w=x-Rhat1 t, c2=Lhat2 w. +``` + +Before the `Ptot` code, the output is + +```text +X=-y-U0 c0-Uhat1 c1, +Y= x-Uhat1 c1+Uhat2 c2. +``` + +The three local rows `L0,L1,L2` have different physical read cuts: + +| Record | Stored argument | Read cut | +| --- | --- | --- | +| `c0` | F0 source `X=x` | completed X, before post-`P0` | +| `c1` | B1 input `Y=P0 t` | current-I Y, before pre-`P1` | +| `c2` | F2 source `X=H w` | completed X, before post-`P2` | + +In particular, `c1=L1(P0 t)`, not `L1 t`. Retaining these records +requires owned fields or a joint invertible code with a decoder for +every displaced arbitrary baseline. Later frame progress is also a +paid operation. + +## Conditional endpoint cleanup + +For physical inputs `X0,Y0`, let `x=q X0`, `y=Y0`, with `q=Q^-1`. +This is a coordinate definition. The retained signed terminal gives + +```text +output=diag(F,F) Qhat D(Ptot) T Qhat^-1 input, +Qhat=diag(Q,I). +``` + +No routed code is commuted through `F`. A logical code `A` at this +endpoint needs the physical implementation `F A F^-1`. + +Since each stage route is port-diagonal, `Ptot` remains supported on +the same 32 ports. Conditional on admitted completed stage views, +remove this code as follows: apply `q` on those 32 X fields, apply +`Ptot^-1` to both banks through the views, then apply `Q` to those +32 X fields. The line subtotal is 64 rank-one children. The six `P` +words cost `6*728=4368` real primitives. This does not remove `T`. + +Saved records would then give the content correction + +```text +X += Q(Uhat1 c1-Uhat2 c2), +Y -= U0 c0+Uhat1 c1. +``` + +The `Q` on the X scatter remains. Three available 16-row records do +not implement the scatter. The number `3*1792+64=5440` is only a +native subtotal under compatible raw-service and view premises. It +is not the price of a complete decoder or supplier. + +## Conditional clean-reflection variant + +Let `S` be the same 32 special ports and `O` the other 80. Let `Pi` +and `J0` be their coordinate projections. Here `J0` is not the metric. +Because `P` is identity on `O`, the ordinary rows of `E` equal those +of `R` and have zero diagonal. The selected set is pair-closed. + +These are local response conditions for a possible clean service. +No native cleanR32 service is emitted in this package. Under that +service premise, use coordinates `x=(a,u)`, `y=(z,v)` and maps + +```text +F_R(x,y)=(-z,(Rx)_O,(Rx)_S,v+(Rx)_O), +B_R(x,y)=(-z,(Rx)_O-v,(Rx)_S,v). +``` + +Selected exchange at both boundaries of `B_R` gives, for `w=R(z,u)`, + +```text +Bswap_R(x,y)=(w_S,w_O-v,-a,v). +``` + +The entry types are `Qx` and `diag(Q_S,I_O)y`. The exit types are +FULL on X and selected Y, and `Fq` on ordinary Y. The selected +exchange uses equal entry types. All target baselines are arbitrary. + +Each source code `diag(R_i,I)` differs from identity by rank 16. +Transport through the invertible ideal stage maps gives a complete +residual rank at most 48, in the same array sense as above. The ideal +terminal has 64 positive rank-one lines; an identity entry requires +32 further selected formation lines. Both counts exclude the +nonidentity reflection residual. + +For the hidden-output test, set final X and selected Y to zero and +let final ordinary logical Y be `h`. Write `i_O` for its inclusion +into the full coordinate space. Exact reversal gives + +```text +unpermuted B: + x_initial=R0 J0 R1 i_O h, + y_initial=(I-R1)i_O h; + +selected-conjugate Bswap: + x_initial=R0 R1 i_O h, + y_initial=J0(I-R1)i_O h. +``` + +The final `R2` drops out. For `Bswap`, the hidden correction depends +on two 16-row families, `L1 i_O h` and `L0 R1 i_O h`, so its rank +is at most 32 arrays. Its selected borrowed row vanishes, but its +ordinary hidden observation remains. Normalizing the ordinary holes +would permit those reads and has a separate cost. + +The exact regression attains residual rank 48 and hidden rank 32. +These are regression ranks, not lower bounds for actual routed +implementations. No unallocated record, clean service, cheap hole +reader, returned code, or complete terminal follows from this algebra. diff --git a/research/reciprocal-native-responses/EXTERNAL-NOTICES.json b/research/reciprocal-native-responses/EXTERNAL-NOTICES.json new file mode 100644 index 0000000000..de2d746073 --- /dev/null +++ b/research/reciprocal-native-responses/EXTERNAL-NOTICES.json @@ -0,0 +1,40 @@ +{ + "files": [ + { + "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "file": "notices/PR2588-NOTICE", + "sha256": "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b", + "source": "research/gmx-t74-borrow43-handoff/NOTICE", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/NOTICE" + }, + { + "commit": "f2927a4b8afcf0701a6b945e14f30de1d94f5176", + "file": "notices/PR3133-NOTICE", + "sha256": "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661", + "source": "research/coupled-carrier-cap740/vendor/PR3133-NOTICE", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/vendor/PR3133-NOTICE" + }, + { + "commit": "f2927a4b8afcf0701a6b945e14f30de1d94f5176", + "file": "notices/PR3133-CREDITS.md", + "sha256": "1d9d8f56d8899f55878e4cb2c4e052b22506444016a51c2e678773505f5189e6", + "source": "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" + }, + { + "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "file": "notices/PR2588-NOTICE-PR2226.md", + "sha256": "6b6730303818f6edc2a253eb4d05471eee58f28b5815fb250c32ae376f774c8a", + "source": "research/gmx-t74-borrow43-handoff/new/code/borrow/NOTICE-PR2226.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/NOTICE-PR2226.md" + }, + { + "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "file": "notices/PR2226-NOTICE.md", + "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422", + "source": "research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/PR2226-NOTICE.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/PR2226-NOTICE.md" + } + ], + "scope": "Unchanged notices from verified historical GitHub file objects." +} diff --git a/research/reciprocal-native-responses/LICENSE b/research/reciprocal-native-responses/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/reciprocal-native-responses/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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All 640 fields have arbitrary initial values. No word reads +or writes the 416 other fields. Their values and frames are unchanged. +This is identity action on those fields, not productive helper progress. + +Let `Q=diag(C_qp)`, `q=Q^-1`, and let `F` be the common nine-axis +advance. Include the pinned input and output adapters. The contracts +are: + +| Word | Physical input | Physical output | +| --- | --- | --- | +| `forward_E` | `(Qx,y)` | `(F x,F q(y+E x))` | +| `backward_transpose_E` | `(Qx,y)` | `(F(x-E^T y),F q y)` | +| `forward_inverse_adjoint_E` | `(Qx,y)` | `(F x,F q(y+E^-T x))` | +| `backward_inverse_E` | `(Qx,y)` | `(F(x-E^-1 y),F q y)` | + +The factor order is part of each contract. In particular, the proof +does not commute `E` through the field-dependent `Q` maps. + +## Direct words + +The pinned odd16 source has a transfer position for every ordered +off-diagonal mode pair in each six-mode block and eight-clique. +The forward emitter retains its native edges, ordered frames, pair +codes, and endpoint adapters. It replaces each transfer coefficient +by the corresponding coefficient of `E`. It deletes zero transfers. +The full replay checks the first contract on all 640 columns. + +The same construction applies to `E^-T`, whose mode diagonal is also +zero. For each forward word, take the literal inverse adjoint. In +chronological order, replace `ADD(t,s,c)` by `ADD(s,t,-c)` and replace +a real `SCALE(c)` by `SCALE(1/c)`. Keep each native unitary, endpoint +monomial, and event order. This gives both backward words, including +their phases and endpoint factors. The two fields of each changed +ADD still have equal ordered frames. + +Each direct word has this original local invoice: + +| Item | Count | +| --- | ---: | +| Native profile | `1520 H1 + 64 H2 + 48 H3` | +| Native rank mass | 1792 | +| Native children | 1632 | +| Real scalar primitives | 6440 | +| Explicit endpoint maps | 224 | +| Native side-map upper bound | 3264 | +| Owned or private fields | 0 | + +The exact common-frame codes are separate from these native words. +On one bank, `E`, `E^-1`, and `E^-T` each cost 3,308 real primitives; +`R` costs 2,892; `P` costs 728. Each such code leaves the other 528 +fields unchanged. These prices include the physical pair codes. + +## Diagonal metric conversion + +Since `E^-T=J E J^-1`, the forward reciprocal word can also use +`J^-1` on both input banks, the `E` forward word, then `J` on both +output banks. The backward reciprocal word can use `J` on both +input banks, the transpose-backward word, then `J^-1` on both +output banks. + +`J` is diagonal on physical fields. Each scale commutes with that +field's spatial map even when different fields have different frames. +Each wrapper adds 128 field-scale instructions and 640 real primitives. +It adds no native child. The total is 7,080 real primitives. A one-bank +conversion costs 320; that price would omit the second bank's baseline +restoration in a native shear. + +| Word | Real scalar primitives | Maximum prefix row one-norm | Binary denominator height | +| --- | ---: | ---: | ---: | +| Forward `E` | 6440 | 46 | 1 | +| Backward transpose `E` | 6440 | 16 | 1 | +| Forward `E^-T` | 6440 | 30 | 1 | +| Backward inverse `E` | 6440 | 30 | 1 | +| Forward metric wrapper | 7080 | 60 | 1 | +| Backward metric wrapper | 7080 | 30 | 2 | + +These bounds cover literal top-level content prefixes. They do not +bound recursive child interiors or prove complete finite precision. + +## Coalesced native cuts + +After zero transfers are removed, some intermediate frames have no +scalar use. For each field, collect consecutive native advances until +the next scalar event that reads or writes that field. Replace this +chain by one advance. At the end, emit any remaining chain. Keep +every scalar instruction, coefficient, scalar frame, and scalar-event +order unchanged. + +Moving a native map past an event on other fields is valid because +the fields are disjoint. The map of the chain is exactly + +```text +(Gamma_k Gamma_(k-1)^-1) ... (Gamma_1 Gamma_0^-1) + = Gamma_k Gamma_0^-1. +``` + +The source subspaces are nested, so the new rank equals the sum of +the old ranks. The emitter compiles the new ordered-frame map and +checks its exact phase. An equal subspace label alone is insufficient. + +The complete coalesced profile is + +```text +971 H1 + 237 H2 + 46 H3 + 12 H4 + 5 H5 + 11 H6 + 10 H7. +``` + +It has 1,292 children and rank mass 1,792. The scalar prices, 224 +endpoint maps, and content-prefix bounds are unchanged. The native +side-map upper bound is 2,584. The payload records the original event +indices in every merged chain, and every original native event occurs +in exactly one chain. + +For `0=3`, `k=n-2`, and `m=n-4`. Use coordinates `(a,b,c)`, where +`a` has `k` entries. Let `s=sum(a)`. Define + +```text +u=(1^k,m,0)^T, ell=(-1^k,1,0), +R=I+u ell, P(a,b,c)=(a,c,b), +E=P R. +``` + +Since `ell u=-2`, we have `R^2=I`. Thus `E^-1=R P`. In coordinates, + +```text +E(a,b,c) = (a-s*1+b*1, c, -m*s+(m+1)*b), +E^-1(a,b,c) = (a-s*1+c*1, -m*s+(m+1)*c, b). +``` + +Both matrices are integer matrices with zero diagonal. Each factor +`P,R` has determinant minus one, so `det(E)=1`. The factorization + +```text +E-I=U V, + +U = [ 1 0 ] repeated k times, + [ 0 1 ], + [ m -1 ], + +V = [ -1 ... -1 1 0 ], + [ 0 ... 0 -1 1 ] +``` + +has two independent columns in `U` and two independent rows in `V`. +Therefore `rank(E-I)=2`. Also `E^-1-I=-E^-1(E-I)`, so the inverse +has the same correction rank. The fixed space is `s=b=c`; it has +dimension `n-2`. Relative to `P`, the difference `E-P=P u ell` has +rank one. This last rank does not remove the cost of `P`. + +## Sharp rank bound in the stated matrix class + +Let `A` be an invertible matrix of size `n>=3` over a field of +characteristic zero. Suppose that both `A` and `A^-1` have zero +diagonal. Rank zero for `A-I` is impossible. If its rank were one, +write `A=I+v w^T`. Each diagonal equation gives `v_i w_i=-1`, so +`w^T v=-n`. The rank-one inverse formula gives + +```text +A^-1=I+v w^T/(n-1). +``` + +Its diagonal is `(n-2)/(n-1)`, which is nonzero. This contradicts +the hypothesis. The construction above therefore attains the minimum +correction rank two. + +The bound applies to `rank(A-I)`. It is not a lower bound on native +children, record fields, or a global supplier. On sixteen independent +blocks of sizes six and eight it gives the sharp sum 32. It gives no +such bound for an arbitrary coupled 112-port response. + +## The rational symmetric six-mode restriction + +Suppose a rational symmetric six-by-six matrix `A` and its inverse +both have zero diagonal. If `rank(A-I)=2`, four eigenvalues are one. +The other two eigenvalues `a,b` obey + +```text +a+b=-4, 1/a+1/b=-4, ab=1, +{a,b}={-2+sqrt(3),-2-sqrt(3)}. +``` + +Let `u,v` be orthonormal eigenvectors for `a,b`. The two diagonal +equations imply `u_i^2=v_i^2=1/6` at every coordinate. Hence +`u=sigma/sqrt(6)` and `v=tau/sqrt(6)` for sign vectors `sigma,tau`. +The spectral expression is + +```text +A=I-(sigma sigma^T+tau tau^T)/2 + +sqrt(3)*(sigma sigma^T-tau tau^T)/6. +``` + +Rationality forces the last coefficient matrix to vanish. The two +rank-one projectors would then be equal, in conflict with orthogonality. +Thus the minimum rank is at least three. Three disjoint exchanges +attain three. The rational-entry hypothesis is needed: the independent +review includes a real, nonrational symmetric example of rank two. + +## Classification of diagonal metrics + +Assume now `n>=5`, so `m=n-4>0`. Set + +```text +J=diag(1^k,-1/m,-1/m), K=J^-1. +``` + +Then `Ju=-ell^T`, `u^T J u=2`, and `ell K ell^T=2`. Expansion +gives `R^T J R=J`. The last two metric entries agree, so +`P^T J P=J`. Consequently + +```text +E^T J E=J, E^-T=J E J^-1. +``` + +Every diagonal invariant real metric is a scalar multiple of `J`. +To prove this, write it as `D=diag(d_0,...,d_(k-1),e,f)`. The last +column norm gives `e=f`. The norm of column `a_i` gives + +```text +sum_j d_j + m^2 f = 2 d_i. +``` + +Thus all `d_i` equal a common value `d`. Since `k=m+2`, the equation +is `m(d+m f)=0`, so `e=f=-d/m`. These necessary conditions are +sufficient by the identity for `J` above. + +A nonzero real scale gives inertia `(n-2,2)` or `(2,n-2)`. In +particular, no positive diagonal metric exists for `n>=5`. A metric +whose entries are units in `Z[1/2]` exists if and only if `m` is a +power of two. The units of this ring are the signed powers of two; +the ratio of `d` and `-d/m` must be a unit. Conversely, the displayed +`J` has unit entries when `m` is a power of two. The allowed sizes are +therefore `n=4+2^h`, `h>=0`. + +The dimension limits are material. At `n=2`, an exchange has correction +rank one. At `n=3`, this construction is a three-cycle and has a +positive diagonal metric. At `n=4`, every diagonal invariant metric +of this construction is singular. The actual native geometry in this +package supplies sizes six and eight; it does not supply every size +in the abstract family. + +## The actual physical response + +The pinned role placement gives eight six-mode blocks and eight +eight-mode blocks. Let `H` be the actual 24 pair codes on the large +48-port sector, with identity on the other 64 ports. In each large +block the mode order is + +```text +centre, pair_difference_a, pair_difference_b, +negative_difference, contrast, negative. +``` + +Use the pinned order for each small eight-clique. Apply the block +formulas above, then set each physical matrix to `H^-1 A H`. +The last two modes in every block form complete physical pairs. +Therefore the physical metric remains diagonal. Its entries are +80 copies of one, 16 copies of `-1/2`, and 16 copies of `-1/4`. + +The pair matrices satisfy `H_pair^T H_pair=2I`. This scale is constant +on the large sector, and each mode response preserves that sector. +These facts preserve the metric identity under the physical basis +change. Similarity alone would not prove it. + +The complete response satisfies both inverse orders and + +```text +E=P R, P^2=R^2=I, +rank(E-P)=16, rank(E-I)=32, +E^-T=J E J^-1. +``` + +Both physical diagonals are zero. Each nonzero response entry joins +orthogonal pinned port labels. Physical `P` is the identity on 80 +ports and acts within the other 32. It has 160 nonzero entries, +including signed halves; it is not a physical field permutation. + +For the physical factor `R-I=U L`, the exact centre Gram is + +```text +L J^-1 L^T=diag(4 I8,2 I8). +``` + +The large-sector factor four comes from the actual pair code. A later +centre encoding must retain this normalization. + +The two correction rows in the six-mode rank-two factor have supports +of sizes five and two. Their union contains all six modes. Only the +first row is the reflection query. The rank-two factorization does +not supply a physical capture or terminal access. + +## Evidence + +The quantified arguments above are proofs. The replay adds exact +regressions in dimensions 3 through 16 for the rank-two construction +and 5 through 24 for the metric classification. It verifies the +actual 48-port pair binding and the complete 112-port model. + +The independent algebra review uses a separate column calculation. +It checks both inverse orders, physical ranks, determinants, query +supports, and meaningful boundary controls. The native results and +their separate verification scope are in [NATIVE.md](NATIVE.md). diff --git a/research/reciprocal-native-responses/README.md b/research/reciprocal-native-responses/README.md new file mode 100644 index 0000000000..873b17cf78 --- /dev/null +++ b/research/reciprocal-native-responses/README.md @@ -0,0 +1,94 @@ +# Reciprocal responses and native words on 112 ports + +This package gives an integer reciprocal response with minimum correction +rank two in every dimension `n>=3`. It classifies the invariant diagonal +metrics of this family for `n>=5`. A diagonal metric of dyadic units exists +exactly for `n=4+2^h`, where `h>=0`. + +The actual construction has eight six-mode blocks and eight eight-mode +blocks. Its 112-port response is `E=P R`, with `P^2=R^2=I`, +`rank(E-P)=16`, and `rank(E-I)=32`. Both `E` and `E^-1` have zero +diagonal in the physical basis and the native mode basis. + +The package also supplies the complete local native words. Each word +acts on 640 arbitrary input fields and leaves the 416 fields outside +the two data banks unchanged. The coalesced word removes unused native +cuts and reduces the child count from 1,632 to 1,292. It retains rank +mass 1,792 and the direct scalar price of 6,440 real primitives. + +These results do not improve the complete kappa calculation. Productive +helper progress, routed record access and restoration, a terminal +decoder, recursive admission, and a complete precision and supplier +calculation remain open. Correction rank is not a native cost. + +Read [the proof](PROOF.md), [the native contracts and prices](NATIVE.md), +[the conditional three-call application](APPLICATION.md), and +[the source notice](SOURCE-NOTICE.md). The exact input list is +[SOURCES.json](SOURCES.json). The completed extraction replay is in +[VALIDATION.json](VALIDATION.json). + +The [low-displacement supplement](annex/README.md) retains the exact +rank-30 and rank-16 responses, their local native words and coded exits, +and two scoped obstructions. It has a separate source manifest and +replay command. Its matrix classes and inverse-grid limits are explicit. + +## Replay + +Use Python 3.10 or later. The replay uses the standard library, one +process at a time, and no network or Git checkout. Run from this directory: + +```sh +python3 -I -B replay.py --out /tmp/reciprocal-native-responses-replay +``` + +The output directory must not exist. The replay copies the frozen inputs +into that directory. It runs nine checks in normal Python and nine checks +with `-O`. It compares every result with its pinned receipt or payload. +The final line must be: + +```text +PASS_RECIPROCAL_NATIVE_RESPONSES +``` + +`REPLAY.json` in the output directory records the environment, commands +by check name, times, and comparison hashes. The replay uses exact bytes +for plain receipts and decompressed bytes for regenerated gzip artifacts. +It verifies the immutable input bytes before and after all checks. + +The checks cover the general-family regression, independent rank-two +review, actual model, original native emission, independent native +review, coalesced native emission with 206 new phase checks, ordered +three-call algebra, and conditional clean-reflection algebra. The +negative controls include a deleted nonzero transfer in each principal +direction, a changed inherited recipe, a wrong reciprocal direction, +and omitted pair-code restoration. + +The original native review inherits the phases of 1,561 pinned recipes +and 224 endpoint adapters from its accepted predecessor. It does not +repeat the predecessor's spatial replay. The coalesced emitter gives +an exact Pauli and reference-column check for its 206 new recipes. +The clean-reflection checker is a matrix check. It does not emit a +native clean service. No complete supplier target runs here. + +The files in `frozen/` retain their original bytes, dates, and local +scope statements. Their historical permission statements do not govern +this extracted package. The current claim limits are stated here. + +## Open next questions + +- Can the three 16-row source records be retained and restored by a + paid invertible code? The first step is an explicit schedule at the + three read cuts in `APPLICATION.md`. Arbitrary borrowed baselines + and later frame progress are the current blockers. +- Can the rank-48 ordered residual be removed with a complete native + terminal invoice? Start with the three inverse shears in + `APPLICATION.md`. The output `Q` factors and ordinary hole access + must remain in the calculation. +- Can the lower native moment of the coalesced words improve a complete + supplier? Start with an admitted recursive host and include all + helpers, views, scalars, side maps, and precision guards. The local + child count alone does not answer this question. + +OpenAI Codex gave substantial assistance in the construction, proofs, +code, checks, independent agent reviews, and package extraction. + diff --git a/research/reciprocal-native-responses/SOURCE-NOTICE.md b/research/reciprocal-native-responses/SOURCE-NOTICE.md new file mode 100644 index 0000000000..24b1492bc5 --- /dev/null +++ b/research/reciprocal-native-responses/SOURCE-NOTICE.md @@ -0,0 +1,108 @@ +# Sources, credit, and review scope + +This package extracts a bounded result from the centre-encoding campaign +of October 2026. It keeps consumed frozen files byte for byte in +`frozen/` and `annex/frozen/`. [SOURCES.json](SOURCES.json) and the +[supplement manifest](annex/SOURCES.json) record their original campaign +paths, byte hashes, sizes, and decompressed payload hashes where needed. +No moving source head replaces a historical input. + +The package contains the full input closure for `replay.py`. It does not +contain every predecessor experiment or every input needed to regenerate +the older spatial review. The replay inherits that review through exact +native-record equality and its pinned receipt. This boundary is stated +in [NATIVE.md](NATIVE.md). + +## Contribution within this campaign + +- The coordinating lane supplied the integer `E=P R` family, its + rank-two proof, the rational symmetric six-mode restriction, and the + signed-metric candidate. The independent-review lane checked these + results by a separate column method and corrected the union of the + two query supports from five modes to six. +- The oblique-native lane supplied the diagonal-metric classification, + actual 112-port response, paid common-frame words, native reciprocal + coefficient words, metric wrappers, and removal of unused native cuts. +- The new-core-transfer lane supplied the pair-closed role placement and + the odd16 native predecessor. The independent-review cyclic-flag + construction supplied the off-diagonal transfer grammar. The native + review supplied the accepted predecessor phase evidence. +- The independent-review lane supplied a separate complete content, + frame, inherited-phase, and price review of the original twelve words. + The coalesced producer supplies fresh exact checks of its new recipes; + its historical freeze has no separate complete independent review. +- The cover-algebra lane supplied the ordered three-call and conditional + clean-reflection identities. The bridge-access lane supplied the + stage-view premise. These results do not allocate source records or + give a complete terminal decoder. +- The new-core-transfer lane supplied the rank-30 response, rank-16 + extension, reciprocal-large words, coded exits, and the two scoped + obstructions in the supplement. The independent-review lane supplied + the separate matrix and scalar checks. The new-native-recipes lane + supplied the separate native and coded-exit spatial reviews. Their + original receipts remain separate from the new publication review. + +The separate centre-metric encoder package supplies later signed and +unitary encodings. Those later encodings are not consumed dependencies +of the response or native results here. + +## Historical external sources + +The retained [native source notice](frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md) +identifies these material predecessors: + +- [PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), + at commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`, supplied the + core used by the native lane. +- [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), + at commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`, supplied the + byte-equal provider words: + [base](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz) + and + [extra](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz). +- [PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), + at commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`, supplied the + retained exact recipe tools. This package directly imports the + [exact Clifford compiler](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py). + Its byte hash is + `2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962`. + +These are historical dependency pins, not claims about current PR +heads or the selected bound. The source notice also retains earlier +wrapper and warp credit. No contributor handle is inferred from a +submitter account. + +The publication refresh used main commit +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`. Its +[selected record](https://github.com/CrocSwap/integer-mult-bounds/blob/b58ad9ef4d4e861b0eaa5dba41742bdc072dca51/certificates/selected-result.json) +names [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470), +with conditional kappa `0.00302015`. That construction has different +source and caller contracts. This package preserves the historical +inputs and proves no transfer to the selected construction. + +The unchanged [PR #2588 notice](notices/PR2588-NOTICE), +[provider notice](notices/PR3133-NOTICE), and +[provider credits](notices/PR3133-CREDITS.md) retain the full predecessor +credit. [EXTERNAL-NOTICES.json](EXTERNAL-NOTICES.json) records their +verified GitHub source pins and byte hashes. These notices include the +dirty-borrowing, native-lowering, owner-fill, and core-construction +lineage. They do not establish an individual author of every imported +helper file. + +The retained [PR #2226 port notice](notices/PR2588-NOTICE-PR2226.md) +identifies `clifford_exact.py` as an unchanged copy from vendor531. +Its [earlier notice](notices/PR2226-NOTICE.md) retains the phase and +compiler lineage. Both files come from the same pinned PR #2588 tree. +They give source context; this package does not import `bw_gauss.py` +or the dirty-borrowing replay. + +## License and AI assistance + +The package uses the repository's Apache-2.0 license. The license text +is in [LICENSE](LICENSE). All retained source notices remain unchanged. + +OpenAI Codex gave substantial assistance in the mathematical construction, +proofs, code, regression checks, independent agent reviews, and package +extraction. An independent agent review is a separate calculation. 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5288 + } + }, + "response_models": { + "rank16": { + "determinant": "2251875390625", + "ordinary_determinant": "5323914784321/16", + "rank": 16 + }, + "rank30": { + "determinant": "33554432", + "ordinary_determinant": "2097152", + "rank": 30 + }, + "reciprocal_large": { + "determinant": "33554432", + "ordinary_determinant": "2097152", + "rank": 30 + } + }, + "scope": "Independent rational maps, scalar prices, typed frame ledger, and 352 changed-exit phases with the existing compiler-independent engine. Inherited raw phases and physical endpoints retain the pinned predecessor reviews. No odd-grid admission or supplier replay.", + "status": "PASS_SUPPORTING_LOW_DISPLACEMENT_REVIEW" +} diff --git a/research/reciprocal-native-responses/annex/PUBLICATION-CHECKS.json b/research/reciprocal-native-responses/annex/PUBLICATION-CHECKS.json new file mode 100644 index 0000000000..6887905c8a --- /dev/null +++ b/research/reciprocal-native-responses/annex/PUBLICATION-CHECKS.json @@ -0,0 +1,21 @@ +{ + "files": { + "NATIVE-CHECKS.json": { + "bytes": 11162, + "review_source": "ANNEX-INDEPENDENT-CHECKS.json", + "sha256": "469e886b99c068737e4d2c0d3d0c7dc10d484f051aecb27f5236932c88dbdb84" + }, + "check_native.py": { + "bytes": 14708, + "review_source": "check_low_displacement_annex.py", + "sha256": "422fcba4ef902417248859b99394f9e59bf2154b9dd6771220637b17f6a2cc5c" + }, + "check_publication_review.py": { + "bytes": 16547, + "review_source": "check_publication_review.py", + "sha256": "19c50e2cc940dbf7f61749f19d5f1bd286ac7c75e0de5aadda5556f67a1b0503" + } + }, + "schema": "low-displacement-publication-checks-v1", + "scope": "Unchanged independent publication checkers and first accepted receipt. Runtime metadata are separate from the mathematical receipt." +} diff --git a/research/reciprocal-native-responses/annex/README.md b/research/reciprocal-native-responses/annex/README.md new file mode 100644 index 0000000000..0e5529fdf0 --- /dev/null +++ b/research/reciprocal-native-responses/annex/README.md @@ -0,0 +1,175 @@ +# Low-displacement response supplement + +This supplement preserves the completed rank-30 and rank-16 response +results. It gives different response classes from the reciprocal +zero-diagonal family in the main package. The frozen files keep their +original bytes and source pins. + +These are matrix constructions, local native words, and two scoped +obstructions. They do not expose a productive centre cohort, remove the +output code, or improve the complete kappa calculation. The moving +section and rational code-service constructions are separate results. + +## Exact matrix statements + +The [rank-30 response proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md) +constructs a dyadic unit `E` on the actual 112 ports, with +`rank(E-I)=30`. Its selected eight-port block is the original `L`, +with `L^2=I/2`, in both `E` and `E^-1`. The full determinant is +`2^25`; the ordinary 104-port determinant is `2^21`. Each literal +common-frame word for `E`, `E^-1`, `E^T`, and `E^-T` costs 3,210 +real scalar primitives on arbitrary input fields. + +The large 48-port part contributes rank 16. The small part uses eleven +five-cliques and three three-cliques. Fourteen blocks are optimal only +among disjoint rank-one dyadic clique blocks of sizes 2, 3, and 5 on +this fixed small support. This is not a native optimum or a lower bound +for all response matrices. The small inverse has a nonzero diagonal. + +The [extension proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md) +also gives a reciprocal-large response. It replaces the large block by +its inverse transpose and keeps the small response. The backward cross +block uses the large inverse and the original small response. It does +not implement the inverse of the complete 112-port response. + +The rank-16 extension is symmetric and has determinant `35^8` and +`rank(E-I)=16`. Its large part is `I-K^T K/2`, where `K K^T=12I`. +Its inverse is `I-K^T K/10`. The small part has eight blocks `I-J_8`, +with inverses `I-J_8/7`. The selected block of `E` is `L`; the +selected block of `E^-1` is `(4I+L)/5`. + +Rank 16 relaxes both the inverse-diagonal requirement and the grid +requirement. The inverse diagonal on each six-mode block is `4/5`. +The inverse needs primes 5 and 7 in the stored grid. The ordinary +normalization also needs prime 31: its inverse has denominators 7, +31, and 62. Odd denominators alone do not evade the reciprocal +rank-two theorem. The native data word does not supply or price these +inverse conversions. + +## Local native contracts and costs + +The [raw native proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE.md) +and the extension proof give both directions for both retained +providers. Each local word checks all 640 arbitrary input fields and +leaves the 416 fields outside the two data banks unchanged. Each uses +zero owned fields and zero private fields. There is no clean-field +premise. The following prices are per word. + +| Response | Native profile | Children | Rank mass | Real scalar primitives | External endpoint maps | +| --- | --- | ---: | ---: | ---: | ---: | +| Rank 30 | `1036 H1 + 48 H3 + 55 H4 + 55 H5 + 9 H6 + 9 H7` | 1,212 | 1,792 | 5,288 | 224 | +| Reciprocal-large | Same as rank 30 | 1,212 | 1,792 | 5,288 | 224 | +| Rank 16 | `1520 H1 + 64 H2 + 48 H3` | 1,632 | 1,792 | 7,384 | 224 | + +The separate upper bound of two side maps per native child is 2,424 +for rank 30 and reciprocal-large, and 3,264 for rank 16. These side +maps are additional to the displayed external endpoint maps. The +array prefix bounds are 46 forward and 30 backward for rank 30, 30 +forward and 46 backward for reciprocal-large, and 22 in both +directions for rank 16. + +The [coded-exit proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS.md) +keeps `W=S_e0 C_45 S_e0` on the large 48 ports or on all 112 ports. +On a coded port, the exact output contracts are +`X_p=W F9 x'_p` and `Y_p=W F9 Q_p^-1 y'_p`. The operator order is +literal. The code is not removed and `W` does not commute freely +through `Q_p`. Thus these are changed output contracts. + +| Response and output code | Native profile | Children | Rank mass | Real scalar primitives | +| --- | --- | ---: | ---: | ---: | +| Rank 30, `W48_I64` | `988 H1 + 48 H2 + 55 H4 + 55 H5 + 9 H6 + 9 H7` | 1,164 | 1,696 | 5,288 | +| Rank 30, `W112` | `988 H1 + 48 H2 + 55 H5 + 55 H6 + 9 H7 + 9 H8` | 1,164 | 1,824 | 5,288 | +| Rank 16, `W48_I64` | `1472 H1 + 112 H2` | 1,584 | 1,696 | 7,384 | +| Rank 16, `W112` | `1408 H1 + 112 H2 + 64 H3` | 1,584 | 1,824 | 7,384 | + +Each coded word has 48 explicit inline monomial exits. `W48_I64` +retains 176 external endpoint maps; `W112` retains 112. The side-map +upper bound is twice the child count. These counts do not pay for +future code removal, terminal access, or a recursive caller. + +## Two scoped limits + +The [cross-Gram proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EVEN-CLIQUE-GRAM.md) +shows that the current rank-16 factor cannot support a section-swap +code that requires an everywhere invertible `V Q^2 U`. Its ranks on +all 512 characters are 0, 4, 8, 14, and 16, with counts 32, 96, 12, +256, and 116. A change of minimal scalar factor basis cannot remove +the obstruction. This does not rule out a different encoding method. + +The [paired-line proof](frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/PAIRED-LINE-TENSOR-SCOPE.md) +proves that the scalar two-field identity retains a tensor-width +cost. A word with arbitrary monomial views and no native calls needs +at least `f` scalar ADDs to implement `Q_f` or +`diag(Q_f,Q_f^-1)`. A separate one-call determinant obstruction +requires translation-only views. It does not apply to general native +views. The finite checks cover widths 1 through 6. + +The paired-line freeze retains its historical status +`FROZEN_PRODUCER_NOTE_INDEPENDENT_REVIEW_NOT_RUN`. The new publication +proof review is separate evidence and does not rewrite that status. + +## Evidence and replay + +[SOURCES.json](SOURCES.json) pins 59 additional frozen files and 14 +shared files from the main package. It retains the exact proofs, +payloads, checks, and five historical independent reviews: + +- [Rank-30 matrix and scalar review](frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md). +- [Extension matrix review](frozen/lanes/independent-review-20261017/response-extensions-review-20261020/REVIEW.md). +- [Rank-30 native review](frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md) and [extension native review](../frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md). +- [Coded-exit review](frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/REVIEW.md). + +The historical raw native review checks 1,141 native recipes and 224 +endpoint adapters with complete spatial columns. The extension review +inherits the unchanged reciprocal-large paths and checks 876 new +rank-16 phases, with 685 exact inherited recipes. The coded review +checks 352 changed exits: 48 exact inherited exits and 304 complete +spatial checks. These historical spatial replays are not repeated by +the four frozen matrix and scope checks below. + +The new [publication checker](check_native.py) uses separate rational +arithmetic from [its review helper](check_publication_review.py). It +checks all 12 raw words, 16 coded words, the exact changed output +order, and all 352 changed-exit phases with the retained exact phase +engine. It also checks the three matrix models and all 512 cross-Gram +ranks. Raw phase and endpoint inheritance remains tied to the historical +reviews. [PUBLICATION-CHECKS.json](PUBLICATION-CHECKS.json) pins the +unchanged checkers and [their accepted receipt](NATIVE-CHECKS.json). + +From the main package directory, use Python 3.10 or later: + +```sh +python3 -I -B replay_annex.py --out /tmp/reciprocal-response-annex-replay +``` + +The output directory must not exist. The runner copies the two frozen +trees into a new directory and checks every source hash. It runs the +two independent matrix checks, the cross-Gram checker, and the +paired-line checker in normal Python and with `-O`. It compares all +eight receipts byte for byte with their frozen values. It also runs +the new publication checker in both modes. For those two receipts, +it compares every field except Python version and elapsed time. The +expected final line is: + +```text +PASS_LOW_DISPLACEMENT_RESPONSE_ANNEX +``` + +[VALIDATION.json](VALIDATION.json) records the ten completed checks, +commands, source-manifest hashes, and receipt hashes. + +The main package replay remains separate. Source credits, retained +licenses, and the AI-assistance disclosure are in +[the source notice](../SOURCE-NOTICE.md). This supplement makes no +claim of independent human review. + +## Open next questions + +- Can a paid code expose and restore the rank-16 or rank-30 records + at an actual caller cut? A displacement factor alone gives no such + interface. +- Can a caller retain `W` with a complete endpoint and terminal + calculation? The coded words leave this operator present. +- Can the rank-16 inverse use an admitted odd grid, including its + selected normalization, with every conversion and precision cost? + The raw native response does not settle that task. diff --git a/research/reciprocal-native-responses/annex/SOURCES.json b/research/reciprocal-native-responses/annex/SOURCES.json new file mode 100644 index 0000000000..64adda0ad8 --- /dev/null +++ b/research/reciprocal-native-responses/annex/SOURCES.json @@ -0,0 +1,306 @@ +{ + "frozen_files": { + "lanes/coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json": { + "bytes": 341474, + "sha256": "20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701" + }, + "lanes/controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": { + "bytes": 42897, + "sha256": "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902" + }, + "lanes/independent-review-20261017/rank-thirty-review-20261020/CHECKS.json": { + 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Two publication-native comparisons omit only Python version and elapsed time. Compressed source files also have payload hashes.", + "core_manifest_sha256": "44861ce503d2268acd85ec4c202d7438f83755761772d5e715ba4abc54abd931", + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "publication_checker_manifest_sha256": "1ac981962cc5c86736361cf29afbe94b528cb9c6f6d41ced912884de9b19ca02", + "python": "3.14.7 (main, Aug 5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]", + "replay_sha256": "c703505b9ebe91c7c8d4ad84694003c68d7d1571efc3d20927f3c5a29e08ebc0", + "runs": [ + { + "check": "rank30-matrix", + "command": [ + "python3", + "-I", + "-B", + "lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py" + ], + "elapsed_seconds": 1.795, + "mode": "normal", + "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97" + }, + { + "check": "extension-matrices", + "command": [ + "python3", + "-I", + "-B", + "lanes/independent-review-20261017/response-extensions-review-20261020/check_extensions.py" + ], + "elapsed_seconds": 5.823, + "mode": "normal", + "receipt_sha256": "e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a" + }, + { + "check": "cross-gram", + "command": [ + "python3", + "-I", + "-B", + "lanes/new-core-transfer-20261017/low-displacement-20261020/check_even_clique_gram.py", + "--out", + "results/cross-gram.json" + ], + "elapsed_seconds": 0.653, + "mode": "normal", + "receipt_sha256": "1172ad3de9fd5e15d6f8056d3a774bcbdfa84d0eb55c3c3e7b711e5d49659da8" + }, + { + "check": "paired-line", + "command": [ + "python3", + "-I", + "-B", + "lanes/new-core-transfer-20261017/low-displacement-20261020/check_paired_line_scope.py", + "--out", + "results/paired-line.json" + ], + "elapsed_seconds": 0.295, + "mode": "normal", + "receipt_sha256": "f12a1e740a4ea6d7b13a99d14e26578c0fc2b17f30ce07551678d8a56487253f" + }, + { + "check": "publication-native", + "command": [ + "python3", + "-I", + "-B", + "publication-checks/check_native.py", + "--source-root", + ".", + "--out", + "results/native.json" + ], + "elapsed_seconds": 5.394, + "mathematical_receipt_sha256": "8155d13cff0d3807980a12c4106763b144e6e86f1d7fa196a7e16c781599ffd3", + "mode": "normal", + "receipt_sha256": "20335655e59f17da26956cdaa9f459b9f00e96174e62c282ce5a8a9a8b98483d" + }, + { + "check": "rank30-matrix", + "command": [ + "python3", + "-I", + "-B", + "-O", + "lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py" + ], + "elapsed_seconds": 1.513, + "mode": "optimized", + "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97" + }, + { + "check": "extension-matrices", + "command": [ + "python3", + "-I", + "-B", + "-O", + "lanes/independent-review-20261017/response-extensions-review-20261020/check_extensions.py" + ], + "elapsed_seconds": 4.999, + "mode": "optimized", + "receipt_sha256": "e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a" + }, + { + "check": "cross-gram", + "command": [ + "python3", + "-I", + "-B", + "-O", + "lanes/new-core-transfer-20261017/low-displacement-20261020/check_even_clique_gram.py", + "--out", + "results/cross-gram.json" + ], + "elapsed_seconds": 0.724, + "mode": "optimized", + "receipt_sha256": "1172ad3de9fd5e15d6f8056d3a774bcbdfa84d0eb55c3c3e7b711e5d49659da8" + }, + { + "check": "paired-line", + "command": [ + "python3", + "-I", + "-B", + "-O", + "lanes/new-core-transfer-20261017/low-displacement-20261020/check_paired_line_scope.py", + "--out", + "results/paired-line.json" + ], + "elapsed_seconds": 0.305, + "mode": "optimized", + "receipt_sha256": "f12a1e740a4ea6d7b13a99d14e26578c0fc2b17f30ce07551678d8a56487253f" + }, + { + "check": "publication-native", + "command": [ + "python3", + "-I", + "-B", + "-O", + "publication-checks/check_native.py", + "--source-root", + ".", + "--out", + "results/native.json" + ], + "elapsed_seconds": 6.875, + "mathematical_receipt_sha256": "8155d13cff0d3807980a12c4106763b144e6e86f1d7fa196a7e16c781599ffd3", + "mode": "optimized", + "receipt_sha256": "45f6079828adcd848d647b158f38a461d517a52ea7a8bba1446b4baaec10ceab" + } + ], + "scope": "Independent matrices, scalar prices, native frame ledgers, 352 changed-exit phases, exact cross-Gram ranks, and finite paired-line checks. The historical raw native spatial replays are separate.", + "shared_core_source_count": 14, + "status": "PASS_LOW_DISPLACEMENT_RESPONSE_ANNEX" +} diff --git a/research/reciprocal-native-responses/annex/check_native.py b/research/reciprocal-native-responses/annex/check_native.py new file mode 100644 index 0000000000..51df3e6644 --- /dev/null +++ b/research/reciprocal-native-responses/annex/check_native.py @@ -0,0 +1,235 @@ +#!/usr/bin/env python3 +"""Review the frozen supporting responses and changed exits.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys +import time + + +HERE = Path(__file__).resolve().parent +spec = importlib.util.spec_from_file_location("publication_arithmetic", HERE/"check_publication_review.py") +a = importlib.util.module_from_spec(spec) +spec.loader.exec_module(a) +PINS = { + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c", + "native-normal-v2/NATIVE-PROGRAM.json.gz": "aca3b3364b73e3c2115ede3082088e7566d789273711031381e44406c0ae793c", + "reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz": "825f27e5b3705dace14c75ae53aa21ea94b9dc69284bbdbd3377591fbcce7439", + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b", + "coded-normal/CODED-EXITS-PROGRAM.json.gz": "aad4decc178d7b9ac19ef4b97d3b77d56854c26714f063e1ff6fa762cf2b6b08", +} + + +def determinant(matrix): + work = [dict(row) for row in matrix] + result = F(1) + for column in range(len(work)): + pivot = next((i for i in range(column, len(work)) if work[i].get(column)), None) + if pivot is None: + return F(0) + if pivot != column: + work[column], work[pivot] = work[pivot], work[column] + result = -result + value = work[column][column] + result *= value + for i in range(column+1, len(work)): + scale = work[i].get(column, 0)/value + if scale: + for j, entry in work[column].items(): + a.put(work[i], j, -scale*entry) + return result + + +def restrict(matrix, indices): + return [{j: matrix[p][q] for j, q in enumerate(indices) if q in matrix[p]} for p in indices] + + +def expected_map(response, backward): + result = a.eye(640) + for i, row in enumerate(response): + for j, value in row.items(): + a.put(result[j if backward else 112+i], 112+i if backward else j, -value if backward else value) + return result + + +def physical_model(model, correction_rank): + e, ei = a.rows(model["response"]), a.rows(model["response_inverse"]) + a.need(a.mul(e, ei) == a.mul(ei, e) == a.eye(112), "Supporting inverse orders") + delta = a.plus(e, a.eye(112), -1) + a.need(a.rank(delta) == correction_rank, "Supporting correction rank") + if "correction_U" in model: + u, v = a.rows(model["correction_U"]), a.rows(model["correction_V"]) + a.need(a.mul(u, v) == delta and a.rank(u) == a.rank(v) == correction_rank, "Supporting correction factor") + ordinary = model["ordinary_ports"] + principal = restrict(e, ordinary) + inverse = a.rows(model["ordinary_inverse"]) + a.need(a.mul(principal, inverse) == a.mul(inverse, principal) == a.eye(104), "Ordinary inverse orders") + selected = model["selected_ports"] + l = a.rows(model["selected_block"]) + a.need(restrict(e, selected) == l and a.mul(l, l) == [{i: F(1, 2)} for i in range(8)], "Selected block") + expected_det = 2**25 if correction_rank == 30 else 35**8 + expected_ordinary = F(2**21) if correction_rank == 30 else F(7**8*31**4, 16) + a.need(determinant(e) == expected_det and determinant(principal) == expected_ordinary, "Supporting determinants") + if correction_rank == 16: + inverse_selected = a.plus([{i: F(4, 5)} for i in range(8)], l, F(1, 5)) + a.need(restrict(ei, selected) == inverse_selected, "Changed selected inverse") + denominators = Counter(value.denominator for row in inverse for value in row.values()) + a.need(denominators == {7: 512, 31: 568, 62: 640}, "Prime 31 in ordinary inverse") + a.need(a.transpose(e, 112) == e, "Rank16 symmetry") + else: + a.need(restrict(ei, selected) == l, "Rank30 inverse selected block") + return {"rank": correction_rank, "determinant": str(expected_det), "ordinary_determinant": str(expected_ordinary)} + + +def as_tuple(value): + return tuple(map(as_tuple, value)) if isinstance(value, list) else value + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--source-root", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + start = time.monotonic() + source_dir = args.source_root/"lanes/new-core-transfer-20261017/low-displacement-20261020" + for name, digest in PINS.items(): + a.need(sha256((source_dir/name).read_bytes()).hexdigest() == digest, "Supporting input " + name) + base = a.read(source_dir/"run-normal/RESPONSE-PROGRAM.json") + raw = a.read(source_dir/"native-normal-v2/NATIVE-PROGRAM.json.gz") + reciprocal = a.read(source_dir/"reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz") + odd = a.read(source_dir/"odd16-normal-v2/EXTENSION-PROGRAM.json.gz") + coded = a.read(source_dir/"coded-normal/CODED-EXITS-PROGRAM.json.gz") + reports = {"rank30": physical_model(base, 30), "reciprocal_large": physical_model(reciprocal["model"], 30), + "rank16": physical_model(odd["model"], 16)} + raw_reports = {} + for name, model, packet, scalar, profile in ( + ("rank30", base, raw, 5288, {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}), + ("reciprocal_large", reciprocal["model"], reciprocal, 5288, {1: 1036, 3: 48, 4: 55, 5: 55, 6: 9, 7: 9}), + ("rank16", odd["model"], odd, 7384, {1: 1520, 2: 64, 3: 48}), + ): + for provider, directions in packet["providers"].items(): + for direction, word in directions.items(): + expected = expected_map(a.rows(model["response"]), direction == "backward") + raw_reports[name+"/"+provider+"/"+direction] = a.word_check(word, expected, profile, scalar) + for word_name, gates in model.get("common_frame_words", {}).items(): + state, cost, _, _ = a.scalar_replay(gates, 112) + expected = a.rows(model["response_inverse"] if "inverse" in word_name else model["response"]) + if "transpose" in word_name: + expected = a.transpose(expected, 112) + a.need(state == expected and cost == 3210, "Supporting common-frame scalar code") + + model = odd["model"] + u, v, q = a.rows(model["correction_U"]), a.rows(model["correction_V"]), model["ports"] + histogram = Counter() + for character in range(512): + moved = [{j: value*(-1 if (q[p] & character).bit_count() % 2 else 1) for j, value in row.items()} for p, row in enumerate(u)] + histogram[a.rank(a.mul(v, moved))] += 1 + a.need(histogram == {0: 32, 4: 96, 8: 12, 14: 256, 16: 116}, "Independent cross-Gram rank census") + + phase_path = args.source_root/"lanes/interface-proof/verify_native_lift.py" + phase_spec = importlib.util.spec_from_file_location("supporting_phase_engine", phase_path) + phase = importlib.util.module_from_spec(phase_spec) + phase_spec.loader.exec_module(phase) + changed = {} + coded_reports = {} + raw_packets = {"rank30": raw, "rank16": odd} + a.need(base["ports"] == odd["model"]["ports"], "Same physical directions") + fourier = [["C", 1 << i, 1] for i in range(9)] + s0 = ["D", [1]+[0]*8, [1]+[0]*8] + gauge = [s0, ["C", 45, 1], s0] + profiles = { + ("rank30", "W48_I64"): {1: 988, 2: 48, 4: 55, 5: 55, 6: 9, 7: 9}, + ("rank30", "W112"): {1: 988, 2: 48, 5: 55, 6: 55, 7: 9, 8: 9}, + ("rank16", "W48_I64"): {1: 1472, 2: 112}, + ("rank16", "W112"): {1: 1408, 2: 112, 3: 64}, + } + for name, codes in coded["providers_by_response_and_code"].items(): + for code, providers in codes.items(): + for provider, directions in providers.items(): + for direction, word in directions.items(): + raw_word = raw_packets[name]["providers"][provider][direction] + coded_ports = set(range(112)) if code == "W112" else set(base["large_ports"]) + a.need(set(word["left_W_ports"]) == coded_ports and set(word["raw_output_ports"]) == set(range(112))-coded_ports, "Exact coded port set") + a.need(word["gauge_circuit"] == gauge, "Literal S_e0 C_45 S_e0 code") + a.need(word["start"] == raw_word["start"], "Unchanged input frame ids") + a.need(word["frames"][:len(raw_word["frames"])] == [{"kind": "canonical", "basis": f} for f in raw_word["frames"]], "Unchanged ordered canonical frames") + endpoints = [record for record in raw_word["endpoint_adapters"] if record["role"] == "source" or record["port"] not in coded_ports] + a.need(word["endpoint_adapters"] == endpoints, "Exact retained endpoint records") + for p in range(112): + if p in coded_ports: + for field, circuit in ((p, fourier+gauge), (112+p, [["C", base["ports"][p], -1]]+fourier+gauge)): + frame = word["frames"][word["final"][field]] + a.need(frame["kind"] == "literal" and frame["circuit"] == circuit, "Literal W F9 Q inverse output order") + else: + a.need(word["final"][p] == raw_word["final"][p] and word["final"][112+p] == raw_word["final"][112+p], "Unchanged uncoded exits") + current, census, monomials, gates = list(word["start"]), Counter(), 0, [] + a.need(len(word["events"]) == len(raw_word["events"]), "One event per original position") + for event, raw_event in zip(word["events"], raw_word["events"]): + if event[0] == "scalar": + gate, frame = event[1:] + if gate[0] == "add": + _, target, source, num, den = gate + a.need(current[source] == frame and 0 <= source < 224, "Coded source access") + else: + _, target, num, den = gate + source = None + a.need(current[target] == frame and 0 <= target < 224, "Coded target access") + gates.append([gate[0], target, source, str(F(num, den))]) + a.need(raw_event[:2] == ["scalar", gates[-1]], "Scalar operation and coefficient unchanged") + if raw_event[2] != frame: + fields = [target] if source is None else [target, source] + a.need(all(raw_event[2] == raw_word["final"][p] and frame == word["final"][p] + and p % 112 in coded_ports for p in fields), "Scalar access changes only to its completed coded output frame") + continue + field, old, new, key = event[1], event[2], event[3], event[-1] + a.need(0 <= field < 224 and current[field] == old, "Coded transformation entry") + current[field] = new + record = word["native_recipes"][key] + if event[0] == "native": + a.need(event[4] == record["rank"] > 0, "Coded native rank") + census[event[4]] += 1 + else: + a.need(event[0] == "monomial" and record["rank"] == 0, "Explicit rank-zero map") + monomials += 1 + if key.startswith("coded:"): + a.need(raw_event[0] == "native" and raw_event[1:3] == event[1:3] and raw_event[3] == raw_word["final"][field], "Only the final physical exit changes") + objects = [word["frames"][old], word["frames"][new], record] + changed[json.dumps(objects, sort_keys=True)] = objects + else: + a.need(event == raw_event and record == raw_word["native_recipes"][key], "Exact inherited native occurrence and recipe") + state, scalar, peak, height = a.scalar_replay(gates, 640) + a.need(state == expected_map(a.rows(coded["responses"][name]), direction == "backward"), "Coded 640-column content") + a.need(current == word["final"] and current[224:] == word["start"][224:], "Coded final frames and outside restoration") + a.need(census == profiles[name, code] and monomials == 48, "Coded profile and monomial count") + a.need(scalar == (5288 if name == "rank30" else 7384), "Coded scalar invoice") + a.need(len(word["endpoint_adapters"]) == (112 if code == "W112" else 176), "Coded endpoint census") + coded_reports[name+"/"+code+"/"+provider+"/"+direction] = { + "profile": dict(census), "children": sum(census.values()), "mass": sum(k*v for k, v in census.items()), + "scalar": scalar, "inline_monomials": monomials, "endpoints": len(word["endpoint_adapters"]), + "prefix_one_norm": str(peak), "binary_height": height, + } + a.need(len(changed) == 352, "Changed exit recipe count") + for old, new, record in changed.values(): + def frame(value): + return phase.frame(value["basis"], 9) if value["kind"] == "canonical" else as_tuple(value["circuit"]) + phase.equal(phase.recipe(record), phase.adjoint(frame(old))+frame(new), "Supporting changed exit") + for name, digest in PINS.items(): + a.need(sha256((source_dir/name).read_bytes()).hexdigest() == digest, "Supporting input unchanged") + result = {"status": "PASS_SUPPORTING_LOW_DISPLACEMENT_REVIEW", "python": sys.version, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), "input_sha256": PINS, + "response_models": reports, "raw_native_words": raw_reports, "cross_gram_rank_census": dict(histogram), + "coded_words": coded_reports, "changed_exit_exact_phase_checks": len(changed), + "phase_engine_sha256": sha256(phase_path.read_bytes()).hexdigest(), + "scope": "Independent rational maps, scalar prices, typed frame ledger, and 352 changed-exit phases with the existing compiler-independent engine. Inherited raw phases and physical endpoints retain the pinned predecessor reviews. No odd-grid admission or supplier replay.", + "elapsed_seconds": round(time.monotonic()-start, 3)} + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(result["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annex/check_publication_review.py b/research/reciprocal-native-responses/annex/check_publication_review.py new file mode 100644 index 0000000000..7df119e9d4 --- /dev/null +++ b/research/reciprocal-native-responses/annex/check_publication_review.py @@ -0,0 +1,366 @@ +#!/usr/bin/env python3 +"""Check the extracted response and native words with separate arithmetic.""" + +import argparse +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from functools import lru_cache +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import sys +import time + + +def need(value, label): + if not value: + raise ValueError(label) + + +def read(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == ".gz" else data) + + +def rows(value): + return [{int(j): F(v) for j, v in row.items() if F(v)} for row in value] + + +def eye(n): + return [{i: F(1)} for i in range(n)] + + +def put(row, j, v): + value = row.get(j, F(0)) + v + if value: + row[j] = value + else: + row.pop(j, None) + + +def plus(a, b, c=1): + out = deepcopy(a) + for row, extra in zip(out, b): + for j, v in extra.items(): + put(row, j, c*v) + return out + + +def mul(a, b): + out = [] + for row in a: + result = {} + for j, v in row.items(): + for k, w in b[j].items(): + put(result, k, v*w) + out.append(result) + return out + + +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 rank(a): + basis = {} + for original in a: + row = dict(original) + while row: + j = min(row) + v = row[j] + if j not in basis: + basis[j] = {k: w/v for k, w in row.items()} + break + for k, w in basis[j].items(): + put(row, k, -v*w) + return len(basis) + + +def family(n): + u = [F(1)]*(n-2) + [F(n-4), F(0)] + ell = [F(-1)]*(n-2) + [F(1), F(0)] + r = plus(eye(n), [{j: a*b for j, b in enumerate(ell) if a*b} for a in u]) + p = eye(n) + p[-2], p[-1] = p[-1], p[-2] + return mul(p, r), mul(r, p), p, r + + +def check_model(model): + generic = [] + for n in range(3, 25): + e, ei, p, r = family(n) + need(mul(e, ei) == mul(ei, e) == eye(n), "Family inverse orders") + need(all(i not in a[i] for a in (e, ei) for i in range(n)), "Family zero diagonals") + need(rank(plus(e, eye(n), -1)) == 2, "Family correction rank") + if n >= 5: + metric = [{i: F(1) if i < n-2 else F(-1, n-4)} for i in range(n)] + need(mul(transpose(e, n), mul(metric, e)) == metric, "Family metric identity") + equations = [] + for i in range(n): + for j in range(i, n): + row = {k: e[k].get(i, 0)*e[k].get(j, 0) for k in range(n)} + if i == j: + put(row, i, -1) + equations.append({k: v for k, v in row.items() if v}) + need(rank(equations) == n-1, "One-dimensional invariant diagonal metric space") + generic.append(n) + + h, hi = eye(112), eye(112) + for pair in model["pair_codes"]: + a, b = pair["ports"] + local = [[F(x) for x in row] for row in pair["matrix"]] + for i, target in enumerate((a, b)): + h[target] = {origin: local[i][j] for j, origin in enumerate((a, b)) if local[i][j]} + hi[target] = {origin: local[j][i]/2 for j, origin in enumerate((a, b)) if local[j][i]} + need(mul(h, hi) == eye(112), "Pair inverse from pair records") + need(h == rows(model["pair_code"]) and hi == rows(model["pair_code_inverse"]), "Serialized pair code") + mode = {name: eye(112) for name in ("E", "inverse_E", "P", "R", "J")} + sizes = Counter() + for block in model["blocks"]: + ports = block["ports"] + n = len(ports) + sizes[n] += 1 + matrices = family(n) + ([{i: F(1) if i < n-2 else F(-1, n-4)} for i in range(n)],) + for name, matrix in zip(mode, matrices): + for i, p in enumerate(ports): + mode[name][p] = {ports[j]: v for j, v in matrix[i].items()} + need(sizes == {6: 8, 8: 8}, "Actual block census") + physical = {name: mul(hi, mul(matrix, h)) for name, matrix in mode.items()} + for name, value in physical.items(): + need(value == rows(model["physical"][name]), "Independent physical reconstruction " + name) + e, ei, p, r, j = (physical[name] for name in mode) + need(mul(e, ei) == mul(ei, e) == eye(112), "Physical inverse orders") + need(mul(p, r) == e and mul(p, p) == mul(r, r) == eye(112), "Physical factors") + need(rank(plus(e, p, -1)) == 16 and rank(plus(e, eye(112), -1)) == 32, "Physical displacement ranks") + need(all(i not in a[i] for a in (e, ei) for i in range(112)), "Physical zero diagonals") + need(mul(transpose(e, 112), mul(j, e)) == j, "Physical metric after pair normalization") + need(Counter(j[i][i] for i in range(112)) == {F(1): 80, F(-1, 2): 16, F(-1, 4): 16}, "Metric weights") + need(sum(map(len, p)) == 160 and any(len(row) > 1 for row in p), "P is not a permutation") + u, ell = rows(model["reflection_U"]), rows(model["reflection_L"]) + ji = [{i: 1/j[i][i]} for i in range(112)] + need(mul(u, ell) == plus(r, eye(112), -1), "Reflection rank factor") + need(mul(ell, mul(ji, transpose(ell, 112))) == [{i: F(4 if i < 8 else 2)} for i in range(16)], "Centre Gram normalization") + for name, word in model["scalar_words"].items(): + state, cost, _, _ = scalar_replay(word, 640) + wanted = rows(model["physical"][name]) if name in model["physical"] else transpose(ei, 112) + need(state[:112] == wanted and state[112:] == eye(640)[112:], "Common-frame map and restoration " + name) + expected = {"P": 728, "R": 2892, "metric_inverse_adjoint_E": 3628}.get(name, 3308) + need(cost == expected, "Common-frame price " + name) + return {"family_dimensions": generic, "invariant_diagonal_space_dimensions": list(range(5, 25)), + "actual_blocks": dict(sizes), "rank_E_minus_P": 16, "rank_E_minus_I": 32, + "physical_P_nonzeros": 160, "physical_Gram": [4]*8 + [2]*8} + + +def tariff(gate): + op, _, _, raw = gate + c = F(raw) + a, b = abs(c.numerator), c.denominator + need(a > 0 and b & (b-1) == 0, "Dyadic coefficient") + if op == "scale": + need(a & (a-1) == 0, "Unit scale") + return 2*(abs(a.bit_length()-b.bit_length()) + (c < 0)) + need(op == "add", "Scalar grammar") + return 2*(1+a.bit_length()+a.bit_count()+b.bit_length()) + + +def scalar_replay(gates, n): + state, cost, peak, height = eye(n), 0, F(1), 0 + for gate in gates: + op, target, origin, raw = gate + c = F(raw) + if op == "add": + need(target != origin, "Distinct fields") + for j, v in state[origin].items(): + put(state[target], j, c*v) + else: + need(op == "scale" and origin is None, "Scale grammar") + state[target] = {j: c*v for j, v in state[target].items() if c*v} + cost += tariff(gate) + peak = max(peak, sum(map(abs, state[target].values()), F(0))) + for v in state[target].values(): + need(v.denominator & (v.denominator-1) == 0, "Dyadic prefix") + height = max(height, v.denominator.bit_length()-1) + return state, cost, peak, height + + +@lru_cache(None) +def span(vectors): + values = {0} + for v in vectors: + values |= {x ^ v for x in values} + return frozenset(values) + + +def word_check(word, expected, profile, scalar): + current = list(word["start"]) + progress, census, gates = Counter(), Counter(), [] + for event in word["events"]: + if event[0] == "native": + _, field, old, new, dimension, key = event + need(0 <= field < 224 and current[field] == old, "Native entry") + need(span(tuple(word["frames"][old])) < span(tuple(word["frames"][new])), "Strict nested advance") + need(dimension == len(word["frames"][new])-len(word["frames"][old]) == word["native_recipes"][key]["rank"], "Native rank") + need(key == str(old)+":"+str(new), "Ordered recipe") + current[field] = new + progress[field] += dimension + census[dimension] += 1 + else: + need(event[0] == "scalar", "Event grammar") + _, gate, frame = event + _, target, origin, _ = gate + need(0 <= target < 224 and current[target] == frame, "Scalar target access") + if origin is not None: + need(0 <= origin < 224 and current[origin] == frame, "Scalar source access") + gates.append(gate) + need(current == word["final"] and census == profile, "Final frames and native census") + need(all(progress[p] == 8 for p in range(224)), "Data advance mass") + state, cost, peak, height = scalar_replay(gates, 640) + need(state == expected, "All 640 arbitrary columns") + need(state[224:] == eye(640)[224:] and current[224:] == word["start"][224:], "Outside values and frames restored") + need(cost == scalar, "Native scalar price") + return {"scalar_real": cost, "prefix_one_norm": str(peak), "binary_height": height, + "native_profile": dict(census), "native_mass": sum(k*v for k, v in census.items()), + "native_children": sum(census.values()), "columns": 640, "outside_fields": 416} + + +def field_projection(word, combine): + projected = [[] for _ in range(224)] + scalar_index = 0 + for index, event in enumerate(word["events"]): + if event[0] == "native": + _, field, old, new, dimension, _ = event + seq = projected[field] + if combine and seq and seq[-1][0] == "native": + need(seq[-1][2] == old, "Original chain joins") + seq[-1][2] = new + seq[-1][3] += dimension + seq[-1][4].append(index) + else: + seq.append(["native", old, new, dimension, [index]]) + else: + for field in (event[1][1], event[1][2]): + if field is not None: + projected[field].append(["scalar", scalar_index]) + scalar_index += 1 + return projected + + +def coalescing_check(original, result): + old_scalars = [e for e in original["events"] if e[0] == "scalar"] + new_scalars = [e for e in result["events"] if e[0] == "scalar"] + need(old_scalars == new_scalars, "Every scalar gate and its global order") + old, new = field_projection(original, True), field_projection(result, False) + chains = {row["event"]: row for row in result["coalesced_native_chains"]} + need(len(chains) == sum(e[0] == "native" for e in result["events"]), "One chain record per new native event") + for field, (a, b) in enumerate(zip(old, new)): + need(len(a) == len(b), "Same per-field scalar barriers") + for source, target in zip(a, b): + if source[0] == "scalar": + need(source == target, "Same scalar use cut") + continue + need(source[:4] == target[:4], "Same total frame map between scalar uses") + chain = chains[target[4][0]] + need(chain["source_events"] == source[4], "Independent source-event chain") + need((chain["field"], chain["old"], chain["new"], chain["rank"]) == (field, *source[1:4]), "Chain metadata") + for key in ("frames", "start", "final", "endpoint_adapters"): + need(original[key] == result[key], "Same physical boundary " + key) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--package", type=Path, required=True) + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + start = time.monotonic() + package = args.package.resolve() + frozen = package / "frozen" + manifest = read(package / "SOURCES.json") + for name, entry in manifest["frozen_files"].items(): + need(sha256((frozen/name).read_bytes()).hexdigest() == entry["sha256"], "Frozen input pin " + name) + directory = frozen / "lanes/oblique-native-20261017/signed-metric-reciprocal-20261020" + original = read(directory / "native-normal/NATIVE.json.gz") + coalesced = read(directory / "coalesced-normal/NATIVE.json.gz") + model = read(directory / "model-normal-v2/RESPONSE.json.gz") + need(original["model"] == coalesced["model"] == model, "Same model in all payloads") + model_report = check_model(model) + word_reports = {} + for provider in ("base", "extra"): + for name, old in original["providers"][provider].items(): + response = rows(model["physical"]["E" if name in ("forward_E", "backward_transpose_E") else "inverse_adjoint_E"]) + expected = eye(640) + for i, row in enumerate(response): + for j, value in row.items(): + put(expected[j if name.startswith("backward") else 112+i], 112+i if name.startswith("backward") else j, + -value if name.startswith("backward") else value) + scalar = 7080 if name.endswith("by_metric") else 6440 + old_report = word_check(old, expected, {1: 1520, 2: 64, 3: 48}, scalar) + new = coalesced["providers"][provider][name] + new_report = word_check(new, expected, {1: 971, 2: 237, 3: 46, 4: 12, 5: 5, 6: 11, 7: 10}, scalar) + coalescing_check(old, new) + need((old_report["prefix_one_norm"], old_report["binary_height"]) == + (new_report["prefix_one_norm"], new_report["binary_height"]), "Unchanged prefix bounds") + word_reports[provider+"/"+name] = {"original": old_report, "coalesced": new_report} + + phase_path = frozen / "lanes/interface-proof/verify_native_lift.py" + spec = importlib.util.spec_from_file_location("frozen_exact_phase", phase_path) + phase = importlib.util.module_from_spec(spec) + spec.loader.exec_module(phase) + first = coalesced["providers"]["base"]["forward_E"] + inherited = original["providers"]["base"]["forward_E"]["native_recipes"] + fresh = [] + for key, record in first["native_recipes"].items(): + if key in inherited: + need(record == inherited[key], "Inherited phase record") + continue + a, b = map(int, key.split(":")) + actual = phase.recipe(record) + target = phase.adjoint(phase.frame(first["frames"][a], 9)) + phase.frame(first["frames"][b], 9) + phase.equal(actual, target, "Fresh recipe " + key) + fresh.append(key) + need(len(fresh) == 206, "Fresh phase census") + for provider in coalesced["providers"].values(): + for word in provider.values(): + need(word["native_recipes"] == first["native_recipes"], "All words use the checked recipes") + + bad = deepcopy(first["native_recipes"][fresh[0]]) + bad["left"]["phase"] = (bad["left"]["phase"]+1) % 4 + a, b = map(int, fresh[0].split(":")) + try: + phase.equal(phase.recipe(bad), phase.adjoint(phase.frame(first["frames"][a], 9)) + phase.frame(first["frames"][b], 9), "Changed phase") + except ValueError: + phase_rejected = True + else: + raise ValueError("Changed phase accepted") + bad = deepcopy(first) + scalar_event = next(e for e in bad["events"] if e[0] == "scalar") + scalar_event[2] = (scalar_event[2]+1) % len(bad["frames"]) + try: + coalescing_check(original["providers"]["base"]["forward_E"], bad) + except ValueError: + scalar_rejected = True + else: + raise ValueError("Changed scalar cut accepted") + + for name, entry in manifest["frozen_files"].items(): + need(sha256((frozen/name).read_bytes()).hexdigest() == entry["sha256"], "Input unchanged " + name) + result = {"status": "PASS_INDEPENDENT_PUBLICATION_REVIEW", "python": sys.version, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_manifest_sha256": sha256((package/"SOURCES.json").read_bytes()).hexdigest(), + "model": model_report, "words": word_reports, "fresh_phase_checks": len(fresh), + "phase_engine_sha256": sha256(phase_path.read_bytes()).hexdigest(), + "phase_engine_scope": "Reused pinned compiler-independent exact Pauli and reference-column engine. No producer interpreter was imported.", + "negative_controls": {"changed_global_phase_rejected": phase_rejected, "changed_scalar_cut_rejected": scalar_rejected}, + "frozen_inputs_unchanged": len(manifest["frozen_files"]), "elapsed_seconds": round(time.monotonic()-start, 3)} + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n") + print(result["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json b/research/reciprocal-native-responses/annex/frozen/lanes/coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json new file mode 100644 index 0000000000..b28691cbe6 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json @@ -0,0 +1,22959 @@ +{ + "W": { + "circuit": [ + [ + "D", + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + ], + [ + "C", + 45, + 1 + ], + [ + "D", + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + ] + ], + "native_recipe": { + "left": { + "linear_Z4": [ + 3, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 3, + 4, + 9, + 17, + 32, + 1, + 64, + 128, + 256 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + }, + "rank": 1, + "right": { + "linear_Z4": [ + 1, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 1, + 33, + 2, + 36, + 40, + 16, + 64, + 128, + 256 + ], + "offset": 1, + "phase": 1, + "quadratic_rows": [ + 33, + 0, + 0, + 0, + 0, + 1, + 0, + 0, + 0 + ] + } + } + }, + "a": 45, + "alignments": { + "W_Z_inverse": { + "circuit": [ + [ + "D", + [ + 12, + 0, + 1, + 1, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 13, + 2, + 8, + 4, + 16, + 44, + 64, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "record": { + "linear_Z4": [ + 2, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 13, + 2, + 8, + 4, + 16, + 44, + 64, + 128, + 256 + ], + "offset": 0, + "phase": 0, + "quadratic_rows": [ + 12, + 0, + 1, + 1, + 0, + 0, + 0, + 0, + 0 + ] + } + }, + "Z_inverse_W": { + "circuit": [ + [ + "D", + [ + 12, + 0, + 1, + 1, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 13, + 2, + 8, + 4, + 16, + 44, + 64, + 128, + 256 + ] + ], + [ + "X", + 45 + ], + [ + "phase", + 0 + ] + ], + "record": { + "linear_Z4": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + "matrix_rows": [ + 13, + 2, + 8, + 4, + 16, + 44, + 64, + 128, + 256 + ], + "offset": 45, + "phase": 0, + "quadratic_rows": [ + 12, + 0, + 1, + 1, + 0, + 0, + 0, + 0, + 0 + ] + } + } + }, + "b": 1, + "canonical_Z": [ + [ + "D", + [ + 32, + 0, + 32, + 32, + 0, + 45, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 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Native phases and routed terminal are separate.", + "source_pins": { + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + }, + "status": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE", + "word_checks": { + "E": { + "columns": 112, + "prefix_row_norm": "44", + "scalar": 3210 + }, + "inverse_E": { + "columns": 112, + "prefix_row_norm": "44", + "scalar": 3210 + }, + "inverse_transpose_E": { + "columns": 112, + "prefix_row_norm": "14", + "scalar": 3210 + }, + "transpose_E": { + "columns": 112, + "prefix_row_norm": "14", + "scalar": 3210 + } + } +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json new file mode 100644 index 0000000000..a60bd1ddf8 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "CHECKS.json": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97", + "REPRODUCTION.json": "6f67d5ce7a2b8c3764da8134a85464cac5805c1086eed309632f01e74b4491c7", + "REVIEW.md": "e16a0cd145879805481391e9273301d89a88a6b4731ec5efe0e3cf67a38380d8", + "check_review.py": "118088a1b6d7126d50fb4c05a59fc7f69d792a8c0530ddb066d17434c3d9fff2" + }, + "scope": "Native phases, routed terminal, and full supplier price are separate.", + "status": "PASS_INDEPENDENT_MATRIX_SCALAR_AND_GEOMETRY" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..5e36b7c6ba --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REPRODUCTION.json @@ -0,0 +1,15 @@ +{ + "runs": [ + { + "mode": "normal", + "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97", + "stdout": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE\nreceipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97\n" + }, + { + "mode": "optimized", + "receipt_sha256": "898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97", + "stdout": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE\nreceipt_sha256=898cbd6b6a1cc6c5bd3aa8dba6ae078c6336f797ba2238a35ea95175593bee97\n" + } + ], + "status": "PASS_BYTE_IDENTICAL" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md new file mode 100644 index 0000000000..335ceedf21 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/REVIEW.md @@ -0,0 +1,158 @@ +# Independent review of the full rank-thirty response + +The frozen matrix and scalar-code packet passes. It gives an exact +dyadic unit on all 112 ports, with correction rank 30. Both its response +and its inverse retain the specified selected eight-port block. The +ordinary 104-port block has an exact dyadic inverse. All four supplied +common-frame scalar words have the stated map and price. + +No material finding remains in this scope. This review does not certify +the separate native packet, helper progress, a routed cut, a terminal, +or a complete supplier cost. + +## Response and selected interface + +The response on 48 ports is the signed pair conjugate of eight copies +of the root's integer six-mode unit. At each vertex the two modes that +meet selected physical ports occupy the first two a positions. The +sign diagonal gives their two off-diagonal coefficients -alpha_v. +The response and its inverse have the same a-to-a block. These facts +preserve the old selected block in both physical matrices. + +The independent checker derives each vertex assignment from the +pinned mode support and the original selected set. It then acts on +physical basis columns in this order: + +```text +signed pair code, +selected sign diagonal, +rank-one reflection and final coordinate exchange, +selected sign diagonal, +inverse pair code. +``` + +For the inverse it reverses the reflection and exchange. It does not +import the producer or use the producer's matrix to define this action. +All 112 columns in each direction agree with the frozen matrices, +including the disjoint small-port response. Both full inverse orders +are the identity. + +The selected block L is the old block, and L^-1 is the old inverse. +Both multiplication orders are checked. For the ordinary block H, +write the full inverse as + +```text +E^-1 = [[L,N],[P,Q]]. +``` + +The block inverse identity gives H^-1=Q-P L^-1 N. The supplied ordinary +inverse passes both multiplication orders on all 104 columns; every +coefficient is dyadic. The exact determinants are + +```text +det(L)=1/16, det(H)=2^21, det(E)=2^25. +``` + +They also satisfy Jacobi's principal-minor identity +det(H)=det(E) det((E^-1)_SS). No Schur-complement determinant has been +substituted for the ordinary determinant. + +The supplied U and V have ranks 30 and satisfy E-I=UV on every physical +column. The two disjoint parts contribute ranks 16 and 14. Since U is +injective and V is onto its 30-dimensional output, this proves that +the correction rank is exactly 30. + +## The small-port cover and its restricted optimum + +The fourteen cliques partition the 64 small ports. Eleven have size +five and three have size three. The checker verifies each pairwise +binary inner product from the actual q labels. + +On a clique of size k, I-J has eigenvalue 1-k on the constant vector +and eigenvalue one on its complement. Therefore its inverse is +I-J/(k-1), its determinant is 1-k, and its correction rank is one. +For k=3 and k=5 these are dyadic units. The complete small determinant +is (-4)^11(-2)^3=2^25. + +There is a short structural proof that the actual support has no +nine-clique. Every small q satisfies q dot q=1 and q dot z=1 for z=45. +The vector z is nonzero and isotropic. Nine pairwise orthogonal odd +vectors in the nine-dimensional binary space would be an orthonormal +basis. Expanding z in that basis would give z=sum(q_i), and hence +z dot z=1. This contradicts z dot z=0. + +As a separate finite check, this review enumerates all cliques by +increasing vertex extension. This differs from the producer's +pivoted maximal-clique method. It finds exactly the same maximal +cliques: 896 of size four and 64 of size eight. It also compares every +maximal clique, not just the two counts. + +The fourteen-block optimum is valid within the stated disjoint +dyadic rank-one clique model. More generally, if a k by k zero-diagonal +block has rank(A-I)=1, write A=I+u*v. The diagonal equations imply +v*u=-k, so det(A)=1-k. Dyadic invertibility requires k-1 to be a power +of two. The clique-size bound leaves k=2,3,5. Twelve blocks cover at +most sixty ports. Thirteen size-five blocks would cover sixty-five; +replacing a size-five block by size three or two reduces the total by +two or three, and cannot give sixty-four. Fourteen is therefore +necessary and the supplied cover attains it. + +This argument does not apply to an odd-denominator representation, +overlapping blocks, a correction of higher rank within a block, or a +different native encoding. It is not a lower bound for the required +computation. + +## Literal scalar words + +The review executes every supplied gate on each of the 112 independent +input columns. Every input is arbitrary. All target and source indices +are data fields; no initial zero, borrowed helper, or owned scratch is +used. It checks E, E^-1, E^T, and E^-T separately. + +For a signed six-mode block, the in-place reflection code has twelve +unit additions and one negation. The final exchange has three unit +additions and one negation. This costs 124 real scalar primitives per +vertex. The eight blocks cost 992. The physical pair code and inverse +cost 940, so the 48-port scalar code costs 1932. + +For a clique of size k, the three groups of k-1 unit additions and +one scale by -(k-1) implement I-J. Their costs are 102 for k=5 and +52 for k=3. Thus the small code costs 1278 and each full word costs +1932+1278=3210. Reversing or transposing the word preserves this +invoice under the stated tariff. + +The independent column replay also accumulates the absolute row sums +at every changed row. The maximum prefix row norms are 44 for E and +E^-1, and 14 for E^T and E^-T. These bounds concern the scalar code +alone. They do not bound a recursive child's internal state. + +The four words are valid at a common frame. This phrase is a binding +premise. It does not provide access to fields in different hole frames, +or make an accumulated controller chart free to change. + +## Reproduction + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py +``` + +The expected status is `PASS_INDEPENDENT_RANK_THIRTY_RESPONSE`. +The two receipts must be byte-identical. The checker authenticates +the producer proof, checker, payload, receipt, freeze, and the two +underlying input payloads. It does not run or import producer code. +It uses exact integers and fractions. + +The new-core-transfer lane supplied the full response, clique cover, +scalar words, and their producer checks. The root supplied the +reciprocal six-mode construction. The actual pair coordinates and +selected block come from the pinned cyclic and matching packets. +This lane supplied the distinct column replay, clique enumeration, +and the isotropic proof of the clique-size bound. OpenAI Codex +assisted this work. + +No PR, push, or publication is authorized. Before any PR description, +read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py new file mode 100644 index 0000000000..8d27eb2ff8 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/rank-thirty-review-20261020/check_review.py @@ -0,0 +1,233 @@ +#!/usr/bin/env python3 +"""Check the full response with independent columns and clique extension.""" + +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / "new-core-transfer-20261017/low-displacement-20261020" +PINS = { + "RESPONSE-FREEZE.json": "59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9", + "RESPONSE.md": "5ea5866231992c389ae2796f1534e0af90ca88bcedfa3fa9758d78f9457d2981", + "check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c", + "run-normal/RESPONSE-CHECKS.json": "7f84440d79200b8c060aad07b910bb96f2bcdde95b07ddb8d41bcea1fcb09d5c", +} + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def unit(n, j): + return [F(i == j) for i in range(n)] + + +def sparse(rows): + return [{int(k): F(v) for k, v in row.items()} for row in rows] + + +def apply(rows, x): + return [sum((v * x[j] for j, v in row.items()), F(0)) for row in rows] + + +def eliminate(rows, width): + a = [dict(row) for row in rows] + pivot, det = 0, F(1) + for j in range(width): + p = next((i for i in range(pivot, len(a)) if a[i].get(j)), None) + if p is None: + continue + if p != pivot: + a[p], a[pivot] = a[pivot], a[p] + det = -det + value = a[pivot][j] + det *= value + for i in range(pivot + 1, len(a)): + value_i = a[i].get(j, F(0)) / value + if not value_i: + continue + for k, c in a[pivot].items(): + new = a[i].get(k, F(0)) - value_i * c + if new: + a[i][k] = new + else: + a[i].pop(k, None) + pivot += 1 + if pivot == len(a): + break + return pivot, det if pivot == width == len(a) else None + + +def restrict(rows, ports): + return [{j: rows[p][q] for j, q in enumerate(ports) if q in rows[p]} for p in ports] + + +def main(): + for name, digest in PINS.items(): + need(sha256((SOURCE / name).read_bytes()).hexdigest() == digest, "Producer pin") + packet = json.loads((SOURCE / "run-normal/RESPONSE-PROGRAM.json").read_text()) + inputs = {} + for name, digest in packet["source_pins"].items(): + raw = (LANES / name).read_bytes() + need(sha256(raw).hexdigest() == digest, "Inherited source pin") + inputs[Path(name).name] = json.loads(raw) + cyclic = inputs["CYCLIC-FLAGS.json"] + matching = inputs["MATCHED-INVOLUTION-PROGRAM.json"] + selected = matching["selected_ports"] + need(packet["selected_ports"] == selected, "Original selected set") + need(packet["ports"] == cyclic["ports"], "Actual binary directions") + assignments = [] + for v, c in enumerate(cyclic["cyclic_carriers"]): + chosen = [p for p in c if set(map(int, cyclic["mode_rows"][str(p)])) & set(selected)] + need(len(chosen) == 2, "Selected mode count") + assignments.append({"vertex": v, "ordered_carriers_a_b_c": + chosen + [p for p in c if p not in chosen], + "signs": [1, (-1) ** v, 1, 1, 1, 1]}) + need(assignments == packet["vertex_assignments"], "Selected-mode assignment") + + def pair(x, inverse=False): + out = list(x) + for entry in cyclic["pair_codes"]: + ps, h = entry["ports"], entry["matrix"] + for i, p in enumerate(ps): + out[p] = sum((F(h[j][i], 2) if inverse else F(h[i][j])) * x[ps[j]] + for j in range(2)) + return out + + def formula(x, inverse=False, wrong_sign=False): + coded, result = pair(x), list(x) + mixed = list(coded) + for entry in assignments: + ps, d = entry["ordered_carriers_a_b_c"], list(entry["signs"]) + if wrong_sign: + d[1] = 1 + values = [coded[p] * sign for p, sign in zip(ps, d)] + if inverse: + values[-2], values[-1] = values[-1], values[-2] + query = values[-2] - sum(values[:4]) + values = [a + query for a in values[:4]] + [values[-2] + 2 * query, values[-1]] + if not inverse: + values[-2], values[-1] = values[-1], values[-2] + for p, sign, value in zip(ps, d, values): + mixed[p] = sign * value + result = pair(mixed, True) + for c in packet["small_cliques"]: + total = sum(x[p] for p in c) / (len(c) - 1 if inverse else 1) + for p in c: + result[p] = x[p] - total + return result + + e, ei = sparse(packet["response"]), sparse(packet["response_inverse"]) + columns, inverse_columns = [], [] + for j in range(112): + x = unit(112, j) + a, b = formula(x), formula(x, True) + need(a == apply(e, x) and b == apply(ei, x), "Independent response columns") + need(formula(a, True) == formula(b) == x, "Full inverse orders") + columns.append(a) + inverse_columns.append(b) + need(any(formula(unit(112, p), wrong_sign=True) != formula(unit(112, p)) for p in selected), + "Reject omitted selected sign") + old_l = sparse(matching["selected_block"]) + li = sparse(packet["selected_inverse"]) + need(restrict(e, selected) == restrict(ei, selected) == old_l, "Both selected blocks") + need(all(apply(old_l, apply(li, unit(8, j))) == apply(li, apply(old_l, unit(8, j))) == unit(8, j) + for j in range(8)), "Selected inverse orders") + ordinary = sorted(set(range(112)) - set(selected)) + need(ordinary == packet["ordinary_ports"], "Ordinary partition") + h, hi = restrict(e, ordinary), sparse(packet["ordinary_inverse"]) + need(all(c.denominator & (c.denominator - 1) == 0 for row in hi for c in row.values()), + "Dyadic ordinary inverse") + need(all(apply(h, apply(hi, unit(104, j))) == apply(hi, apply(h, unit(104, j))) == unit(104, j) + for j in range(104)), "Ordinary inverse orders") + need(eliminate(old_l, 8)[1] == F(1, 16), "Selected determinant") + need(eliminate(e, 112)[1] == 2 ** 25, "Full determinant") + need(eliminate(h, 104)[1] == 2 ** 21, "Ordinary determinant") + u, v = sparse(packet["correction_U"]), sparse(packet["correction_V"]) + need(eliminate(u, 30)[0] == eliminate(v, 112)[0] == 30, "Factor ranks") + for j in range(112): + x = unit(112, j) + need(apply(u, apply(v, x)) == [a - b for a, b in zip(columns[j], x)], "Correction factor") + + word_receipts = {} + for name, gates in packet["common_frame_words"].items(): + expected = inverse_columns if "inverse" in name else columns + if "transpose" in name: + expected = [list(row) for row in zip(*expected)] + prefix_norms = [F(0)] * len(gates) + price = 0 + parsed = [] + for kind, target, origin, text in gates: + c = F(text) + need(0 <= target < 112 and c != 0, "Literal field and coefficient") + need(c.denominator & (c.denominator - 1) == 0, "Dyadic gate") + a, b = abs(c.numerator), c.denominator + if kind == "add": + need(isinstance(origin, int) and 0 <= origin < 112 and origin != target, + "Arbitrary-input addition") + price += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + else: + need(kind == "scale" and origin is None and a & (a - 1) == 0, "Unit scale") + price += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) + parsed.append((kind, target, origin, c)) + for j in range(112): + x = unit(112, j) + for k, (kind, target, origin, c) in enumerate(parsed): + x[target] = x[target] * c if kind == "scale" else x[target] + c * x[origin] + prefix_norms[k] += abs(x[target]) + need(x == expected[j], "Literal word column " + name) + norm = max([F(1)] + prefix_norms) + need(price == 3210 and norm == (14 if "transpose" in name else 44), "Scalar invoice") + word_receipts[name] = {"columns": 112, "scalar": price, "prefix_row_norm": str(norm)} + + small, q = packet["small_ports"], packet["ports"] + need(sorted(p for c in packet["small_cliques"] for p in c) == small, "Disjoint small cover") + need(Counter(map(len, packet["small_cliques"])) == {3: 3, 5: 11}, "Clique cover sizes") + need(all((q[p] & q[r]).bit_count() % 2 == (p == r) + for c in packet["small_cliques"] for p in c for r in c), "Actual clique cover") + need(all(q[p].bit_count() % 2 == (q[p] & 45).bit_count() % 2 == 1 for p in small) + and (45).bit_count() % 2 == 0, "Affine isotropic obstruction to size nine") + adjacent = [{r for r in small if r != p and (q[p] & q[r]).bit_count() % 2 == 0} + for p in range(112)] + maxima, visited = [], Counter() + + def extend(chosen, options, common): + visited[len(chosen)] += 1 + if not common: + maxima.append(tuple(chosen)) + for i, p in enumerate(options): + extend(chosen + [p], [r for r in options[i + 1:] if r in adjacent[p]], + common & adjacent[p]) + + extend([], small, set(small)) + need(Counter(map(len, maxima)) == {4: 896, 8: 64}, "Separate maximal clique census") + need(sorted(maxima) == sorted(tuple(sorted(c)) for c in packet["maximal_small_cliques"]), + "Every reported maximal clique") + need(max(visited) == 8, "Maximum clique dimension") + receipt = { + "status": "PASS_INDEPENDENT_RANK_THIRTY_RESPONSE", + "producer_pins": PINS, + "source_pins": packet["source_pins"], + "response_columns_per_direction": 112, + "correction_rank": 30, + "determinants": {"selected": "1/16", "ordinary": str(2 ** 21), "full": str(2 ** 25)}, + "word_checks": word_receipts, + "all_clique_sizes": dict(sorted(visited.items())), + "maximal_clique_sizes": dict(sorted(Counter(map(len, maxima)).items())), + "scope": "Matrix, scalar words, and actual graph. Native phases and routed terminal are separate.", + } + raw = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (HERE / "CHECKS.json").write_bytes(raw) + print(receipt["status"]) + print("receipt_sha256=" + sha256(raw).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/CHECKS.json b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/CHECKS.json new file mode 100644 index 0000000000..c45523bab9 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/CHECKS.json @@ -0,0 +1,71 @@ +{ + "payload_decompressed_pins": { + "odd16-normal-v2": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "reciprocal-normal-v2": "e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416" + }, + "reports": { + "odd-grid-rank16": { + "columns_per_direction": 112, + "correction_rank": 16, + "full_determinant": "2251875390625", + "inverse_denominators": { + "5": 48, + "7": 512, + "10": 960 + }, + "ordinary_determinant": "5323914784321/16", + "ordinary_inverse_denominators": { + "7": 512, + "31": 568, + "62": 640 + }, + "scalar_words": {} + }, + "reciprocal-large": { + "columns_per_direction": 112, + "correction_rank": 30, + "full_determinant": "33554432", + "inverse_denominators": { + "1": 128, + "2": 603, + "4": 275 + }, + "ordinary_determinant": "2097152", + "ordinary_inverse_denominators": { + "1": 280, + "2": 427, + "4": 275 + }, + "scalar_words": { + "E": { + "columns": 112, + "prefix_row_norm": "20", + "scalar": 3210 + }, + "inverse_E": { + "columns": 112, + "prefix_row_norm": "14", + "scalar": 3210 + }, + "inverse_transpose_E": { + "columns": 112, + "prefix_row_norm": "44", + "scalar": 3210 + }, + "transpose_E": { + "columns": 112, + "prefix_row_norm": "44", + "scalar": 3210 + } + } + } + }, + "scope": "Exact matrices and reciprocal-large scalar words. Native phases and odd-grid implementation are separate.", + "source_pins": { + "EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689", + "EXTENSIONS.md": "2328ec60c1cf89efe7661b3696839f8eb32a95e11c67a62dd653781a8b0ed5fb", + "emit_followthrough.py": "b03568530696ab810070ba3243b59dd74740fb634fe7f26b2cbdb1d3283d045f", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c" + }, + "status": "PASS_INDEPENDENT_RESPONSE_EXTENSIONS" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/FREEZE.json new file mode 100644 index 0000000000..cf7e6ad7d9 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "CHECKS.json": "e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a", + "REPRODUCTION.json": "39c6300f307be4edf100a0ad53ca163f6d28ca0f01f51fce65ab5b200c09b731", + "REVIEW.md": "ab9192c4e9a6cec5a864189bd24a4f208a9242c55c5a6a329b4f4e3e25edb8b7", + "check_extensions.py": "97e6c35e916b3cc6b4512e82b554ca33189fe91c89d00a269cf83719f61a073c" + }, + "scope": "Native words, odd-grid implementation, and complete supplier price are separate.", + "status": "PASS_EXTENSION_MATRICES_AND_PRINCIPAL_INVERSES" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/REPRODUCTION.json b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..f64ad3939f --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/REPRODUCTION.json @@ -0,0 +1,15 @@ +{ + "runs": [ + { + "mode": "normal", + "receipt_sha256": "e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a", + "stdout": "PASS_INDEPENDENT_RESPONSE_EXTENSIONS\nreceipt_sha256=e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a\n" + }, + { + "mode": "optimized", + "receipt_sha256": "e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a", + "stdout": "PASS_INDEPENDENT_RESPONSE_EXTENSIONS\nreceipt_sha256=e2660de3472640fb41c673761df58f251f720f988bec4e2fab6b3871b4d29a3a\n" + } + ], + "status": "PASS_BYTE_IDENTICAL" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/REVIEW.md b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/REVIEW.md new file mode 100644 index 0000000000..3ada35cc45 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/REVIEW.md @@ -0,0 +1,168 @@ +# Independent review of the reciprocal and rank-sixteen matrices + +Both final v2 extension models pass the matrix review. The reciprocal +extension gives the stated inverse response on the large 48-port +sector. The odd-grid extension gives an integer native response whose +full correction rank is 16 and whose exact inverse uses primes five +and seven. The selected ordinary normalization requires prime 31. + +This review covers exact response algebra, actual clique geometry, +principal inverses, and the reciprocal extension's four scalar words. +The native phase and frame review is separate. The retained odd-grid +contract and a complete inverse-code implementation are also separate. +Earlier draft extension directories are not inputs to this review. + +## Reciprocal large sector + +Let E48 be the previously reviewed large response and C be the +fourteen-clique small response. The new response is + +```text +A = E48^-T direct_sum C, +A^-1 = E48^T direct_sum C^-1. +``` + +The independent checker derives these actions from the pinned base +matrices. All 112 columns of each action equal the final extension +payload. Both full inverse orders pass. The raw backward convention +uses -A^T, so its large response is -E48^-1 as claimed. + +This is reciprocal native access on the large sector only. The small +response remains C in the raw backward map, whereas C^-1 has nonzero +diagonal and is not the small response emitted by these paths. + +Both selected principal blocks remain L. The ordinary inverse passes +both 104-column multiplication orders. The full and ordinary +determinants remain 2^25 and 2^21. The full correction rank remains 30. + +The four literal common-frame scalar words are checked on all 112 +columns each. Their instructions use arbitrary data fields only and +legal dyadic coefficients. Each costs 3210 real scalar primitives. +The receipt also gives the separately computed prefix row norms. +This scalar check does not establish access to a common frame in a +routed call. + +## Rank sixteen from actual signed queries and eight-cliques + +The checker constructs eight physical rows K directly from the pinned +pair-code rows and the selected-compatible vertex signs. Every row +has twelve signed unit entries. It verifies + +```text +K K^T = 12 I. +``` + +On the large sector the two independently evaluated actions are + +```text +E48 x = x-K^T Kx/2, +E48^-1 x = x-K^T Kx/10. +``` + +The inverse formula follows from +(K^T K)^2=12 K^T K. Each row direction has eigenvalue -5 under E48; +the complementary directions have eigenvalue one. Thus the large +determinant is 5^8 and its correction rank is eight. + +The checker also verifies the actual partition of all 64 small ports +into eight orthonormal eight-cliques. On each clique the response is +I-J and its inverse is I-J/7. Each contributes determinant -7 and +one correction coordinate. The full response is symmetric, has +determinant 35^8, and has correction rank 16. + +These formulas are evaluated on every physical basis column and +compared with the final matrices. Both full inverse orders pass. +The supplied U,V factors satisfy E-I=UV on all 112 columns; each +factor has rank 16. + +## Which restriction is relaxed + +The rank-two theorem requires both the native response and its +inverse to have zero diagonal. It holds over every field of +characteristic zero, including the rationals. Odd denominators +alone do not remove that restriction. + +In the rank-sixteen extension, the six-mode response is I-dd^T and +its inverse is I-dd^T/5. The inverse has diagonal 4/5. The construction +therefore uses the inverse as a later scalar code, rather than as +another zero-diagonal response in the cyclic native family. + +Its intended opportunity depends on both changes: the general +raw-backward controller must permit this use of scalar inverse codes, +and the retained representation must admit their odd denominators. +The local matrix packet does not prove either complete global duty. +It does not contradict the reviewed reciprocal rank-two minimum or +the disjoint dyadic clique bound. + +## The selected split introduces 31 + +The selected block of E is still L, with L²=I/2. Restricting the +large inverse gives + +```text +(E^-1)_SS = (4I+L)/5, +((E^-1)_SS)^-1 = 10(4I-L)/31. +``` + +Both orders of this eight-dimensional inverse are checked. The +identity uses +(4I+L)(4I-L)=16I-L²=(31/2)I. + +Jacobi's identity now gives + +```text +det(E_UU) = det(E) det((E^-1)_SS) + = 7^8 * 31^4 / 16. +``` + +The supplied ordinary inverse passes both multiplication orders on +all 104 columns and has precisely these reduced denominators: + +| Denominator | Nonzero entries | +| ---: | ---: | +| 7 | 512 | +| 31 | 568 | +| 62 | 640 | + +Prime five cancels in this ordinary inverse. Prime 31 is present, +not just a possible denominator in a formula. By comparison, the +full E^-1 uses denominators 5, 7, and 10 only. + +A grid contract that includes only primes five and seven can cover +the full inverse code, subject to its other obligations. It does not +cover this selected ordinary normalization. An interface with empty +selection can avoid that extra principal-inverse operation. It must +still prove and price its actual controller and terminal. + +## Verification and inherited limits + +The checker imports only matrix helpers from this lane's pinned +independent base review. It imports no producer or native compiler. +It authenticates the final extension proof, emitter, freeze, and both +decompressed payloads. It also authenticates the underlying base +matrix and geometry. + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/response-extensions-review-20261020/check_extensions.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/response-extensions-review-20261020/check_extensions.py +``` + +The expected status is `PASS_INDEPENDENT_RESPONSE_EXTENSIONS`. +The receipts must be byte-identical. + +This review does not check the native event streams, their borrowed +state, exact phases, frame adapters, or recursive child invoices. +Those belong to the separate native review. It also does not price +division by five, seven, or 31, prove root-stream conversion, or give +an odd-denominator height bound. The native-escape grid packet owns +those representation duties. No completed supplier or exponent +improvement follows from this matrix review alone. + +The new-core-transfer lane supplied the two extension models. The +root and earlier pair-code work supplied the underlying responses. +This lane supplied the independent matrix and principal-inverse +checks. OpenAI Codex assisted the work. No PR or publication is +authorized. Before any PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/check_extensions.py b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/check_extensions.py new file mode 100644 index 0000000000..9ba3a98e14 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/independent-review-20261017/response-extensions-review-20261020/check_extensions.py @@ -0,0 +1,192 @@ +#!/usr/bin/env python3 +"""Check the changed matrices and principal inverses without native replay.""" + +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / "new-core-transfer-20261017/low-displacement-20261020" +REVIEW = HERE.parent / "rank-thirty-review-20261020/check_review.py" +PINS = { + "EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689", + "EXTENSIONS.md": "2328ec60c1cf89efe7661b3696839f8eb32a95e11c67a62dd653781a8b0ed5fb", + "emit_followthrough.py": "b03568530696ab810070ba3243b59dd74740fb634fe7f26b2cbdb1d3283d045f", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c", +} +PAYLOADS = { + "reciprocal-normal-v2": "e4df61bf4e121364ba53538eb2ad612bd314807cfb2050050d4595efce9cf416", + "odd16-normal-v2": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", +} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def main(): + need(sha256(REVIEW.read_bytes()).hexdigest() == + "118088a1b6d7126d50fb4c05a59fc7f69d792a8c0530ddb066d17434c3d9fff2", + "Independent base-review helper pin") + spec = importlib.util.spec_from_file_location("independent_rank_thirty", REVIEW) + helper = importlib.util.module_from_spec(spec) + spec.loader.exec_module(helper) + apply, rows, unit = helper.apply, helper.sparse, helper.unit + for name, digest in PINS.items(): + need(sha256((SOURCE / name).read_bytes()).hexdigest() == digest, "Source pin") + old = json.loads((SOURCE / "run-normal/RESPONSE-PROGRAM.json").read_text()) + for name, digest in old["source_pins"].items(): + raw = (LANES / name).read_bytes() + need(sha256(raw).hexdigest() == digest, "Geometry pin") + if "CYCLIC" in name: + cyclic = json.loads(raw) + old_e, old_ei = rows(old["response"]), rows(old["response_inverse"]) + large, small, selected = old["large_ports"], old["small_ports"], old["selected_ports"] + ordinary = old["ordinary_ports"] + l, li = rows(old["selected_block"]), rows(old["selected_inverse"]) + k_rows = [] + for entry in old["vertex_assignments"]: + k = {} + for p, sign in zip(entry["ordered_carriers_a_b_c"], entry["signs"]): + for q, coefficient in cyclic["mode_rows"][str(p)].items(): + k[int(q)] = k.get(int(q), F(0)) + sign * F(coefficient) + k_rows.append({p: c for p, c in k.items() if c}) + need(all(len(k) == 12 and set(k.values()) <= {-1, 1} for k in k_rows), + "Eight signed twelve-port queries") + need([[sum(c * other.get(p, 0) for p, c in k.items()) for other in k_rows] + for k in k_rows] == [[12 * (i == j) for j in range(8)] for i in range(8)], + "Exact K Gram matrix") + reports = {} + for folder, digest in PAYLOADS.items(): + raw = gzip.decompress((SOURCE / folder / "EXTENSION-PROGRAM.json.gz").read_bytes()) + need(sha256(raw).hexdigest() == digest, "Final extension payload") + packet = json.loads(raw) + model = packet["model"] + odd = packet["kind"] == "odd-grid-rank16" + e, ei = rows(model["response"]), rows(model["response_inverse"]) + need(model["selected_ports"] == selected and model["ordinary_ports"] == ordinary, + "Unchanged principal partition") + + def formula(x, inverse=False): + if not odd: + out = apply(old_ei if inverse else old_e, x) + source = old_e if inverse else old_ei + for p in large: + out[p] = sum(source[q].get(p, F(0)) * x[q] for q in large) + return out + values = apply(k_rows, x) + out = list(x) + for p in large: + out[p] -= sum(k.get(p, 0) * v for k, v in zip(k_rows, values)) / (10 if inverse else 2) + for group in model["small_cliques"]: + total = sum(x[p] for p in group) / (7 if inverse else 1) + for p in group: + out[p] = x[p] - total + return out + + columns, inverse_columns = [], [] + for j in range(112): + x = unit(112, j) + a, b = formula(x), formula(x, True) + need(a == apply(e, x) and b == apply(ei, x), "Independent extension column") + need(formula(a, True) == formula(b) == x, "Two extension inverse orders") + columns.append(a) + inverse_columns.append(b) + need(helper.restrict(e, selected) == l, "Original selected block") + inverse_l = helper.restrict(ei, selected) + wanted = [{j: (4 * (i == j) + l[i].get(j, 0)) / F(5) + for j in range(8) if i == j or j in l[i]} for i in range(8)] if odd else l + need(inverse_l == wanted == rows(model["selected_inverse_block"]), "Inverse selected block") + p_inverse = [{j: F(10, 31) * (4 * (i == j) - l[i].get(j, 0)) + for j in range(8) if i == j or j in l[i]} for i in range(8)] if odd else li + need(all(apply(inverse_l, apply(p_inverse, unit(8, j))) == + apply(p_inverse, apply(inverse_l, unit(8, j))) == unit(8, j) for j in range(8)), + "Inverse selected principal inverse") + h, hi = helper.restrict(e, ordinary), rows(model["ordinary_inverse"]) + need(all(apply(h, apply(hi, unit(104, j))) == + apply(hi, apply(h, unit(104, j))) == unit(104, j) for j in range(104)), + "Two ordinary inverse orders") + full_det = 35 ** 8 if odd else 2 ** 25 + ordinary_det = F(7 ** 8 * 31 ** 4, 16) if odd else F(2 ** 21) + need(helper.eliminate(e, 112)[1] == full_det == F(model["full_determinant"]), + "Full determinant") + need(helper.eliminate(h, 104)[1] == ordinary_det == F(model["ordinary_determinant"]), + "Ordinary determinant") + correction = [{q: c - (p == q) for q, c in row.items()} for p, row in enumerate(e)] + for p, row in enumerate(correction): + if p not in e[p]: + row[p] = F(-1) + correction[p] = {q: c for q, c in row.items() if c} + need(helper.eliminate(correction, 112)[0] == (16 if odd else 30), "Correction rank") + code_reports = {} + if odd: + need(sorted(p for c in model["small_cliques"] for p in c) == small and + len(model["small_cliques"]) == 8 and all(len(c) == 8 for c in model["small_cliques"]), + "Eight-clique partition") + need(all((model["ports"][p] & model["ports"][q]).bit_count() % 2 == (p == q) + for c in model["small_cliques"] for p in c for q in c), "Actual eight-cliques") + u, v = rows(model["correction_U"]), rows(model["correction_V"]) + need(helper.eliminate(u, 16)[0] == helper.eliminate(v, 112)[0] == 16, "Rank16 factors") + need(all(apply(u, apply(v, unit(112, j))) == + [c - (i == j) for i, c in enumerate(columns[j])] for j in range(112)), "UV factor") + need(all(columns[j][i] == columns[i][j] and + inverse_columns[j][i] == inverse_columns[i][j] for i in range(112) for j in range(112)), + "Symmetric response and inverse") + need("common_frame_words" not in model, "No unverified odd scalar word") + need(any(c.denominator % 31 == 0 for row in hi for c in row.values()), "Prime31 is present") + else: + for name, word in model["common_frame_words"].items(): + expect = inverse_columns if "inverse" in name else columns + if "transpose" in name: + expect = [list(r) for r in zip(*expect)] + norm_sums, tariff = [F(0)] * len(word), 0 + for op, target, origin, text in word: + c = F(text) + a, b = abs(c.numerator), c.denominator + need(0 <= target < 112 and a != 0 and b & (b - 1) == 0, "Data-only dyadic word") + need((op == "scale" and origin is None and a & (a - 1) == 0) or + (op == "add" and isinstance(origin, int) and + 0 <= origin < 112 and origin != target), "Literal scalar grammar") + tariff += (2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) if op == "scale" + else 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length())) + for j in range(112): + x = unit(112, j) + for t, (op, target, origin, text) in enumerate(word): + c = F(text) + x[target] = c * x[target] if op == "scale" else x[target] + c * x[origin] + norm_sums[t] += abs(x[target]) + need(x == expect[j], "Reciprocal literal scalar word") + need(tariff == 3210, "Reciprocal scalar invoice") + code_reports[name] = {"columns": 112, "scalar": tariff, + "prefix_row_norm": str(max([F(1)] + norm_sums))} + reports[packet["kind"]] = { + "columns_per_direction": 112, + "correction_rank": 16 if odd else 30, + "full_determinant": str(full_det), + "ordinary_determinant": str(ordinary_det), + "inverse_denominators": dict(sorted(Counter(c.denominator for row in ei for c in row.values()).items())), + "ordinary_inverse_denominators": dict(sorted(Counter(c.denominator for row in hi for c in row.values()).items())), + "scalar_words": code_reports, + } + receipt = { + "status": "PASS_INDEPENDENT_RESPONSE_EXTENSIONS", + "source_pins": PINS, + "payload_decompressed_pins": PAYLOADS, + "reports": reports, + "scope": "Exact matrices and reciprocal-large scalar words. Native phases and odd-grid implementation are separate.", + } + output = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (HERE / "CHECKS.json").write_bytes(output) + print(receipt["status"]) + print("receipt_sha256=" + sha256(output).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..c6c54dc3bdef3d7bf56c36885a45b98cdeb1e74c GIT binary patch literal 583358 zcmZU&18^i@+a(&?=ESy*iEZ09Cbn(cwrxyoI}>waXOsE9fA`+qRM%VS>U1ZS_dG`r zUIYZd_ZQITLf2$94VM+^1FcIZn%qkYx1wkq0Usbdg47Z#{0|PD3>V?4FtrJD3eSQgxg7 zyXzSjTwGXt&t7>><4(&b^n5mypRYf?vN}A~8TVA1&%fSU&kn6^wQjdK55!2nI9tD< z<)|FYpX;_Ne=cyX*c zm+CPyH=EjSS?n3j)i0PfQE$#dAumo&+5BV7=Jrg*(Ziwvo3!kkeB>Lv_H2DfhXty? 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"1860726ae7a210bc7ed8c4afc93cdf251bad8a7d90fd8b353157752434c2c4c8", + "EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689", + "NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24", + "coded-normal/CODED-EXITS-CHECKS.json": "b36bee542add54bac48e409c6a4a054b3bca5fba9c98d5513a90a6a92628d576", + "coded-normal/CODED-EXITS-PROGRAM.json.gz": "aad4decc178d7b9ac19ef4b97d3b77d56854c26714f063e1ff6fa762cf2b6b08", + "emit_coded_exits.py": "3d6c9283a2217306bae8f998891439e5cff435a7b3d7575c9481c115f411a282" + }, + "normal_optimized_byte_identical": true, + "scope": "Exact changed output contracts; independent review and complete supplier duties remain separate.", + "status": "PASS_CHANGED_NATIVE_EXITS" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS.md new file mode 100644 index 0000000000..7ea08ea65b --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS.md @@ -0,0 +1,115 @@ +# Exact output codes for both low-displacement responses + +The native exits of both new responses admit the previous common +left output code W. The uniform output code no longer requires +rank-nine children. For the rank-sixteen response, its maximum child +rank is three. This is a local representation result. It does not +remove W or prove a complete supplier. + +Let + +```text +W = S_e0 C_45 S_e0 +``` + +be the literal circuit in the pinned isotropic-pair-gauge packet. +The new emitter uses the frozen exit compiler and its exact physical +phase checks. It applies that compiler to the new words' actual +ordered source bases. + +Two output representations are emitted: + +* W48_I64 applies W to both data banks on the 48 paired ports. +* W112 applies W to both data banks on all 112 data ports. + +At a coded port p, the exact physical output is + +```text +X_p = W F9 x'_p, +Y_p = W F9 Q_p^-1 y'_p. +``` + +At an uncoded port, omit the initial W. The input convention remains +X=Qx, Y=y. The response itself does not change. In particular, there +is no commutation of W with Q and no free re-interpretation as a raw +endpoint. + +## Actual exit replacement + +For each coded source with last canonical frame Gamma_U, the final +edge is the exact operator W F9 Gamma_U^-1. All such sources share +the same W F9 frame. The inverse physical pair code remains legal. + +For each coded target with last frame Gamma_V, the new intrinsic +exit is W F9 Q_p^-1 Gamma_V^-1. The old external target adapter is +removed. A rank-zero intrinsic exit is an explicit monomial event; +it is not omitted. + +The new six-mode paths reach rank six before the source exit. +The exact coded source exit has rank two, in place of rank three. +The 48 pair-mode target exits become monomial. These calculations +use the actual source bases and phase maps; the result is not +inferred from a mass subtraction. + +The small-clique exits depend on the clique size. In the +rank-sixteen word they start from rank-seven flags. Under the +uniform W output, the source exits have rank three and the target +exits rank two. The earlier matching word started its small sources +on lines and required rank-nine exits under the same W output. +The new flags therefore resolve that specific native-rank issue. +Recursive hosting remains a separate obligation. + +## Complete local invoices + +Every row below applies to both providers and both directions. +The scalar operation sequence is unchanged. + +| Response and output code | Native profile | Children | Mass | Real scalar primitives | +| --- | --- | ---: | ---: | ---: | +| Rank30, W48_I64 | 988 H1 + 48 H2 + 55 H4 + 55 H5 + 9 H6 + 9 H7 | 1164 | 1696 | 5288 | +| Rank30, W112 | 988 H1 + 48 H2 + 55 H5 + 55 H6 + 9 H7 + 9 H8 | 1164 | 1824 | 5288 | +| Rank16, W48_I64 | 1472 H1 + 112 H2 | 1584 | 1696 | 7384 | +| Rank16, W112 | 1408 H1 + 112 H2 + 64 H3 | 1584 | 1824 | 7384 | + +Each word has 48 inline monomial exits. W48_I64 retains 176 external +endpoint adapters; W112 retains 112. There are at most two side maps +per native child, in addition to the listed inline monomial and +external endpoint maps. These maps are not claimed to be free. + +All 640 input columns remain independent. The 416 other fields keep +their original values and frames. There is no owned or private +workspace. The forward and backward scalar prefix bounds remain +46 and 30 for rank thirty, and 22 in both directions for rank sixteen. + +## Verification and use + +The source event schema is converted exactly to the frozen exit +compiler's rational scalar schema. The converted raw word is +replayed before any exit changes. Each output word is then checked +on all 640 columns, including every equal-frame scalar access and +every exact native or monomial source frame. The serialized packet +is read back and replayed again. + +Every changed physical exit receives a fresh compiler lowering and +an independent Pauli and exact Gaussian-state comparison. The old +native phases remain pinned. The source pair-code metadata comes +from the exact cyclic-family payload. + +Run emit_coded_exits.py with --out naming a new directory. Repeat +with optimized Python and a different new output directory. The +expected status is PASS_LOW_DISPLACEMENT_CODED_EXITS. Both payloads +and receipts must be byte-identical. + +The W48_I64 mass saving is useful only if the caller can consume the +mixed representation. The uniform W112 representation has a larger +mass but a uniform exterior code. Neither word proves a free stage +transition, a free terminal inverse, helper progress, or the final +recursive cost. The complete controller must retain the stated +ordered physical outputs. + +The coherent-port and root lanes supplied W. The oblique-native +lane supplied the exact exit compiler and its previous matching +application. This packet binds that construction to the new cyclic +paths and proves the resulting profiles. AI assistance was used. +No PR or publication is authorized. Before any future description, +read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EVEN-CLIQUE-GRAM.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EVEN-CLIQUE-GRAM.md new file mode 100644 index 0000000000..c73f55fa5e --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EVEN-CLIQUE-GRAM.md @@ -0,0 +1,130 @@ +# Cross-Gram obstruction for the rank-sixteen response + +The current rank-sixteen response admits a complete native data word. +This note tests a different obligation: inversion of the cross-Gram +matrix used by the proposed centre section-swap code. + +Let E-I=UV be the exact factorization in the frozen rank-sixteen +payload. The matrices U and V have sizes 112 by 16 and 16 by 112. +Both have rank 16. Let Q be the diagonal matrix of the physical line +operators. Then Q_p squared is translation by the actual binary +direction q_p. The cross-Gram matrix is + +```text +T = V Q^2 U. +``` + +On the character indexed by w in F2^9, it is the rational matrix + +```text +T(w) = V diag((-1)^(q_p dot w)) U. +``` + +The exact ranks of these 512 matrices are: + +| Rank | Number of characters | +| --- | ---: | +| 0 | 32 | +| 4 | 96 | +| 8 | 12 | +| 14 | 256 | +| 16 | 116 | + +Thus T is not an invertible operator on the full spatial field. +This rules out a section-swap construction that requires T inverse +for this response and this complete spatial domain. It does not +rule out the response, its retained-grid inverse, or a different +terminal construction. + +## The eight small clique coordinates + +For each of the eight disjoint small cliques C_j, the query row is +the indicator of C_j. The scatter column is its negative. No other +query or scatter uses these ports. Therefore these eight coordinates +are separate one-dimensional blocks of T(w), with entries + +```text +t_j(w) = -sum_{p in C_j} (-1)^(q_p dot w). +``` + +Each actual clique contains eight orthonormal directions. They are +linearly independent. The map from w to its eight dot products is +therefore onto F2^8, with two preimages for each output. A zero sum +requires four negative signs. It occurs on + +```text +2 * binomial(8,4) = 140 +``` + +of the 512 characters for each clique. This argument applies to any +orthonormal eight-clique in this nine-axis space. + +In the actual partition, all eight zero sets are equal. The checker +tests this additional source-specific fact on all 512 characters. +Its complete zero-mask distribution is 372 copies of mask 0 and +140 copies of mask 255. On those 140 characters, the full cross-Gram +has rank 0, 4, or 8, with counts 32, 96, and 12. + +Each clique sums to z=45. This vector is isotropic, and every clique +direction has dot product one with z. On a zero character, +the product of the eight signs is positive. Thus every small-block +zero is in the positive-z sector. In the negative-z sector all +eight small blocks are nonzero, but the full cross-Gram has rank 14 +on all 256 characters. The exact checker evaluates the large block +as well; it does not infer this latter rank from the small blocks. + +For example, w=2 gives signs + +```text +(-1,-1,+1,+1,+1,+1,-1,-1) +``` + +on the first clique, whose ports are +`[1,5,19,54,64,73,82,83]`. Its cross-Gram entry is zero. + +## Changing the factor basis does not remove the obstruction + +Let E-I=U'V' be another factorization through 16 scalar coordinates, +with both factors of full rank. The image of U and the image of U' +are both the image of E-I. There is an invertible 16 by 16 matrix M +with U'=UM. Since U is injective, V'=M inverse V. Consequently, + +```text +V' Q^2 U' = M^-1 (V Q^2 U) M. +``` + +The ranks in the table do not depend on the choice of minimal +scalar factors. + +More coordinates do not make this particular cross-Gram invertible. +If E-I=AB factors through r coordinates and B Q^2 A is invertible, +then A is injective and B is onto. Hence rank(AB)=r. Since E-I has +rank 16, necessarily r=16. An extension that changes the encoded +operation or adds a separate data response is outside this argument. + +## Exact evidence and scope + +The source is `odd16-normal-v2/EXTENSION-PROGRAM.json.gz`, with +decompressed SHA256 +`d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4`. +`EXTENSIONS-FREEZE.json` pins the native producer. The separate +extension matrix review checks E-I=UV and the complete inverse. + +`check_even_clique_gram.py` checks the source hash, both factor ranks, +the actual clique cover, all orthogonality and support claims, all +512 zero masks, and all 512 complete rational matrix ranks. It uses +exact fractions and explicit checks that remain active under +optimized Python. The two final receipts are +`gram-v2-normal.json` and `gram-v2-optimized.json`; they are +byte-identical. The earlier two receipts are retained as draft +small-block checks. + +This note supplies no centre formation or capture operation. The +native words have 112 productive fields in each data bank and 416 +unchanged auxiliary fields. They do not expose a separate 16-field +or 30-field productive centre cohort. + +The response uses the root's low-displacement proposal, the actual +clique partition in the native extension, and the proposed section +code from the root and coherent-port lane. AI assistance was used. +No complete supplier bound or publication claim is made. diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json new file mode 100644 index 0000000000..61c4e93cc1 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS-FREEZE.json @@ -0,0 +1,14 @@ +{ + "files": { + "EXTENSIONS.md": "2328ec60c1cf89efe7661b3696839f8eb32a95e11c67a62dd653781a8b0ed5fb", + "NATIVE-FREEZE.json": "efdf8acc943934e83374f986a4a9a6f49ab7607a4f4e8d2973ec71cd5e1c5e24", + "emit_followthrough.py": "b03568530696ab810070ba3243b59dd74740fb634fe7f26b2cbdb1d3283d045f", + "odd16-normal-v2/EXTENSION-CHECKS.json": "a502af8c80df714e4d06012bedba0433f977a402c1093e210c0cb28cb4044197", + "odd16-normal-v2/EXTENSION-PROGRAM.json.gz": "7160a8764f0b12131e30dd1ca90a28b781b9dd99e8eb2f1935b8592aaf48037b", + "reciprocal-normal-v2/EXTENSION-CHECKS.json": "cfea59ca775a7350c2e9bcded1c52f2f19df12465f6d8736fd2a907599839adc", + "reciprocal-normal-v2/EXTENSION-PROGRAM.json.gz": "825f27e5b3705dace14c75ae53aa21ea94b9dc69284bbdbd3377591fbcce7439" + }, + "normal_optimized_byte_identical": true, + "scope": "Independent native review, odd-grid admission and the global supplier remain separate.", + "status": "PASS_RECIPROCAL_LARGE_AND_ODD_GRID_NATIVE" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md new file mode 100644 index 0000000000..af1bd759d0 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/EXTENSIONS.md @@ -0,0 +1,190 @@ +# Reciprocal and odd-grid extensions + +These are two separate extensions of the frozen native paths. +The first realizes the reciprocal response on the 48 paired ports. +The second lowers the full correction rank from thirty to sixteen +by permitting odd denominators in later scalar inverse codes. +The original rank-thirty packets remain unchanged. + +## A native reciprocal response on the large sector + +Replace the six-mode matrix B by B^-T on the 48 paired ports. +Both matrices have zero diagonal, so every new nonzero coefficient +has its own existing cyclic transfer event. Keep the small +fourteen-clique response C. + +The new complete response is + +```text +A = E48^-T direct_sum C. +``` + +The raw backward native call therefore gives + +```text +x <- x - (E48^-1 direct_sum C) y. +``` + +This proves native reciprocal access on the large sector. It does +not prove a reciprocal response on all 112 ports, because C^-1 has +nonzero diagonal and is not emitted by the small-clique paths. + +Every native frame, edge, recipe, and endpoint adapter is identical +to the frozen rank-thirty path. Only scalar coefficients and their +nonzero event positions change. The full response, its inverse, all +640 input columns in both directions, and all four common-frame +scalar codes are checked. Every scalar code costs 3210. The native +invoice remains 5288 real scalar primitives and + +```text +1036 H1 + 48 H3 + 55 H4 + 55 H5 + 9 H6 + 9 H7. +``` + +The original selected block L and the ordinary principal unit are +preserved. The forward prefix row one-norm is 30; the backward +bound is 46. The proof uses the 1141 frozen native phase records +and 224 frozen endpoint records, with exact binary-frame matching. + +## Sixteen correction coordinates with odd-grid inverses + +The actual small-port orthogonality graph has a disjoint partition +into eight eight-cliques. The literal partition is in the payload. +The checker verifies every pairwise orthogonality equation and the +complete disjoint cover. + +At each large vertex use + +```text +B_v = I6-d_v d_v^T, +B_v^-1 = I6-d_v d_v^T/5, +``` + +where d_v is the same sign vector used for the selected-compatible +rank-two block. Conjugate by the actual physical pair code H. +The physical large response has eight correction coordinates. +Equivalently, let K contain the eight signed twelve-port rows +d_v^T H. Then + +```text +K K^T = 12 I8, +E48 = I48-K^T K/2, +E48^-1 = I48-K^T K/10. +``` + +On each small eight-clique use + +```text +C8 = I8-J8, +C8^-1 = I8-J8/7. +``` + +Each clique contributes one correction coordinate. The full +response E is symmetric, has determinant 35^8, and satisfies +rank(E-I)=16. The payload contains exact factors U,V with +E-I=UV and ranks sixteen. Both full inverse products are checked. + +The selected block of E remains the previous L. However, the +selected block of E^-1 is (4I+L)/5. Therefore + +```text +det(E_U,U) = 7^8 * 31^4 / 16, +((E^-1)_S,S)^-1 = 10(4I-L)/31. +``` + +The payload includes the new ordinary inverse and checks both of +its 104-column inverse products. This exposes the factor 31 needed +by the selected ordinary normalization. A controller with no +selected split can avoid that additional principal-inverse +requirement. It still needs its own complete code and terminal +construction. + +The inverse coefficients 1/5 and 1/7 are not ordinary dyadic unit +scales. Their exact implementation needs the retained odd-grid +contract, conversion of all relevant root streams including +borrowed streams, a bound on odd denominator height, complete +native-child endpoint closure, and exact final conversion. Those +obligations belong to the separate odd-grid packet. This native +packet neither prices those divisions as free nor assumes them to +be forbidden. + +## Literal native implementation and invoice + +All native transfer coefficients in the rank-sixteen word are signed +integers of absolute value one. The large sector uses the frozen +six-mode cyclic paths, with all 240 off-diagonal coefficients. +Its pair-code cost is 1880 and its transfer cost is 1920. + +For each eight-clique, use the same cyclic line-flag construction as +in NATIVE.md, now with depths one through seven. The source and +target flags are equal at each transfer and remain nested. A source +finishes with rank two after its rank-seven flag. A target finishes +with rank one in its own rank-eight hole. + +Each small port contributes fourteen H1 children and one H2 child. +The complete local word has the following invoice in either +direction: + +| Quantity | Count | +| --- | ---: | +| Rank-one children | 1520 | +| Rank-two children | 64 | +| Rank-three children | 48 | +| All native children | 1632 | +| Native mass | 1792 | +| Real scalar primitives | 7384 | +| Endpoint adapters | 224 | +| Native side-map upper bound | 3264 | + +The small transfer cost is 448 unit ADDs, or 3584 real primitives. +The complete scalar count is 1880+1920+3584=7384. This is the +native word's scalar count only. + +The phase table contains 685 entries inherited by exact frame-pair +identity and 876 new entries. Each new entry is compiled and checked +with the independent Pauli and exact Gaussian-state interpreter. +The 224 endpoint adapters are unchanged. Both providers have the +same actual data directions and receive the complete checked word. + +Every output is replayed on all 640 independent input columns. +The 416 other fields remain arbitrary and unchanged. No owned or +private field is used. The complete prefix row one-norm is at most +22 in either direction. Every native child still has a Gaussian +dyadic endpoint. This last statement does not replace the global +odd-grid precision proof. + +The exact physical conventions remain X=Qx at entry and +(F9 x', F9 Q^-1 y') at exit. No changed-exit W48/I64 histogram is +claimed in this packet. No source response is moved through Q. + +## Reproduction and scope + +Run emit_followthrough.py with --kind reciprocal-large or +--kind odd-grid-rank16, and --out naming a new directory. Repeat +with optimized Python and a different new directory. The expected +statuses are PASS_RECIPROCAL_LARGE and PASS_ODD_GRID_RANK16. +The final v2 outputs must be byte-identical between the two modes. + +The earlier extension directories are retained as drafts. Their +scalar/native maps passed, but their copied matrix metadata included +an old ordinary inverse. The final emitter constructs a new model +from only valid shared geometry, computes the new inverse, and +checks both inverse products. Only the v2 outputs are frozen. + +The rank-sixteen extension changes the allowed representation. It +does not contradict a dyadic-only obstruction. Its native child +distribution also differs from the rank-thirty and matching words; +mass alone is not a recursive price comparison. + +The generic current-cut controller still leaves the ordered code +E2 E1^-T E0 and the physical conjugation Q(...)Q^-1. Native local +correctness does not supply access to that code's queries or +scatters. Helper progress, recursive hosting, the complete precision +bound, terminal removal, and the final supplier bound remain open. + +The root identified odd-grid admission as the relevant escape. The +native-escape lane is responsible for that contract. The root's +reciprocal matrix, the independent-review cyclic flag family, and +the earlier pair-code and common-frame scalar constructions are +the other predecessors. 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/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/GRAM-OBSTRUCTION-FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/GRAM-OBSTRUCTION-FREEZE.json new file mode 100644 index 0000000000..7aa8cee128 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/GRAM-OBSTRUCTION-FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "EVEN-CLIQUE-GRAM.md": "de9d44d1c722702c99a2b382065688ca52420b732fe4b4522b7a278021b9e127", + "EXTENSIONS-FREEZE.json": "aec99dd0638e635619b14ffd056ab2581424d765d435462aed94b8c8f882a689", + "check_even_clique_gram.py": "19f2c008b561b6aaf913b02bf369619df689f24b57bb9336f6e6e764156b3433", + "gram-v2-normal.json": "1172ad3de9fd5e15d6f8056d3a774bcbdfa84d0eb55c3c3e7b711e5d49659da8" + }, + "normal_optimized_byte_identical": true, + "scope": "The exact current rank16 response cannot use an everywhere invertible cross-Gram of factors of E-I. Other encoding mechanisms remain open.", + "status": "PASS_RANK16_CROSS_GRAM_OBSTRUCTION" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json new file mode 100644 index 0000000000..26466669a7 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE-FREEZE.json @@ -0,0 +1,12 @@ +{ + "files": { + "NATIVE.md": "6c6d0cd1d93f270f16765183b8512a81a533b0bb5a2712506d677e27bbfa74d5", + "RESPONSE-FREEZE.json": "59e43eb802114070aa40b39a7e355b3271a744b713a32c5a3e09c2e46ec7fdc9", + "emit_native.py": "599987ddfe2fdb8fd4be533d783e24bf40a95b6c69118ec1552a10b06f1d5745", + "native-normal-v2/NATIVE-CHECKS.json": "8acc084b5cd1d9513fdd3373eede998bd08e7f3fe1624f9fd41f758d4de7cb82", + "native-normal-v2/NATIVE-PROGRAM.json.gz": "aca3b3364b73e3c2115ede3082088e7566d789273711031381e44406c0ae793c" + }, + "normal_optimized_byte_identical": true, + "scope": "Independent producer review and global supplier duties remain separate.", + "status": "PASS_NATIVE_DATA_RESPONSE_AND_PHASES" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE.md new file mode 100644 index 0000000000..f547931fc9 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/NATIVE.md @@ -0,0 +1,149 @@ +# Native realization of the rank-thirty response + +The literal native word implements the full response E from +RESPONSE.md in both directions: + +```text +F(x,y,h) = (x, y+E x, h), +B(x,y,h) = (x-E^T y, y, h). +``` + +The physical input convention is X=Qx and Y=y. The physical output +convention is X=F9 x' and Y=F9 Q^-1 y'. All 640 input columns are +independent. The 416 fields outside the two data banks remain +unchanged. No owned field or private field is used. This is a local +data service; it does not supply productive progress for those other +fields. + +The exact local invoice, in either direction, is + +| Quantity | Count | +| --- | ---: | +| Rank-one children | 1036 | +| Rank-three children | 48 | +| Rank-four children | 55 | +| Rank-five children | 55 | +| Rank-six children | 9 | +| Rank-seven children | 9 | +| All native children | 1212 | +| Native mass | 1792 | +| Real scalar primitives | 5288 | +| Endpoint adapters | 224 | +| Native side-map upper bound | 2424 | + +The implementation checks 1141 distinct native edges and 224 endpoint +adapters with the independent Pauli and exact Gaussian-state +interpreter. These checks include global phase. They are separate +from the scalar-column replay. + +## The large 48-port word + +The pinned cyclic family supplies the exact paths and the +parameterized scalar events. At each of eight vertices there are six +pair-mode carriers. For every ordered pair of distinct modes, one +source flag and one target flag have the same actual binary frame. +The corresponding coefficient of the signed rank-two block is +substituted at that event. A zero coefficient omits that ADD only; +the fixed native path is retained. + +The source and target pair codes use the exact pinned short factors. +The source pair code is applied after the two source lines reach +their pair plane. The target code is applied while both targets are +at I. The inverse source code is applied at FULL. The inverse target +code is applied at the common pair-perpendicular frame, before the +two targets reach their individual holes. + +There are 176 nonzero mode coefficients. Of these, 136 are signed +units, 32 have absolute value two, and eight have absolute value +three. Their real ADD cost is 1504. The pair codes and inverse codes +cost 1880 across both data banks. The large-sector scalar cost is +therefore 3384. Its native profile is 624 H1 + 48 H3. + +In the backward word, each source carrier receives the negative +coefficient times the corresponding target carrier. Since the pair +code H obeys H H^T=2I, removal of both codes gives the exact negative +transpose -E^T. No scalar response is moved through Q. + +## The 64-port clique word + +For each clique q0,...,q(k-1), the labels are orthonormal over F2. +At depth d=1,...,k-1, advance source i to + +```text +S_i(d) = span(q_i,...,q_(i+d-1)) +``` + +and target j to + +```text +T_j(d) = span(q_(j-d),...,q_(j-1)). +``` + +Indices are cyclic. Then S_i(d)=T_(i+d)(d). Apply the signed unit +coefficient of I-J_k at this common frame. Every off-diagonal ordered +pair occurs exactly once. + +Each source starts at its own line. Each target starts at I. After +the last transfer, advance each source to FULL and each target to +its own hole. Every target flag excludes its own q label and is +contained in that hole. Thus every native edge is nested, with +positive rank. No frame change on nonzero data is free. + +For a five-clique, each port contributes seven H1 children, one H4, +and one H5. For a three-clique, each port contributes three H1, one +H6, and one H7. The eleven five-cliques and three three-cliques give + +```text +412 H1 + 55 H4 + 55 H5 + 9 H6 + 9 H7. +``` + +There are 238 signed unit ADDs, with real scalar cost 1904. + +## Phase and complete replay + +The frame table is in canonical binary row form. For each native +edge old -> new, the compiler lowers the exact operator +Gamma_new Gamma_old^-1. A separate interpreter checks all Pauli +images and one exact Gaussian-state column. Together these checks +determine the complete Clifford operator and its global phase. +The child rank is independently checked against the frame-dimension +difference. + +For each physical source line Q_p and each target convention +F9 Q_p^-1, an explicit rank-zero adapter relates the convention to +the canonical endpoint frame. All 224 adapters receive the same +independent exact phase check. Both pinned providers have the same +data directions. The new word is consequently the same for both; +the checker verifies that premise from each provider. + +The serialized words are read back and replayed on all 640 input +columns. Every scalar ADD has exactly equal source and target +frames. Every native edge has the declared entry frame and a +nested exit. Every final data frame and every untouched field is +checked. Deletion of one nonzero transfer is rejected. + +The maximum top-level prefix row one-norm is 46 forward and 30 +backward. This does not bound the internal state of recursive +children. The complete recursive precision and host invoice remain +separate. + +Run emit_native.py with --out and a new directory. Repeat with +optimized Python and a different new directory. The expected status +is PASS_LOW_DISPLACEMENT_NATIVE. Both payloads and receipts must be +byte-identical. The empty first-attempt directory is retained. That +attempt stopped before phase compilation because its temporary +binary-basis routine did not produce a unique row form. The final +emitter uses complete binary row reduction and checks every common +frame explicitly. + +The response remains asymmetric on the 48-port sector. This packet +emits the raw backward transpose. It does not emit the full inverse +as a native response: the small clique inverse has nonzero diagonal. +The general-unit controller can use the explicit common-frame +inverse codes, subject to its own routed access and terminal duties. + +The root reciprocal response, the independent-review cyclic flags, +the controller's pair geometry, and the oblique-native phase +construction are the predecessors. AI assistance was used. This +packet does not change the selected frontier or claim a complete +kappa improvement. No publication is authorized. diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/PAIRED-LINE-SCOPE-FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/PAIRED-LINE-SCOPE-FREEZE.json new file mode 100644 index 0000000000..a81a1fc18e --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/PAIRED-LINE-SCOPE-FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "PAIRED-LINE-TENSOR-SCOPE.md": "ffb792832009ce817c057e3e518b0206d530756668ca6fb76e8680a557002d46", + "check_paired_line_scope.py": "f8ee8d5734a9840b47914882821cc4ce9dac4639c8a344a94e65251e5d0a7d3d", + "paired-line-scope-normal.json": "f12a1e740a4ea6d7b13a99d14e26578c0fc2b17f30ce07551678d8a56487253f", + "paired-line-scope-optimized.json": "f12a1e740a4ea6d7b13a99d14e26578c0fc2b17f30ce07551678d8a56487253f" + }, + "normal_optimized_byte_identical": true, + "scope": "General scalar row-support lower bound; a separate one-call determinant obstruction only for translation views; exact finite checks f=1..6. No obstruction for general native views.", + "status": "FROZEN_PRODUCER_NOTE_INDEPENDENT_REVIEW_NOT_RUN" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/PAIRED-LINE-TENSOR-SCOPE.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/PAIRED-LINE-TENSOR-SCOPE.md new file mode 100644 index 0000000000..1a2f618c4a --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/PAIRED-LINE-TENSOR-SCOPE.md @@ -0,0 +1,117 @@ +# Tensor scope of a paired-line scalar factor + +This note records a limit of a proposed terminal factor. It does not +exclude a native construction that uses more general views or a changed +interface. + +Let Q be an invertible operator and let q=Q^-1. Define two elementary +field operations by + +```text +U(c) = [[I,c],[0,I]], L(c) = [[I,0],[c,I]], +J = [[0,-I],[I,0]]. +``` + +Direct multiplication gives + +```text +U(Q) L(-q) U(Q) J = diag(Q,q). +``` + +The displayed order is matrix order. Its chronological order starts +with J. This identity accepts arbitrary values in both fields. It does +not need a clean field. + +For one tensor position, the positive line gate has the formula + +```text +Q = ((1+i)I + (1-i)T)/2, +q = ((1-i)I + (1+i)T)/2, +T = Q^2. +``` + +Here T is a translation. Each off-diagonal operation U(Q), L(-q), or +U(Q) can therefore be split into two scalar ADDs with translation +views at that one tensor position. + +This formula does not give a fixed scalar invoice for the recursive +line gate. At tensor width f, the gate is Q_f=Q^tensor f. Its expansion +contains 2^f distinct translations, all with nonzero coefficients. +In particular, + +```text +Q_f != ((1+i)I + (1-i)T^tensor f)/2 +``` + +when f is greater than one. Applying the two-field identity at each +tensor position instead needs a number of field scans proportional +to f. That cost is not a constant scalar toll for a recursive supplier. + +## A scalar support bound + +Consider a word on any finite number of fields. Admit arbitrary +monomial maps within fields, nonzero scalar scales, field permutations, +and scalar ADDs from one field to another. A monomial map has exactly +one nonzero matrix entry in each row and column. Admit arbitrary input +values in every borrowed field. + +After m scalar ADDs, each matrix row of the word has at most 2^m +nonzero input coefficients. To prove this, start with the identity +matrix, whose rows have support one. A monomial map, scalar scale, or +field permutation does not increase the maximum row support. One ADD +replaces a target row by the sum of two rows, so it can at most double +the maximum. + +Every row of Q_f on its input field has 2^f nonzero coefficients. The +translations in its tensor expansion are distinct. Thus any word in +this class that implements Q_f, or diag(Q_f,Q_f^-1), needs at least f +scalar ADDs. + +The bound permits extra arbitrary fields and arbitrary monomial views. +It rules out a fixed number of scalar ADDs with no native operation. +It does not give a lower bound on the number or ranks of native calls. + +## A narrower one-call obstruction + +There is also a simple exact statement when every free view is a +translation. Let R be the commutative complex group algebra of the +spatial translation group. Treat a word on two fields as a two-by-two +matrix over R. + +Admit scalar elementary ADDs with translated sources, constant nonzero +scales, field translations, and field exchanges. Each such word has +determinant c T for a nonzero scalar c and a single translation T. +An elementary ADD has determinant one. The other generators have the +stated determinant form, which is closed under multiplication. + +One native call Q_f or Q_f^-1 on one field multiplies the determinant +by Q_f or Q_f^-1. A complete word with exactly one such call therefore +has determinant + +```text +c T Q_f or c T Q_f^-1. +``` + +Neither expression is one: Q_f and Q_f^-1 have 2^f nonzero translation +coefficients, whereas a scalar translation has one. The target +diag(Q_f,Q_f^-1) has determinant one. It cannot be realized with exactly +one line call in this translation-only class. Two direct line calls +realize the target. + +This determinant argument does not admit general orthogonal address +maps or coordinate-dependent phases as free generators. Such maps can +make the operator entries noncommutative. The argument must not be +used as a lower bound for that larger construction family. + +## Research consequence + +The one-position paired-line factor is exact. Its proposed fixed-cost +tensor lift was invalid. The scalar support bound explains the lost +factor f. The determinant argument gives a separate, narrower limit +for one-call constructions with translation views. + +These statements do not settle the actual terminal problem. A useful +escape can change a native endpoint, use a different type of view, +combine several native fields, or carry an encoded interface through a +recursive call. Each escape still needs its own complete cost and +physical proof. AI assistance was used to derive and check this note. diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE-FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE-FREEZE.json new file mode 100644 index 0000000000..f3cd7e48e4 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE-FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "RESPONSE.md": "5ea5866231992c389ae2796f1534e0af90ca88bcedfa3fa9758d78f9457d2981", + "check_response.py": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + "run-normal/RESPONSE-CHECKS.json": "7f84440d79200b8c060aad07b910bb96f2bcdde95b07ddb8d41bcea1fcb09d5c", + "run-normal/RESPONSE-PROGRAM.json": "5832788135e16c2427f8c746f251501621684a02ef88b0a14322056653dc2d7c" + }, + "normal_optimized_byte_identical": true, + "scope": "Native phase and routed terminal review remain open.", + "status": "PASS_EXACT_RESPONSE_AND_SCALAR_CODES" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md new file mode 100644 index 0000000000..0ee7aebbb6 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/RESPONSE.md @@ -0,0 +1,165 @@ +# A rank-thirty correction on the actual 112 ports + +This packet gives an exact unit response E on the actual 112 data ports. +It has rank(E-I)=30. The previous signed matching has correction rank +56. The new response keeps the useful selected eight-port principal +block L. Both E and E^-1 have selected block L. The ordinary principal +block is also a dyadic unit. + +The packet also gives complete in-place scalar words for E, E^-1, E^T, +and E^-T. Each word costs 3210 real scalar primitives at a common +frame. It uses no owned or borrowed field. These are port-code and +matrix results. Native phase lowering, routed access, the physical +terminal, helper progress, and the complete supplier cost are separate. + +## The 48-port reciprocal part + +The signed pair code H comes from the pinned cyclic family. Its 24 +two-field blocks satisfy H H^T=2I. The six coded fields at each of +eight vertices have their actual carrier labels in the payload. + +Use the root's reciprocal six-mode matrix. Write a=(a0,a1,a2,a3), +s=sum(a), and define + +```text +E6(a,b,c) = (a-s*1+b*1, c, -2s+3b), +E6^-1(a,b,c) = (a-s*1+c*1, -2s+3c, b). +``` + +Both matrices are integer units with determinant one and zero +diagonal. Their correction rank is two. The root proof establishes +the general construction and the sharp rank-two lower bound. + +At each vertex, put its two modes that meet the selected physical +ports in the first two a positions. Fill the other four positions in +the source order. Conjugate the block by the sign diagonal + +```text +D_v = diag(1, alpha_v, 1, 1, 1, 1), +alpha_v = (-1)^v. +``` + +The two selected-mode off-diagonal entries of both D_v E6 D_v and +D_v E6^-1 D_v are -alpha_v. All their diagonal entries are zero. +Consequently the physical selected block is exactly the old L after +the pair code is removed. The full physical 48-port response is +H^-1 (direct_sum_v D_v E6 D_v) H. It has determinant one and +correction rank sixteen. Its inverse is explicitly given by the same +formula with E6^-1. + +This assignment is significant for the existing selected interface: +L^2=I/2 and det(L)=1/16 remain valid. It is not an arbitrary rank-two +block that loses the selected principal unit. + +The mode word uses E6=P R, where P exchanges b and c. The reflection +R is implemented without a scratch field. With d_i the four a signs, +execute + +```text +b -= sum_i d_i a_i +a_i += d_i b for each i +b *= -1 +b += sum_i d_i a_i +exchange b,c +``` + +The exchange is four priced scalar instructions: three unit ADDs and +one negative unit scale. Thus each six-mode word costs 124. The eight +words cost 992. The physical pair code and its inverse cost 940 on +one bank. This gives 1932 for the complete 48-port scalar code. + +The reflection factor alone has nonzero diagonal. Its scalar code +does not prove that it can be used as a free native transfer. + +## A fourteen-block cover of the other 64 ports + +The exact orthogonality graph joins ports p,r when q_p dot q_r=0. +All 64 q labels have odd norm. Exhaustive maximal-clique enumeration +finds 896 maximal cliques of size four and 64 of size eight. In +particular, this fixed support has no nine-clique. + +The payload gives a disjoint cover by eleven five-cliques and three +three-cliques. On a clique of size k use + +```text +C_k = I-J_k, C_k^-1 = I-J_k/(k-1). +``` + +Here J_k is the all-ones matrix. Each C_k is a dyadic unit, has zero +diagonal, and differs from identity by rank one. Thus the 64-port +part has correction rank fourteen and determinant 2^25. + +Fourteen is optimal within disjoint dyadic rank-one clique blocks of +sizes two, three, and five. A cover with at most twelve blocks covers +at most sixty ports. Thirteen five-blocks cover sixty-five ports, and +replacing a size five by size three or two decreases this number by +two or three, never by one. The graph has no size nine block. This is +a lower bound for this stated clique model, not a lower bound for all +native constructions or terminal decoders. + +An in-place word for C_k is + +```text +a += sum(rest) +b -= a for each remaining field b +a *= -(k-1) +a -= sum(rest) +``` + +The word uses 3(k-1) unit ADDs and one dyadic scale. Its cost is 102 +when k=5 and 52 when k=3. The complete small code costs +11*102+3*52=1278. Reverse the word and invert its instructions to +obtain the inverse. The inverse has nonzero diagonal and is not +claimed to belong to the direct native zero-diagonal family. + +## Complete code and principal inverse + +Combine the two disjoint responses. The resulting E has determinant +2^25 and correction rank thirty. The payload gives exact matrices U,V +with 30 columns and rows, respectively, such that E-I=UV. Both U and +V have rank thirty. + +Let S be the old selected eight ports and U0 its complement. Partition +E^-1 as [[L,N],[P,Q]]. Then + +```text +(E_U0,U0)^-1 = Q-P L^-1 N. +``` + +Both multiplication orders are checked on all 104 ordinary columns. +Every inverse coefficient is dyadic. The ordinary determinant is +2^21. The selected determinant is 1/16. + +The combined scalar word costs 1932+1278=3210. Its reverse gives +E^-1. Reverse the instruction order and transpose each elementary +operation to give E^T; apply both operations to give E^-T. Every word +is checked on all 112 columns. The maximum prefix row one-norm is +44 for E and E^-1, and 14 for E^T and E^-T. These are bounds for the +top-level scalar word only. + +The generic five-code controller can use a native forward response +E and raw backward response E^T, provided each common-frame code is +legally bound at its stated cut. Its residual is still the ordered +operator E2 E1^-T E0. The physical terminal sees +Q(E2 E1^-T E0)Q^-1. Rank thirty in one local chart does not provide +free access to those correction coordinates in a routed hole frame. + +## Reproduction and credit + +The checker requires a new output directory and preserves all source +packets. Run it once with ordinary Python and once with optimized +Python, with different output directories. The expected status is +PASS_LOW_DISPLACEMENT_RESPONSE. The two payloads and receipts must +be byte-identical. + +The root supplied the reciprocal rank-two matrix and its proof. The +independent-review lane supplied the complete cyclic zero-diagonal +family. The controller and oblique-native lanes supplied the actual +signed pair coordinates and the selected matching interface. The +encoded-controller lane supplied the legal-cut general-unit +controller and the three-field I-J code. This packet binds the +selected principal units, gives the actual fourteen-clique cover, +and extends the scalar code to five fields. AI assistance was used. + +No PR or publication is authorized. Before any future PR description, +read /Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_even_clique_gram.py b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_even_clique_gram.py new file mode 100644 index 0000000000..bae16816b6 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_even_clique_gram.py @@ -0,0 +1,128 @@ +#!/usr/bin/env python3 +"""Check the exact character obstruction for the rank-sixteen factor.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +SOURCE = HERE / "odd16-normal-v2/EXTENSION-PROGRAM.json.gz" +SOURCE_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" + + +def need(test, message): + if not test: + raise ValueError(message) + + +def rank(rows, columns): + data = [[row.get(j, F(0)) for j in range(columns)] for row in rows] + used = 0 + for column in range(columns): + pivot = next((i for i in range(used, len(data)) if data[i][column]), None) + if pivot is None: + continue + data[used], data[pivot] = data[pivot], data[used] + scale = data[used][column] + data[used] = [value / scale for value in data[used]] + for i in range(used + 1, len(data)): + scale = data[i][column] + if scale: + data[i] = [a - scale * b for a, b in zip(data[i], data[used])] + used += 1 + return used + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + need(not args.out.exists(), "Use a new receipt path") + raw = gzip.decompress(SOURCE.read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_PIN, "Exact rank16 source") + model = json.loads(raw)["model"] + q, cliques = model["ports"], model["small_cliques"] + u = [{int(p): F(c) for p, c in row.items()} for row in model["correction_U"]] + v = [{int(p): F(c) for p, c in row.items()} for row in model["correction_V"]] + need(rank(u, 16) == rank(v, 112) == 16, "Both factors have full rank") + z = 45 + need(z.bit_count() % 2 == 0, "The common direction is isotropic") + need(sorted(p for clique in cliques for p in clique) == sorted(model["small_ports"]), + "The eight cliques partition the actual small ports") + for i, clique in enumerate(cliques): + need(len(clique) == 8 and all( + (q[p] & q[t]).bit_count() % 2 == int(p == t) for p in clique for t in clique), + "Each clique contains eight orthonormal directions") + total = 0 + for p in clique: + total ^= q[p] + need(total == z and all((q[p] & z).bit_count() % 2 == 1 for p in clique), + "Each actual orthonormal clique sums to the same isotropic direction") + need(v[8 + i] == {p: F(1) for p in clique}, "Exact small query row") + need(all(u[p].get(8 + i, 0) == (-1 if p in clique else 0) for p in range(112)), + "Exact small scatter column") + need(all(u[p] == {8 + i: F(-1)} for p in clique), "No other scatter uses this clique") + need(all(not set(v[j]).intersection(clique) for j in range(16) if j != 8 + i), + "The small cross-Gram block is isolated") + counts = [0] * 8 + character_masks = [] + character_ranks = [] + sector_ranks = [Counter(), Counter()] + witness = None + for w in range(512): + gram = [{} for _ in range(16)] + for i, row in enumerate(v): + for p, coefficient in row.items(): + sign = (-1) ** ((q[p] & w).bit_count() % 2) + for j, value in u[p].items(): + gram[i][j] = gram[i].get(j, F(0)) + coefficient * sign * value + gram = [{j: value for j, value in row.items() if value} for row in gram] + current_rank = rank(gram, 16) + character_ranks.append(current_rank) + sector_ranks[(z & w).bit_count() % 2][current_rank] += 1 + mask = 0 + for i, clique in enumerate(cliques): + signs = [(-1) ** ((q[p] & w).bit_count() % 2) for p in clique] + value = -sum(signs) + if value == 0: + counts[i] += 1 + mask |= 1 << i + need((z & w).bit_count() % 2 == 0, "Every zero is in the positive Z sector") + if witness is None: + witness = {"character": w, "clique_index": i, "ports": clique, + "directions": [q[p] for p in clique], "signs": signs, + "cross_gram_column": 8 + i} + character_masks.append(mask) + need(counts == [140] * 8 and witness is not None, "Exact balanced-sign counts") + need(Counter(character_masks) == {0: 372, 255: 140}, "All eight small zeros occur together") + need(all(character_masks[w] == 0 for w in range(512) if (z & w).bit_count() % 2), + "No small-block zero in the negative Z sector") + need(sector_ranks == [{0: 32, 4: 96, 8: 12, 16: 116}, {14: 256}], + "Exact full cross-Gram ranks in both Z sectors") + output = { + "status": "PASS_EVEN_CLIQUE_CROSS_GRAM_OBSTRUCTION", + "source_decompressed_sha256": SOURCE_PIN, + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "zero_characters_per_clique": counts, + "characters_with_at_least_one_zero_small_block": sum(bool(mask) for mask in character_masks), + "character_zero_block_masks": character_masks, + "character_full_cross_gram_ranks": character_ranks, + "full_cross_gram_rank_counts": dict(sorted(Counter(character_ranks).items())), + "positive_Z_rank_counts": dict(sorted(sector_ranks[0].items())), + "negative_Z_rank_counts": dict(sorted(sector_ranks[1].items())), + "invertible_characters": character_ranks.count(16), + "witness": witness, + "scope": "The exact minimal cross-Gram V Q^2 U is not an everywhere unit in the local nine-axis character algebra. Other terminal mechanisms remain open.", + } + args.out.parent.mkdir(parents=True, exist_ok=True) + args.out.write_text(json.dumps(output, indent=2, sort_keys=True) + "\n") + print(output["status"], output["full_cross_gram_rank_counts"], witness) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_paired_line_scope.py b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_paired_line_scope.py new file mode 100644 index 0000000000..d47a828e8b --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_paired_line_scope.py @@ -0,0 +1,111 @@ +#!/usr/bin/env python3 +"""Check the exact group-algebra paired-line identity at small widths.""" + +import argparse +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +ZERO = (F(0), F(0)) +ONE = (F(1), F(0)) +ID = {0: ONE} + + +def need(value, message): + if not value: + raise ValueError(message) + + +def zadd(a, b): + return (a[0] + b[0], a[1] + b[1]) + + +def zmul(a, b): + return (a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]) + + +def add(a, b): + out = dict(a) + for j, value in b.items(): + out[j] = zadd(out.get(j, ZERO), value) + if out[j] == ZERO: + del out[j] + return out + + +def multiply(a, b): + out = {} + for i, x in a.items(): + for j, y in b.items(): + k = i ^ j + out[k] = zadd(out.get(k, ZERO), zmul(x, y)) + if out[k] == ZERO: + del out[k] + return out + + +def negative(a): + return {j: (-x, -y) for j, (x, y) in a.items()} + + +def product(a, b): + return [[add(multiply(a[i][0], b[0][j]), multiply(a[i][1], b[1][j])) + for j in range(2)] for i in range(2)] + + +def determinant(a): + return add(multiply(a[0][0], a[1][1]), negative(multiply(a[0][1], a[1][0]))) + + +def line(f, sign): + out = dict(ID) + for j in range(f): + out = multiply(out, {0: (F(1, 2), F(sign, 2)), + 1 << j: (F(1, 2), F(-sign, 2))}) + return out + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + need(not args.out.exists(), "Use a new output path") + args.out.parent.mkdir(parents=True, exist_ok=True) + checks = [] + for f in range(1, 7): + qpos, qneg = line(f, 1), line(f, -1) + need(multiply(qpos, qneg) == ID, "The exact line inverse") + need(len(qpos) == len(qneg) == 2 ** f, "The complete tensor support") + upper = [[ID, qpos], [{}, ID]] + lower = [[ID, {}], [negative(qneg), ID]] + rotation = [[{}, negative(ID)], [ID, {}]] + target = [[qpos, {}], [{}, qneg]] + need(product(product(product(upper, lower), upper), rotation) == target, + "The exact paired-line factor") + need(determinant(target) == ID, "The target determinant") + need(determinant([[qpos, {}], [{}, ID]]) == qpos + and determinant([[qneg, {}], [{}, ID]]) == qneg, + "The one-call determinant factors") + shortcut = {0: (F(1, 2), F(1, 2)), + (1 << f) - 1: (F(1, 2), F(-1, 2))} + need((shortcut == qpos) == (f == 1), "The one-position shortcut fails above width one") + wrong = [[ID, {}], [qneg, ID]] + need(product(product(product(upper, wrong), upper), rotation) != target, + "The wrong lower sign is rejected") + checks.append({"tensor_width": f, "line_support": len(qpos), + "paired_identity": True, "inverse": True, + "shortcut_rejected": f > 1}) + receipt = { + "status": "PASS_PAIRED_LINE_SCOPE", + "producer_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "checks": checks, + "scope": "Exact finite examples support the algebraic proof. The general support and translation-only determinant arguments are in PAIRED-LINE-TENSOR-SCOPE.md.", + } + args.out.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/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json new file mode 100644 index 0000000000..327a949b0b --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/coded-normal/CODED-EXITS-CHECKS.json @@ -0,0 +1,430 @@ +{ + "cyclic_geometry_sha256": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "exit_compiler_sha256": "cb8c0880051b24175d2b84080f51ad65a12e85755b6237e7439d12576ffe9bbf", + "exit_compiler_source_pins": { + "coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json": [ + "plain", + "20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701" + ], + "oblique-native-20261017/matched-native-involution/FREEZE.json": [ + "plain", + "b35eae3fb4b53f51cfbed6bec8968b950c70e65bfe777cbe0d15e86c36dd4ab5" + ], + "oblique-native-20261017/matched-native-involution/MATCHED-NATIVE-PROGRAM.json.gz": [ + "decompressed", + "95f11d2b13fc75cb0d07e79ea17afdf3f46b4aca294117ffe1a988779e99f025" + ] + }, + "fresh_changed_exit_phases": 352, + "payload_decompressed_sha256": "7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d", + "producer_sha256": "3d6c9283a2217306bae8f998891439e5cff435a7b3d7575c9481c115f411a282", + "receipts": { + "rank16": { + "W112": { + "base": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 3, + "native_children": 1584, + "native_mass": 1824, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1408, + "2": 112, + "3": 64 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 3, + "native_children": 1584, + "native_mass": 1824, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1408, + "2": 112, + "3": 64 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + } + }, + "extra": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 3, + "native_children": 1584, + "native_mass": 1824, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1408, + "2": 112, + "3": 64 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 3, + "native_children": 1584, + "native_mass": 1824, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1408, + "2": 112, + "3": 64 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + } + } + }, + "W48_I64": { + "base": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 2, + "native_children": 1584, + "native_mass": 1696, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1472, + "2": 112 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 2, + "native_children": 1584, + "native_mass": 1696, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1472, + "2": 112 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + } + }, + "extra": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 2, + "native_children": 1584, + "native_mass": 1696, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1472, + "2": 112 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 2, + "native_children": 1584, + "native_mass": 1696, + "native_side_map_bound": 3168, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 1472, + "2": 112 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 7384, + "top_level_max_array_l2_amplification_bound": "22" + } + } + } + }, + "rank30": { + "W112": { + "base": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 8, + "native_children": 1164, + "native_mass": 1824, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "5": 55, + "6": 55, + "7": 9, + "8": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "30" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 8, + "native_children": 1164, + "native_mass": 1824, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "5": 55, + "6": 55, + "7": 9, + "8": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "46" + } + }, + "extra": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 8, + "native_children": 1164, + "native_mass": 1824, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "5": 55, + "6": 55, + "7": 9, + "8": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "30" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 112, + "external_endpoint_maps": 112, + "inline_monomial_maps": 48, + "maximum_native_rank": 8, + "native_children": 1164, + "native_mass": 1824, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 112, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "5": 55, + "6": 55, + "7": 9, + "8": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "46" + } + } + }, + "W48_I64": { + "base": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 7, + "native_children": 1164, + "native_mass": 1696, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "4": 55, + "5": 55, + "6": 9, + "7": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "30" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 7, + "native_children": 1164, + "native_mass": 1696, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "4": 55, + "5": 55, + "6": 9, + "7": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "46" + } + }, + "extra": { + "backward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 7, + "native_children": 1164, + "native_mass": 1696, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "4": 55, + "5": 55, + "6": 9, + "7": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "30" + }, + "forward": { + "all_input_columns": 640, + "arbitrary_untouched_helpers": 416, + "coded_ports_per_bank": 48, + "external_endpoint_maps": 176, + "inline_monomial_maps": 48, + "maximum_native_rank": 7, + "native_children": 1164, + "native_mass": 1696, + "native_side_map_bound": 2328, + "old_target_adapters_removed": 48, + "owned_fields": 0, + "private_fields": 0, + "profile": { + "1": 988, + "2": 48, + "4": 55, + "5": 55, + "6": 9, + "7": 9 + }, + "rank_nine_admission": "not needed", + "real_scalar_primitives": 5288, + "top_level_max_array_l2_amplification_bound": "46" + } + } + } + } + }, + "scope": "Exact changed output representations. 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1, + 1 + ], + "vertex": 2 + }, + { + "ordered_carriers_a_b_c": [ + 111, + 89, + 9, + 51, + 37, + 43 + ], + "signs": [ + 1, + -1, + 1, + 1, + 1, + 1 + ], + "vertex": 3 + }, + { + "ordered_carriers_a_b_c": [ + 20, + 79, + 25, + 16, + 47, + 99 + ], + "signs": [ + 1, + 1, + 1, + 1, + 1, + 1 + ], + "vertex": 4 + }, + { + "ordered_carriers_a_b_c": [ + 7, + 94, + 61, + 10, + 63, + 92 + ], + "signs": [ + 1, + -1, + 1, + 1, + 1, + 1 + ], + "vertex": 5 + }, + { + "ordered_carriers_a_b_c": [ + 57, + 42, + 44, + 106, + 104, + 87 + ], + "signs": [ + 1, + 1, + 1, + 1, + 1, + 1 + ], + "vertex": 6 + }, + { + "ordered_carriers_a_b_c": [ + 46, + 105, + 62, + 52, + 110, + 90 + ], + "signs": [ + 1, + -1, + 1, + 1, + 1, + 1 + ], + "vertex": 7 + } + ] +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/isotropic-pair-review-20261018/check.py b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/isotropic-pair-review-20261018/check.py new file mode 100644 index 0000000000..3baaa8e3f3 --- /dev/null +++ b/research/reciprocal-native-responses/annex/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/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/FREEZE.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/FREEZE.json new file mode 100644 index 0000000000..21407850f1 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/FREEZE.json @@ -0,0 +1,18 @@ +{ + "base_review_freeze": "cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976", + "earlier_carry_W_review_freeze": "bc0352b29a7a7244ebea40e8b53e44fa5d16dbb645db87eecbe3e02cf3bbaf46", + "extension_review_freeze": "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c", + "files": { + "REPRODUCTION.json": "fd17482fa2c299d87c91b54fac4ba25420d9a02569addbc21aa654a5c52c2b27", + "REVIEW.md": "784e84e17f331eb182a85aa70c26c024fd4a0b7f6d305fd99dda84d36c569e95", + "check.py": "b292828dedc9026f17c436ca2926e44c097672a17b7c2035bd5b280702a9a170", + "normal/INPUTS.json": "1854925de8ff7604651edad157ec9a8f06c2d1f12ea04e5a6d221742c5437372", + "normal/REVIEW.json": "de83b96108ba4633d3d089a487a879f543212e1c802030ae8d69003ce747c061", + "optimized/INPUTS.json": "1854925de8ff7604651edad157ec9a8f06c2d1f12ea04e5a6d221742c5437372", + "optimized/REVIEW.json": "de83b96108ba4633d3d089a487a879f543212e1c802030ae8d69003ce747c061" + }, + "producer_freeze": "f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936", + "publication": "No PR, push, commit, or publication.", + "scope": "All sixteen local coded words, 640 input columns, 352 changed exits (48 exact inherited and 304 full spatial checks), all physical phases, explicit coded outputs and local invoices. No free output-code removal, stage transition, productive helper progress, recursive hosting, or complete supplier claim.", + "status": "FROZEN_INDEPENDENT_LOW_DISPLACEMENT_CODED_EXITS" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/REPRODUCTION.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..3281cc6a23 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/REPRODUCTION.json @@ -0,0 +1,8 @@ +{ + "normal_optimized_byte_identical": { + "INPUTS.json": "1854925de8ff7604651edad157ec9a8f06c2d1f12ea04e5a6d221742c5437372", + "REVIEW.json": "de83b96108ba4633d3d089a487a879f543212e1c802030ae8d69003ce747c061" + }, + "source_files_rechecked": 37, + "status": "PASS" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/REVIEW.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/REVIEW.md new file mode 100644 index 0000000000..beeda7241d --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/REVIEW.md @@ -0,0 +1,206 @@ +# Independent review of the low-displacement coded exits + +All stated local checks pass. There is no material finding. + +This review checks the exact output codes of the rank-thirty and +rank-sixteen native responses. The two codes act on both data banks: +`W48_I64` applies W on the 48 paired ports, and `W112` applies W on all +112 ports. The response matrix does not change. + +The rank-sixteen uniform code uses children of rank at most three. +This resolves the rank-nine exit requirement of the earlier matching +path. It does not remove the output code or provide a recursive host. + +## Inputs and independent method + +The producer input is +[CODED-EXITS-FREEZE.json](../../new-core-transfer-20261017/low-displacement-20261020/CODED-EXITS-FREEZE.json), +at SHA256 +`f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936`. +The decompressed payload SHA256 is +`7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d`. + +The accepted raw phases are fixed by +[NATIVE-REVIEW-FREEZE.json](../low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json) +and +[EXTENSIONS-REVIEW-FREEZE.json](../low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json). +Their SHA256 values are +`cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976` +and +`c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c`. +The earlier carry-W phases are fixed by +[the matching-code review](../matched-left-gauge-review-20261018/FREEZE.json), +at SHA256 +`bc0352b29a7a7244ebea40e8b53e44fa5d16dbb645db87eecbe3e02cf3bbaf46`. + +The checker imports no producer or Clifford compiler. It uses the +previously frozen reverse coefficient interpreter for the complete +field map. It uses a separate sparse Gaussian interpreter for each +fresh physical exit. + +An inherited exit must have the same ordered entry basis, literal +output circuit, and complete phase recipe. Equal spaces or equal ranks +are not sufficient. The new packet has 352 distinct changed exits. +Of these, 48 are exact entries from the earlier accepted carry-W table. +The other 304 require fresh checks. + +For each fresh exit, the check is + +\[ + R T_{\rm old}=T_{\rm final} +\] + +on every one of the 512 spatial basis vectors. Since \(T_{\rm old}\) +is invertible, this checks the entire operator +\(R=T_{\rm final}T_{\rm old}^{-1}\), including its global phase. +The recipe acts on arbitrary field contents. No zero input or clean +helper assumption is used. + +The 304 fresh checks cover 155648 spatial columns and 56623104 exact +nonzero Gaussian coefficients. The word checks bind all 2560 changed +exit occurrences across the sixteen complete words. + +Under the inherited tensor model, the complete one-column identity +extends to every field width. The constant phase is part of the +operator. In particular, a factor \(i^c\) in each of f tensor columns +gives \(i^{cf}\), and \(W_f^2=i^fI\). The finite check does not replace +these factors by width-independent phases. + +## Exact physical output + +Let \(A\) be the accepted response of the chosen family. The logical +forward and backward maps remain + +\[ + F_A(x,y)=(x,y+Ax),\qquad + B_A(x,y)=(x-A^{\mathsf T}y,y). +\] + +The physical input is \(X=Qx,\ Y=y\). On a coded port p, the output is + +\[ + X_p=W F_9 x'_p,\qquad + Y_p=W F_9 Q_p^{-1}y'_p. +\] + +On an uncoded port, omit W. The literal W circuit is +\(S_{e_0}C_{45}S_{e_0}\), with the phase convention of the pinned +gauge packet. W is placed on the left of the complete raw output. +No Q is moved through W or through the response matrix. + +The checker binds every changed source exit to its actual last +ordered canonical basis and to the literal output circuit \(W F_9\). +It binds every changed target exit to +\(W F_9Q_p^{-1}\). This target replacement includes the old inverse +target adapter. The old adapter must be removed. + +Every source adapter is retained. Every uncoded target adapter is +retained. Every rank-zero exit is an explicit monomial operation with +one side map. It is not an absent operation. + +The same unitary code on both directions preserves the physical +inverse-adjoint relation. To see this, let +\(S=\operatorname{diag}(Q,I)\) be the physical input map and let T be +the declared output map, including the chosen W code. Both S and T +are unitary. The physical maps are \(T F_A S^{-1}\) and +\(T B_A S^{-1}\). Since \(B_A^*F_A=I\), their adjoint product is I. +This statement uses the same declared input and output maps. It does +not turn the coded output into the raw output. + +## Complete event stream and arbitrary workspace + +All sixteen words are checked: two responses, two codes, two providers, +and two directions. The new and raw event streams have the same event +positions. The checker compares every scalar coefficient and access. +It compares every unchanged native occurrence and its full recipe. +Only the declared final coded exits can change. + +The typed frame ledger checks every transformation entry, every final +frame, and every equal-frame scalar ADD. The rational scalar schema +conversion is exact. A reverse pass checks all 640 independent input +columns against the accepted response. + +All operations act on the 224 data fields. The other 416 roles retain +their arbitrary values and frames. There are no private fields, +owned fields, CLEAR operations, or hidden helper accesses. In +particular, unchanged helper state is not productive helper progress. + +## Complete local invoices + +Each row applies to both providers and both directions. + +| Response and code | Native profile | Children | Mass | Real scalar primitives | +| --- | --- | ---: | ---: | ---: | +| Rank30, W48_I64 | 988 H1 + 48 H2 + 55 H4 + 55 H5 + 9 H6 + 9 H7 | 1164 | 1696 | 5288 | +| Rank30, W112 | 988 H1 + 48 H2 + 55 H5 + 55 H6 + 9 H7 + 9 H8 | 1164 | 1824 | 5288 | +| Rank16, W48_I64 | 1472 H1 + 112 H2 | 1584 | 1696 | 7384 | +| Rank16, W112 | 1408 H1 + 112 H2 + 64 H3 | 1584 | 1824 | 7384 | + +Each word has 48 inline monomial exits. The mixed code has 176 +external endpoint maps, and the uniform code has 112. Each native +child has at most two side maps. These maps are not assigned zero cost. +The child side-map upper bounds are 2328 and 3168 for the rank-thirty +and rank-sixteen families. + +The scalar prefix array norm bounds are 46 forward and 30 backward +for rank thirty, and 22 in both directions for rank sixteen. These +bounds apply at the top-level event boundaries. They do not bound +primitive internals, recursive child internals, or roundoff growth. + +The exact profiles explain the native-rank improvement. The large +paired source flags reach dimension six before the exit. W changes +their rank-three source exits to rank two, while their 48 target +exits become monomial. The rank-sixteen small-clique source flags +reach dimension seven. Their uniform-code source exits have rank +three, and their target exits have rank two. + +The earlier matching path started the corresponding small source +exits at dimension one and needed rank nine. These are different +literal paths. The new result does not change the old phase result. + +## Scope + +The response matrix results and their inverses remain dependencies of +the accepted raw reviews. This packet changes only the local output +representation and its exact native profile. No odd division is added +to the native word. + +The mixed code saves 96 units of native mass relative to the raw +1792-mass word. The uniform code uses 32 more units. A recursive cost +cannot be inferred from these mass differences alone. The profile, +side maps, source access, and child hosting must be included. + +This review does not provide a free W inverse, a free stage transition, +a terminal decoder, productive helper progress, a complete precision +bound, or the complete supplier. It does not change the selected +frontier or establish an improvement in the complete kappa calculation. + +## Reproduction + +Run from the workspace root, with one CPU: + +```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-coded-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-coded-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-coded-review-20261020/check.py --out work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/optimized +``` + +The required final line is: + +```text +PASS_INDEPENDENT_LOW_DISPLACEMENT_CODED_EXITS +``` + +The checker also rejects retention of the old coded target adapter, +placement of W on the wrong side, and reduction of a child rank +without a new recipe. `REPRODUCTION.json` records the final comparison +of both runs and the final input hashes. + +Both normal and optimized runs passed. Their result and input receipts +are byte-identical. The final hash check confirms that all 37 consumed +source files are unchanged. + +The source packets retain credit for the cyclic paths, responses, +pair factors, and W 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/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/check.py b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/check.py new file mode 100644 index 0000000000..f56ff1175d --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/check.py @@ -0,0 +1,283 @@ +#!/usr/bin/env python3 +"""Check the complete coded exits on the frozen low-displacement paths.""" +from collections import Counter +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 +LANES = HERE.parents[1] +BASE = HERE.parent/'low-displacement-review-20261020' +SOURCE = LANES/'new-core-transfer-20261017/low-displacement-20261020' +OLD = HERE.parent/'matched-left-gauge-review-20261018' + + +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 parse(event): + gate = event[1] + return gate[0], gate[1], None if gate[0] == 'scale' else gate[2], F(*gate[-2:]) + + +def phase_key(basis, circuit): + return json.dumps([basis, circuit], sort_keys=True, separators=(',', ':')) + + +def accepted_exits(payload, need): + records = {} + for providers in payload['providers_by_output_code'].values(): + for directions in providers.values(): + for word in directions.values(): + for event in word['events']: + if event[0] == 'scalar': + continue + before, after = word['frames'][event[2]], word['frames'][event[3]] + if after['kind'] != 'literal': + continue + key = phase_key(before['basis'], after['circuit']) + record = word['native_recipes'][event[-1]] + need(key not in records or records[key] == record, 'Unambiguous accepted exit') + records[key] = record + need(len(records) == 200, 'Complete earlier carry-W phase table') + return records + + +def ledger(word, response, direction, review): + current = list(word['start']) + review.need(len(current) == len(word['final']) == 640, 'Exactly 640 live roles') + rows = [{i: F(1)} for i in range(224)] + maximum = F(1) + converted = [] + for event in word['events']: + if event[0] == 'scalar': + op, target, origin, value = parse(event) + frame = event[2] + review.need(0 <= target < 224 and current[target] == frame, 'Actual scalar target frame') + if op == 'add': + review.need(0 <= origin < 224 and origin != target and current[origin] == frame, + 'Actual equal scalar frames') + review.add(rows[target], rows[origin], value) + else: + review.need(op == 'scale' and origin is None, 'Closed scalar grammar') + rows[target] = {j: value*c for j, c in rows[target].items()} + maximum = max(maximum, sum(abs(c) for c in rows[target].values())) + converted.append(['scalar', [op, target, origin, str(value)], frame]) + else: + review.need(event[0] in ('native', 'monomial'), 'Closed transformation grammar') + target, before, after = event[1:4] + review.need(0 <= target < 224 and current[target] == before, 'Actual transformation entry') + rank = event[4] if event[0] == 'native' else 0 + record = word['native_recipes'][event[-1]] + review.need(record['rank'] == rank and (rank > 0) == (event[0] == 'native'), + 'Exact native or monomial rank') + review.need(rank > 0 or record['right'] is None, 'One map for each zero-rank exit') + current[target] = after + converted.append(event) + review.need(current == word['final'] and current[224:] == word['start'][224:], + 'All final frames and all 416 unchanged other roles') + review.need(review.reverse(converted) == review.response_columns(response, direction), + 'Every input column of the complete coded word') + profile = Counter(e[4] for e in word['events'] if e[0] == 'native') + return { + 'all_input_columns': 640, 'untouched_arbitrary_roles': 416, + 'owned_fields': 0, 'private_fields': 0, 'native_profile': dict(sorted(profile.items())), + 'native_children': sum(profile.values()), 'native_mass': sum(r*n for r, n in profile.items()), + 'inline_monomials': sum(e[0] == 'monomial' for e in word['events']), + 'external_endpoint_maps': len(word['endpoint_adapters']), + 'native_side_map_bound': 2*sum(profile.values()), + 'real_scalar_primitives': review.scalar_price(converted), + 'maximum_child_rank': max(profile), 'top_level_array_norm_bound': str(maximum), + } + + +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('accepted_low_native_review', BASE/'check_native.py', + 'e397b24015a75b61b71562560d82db22dd02c754840a35d2b74fc668180a2a56') + need = review.need + review.frozen(BASE, 'NATIVE-REVIEW-FREEZE.json', + 'cfdc4fa0361aa79c1d53a59ff48bdde1715ea8e3eb6b9efbc109c97bcc44a976') + review.frozen(BASE, 'EXTENSIONS-REVIEW-FREEZE.json', + 'c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c') + review.frozen(OLD, 'FREEZE.json', + 'bc0352b29a7a7244ebea40e8b53e44fa5d16dbb645db87eecbe3e02cf3bbaf46') + review.frozen(SOURCE, 'CODED-EXITS-FREEZE.json', + 'f466ce7bc9d6f5459462acd1799f269a6c2685aea124a3d18f579d542f269936') + payload = json.loads(review.read(SOURCE/'coded-normal/CODED-EXITS-PROGRAM.json.gz', + '7f7efbd4a080f641b7ffcb774c677c66344de60d57c6ecc67cdfc0e6f2f6f73d', True)) + native = json.loads(review.read(SOURCE/'native-normal-v2/NATIVE-PROGRAM.json.gz', + 'e387b082422f085efc8122497cdda0b5211a86b0418af4b9fdbc1da15ac71558', True)) + odd = json.loads(review.read(SOURCE/'odd16-normal-v2/EXTENSION-PROGRAM.json.gz', + 'd466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4', True)) + previous = json.loads(review.read(LANES/'oblique-native-20261017/matched-left-gauge/LEFT-GAUGE-PROGRAM.json.gz', + '437f96b00ae04f410c55f3501ac28bc103e0b416005459c661ac02794c0f9891', True)) + known = accepted_exits(previous, need) + cyclic = json.loads(review.read(LANES/'independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json', + '3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585')) + gauge = json.loads(review.read(LANES/'coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json', + '20f14f021623761160b0ef461904b38f82efdc7dd0c4008271620415bf747701')) + phase_path = HERE.parent/'isotropic-pair-review-20261018/check.py' + phase_pin = 'e428f575ad93a8ade3a92b641a2b5eef111519f03ba5cceca4cd4957f008ba18' + review.read(phase_path, phase_pin) + phase = load('coded_full_spatial', phase_path, phase_pin) + raw = {'rank30': native['providers'], 'rank16': odd['providers']} + need(payload['responses'] == {'rank30': native['response'], 'rank16': odd['model']['response']}, + 'Exact accepted response matrices') + families = payload['providers_by_response_and_code'] + need(set(families) == {'rank30', 'rank16'}, 'Both response families') + full = [['C', 1 << j, 1] for j in range(9)] + w = gauge['W']['circuit'] + need(phase.compile_circuit(w) == phase.gauge(9, 45, 1), 'Exact W phase convention') + large = {p for pair in cyclic['pair_codes'] for p in pair['ports']} + need(len(large) == 48, 'Exact 48-port code support') + q = cyclic['ports'] + cases, reports, controls = {}, {}, {} + for name, codes in families.items(): + need(set(codes) == {'W48_I64', 'W112'}, 'Both output representations') + reports[name] = {} + response = [{int(k): F(v) for k, v in row.items()} for row in payload['responses'][name]] + for code, providers in codes.items(): + selection = large if code == 'W48_I64' else set(range(112)) + need(set(providers) == {'base', 'extra'}, 'Both physical providers') + reports[name][code] = {} + for provider, directions in providers.items(): + need(set(directions) == {'forward', 'backward'}, 'Both directions') + reports[name][code][provider] = {} + for direction, word in directions.items(): + old = raw[name][provider][direction] + need(word['start'] == old['start'] and word['source_pair_codes'] == cyclic['pair_codes'], + 'Exact input frames and source pair-code metadata') + need(word['gauge_circuit'] == w and word['left_W_ports'] == sorted(selection) + and word['raw_output_ports'] == sorted(set(range(112))-selection), + 'Exact output gauge and port partition') + need(word['frames'][:len(old['frames'])] == + [{'kind': 'canonical', 'basis': basis} for basis in old['frames']], + 'Exact original ordered frame bases') + need(len(word['frames']) == len(old['frames'])+1+len(selection), + 'Only the required output frames are added') + adapters = [r for r in old['endpoint_adapters'] + if r['role'] == 'source' or r['port'] not in selection] + need(word['endpoint_adapters'] == adapters, 'Only coded target adapters are removed') + need(len(word['events']) == len(old['events']), 'Same event positions') + changed_x, changed_y = [], [] + for a, b in zip(old['events'], word['events']): + if a[0] == 'scalar': + op, target, origin, value = a[1] + need(b[0] == 'scalar' and parse(b) == (op, target, origin, F(value)), + 'Exact scalar schema conversion and unchanged content') + continue + _, target, before, after, rank, key = a + is_x = target in selection and after == 1 + is_y = 112 <= target < 224 and target-112 in selection and after == old['final'][target] + if not (is_x or is_y): + need(b == a and word['native_recipes'][key] == old['native_recipes'][key], + 'Exact inherited native occurrence and recipe') + continue + need(b[1:3] == a[1:3], 'Changed exit has the exact old role and entry frame') + if is_x: + circuit = full+w + changed_x.append(target) + else: + circuit = [['C', q[target-112], -1]]+full+w + changed_y.append(target-112) + after_frame = word['frames'][b[3]] + need(after_frame['kind'] == 'literal' and after_frame['circuit'] == circuit, + 'Exact ordered physical output circuit') + basis = old['frames'][before] + identity = phase_key(basis, circuit) + record = word['native_recipes'][b[-1]] + if identity in cases: + need(cases[identity]['record'] == record, 'Repeated physical exit is exact') + else: + cases[identity] = {'basis': basis, 'circuit': circuit, 'record': record, 'uses': 0} + cases[identity]['uses'] += 1 + if is_y and len(controls) < 2: + expected = phase.compile_circuit(circuit) + adapter = next(r for r in old['endpoint_adapters'] + if r['role'] == 'target' and r['port'] == target-112) + wrong = { + 'old_target_adapter_retained': expected+phase.inverse(phase.recipe(adapter)), + 'W_on_wrong_side': phase.compile_circuit(w+full+[['C', q[target-112], -1]]), + } + for label, operation in wrong.items(): + if label not in controls: + column = next((x for x in range(512) + if phase.run(operation, x) != phase.run(expected, x)), None) + if column is not None: + controls[label] = {'spatial_column': column, 'port': target-112} + need(sorted(changed_x) == sorted(selection) and sorted(changed_y) == sorted(selection), + 'Exactly one coded exit per selected bank role') + for p in range(112): + if p in selection: + need(word['frames'][word['final'][p]]['circuit'] == full+w + and word['frames'][word['final'][112+p]]['circuit'] == + [['C', q[p], -1]]+full+w, 'Every coded final physical frame') + else: + need(word['final'][p] == old['final'][p] + and word['final'][112+p] == old['final'][112+p], 'Every raw final frame') + report = ledger(word, response, direction, review) + profile = { + ('rank30', 'W48_I64'): {1: 988, 2: 48, 4: 55, 5: 55, 6: 9, 7: 9}, + ('rank30', 'W112'): {1: 988, 2: 48, 5: 55, 6: 55, 7: 9, 8: 9}, + ('rank16', 'W48_I64'): {1: 1472, 2: 112}, + ('rank16', 'W112'): {1: 1408, 2: 112, 3: 64}, + }[name, code] + need(report['native_profile'] == profile and report['native_mass'] == + (1696 if code == 'W48_I64' else 1824), 'Complete changed native profile and mass') + need(report['real_scalar_primitives'] == (5288 if name == 'rank30' else 7384) + and report['inline_monomials'] == 48 + and report['external_endpoint_maps'] == 224-len(selection), 'Complete local invoice') + bound = ('46' if direction == 'forward' else '30') if name == 'rank30' else '22' + need(report['top_level_array_norm_bound'] == bound, 'Unchanged complete prefix bound') + reports[name][code][provider][direction] = report + need(len(cases) == 352, 'All distinct changed physical exits') + inherited, fresh = [], [] + for identity, case in cases.items(): + record = case['record'] + if identity in known: + need(record == known[identity], 'Exact accepted old exit recipe') + inherited.append(identity) + continue + source = phase.canonical(case['basis']) + target = phase.compile_circuit(case['circuit']) + result = phase.compare(source+phase.recipe(record), target, 'Fresh coded exit') + fresh.append({'ordered_frame_and_output': json.loads(identity), 'rank': record['rank'], + 'occurrences': case['uses'], **result}) + if record['rank'] > 0 and 'rank_reduced_without_new_recipe' not in controls: + bad_record = dict(record, rank=record['rank']-1) + bad = source+phase.recipe(bad_record) + column = next((x for x in range(512) if phase.run(bad, x) != phase.run(target, x)), None) + need(column is not None, 'A claimed smaller child is rejected') + controls['rank_reduced_without_new_recipe'] = {'spatial_column': column} + if len(fresh) % 16 == 0: + print('Independent fresh coded exits', len(fresh), '/ 304', flush=True) + need(len(inherited) == 48 and len(fresh) == 304, 'Exact old and fresh coded phase split') + need(len(controls) == 3, 'All physical negative controls') + result = { + 'status': 'PASS_INDEPENDENT_LOW_DISPLACEMENT_CODED_EXITS', + 'literal_words': reports, 'distinct_changed_exits': 352, + 'accepted_previous_exits': [json.loads(key) for key in inherited], + 'fresh_exit_checks': fresh, 'changed_exit_occurrences': sum(c['uses'] for c in cases.values()), + 'negative_controls': controls, 'spatial_columns_per_fresh_exit': 512, + 'scope': 'Exact changed local output contracts and native profiles. No free code removal, stage transition, productive helper progress, recursive hosting, or complete supplier claim.', + } + for name, value in (('REVIEW.json', result), ('INPUTS.json', review.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/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/normal/INPUTS.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/normal/INPUTS.json new file mode 100644 index 0000000000..42e1926ce3 --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-coded-review-20261020/normal/INPUTS.json @@ -0,0 +1,117 @@ +{ + "coherent-port/isotropic-pair-gauge-20261018/GAUGE-PROGRAMS.json": { + "sha256": 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No free code removal, stage transition, productive helper progress, recursive hosting, or complete supplier claim.", + "spatial_columns_per_fresh_exit": 512, + "status": "PASS_INDEPENDENT_LOW_DISPLACEMENT_CODED_EXITS" +} diff --git a/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REPRODUCTION.json new file mode 100644 index 0000000000..f19774d033 --- /dev/null +++ b/research/reciprocal-native-responses/annex/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/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/NATIVE-REVIEW-FREEZE.json b/research/reciprocal-native-responses/annex/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/reciprocal-native-responses/annex/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/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/REVIEW.md new file mode 100644 index 0000000000..affe6325a2 --- /dev/null +++ b/research/reciprocal-native-responses/annex/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/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_native.py new file mode 100644 index 0000000000..d8a4b0dd76 --- /dev/null +++ b/research/reciprocal-native-responses/annex/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/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json new file mode 100644 index 0000000000..a6d8312b0f --- /dev/null +++ b/research/reciprocal-native-responses/annex/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/normal/INPUTS.json @@ -0,0 +1,64 @@ +{ + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.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/reciprocal-native-responses/frozen/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md b/research/reciprocal-native-responses/frozen/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md new file mode 100644 index 0000000000..9b57035450 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md @@ -0,0 +1,195 @@ +# Exact stage views in every dimension 9+8T + +The actual D25 and D73 DATA routes are instances of one exact formula. +The formula works for every positive integer T in dimension \(D=9+8T\). +It retains the actual root chart of each of the 112 ports. It gives the +complete payload phase and the regular-cover owner map. + +This result supplies the stage boundary identities needed to carry the +same local nine-dimensional service to later stages. It does not make +the routed response constant. It does not supply a complete caller, +a new recursive host, a finite map cost, or an exponent. + +## Root quadratic refinement + +Fix an actual port with intrinsic unit vector q. The root chart is the +pinned orthonormal basis + +\[ +B=(q,b_1,\ldots,b_8) +\] + +of the first nine coordinates. Its q has Hamming weight 3 or 7. +For any unit vector v, define + +\[ +\beta(v)=\frac{|v|-1}{2}\pmod 2. +\] + +Put \(\beta_j=\beta(b_j)\) and + +\[ +\delta_0=q+\sum_{j=1}^{8}\beta_jb_j. +\tag{1} +\] + +The coefficient of q is one because its weight is 3 or 7. +Let \(C_v\) be the exact line transform with Fourier multiplier +\(i^{v\cdot z}\). Let \(X_v=C_v^2\) be the translation by v. +All these operators commute. If \(F_0\) is FULL on the root axes, then + +\[ +Q\prod_{j=1}^{8}C_{b_j}=X_{\delta_0}F_0,\qquad Q=C_q. +\tag{2} +\] + +To prove (2), compare the Z4 functions +\(\sum_{v\in B}(v\cdot z)\) and \(|z|\). Their difference has zero +quadratic part modulo four because B is orthonormal. Its linear part +is even. Evaluate it at each basis vector \(v\in B\): the value is +\(1-|v|=2\beta(v)\pmod4\). Thus the difference is +\(2\delta_0\cdot z\). This proves the full phase, including its sign. + +## The route and its two translations + +Let \(E_s=(e_{s,1},\ldots,e_{s,8})\) be the fresh coordinate block for +stage s, where \(1\leq s\leq T\). Define \(\rho_s\) to exchange +\(b_j\) with \(e_{s,j}\), for each j, and to fix q and all other fresh +blocks. This is an orthogonal involution. An explicit matrix is + +\[ +\rho_s=I+\sum_{j=1}^{8} + (b_j+e_{s,j})(b_j+e_{s,j})^{\mathsf T}. +\tag{3} +\] + +The eight vectors in the sum are isotropic and pairwise orthogonal. +Equation (3) therefore has the stated action on the complete +orthonormal basis. + +The two physical translations are + +\[ +\delta_{\rm in}(s)=\rho_s\delta_0 + =q+\sum_j\beta_je_{s,j},\qquad +\delta_{\rm out}(s)=\delta_0+\rho_s\delta_0. +\tag{4} +\] + +Let \(P_{\rho_s}\) be the payload address permutation. The entry map is +\(V_{\rm in}=X_{\delta_{\rm in}}P_{\rho_s}\). Its equivalent order is +\(P_{\rho_s}X_{\delta_0}\). The exit map is +\(V_{\rm out}=X_{\delta_{\rm out}}P_{\rho_s}\). +The exit translation is fixed by \(\rho_s\), so the exit map is its +own inverse. + +## Adjacent-stage identities + +Let \(F_\ell\) be FULL on the root and fresh blocks 1 through \(\ell\). +Let \(F_{{\rm ext},s}\) be FULL on fresh blocks 1 through s. +The exact adjacent identities are + +\[ +\begin{aligned} +V_{\rm in}(s)F_{s-1} + &=F_{{\rm ext},s}\,Q\,P_{\rho_s},\\ +V_{\rm in}(s)F_{s-1}q + &=F_{{\rm ext},s}\,P_{\rho_s},\\ +V_{\rm out}(s)F_s + &=F_sP_{\rho_s},\\ +V_{\rm out}(s)F_sq + &=F_sqP_{\rho_s}. +\end{aligned} +\tag{5} +\] + +For the first identity, conjugate (2) by \(P_{\rho_s}\). +The eight root-complement line factors become the fresh block s. +The other completed fresh blocks are fixed. The entry translation +in (4) cancels the translated factor in (2). +The second identity follows because \(\rho_s q=q\) and \(Qq=I\). + +For the third identity, the factors from both the root and fresh +block s are present. Exchanging these factors changes FULL by precisely +\(X_{\delta_0+\rho_s\delta_0}\), which the exit map cancels. +The fourth identity follows again from \(\rho_s q=q\). + +All remaining coordinates are spectators. None of these arguments +depends on T or on the number of preceding completed blocks. + +The same proof gives the complete access cones. A FULL field at level +\(\ell\geq s\) admits the stage-s exit map. A hole field \(F_\ell q\) +at level \(\ell` in +normal Python and in `python3 -O`; both payload and receipt must be +byte equal. + +The root charts, D25 records, and D73 records come from the actual +supplier access calculations. The retained-reader consequence uses +the complete forward service and its emitted inverse-adjoint. All +source hashes are explicit in the payload. This work uses AI assistance +and exact finite-field and Z4 computation. + +No PR or publication is authorized. Before any future PR description, +read `/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CHECKS-OPTIMIZED.json b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CHECKS-OPTIMIZED.json new file mode 100644 index 0000000000..5c3ad48f01 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CHECKS-OPTIMIZED.json @@ -0,0 +1,61 @@ +{ + "actual_E_minus_I_rank": 32, + "actual_ports": 112, + "actual_reflection_rank": 16, + "both_inverse_orders": true, + "factor_ranks": [ + 16, + 16, + 16 + ], + "model_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "native_record_or_scatter_claim": false, + "negative_controls": { + "omit_P_transport": true, + "omit_first_query_transport": true, + "reverse_reflection_factors": true, + "use_E_as_involution": true + }, + "ordered_source_queries": 3, + "physical_P_nonzeros": 160, + "physical_P_support": [ + 2, + 10, + 11, + 13, + 25, + 42, + 43, + 51, + 62, + 63, + 70, + 78, + 80, + 82, + 83, + 84, + 85, + 86, + 91, + 93, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 104, + 105, + 108, + 109 + ], + "regression_residual_rank": 48, + "schema": "reciprocal-selected-baseline-check-v1", + "scope": "Exact matrix and ordered caller proof. The native service, saved records, phase scatter, host and full supplier remain separate.", + "status": "PASS", + "three_stage_regression": "Independent signed conjugations of the actual112 model; not D25 routes.", + "two_bank_columns": 224 +} diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CHECKS.json b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CHECKS.json new file mode 100644 index 0000000000..5c3ad48f01 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CHECKS.json @@ -0,0 +1,61 @@ +{ + "actual_E_minus_I_rank": 32, + "actual_ports": 112, + "actual_reflection_rank": 16, + "both_inverse_orders": true, + "factor_ranks": [ + 16, + 16, + 16 + ], + "model_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "native_record_or_scatter_claim": false, + "negative_controls": { + "omit_P_transport": true, + "omit_first_query_transport": true, + "reverse_reflection_factors": true, + "use_E_as_involution": true + }, + "ordered_source_queries": 3, + "physical_P_nonzeros": 160, + "physical_P_support": [ + 2, + 10, + 11, + 13, + 25, + 42, + 43, + 51, + 62, + 63, + 70, + 78, + 80, + 82, + 83, + 84, + 85, + 86, + 91, + 93, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 104, + 105, + 108, + 109 + ], + "regression_residual_rank": 48, + "schema": "reciprocal-selected-baseline-check-v1", + "scope": "Exact matrix and ordered caller proof. The native service, saved records, phase scatter, host and full supplier remain separate.", + "status": "PASS", + "three_stage_regression": "Independent signed conjugations of the actual112 model; not D25 routes.", + "two_bank_columns": 224 +} diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-CHECKS-OPTIMIZED.json b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-CHECKS-OPTIMIZED.json new file mode 100644 index 0000000000..bacc377f28 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-CHECKS-OPTIMIZED.json @@ -0,0 +1,58 @@ +{ + "actual_model_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "schema": "clean-reflection-hidden-check-v1", + "scope": "Exact ordered content. Signed stage conjugations are a regression, not an actual routed lower bound. No new native service or decoder.", + "selected_ports": [ + 2, + 10, + 11, + 13, + 25, + 42, + 43, + 51, + 62, + 63, + 70, + 78, + 80, + 82, + 83, + 84, + 85, + 86, + 91, + 93, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 104, + 105, + 108, + 109 + ], + "status": "PASS", + "variants": { + "selected_conjugate": { + "arbitrary_two_bank_columns": 224, + "hidden_X_rank": 32, + "hidden_Y_rank": 16, + "hidden_columns": 80, + "hidden_rank_regression": 32, + "residual_rank_regression": 47 + }, + "unpermuted": { + "arbitrary_two_bank_columns": 224, + "hidden_X_rank": 32, + "hidden_Y_rank": 16, + "hidden_columns": 80, + "hidden_rank_regression": 32, + "residual_rank_regression": 48 + } + } +} diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-CHECKS.json b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-CHECKS.json new file mode 100644 index 0000000000..bacc377f28 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-CHECKS.json @@ -0,0 +1,58 @@ +{ + "actual_model_sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "schema": "clean-reflection-hidden-check-v1", + "scope": "Exact ordered content. Signed stage conjugations are a regression, not an actual routed lower bound. No new native service or decoder.", + "selected_ports": [ + 2, + 10, + 11, + 13, + 25, + 42, + 43, + 51, + 62, + 63, + 70, + 78, + 80, + 82, + 83, + 84, + 85, + 86, + 91, + 93, + 95, + 96, + 97, + 98, + 99, + 100, + 101, + 102, + 104, + 105, + 108, + 109 + ], + "status": "PASS", + "variants": { + "selected_conjugate": { + "arbitrary_two_bank_columns": 224, + "hidden_X_rank": 32, + "hidden_Y_rank": 16, + "hidden_columns": 80, + "hidden_rank_regression": 32, + "residual_rank_regression": 47 + }, + "unpermuted": { + "arbitrary_two_bank_columns": 224, + "hidden_X_rank": 32, + "hidden_Y_rank": 16, + "hidden_columns": 80, + "hidden_rank_regression": 32, + "residual_rank_regression": 48 + } + } +} diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-FREEZE.json b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-FREEZE.json new file mode 100644 index 0000000000..c0a7935b4e --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "CLEAN-CHECKS-OPTIMIZED.json": "2cad019620b5cffe1596c066fc15a8dc36eedb0afab9e8bf2dce01d26504e3a5", + "CLEAN-CHECKS.json": "2cad019620b5cffe1596c066fc15a8dc36eedb0afab9e8bf2dce01d26504e3a5", + "CLEAN-REFLECTION.md": "ec2aeb53ade7ba8892e660ba53a3830cd782e35e7fdf66198025c4e41f47cbd7", + "check_clean_reflection.py": "4c82b16bbc73394df35e3d4e3febbee8b1bd771ffcad762631c6acc35434d27e" + }, + "scope": "Bounded existing result completed before publication audit. No new native or supplier claim.", + "status": "PASS" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-REFLECTION.md b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-REFLECTION.md new file mode 100644 index 0000000000..53e49d093b --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/CLEAN-REFLECTION.md @@ -0,0 +1,159 @@ +# A clean reflection and its two hidden query families + +This note uses the same actual R=I+U L as RECIPROCAL-CALLER.md. +Let S be the 32 special ports of the reciprocal model and let +O be the other 80 ports. Write Pi and J0 for their coordinate +projections. J0 is not the signed metric J. + +The matrix P is the identity on O. Therefore the ordinary rows +of E=P R equal the ordinary rows of R. They have zero diagonal. +The selected set S is closed under the actual physical pair code. +These are the local response conditions for a possible clean +R service. They do not by themselves emit that service. + +## Conditional local maps + +Use x=(a,u) and y=(z,v), with selected coordinates first. The +clean forward map and its metric-converted inverse-adjoint are + +```text +F_R(x,y)=(-z,(Rx)_O,(Rx)_S,v+(Rx)_O), +B_R(x,y)=(-z,(Rx)_O-v,(Rx)_S,v). +``` + +Selected wire exchange at both boundaries of B gives + +```text +w=R(z,u), +Bswap_R(x,y)=(w_S,w_O-v,-a,v). +``` + +The input types are Qx and Z y, where + +```text +Z=diag(Q_S,I_O). +``` + +The output types are FULL on X and selected Y, and Fq on ordinary +Y. Both selected input fields have the same Q type. Thus the +selected exchange is a valid wire exchange under this local +contract. The initial selected target is arbitrary. + +The signed metric gives C=R, G=J^-1 in the clean metric formula +of RECIPROCAL-CALLER.md. No positive-definite metric is needed. +No helper is used as a new cache. + +## A rank-48 residual + +Let A=F_I and B=B_I. Then + +```text +F_R=A diag(R,I), B_R=B diag(R,I). +``` + +Since rank(R-I)=16, each source code differs from I by rank 16. +In the three-call product F_R2 B_R1 F_R0, transport each source +code through the invertible ideal factors. The result, after +removing A B A, is a product of three conjugates of diag(R_i,I). +Each difference has rank 16. The complete residual has rank +at most 48. + +The same argument applies with the selected-conjugate Bswap. +No stage matrices have been commuted. This is an array-rank bound, +not a native invoice. + +For the unpermuted B, the ideal product A B A is the signed swap +W on ordinary coordinates and -W on selected coordinates. For +Bswap, its ideal product is W on both sets. These selected signs +are scalar operations. + +At the ideal endpoint, the ordinary Y q factor is converted to +the required Q by Q^2, a translation. Both selected output banks +need one positive Q line each. Thus the ideal terminal has 64 +rank-one lines. This count excludes the nonidentity reflection +residual. With I entry, the 32 initial selected formation lines +are an additional cost. + +## Exact hidden-output test + +Use a triple with arbitrary routed R0,R1,R2. Set all final X +coordinates and all final selected Y coordinates to zero. Let +the final ordinary logical Y be h. Its physical field is Fq h. +Let i_O embed h into the full 112-coordinate vector. + +Reverse the last forward map. Its coded source is reconstructed +from final selected Y and final ordinary X. Both are zero, so +the input X to that last call is zero. R2 drops out exactly. + +For the unpermuted B, the remaining inverse is + +```text +x_initial=R0 J0 R1 i_O h, +y_initial=(I-R1)i_O h. +``` + +For the selected-conjugate Bswap, it is + +```text +x_initial=R0 R1 i_O h, +y_initial=J0(I-R1)i_O h. +``` + +In the second formula, the selected initial borrowed baseline +is zero. Thus Bswap removes the hidden selected borrowed row. +It does not remove the ordinary hidden observation. + +For Bswap the difference from the ideal inverse factors as + +```text +x_initial-i_O h + =U1 L1 i_O h + U0 L0 R1 i_O h, +y_initial + =-J0 U1 L1 i_O h. +``` + +Only two 16-row query families occur: + +```text +L1 i_O h, L0 R1 i_O h. +``` + +This gives a 32-array-rank bound for the hidden correction. +The two rows must not be identified across stages. They can be +formed freely after all ordinary holes are normalized, but that +normalization is a paid operation. This note supplies no cheaper +reader. + +The unpermuted B also has a 32-row bound, from + +```text +R0 J0 R1 i_O-i_O + =U0 L0 i_O+R0 J0 U1 L1 i_O. +``` + +It has an additional selected borrowed response +`-Pi U1 L1 i_O h`. This is why retaining an old selected data +query by that orientation does not settle arbitrary borrowed +state restoration. + +## Exact check + +The checker uses the pinned physical 112-port R and three +different signed conjugations. It verifies all 224 two-bank +columns, both local inverse orders, both full inverse orders, +the two hidden formulas, and the 48/32 rank bounds. + +The signed stage conjugations are an order regression, not an +actual D25 route replay. In this regression the complete residual +has rank 48 and the hidden correction has rank 32. The proof +above supplies the general bounds. It does not claim that these +regression ranks are actual routed lower bounds. + +The native lane has a separate census for a possible clean R +word. The controller lane owns the physical joint decoder. This +note does not claim a complete native service, a returned code, +an admitted helper schedule, or a kappa 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/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/FREEZE.json b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/FREEZE.json new file mode 100644 index 0000000000..32359ce078 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/FREEZE.json @@ -0,0 +1,20 @@ +{ + "files": { + "CHECKS-OPTIMIZED.json": "c418cfbbf92f423cd2e5bcd8639c7d5b523376dad4a1d09c9a531157fed06fee", + "CHECKS.json": "c418cfbbf92f423cd2e5bcd8639c7d5b523376dad4a1d09c9a531157fed06fee", + "RECIPROCAL-CALLER.md": "1c54d18b4a0601dae03064cc03029bc5f2c7e53c3befbc978f163d009f24d99b", + "check_reciprocal_caller.py": "8c107239cbc9f7d491a8ef455a53826aeccd2e8c33eccfb43e9625101ceb87fc" + }, + "schema": "reciprocal-selected-baseline-freeze-v1", + "scope": { + "actual112_matrix": true, + "complete_decoder": false, + "complete_supplier": false, + "new_native_word": false, + "ordered_caller": true, + "publication": false, + "rank48_array_residual": true, + "stored_records": false + }, + "status": "PASS" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/RECIPROCAL-CALLER.md b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/RECIPROCAL-CALLER.md new file mode 100644 index 0000000000..748901f33b --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/RECIPROCAL-CALLER.md @@ -0,0 +1,306 @@ +# A reciprocal caller with a 48-row residual + +The actual 112-port response has a factorization E=P R. The matrix P +is an involution on 32 ports. The matrix R is an involution with +rank(R-I)=16. A three-call caller can keep P as a common bank code +and leave only three rank-16 shear corrections. + +This is an ordered caller theorem. The actual matrix is checked +independently. A new native word, stored query records, and a complete +terminal decoder are separate obligations. Rank 48 is not a native +cost of 48. + +## Source and metric + +The matrix source is + +```text +oblique-native-20261017/signed-metric-reciprocal-20261020/ +model-normal-v2/RESPONSE.json.gz +``` + +Its decompressed SHA256 is +`df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0`. +The root construction is in +`root/RECIPROCAL-RANK-TWO-20261020.md`. + +Write the physical row and column factors as L and U. They satisfy + +```text +R=I+U L, L U=-2I16, P^2=R^2=I, +E=P R, E^-1=R P. +``` + +The source also supplies a real diagonal matrix J with + +```text +P* J P=J, R* J R=J, E* J E=J. +``` + +Its diagonal entries are 1 on 80 ports, -1/2 on 16 ports, and -1/4 +on 16 ports. Thus all metric scales and inverse scales are dyadic. +The order of the inverse formulas is + +```text +E^-*=J E J^-1, E^-1=J^-1 E* J. +``` + +Do not replace E by an involution. In general E^2 is not I. + +Every nonidentity row or column of P lies in the same 32-port set S. +The physical P has 160 nonzero entries. It is not a monomial matrix. +Its accepted common-frame scalar word costs 728 real primitives. +This cost does not include global address views. + +## A local P wrapper + +Let D(A)=diag(A,A), and define + +```text +L_A=[[I,0],[A,I]], U_A=[[I,A],[0,I]]. +``` + +Assume a raw forward service has response E. Apply P to the +current-I Y input. Apply P to the completed-FULL X output. The +result is + +```text +F^P = [[P,0],[E,P]] = D(P) L_R. +``` + +For a raw backward response E^-1, the same input and output +wrappers give + +```text +B^P = [[P,-P R],[0,P]] = D(P) U_-R. +``` + +There is also an exact conversion from the chronological +inverse-adjoint of the whole wrapped forward word: + +```text +D(J^-1) (F^P)^-* D(J) = B^P. +``` + +This conversion uses only physical diagonal scales. It does not +commute a port-mixing code through a hole phase. The complete +inverse-adjoint must retain the complete helper and phase contract. + +The current-I pre-Y and completed-FULL post-X placements use the +standard stage-view contract. Its source is +`bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md`, +SHA256 `5da866eb2802e8a30ea77d2f88877b5005a2eb04632514c897a426e76277db2e`. +No wrapper is granted on a retired ordinary Y hole. + +## Three different stages + +Keep all stage labels. Set + +```text +H=P1 P0, Ptot=P2 P1 P0, +Rhat0=R0, +Rhat1=P0^-1 R1 P0, +Rhat2=H^-1 R2 H. +``` + +Then + +```text +F2^P B1^P F0^P + =D(Ptot) L_Rhat2 U_-Rhat1 L_Rhat0. +``` + +This identity holds over an ordered operator ring. It uses no +commutation between stages. + +Write K_i=Rhat_i-I. Each K_i has at most 16 array columns. Let + +```text +W=L_I U_-I L_I=[[0,-I],[I,0]]. +``` + +The normalized defect is + +```text +T=W^-1 L_Rhat2 U_-Rhat1 L_Rhat0=A2 A1 A0, + +A0=[[I,0],[K0,I]], +A1=[[I-K1,-K1],[K1,I+K1]], +A2=[[I,-K2],[0,I]]. +``` + +Each A_i-I has square zero. For A1 this follows from the ordered +factorization + +```text +A1-I=[-I;I] K1 [I,I], +``` + +because [I,I][-I;I]=0. Therefore + +```text +rank(T-I) <= rank(K0)+rank(K1)+rank(K2) <=48. +``` + +For a payload field of dimension d, the bound is 48d. It is an +array-rank bound, not a count of scalar coordinates. + +An exact inverse applies these operations in this order: + +```text +X += K2 Y +q = K1(X+Y); X += q; Y -= q +Y -= K0 X. +``` + +The middle sum X+Y is unchanged by its two writes. A serial +implementation must use the complete query before either write +changes its required source. + +## Three queries at actual source cuts + +Factor the transported K_i as Uhat_i Lhat_i, where + +```text +Uhat0=U0, Lhat0=L0, +Uhat1=P0^-1 U1, Lhat1=L1 P0, +Uhat2=H^-1 U2, Lhat2=L2 H. +``` + +For arbitrary initial logical data x,y, define + +```text +c0=L0 x, +t=y+R0 x, +c1=Lhat1 t, +w=x-Rhat1 t, +c2=Lhat2 w. +``` + +Direct substitution gives the output before Ptot: + +```text +X=-y-U0 c0-Uhat1 c1, +Y= x-Uhat1 c1+Uhat2 c2. +``` + +Thus the normalized defect is also + +```text +T(x,y)=(x-Uhat1 c1+Uhat2 c2, + y+U0 c0+Uhat1 c1). +``` + +These records have three different literal read cuts: + +| Record | Actual stored argument | Read cut | +| --- | --- | --- | +| c0 | native F0 source X=x | completed X, before post-P0 | +| c1 | B1 input Y=P0 t | current-I Y, before pre-P1 | +| c2 | native F2 source X=H w | completed X, before post-P2 | + +The local rows at these cuts are L0,L1,L2. In particular, c1 is +L1 applied to the stored B1 input. It is not L1 applied to the +uncoded t. This distinction accounts for P0 without an extra old +query. + +No read discards an arbitrary baseline. To retain these records, +one must specify either owned fields or a joint invertible code +with a decoder for every displaced baseline. The c1 record starts +at the current-I cut. Its later frame progress is not free. + +## Physical endpoint and the 32-port code + +Use the all-hole raw service contract. Let Q be the diagonal +positive input line operator and q=Q^-1. For arbitrary physical +inputs X0,Y0, the first logical source is x=q X0 and y=Y0. +This is a coordinate definition; it needs no formation gate. + +Let F be the complete native Fourier progress and +Qhat=diag(Q,I). The retained signed terminal, including its +old Y Q^2 maps, gives + +```text +output = diag(F,F) Qhat D(Ptot) T Qhat^-1 input. +``` + +Do not commute F with the routed code. A logical code A at this +boundary is implemented physically as F A F^-1. + +Because each stage route is port-diagonal, it does not enlarge +the 32-port support of P. Hence Ptot is the identity outside S. +The conjugated Ptot code can be removed with the following +conditional complete-FULL recipe: + +1. Apply q to the 32 affected X fields. +2. Apply Ptot^-1 to both banks through the completed stage views. +3. Apply Q to the same 32 X fields. + +The line subtotal is 64 rank-one children. The scalar subtotal +for the six P words is 6*728=4,368 real primitives. The stage views, +helper host, precision, and line-child admission remain separate. +The operations do not remove T. + +After this code removal, a saved-record decoder would add +Q(Uhat1 c1-Uhat2 c2) to X and subtract U0 c0+Uhat1 c1 from Y, +in the complete F frame. The X scatter still contains Q on its +output ports. The availability of three 16-row records alone +does not implement those scatters. + +In particular, 3*1792+64 is only a native subtotal under a +compatible raw-service premise. No 96-child residual decoder is +claimed, and no supplier or kappa gain follows from this note. + +## A separate signed clean interface + +Suppose a completion C satisfies C J^-1 C*=G, with physical +diagonal dyadic units J,G. Suppose its ordinary rows have a legal +zero-diagonal native response and a clean selected exchange. +For x=(a,u), y=(z,v), its clean map is + +```text +F_C(x,y)=(-z,(Cx)_R,(Cx)_P,v+(Cx)_R). +``` + +Since C^-*=G^-1 C J^-1, its exact metric conversion is + +```text +D(G) F_C^-* diag(J,G^-1) + =(-z,(Cx)_R-v,(Cx)_P,v). +``` + +Selected input/output exchange then gives + +```text +w=C(z,u), +Bswap_C=(w_P,w_R-v,-a,v). +``` + +All added metric operations are diagonal field scales. This local +identity does not identify C_s and C_t at different stages. +The selected FULL and ordinary hole types must still be kept. +It does not change the all-hole reciprocal theorem above. + +## Validation and limits + +The checker independently reads the actual 112-port model. It +checks both inverse orders, the metric identities, the exact P +support, the U L factor, and the scalar P word. A regression uses +three different signed conjugations of these actual matrices. It +checks all 224 two-bank columns, the ordered factorization, both +inverse orders, and the three source-record formulas. These +signed conjugations test order; they are not the actual D25 routes. + +The proof covers general routed operator coefficients. The native +stage-view theorem is an inherited premise. This checker does not +emit a raw service, allocate records, restore dirty record fields, +or certify a complete decoder. + +The root lane supplied E=P R and its signed metric. The oblique +lane supplied the actual 112-port model and its scalar words. +The bridge lanes supply the stage-view contract and study native +record access. 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/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/check_clean_reflection.py b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/check_clean_reflection.py new file mode 100644 index 0000000000..49dbe9bd47 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/check_clean_reflection.py @@ -0,0 +1,145 @@ +#!/usr/bin/env python3 +"""Check clean reflection maps and their hidden output columns.""" + +import argparse +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +HELPER = HERE / "check_reciprocal_caller.py" +PIN = "8c107239cbc9f7d491a8ef455a53826aeccd2e8c33eccfb43e9625101ceb87fc" +if sha256(HELPER.read_bytes()).hexdigest() != PIN: + raise ValueError("The pinned independent arithmetic helper") +SPEC = importlib.util.spec_from_file_location("reciprocal_check", HELPER) +G = importlib.util.module_from_spec(SPEC) +SPEC.loader.exec_module(G) +N = 112 + + +def local(r, selected, backward=False, swap=False): + out = [] + for p in range(N): + if p in selected: + out.append({N+p: G.F(-1)}) + else: + row = dict(r[p]) + if backward: + row[N+p] = G.F(-1) + out.append(row) + for p in range(N): + if p in selected: + out.append(dict(r[p])) + elif backward: + out.append({N+p: G.F(1)}) + else: + row = dict(r[p]) + row[N+p] = G.F(1) + out.append(row) + return conjugate_selected(out, selected) if swap else out + + +def inverse(r, selected, backward=False, swap=False): + w = [ + {N+p: G.F(1)} if p in selected else + ({p: G.F(1), N+p: G.F(1)} if backward else {p: G.F(1)}) + for p in range(N) + ] + out = G.mul(r, w) + for p in range(N): + out.append({p: G.F(-1)} if p in selected else + ({N+p: G.F(1)} if backward else {N+p: G.F(1), p: G.F(-1)})) + return conjugate_selected(out, selected) if swap else out + + +def conjugate_selected(a, selected): + permutation = [p+N if p in selected else p-N if p-N in selected else p + for p in range(2*N)] + return [{permutation[j]: x for j, x in a[permutation[p]].items()} + for p in range(2*N)] + + +def check(): + raw = gzip.decompress(G.MODEL.read_bytes()) + G.need(sha256(raw).hexdigest() == G.PIN, "The actual112 source pin") + source = json.loads(raw) + r = G.rows(source["physical"]["R"]) + selected = set(source["special_ports"]) + ordinary = [p for p in range(N) if p not in selected] + rs, us, ls = [], [], [] + for stage in range(3): + s = G.eye(N) if stage == 0 else G.sign_matrix(N, stage) + rs.append(G.mul(s, G.mul(r, s))) + us.append(G.mul(s, G.rows(source["reflection_U"]))) + ls.append(G.mul(G.rows(source["reflection_L"]), s)) + proj = [{p: G.F(1)} if p in ordinary else {} for p in range(N)] + i_o = [{ordinary.index(p): G.F(1)} if p in ordinary else {} for p in range(N)] + results = {} + for swap in (False, True): + forwards = [local(rs[0], selected), + local(rs[1], selected, True, swap), + local(rs[2], selected)] + inverses = [inverse(rs[0], selected), + inverse(rs[1], selected, True, swap), + inverse(rs[2], selected)] + for a, ai in zip(forwards, inverses): + G.need(G.mul(a, ai) == G.mul(ai, a) == G.eye(2*N), "Both local inverse orders") + total = G.mul(forwards[2], G.mul(forwards[1], forwards[0])) + total_inverse = G.mul(inverses[0], G.mul(inverses[1], inverses[2])) + G.need(G.mul(total, total_inverse) == G.mul(total_inverse, total) == G.eye(2*N), + "Both complete inverse orders") + ident = G.eye(N) + ideal = G.mul(local(ident, selected), + G.mul(local(ident, selected, True, swap), local(ident, selected))) + ideal_inverse = G.trans(ideal, 2*N) + defect = G.add(G.mul(ideal_inverse, total), G.eye(2*N), -1) + G.need(G.rank(defect) <= 48, "The complete rank bound") + hidden = G.zero(N) + i_o + actual = G.mul(total_inverse, hidden) + r1_o = G.mul(rs[1], i_o) + want_x = G.mul(rs[0], r1_o if swap else G.mul(proj, r1_o)) + want_y = G.add(i_o, r1_o, -1) + if swap: + want_y = G.mul(proj, want_y) + G.need(actual == want_x + want_y, "The exact hidden-column formula") + relative = G.add(actual, i_o + G.zero(N), -1) + G.need(G.rank(relative) <= 32, "The hidden rank bound") + if swap: + q1 = G.mul(ls[1], i_o) + q0 = G.mul(ls[0], r1_o) + dx = G.add(G.mul(us[1], q1), G.mul(us[0], q0)) + dy = G.neg(G.mul(proj, G.mul(us[1], q1))) + G.need(relative == dx + dy, "The two query factorization") + G.need(all(not actual[N+p] for p in selected), "No selected borrowed hidden row") + results["selected_conjugate" if swap else "unpermuted"] = { + "arbitrary_two_bank_columns": 224, + "hidden_columns": len(ordinary), + "residual_rank_regression": G.rank(defect), + "hidden_rank_regression": G.rank(relative), + "hidden_X_rank": G.rank(relative[:N]), + "hidden_Y_rank": G.rank(relative[N:]), + } + return { + "schema": "clean-reflection-hidden-check-v1", + "status": "PASS", + "actual_model_sha256": G.PIN, + "selected_ports": sorted(selected), + "variants": results, + "scope": "Exact ordered content. Signed stage conjugations are a regression, not an actual routed lower bound. No new native service or decoder.", + } + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + result = check() + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(json.dumps({"status": result["status"], "sha256": sha256(args.out.read_bytes()).hexdigest()})) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/check_reciprocal_caller.py b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/check_reciprocal_caller.py new file mode 100644 index 0000000000..f97b85bc6d --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/check_reciprocal_caller.py @@ -0,0 +1,260 @@ +#!/usr/bin/env python3 +"""Check the reciprocal caller with exact rational matrices.""" + +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 +LANES = HERE.parents[1] +MODEL = LANES / "oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz" +PIN = "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0" + + +def need(value, text): + if not value: + raise ValueError(text) + + +def rows(raw): + return [{int(j): F(x) for j, x in row.items() if F(x)} for row in raw] + + +def eye(n): + return [{i: F(1)} for i in range(n)] + + +def zero(n): + return [{} for _ in range(n)] + + +def put(row, j, x): + value = row.get(j, F(0)) + x + if value: + row[j] = value + else: + row.pop(j, None) + + +def add(a, b, scale=1): + out = [dict(row) for row in a] + for row, extra in zip(out, b): + for j, x in extra.items(): + put(row, j, scale * x) + return out + + +def mul(a, b): + out = [] + for row in a: + result = {} + for j, x in row.items(): + for k, y in b[j].items(): + put(result, k, x * y) + out.append(result) + return out + + +def trans(a, width): + out = zero(width) + for i, row in enumerate(a): + for j, x in row.items(): + out[j][i] = x + return out + + +def block(a, b, c, d): + n = len(a) + return [ + dict(list(left.items()) + [(n + j, x) for j, x in right.items()]) + for left, right in zip(a + c, b + d) + ] + + +def diag(a): + z = zero(len(a)) + return block(a, z, z, a) + + +def lower(a): + n = len(a) + return block(eye(n), zero(n), a, eye(n)) + + +def upper(a): + n = len(a) + return block(eye(n), a, zero(n), eye(n)) + + +def neg(a): + return [{j: -x for j, x in row.items()} for row in a] + + +def rank(a): + basis = {} + for source in a: + row = dict(source) + while row: + p = min(row) + x = row[p] + if p not in basis: + basis[p] = {j: y / x for j, y in row.items()} + break + for j, y in basis[p].items(): + put(row, j, -x * y) + return len(basis) + + +def sign_matrix(n, stage): + return [{p: F(-1 if ((p * (stage + 3) + p // (stage + 2)) % 5) < 2 else 1)} + for p in range(n)] + + +def replay(word, n): + state = eye(n) + for op, target, source, raw in word: + value = F(raw) + if op == "add": + need(target != source, "Distinct ADD fields") + for j, x in state[source].items(): + put(state[target], j, value * x) + else: + need(op == "scale" and value, "An invertible scalar scale") + state[target] = {j: value * x for j, x in state[target].items()} + return state + + +def check(): + raw = gzip.decompress(MODEL.read_bytes()) + need(sha256(raw).hexdigest() == PIN, "The actual model pin") + source = json.loads(raw) + matrices = {name: rows(value) for name, value in source["physical"].items()} + e, p, r, j, ji = (matrices[name] for name in ("E", "P", "R", "J", "inverse_J")) + ei = matrices["inverse_E"] + u, ell = rows(source["reflection_U"]), rows(source["reflection_L"]) + n = 112 + i, z = eye(n), zero(n) + need(mul(p, p) == mul(r, r) == i, "The two involutions") + need(mul(p, r) == e and mul(r, p) == ei, "The ordered E factors") + need(mul(e, ei) == mul(ei, e) == i, "Both E inverse orders") + need(mul(ji, j) == mul(j, ji) == i, "Both metric inverse orders") + need(mul(trans(e, n), mul(j, e)) == j, "The E metric") + need(mul(trans(p, n), mul(j, p)) == j, "The P metric") + need(mul(trans(r, n), mul(j, r)) == j, "The R metric") + need(mul(ji, mul(trans(e, n), j)) == ei, "The inverse metric order") + need(mul(j, mul(e, ji)) == trans(ei, n), "The inverse-adjoint metric order") + need(mul(ell, u) == [{k: F(-2)} for k in range(16)], "L U=-2I") + need(add(i, mul(u, ell)) == r, "The actual reflection factor") + need(rank(add(r, i, -1)) == 16 and rank(add(e, i, -1)) == 32, + "The actual correction ranks") + special = set(source["special_ports"]) + need(len(special) == 32, "The exact special-port count") + for row, delta in enumerate(add(p, i, -1)): + need(not delta or row in special, "P changed rows stay selected") + need(all(col in special for col in delta), "P changed columns stay selected") + need(sum(len(row) for row in p) == 160, "P is not a monomial") + need(replay(source["scalar_words"]["P"], n) == p, "The actual scalar P word") + need(all(e[k].get(k, 0) == ei[k].get(k, 0) == 0 for k in range(n)), + "Both actual response diagonals") + + ps, rs, us, ls = [], [], [], [] + for stage in range(3): + s = eye(n) if stage == 0 else sign_matrix(n, stage) + ps.append(mul(s, mul(p, s))) + rs.append(mul(s, mul(r, s))) + us.append(mul(s, u)) + ls.append(mul(ell, s)) + need(mul(rs[0], rs[1]) != mul(rs[1], rs[0]), "A noncommuting stage test") + h, hi = mul(ps[1], ps[0]), mul(ps[0], ps[1]) + pt, pti = mul(ps[2], h), mul(hi, ps[2]) + rh = [rs[0], mul(ps[0], mul(rs[1], ps[0])), mul(hi, mul(rs[2], h))] + uh = [us[0], mul(ps[0], us[1]), mul(hi, us[2])] + lh = [ls[0], mul(ls[1], ps[0]), mul(ls[2], h)] + ks = [add(a, i, -1) for a in rh] + for k, col, row in zip(ks, uh, lh): + need(mul(col, row) == k, "The transported rank factor") + fs = [mul(diag(ps[s]), lower(rs[s])) for s in range(3)] + b1 = mul(diag(ps[1]), upper(neg(rs[1]))) + f1i = mul(lower(neg(rs[1])), diag(ps[1])) + need(mul(diag(ji), mul(trans(f1i, 2*n), diag(j))) == b1, + "The whole wrapped inverse-adjoint metric conversion") + triple = mul(fs[2], mul(b1, fs[0])) + stripped = mul(diag(pti), triple) + expected = mul(lower(rh[2]), mul(upper(neg(rh[1])), lower(rh[0]))) + need(stripped == expected, "The ordered transported triple") + wi = block(z, i, neg(i), z) + t = mul(wi, stripped) + a0 = lower(ks[0]) + a1 = block(add(i, ks[1], -1), neg(ks[1]), ks[1], add(i, ks[1])) + a2 = upper(neg(ks[2])) + need(mul(a2, mul(a1, a0)) == t, "The three square-zero factors") + for a in (a0, a1, a2): + delta = add(a, eye(2*n), -1) + need(mul(delta, delta) == zero(2*n), "A square-zero difference") + need(rank(delta) == 16, "Each exact factor rank") + a0i = lower(neg(ks[0])) + a1i = block(add(i, ks[1]), ks[1], neg(ks[1]), add(i, ks[1], -1)) + a2i = upper(ks[2]) + ti = mul(a0i, mul(a1i, a2i)) + need(mul(ti, t) == mul(t, ti) == eye(2*n), "Both residual inverse orders") + + x = [dict(row) for row in eye(2*n)[:n]] + y = [dict(row) for row in eye(2*n)[n:]] + c0 = mul(ls[0], x) + after0 = mul(fs[0], x + y) + c1 = mul(ls[1], after0[n:]) + after1 = mul(b1, after0) + c2 = mul(ls[2], after1[:n]) + want_x = add(add(x, mul(uh[1], c1), -1), mul(uh[2], c2)) + want_y = add(add(y, mul(uh[0], c0)), mul(uh[1], c1)) + need(t == want_x + want_y, "All224 source-record columns") + need(rank(add(t, eye(2*n), -1)) <= 48, "The residual rank bound") + need(mul(pt, pti) == mul(pti, pt) == i, "Both common-code inverse orders") + for row, delta in enumerate(add(pt, i, -1)): + need(not delta or row in special, "The common code has selected rows") + need(all(col in special for col in delta), "The common code has selected columns") + + controls = { + "omit_P_transport": mul(lower(rs[2]), mul(upper(neg(rs[1])), lower(rs[0]))) != stripped, + "reverse_reflection_factors": mul(a0, mul(a1, a2)) != t, + "use_E_as_involution": mul(e, e) != i, + "omit_first_query_transport": mul(ls[1], add(y, mul(rs[0], x))) != c1, + } + need(all(controls.values()), "Every negative control rejects") + return { + "schema": "reciprocal-selected-baseline-check-v1", + "status": "PASS", + "model_sha256": PIN, + "actual_ports": n, + "actual_reflection_rank": 16, + "actual_E_minus_I_rank": 32, + "physical_P_nonzeros": 160, + "physical_P_support": sorted(special), + "three_stage_regression": "Independent signed conjugations of the actual112 model; not D25 routes.", + "two_bank_columns": 224, + "ordered_source_queries": 3, + "factor_ranks": [16, 16, 16], + "regression_residual_rank": rank(add(t, eye(2*n), -1)), + "both_inverse_orders": True, + "negative_controls": controls, + "native_record_or_scatter_claim": False, + "scope": "Exact matrix and ordered caller proof. The native service, saved records, phase scatter, host and full supplier remain separate.", + } + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + result = check() + args.out.parent.mkdir(parents=True, exist_ok=True) + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(json.dumps({"status": result["status"], "sha256": sha256(args.out.read_bytes()).hexdigest()})) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json new file mode 100644 index 0000000000..3924fe2465 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json @@ -0,0 +1,27210 @@ 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No separate centre-query child is needed. Every data +field receives total native rank eight. This packet proves the exact +scalar maps and the nested-frame schedule. It does not yet certify the +native phases, the ordinary response on the other 64 ports, a recursive +host, or a complete supplier. + +The full 48-port signed response is in this family. The family also +contains nontrivial responses whose inverses remain in the family. Thus +the schedule is not limited to one centre correction or one matrix. + +## Actual pair coordinates + +Use the pinned pair incidence and signed centre rows K. For each physical +pair e=(a,b), incident to vertices v,w, set + +```text +A_e = [[K_va, K_vb], [K_wa, K_wb]]. +A_e A_e^T = 2I, A_e^-1 = A_e^T/2. +``` + +Let A be the direct sum of these 24 two-field codes. The two coded +carriers use the original physical field labels a,b. Carrier a belongs +to v and carrier b belongs to w. At each vertex, order its six carriers +by their occurrence in the pinned `pair_edges` list. The payload records +these orders in `cyclic_carriers`. + +Let z=45. On a pair, q_a+q_b=z over F_2. Its plane is +P_e=span(z,q_a)=span(z,q_b). At each vertex the six chosen representatives +q_0,...,q_5 are orthonormal. They are all orthogonal to z. The seven +vectors z,q_0,...,q_5 are independent and span U_v. These are exact facts +about the pinned 9-bit directions. + +The current signed response J and signed ordinary term G satisfy + +```text +A G A^-1 = direct_sum_v alpha_v I_6, +A J A^-1 = direct_sum_v alpha_v (I_6 - 1_6 1_6^T). +``` + +Each J block has zero diagonal. The checker verifies the two identities +by applying each inverse pair-code column in original coordinates, then +applying G or J and the pair code. It checks all 2304 entries of each +conjugation. + +## The cyclic schedule + +Indices in this section are modulo six. For k=1,...,5 define + +```text +S_i(k) = span(z,q_i,q_(i+1),...,q_(i+k-1)), +T_j(k) = span(z,q_(j-k),...,q_(j-1)). +``` + +Both spaces have dimension k+1. They increase with k. The decisive +identity is S_i(k)=T_(i+k)(k). + +First advance both source fields of each physical pair from their +entry lines to P_e. Apply A_e there. Apply the same pair code to the two +target fields while both are still at I. Advance every affected coded +target to Z=span(z). + +For k=1,...,5, advance coded source i to S_i(k), and coded target j to +T_j(k). At this step add + +```text +Y_(i+k) += B_v[i+k,i] X_i +``` + +for all six i and all eight vertices. The two fields in each addition +have exactly the same frame. Each ordered off-diagonal pair occurs once. +There is no update to a source value. Hence the order of these additions +does not impose a relation between their coefficients. + +After step five, advance each coded source directly from its rank-six +frame to FULL, with rank three. Apply the inverse pair codes at FULL. + +For target i the last frame is + +```text +T_i(5) = U_v intersect P_i^perp. +``` + +It is contained in P_i^perp. Advance both coded fields of each physical +pair to that common rank-seven frame. Apply the inverse pair code there. +Each restored physical target then advances to its own rank-eight hole +q_p^perp. The inclusion P_e^perp subset q_p^perp holds for both endpoints +of the pair. No nonzero value receives a free change of frame. + +The other 64 fields of each data bank advance directly with rank eight. +Their response coefficient is zero in this packet. All 416 other fields, +including the eight unused C labels, are arbitrary and unchanged. The +word does not use owned or private fields. + +## Full forward and backward maps + +Let B be any direct sum of eight zero-diagonal six by six matrices, and +let E=A^-1 B A on the affected ports. Extend E by zero on the other +64 ports. The forward logical map is + +```text +(x,y,h) -> (x,y+E x,h). +``` + +The same frame paths give the backward map. At each common-frame step, +replace the forward addition by + +```text +X_i -= B_v[i+k,i] Y_(i+k). +``` + +The logical result is (x-E^T y,y,h). To see the transpose, use +AA^T=2I. It gives A^-1 B^T A=E^T. No response matrix is commuted through +a source C_q map. With the current source and target endpoint adapters, +the intended physical entries and exits are the same as the earlier +pair-coded service. Those adapters and every new native edge still need +their exact phase certificate. + +The checker represents each of the 240 entries of B by a separate +formal parameter. A reverse event replay checks all 640 columns in both +directions. It permits no product of two parameters. It then compares +each coefficient with A^-1 B A or its negative transpose. This proves +the full coefficient family, not only the signed J example. + +## Reciprocal responses inside the family + +Let M and N be any three by three units over Z[1/2]. Then + +```text +B = [[0,M], [N,0]], +B^-1 = [[0,N^-1], [M^-1,0]]. +``` + +Both matrices have zero diagonal. They therefore use this same frame +schedule. Taking N=M^-1 gives an involution. Taking N=M^T gives a +symmetric reciprocal pair. Transposes also have zero diagonal, so an +inverse-adjoint response remains available. The scalar invoice depends +on the exact dyadic coefficients chosen. + +This gives an inverse-closed block family with two free three by three +units per vertex. It is a sufficient family, not a classification of all +invertible zero-diagonal matrices with zero-diagonal inverse. The checker +includes explicit nontrivial triangular dyadic M,N and checks both +inverse orders and an involution. These statements concern the affected +48-port block. A unit on all 112 ports also requires a compatible unit +on the other 64 ports. + +## Local invoice and limits + +For either direction, the fixed schedule has the profile + +| Native rank | Children | +| --- | ---: | +| 1 | 624 | +| 3 | 48 | +| 8 | 128 | + +There are 800 children and native mass 1792. All this mass is productive +progress on the 224 data fields. The 48 affected source paths use ranks +1,1,1,1,1,3. The 48 affected target paths use eight ranks of one. The +other 128 fields each use one rank-eight child. There is no query rank. + +The literal pair codes and inverse codes cost 1880 real scalar +primitives across both data banks. For a nonzero dyadic coefficient +c=a/2^k in lowest terms, the stated scalar lowering charges its complex +ADD as + +```text +2 (1 + bit_length(abs(a)) + popcount(abs(a)) + bit_length(2^k)). +``` + +Sum that charge over the nonzero entries of B. Zero entries need no ADD. +The full signed J48 uses 240 signed unit additions, so its scalar count +is 3800 in either direction. Exact prefix row-sum bounds for this example +are in `CHECKS.json`. They bound top-level array norms, not the internal +state of a recursive child. + +There are 224 endpoint maps and at most 1600 native side maps. This +schedule trades extra children and side maps for zero separate query +rank. Native mass alone does not give its recursive cost or an exponent. +The full 64-port response, native phases, helper completion, memory host, +recursive precision, and final assembly are separate duties. No selected +frontier or complete kappa calculation changes in this packet. + +## Verification and credit + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/check_cyclic_flags.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/cyclic-pair-flags-20261018/check_cyclic_flags.py +``` + +The expected output is `PASS_CYCLIC_PAIR_FLAGS`. Both runs must produce +the same payload and receipt bytes. The checker rejects omission of one +cyclic transfer. It also checks the direct diagonal obstruction: q_i is +in P_i but not in q_i^perp, since q_i has odd norm. This last fact concerns +this monotone direct-transfer schedule only. + +The root lane supplied the common radical and pair conjugation. The +oblique-native lane supplied the productive pair-code construction. The +controller lane supplied the actual signed centre and pair geometry. +This lane derived the cyclic schedule. The root lane identified its +general zero-diagonal family and asked for reciprocal extensions. This +work was produced with AI assistance. Independent review and native +phase lowering are requested separately. No publication is authorized. diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/CHECKS.json b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/CHECKS.json new file mode 100644 index 0000000000..e038735717 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/CHECKS.json @@ -0,0 +1,185 @@ +{ + "balanced_response": [ + { + "inverse": false, + "row_norms": [ + 11, + 7 + ], + "transfer_tariff": 188 + }, + { + "inverse": true, + "row_norms": [ + 11, + 7 + ], + "transfer_tariff": 188 + } + ], + "dimensions_checked": [ + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16, + 17, + 18, + 19, + 20, + 21, + 22, + 23, + 24, + 25, + 26, + 27, + 28, + 29, + 30, + 31, + 32 + ], + "negative_controls": [ + "wrong reflection coefficient", + "E as its inverse", + "omitted pair undo", + "inverse without transpose", + "n=2 rank-one exception", + "real nonrational symmetric example" + ], + "physical_columns_per_direction": 48, + "physical_correction_ranks": [ + 16, + 16 + ], + "physical_determinants": [ + "1", + "1" + ], + "query_geometry": [ + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 0 + }, + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 1 + }, + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 2 + }, + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 3 + }, + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 4 + }, + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 5 + }, + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 6 + }, + { + "plane_dimensions": [ + 6, + 3, + 7 + ], + "query_supports": [ + 5, + 2 + ], + "union_support": 6, + "vertex": 7 + } + ], + "scope": "Exact response algebra and actual pair binding. No native or terminal price.", + "source_pins": { + "lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "root/RECIPROCAL-RANK-TWO-20261020.json": "971df2cc46160babf79b668c5677ab03e48ae86551d727db05c6f4118fc6658e", + "root/RECIPROCAL-RANK-TWO-20261020.md": "5d7855b2360093629530aceb91d38204a9a0a42654f53a150f35279efc8de172", + "root/RECIPROCAL-RANK-TWO-ADDENDUM-20261020.md": "7c7bf50e6f61af68ecda8a4c0cc4d6ba0cbf9a89aec9ccbeedc3eec794da486d", + "root/RECIPROCAL-RANK-TWO-FREEZE-20261020.json": "4cc076c7b551ee2f4259de10ef3cd0e00fa395882b4175f12af948f7eefb5b75", + "root/check_reciprocal_rank_two_20261020.py": "2fc272bf47b7840f5464b1f589f16d069e66b6cd41c8d2fce03f9f04878635bc" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_RANK_TWO" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/FREEZE.json b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/FREEZE.json new file mode 100644 index 0000000000..41b71e1cf6 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/FREEZE.json @@ -0,0 +1,10 @@ +{ + "files": { + "CHECKS.json": "6c24c5a9ae096409998da667f1d237231c82aba43383853e2e1b96565cb7e978", + "REPRODUCTION.json": "e24d55be9675c4b86659d0b1962832c54fdbb0b875b6d3f9bfae4d4829cccdff", + "REVIEW.md": "433986a1cb73d646ab53f7bc14708cff44ef63e61648bf253ccf81e3325ee557", + "check_review.py": "1865f145988de9702474a0f2ff042725d1001ad15ddd216c58a61199c5a7a88e" + }, + "scope": "No native phases, terminal implementation, or complete supplier price.", + "status": "PASS_INDEPENDENT_ALGEBRA_AND_BINDING" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/REPRODUCTION.json b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/REPRODUCTION.json new file mode 100644 index 0000000000..718c2786be --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/REPRODUCTION.json @@ -0,0 +1,15 @@ +{ + "runs": [ + { + "mode": "normal", + "receipt_sha256": "6c24c5a9ae096409998da667f1d237231c82aba43383853e2e1b96565cb7e978", + "stdout": "PASS_INDEPENDENT_RECIPROCAL_RANK_TWO\nreceipt_sha256=6c24c5a9ae096409998da667f1d237231c82aba43383853e2e1b96565cb7e978\n" + }, + { + "mode": "optimized", + "receipt_sha256": "6c24c5a9ae096409998da667f1d237231c82aba43383853e2e1b96565cb7e978", + "stdout": "PASS_INDEPENDENT_RECIPROCAL_RANK_TWO\nreceipt_sha256=6c24c5a9ae096409998da667f1d237231c82aba43383853e2e1b96565cb7e978\n" + } + ], + "status": "PASS_BYTE_IDENTICAL" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/REVIEW.md b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/REVIEW.md new file mode 100644 index 0000000000..0cc67767f9 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/REVIEW.md @@ -0,0 +1,167 @@ +# Independent review of the reciprocal rank-two response + +The response theorem passes. The construction is an integer unit in each +dimension n at least three. Both the response and its inverse have zero +diagonal. Each differs from the identity by rank two, which is the least +possible rank under these hypotheses. The literal 48-port pair code gives +rank 16 in each direction. + +The frozen proof has one wording defect about query support. Its addendum +corrects that defect. The first correction coordinate uses five modes; +the second uses two; their union uses all six. Only the first coordinate +has the stated proposed rank-five capture to the common radical. No +capture implementation or price follows from this observation. + +This review covers exact response algebra, the pair-coordinate binding, +and the balanced response in the addendum. It does not cover new native +phases, a response on the other 64 ports, a controller, a terminal decoder, +or the complete recursive cost. + +## Independent derivation + +Put m=n-2. Let P exchange the final two coordinates. Let +u=(1,...,1,m-2,0) and l=(-1,...,-1,1,0). Their product l*u is -2. +Thus R=I+u*l is an involution: + +```text +R² = I + (2+l*u)u*l = I. +``` + +R has eigenvalue -1 on u and is the identity on the kernel of l. Its +determinant is -1. Since det(P)=-1, E=P*R has determinant one, with inverse +R*P. Direct action on a basis vector gives the two displayed formulas in +the producer proof. This also proves their zero diagonals. + +For the displayed E-I=UV factor, U is injective and V is onto its +two-dimensional range: their indicated two by two minors are units. +Therefore rank(UV)=2. This uses the injectivity of U, not just the separate +rank statements. Also E^-1-I=-E^-1(E-I), so the inverse has the same +correction rank. The equation Vx=0 is exactly sum(a)=b=c. + +For the lower bound, rank zero contradicts a zero diagonal. In rank one, +A=I+u*v and u_i*v_i=-1 for each i. Therefore v*u=-n. The inverse formula +has denominator 1-n, which is nonzero in characteristic zero. Its +diagonal is (n-2)/(n-1), which is nonzero for n at least three. The +dimension and characteristic hypotheses matter. The two-dimensional +coordinate exchange has correction rank one and is its own inverse. + +No commutation between P and R is used. In fact E is not an involution +in dimension six. Replacing the inverse by E fails the exact check. + +## The symmetry restriction + +The producer's six-dimensional proof is valid. A stronger statement also +holds: for every integer n at least five, a symmetric rational unit with +zero diagonal and zero-diagonal inverse cannot have rank(A-I)=2. + +To prove it, diagonalize A over the reals. There are n-2 eigenvalues equal +to one and two other eigenvalues a,b. The two trace equations give + +```text +a+b=-(n-2), 1/a+1/b=-(n-2), ab=1. +``` + +For n at least five the two eigenvalues are distinct and real. Their +difference is sqrt(n(n-4)). Let u,v be their orthonormal eigenvectors. +The diagonal equations for A and A^-1 have the coefficients of u_i² +and v_i² exchanged. Their difference gives u_i²=v_i². Either equation +then gives u_i²=v_i²=1/n. Write u=sigma/sqrt(n) and v=tau/sqrt(n), where +sigma,tau are sign vectors. The spectral formula is + +```text +A = I - (sigma*sigma^T+tau*tau^T)/2 + + sqrt(n(n-4)) (sigma*sigma^T-tau*tau^T)/(2n). +``` + +For every n at least five, + +```text +(n-3)² < n(n-4) < (n-2)². +``` + +The left difference is 2n-9, and the right difference is 4. Thus the +square root is irrational. Rational entries of A force the last +coefficient matrix to vanish. The two rank-one projectors would then +be equal, in conflict with u perpendicular to v. This proves the claim. +For odd n, orthogonality of the two sign vectors already fails over +the reals. + +This extension gives a lower bound of three, not a claim of attainment +in every dimension. In dimension six, three disjoint exchanges attain +rank three. The rational premise is necessary: with n=6, sigma all +positive, and tau=(1,1,1,-1,-1,-1), the displayed formula gives a real +symmetric rank-two example over Q(sqrt(3)). The checker verifies its +zero diagonals and both inverse orders with exact pairs of rationals. + +## Actual pair coordinates and orientation + +The review pins the cyclic-family payload and checks its two partitions: +24 signed physical pairs and eight six-mode vertex lists. It applies +each pair code to a physical basis column, applies P and R directly to +each vertex's six values, and applies the inverse pair code. It does +not import the producer or multiply the producer's response matrices. + +All 48 forward columns and all 48 inverse columns equal the frozen +producer matrices. Both composition orders are the identity. The two +physical determinants are one; both correction ranks are 16; both +physical diagonals are zero. The checker also verifies the actual +binary query-plane dimensions. They are six for the first query, +three for the second query, and seven for their combined support, +including the common radical in each case. + +The cyclic transfer family requires zero diagonal in the mode matrix. +Both E and E^-1 meet this condition. The backward transfer computes the +negative transpose of its mode matrix. A reciprocal backward response +therefore uses E^-T as its generator. The pair code satisfies AA^T=2I, +which gives A^-1 B^T A=(A^-1 B A)^T. This is the required compatibility +with the physical transpose. It does not move a matrix through a C_q +chart. The physical inverse is not symmetric, so omitting the transpose +would change the required map. + +The rank reduction is a response-space result. A scalar rank-two factor +does not grant access to the two values at a hole frame. The reflection +and the coordinate exchange each have nonzero diagonal entries, so they +cannot each be substituted into the zero-diagonal transfer schedule. + +## Balanced response + +The addendum's conjugation D^-1 E D, with +D=diag(1,1,1,1,-2,2), gives its two stated formulas. Both are integer +units; both have correction rank two and zero diagonal. The maximum +absolute row sums fall from 11 to 7 in each direction. The four by four +a-to-a block stays unchanged. + +The independent coefficient invoice is 188 real scalar primitives per +six-mode transfer in either direction, before and after this change. +This is the sum of the cyclic family's stated ADD tariffs. It is not a +complete native invoice. In particular, it does not price the pair +codes, source access, frame changes, or a terminal. The row-sum bound is +a bound on this matrix, not on all prefixes or a recursive child's state. + +## Reproduction and scope + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/check_review.py +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/check_review.py +``` + +Expected output starts with `PASS_INDEPENDENT_RECIPROCAL_RANK_TWO`. +The receipt must be byte-identical in the two modes. The checker verifies +the source hashes before it uses any data. Its arithmetic uses exact +integers and fractions. Finite checks in dimensions 3 through 32 support +the all-dimension derivation above; they do not replace it. + +Controls reject a changed reflection coefficient, the use of E as its +inverse, and an omitted pair undo. The checker also distinguishes the +inverse from its transpose, the excluded n=2 case, and the real +nonrational symmetric example. No producer code is imported. + +The root lane supplied the reciprocal response and its balanced form. +The cyclic family supplies the actual coordinate system and transfer +condition. This lane supplied a separate derivation, column check, +support correction, and the symmetry extension. OpenAI Codex assisted +this work. No PR, push, or publication is authorized. Before any PR +description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/check_review.py b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/check_review.py new file mode 100644 index 0000000000..9f5c912c03 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/reciprocal-rank-two-review-20261020/check_review.py @@ -0,0 +1,269 @@ +#!/usr/bin/env python3 +"""Check the reciprocal response with a separate column method.""" + +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +CAMPAIGN = HERE.parents[2] +PINS = { + "root/RECIPROCAL-RANK-TWO-20261020.md": + "5d7855b2360093629530aceb91d38204a9a0a42654f53a150f35279efc8de172", + "root/check_reciprocal_rank_two_20261020.py": + "2fc272bf47b7840f5464b1f589f16d069e66b6cd41c8d2fce03f9f04878635bc", + "root/RECIPROCAL-RANK-TWO-20261020.json": + "971df2cc46160babf79b668c5677ab03e48ae86551d727db05c6f4118fc6658e", + "root/RECIPROCAL-RANK-TWO-FREEZE-20261020.json": + "4cc076c7b551ee2f4259de10ef3cd0e00fa395882b4175f12af948f7eefb5b75", + "root/RECIPROCAL-RANK-TWO-ADDENDUM-20261020.md": + "7c7bf50e6f61af68ecda8a4c0cc4d6ba0cbf9a89aec9ccbeedc3eec794da486d", + "lanes/independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", +} + + +def need(ok, reason): + if not ok: + raise ValueError(reason) + + +def rank(rows): + rows = [list(map(F, row)) for row in rows] + k = 0 + for j in range(len(rows[0])): + p = next((i for i in range(k, len(rows)) if rows[i][j]), None) + if p is None: + continue + rows[k], rows[p] = rows[p], rows[k] + lead = rows[k][j] + rows[k] = [x / lead for x in rows[k]] + for i in range(k + 1, len(rows)): + lead = rows[i][j] + rows[i] = [x - lead * y for x, y in zip(rows[i], rows[k])] + k += 1 + if k == len(rows): + break + return k + + +def bitrank(values): + basis = {} + for x in values: + while x: + k = x.bit_length() + if k not in basis: + basis[k] = x + break + x ^= basis[k] + return len(basis) + + +def determinant(rows): + a = [list(map(F, r)) for r in rows] + answer = F(1) + for k in range(len(a)): + p = next((i for i in range(k, len(a)) if a[i][k]), None) + if p is None: + return F(0) + if p != k: + a[p], a[k] = a[k], a[p] + answer = -answer + d = a[k][k] + answer *= d + for i in range(k + 1, len(a)): + c = a[i][k] / d + a[i] = [x - c * y for x, y in zip(a[i], a[k])] + return answer + + +def unit(n, j): + return [F(i == j) for i in range(n)] + + +def reflect(x, wrong=False): + m = len(x) - 2 + value = x[m] - sum(x[:m]) + u = [1] * m + [m - 2 + int(wrong), 0] + return [a + b * value for a, b in zip(x, u)] + + +def swap(x): + return list(x[:-2]) + [x[-1], x[-2]] + + +def act(x, inverse=False): + return reflect(swap(x)) if inverse else swap(reflect(x)) + + +def correction_rank(columns): + n = len(columns) + return rank([[columns[j][i] - (i == j) for j in range(n)] + for i in range(n)]) + + +def quad_add(x, y): + return x[0] + y[0], x[1] + y[1] + + +def quad_mul(x, y): + return x[0] * y[0] + 3 * x[1] * y[1], x[0] * y[1] + x[1] * y[0] + + +def main(): + for name, expected in PINS.items(): + need(sha256((CAMPAIGN / name).read_bytes()).hexdigest() == expected, + "Source pin: " + name) + source = json.loads((CAMPAIGN / next(p for p in PINS if p.endswith("CYCLIC-FLAGS.json"))).read_text()) + producer = json.loads((CAMPAIGN / "root/RECIPROCAL-RANK-TWO-20261020.json").read_text()) + dimensions = [] + for n in range(3, 33): + e = [act(unit(n, j)) for j in range(n)] + inverse = [act(unit(n, j), True) for j in range(n)] + for j in range(n): + need(act(e[j], True) == act(inverse[j]) == unit(n, j), "Two inverse orders") + need(e[j][j] == inverse[j][j] == 0, "Two zero diagonals") + need(reflect(reflect(unit(n, j))) == unit(n, j), "Reflection square") + need(correction_rank(e) == correction_rank(inverse) == 2, "Two correction ranks") + need(determinant(e) == determinant(inverse) == 1, "Integer unit") + for j in range(n - 2): + x = unit(n - 2, j) + [F(1), F(1)] + need(act(x) == x, "Fixed basis") + dimensions.append(n) + # The n=2 exchange is the excluded rank-one example. + need(correction_rank([unit(2, 1), unit(2, 0)]) == 1, "Dimension hypothesis") + need(any(swap(reflect(swap(reflect(unit(6, j))))) != unit(6, j) + for j in range(6)), "Reject E in place of its inverse") + need(any(reflect(reflect(unit(6, j), True), True) != unit(6, j) + for j in range(6)), "Reject changed reflection coefficient") + + def balanced(x, inverse=False): + d = [1, 1, 1, 1, -2, 2] + return [y / t for y, t in zip(act([t * y for t, y in zip(d, x)], inverse), d)] + + def tariff(columns): + return sum(2 * (1 + abs(x.numerator).bit_length() + + abs(x.numerator).bit_count() + x.denominator.bit_length()) + for col in columns for x in col if x) + + balanced_counts = [] + for inverse in [False, True]: + original = [act(unit(6, j), inverse) for j in range(6)] + adjusted = [balanced(unit(6, j), inverse) for j in range(6)] + for j in range(6): + x = unit(6, j) + a, b, c = x[:4], x[4], x[5] + s = sum(a) + formula = ([v - s + 2 * c for v in a] + [s - 3 * c, -b] + if inverse else [v - s - 2 * b for v in a] + [-c, -s - 3 * b]) + need(adjusted[j] == formula, "Balanced displayed formula") + need(balanced(adjusted[j], not inverse) == x, "Balanced inverse order") + norms = [max(sum(abs(col[i]) for col in cs) for i in range(6)) + for cs in [original, adjusted]] + need(norms == [11, 7], "Original and balanced row norms") + need(tariff(original) == tariff(adjusted) == 188, "Equal transfer tariff") + need(correction_rank(adjusted) == 2, "Balanced correction rank") + need(all(original[j][i] == adjusted[j][i] for i in range(4) for j in range(4)), + "The a-to-a minor is unchanged") + balanced_counts.append({"inverse": inverse, "row_norms": [11, 7], "transfer_tariff": 188}) + + ports = source["affected_ports"] + carriers = source["cyclic_carriers"] + need(len(carriers) == 8 and all(len(c) == 6 for c in carriers), "Eight six-mode blocks") + need(sorted(p for c in carriers for p in c) == ports, "Mode partition") + need(sorted(p for pair in source["pair_codes"] for p in pair["ports"]) == ports, + "Pair partition") + + def pair_code(x, inverse=False): + answer = {} + for pair in source["pair_codes"]: + ps, h = pair["ports"], pair["matrix"] + for i, p in enumerate(ps): + answer[p] = sum(F(h[j][i], 2) * x[ps[j]] if inverse + else F(h[i][j]) * x[ps[j]] for j in range(2)) + return answer + + def physical(x, inverse=False, omit_undo=False): + coded = pair_code(x) + mixed = {} + for c in carriers: + mixed.update(zip(c, act([coded[p] for p in c], inverse))) + return mixed if omit_undo else pair_code(mixed, True) + + columns = [] + inverse_columns = [] + for j, p in enumerate(ports): + x = {q: F(p == q) for q in ports} + need(pair_code(pair_code(x), True) == x, "Actual pair inverse") + y, z = physical(x), physical(x, True) + need(physical(y, True) == physical(z) == x, "Physical inverse orders") + columns.append([y[q] for q in ports]) + inverse_columns.append([z[q] for q in ports]) + need([y[q] for q in ports] == [F(row[j]) for row in producer["physical_response"]], + "Independent physical response column") + need([z[q] for q in ports] == [F(row[j]) for row in producer["physical_inverse"]], + "Independent physical inverse column") + need(correction_rank(columns) == correction_rank(inverse_columns) == 16, + "Physical correction ranks") + need(determinant(columns) == determinant(inverse_columns) == 1, "Physical determinants") + need(all(columns[j][j] == inverse_columns[j][j] == 0 for j in range(48)), + "Physical zero diagonals") + need(any(physical({p: F(p == q) for p in ports}, omit_undo=True) != + physical({p: F(p == q) for p in ports}) for q in ports), + "Reject omitted pair undo") + need(columns != [list(row) for row in zip(*columns)], "Response is asymmetric") + need(inverse_columns != [list(row) for row in zip(*inverse_columns)], + "Backward inverse needs a transpose in the generator") + + query_geometry = [] + for v, c in enumerate(carriers): + qs = [source["ports"][p] for p in c] + z = source["common_line"] + need(all((a & b).bit_count() % 2 == (i == j) + for i, a in enumerate(qs) for j, b in enumerate(qs)), + "Orthonormal mode representatives") + ranks = [bitrank([z] + qs[:5]), bitrank([z] + qs[4:]), bitrank([z] + qs)] + need(ranks == [6, 3, 7], "First, second, and combined query planes") + query_geometry.append({"vertex": v, "query_supports": [5, 2], "union_support": 6, + "plane_dimensions": ranks}) + + # A real symmetric example shows why rational entries are a material premise. + signs = [1, 1, 1, -1, -1, -1] + a = [[(F(i == j) - F(1 + signs[i] * signs[j], 2), + F(1 - signs[i] * signs[j], 6)) for j in range(6)] for i in range(6)] + b = [[(x, -y) for x, y in row] for row in a] + for x, y in [(a, b), (b, a)]: + for i in range(6): + for j in range(6): + entry = (F(0), F(0)) + for k in range(6): + entry = quad_add(entry, quad_mul(x[i][k], y[k][j])) + need(entry == (F(i == j), F(0)), "Quadratic-field inverse") + need(all(a[i][i] == b[i][i] == (0, 0) for i in range(6)), "Real example diagonals") + need(any(y for row in a for _, y in row), "The real example is not rational") + need(all((n - 3) ** 2 < n * (n - 4) < (n - 2) ** 2 for n in range(5, 101)), + "Discriminant inequalities corroboration") + receipt = { + "status": "PASS_INDEPENDENT_RECIPROCAL_RANK_TWO", + "source_pins": PINS, + "dimensions_checked": dimensions, + "physical_columns_per_direction": 48, + "physical_correction_ranks": [16, 16], + "physical_determinants": ["1", "1"], + "balanced_response": balanced_counts, + "query_geometry": query_geometry, + "negative_controls": ["wrong reflection coefficient", "E as its inverse", + "omitted pair undo", "inverse without transpose", + "n=2 rank-one exception", "real nonrational symmetric example"], + "scope": "Exact response algebra and actual pair binding. No native or terminal price.", + } + raw = (json.dumps(receipt, indent=2, sort_keys=True) + "\n").encode() + (HERE / "CHECKS.json").write_bytes(raw) + print(receipt["status"]) + print("receipt_sha256=" + sha256(raw).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/CHECKS-OPTIMIZED.json b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/CHECKS-OPTIMIZED.json new file mode 100644 index 0000000000..972cfeaeb7 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/CHECKS-OPTIMIZED.json @@ -0,0 +1,228 @@ +{ + "accepted_phase_review_freeze": "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c", + "new_spatial_phase_checks": 0, + "old_native_payload": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "phase_scope": "Complete ordered frames, native occurrences, full recipes and endpoint records are byte-equal to the accepted source. No new phase recipe is introduced.", + "reports": { + "base": { + "backward_inverse_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "backward_inverse_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 2, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 7080 + }, + "backward_transpose_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "16", + "scalar_real": 6440 + }, + "forward_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "46", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "60", + "scalar_real": 7080 + } + }, + "extra": { + "backward_inverse_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "backward_inverse_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 2, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 7080 + }, + "backward_transpose_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "16", + "scalar_real": 6440 + }, + "forward_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "46", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "60", + "scalar_real": 7080 + } + } + }, + "scope": "Complete local data service. Outside fields are identity, without productive helper progress. Routed controller, terminal, child host and precision are separate.", + "source_pins": { + "MODEL-FREEZE.json": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7", + "NATIVE-FREEZE.json": "ced70c0c6fe961b1a840819ee5e8cce2756a229d4eee7ec3b5a6f8e4bac6c6eb", + "NATIVE.md": "1fe48a47d0dca937f8ccc5c27936b3d679cf6c997c6f9156ca4158554a9f19a7", + "emit_native.py": "b6db27a1a7e990ac297972f0306efa624bfa317d70bcb18615a38a4b8d2aac03", + "model-normal-v2/RESPONSE.json.gz": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "native-normal/CHECKS.json": "e3e6b18efae3b93fa48b95c0c2f238caff1ec3f5a9948bd880e21c9cf75d31b0", + "native-normal/NATIVE.json.gz": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e" + }, + "status": "PASS_INDEPENDENT_SIGNED_METRIC_NATIVE", + "words": 12 +} diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/FINAL-CHECKS.json b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/FINAL-CHECKS.json new file mode 100644 index 0000000000..972cfeaeb7 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/FINAL-CHECKS.json @@ -0,0 +1,228 @@ +{ + "accepted_phase_review_freeze": "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c", + "new_spatial_phase_checks": 0, + "old_native_payload": "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4", + "phase_scope": "Complete ordered frames, native occurrences, full recipes and endpoint records are byte-equal to the accepted source. No new phase recipe is introduced.", + "reports": { + "base": { + "backward_inverse_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "backward_inverse_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 2, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 7080 + }, + "backward_transpose_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "16", + "scalar_real": 6440 + }, + "forward_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "46", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "60", + "scalar_real": 7080 + } + }, + "extra": { + "backward_inverse_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "backward_inverse_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 2, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 7080 + }, + "backward_transpose_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "16", + "scalar_real": 6440 + }, + "forward_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "46", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_E": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "30", + "scalar_real": 6440 + }, + "forward_inverse_adjoint_by_metric": { + "arbitrary_outside_fields": 416, + "binary_height": 1, + "endpoint_maps": 224, + "exact_inherited_recipes": 1561, + "input_columns": 640, + "native_children": 1632, + "native_mass": 1792, + "native_profile": { + "1": 1520, + "2": 64, + "3": 48 + }, + "native_side_map_bound": 3264, + "prefix_row_one_norm": "60", + "scalar_real": 7080 + } + } + }, + "scope": "Complete local data service. Outside fields are identity, without productive helper progress. Routed controller, terminal, child host and precision are separate.", + "source_pins": { + "MODEL-FREEZE.json": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7", + "NATIVE-FREEZE.json": "ced70c0c6fe961b1a840819ee5e8cce2756a229d4eee7ec3b5a6f8e4bac6c6eb", + "NATIVE.md": "1fe48a47d0dca937f8ccc5c27936b3d679cf6c997c6f9156ca4158554a9f19a7", + "emit_native.py": "b6db27a1a7e990ac297972f0306efa624bfa317d70bcb18615a38a4b8d2aac03", + "model-normal-v2/RESPONSE.json.gz": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "native-normal/CHECKS.json": "e3e6b18efae3b93fa48b95c0c2f238caff1ec3f5a9948bd880e21c9cf75d31b0", + "native-normal/NATIVE.json.gz": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e" + }, + "status": "PASS_INDEPENDENT_SIGNED_METRIC_NATIVE", + "words": 12 +} diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/FREEZE.json b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/FREEZE.json new file mode 100644 index 0000000000..7e177a3c29 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/FREEZE.json @@ -0,0 +1,13 @@ +{ + "files": { + "CHECKS-OPTIMIZED.json": "18ede33f0dcfbcceb57ea2b8c2b82e06afe173000defd42fd7af39a607ef5e12", + "FINAL-CHECKS.json": "18ede33f0dcfbcceb57ea2b8c2b82e06afe173000defd42fd7af39a607ef5e12", + "REVIEW.md": "01bc6ca15a488f3e92dbc237e07433343f3f10c2a3af6a6b6e9708f9cd85f0fd", + "check_review.py": "27e995087c5d5d8642a8ef52a849964fa107f0d3340fe88bca63dabb5399e4a8" + }, + "normal_optimized_bytes_equal": true, + "scope": "All12 local native words,640 arbitrary fields, inherited exact phases, literal inverse adjoints and metric wrappers. No global controller, productive helper progress, host or supplier.", + "source_native_decompressed_sha256": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e", + "source_native_freeze": "ced70c0c6fe961b1a840819ee5e8cce2756a229d4eee7ec3b5a6f8e4bac6c6eb", + "status": "FROZEN_INDEPENDENT_SIGNED_METRIC_NATIVE" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/REVIEW.md b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/REVIEW.md new file mode 100644 index 0000000000..3733a1473a --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/REVIEW.md @@ -0,0 +1,220 @@ +# Independent native review of the signed reciprocal response + +All twelve frozen local words pass the independent check. This covers +both providers, the four direct shear words, and the two metric +wrappers per provider. Each word has the stated map on all 640 +arbitrary input fields. The 416 fields outside the two data banks +retain their values and frames. + +No material error was found. The four direct words cost 6,440 +existing real scalar primitives each. Each metric wrapper costs +7,080. All words have native profile 1520 H1+64 H2+48 H3, rank mass +1,792, and 1,632 children. + +This is a complete local data-service review. It does not establish +productive progress on the unchanged helpers, a routed controller, +a terminal, a recursive child host, or a complete supplier bound. + +## Pins and independent method + +The reviewed producer freeze is +`oblique-native-20261017/signed-metric-reciprocal-20261020/NATIVE-FREEZE.json`, +with digest +`ced70c0c6fe961b1a840819ee5e8cce2756a229d4eee7ec3b5a6f8e4bac6c6eb`. +The model freeze has digest +`9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7`. +The native payload has decompressed digest +`f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e`. + +The preceding accepted native source is +`new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz`, +with decompressed digest +`d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4`. +Its independent phase review is +`new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json`, +with digest +`c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c`. +The accepted review's input manifest binds this exact source. +Paths in this section are relative to the campaign `lanes` directory. + +The new checker imports no producer, compiler, or prior interpreter. +It uses exact fractions and separate forward-row and reverse-column +calculations. It also reconstructs both direct retunings from the +physical response through the actual pair matrices. Every unchanged +source event is compared directly. + +The bridge-review lane separately owns the signed-metric matrix +theorem and the later completion. This review checks the matrix +identities needed by the native words and their complete literal use. +It does not substitute for that broader theorem review. +That companion review is frozen in +`bridge-review-20261017/signed-metric-review-20261020`, with freeze +`b44b5a95c1fa8372bbd979f360fde743df10c16bd07ac4d5015c048982539762` +and proof +`79ffc65f3037d00a03fbfa99e0a24ab3c889412602be21a022399ad59f8599f1`. + +## Response and physical contracts + +Let E be the actual physical response and J its physical diagonal +metric. The checker confirms both inverse orders, the exact +inverse-transpose matrix, and + +```text +E^-T = J E J^-1. +``` + +The physical metric has 80 entries 1, sixteen entries -1/2, and +sixteen entries -1/4. Thus J and its inverse are dyadic units. +The actual pair basis gives zero mode diagonal for both E and E^-T. + +With Q the positive portwise line, q=Q^-1, and F the common +nine-axis advance, the direct contracts are + +| Word | Input | Output | +|---|---|---| +| forward E | (Qx,y) | (Fx,Fq(y+Ex)) | +| backward transpose E | (Qx,y) | (F(x-E^T y),Fq y) | +| forward inverse adjoint E | (Qx,y) | (Fx,Fq(y+E^-T x)) | +| backward inverse E | (Qx,y) | (F(x-E^-1 y),Fq y) | + +All factors keep this order. In particular, the response matrix is +not moved through the field-dependent Q. + +For each direct forward word, the checker takes the accepted source +transfer positions and obtains the new coefficient from H E H^-1 +or H E^-T H^-1. It removes exactly the zero transfers. All other +scalar events and all native events retain their exact source bytes. +The complete resulting event lists equal the emitted lists. + +## Literal inverse adjoint + +For a chronological word G1,...,Gn, the physical operator is +M=Gn...G1. Its inverse adjoint is + +```text +M^-* = Gn^-* ... G1^-*. +``` + +Thus the chronological order stays fixed. A real ADD(t,s,c) +becomes ADD(s,t,-c), and a real SCALE(c) becomes SCALE(1/c). +Each native unitary and each endpoint monomial is unchanged, +including its phase. + +The checker compares both complete backward event lists with this +literal transformation. It does not merely check their expected +cross blocks. At each transposed ADD, the two fields still have the +same ordered frame. Scalar instructions do not change a frame, so +the unchanged native chronology gives the same full frame ledger. + +The endpoint adapters are also unitary and unchanged. If + +```text +M = diag(F,Fq) S_E diag(q,I), +``` + +then the same two endpoint factors occur in M^-*. The content shear +changes from `(x,y+Ex)` to `(x-E^T y,y)`. Applying the same argument +to the E^-T forward word gives `(x-E^-1 y,y)`. This proves the +physical table without an extra chart transition. + +## Metric wrappers + +The forward metric wrapper applies J^-1 to both input banks, +runs the forward E word, then applies J to both output banks. +Its cross block is J E J^-1=E^-T. + +The backward metric wrapper applies J to both input banks, +runs the backward transpose word, then applies J^-1 to both +output banks. Its cross block is + +```text +-J^-1 E^T J = -E^-1. +``` + +J is a scalar diagonal on physical fields. It therefore commutes +with every field's spatial operator even when different fields have +different frames. This is not an assumption that J commutes with E. + +The checker verifies every prefix and suffix scale, its actual +field, and its actual input or output frame. It verifies that the +whole core between those scales is unchanged. Scales on distinct +fields can occur in different orders; the exact per-field action +is checked. Each wrapper contains 128 added complex-field SCALE +instructions, with a cost of 640 real scalar primitives. A +one-bank metric price would omit the baseline restoration in +the other bank. + +## Frames, phases, and arbitrary fields + +Every native occurrence has the same field, ordered old frame, +ordered new frame, rank, and recipe key as the accepted source. +Every complete frame table, start vector, final vector, native +recipe table, and endpoint adapter table is byte-equal to it. + +There are 1,561 inherited recipe records and 224 inherited endpoint +records. The accepted spatial review covers 685 inherited pairs +and 876 further pairs checked on all 512 spatial columns. The +union of those accepted keys is exactly the table used here. +No new native operator or endpoint phase is introduced. + +This review therefore uses exact phase inheritance. It does not +claim a fresh spatial replay. Equal subspaces or equal ranks would +not have been enough; the ordered frames and complete recipes +must agree. + +The independent ledger checks strict nested progress, each rank +difference, every ADD's equal ordered frames, and all final frames. +Each data field receives exactly eight productive ranks. No event +reads or writes any of the other 416 fields. There is no CLEAR, +private field, owned field, or zero-input premise. + +The reverse calculation checks all 640 input columns of each +complete scalar content word. A forward calculation checks the +same map and all scalar prefixes. Since the coefficients are real, +the content equations hold on arbitrary complex fields; the +inherited frame operators retain the complete complex phases. + +## Local cost and bounds + +| Word | Real scalar cost | Prefix row one-norm | Binary height | +|---|---:|---:|---:| +| forward E | 6440 | 46 | 1 | +| backward transpose E | 6440 | 16 | 1 | +| forward inverse adjoint E | 6440 | 30 | 1 | +| backward inverse E | 6440 | 30 | 1 | +| forward metric wrapper | 7080 | 60 | 1 | +| backward metric wrapper | 7080 | 30 | 2 | + +The native profile is 1520 H1+64 H2+48 H3 in every row. It has +1,632 children and rank mass 1,792. There are 224 explicit +endpoint maps and an upper bound of 3,264 native side maps. +The direct retuning avoids the wrapper's 640-unit surcharge. + +The norms and heights above concern literal top-level content +prefixes. They do not include recursive child interiors or a +complete finite-precision analysis. The unchanged helpers have +identity action, not the productive progress required by some +outer constructions. + +## Reproduction + +Run the checker twice with new output files: + +```text +python3 check_review.py --out FINAL-CHECKS.json +python3 -O check_review.py --out CHECKS-OPTIMIZED.json +``` + +Both runs pass with identical receipts. The checker rejects an +omitted nonzero transfer in each principal direction and provider. +It also checks that a changed recipe record cannot inherit the +accepted table. All producer and predecessor bytes are preserved. + +The producer supplied the reciprocal coefficient words and metric +wrappers. Earlier lanes supplied the pair geometry, cyclic paths, +and phase recipes. This lane supplied the independent native +composition and invoice check. AI assistance was used. + +No PR, push, commit, or publication is authorized. Before a future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/check_review.py b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/check_review.py new file mode 100644 index 0000000000..549d9fff18 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/independent-review-20261017/signed-metric-native-review-20261020/check_review.py @@ -0,0 +1,312 @@ +"""Review all signed reciprocal native words without the producer interpreter.""" + +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 / "oblique-native-20261017/signed-metric-reciprocal-20261020" +PINS = { + "NATIVE-FREEZE.json": "ced70c0c6fe961b1a840819ee5e8cce2756a229d4eee7ec3b5a6f8e4bac6c6eb", + "MODEL-FREEZE.json": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7", + "NATIVE.md": "1fe48a47d0dca937f8ccc5c27936b3d679cf6c997c6f9156ca4158554a9f19a7", + "emit_native.py": "b6db27a1a7e990ac297972f0306efa624bfa317d70bcb18615a38a4b8d2aac03", + "model-normal-v2/RESPONSE.json.gz": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + "native-normal/NATIVE.json.gz": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e", + "native-normal/CHECKS.json": "e3e6b18efae3b93fa48b95c0c2f238caff1ec3f5a9948bd880e21c9cf75d31b0", +} +OLD = LANES / "new-core-transfer-20261017/low-displacement-20261020/odd16-normal-v2/EXTENSION-PROGRAM.json.gz" +OLD_PIN = "d466cea24be92fb7f749d686c5efc63f44ea82575c15f78c38e9d6d4c972eba4" +PEER = LANES / "new-native-recipes-20261017/low-displacement-review-20261020" +PEER_PIN = "c8fccfbe49ddd8747095a43aa1c1c59b0270bbbf73d94a317a79113191e4e34c" + + +def need(value, label): + if not value: + raise ValueError(label) + + +def read(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 rows(raw): + return [{int(j): F(value) for j, value in row.items()} for row in raw] + + +def eye(size): + return [{j: F(1)} for j in range(size)] + + +def add(target, source, value): + for j, x in source.items(): + result = target.get(j, F(0)) + value*x + if result: + target[j] = result + else: + target.pop(j, None) + + +def multiply(a, b): + result = [] + for row in a: + target = {} + for j, value in row.items(): + add(target, b[j], value) + result.append(target) + return result + + +def transpose(a, width): + result = [{} for _ in range(width)] + for i, row in enumerate(a): + for j, value in row.items(): + result[j][i] = value + return result + + +def span(vectors): + result = {0} + for v in vectors: + result |= {x ^ v for x in result} + return result + + +def tariff(gate): + op, _, _, raw = gate + value = F(raw) + a, b = abs(value.numerator), value.denominator + need(a and b & (b-1) == 0, "Nonzero dyadic coefficient") + if op == "scale": + need(a & (a-1) == 0, "Dyadic unit scale") + return 2*(abs(a.bit_length()-b.bit_length()) + (value < 0)) + need(op == "add", "Known scalar primitive") + return 2*(1+a.bit_length()+a.bit_count()+b.bit_length()) + + +def reverse_columns(events): + columns = eye(640) + for event in reversed(events): + if event[0] == "native": + continue + op, target, origin, raw = event[1] + value = F(raw) + if op == "scale": + columns[target] = {j: value*x for j, x in columns[target].items()} + else: + add(columns[origin], columns[target], value) + return columns + + +def shear_columns(response, backward): + result = eye(640) + for target, row in enumerate(response): + for origin, value in row.items(): + if backward: + add(result[112+target], {origin: -value}, F(1)) + else: + add(result[origin], {112+target: value}, F(1)) + return result + + +def inverse_adjoint_events(events): + result = [] + for event in events: + if event[0] == "native": + result.append(event) + continue + _, gate, frame = event + op, target, origin, raw = gate + value = F(raw) + new = [op, origin, target, str(-value)] if op == "add" else [op, target, None, str(1/value)] + result.append(["scalar", new, frame]) + return result + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + need(not args.out.exists(), "New output path") + saved = {name: read(SOURCE/name, pin) for name, pin in PINS.items()} + native = json.loads(saved["native-normal/NATIVE.json.gz"]) + model = json.loads(saved["model-normal-v2/RESPONSE.json.gz"]) + old = json.loads(read(OLD, OLD_PIN)) + need(native["model"] == model, "Exact model binding") + peer = json.loads(read(PEER/"EXTENSIONS-REVIEW-FREEZE.json", PEER_PIN)) + for name, pin in peer["files"].items(): + read(PEER/name, pin) + accepted_inputs = json.loads((PEER/"extensions-normal/EXTENSIONS-INPUTS.json").read_bytes()) + need(accepted_inputs[str(OLD.relative_to(LANES))]["decompressed_sha256"] == OLD_PIN, + "The accepted spatial review consumed this exact native source") + accepted = json.loads((PEER/"extensions-normal/EXTENSIONS-REVIEW.json").read_bytes())["extensions"]["odd-grid-rank16"] + fresh = accepted["fresh_native_phase_checks"] + need(len(fresh) == 876 and all(row["spatial_columns"] == 512 for row in fresh), + "Accepted complete spatial checks") + accepted_keys = set(accepted["exact_inherited_frame_pairs"]) | {row["edge"] for row in fresh} + + e, ei = rows(model["physical"]["E"]), rows(model["physical"]["inverse_E"]) + ej = rows(model["physical"]["inverse_adjoint_E"]) + j, ji = rows(model["physical"]["J"]), rows(model["physical"]["inverse_J"]) + h, hi = rows(model["pair_code"]), rows(model["pair_code_inverse"]) + need(multiply(e, ei) == multiply(ei, e) == eye(112), "Actual inverse orders") + need(ej == transpose(ei, 112), "Exact inverse adjoint") + need(multiply(j, ji) == multiply(ji, j) == eye(112), "Metric unit") + need(all(set(row) == {p} for p, row in enumerate(j)), "Physical diagonal metric") + need(multiply(multiply(j, e), ji) == ej, "Actual physical metric conversion") + need(Counter(row[p] for p, row in enumerate(j)) == Counter({F(1): 80, F(-1, 2): 16, F(-1, 4): 16}), + "Actual signed metric entries") + modes = {"forward_E": multiply(multiply(h, e), hi), + "forward_inverse_adjoint_E": multiply(multiply(h, ej), hi)} + need(all(p not in row for matrix in modes.values() for p, row in enumerate(matrix)), + "Both complete mode diagonals vanish") + + def wrapped_events(events, frames_in, frames_out, forward): + pre, post = (ji, j) if forward else (j, ji) + result = [] + for bank in (0, 112): + for p, row in enumerate(pre): + if row[p] != 1: + result.append(["scalar", ["scale", bank+p, None, str(row[p])], frames_in[bank+p]]) + prefix = len(result) + result += events + for bank in (0, 112): + for p, row in enumerate(post): + if row[p] != 1: + result.append(["scalar", ["scale", bank+p, None, str(row[p])], frames_out[bank+p]]) + return result, prefix + + reports = {} + for provider in ("base", "extra"): + original = old["providers"][provider]["forward"] + words = native["providers"][provider] + need(set(original["native_recipes"]) == accepted_keys, "Accepted phase recipe coverage") + need(len(original["native_recipes"]) == 1561 and len(original["endpoint_adapters"]) == 224, + "Complete inherited phase and endpoint tables") + transfer_slots = {record["event"] for record in original["transfer_records"]} + need(len(transfer_slots) == len(original["transfer_records"]), "Unique transfer positions") + for name, mode in modes.items(): + expected_events = [] + for index, event in enumerate(original["events"]): + if index not in transfer_slots: + expected_events.append(event) + continue + need(event[0] == "scalar" and event[1][0] == "add", "Actual source transfer slot") + _, target, origin, _ = event[1] + need(112 <= target < 224 and 0 <= origin < 112, "Actual forward transfer addresses") + coefficient = mode[target-112].get(origin, F(0)) + if coefficient: + expected_events.append(["scalar", ["add", target, origin, str(coefficient)], event[2]]) + need(words[name]["events"] == expected_events, "Independent complete retuning: " + name) + need(words["backward_transpose_E"]["events"] == inverse_adjoint_events(words["forward_E"]["events"]), + "First literal inverse-adjoint chronology") + need(words["backward_inverse_E"]["events"] == inverse_adjoint_events(words["forward_inverse_adjoint_E"]["events"]), + "Second literal inverse-adjoint chronology") + for name, base, forward in ( + ("forward_inverse_adjoint_by_metric", "forward_E", True), + ("backward_inverse_by_metric", "backward_transpose_E", False)): + expected, prefix = wrapped_events(words[base]["events"], original["start"], original["final"], forward) + actual = words[name]["events"] + need(prefix == 64 and len(actual) == len(expected), "Complete two-bank wrapper size") + need(actual[prefix:-prefix] == words[base]["events"], "Unchanged core inside wrapper") + for left, right in ((actual[:prefix], expected[:prefix]), (actual[-prefix:], expected[-prefix:])): + need(sorted(left, key=lambda event: event[1][1]) == + sorted(right, key=lambda event: event[1][1]), + "Exact per-field diagonal wrapper: " + name) + + reports[provider] = {} + for name, word in words.items(): + for key in ("native_recipes", "endpoint_adapters", "frames", "start", "final"): + need(word[key] == original[key], "Exact inherited physical object: " + key) + need([e for e in word["events"] if e[0] == "native"] == + [e for e in original["events"] if e[0] == "native"], "Exact native occurrence order") + current, state = list(word["start"]), eye(640) + need(len(current) == 640, "All640 arbitrary roles") + profile, progress = Counter(), Counter() + scalar, maximum, height = 0, F(1), 0 + spaces = [span(frame) for frame in word["frames"]] + for event in word["events"]: + if event[0] == "native": + _, field, before, after, rank, key = event + need(0 <= field < 224 and current[field] == before, "Native field and old frame") + need(spaces[before] < spaces[after], "Strict nested native progress") + need(rank == len(word["frames"][after])-len(word["frames"][before]) == + word["native_recipes"][key]["rank"], "Actual native rank") + need(key == str(before)+":"+str(after), "Ordered recipe key") + current[field] = after + profile[rank] += 1 + progress[field] += rank + continue + need(event[0] == "scalar", "Only scalar and native events") + _, gate, frame = event + op, target, origin, raw = gate + value = F(raw) + need(0 <= target < 224 and current[target] == frame, "Scalar target frame") + if op == "add": + need(0 <= origin < 224 and origin != target and current[origin] == frame, + "Equal ordered source and target frames") + add(state[target], state[origin], value) + else: + need(op == "scale" and origin is None, "Scale syntax") + state[target] = {p: value*x for p, x in state[target].items()} + scalar += tariff(gate) + maximum = max(maximum, sum(map(abs, state[target].values()), F(0))) + for value in state[target].values(): + need(value.denominator & (value.denominator-1) == 0, "Dyadic scalar prefix") + height = max(height, value.denominator.bit_length()-1) + need(current == word["final"], "Complete final frames") + need(all(progress[p] == 8 for p in range(224)), "Eight productive ranks on each data field") + need(profile == Counter({1: 1520, 2: 64, 3: 48}), "Complete native profile") + need(all(current[p] == word["start"][p] and state[p] == {p: F(1)} for p in range(224, 640)), + "All416 arbitrary outside fields and frames unchanged") + response = e if name in ("forward_E", "backward_transpose_E") else ej + backward = name.startswith("backward") + expected_columns = shear_columns(response, backward) + need(reverse_columns(word["events"]) == expected_columns, "All640 independent reverse columns") + need(transpose(state, 640) == expected_columns, "All640 forward rows agree") + expected_scalar = 7080 if name.endswith("by_metric") else 6440 + need(scalar == expected_scalar, "Exact complete scalar invoice") + reports[provider][name] = { + "input_columns": 640, "arbitrary_outside_fields": 416, "scalar_real": scalar, + "prefix_row_one_norm": str(maximum), "binary_height": height, + "native_profile": dict(sorted(profile.items())), "native_children": sum(profile.values()), + "native_mass": sum(k*v for k, v in profile.items()), "endpoint_maps": 224, + "native_side_map_bound": 2*sum(profile.values()), "exact_inherited_recipes": 1561, + } + for name in ("forward_E", "backward_inverse_E"): + events = list(words[name]["events"]) + index = next(record["event"] for record in words[name]["transfer_records"]) + del events[index] + response = e if name == "forward_E" else ej + need(reverse_columns(events) != shear_columns(response, name.startswith("backward")), + "Missing-transfer negative control") + malformed = dict(words["forward_E"]["native_recipes"]) + key = next(iter(malformed)) + malformed[key] = dict(malformed[key]) + malformed[key]["rank"] += 1 + need(malformed != original["native_recipes"], "Altered recipe negative control") + need(reports["base"] == reports["extra"], "Both provider receipts") + receipt = { + "status": "PASS_INDEPENDENT_SIGNED_METRIC_NATIVE", + "source_pins": PINS, "old_native_payload": OLD_PIN, "accepted_phase_review_freeze": PEER_PIN, + "reports": reports, "words": 12, + "new_spatial_phase_checks": 0, + "phase_scope": "Complete ordered frames, native occurrences, full recipes and endpoint records are byte-equal to the accepted source. No new phase recipe is introduced.", + "scope": "Complete local data service. Outside fields are identity, without productive helper progress. Routed controller, terminal, child host and precision are separate.", + } + args.out.write_text(json.dumps(receipt, sort_keys=True, indent=2)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/frozen/lanes/interface-proof/verify_native_lift.py b/research/reciprocal-native-responses/frozen/lanes/interface-proof/verify_native_lift.py new file mode 100644 index 0000000000..fb72255b9c --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/interface-proof/verify_native_lift.py @@ -0,0 +1,336 @@ +"""Check the exact native lift and the finite local bill. + +The checker does not import the emitter or the Clifford compiler. It uses +Pauli conjugation and a separate exact state interpreter. The scalar map is +owned by the independent transpose replay in the adjacent review lane. +""" +from collections import Counter +from fractions import Fraction +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json +import resource +import subprocess +import tarfile +import time + +BASE = 'bce54fb3f895cbe5cd4c0eb477c3afeed100190f' +ARCHIVE = 'research/community-frontier1042-audit/selected-replay.tar.gz' +ARCHIVE_HASH = '22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754' +PINS = { + 'CANONICAL-WORD.json.gz': '16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219', + 'LOCAL-PROGRAMS.json.gz': '241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a', + 'CLIFFORD-RECIPES.json': 'd0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731', + 'RESIDUAL-ADAPTERS.json': '383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c', +} + + +def require(condition, label): + if not condition: + raise ValueError(label) + + +def load(repo): + args = ['git', 'show', BASE + ':' + ARCHIVE] + proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE) + digest = sha256() + while chunk := proc.stdout.read(65536): + digest.update(chunk) + require(proc.wait() == 0 and digest.hexdigest() == ARCHIVE_HASH, 'archive pin') + proc = subprocess.Popen(args, cwd=repo, stdout=subprocess.PIPE) + values = {} + with tarfile.open(fileobj=proc.stdout, mode='r|gz') as archive: + for entry in archive: + name = entry.name.removeprefix('slots/local/') + if entry.name.startswith('slots/local/') and name in PINS: + raw = archive.extractfile(entry).read() + require(sha256(raw).hexdigest() == PINS[name], name + ' pin') + values[name] = json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw) + require(proc.wait() == 0 and set(values) == set(PINS), 'source extraction') + return values + + +def parity(value): + return value.bit_count() % 2 + + +def mul(matrix, vector): + return sum(parity(row & vector) << i for i, row in enumerate(matrix)) + + +def transpose(matrix): + return tuple(sum(((row >> j) & 1) << i for i, row in enumerate(matrix)) for j in range(len(matrix))) + + +def inverse(matrix): + n = len(matrix) + rows = [row | (1 << (n+i)) for i, row in enumerate(matrix)] + for j in range(n): + pivot = next((i for i in range(j, n) if rows[i] >> j & 1), None) + require(pivot is not None, 'singular binary chart') + rows[j], rows[pivot] = rows[pivot], rows[j] + for i in range(n): + if i != j and rows[i] >> j & 1: + rows[i] ^= rows[j] + require([row & ((1 << n)-1) for row in rows] == [1 << i for i in range(n)], 'binary inverse') + return tuple(row >> n for row in rows) + + +def extend(vectors, n): + columns, pivots = [], {} + for value in tuple(vectors) + tuple(1 << i for i in range(n)): + reduced = value + while reduced: + j = reduced.bit_length()-1 + if j not in pivots: + pivots[j] = reduced + columns.append(value) + break + reduced ^= pivots[j] + require(len(columns) == n, 'frame basis extension') + return tuple(columns) + + +def adjoint(circuit): + out = [] + for gate in reversed(circuit): + if gate[0] == 'P': + out.append(('P', inverse(gate[1]))) + elif gate[0] == 'D': + out.append(('D', gate[1], tuple(-a % 4 for a in gate[2]))) + elif gate[0] == 'C': + out.append(('C', gate[1], -gate[2])) + elif gate[0] == 'phase': + out.append(('phase', -gate[1] % 4)) + else: + require(gate[0] == 'X', 'adjoint gate type') + out.append(gate) + return tuple(out) + + +def fourier(rank): + return tuple(('C', 1 << i, 1) for i in range(rank)) + + +def frame(vectors, n): + rank = len(vectors) + if rank == 0: + return () + if rank == n: + return fourier(n) + matrix = transpose(extend(vectors, n)) + columns = transpose(inverse(matrix)) + quadratic = tuple((1 << i) ^ sum(parity(a & b) << j for j, b in enumerate(columns)) for i, a in enumerate(columns)) + diagonal = tuple((row >> i) & 1 for i, row in enumerate(quadratic)) + chart = (('P', matrix), ('D', quadratic, diagonal)) + return adjoint(chart) + fourier(rank) + chart + + +def monomial(record): + matrix = tuple(record['matrix_rows']) + quadratic = tuple(record['quadratic_rows']) + linear = tuple(record['linear_Z4']) + require(transpose(quadratic) == quadratic, 'quadratic symmetry') + require(len(matrix) == len(quadratic) == len(linear) == 9, 'monomial dimension') + require(all(a % 2 == (quadratic[i] >> i) & 1 for i, a in enumerate(linear)), 'diagonal parity') + inverse(matrix) + return (('D', quadratic, linear), ('P', matrix), ('X', record['offset']), ('phase', record['phase'])) + + +def recipe(record): + rank = record['rank'] + require(isinstance(rank, int) and 0 <= rank <= 9, 'child rank') + if rank == 0: + require(record['right'] is None, 'rank zero right factor') + return monomial(record['left']) + return monomial(record['right']) + fourier(rank) + monomial(record['left']) + + +def tableau(circuit, n=9): + rows = [(1 << i, 0, 0) for i in range(n)] + [(0, 1 << i, 0) for i in range(n)] + for gate in circuit: + tag = gate[0] + out = [] + inverse_transpose = transpose(inverse(gate[1])) if tag == 'P' else None + for x, z, phase in rows: + if tag == 'P': + x, z = mul(gate[1], x), mul(inverse_transpose, z) + elif tag == 'X': + phase += 2 * parity(z & gate[1]) + elif tag == 'C': + if parity(z & gate[1]): + x ^= gate[1] + phase += 3 * gate[2] + elif tag == 'D': + quadratic, linear = gate[1:] + phase += sum(linear[i] for i in range(n) if x >> i & 1) + phase += 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(n) if x >> i & 1) + z ^= mul(quadratic, x) + else: + require(tag == 'phase', 'tableau gate type') + out.append((x, z, phase % 4)) + rows = out + return tuple(rows) + + +@lru_cache(maxsize=512) +def action(gate): + if gate[0] == 'P': + return tuple(mul(gate[1], x) for x in range(512)) + require(gate[0] == 'D', 'state action type') + quadratic, linear = gate[1:] + return tuple((sum(linear[i] for i in range(9) if x >> i & 1) + + 2 * sum(parity((quadratic[i] >> (i+1)) & (x >> (i+1))) for i in range(9) if x >> i & 1)) % 4 for x in range(512)) + + +def rotate(pair, power): + a, b = pair + return ((a, b), (-b, a), (-a, -b), (b, -a))[power % 4] + + +def state(circuit, basis=0): + value = [(0, 0)] * 512 + value[basis] = (1, 0) + denominator = 0 + for gate in circuit: + tag = gate[0] + if tag == 'P': + moved = [(0, 0)] * 512 + for source, target in enumerate(action(gate)): + moved[target] = value[source] + value = moved + elif tag == 'X': + value = [value[x ^ gate[1]] for x in range(512)] + elif tag == 'D': + value = [rotate(pair, p) for pair, p in zip(value, action(gate))] + elif tag == 'phase': + value = [rotate(pair, gate[1]) for pair in value] + elif tag == 'C': + direction, sign = gate[1:] + moved = [] + for x, (a, b) in enumerate(value): + c, d = value[x ^ direction] + moved.append((a-sign*b+c+sign*d, b+sign*a+d-sign*c)) + value = moved + denominator += 1 + else: + raise ValueError('state gate type') + while denominator and all((a | b) % 2 == 0 for a, b in value): + value = [(a//2, b//2) for a, b in value] + denominator -= 1 + return value, denominator + + +def equal(actual, expected, label): + require(tableau(actual) == tableau(expected), label + ': Pauli action') + require(state(actual) == state(expected), label + ': global phase') + + +def scalar_cost(gate): + if gate[0] in ('copy', 'clear'): + return 1 + value = Fraction(*gate[-2:]) + numerator, denominator = abs(value.numerator), value.denominator + require(numerator > 0 and denominator & (denominator-1) == 0, 'nonzero dyadic scalar') + if gate[0] == 'scale': + require(numerator & (numerator-1) == 0, 'dyadic scale unit') + return abs(numerator.bit_length()-denominator.bit_length()) + (value < 0) + require(gate[0] == 'add', 'scalar type') + return 3 + numerator.bit_length()-1 + numerator.bit_count() + denominator.bit_length()-1 + + +def main(args): + start = time.monotonic() + data = load(args.repo) + word = data['CANONICAL-WORD.json.gz'] + old = data['LOCAL-PROGRAMS.json.gz'] + phase = data['CLIFFORD-RECIPES.json'] + residual = data['RESIDUAL-ADAPTERS.json']['recipes'] + changed_raw = gzip.decompress(args.changed.read_bytes()) + require(sha256(changed_raw).hexdigest() == 'fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877', 'changed payload pin') + changed = json.loads(changed_raw) + require(set(changed) == {'forward', 'backward'}, 'orientation inventory') + native = lambda events: [e for e in events if e[0] in ('climb', 'adapter', 'residual_adapter')] + invoices = {} + for name, events in changed.items(): + require(native(events) == native(old[name]), 'persistent native stream') + require(all(e[0] in ('scalar', 'phase', 'climb', 'adapter', 'residual_adapter') for e in events), 'event grammar') + first = events.index(['phase', 'centre_dirty_correction']) + last = events.index(['phase', 'A']) + prefix = [e[1] for e in events[first+1:last]] + require(all(e[0] == 'scalar' and e[2] == 0 for e in events[first+1:last]), 'correction frame') + scalars = [e[1] for e in events if e[0] == 'scalar'] + paid = Counter(e[5] for e in events if e[0] == 'climb') + invoices[name] = { + 'events': len(events), 'scalar_macros': len(scalars), + 'real_component_primitive_bound': 2*sum(map(scalar_cost, scalars)), + 'prefix_macros': dict(Counter(e[0] for e in prefix)), + 'prefix_real_component_primitive_bound': 2*sum(map(scalar_cost, prefix)), + 'paid_profile': dict(sorted(paid.items())), + 'paid_rank_sum': sum(rank*count for rank, count in paid.items()), + 'persistent_native_events': len(native(events)), + } + used = {(e[3], e[4]) for e in changed['forward'] if e[0] == 'climb'} + children = {(r['old'], r['new']): r for r in phase['children']} + require(len(children) == len(phase['children']) and used <= set(children), 'child recipe binding') + frames = [frame(tuple(vectors), 9) for vectors in word['frames']] + for i, (a, b) in enumerate(sorted(used)): + record = children[a, b] + require(record['rank'] == len(word['frames'][b])-len(word['frames'][a]), 'paid frame difference') + equal(recipe(record), adjoint(frames[a])+frames[b], 'child '+str((a, b))) + if i % 500 == 0: + print('phase edges', i, '/', len(used), flush=True) + endpoints = {(r['role'], r['port']): r for r in phase['endpoint_adapters']} + require(set(endpoints) == {(role, p) for role in ('source', 'target') for p in range(112)}, 'endpoint coverage') + for (role, port), record in endpoints.items(): + q = word['ports'][port] + conventional = (('C', q, 1),) if role == 'source' else (('C', q, -1),)+fourier(9) + expected_frame = word['start'][port] if role == 'source' else word['final'][112+port] + require(record['frame'] == expected_frame and record['rank'] == 0, 'endpoint frame binding') + equal(recipe(record), adjoint(conventional)+frames[expected_frame], 'endpoint '+str((role, port))) + used_residual = set() + for event in changed['forward']: + if event[0] == 'residual_adapter': + _, position, register, entry, *tail = event + terminal = tail[0] if tail else 1 + key = str(entry) if terminal == 1 else str(entry)+':'+str(terminal) + require(key in residual and position in ('pre', 'post'), 'residual binding') + require(entry == word['start'][register] and terminal == word['final'][register], 'residual boundary') + used_residual.add(key) + for key in sorted(used_residual): + record = residual[key] + entry = record['frame'] + terminal = record.get('terminal', 1) + equal(recipe(record), adjoint(frames[entry])+frames[terminal], 'residual '+key) + probe = next(r for r in children.values() if r['left']['phase'] != 0 or r['right'] and r['right']['phase'] != 0) + correct = recipe(probe) + corrupt = tuple(gate for gate in correct if gate[0] != 'phase') + if state(corrupt) == state(correct): + corrupt = correct+(('phase', 1),) + require(tableau(corrupt) == tableau(correct) and state(corrupt) != state(correct), 'global phase negative control') + require(state(corrupt, 1) != state(correct, 1), 'phase control second input') + report = { + 'status': 'PASS_INDEPENDENT_NATIVE_FRAME_LIFT_AND_FINITE_LOCAL_BILL', + 'base': BASE, 'archive_sha256': ARCHIVE_HASH, 'member_sha256': PINS, + 'changed_payload_sha256': sha256(changed_raw).hexdigest(), + 'checked_unique_persistent_edges': len(used), 'checked_endpoint_adapters': len(endpoints), + 'checked_residual_recipes': len(used_residual), 'finite_local_invoice': invoices, + 'exact_operator_method': 'Pauli conjugation and exact Gaussian dyadic zero state; no compiler import', + 'negative_controls': ['wrong global phase with the same Pauli action, on basis inputs 0 and 1'], + 'all_tensor_powers': 'Base operators are exactly equal, so their tensor powers are equal for every positive integer. The common frame conjugation proof gives the full array map.', + 'not_claimed': ['global chart or owner admission', 'recursive supplier admission', 'new kappa', 'fresh all-size compiler proof'], + 'seconds': time.monotonic()-start, 'max_rss_bytes': resource.getrusage(resource.RUSAGE_SELF).ru_maxrss, + } + args.out.write_text(json.dumps(report, indent=2, sort_keys=True)+'\n') + print(report['status'], flush=True) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--repo', type=Path, required=True) + parser.add_argument('--changed', type=Path, required=True) + parser.add_argument('--out', type=Path, required=True) + main(parser.parse_args()) diff --git a/research/reciprocal-native-responses/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py b/research/reciprocal-native-responses/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py new file mode 100644 index 0000000000..17a70cda41 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py @@ -0,0 +1,339 @@ +#!/usr/bin/env python3 +"""Bind the rank-two response and the small clique cover to actual ports.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": + "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", +} +CLIQUES = [ + [5, 34, 40, 85, 97], [3, 32, 38, 50, 95], [24, 48, 67, 80, 82], + [23, 35, 55, 65, 68], [1, 17, 66, 75, 83], [8, 12, 45, 107, 109], + [29, 49, 54, 56, 108], [26, 30, 64, 73, 96], [4, 33, 69, 74, 88], + [18, 22, 84], [19, 28, 77], [39, 58, 86], [6, 98, 100, 101, 102], + [31, 59, 60, 93, 103], +] + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(relative): + raw = (LANES / relative).read_bytes() + need(sha256(raw).hexdigest() == PINS[relative], "Source pin " + relative) + return json.loads(raw) + + +def identity(n): + return [{i: F(1)} for i in range(n)] + + +def add(target, source, coefficient=F(1)): + for key, value in source.items(): + target[key] = target.get(key, F(0)) + coefficient * value + if not target[key]: + del target[key] + + +def product(a, b): + result = [] + for row in a: + value = {} + for j, coefficient in row.items(): + add(value, b[j], coefficient) + result.append(value) + return result + + +def transpose(a, n): + result = [{} for _ in range(n)] + for i, row in enumerate(a): + for j, value in row.items(): + result[j][i] = value + return result + + +def restrict(a, ports): + index = {p: i for i, p in enumerate(ports)} + return [{index[p]: value for p, value in a[row].items() if p in index} + for row in ports] + + +def rank(rows, columns): + rows = [dict(row) for row in rows] + pivot = 0 + for column in range(columns): + found = next((i for i in range(pivot, len(rows)) if rows[i].get(column)), None) + if found is None: + continue + rows[pivot], rows[found] = rows[found], rows[pivot] + c = rows[pivot][column] + rows[pivot] = {p: v / c for p, v in rows[pivot].items()} + for i in range(pivot + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[pivot], -rows[i][column]) + pivot += 1 + return pivot + + +def determinant(rows): + rows = [dict(row) for row in rows] + result = F(1) + for column in range(len(rows)): + found = next((i for i in range(column, len(rows)) if rows[i].get(column)), None) + if found is None: + return F(0) + if found != column: + rows[column], rows[found] = rows[found], rows[column] + result = -result + c = rows[column][column] + result *= c + for i in range(column + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[column], -rows[i][column] / c) + return result + + +def inverse_word(word): + return [[op, target, origin, str(1 / F(c) if op == "scale" else -F(c))] + for op, target, origin, c in reversed(word)] + + +def transpose_word(word): + return [[op, target if op == "scale" else origin, + origin if op == "scale" else target, c] + for op, target, origin, c in reversed(word)] + + +def replay(word): + state = identity(112) + maximum = F(1) + for op, target, origin, coefficient in word: + c = F(coefficient) + if op == "scale": + state[target] = {p: c * v for p, v in state[target].items() if c * v} + else: + need(op == "add" and target != origin, "Scalar word grammar") + add(state[target], state[origin], c) + maximum = max(maximum, sum(abs(c) for c in state[target].values())) + return state, maximum + + +def price(word): + result = 0 + for op, _, _, coefficient in word: + c = F(coefficient) + a, b = abs(c.numerator), c.denominator + need(a and not b & (b - 1), "Dyadic coefficient") + if op == "scale": + need(not a & (a - 1), "Dyadic unit scale") + result += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) + else: + result += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + return result + + +def maximal_cliques(ports, q): + n = len(ports) + adjacent = [sum(1 << j for j, r in enumerate(ports) + if i != j and not (q[p] & q[r]).bit_count() % 2) + for i, p in enumerate(ports)] + result = [] + + def visit(chosen, possible, excluded): + if not possible and not excluded: + result.append(chosen) + return + options = possible | excluded + pivot = max((i for i in range(n) if options >> i & 1), + key=lambda i: (adjacent[i] & possible).bit_count(), default=0) + todo = possible & ~adjacent[pivot] + while todo: + bit = todo & -todo + i = bit.bit_length() - 1 + todo -= bit + visit(chosen | bit, possible & adjacent[i], excluded & adjacent[i]) + possible -= bit + excluded |= bit + + visit(0, (1 << n) - 1, 0) + return [[ports[i] for i in range(n) if mask >> i & 1] for mask in sorted(result)] + + +def encoded(rows): + return [{str(p): str(c) for p, c in sorted(row.items())} for row in rows] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = read(next(name for name in PINS if "CYCLIC" in name)) + matching = read(next(name for name in PINS if "MATCHED" in name)) + selected, small = matching["selected_ports"], matching["small_ports"] + selected_set = set(selected) + q = cyclic["ports"] + h = identity(112) + codes = [] + for pair in cyclic["pair_codes"]: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + h[a], h[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)} + if aa != 1: + codes.append(["scale", a, None, str(aa)]) + codes.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + hi = transpose(h, 112) + for p in cyclic["affected_ports"]: + hi[p] = {k: v / 2 for k, v in hi[p].items()} + need(product(h, hi) == identity(112), "Actual pair inverse") + mode = identity(112) + mode_inverse = identity(112) + mode_u, mode_v = [{} for _ in range(112)], [] + mode_word, assignments = [], [] + for vertex, group in enumerate(cyclic["cyclic_carriers"]): + chosen = [p for p in group if selected_set.intersection(map(int, cyclic["mode_rows"][str(p)]))] + rest = [p for p in group if p not in chosen] + need(len(chosen) == 2 and len(rest) == 4, "Two selected modes per vertex") + order = chosen + rest + signs = [1, 1 if vertex % 2 == 0 else -1, 1, 1, 1, 1] + e = [{j: F((i == j) - 1) for j in range(4) if i != j} | {4: F(1)} + for i in range(4)] + e += [{5: F(1)}, {0: F(-2), 1: F(-2), 2: F(-2), 3: F(-2), 4: F(3)}] + swap = [0, 1, 2, 3, 5, 4] + ei = [{swap[j]: c for j, c in e[swap[i]].items()} for i in range(6)] + need(product(e, ei) == product(ei, e) == identity(6), "Six-mode reciprocal pair") + for i, p in enumerate(order): + mode[p] = {order[j]: c * signs[i] * signs[j] for j, c in e[i].items()} + mode_inverse[p] = {order[j]: c * signs[i] * signs[j] for j, c in ei[i].items()} + offset = len(mode_v) + local_u = [[1, 0]] * 4 + [[0, 1], [2, -1]] + local_v = [[-1, -1, -1, -1, 1, 0], [0, 0, 0, 0, -1, 1]] + for i, p in enumerate(order): + mode_u[p].update({offset + j: F(value * signs[i]) + for j, value in enumerate(local_u[i]) if value}) + mode_v.extend([{order[j]: F(value * signs[j]) for j, value in enumerate(row) if value} + for row in local_v]) + a, b, c = order[:4], order[4], order[5] + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(-signs[i])]) + for i, p in enumerate(a): + mode_word.append(["add", p, b, str(signs[i])]) + mode_word.append(["scale", b, None, "-1"]) + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(signs[i])]) + mode_word.extend([["add", b, c, "1"], ["add", c, b, "-1"], + ["add", b, c, "1"], ["scale", c, None, "-1"]]) + assignments.append({"vertex": vertex, "ordered_carriers_a_b_c": order, "signs": signs}) + need(replay(mode_word)[0] == mode, "In-place rank-two mode code") + response, response_inverse = product(hi, product(mode, h)), product(hi, product(mode_inverse, h)) + u, v = product(hi, mode_u), product(mode_v, h) + small_word = [] + need(sorted(p for group in CLIQUES for p in group) == sorted(small), "Exact disjoint64 cover") + for group in CLIQUES: + k = len(group) + need(k in (3, 5), "Dyadic clique size") + need(all((q[p] & q[r]).bit_count() % 2 == int(p == r) + for p in group for r in group), "Actual orthonormal clique") + for p in group: + response[p] = {r: F(-1) for r in group if r != p} + response_inverse[p] = {r: F(int(p == r)) - F(1, k - 1) for r in group} + u[p] = {len(v): F(-1)} + v.append({p: F(1) for p in group}) + a, rest = group[0], group[1:] + small_word.extend([["add", a, p, "1"] for p in rest]) + small_word.extend([["add", p, a, "-1"] for p in rest]) + small_word.append(["scale", a, None, str(1 - k)]) + small_word.extend([["add", a, p, "-1"] for p in rest]) + word = codes + mode_word + inverse_word(codes) + small_word + common_words = {"E": word, "inverse_E": inverse_word(word), + "transpose_E": transpose_word(word), + "inverse_transpose_E": transpose_word(inverse_word(word))} + expected = {"E": response, "inverse_E": response_inverse, + "transpose_E": transpose(response, 112), + "inverse_transpose_E": transpose(response_inverse, 112)} + word_receipts = {} + for name, gates in common_words.items(): + actual, maximum = replay(gates) + need(actual == expected[name], "Full112 scalar code " + name) + need(replay(gates + inverse_word(gates))[0] == identity(112), "Both code orders " + name) + word_receipts[name] = {"real_scalar_primitives": price(gates), + "prefix_row_l1_bound": str(maximum), "owned_fields": 0} + need(product(response, response_inverse) == product(response_inverse, response) == identity(112), + "Full112 reciprocal products") + correction = [dict(row) for row in response] + for i in range(112): + add(correction[i], {i: F(-1)}) + need(product(u, v) == correction and rank(u, 30) == rank(v, 112) == 30, + "Exact full rank30 correction factor") + l = restrict(response, selected) + li = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_inverse"]] + old_l = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_block"]] + need(l == restrict(response_inverse, selected) == old_l, "Both selected blocks retain L") + need(product(l, li) == identity(8), "Selected inverse") + ordinary = sorted(set(range(112)) - selected_set) + p = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(selected) + if response_inverse[r].get(s)} for r in ordinary] + n = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(ordinary) + if response_inverse[r].get(s)} for r in selected] + ordinary_inverse = restrict(response_inverse, ordinary) + for row, update in zip(ordinary_inverse, product(product(p, li), n)): + add(row, update, -1) + ordinary_block = restrict(response, ordinary) + need(product(ordinary_block, ordinary_inverse) == product(ordinary_inverse, ordinary_block) + == identity(104), "Both ordinary104 inverse orders") + need(all(not c.denominator & (c.denominator - 1) + for row in ordinary_inverse for c in row.values()), "Dyadic ordinary inverse") + maxima = maximal_cliques(small, q) + histogram = Counter(map(len, maxima)) + need(histogram == {4: 896, 8: 64}, "Exhaustive maximal clique census") + # A separate exhaustive extension pass checks the absence of a ninth vertex. + need(all(not any(p not in clique and all(not (q[p] & q[r]).bit_count() % 2 for r in clique) + for p in small) for clique in maxima), "Each reported clique is maximal") + receipt = { + "status": "PASS_LOW_DISPLACEMENT_RESPONSE", + "source_pins": PINS, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "correction_rank_large48": 16, "correction_rank_small64": 14, "correction_rank_full112": 30, + "selected_determinant": str(determinant(l)), + "full_determinant": str(determinant(response)), + "ordinary104_determinant": str(determinant(ordinary_block)), + "small_clique_sizes": dict(sorted(Counter(map(len, CLIQUES)).items())), + "all_maximal_small_clique_sizes": dict(sorted(histogram.items())), + "common_frame_scalar_codes": word_receipts, + "scope": "Exact port matrices, principal units, scalar codes and geometry. Native phases and terminal access are separate.", + } + payload = { + "source_pins": PINS, "ports": q, "selected_ports": selected, "ordinary_ports": ordinary, + "large_ports": cyclic["affected_ports"], "small_ports": small, + "vertex_assignments": assignments, "mode_response": encoded(mode), + "mode_inverse": encoded(mode_inverse), "small_cliques": CLIQUES, + "response": encoded(response), "response_inverse": encoded(response_inverse), + "correction_U": encoded(u), "correction_V": encoded(v), + "selected_block": encoded(l), "selected_inverse": encoded(li), + "ordinary_inverse": encoded(ordinary_inverse), "common_frame_words": common_words, + "maximal_small_cliques": maxima, + } + raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode() + (args.out / "RESPONSE-PROGRAM.json").write_bytes(raw) + receipt["payload_sha256"] = sha256(raw).hexdigest() + (args.out / "RESPONSE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py b/research/reciprocal-native-responses/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/emit_native.py new file mode 100644 index 0000000000..532c8709eb --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/METRIC-COMPLETION.json.gz b/research/reciprocal-native-responses/frozen/lanes/new-core-transfer-20261017/low-displacement-20261020/metric-completion-20261020/signed-probe/METRIC-COMPLETION.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..a2e0a3622e80b9bf86fdbc603d3f0e72aac67ba7 GIT binary patch literal 17389 zcmce6<8xA4-v+RHL$LbsCRYs6>%d{&yuw{! z*7cmERw3`V+GeKNs?Tdr%uR@a#j6w5JS2y)>azdYVf;@G!m>g=v&&PPA)$Gq6T z;jYc_d^6wMs%jWk^5$FfYJ{Jzo3@ruwzy7LILls|mhwhgiKT33e7@G(0zTR7cOh<8 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b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md @@ -0,0 +1,140 @@ +# Native recipes for the new centre-deleted core + +This lane checks the native operators for both PR3133 provider words. +The words are the byte-equal copies in PR3148. It uses the new frame and +warp data. It does not use the earlier T74 frame data. + +Fresh generation passed for both providers. Each run checked 1130 frames, +3036 directed child edges, 224 endpoint adapters, 180 signed physical warp +classes, 72 logical warp operators, and 56 residual wrapper classes. The +residual classes include 32 proper terminal pairs, of which 24 are cold. +Each source run rejected 25 wrapper mutations and 13 warp mutations. + +The fresh child and residual recipe files have the same hashes as the +authenticated PR3133 native receipt. Both literal dual runs also passed: +each checked all 180 signed classes on all 512 columns. In each provider, +172 literal dual recipes differ from the forward recipes. All literal +dual recipes have rank zero. Thus the choice of logical warp orientation +does affect the phase tables, but it does not add native children. + +The independent interpreter review is a separate calculation. The scalar +map, stock, controller, precision, and complete kappa calculation are also +separate checks. `RESULT.json` gives the generation result; `FREEZE.json` +pins its inputs, scripts, proofs, and outputs. + +## Exact operator test + +For a binary subspace U, let T_U be the canonical Clifford frame in the +pinned source. A child from U to V must implement T_V T_U^{-1}. The +generator derives its recipe from this product. It checks the full Pauli +table and the exact Gaussian dyadic image of the zero basis vector. These +two checks include the global phase. + +To see this, let A and B be unitary operators with the same action on all +Pauli generators. Then B^{-1} A commutes with every X and Z generator. An +operator that commutes with every Z generator is diagonal in the standard +basis. If it also commutes with every X generator, all diagonal entries +are equal. Thus A is a scalar multiple of B. Equality on the zero basis +vector fixes that scalar as one. The argument applies to each generated +Clifford product. It also proves equality of all positive tensor powers. + +Each child recipe has the form L C_[r] R, with R applied first. The +serialized L and R are monomial Clifford operators. For a nested frame +change, the checked r is the difference of the frame dimensions. The +physical warp product is T_V K_G^{sign} T_U^{-1}. Its checked r is zero. +The separate Gaussian matrix implementation checks every one of its 512 +columns. + +A helper that enters at E and leaves at V has residual T_V T_E^{-1}. +The recipes include the proper terminal subspaces of the new words. They +also include the cold pairs with E equal to zero. The exact wrapper test +checks R^{-1}, then the residual, then L^{-1}; the result is C_[r]. It does +not replace a proper terminal frame by FULL. + +## Literal dual warps + +The backward scalar proof uses the inverse transpose of each logical +warp. For a unitary warp K this is the entrywise conjugate of K. The +source emitter stores the same signed warp labels for both orientations. +The orientation must therefore select a physical implementation. + +There are two valid routes. The free-operator proof can establish the +endpoint identity for an arbitrary consistent choice of invertible warp +generators. The physical implementation can then use the forward K in +both orientations. Alternatively, the literal dual implementation can +use conjugate(K) in the backward orientation. This lane supplies exact +recipes for the second route as well. + +The literal dual route has a general rank-zero closure property. Let K +be a monomial Clifford operator whose nonzero entries are fourth roots of +unity. Every source K_G has this property. In a standard basis, K is an affine +permutation with a phase of the form + + i^(c + alpha.x + 2 q(x)), + +where q is a binary quadratic form. Conjugation changes this phase by +2(c + alpha.x) modulo 4. The quadratic term vanishes. After the affine +permutation, this phase is a signed Z Pauli. Thus + + conjugate(K) K^{-1} = P + +for a Pauli P. Suppose the accepted physical warp is + + W = T_V K T_U^{-1} + +and W is monomial. Then its literal dual counterpart is + + T_V conjugate(K) T_U^{-1} = (T_V P T_V^{-1}) W. + +A Clifford frame maps a Pauli to a Pauli. A Pauli is monomial. Hence the +literal dual counterpart is monomial and needs no native child. Apply the +same argument to K^{-1} for a negative signed occurrence. This proof does +not require U and V to be FULL, or require the Pauli to be diagonal after +frame conjugation. + +`generate_dual_warps.py` also checks this conclusion directly for each +signed class of each new provider. It uses the physical product +T_V conjugate(K_G)^{sign} T_U^{-1}. A separate Gaussian matrix calculation +compares all 512 columns. A wrong global phase must fail. + +## Source and credit + +The core comes from +[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), at +commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. The byte-equal provider +words are in +[PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), at +commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`: + +- [Base word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz). +- [Extra word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz). + +The unchanged recipe sources come from +[PR2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), at +commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`: + +- [Phase compiler](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_phases.py). +- [Residual wrappers](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_adapters.py). +- [Gaussian matrix implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_gauss.py). +- [Serialized warp checker](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_check_recipes.py). +- [Exact Clifford implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py). + +The source files retain their original author and AI-assistance notices. +The wrapper source credits the PR458 construction. The warp source credits +Cinna Davis and PR2226. OpenAI Codex assisted this lane's driver, literal +dual calculation, proof, and local checks. The independent review is a +separate agent calculation. It is not a maintainer review. + +## Reproduction + +Use one process and the workspace Python that has NumPy: + + work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_recipes.py + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_dual_warps.py + python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/freeze_results.py + +The first command checks every source and input pin before generation. +It runs the wrapper, phase, and serialized warp checks for each provider. +The second command checks the source and first-stage output pins before +it generates the literal dual recipes. The scripts write results only +inside this lane. No PR, push, or publication commit is part of this work. diff --git a/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json new file mode 100644 index 0000000000..c3df9a69e7 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json @@ -0,0 +1,10 @@ +{ + "source_commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "source_sha256": { + "bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce", + "bw_check_recipes.py": "d600b959a0ac462dc28deb8c0d5d8f9e0c76d7f7d7b6f92a296c5ef9e0a1de19", + "bw_gauss.py": "0884b14d6d77cde419a3c773ad9b21d0d18de1e6e20e6b6d5add458ed32ba4cb", + "bw_phases.py": "9d1a620e26715f4c42fd0347ecc14ef5a4a9031867869b64e8bae4d8526a821e", + "vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } +} diff --git a/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REPRODUCTION.json new file mode 100644 index 0000000000..1781475f6e --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW-FREEZE.json b/research/reciprocal-native-responses/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/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/EXTENSIONS-REVIEW.md new file mode 100644 index 0000000000..8a7aaff05c --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/check_extensions.py new file mode 100644 index 0000000000..33c667c847 --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/low-displacement-review-20261020/extensions-normal/EXTENSIONS-INPUTS.json @@ -0,0 +1,74 @@ +{ + 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"used_native_edges": 1141 + } + }, + "owned_fields": 0, + "private_fields": 0, + "untouched_arbitrary_roles": 416 + } + }, + "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.", + "spatial_columns_per_fresh_edge": 512, + "status": "PASS_INDEPENDENT_NATIVE_EXTENSIONS" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/new-native-recipes-20261017/sources/vendor/clifford/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<` and repeat +with `-O`. Compare the decompressed native payload and receipt bytes. + +The full native contracts, scalar words, and all open caller obligations +are those in `NATIVE.md`. In particular, this packet does not supply +centre retention, helper progress, a terminal decoder, or a recursive +host. + +The source response and cyclic path came from the coordinating, +new-core-transfer, and independent-review lanes, as cited in the frozen +model and native packets. This lane supplies the legal cut removal and +its full phase and content check. 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/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY-FREEZE.json b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY-FREEZE.json new file mode 100644 index 0000000000..9fc9811495 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY-FREEZE.json @@ -0,0 +1,11 @@ +{ + "files": { + "FAMILY.md": "d5764b5fd29ccd897a7a666b22d8e77bdca415f65072d44974b0ff7b70f37e43", + "MODEL-FREEZE.json": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7", + "check_family.py": "4b3769563f024e3a3a3728c5f640f44697ec418a64dc53bff9ae1320167eabed", + "family-normal/CHECKS.json": "ab34f72669e44f1615514511402bf77b637382d874e5a19cd813d96bed1bbdfb", + "family-optimized/CHECKS.json": "ab34f72669e44f1615514511402bf77b637382d874e5a19cd813d96bed1bbdfb" + }, + "normal_optimized_bytes_equal": true, + "status": "FROZEN_FAMILY_THEOREM" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY.md b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY.md new file mode 100644 index 0000000000..d08fc4f800 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/FAMILY.md @@ -0,0 +1,133 @@ +# The reciprocal family and its sharp blockwise restrictions + +Let n be an integer with n>=5. 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/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL-FREEZE.json new file mode 100644 index 0000000000..7126204dcc --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL.md b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/MODEL.md new file mode 100644 index 0000000000..cd2fd125cc --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/NATIVE-FREEZE.json b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/NATIVE-FREEZE.json new file mode 100644 index 0000000000..c5114015bc --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/NATIVE-FREEZE.json @@ -0,0 +1,29 @@ +{ + "files": { + "MODEL-FREEZE.json": { + "sha256": "9dbff19fa68567eadea82cef2add71fda3ffe7228944028d06d53880da8b70f7" + }, + "NATIVE.md": { + "sha256": "1fe48a47d0dca937f8ccc5c27936b3d679cf6c997c6f9156ca4158554a9f19a7" + }, + "emit_native.py": { + "sha256": "b6db27a1a7e990ac297972f0306efa624bfa317d70bcb18615a38a4b8d2aac03" + }, + "native-normal/CHECKS.json": { + "sha256": "e3e6b18efae3b93fa48b95c0c2f238caff1ec3f5a9948bd880e21c9cf75d31b0" + }, + "native-normal/NATIVE.json.gz": { + "decompressed_sha256": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e", + "sha256": "e84b7f009339b44110e8658b1d4073dd903d1b2bf5f9550402070ca15dca6226" + }, + "native-optimized/CHECKS.json": { + "sha256": "e3e6b18efae3b93fa48b95c0c2f238caff1ec3f5a9948bd880e21c9cf75d31b0" + }, + "native-optimized/NATIVE.json.gz": { + "decompressed_sha256": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e", + "sha256": "e84b7f009339b44110e8658b1d4073dd903d1b2bf5f9550402070ca15dca6226" + } + }, + "normal_optimized_bytes_equal": true, + "status": "FROZEN_NATIVE" +} diff --git a/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/NATIVE.md b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/NATIVE.md new file mode 100644 index 0000000000..0b3e7fd758 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/NATIVE.md @@ -0,0 +1,128 @@ +# Native reciprocal words with a dyadic signed metric + +This packet implements the actual112 response E from `MODEL.md` and its +reciprocal in the two native shear directions. All640 input fields are +arbitrary. The416 fields outside the224 data fields are unchanged. + +Write Q=diag(C_qp), q=Q^-1, and let F be the common9-axis advance. +The complete words include the conventional input and output adapters. +They have these physical contracts: + +| Word | Physical input | Physical output | +| --- | --- | --- | +| `forward_E` | (Qx,y) | (F x,F q(y+E x)) | +| `backward_transpose_E` | (Qx,y) | (F(x-E^T y),F q y) | +| `forward_inverse_adjoint_E` | (Qx,y) | (F x,F q(y+E^-T x)) | +| `backward_inverse_E` | (Qx,y) | (F(x-E^-1 y),F q y) | + +The order of F,q, and E in this table is part of the contract. The +packet does not commute E through the field-dependent Q maps. + +## Construction + +The frozen odd16 native source has a transfer position for every ordered +off-diagonal pair in each large6-mode block and each small8-clique. +This packet retains every native edge, ordered frame, and endpoint +adapter from its forward word. + +At each transfer position, replace the coefficient by the corresponding +entry of E in the native mode basis. Delete a transfer when its new +coefficient is zero. The physical pair-code steps are unchanged. The +all640-column replay proves the first contract. + +For the second forward word, use E^-T. This matrix has zero diagonal in +the same mode and physical bases. Thus the same transfer positions +implement it. No new native path is needed. + +For each forward word, construct its literal inverse adjoint. Keep the +event order and every native unitary. Replace ADD(target,source,c) by +ADD(source,target,-c). Replace each real SCALE(c) by SCALE(1/c). +All scalar coefficients in this packet are real. Each new ADD has equal +source and target frames because the original ADD did. This proves the +complete native inverse-adjoint relation, including all endpoint +monomials. The two resulting backward words also pass the full content +and frame replay. + +This is a direct reciprocal implementation. It does not require the +two-bank metric wrapper described below. + +## Full local invoice + +Each of the four words has: + +```text +1520 H1 + 64 H2 + 48 H3, +native mass 1792, +1632 native children, +6440 real scalar primitives, +224 explicit endpoint monomial maps, +at most3264 native side maps, +zero owned fields and zero private outer fields. +``` + +Every content prefix is dyadic, with binary denominator height at most1. +The maximum row one-norm is46 for `forward_E`,16 for +`backward_transpose_E`, and30 for each directly retuned reciprocal word. +The invoice is the same for both actual providers. + +All1561 inherited native recipe records and all224 endpoint adapter +records are byte-equal to the pinned source. Every actual native event +has the same field, old ordered frame, new ordered frame, rank, and +recipe key as that source. The source phase proofs therefore apply +without a changed hypothesis. This run checks that exact inheritance; +it does not claim a fresh spatial replay of those recipes. + +The416 unchanged fields include the existing helper fields and the eight +extra named fields in the source schema. No event reads or writes any +of them. This proves restoration on arbitrary state. It does not supply +the separate productive progress that an outer supplier may assign to +those helpers. + +## Paid diagonal conversion + +The physical diagonal metric commutes with each individual native map. +It is legal to apply its scalar entries even when different fields have +different frames. + +Let D2=diag(J,J). Since E^-T=J E J^-1, the native forward word for +E^-T can also be obtained by pre-scaling both banks by J^-1 and +post-scaling both banks by J. The native backward word with cross term +-E^-1 can be obtained by pre-scaling both banks by J, using the +backward transpose word, then post-scaling both banks by J^-1. + +The packet emits and replays both constructions. Each adds128 scalar +SCALE instructions,640 real scalar primitives, and no native child. +The total is7080 scalar primitives. The backward wrapper has binary +height at most2; the forward wrapper has height at most1. + +The common-frame one-bank conversion in `MODEL.md` costs320 primitives. +The two-bank native wrapper costs640 because it must restore both +baseline banks. Direct transfer-coefficient retuning gives the same +required shear for6440 primitives and avoids the wrapper surcharge. + +## Verification and limits + +Run `python3 -I -B emit_native.py --out ` and repeat with +`-O`. The decompressed payload and receipt must agree. + +The producer checks both providers and all six words. It verifies all640 +input columns, every scalar access, every literal native frame, all final +frames, every unchanged helper column, the full local cost, and the +serialized payload. It also deletes one nonzero transfer in each +principal direction and rejects the changed result. + +No global controller, centre record, terminal decoder, routed stage +composition, helper progress, recursive host, or complete bound is +claimed here. In particular, the rank16 factor E-P does not by itself +make its centre information available at a later cut. + +The native path and phase records come from the new-core-transfer +odd16 packet and its cited cyclic-flag sources. The coordinating agent +supplied the signed-metric identity. The new-core-transfer lane supplied +the physical pair-closed role placement. This lane supplies the actual +reciprocal coefficient words, literal inverse-adjoint directions, +metric wrappers, 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/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_family.py b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_family.py new file mode 100644 index 0000000000..383fdb5bcd --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_model.py b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/check_model.py new file mode 100644 index 0000000000..e361d331b3 --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/coalesced-normal/CHECKS.json b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/coalesced-normal/CHECKS.json new file mode 100644 index 0000000000..368e3e04c4 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/coalesced-normal/CHECKS.json @@ -0,0 +1,330 @@ +{ + "fresh_exact_native_phase_checks": 206, + "inherited_native_records": 1071, + "payload_decompressed_sha256": "308044e47b3456e0fdb80325e3aa26327e5d71e61176d6db9c2d658241d5d255", + "phase_method": "Exact18 Pauli images and the exact reference column fix the full Clifford operator and global phase.", + "producer_sha256": "3b3c1e1a3c33a5391c27d89d3484c0802c63d6ec02c9ac041fde6a4c6b844efb", + "reports": { + "base": { + "backward_inverse_E": { + "all_input_columns": 640, + "binary_height": 1, + "endpoint_maps": 224, + "explicit_endpoint_monomials": 224, + "merged_chain_count": 1292, + "native_children": 1292, + "native_mass": 1792, + "native_profile": { + "1": 971, + "2": 237, + "3": 46, + "4": 12, + "5": 5, + "6": 11, + "7": 10 + }, + "native_side_map_bound": 2584, + "owned_fields": 0, + "prefix_row_l1_bound": "30", + "private_fields": 0, + "real_scalar_primitives": 6440, + "scalar_events_byte_equal": true, + "untouched_arbitrary_fields": 416 + }, + "backward_inverse_by_metric": { + "all_input_columns": 640, + "binary_height": 2, + "endpoint_maps": 224, + "explicit_endpoint_monomials": 224, + 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z=&rI+?DqFLPdIvTS?GFrM$_!Z7<*q5Fs`=i&W(UDPNnu9Yv=iEf9`zz(Drbkwpl%A z3%^K3$J_>SO954XwZKSS|KLJ9p?W4hegX12Sl9RKgZ~fmlZzQ)^z62T>Nw$yYbD#1 zS5{$!?JmpBYbH=@`*d##TzU@j`iq8~iCX=Z?bh?__^+IFglIN@I^#d2OV;>smY0MX znq#_+LB;2D!?wujR5G6Sf_G(u`Y!+LsyYoIQw`dlx~n|h}PwOtd0tVE(G z*bsdH3=m5YMjqwa1|kFv zu?A7fa$c!UX)h!`6g;(lFF zSUcJ~SupAn-FT0Ov-=QP@j@D_t7~o9$D6_PGBErKrM9k1ZP$pn+&!gS>wZ9=y?xGT ziEU?=3, put m=n-2, and write an input as (a,b,c), where a has m +coordinates. Write s for the sum of the coordinates of a. Define + +```text +E(a,b,c) = (a-s*1+b*1, c, -(m-2)*s+(m-1)*b), +E^-1(a,b,c) = (a-s*1+c*1, -(m-2)*s+(m-1)*c, b). +``` + +All coefficients are integers. Both displayed matrices have zero +diagonal. Their two products are I. + +A short factorization proves invertibility and the correction rank. +Let P exchange b and c. Define the column u and row l by + +```text +u = (1,...,1,m-2,0)^T, +l = (-1,...,-1,1,0). +``` + +Then l*u=-2, so R=I+u*l satisfies R^2=I. Direct substitution gives +E=P*R and E^-1=R*P. Each factor has determinant -1. Thus det(E)=1. +The factor R changes only the one scalar l*x. This factorization does +not assert that R or P alone has a legal native transfer schedule. + +An explicit factorization of the complete correction is + +```text +E-I = U V, + +U = [ 1 0 ] repeated m times, + [ 0 1 ], + [ m-2 -1 ], + +V = [ -1 ... -1 1 0 ], + [ 0 ... 0 -1 1 ]. +``` + +Both U and V have rank two, and + +```text +I_2+VU = [[1-m,1],[m-2,-1]] +``` + +has determinant one. The two nonzero rows of V and the first and +(m+1)-st rows of U show that rank(E-I)=2. Also +E^-1-I=-E^-1(E-I), so rank(E^-1-I)=2. The fixed space has dimension +n-2 and is given by s=b=c. In particular, for n=6 each response fixes +four dimensions. + +## Two correction coordinates are necessary + +Work over a field of characteristic zero. Suppose A is an invertible +n by n matrix, and both A and A^-1 have zero diagonal. Rank(A-I) +cannot be zero. If it is one, write A=I+u*v. Each diagonal equation +gives u_i*v_i=-1, so v*u=-n. The rank-one inverse formula gives + +```text +A^-1 = I-u*v/(1-n). +``` + +Every diagonal entry of this inverse is (n-2)/(n-1). It is nonzero +for n>=3. This is a contradiction. The construction therefore attains +the minimum correction rank in this matrix family. + +The statement is about rank(A-I). It is not a lower bound on native +children, storage, or the cost of a routed code. + +## Symmetry forces a third correction coordinate in dimension six + +Suppose A is a symmetric rational six by six unit, with both A and +A^-1 of zero diagonal. Assume rank(A-I)=2. Symmetry gives an +orthogonal eigenbasis. Four eigenvalues are one. Let the other two +be a and b. The two trace equations give + +```text +a+b=-4, 1/a+1/b=-4, +ab=1, {a,b}={-2+sqrt(3),-2-sqrt(3)}. +``` + +Let u and v be unit eigenvectors for a and b. At coordinate i, the +two diagonal equations are + +```text +1+(a-1)*u_i^2+(b-1)*v_i^2=0, +1+(b-1)*u_i^2+(a-1)*v_i^2=0. +``` + +Their difference gives u_i^2=v_i^2, and either equation then gives +u_i^2=v_i^2=1/6. Hence u=sigma/sqrt(6) and v=tau/sqrt(6), where +sigma and tau are sign vectors. The spectral formula is + +```text +A = I - (sigma*sigma^T+tau*tau^T)/2 + + sqrt(3)*(sigma*sigma^T-tau*tau^T)/6. +``` + +Rationality forces the coefficient of sqrt(3) to be zero. The two +rank-one projectors are then equal, which contradicts u perpendicular +to v. Thus the correction rank is at least three. Three disjoint +coordinate exchanges attain it. The symmetric matching response is +optimal under these hypotheses; an asymmetric reciprocal pair escapes +that restriction. + +The proof uses real symmetry and rational entries. It does not assert +the same conclusion for complex symmetric matrices, or for a matrix +whose inverse has a nonzero diagonal. + +## Binding to the actual 48 pair modes + +The pinned cyclic family has eight vertices with six pair modes at +each vertex. Let A_pair be its signed pair code. It satisfies +A_pair*A_pair^T=2I. Put one copy of E_6 on each vertex and set + +```text +B = direct_sum_v E_6, +E_physical = A_pair^-1 B A_pair. +``` + +Both B and B^-1 have zero diagonal, so both belong to the proved +cyclic transfer family. The backward transfer convention produces the +negative transpose of its coefficient matrix. Therefore the native +generator for a reciprocal backward response must use B^-T. + +The physical response has determinant one and +rank(E_physical-I)=16. Its inverse has the same correction rank. +The corresponding symmetric matching has correction rank 24 on these +48 ports. Conjugation by the invertible pair code preserves each rank. +The checker verifies both full 48 by 48 inverse orders and both ranks +from the literal pinned pair code. + +The rank-two coordinates depend on five modes at each vertex. The +rank-one reflection R uses four a modes and the b mode. Their actual +source planes span six binary directions, including the common +radical. A proposed capture to that radical would have rank five. +This observation is not a capture implementation: the permutation P +has fixed modes, and R has nonzero diagonal. Neither factor alone +belongs to the zero-diagonal transfer family. + +The cyclic family proves logical transfers and nested frame access. +Its fixed path gives native mass 1792 on all 224 data fields, with +zero response on the other 64 ports in that family packet. This +theorem does not supply a compatible 64-port unit or a full native +phase replay. The two-coordinate factorization must not be treated +as free physical access at a hole frame. + +## Checks and continuation + +Run the adjacent checker in normal and optimized Python modes. It +checks dimensions three through sixteen, the exact factors, both +inverse orders, the rank-two factor, the fixed space, and the pinned +48-port application. The proof above covers all n>=3; the finite +checks do not replace that proof. + +Next steps are native phase lowering of the actual reciprocal pair, +selection of a compatible ordinary 64-port response, and a costed +capture or terminal scheme that uses the smaller correction space. +The general one-pair controller can also use an arbitrary unit raw +backward response through legal current-stage codes. That result +removes reciprocal native synthesis as a prerequisite, but leaves +the physical output code explicit. + +This result builds on the root pair geometry, the oblique-native +pair-code construction, and the independent-review cyclic flag +theorem. OpenAI Codex assisted the work. No PR or publication is +authorized. Before any PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/reciprocal-native-responses/frozen/root/RECIPROCAL-RANK-TWO-ADDENDUM-20261020.md b/research/reciprocal-native-responses/frozen/root/RECIPROCAL-RANK-TWO-ADDENDUM-20261020.md new file mode 100644 index 0000000000..c0e7264b20 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/root/RECIPROCAL-RANK-TWO-ADDENDUM-20261020.md @@ -0,0 +1,41 @@ +# Scope correction and a balanced response + +This note supplements the frozen reciprocal rank-two proof. It does not +change that proof's matrix identities. + +The statement that the two correction coordinates depend on five modes +needs a more precise form. The first row of V depends on the four a +modes and b. The second row depends on b and c. Their union contains +all six modes. Only the first row, which is the reflection query, has +the proposed rank-five capture to the common radical. The independent +review found this wording defect. No two-coordinate capture was priced +in the frozen proof. + +For n=6, a diagonal conjugation reduces both matrix row norms. Set + +```text +D=diag(1,1,1,1,-2,2), E_balanced=D^-1 E D. +``` + +With s=sum(a), the exact maps are + +```text +E_balanced(a,b,c)=(a-s*1-2*b*1, -c, -s-3*b), +E_balanced^-1(a,b,c)=(a-s*1+2*c*1, s-3*c, -b). +``` + +Both matrices have maximum absolute row sum seven. The unbalanced +pair has maximum absolute row sum eleven. The two diagonals remain +zero and both correction ranks remain two. The a-to-a entries remain +unchanged, so this conjugation preserves a selected minor supported +only on the a modes. + +The coefficient changes exchange four unit ADD coefficients with four +coefficient-two ADD coefficients in each direction. They preserve the +sum of the inherited scalar ADD charges. This is a statement about +the matrix transfer coefficients. Pair codes, intermediate norm bounds, +native paths, and routed use still need their own verification. + +The root checked the two matrices with exact rational arithmetic. +The native-construction lane has the formulas for a full replay. +Do not treat the row-norm bound as a complete finite-precision proof. diff --git a/research/reciprocal-native-responses/frozen/root/RECIPROCAL-RANK-TWO-FREEZE-20261020.json b/research/reciprocal-native-responses/frozen/root/RECIPROCAL-RANK-TWO-FREEZE-20261020.json new file mode 100644 index 0000000000..4fd91400e1 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/root/RECIPROCAL-RANK-TWO-FREEZE-20261020.json @@ -0,0 +1,13 @@ +{ + "files": { + "RECIPROCAL-RANK-TWO-20261020.json": "971df2cc46160babf79b668c5677ab03e48ae86551d727db05c6f4118fc6658e", + "RECIPROCAL-RANK-TWO-20261020.md": "5d7855b2360093629530aceb91d38204a9a0a42654f53a150f35279efc8de172", + "check_reciprocal_rank_two_20261020.py": "2fc272bf47b7840f5464b1f589f16d069e66b6cd41c8d2fce03f9f04878635bc" + }, + "scope": "Response algebra and actual48 pair binding. Independent proof review pending. No native phase, decoder, supplier, or kappa claim.", + "validation": { + "normal": "PASS_RECIPROCAL_RANK_TWO", + "optimized": "PASS_RECIPROCAL_RANK_TWO", + "receipt_bytes_equal": true + } +} diff --git a/research/reciprocal-native-responses/frozen/root/check_reciprocal_rank_two_20261020.py b/research/reciprocal-native-responses/frozen/root/check_reciprocal_rank_two_20261020.py new file mode 100644 index 0000000000..aa170eaaf9 --- /dev/null +++ b/research/reciprocal-native-responses/frozen/root/check_reciprocal_rank_two_20261020.py @@ -0,0 +1,154 @@ +#!/usr/bin/env python3 +"""Check the reciprocal rank-two response and its actual pair code.""" + +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +SOURCE = (HERE.parent / "lanes/independent-review-20261017/" + "cyclic-pair-flags-20261018/CYCLIC-FLAGS.json") +SOURCE_SHA = "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585" + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def identity(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def product(a, b): + return [[sum(x * y for x, y in zip(row, col)) for col in zip(*b)] + for row in a] + + +def subtract(a, b): + return [[x - y for x, y in zip(ra, rb)] for ra, rb in zip(a, b)] + + +def rank(a): + a = [list(map(F, row)) for row in a] + pivot = 0 + for col in range(len(a[0])): + row = next((i for i in range(pivot, len(a)) if a[i][col]), None) + if row is None: + continue + a[pivot], a[row] = a[row], a[pivot] + scale = a[pivot][col] + a[pivot] = [x / scale for x in a[pivot]] + for i in range(len(a)): + if i != pivot and a[i][col]: + scale = a[i][col] + a[i] = [x - scale * y for x, y in zip(a[i], a[pivot])] + pivot += 1 + if pivot == len(a): + break + return pivot + + +def response(n): + m = n - 2 + e = identity(n) + for i in range(m): + for j in range(m): + e[i][j] -= 1 + e[i][m] = F(1) + e[m] = [F(0)] * n + e[m][m + 1] = F(1) + e[m + 1] = [F(-(m - 2))] * m + [F(m - 1), F(0)] + p = identity(n) + p[m], p[m + 1] = p[m + 1], p[m] + inverse = product(product(p, e), p) + return e, inverse, p + + +def main(): + dimensions = [] + for n in range(3, 17): + m = n - 2 + e, inverse, p = response(n) + unit = identity(n) + u = [[F(1), F(0)] for _ in range(m)] + u += [[F(0), F(1)], [F(m - 2), F(-1)]] + v = [[F(-1)] * m + [F(1), F(0)], + [F(0)] * m + [F(-1), F(1)]] + correction = subtract(e, unit) + need(product(u, v) == correction, "Exact rank-two correction") + need(rank(correction) == rank(subtract(inverse, unit)) == 2, + "Both correction ranks are two") + need(product(e, inverse) == product(inverse, e) == unit, + "Both inverse orders") + need(all(e[i][i] == inverse[i][i] == 0 for i in range(n)), + "Both diagonals are zero") + r = product(p, e) + need(product(r, r) == unit and rank(subtract(r, unit)) == 1, + "The reflection has rank one") + small = product(v, u) + small = [[small[i][j] + (i == j) for j in range(2)] + for i in range(2)] + need(small == [[F(1 - m), F(1)], [F(m - 2), F(-1)]], + "The two-coordinate action") + need(small[0][0] * small[1][1] - + small[0][1] * small[1][0] == 1, "Determinant one") + for j in range(m): + fixed = [[F(i == j)] for i in range(m)] + [[F(1)], [F(1)]] + need(product(e, fixed) == fixed, "An explicit fixed-space basis") + dimensions.append({"n": n, "correction_rank": 2, + "fixed_dimension": n - 2, "determinant": 1}) + + raw = SOURCE.read_bytes() + need(sha256(raw).hexdigest() == SOURCE_SHA, "Cyclic family source pin") + source = json.loads(raw) + ports = source["affected_ports"] + need(len(ports) == len(set(ports)) == 48, "48 distinct physical ports") + position = {p: i for i, p in enumerate(ports)} + pair_code = [[F(0)] * 48 for _ in range(48)] + for pair in source["pair_codes"]: + for i, p in enumerate(pair["ports"]): + for j, q in enumerate(pair["ports"]): + pair_code[position[p]][position[q]] = F(pair["matrix"][i][j]) + pair_inverse = [[x / 2 for x in row] for row in zip(*pair_code)] + need(product(pair_code, pair_inverse) == identity(48), "Actual pair inverse") + block = [[F(0)] * 48 for _ in range(48)] + block_inverse = [[F(0)] * 48 for _ in range(48)] + e, inverse, _ = response(6) + for carriers in source["cyclic_carriers"]: + need(len(carriers) == 6, "Six modes at each vertex") + for i, p in enumerate(carriers): + for j, q in enumerate(carriers): + block[position[p]][position[q]] = e[i][j] + block_inverse[position[p]][position[q]] = inverse[i][j] + physical = product(product(pair_inverse, block), pair_code) + physical_inverse = product(product(pair_inverse, block_inverse), pair_code) + need(product(physical, physical_inverse) == identity(48), "Physical right inverse") + need(product(physical_inverse, physical) == identity(48), "Physical left inverse") + need(rank(subtract(physical, identity(48))) == 16, "Physical correction rank") + need(rank(subtract(physical_inverse, identity(48))) == 16, "Inverse correction rank") + need(all(physical[i][i] == physical_inverse[i][i] == 0 for i in range(48)), + "Physical diagonals") + receipt = { + "status": "PASS_RECIPROCAL_RANK_TWO", + "source": str(SOURCE.relative_to(HERE.parent)), + "source_sha256": SOURCE_SHA, + "dimensions": dimensions, + "six_mode_response": [[str(x) for x in row] for row in e], + "six_mode_inverse": [[str(x) for x in row] for row in inverse], + "physical_ports": ports, + "physical_response": [[str(x) for x in row] for row in physical], + "physical_inverse": [[str(x) for x in row] for row in physical_inverse], + "physical_correction_rank": 16, + "scope": "Exact response algebra; no native phase or terminal price claim", + } + output = HERE / "RECIPROCAL-RANK-TWO-20261020.json" + output.write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + print("receipt_sha256=" + sha256(output.read_bytes()).hexdigest()) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/notices/PR2226-NOTICE.md b/research/reciprocal-native-responses/notices/PR2226-NOTICE.md new file mode 100644 index 0000000000..5ea70357a0 --- /dev/null +++ b/research/reciprocal-native-responses/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. diff --git a/research/reciprocal-native-responses/notices/PR2588-NOTICE b/research/reciprocal-native-responses/notices/PR2588-NOTICE new file mode 100644 index 0000000000..46411b80b2 --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/notices/PR2588-NOTICE-PR2226.md b/research/reciprocal-native-responses/notices/PR2588-NOTICE-PR2226.md new file mode 100644 index 0000000000..a14b299ef5 --- /dev/null +++ b/research/reciprocal-native-responses/notices/PR2588-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/reciprocal-native-responses/notices/PR3133-CREDITS.md b/research/reciprocal-native-responses/notices/PR3133-CREDITS.md new file mode 100644 index 0000000000..24f00912d4 --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/notices/PR3133-NOTICE b/research/reciprocal-native-responses/notices/PR3133-NOTICE new file mode 100644 index 0000000000..89c20926ea --- /dev/null +++ b/research/reciprocal-native-responses/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/reciprocal-native-responses/replay.py b/research/reciprocal-native-responses/replay.py new file mode 100644 index 0000000000..e4abd6acb2 --- /dev/null +++ b/research/reciprocal-native-responses/replay.py @@ -0,0 +1,113 @@ +#!/usr/bin/env python3 +"""Replay the pinned response package in a new output directory.""" + +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import platform +import shutil +import subprocess +import sys +import time + + +HERE = Path(__file__).resolve().parent +MODEL = "lanes/oblique-native-20261017/signed-metric-reciprocal-20261020" +REVIEW = "lanes/independent-review-20261017" +CALLER = "lanes/cover-algebra/reciprocal-selected-baseline-20261020" + + +def digest(path): + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + return sha256(raw).hexdigest() + + +def verify_sources(manifest): + for name, record in manifest["frozen_files"].items(): + path = HERE / "frozen" / name + raw = path.read_bytes() + if sha256(raw).hexdigest() != record["sha256"]: + raise ValueError("Frozen source changed: " + name) + if path.suffix == ".gz" and digest(path) != record["decompressed_sha256"]: + raise ValueError("Frozen payload changed: " + name) + + +def tasks(): + return [ + ("rank-two", "root/check_reciprocal_rank_two_20261020.py", [], + [("root/RECIPROCAL-RANK-TWO-20261020.json", "root/RECIPROCAL-RANK-TWO-20261020.json")]), + ("rank-two-review", REVIEW + "/reciprocal-rank-two-review-20261020/check_review.py", [], + [(REVIEW + "/reciprocal-rank-two-review-20261020/CHECKS.json", + REVIEW + "/reciprocal-rank-two-review-20261020/CHECKS.json")]), + ("family", MODEL + "/check_family.py", ["--out", "results/family"], + [("results/family/CHECKS.json", MODEL + "/family-normal/CHECKS.json")]), + ("model", MODEL + "/check_model.py", ["--out", "results/model"], + [("results/model/CHECKS.json", MODEL + "/model-normal-v2/CHECKS.json"), + ("results/model/RESPONSE.json.gz", MODEL + "/model-normal-v2/RESPONSE.json.gz")]), + ("native", MODEL + "/emit_native.py", ["--out", "results/native"], + [("results/native/CHECKS.json", MODEL + "/native-normal/CHECKS.json"), + ("results/native/NATIVE.json.gz", MODEL + "/native-normal/NATIVE.json.gz")]), + ("native-review", REVIEW + "/signed-metric-native-review-20261020/check_review.py", + ["--out", "results/native-review.json"], + [("results/native-review.json", REVIEW + "/signed-metric-native-review-20261020/FINAL-CHECKS.json")]), + ("coalesced", MODEL + "/emit_coalesced.py", ["--out", "results/coalesced"], + [("results/coalesced/CHECKS.json", MODEL + "/coalesced-normal/CHECKS.json"), + ("results/coalesced/NATIVE.json.gz", MODEL + "/coalesced-normal/NATIVE.json.gz")]), + ("ordered-caller", CALLER + "/check_reciprocal_caller.py", ["--out", "results/caller.json"], + [("results/caller.json", CALLER + "/CHECKS.json")]), + ("conditional-clean-reflection", CALLER + "/check_clean_reflection.py", + ["--out", "results/clean-reflection.json"], + [("results/clean-reflection.json", CALLER + "/CLEAN-CHECKS.json")]), + ] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + output = args.out.resolve() + output.mkdir(parents=True, exist_ok=False) + manifest = json.loads((HERE / "SOURCES.json").read_text()) + verify_sources(manifest) + reports = [] + for mode, flags in (("normal", []), ("optimized", ["-O"])): + work = output / mode + shutil.copytree(HERE / "frozen", work) + (work / "results").mkdir() + for name, script, arguments, comparisons in tasks(): + command = [sys.executable, "-I", "-B", *flags, str(work / script), *arguments] + start = time.monotonic() + with (work / "results" / (name + ".log")).open("w") as log: + subprocess.run(command, cwd=work, stdout=log, stderr=subprocess.STDOUT, check=True) + compared = {} + for produced, expected in comparisons: + actual_hash = digest(work / produced) + expected_hash = digest(HERE / "frozen" / expected) + if actual_hash != expected_hash: + raise ValueError("Replay differs from frozen payload: " + mode + "/" + produced) + compared[produced] = actual_hash + reports.append({"mode": mode, "check": name, + "command": ["python3", "-I", "-B", *flags, script, *arguments], + "payloads": compared, + "elapsed_seconds": round(time.monotonic() - start, 3)}) + print("PASS " + mode + " " + name, flush=True) + verify_sources(manifest) + receipt = { + "status": "PASS_RECIPROCAL_NATIVE_RESPONSES", + "python": sys.version, "platform": platform.platform(), + "replay_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "source_manifest_sha256": sha256((HERE / "SOURCES.json").read_bytes()).hexdigest(), + "frozen_source_count": len(manifest["frozen_files"]), "runs": reports, + "comparison": "Exact receipt bytes and decompressed gzip payload bytes.", + "scope": "Response proof checks, local native words, and conditional caller algebra. No complete supplier replay.", + } + (output / "REPLAY.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"], flush=True) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/replay_annex.py b/research/reciprocal-native-responses/replay_annex.py new file mode 100644 index 0000000000..ae19c57214 --- /dev/null +++ b/research/reciprocal-native-responses/replay_annex.py @@ -0,0 +1,133 @@ +#!/usr/bin/env python3 +"""Replay the frozen low-displacement matrix and scope checks.""" + +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import platform +import shutil +import subprocess +import sys +import time + + +HERE = Path(__file__).resolve().parent +SOURCE = "lanes/new-core-transfer-20261017/low-displacement-20261020" +REVIEW = "lanes/independent-review-20261017" + + +def verify_tree(root, records): + for name, record in records.items(): + path = root / name + raw = path.read_bytes() + if len(raw) != record["bytes"] or sha256(raw).hexdigest() != record["sha256"]: + raise ValueError("Frozen source changed: " + name) + if path.suffix == ".gz": + if sha256(gzip.decompress(raw)).hexdigest() != record["decompressed_sha256"]: + raise ValueError("Frozen payload changed: " + name) + + +def tasks(): + return [ + ("rank30-matrix", REVIEW + "/rank-thirty-review-20261020/check_review.py", [], + REVIEW + "/rank-thirty-review-20261020/CHECKS.json"), + ("extension-matrices", REVIEW + "/response-extensions-review-20261020/check_extensions.py", [], + REVIEW + "/response-extensions-review-20261020/CHECKS.json"), + ("cross-gram", SOURCE + "/check_even_clique_gram.py", ["--out", "results/cross-gram.json"], + SOURCE + "/gram-v2-normal.json"), + ("paired-line", SOURCE + "/check_paired_line_scope.py", ["--out", "results/paired-line.json"], + SOURCE + "/paired-line-scope-normal.json"), + ] + + +def mathematical_receipt(path): + result = json.loads(path.read_text()) + del result["python"] + del result["elapsed_seconds"] + return json.dumps(result, sort_keys=True, separators=(",", ":")).encode() + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + output = args.out.resolve() + output.mkdir(parents=True, exist_ok=False) + core = json.loads((HERE / "SOURCES.json").read_text()) + annex = json.loads((HERE / "annex/SOURCES.json").read_text()) + publication = json.loads((HERE / "annex/PUBLICATION-CHECKS.json").read_text()) + records = {**core["frozen_files"], **annex["frozen_files"]} + if set(core["frozen_files"]) & set(annex["frozen_files"]): + raise ValueError("The two frozen trees must have distinct paths") + if any(core["frozen_files"].get(name) != record + for name, record in annex["shared_core_files"].items()): + raise ValueError("Shared source manifest mismatch") + + def verify_sources(): + verify_tree(HERE / "frozen", core["frozen_files"]) + verify_tree(HERE / "annex/frozen", annex["frozen_files"]) + verify_tree(HERE / "annex", publication["files"]) + + verify_sources() + reports = [] + for mode, flags in (("normal", []), ("optimized", ["-O"])): + work = output / mode + shutil.copytree(HERE / "frozen", work) + shutil.copytree(HERE / "annex/frozen", work, dirs_exist_ok=True) + verify_tree(work, records) + (work / "results").mkdir() + (work / "publication-checks").mkdir() + for name in publication["files"]: + shutil.copy2(HERE / "annex" / name, work / "publication-checks" / name) + for name, script, arguments, expected in tasks(): + command = [sys.executable, "-I", "-B", *flags, str(work / script), *arguments] + start = time.monotonic() + with (work / "results" / (name + ".log")).open("w") as log: + subprocess.run(command, cwd=work, stdout=log, stderr=subprocess.STDOUT, check=True) + produced = work / (arguments[-1] if arguments else expected) + actual_hash = sha256(produced.read_bytes()).hexdigest() + if actual_hash != records[expected]["sha256"]: + raise ValueError("Receipt differs from frozen source: " + mode + "/" + name) + reports.append({"mode": mode, "check": name, + "command": ["python3", "-I", "-B", *flags, script, *arguments], + "receipt_sha256": actual_hash, + "elapsed_seconds": round(time.monotonic() - start, 3)}) + print("PASS " + mode + " " + name, flush=True) + script = "publication-checks/check_native.py" + arguments = ["--source-root", ".", "--out", "results/native.json"] + command = [sys.executable, "-I", "-B", *flags, str(work / script), *arguments] + start = time.monotonic() + with (work / "results/native.log").open("w") as log: + subprocess.run(command, cwd=work, stdout=log, stderr=subprocess.STDOUT, check=True) + produced = work / "results/native.json" + content = mathematical_receipt(produced) + if content != mathematical_receipt(HERE / "annex/NATIVE-CHECKS.json"): + raise ValueError("Publication native check differs: " + mode) + reports.append({"mode": mode, "check": "publication-native", + "command": ["python3", "-I", "-B", *flags, script, *arguments], + "receipt_sha256": sha256(produced.read_bytes()).hexdigest(), + "mathematical_receipt_sha256": sha256(content).hexdigest(), + "elapsed_seconds": round(time.monotonic() - start, 3)}) + print("PASS " + mode + " publication-native", flush=True) + verify_sources() + receipt = { + "status": "PASS_LOW_DISPLACEMENT_RESPONSE_ANNEX", + "python": sys.version, "platform": platform.platform(), + "replay_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "core_manifest_sha256": sha256((HERE / "SOURCES.json").read_bytes()).hexdigest(), + "annex_manifest_sha256": sha256((HERE / "annex/SOURCES.json").read_bytes()).hexdigest(), + "publication_checker_manifest_sha256": sha256((HERE / "annex/PUBLICATION-CHECKS.json").read_bytes()).hexdigest(), + "additional_frozen_source_count": len(annex["frozen_files"]), + "shared_core_source_count": len(annex["shared_core_files"]), + "runs": reports, + "comparison": "Eight exact frozen receipt byte comparisons. Two publication-native comparisons omit only Python version and elapsed time. Compressed source files also have payload hashes.", + "scope": "Independent matrices, scalar prices, native frame ledgers, 352 changed-exit phases, exact cross-Gram ranks, and finite paired-line checks. The historical raw native spatial replays are separate.", + } + (output / "REPLAY.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"], flush=True) + + +if __name__ == "__main__": + main() From 4c903ff856e2cfbd6fc91d98b6b430e1b4955e72 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Thu, 22 Oct 2026 14:04:48 -0500 Subject: [PATCH 2/2] Add original-response rank limits and dyadic reciprocal coefficient classification --- .../COMMANDS.json | 32 + .../FINAL-PACKAGE-CHECKS.json | 188 + .../PRE-REPLAY-SOURCES.json | 18 + .../REPLAY.json | 226 + .../REVIEW.json | 136 + .../original-j-rank-readers-review/REVIEW.md | 202 + .../REVIEWED-ANNEX-MANIFEST.json | 630 + .../REVIEWED-BODY-ADDENDUM.template.md | 21 + .../WRAPPER-DELTA.json | 53 + .../WRAPPER-DELTA.patch | 20 + .../cold-replay/REPLAY.json | 226 + .../cold-replay/grid/normal/GRID-CHECKS.json | 67 + .../cold-replay/grid/normal/stdout.log | 1 + 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The added root notice and stopped-product file match their retained SHA256 and declared Git blob identifiers. No independent remote or Git-object existence check was performed in this review.", + "runtime_boundary_method": "Read the six executed checkers and their import paths; isolated fresh-copy execution. No separate runtime access trace.", + "standard_library_only": true + }, + "status": "PASS_INDEPENDENT_ORIGINAL_J_RANK_READERS_REVIEW" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEW.md b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEW.md new file mode 100644 index 0000000000..bfa16612a5 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEW.md @@ -0,0 +1,202 @@ +# Independent review of the original-J rank and reader annex + +The mathematical claims pass this bounded review. The original-J rank +theorem, its local rational words, the common-grid composition theorem, +and the later source-cut reader theorem have the scope stated below. +These results do not improve the complete kappa calculation or admit a +supplier to the current selected result. This review is separate from +the earlier review of the reciprocal package and its low-displacement +annex. + +The reviewed annex is +`packages/reciprocal-native-responses/annexes/original-j-rank-readers`. +`REVIEW.json` binds the final file set, source manifest, proposed body, +and review receipts. All 73 frozen inputs match the campaign originals. +The fresh replay passed all 12 jobs in normal and optimized Python. +The source proofs and all six executed checkers were read. The argument +review below is separate from those finite checks. + +## Original-J rank theorem + +The theorem fixes the actual matrices K and R with RK=14I8 and the +family J=I-KR, E=J+KMR, G=J+KNR. It measures the ranks of the two +specified correction queries MR and NR, which equal rank M and rank N +because R is onto. + +Direct expansion, in the stated order, gives + + EG-I = K [12I-13(M+N)+14MN] R. + +K is injective and R is onto. Thus EG=I is equivalent to the vanishing +of the bracket. The same condition is + + (14M-13I)(14N-13I)=I. + +For square matrices over Q, a right inverse is also a left inverse. +This proves the reversed identity and MN=NM without an assumption that +M and N commute. + +For dyadic M and N, reduction modulo 13 gives MN=I over F13. Both +matrices have rank eight over Q. The correction-rank sum is therefore +16, and M=N=I attains it. This example also makes E=G=I. It prevents +the theorem from being used as a lower bound on every way to implement +the full responses. + +Over Q, the equation + + 12I = 13M+(13I-14M)N + +gives rank M+rank N at least eight. In an equality case, v in ker N +implies Mv=(12/13)v. The rank equality then gives ker N=im M. The +reversed equation gives ker M=im N. These two spaces form a direct +sum. Hence every equality case is + + M=(12/13)P, N=(12/13)(I-P), P^2=P. + +Conversely, each such projection gives a reciprocal pair. Orthogonality +is not required. The proof of the one-sided 13-integral restriction is +also valid: if M is 13-integral, 13M-12I is invertible, so the reciprocal +equation forces N to have full rank. A four/four split therefore needs +a factor 13 in both coefficient sets. + +The independent finite check reconstructs K and R from the clean +payload, tests all 256 coordinate projections, checks nine full +112-column examples in both orders, and rejects three false variants. +The general bound and equality classification follow from the algebra +above, not from this enumeration. + +## Local original-J words and grid scope + +The eight retained words are E and G, in both orientations, for both +providers. The reverse-column checker uses free ordered K and dual_K +words. It only cancels adjacent inverse letters. It checks all 640 +arbitrary input columns, all 408 logical helper fields, every frame, +and all 91 private zero returns. Removing the four inserted centre +blocks leaves the exact clean source word. + +For each selected four-row set S, the checked response is + + T=I-sum(j in S) R_j^T R_j/52 + -sum(j not in S) R_j^T R_j/4. + +The backward contract uses -T^T. It does not replace a transpose with +an inverse. The complementary E and G give the reciprocal pair. The +physical q boundary factors remain in their stated order. + +Each forward word has 165594 dyadic real primitives; each backward +word has 165618. Each also has 16 real /13 scans, 3511 native children, +and rank mass 5105. The scans and full bit-machine cost are separate. +C0 ends at zero at I. C1 through C7 retain arbitrary input values at I. +A contract that requires all eight owned fields to end at zero needs +seven further CLEARs, at a cost of 14 scalar primitives. + +The eight pre-division observables have Gaussian-dyadic coefficients +relative to the input. Each division therefore introduces at most one +new factor 13. Dyadic events cannot increase that height. This proves +one new local denominator level for the literal word, rather than one +level per division. The checker binds all 32 new centre occurrences to +the exact recipes from the prior 3036-class phase review. This replay +does not repeat that phase sweep. + +The common-grid theorem needs exact Gaussian-dyadic full-state +endpoints for completed recursive children, including all permitted +helper inputs. After such children are contracted, unfinished calls +form one active path. If each call adds at most D odd levels and the +depth is L, height at most DL follows without commuting any maps. +The root must scale all numeric fields by a sufficient common power +of 13; arbitrary finest-grid numerators are outside this claim. A +dyadic root endpoint is required before final unscaling. The signed +scan recurrence and its carry bounds are correct. The finite check +covers 32766 signed inputs per scan and five nested test trees, with +three negative controls. E and G individually have rational endpoints +and do not satisfy the completed-provider premise. + +## Later reader cuts use a different response family + +The reader packet uses E=P R, with P^2=R^2=I and R=I+U ell of +rank-16 displacement. Its P has 160 nonzero physical entries and is +not a monomial map. This family is distinct from the original-J +correction-rank theorem above. + +The source-cut derivation retains the order of the entry and exit +maps and the translation in the dimension-25 view. With + + t=y+R0 x, + w=x-P0^-1 R1 P0 t, + +the three logical queries are ell0 x, ell1 P0 t, and ell2 P1 P0 w. +Their physical types are F9, F9 q_anchor, and F25. In particular, the +middle record does not have the FULL frame. + +The independent phase check uses the pinned exact engine, retains +the complete phase polynomial and route order, and tests 1792 typed +identities. It rejects a missing entry translation and a false FULL +middle return. The native endpoint contract is an explicit premise +of this source-cut check; it does not replay the native word. + +The 136 nonzero coefficients of ell give a conditional additive +reader on 16 supplied, independent, correctly typed accumulators. +It leaves all source fields unchanged and retains the arbitrary +accumulator baseline. Its 136 complex ADDs cost 1088 real scalar +units; three formations cost 3264. The prefix row one-norm is 11, +and all coefficients are integral. The independent check covers +the 128 active input columns; the other 528 fields are untouched. +The literal binding check compares all 272 real formation +instructions, all 272 immediate inverse instructions, the three +ordered queries, and their types. + +These facts do not supply the accumulator records, a clean baseline, +their storage or transport, typed views, record leases, a late erase, +or a complete native invoice. The immediate inverse uses an unchanged +source and does not prove that a saved record can be erased later. + +## Fresh replay and package boundary + +`COMMANDS.json` gives the actual fresh-copy command. `REPLAY.json` +and `cold-replay/` retain all receipts and logs. The six jobs were +rank, grid, original-J words, reader producer, independent reader +review, and literal binding. Each ran with `-I -B`, then with `-O` +as well. One child process ran at a time. The 12 jobs used 21.778 +seconds in total on this host. + +After this run, the producer changed only the output-comparison +description in the runner report and source manifest. `WRAPPER-DELTA.json` +and its patch retain this exact change. The final producer replay uses +those final wrapper hashes. This review separately checks its 12 sets +of raw output hashes and normalized contents against the independent +run. The final annex has 126 files and 5,525,013 bytes. Its 125 manifest +entries and exact inventory pass. All 152 previously reviewed parent +files remain unchanged. The proposed body has no claim defect; its +commit placeholders remain outside the annex. + +Files without path metadata use exact byte comparison. Reader +payloads, reader receipts, and source-manifest keys use complete +canonical JSON comparison after the declared path changes. Before +normalization, the raw decompressed reader payload must match its +raw receipt hash. The runner then substitutes the hash of the +canonical payload. It retains every other field and verifies all +four source pins. It does not discard a mathematical field or a +payload binding to make a fresh path pass. + +The executed scripts use the standard library and paths derived +from their copied locations. The independent source-cut checker +imports its retained phase engine; the rank, native-word, and +binding checkers do not import producer code. The historical +absolute paths occur as receipt metadata. They are not runtime +input paths. This boundary was checked by source inspection and +the isolated fresh replay; no separate runtime file-access trace +is claimed. + +The producer native emitter, the original 3036-class phase sweep, +the later reader native-event word, current supplier admission, +global controller, recursive supplier, precision, and complete +kappa calculation were not rerun here. The final GitHub commit +links, rendered PR body, and published readback remain the +coordinator's publication checks. This review makes no Git or +publication change. + +OpenAI Codex performed this independent review under the user's +direction. The retained proofs and notices give predecessor +credit. The earlier reciprocal package review remains valid only +for its own recorded file set; this review records the new annex +separately. diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEWED-ANNEX-MANIFEST.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEWED-ANNEX-MANIFEST.json new file mode 100644 index 0000000000..3d8913e284 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEWED-ANNEX-MANIFEST.json @@ -0,0 +1,630 @@ +{ + "files": [ + { + "bytes": 3404, + "path": "EXTERNAL-NOTICES.json", + "sha256": "164aae3ae2555e9c062162f1e2793cc07d912365d37f3d05f4e6b5b822699ed9" + }, + { + "bytes": 11357, + "path": "LICENSE", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4" + }, + { + "bytes": 3336, + "path": "NOTICE.md", + "sha256": "6527e554ae45eb9431321e04a3ee3d77d11f4a0b2bff33f1bc115cd188e3ba79" + }, 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+ "path": "notices/PR3133-NOTICE", + "sha256": "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661" + }, + { + "bytes": 8465, + "path": "replay.py", + "sha256": "16578a52cb555ce18db1447ac2025c265b1de305f07bf5cbb336548d4dfc2338" + } + ], + "scope": "Additive original-J rank and later reciprocal-reader annex. All accepted parent files and frozen campaign inputs are unchanged." +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEWED-BODY-ADDENDUM.template.md b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEWED-BODY-ADDENDUM.template.md new file mode 100644 index 0000000000..1c8ddd63ba --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEWED-BODY-ADDENDUM.template.md @@ -0,0 +1,21 @@ +The [original-J rank and reader annex](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/original-j-rank-readers/README.md) adds two distinct results. The [rank proof and independent review](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/REVIEW.md) classify reciprocal extensions `E=J+KMR`, `G=J+KNR` of the actual clean `J=I-KR`, where `RK=14I_8`. Dyadic corrections each have rank eight. Over the rationals the minimum rank sum is eight, and every equality case is `M=(12/13)P`, `N=(12/13)(I-P)` for a projection P. This measures the specified correction terms, not the native or query cost of every implementation. The later `E=P R` response is a different family. + +The [literal coordinate rank-four words](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/REVIEW.md) cover both responses, orientations, and historical providers. Each word uses 3,511 native children and rank mass 5,105. Forward words cost 165,594 dyadic real primitives and backward words 165,618, with 16 real division-by-13 scans priced separately. All 408 logical helpers are restored. C0 returns zero at I; C1 through C7 retain their arbitrary inputs. Clearing those seven owned outputs costs 14 more primitives. These rational endpoints are not completed dyadic recursive providers. Ordered physical q factors, controller composition, hosting, a complete precision guard, and the full invoice remain obligations. + +The [reader-cut proof and independent review](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/REVIEW.md) instead use the later signed-metric `E=P R` model. They identify the ordered readers `ell0 x`, `ell1 P0 t`, and `ell2 P1 P0 w` at actual F/B/F cuts. Their returned frames are F9, **F9 q_anchor**, and F25; the middle record is a hole record. Each formation costs 136 complex ADDs, or 1,088 inherited real scalar units, if sixteen separate typed accumulators are supplied. It retains an arbitrary accumulator baseline. The count excludes record supply, accumulator views, preparation, retention, transport, leases, and late erase. No reader native-event replay or complete native invoice is claimed. + +The [fresh receipt](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/REPLAY.json) records twelve normal/optimized checks: the scalar rank cases, conditional grid checks, eight original-J local words, reader producer, independent cut review, and literal binding. The [fresh separate agent review](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/REVIEW.md) records its independent replay and proof limits. The original-J word review binds changed centre calls to the retained native phase evidence; it does not repeat the 3,036-class phase sweep. Reader results with absolute source paths use complete canonical JSON comparison after raw payload-hash binding. All other fields are retained. + +With Python 3.11+, the standard library, at least 3 GiB free space, and a new output directory: + +```sh +python3 -I -B research/reciprocal-native-responses/annexes/original-j-rank-readers/replay.py --out /tmp/original-j-rank-readers +``` + +Expected final line: + +```text +PASS_ORIGINAL_J_RANK_READERS_ANNEX +``` + +All 73 frozen sources and all 152 prior package files stay unchanged. The [notice](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/original-j-rank-readers/NOTICE.md) preserves the campaign credit, [PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), and [PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588) source lineage, and the stopped-product grid credit to @icekylinx. Historical commits and Apache-2.0 notices stay fixed. Substantial OpenAI Codex assistance was used. The refreshed main context remains [b58ad9ef](https://github.com/CrocSwap/integer-mult-bounds/commit/b58ad9ef4d4e861b0eaa5dba41742bdc072dca51); this annex proves no transfer to its selected [PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470) construction and gives **no complete kappa improvement**. diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/WRAPPER-DELTA.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/WRAPPER-DELTA.json new file mode 100644 index 0000000000..44e61734ec --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/WRAPPER-DELTA.json @@ -0,0 +1,53 @@ +{ + "all_73_frozen_inputs_match_campaign": true, + "changes_since_independent_replay": [ + "SOURCES.json comparison description", + "replay.py report comparison description" + ], + "executed_checkers_and_input_bytes_changed": false, + "external_notice_checks": [ + { + "file": "notices/PR2588-NOTICE", + "retained_parent_notice": true, + "sha256": "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b" + }, + { + "file": "notices/PR3133-NOTICE", + "retained_parent_notice": true, + "sha256": "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661" + }, + { + "file": "notices/PR3133-CREDITS.md", + "retained_parent_notice": true, + "sha256": "1d9d8f56d8899f55878e4cb2c4e052b22506444016a51c2e678773505f5189e6" + }, + { + "file": "notices/PR2588-NOTICE-PR2226.md", + "retained_parent_notice": true, + "sha256": "6b6730303818f6edc2a253eb4d05471eee58f28b5815fb250c32ae376f774c8a" + }, + { + "file": "notices/PR2226-NOTICE.md", + "retained_parent_notice": true, + "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422" + }, + { + "file": "notices/HISTORICAL-ROOT-NOTICE", + "retained_parent_notice": false, + "sha256": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd" + }, + { + "file": "frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex", + "retained_parent_notice": false, + "sha256": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a" + } + ], + "external_notice_scope": "Five notices match the prior reviewed parent package. The added root notice and stopped-product file match their retained SHA256 and declared Git blob identifiers. No independent remote or Git-object existence check was performed in this review.", + "final_runner_sha256": "16578a52cb555ce18db1447ac2025c265b1de305f07bf5cbb336548d4dfc2338", + "final_sources_sha256": "5f94525a446f86ca6e52c3187e042f90b69f389a40fb2f6b22298d3614880d63", + "prior_parent_package_files_unchanged": 152, + "prior_review_sha256": "32fd59d6a849cb2ace531936ebe6566bec85ba07dcb95ca1e29602a3982c1d83", + "replayed_runner_sha256": "45cdb69b04a2ea1453a62fa475d7b382ed9a9333e0218509e50d9684dae05204", + "replayed_sources_sha256": "7e941c421f833f8bf24d636e14c3e688483a9e7dc2c12d6cb28555b5faa72f06", + "status": "PASS" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/WRAPPER-DELTA.patch b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/WRAPPER-DELTA.patch new file mode 100644 index 0000000000..000e91720d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/WRAPPER-DELTA.patch @@ -0,0 +1,20 @@ +--- replayed/replay.py ++++ final/replay.py +@@ -153,7 +153,7 @@ + "source_manifest_sha256": digest((HERE / "SOURCES.json").read_bytes()), + "runner_sha256": digest(Path(__file__).read_bytes()), "python": platform.python_version(), + "platform": platform.platform(), "child_processes_run_concurrently": 1, +- "comparison": "Exact bytes except the four reader source paths and SOURCE-MANIFEST keys. The raw decompressed reader payload is first bound to its raw receipt; its canonical hash then replaces that receipt field. All other fields are compared.", ++ "comparison": "Exact bytes for files without source paths. Complete canonical JSON comparison for reader CHECKS, decompressed READERS, and SOURCE-MANIFEST: normalize only the four source paths or manifest keys. Bind the raw reader payload to its raw receipt first, then use the canonical payload hash in the canonical receipt. Compare every other field.", + "omitted": ["Producer native re-emission", "Original 3036-class phase sweep", "Reader native-event replay", "Accumulator supply, transport, and late erasure", "Global controller, recursive supplier, precision, and complete kappa calculation"]} + (out / "REPLAY.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + print(report["status"]) +--- replayed/SOURCES.json ++++ final/SOURCES.json +@@ -1,5 +1,5 @@ + { +- "comparison": "Exact frozen input bytes; decompressed payload comparison for regenerated gzip output.", ++ "comparison": "Exact bytes for frozen inputs. replay.py defines complete output comparisons, including the explicit path normalization for reader JSON and source manifests.", + "files": [ + { + "bytes": 202201, diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/REPLAY.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/REPLAY.json new file mode 100644 index 0000000000..53f7f1887d --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/REPLAY.json @@ -0,0 +1,226 @@ +{ + "checks": [ + { + "all_result_fields_compared": true, + "check": "rank", + "files": { + "CHECKS.json": { + "comparison_sha256": "4cbe8ca3e0af51192fb113a2879467b30af19fc68b0f9713991e1f0bef2b2e7c", + "raw_sha256": "4cbe8ca3e0af51192fb113a2879467b30af19fc68b0f9713991e1f0bef2b2e7c" + } + }, + "mode": "normal", + "seconds": 3.531, + "status": "PASS" + }, + { + "all_result_fields_compared": true, + "check": "rank", + "files": { + "CHECKS.json": { + "comparison_sha256": "4cbe8ca3e0af51192fb113a2879467b30af19fc68b0f9713991e1f0bef2b2e7c", + "raw_sha256": "4cbe8ca3e0af51192fb113a2879467b30af19fc68b0f9713991e1f0bef2b2e7c" + } + }, + "mode": "optimized", + "seconds": 3.458, + "status": "PASS" + }, + { + "all_result_fields_compared": true, + "check": "grid", + "files": { + "GRID-CHECKS.json": { + "comparison_sha256": "4f12b6f0ed60343ad03be226e162df6a918caf813ab46ad88105c85a28fae412", + "raw_sha256": "4f12b6f0ed60343ad03be226e162df6a918caf813ab46ad88105c85a28fae412" + } + }, + "mode": "normal", + "seconds": 0.154, + "status": "PASS" + }, + { + "all_result_fields_compared": true, + "check": "grid", + "files": { + "GRID-CHECKS.json": { + "comparison_sha256": "4f12b6f0ed60343ad03be226e162df6a918caf813ab46ad88105c85a28fae412", + "raw_sha256": "4f12b6f0ed60343ad03be226e162df6a918caf813ab46ad88105c85a28fae412" + } + }, + "mode": "optimized", + "seconds": 0.226, + "status": "PASS" + }, + { + "all_result_fields_compared": true, + "check": "original_j_words", + "files": { + "CHECKS.json": { + "comparison_sha256": "3e2238c8e94c8b20c12c68564e4e9b929d78f485bda66b5835a3e0960dffa63e", + "raw_sha256": "3e2238c8e94c8b20c12c68564e4e9b929d78f485bda66b5835a3e0960dffa63e" + } + }, + "mode": "normal", + "seconds": 5.662, + "status": "PASS" + }, + { + "all_result_fields_compared": true, + "check": "original_j_words", + "files": { + "CHECKS.json": { + "comparison_sha256": "3e2238c8e94c8b20c12c68564e4e9b929d78f485bda66b5835a3e0960dffa63e", + "raw_sha256": "3e2238c8e94c8b20c12c68564e4e9b929d78f485bda66b5835a3e0960dffa63e" + } + }, + "mode": "optimized", + "seconds": 5.631, + "status": "PASS" + }, + { + "all_result_fields_compared": true, + "check": "reader_producer", + "files": { + "CHECKS.json": { + "comparison_sha256": "0097e4ce86d955d43ab926f84ee7407b8f01ba4923293c088e380e369cf8d41b", + "raw_sha256": "e4fa4469bb6cda4922e13c39062cbf57ef1d49049c2fc955266ab710cea31646" + }, + "READERS.json.gz": { + "comparison_sha256": "93d5f28d800f1e11983391e9b8195c2dafa7664cb4c6186c74aa163db07f4ea5", + "decompressed_sha256": "38326f6a18e1d38556a259a47ac94d95fe2caef2c54c57fb3042f442f36eb489", + "raw_sha256": "cbad3f9636e56bade9a5e8994aa677297fd782e5972c3fb62ba1ec8af4ed358d" + } + 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The raw decompressed reader payload is first bound to its raw receipt; its canonical hash then replaces that receipt field. All other fields are compared.", + "frozen_sources_unchanged": true, + "omitted": [ + "Producer native re-emission", + "Original 3036-class phase sweep", + "Reader native-event replay", + "Accumulator supply, transport, and late erasure", + "Global controller, recursive supplier, precision, and complete kappa calculation" + ], + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "python": "3.14.7", + "runner_sha256": "45cdb69b04a2ea1453a62fa475d7b382ed9a9333e0218509e50d9684dae05204", + "source_files": 73, + "source_manifest_sha256": "7e941c421f833f8bf24d636e14c3e688483a9e7dc2c12d6cb28555b5faa72f06", + "status": "PASS_ORIGINAL_J_RANK_READERS_ANNEX" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/normal/GRID-CHECKS.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/normal/GRID-CHECKS.json new file mode 100644 index 0000000000..50cbc391f9 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/normal/GRID-CHECKS.json @@ -0,0 +1,67 @@ +{ + "checker_sha256": "e257f0a984b9e7f4f86f25a9e2991f03e3ff0c93888be9ff75a717186af85641", + "negative_controls": [ + "unscaled finest-grid numerator", + "three rational completed children with a two-level budget", + "final unscaling before a dyadic root endpoint" + ], + "nested_integer_basis_cases": [ + { + "active_levels": 1, + "binary_budget": 8, + "completed_calls": 1, + "divisions": 0, + "events": 1, + "max_active_levels": 1, + "max_height": 0, + "odd_budget": 8 + }, + { + "active_levels": 2, + "binary_budget": 16, + "completed_calls": 3, + "divisions": 8, + "events": 19, + "max_active_levels": 2, + "max_height": 1, + "odd_budget": 16 + }, + { + "active_levels": 3, + "binary_budget": 24, + "completed_calls": 7, + "divisions": 24, + "events": 55, + "max_active_levels": 3, + "max_height": 2, + "odd_budget": 24 + }, + { + "active_levels": 4, + "binary_budget": 32, + "completed_calls": 15, + "divisions": 56, + "events": 127, + "max_active_levels": 4, + "max_height": 3, + "odd_budget": 32 + }, + { + "active_levels": 5, + "binary_budget": 40, + "completed_calls": 31, + "divisions": 120, + "events": 271, + "max_active_levels": 5, + "max_height": 4, + "odd_budget": 40 + } + ], + "scope": "Exact signed scans and test trees. The general active-path bound is proved in ODD-GRID-COMPOSITION.md. These trees are not an emitted supplier controller.", + "signed_inputs_checked_for_each_scan": 32766, + "signed_scan_widths": [ + 1, + 14 + ], + "status": "PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/normal/stdout.log b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/normal/stdout.log new file mode 100644 index 0000000000..b4f6e13eb2 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/optimized/GRID-CHECKS.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/optimized/GRID-CHECKS.json new file mode 100644 index 0000000000..50cbc391f9 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/optimized/GRID-CHECKS.json @@ -0,0 +1,67 @@ +{ + "checker_sha256": "e257f0a984b9e7f4f86f25a9e2991f03e3ff0c93888be9ff75a717186af85641", + "negative_controls": [ + "unscaled finest-grid numerator", + "three rational completed children with a two-level budget", + "final unscaling before a dyadic root endpoint" + ], + "nested_integer_basis_cases": [ + { + "active_levels": 1, + "binary_budget": 8, + "completed_calls": 1, + "divisions": 0, + "events": 1, + "max_active_levels": 1, + "max_height": 0, + "odd_budget": 8 + }, + { + "active_levels": 2, + "binary_budget": 16, + "completed_calls": 3, + "divisions": 8, + "events": 19, + "max_active_levels": 2, + "max_height": 1, + "odd_budget": 16 + }, + { + "active_levels": 3, + "binary_budget": 24, + "completed_calls": 7, + "divisions": 24, + "events": 55, + "max_active_levels": 3, + "max_height": 2, + "odd_budget": 24 + }, + { + "active_levels": 4, + "binary_budget": 32, + "completed_calls": 15, + "divisions": 56, + "events": 127, + "max_active_levels": 4, + "max_height": 3, + "odd_budget": 32 + }, + { + "active_levels": 5, + "binary_budget": 40, + "completed_calls": 31, + "divisions": 120, + "events": 271, + "max_active_levels": 5, + "max_height": 4, + "odd_budget": 40 + } + ], + "scope": "Exact signed scans and test trees. 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These trees are not an emitted supplier controller.", + "signed_inputs_checked_for_each_scan": 32766, + "signed_scan_widths": [ + 1, + 14 + ], + "status": "PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/optimized/stdout.log b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/optimized/stdout.log new file mode 100644 index 0000000000..b4f6e13eb2 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/grid/optimized/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/normal/CHECKS.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/normal/CHECKS.json new file mode 100644 index 0000000000..35105851d5 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/normal/CHECKS.json @@ -0,0 +1,550 @@ +{ + "checker_sha256": "8a9023adc5ebe5ce1f9ff09b5ce02c00ef58cd0bb695c9a26b1b8cee606cf913", + "clean_payload_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "negative_controls": { + "changed_centre_input_frame": true, + "changed_centre_scatter_sign": true, + "erased_untouched_arbitrary_owned_input": true, + "omitted_weighted_entrance_division": true + }, + "payload_decompressed_sha256": "8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013", + "phase_scope": "Exact byte binding to the prior independent all-3036-edge review, including all 32 centre directions and literal backward dual warps. 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adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + } + }, + "scope": "Complete local rational maps, arbitrary logical helper restoration, typed native occurrences, scalar and native invoices, and one new 13-denominator level. No global controller, new recursive provider, owner layout, or kappa claim.", + "source_pins": { + "independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json": "924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d", + "independent-review-20261017/check_new_native.py": "937543157459e5c0eee788feefcf2107acf6bdf660a1209cdecece1ca1f26d01", + "new-native-recipes-20261017/base/CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "reciprocal-centre-20261018/FREEZE.json": "b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd", + "reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md": "322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737", + "reciprocal-centre-20261018/emit_reciprocal_centres.py": "cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc", + "reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-RECEIPT.json": "aafaa8b17be476d521fe4c8eb3cf3af59c72351c3aba60a9413cd2aa0baafdfc" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/normal/stdout.log b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/normal/stdout.log new file mode 100644 index 0000000000..a15817dbaa --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/normal/stdout.log @@ -0,0 +1,9 @@ +base E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/optimized/CHECKS.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/optimized/CHECKS.json new file mode 100644 index 0000000000..35105851d5 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/optimized/CHECKS.json @@ -0,0 +1,550 @@ +{ + "checker_sha256": "8a9023adc5ebe5ce1f9ff09b5ce02c00ef58cd0bb695c9a26b1b8cee606cf913", + "clean_payload_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "negative_controls": { + "changed_centre_input_frame": true, + "changed_centre_scatter_sign": true, + "erased_untouched_arbitrary_owned_input": true, + "omitted_weighted_entrance_division": true + }, + "payload_decompressed_sha256": "8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013", + "phase_scope": "Exact byte binding to the prior independent all-3036-edge review, including all 32 centre directions and literal backward dual warps. No second compiler or phase interpreter is claimed in this run.", + "providers": { + "base": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + }, + "extra": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + } + }, + "scope": "Complete local rational maps, arbitrary logical helper restoration, typed native occurrences, scalar and native invoices, and one new 13-denominator level. No global controller, new recursive provider, owner layout, or kappa claim.", + "source_pins": { + "independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json": "924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d", + "independent-review-20261017/check_new_native.py": "937543157459e5c0eee788feefcf2107acf6bdf660a1209cdecece1ca1f26d01", + "new-native-recipes-20261017/base/CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "reciprocal-centre-20261018/FREEZE.json": "b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd", + "reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md": "322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737", + "reciprocal-centre-20261018/emit_reciprocal_centres.py": "cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc", + "reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-RECEIPT.json": "aafaa8b17be476d521fe4c8eb3cf3af59c72351c3aba60a9413cd2aa0baafdfc" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/optimized/stdout.log b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/optimized/stdout.log new file mode 100644 index 0000000000..a15817dbaa --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/original_j_words/optimized/stdout.log @@ -0,0 +1,9 @@ +base E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/normal/CHECKS.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/normal/CHECKS.json new file mode 100644 index 0000000000..df1ae1872e --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/normal/CHECKS.json @@ -0,0 +1,84 @@ +{ + "actual_K_row_l1": 1, + "actual_R_row_l1": 56, + "checker_sha256": "550330e2c6b5b485f531c9c1f0b633ec55d6a2200839903b4f1fc3d4da9ade1e", + "coordinate_projection_checks": 256, + "coordinate_rank_distribution": { + "0": 1, + "1": 8, + "2": 28, + "3": 56, + "4": 70, + "5": 56, + "6": 28, + "7": 8, + "8": 1 + }, + "full_inverse_cases": [ + { + "basis_columns_per_order": 112, + "label": "coordinate-0", + "rank_M": 0, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-1", + "rank_M": 1, + "rank_N": 7 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-15", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-127", + "rank_M": 7, + "rank_N": 1 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-255", + "rank_M": 8, + "rank_N": 0 + }, + { + "basis_columns_per_order": 112, + "label": "noncoordinate-rank-four", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "general-centre-unit", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "nontrivial-dyadic-full-rank", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "13-integral-rank-four-forces-full-rank-partner", + "rank_M": 4, + "rank_N": 8 + } + ], + "method": "Independent dense centre algebra and 112-column vector interpreter; no producer imports.", + "negative_controls": [ + "wrong coefficient", + "repeated response", + "arbitrary noncommuting pair" + ], + "ordered_noncommuting_identity_columns": 112, + "scope": "Exact scalar family and query ranks. No full native word, phase terminal, controller, or complete supplier price is certified here.", + "source_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "source_proof_sha256": "d2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9", + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_RANK" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/normal/stdout.log b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/normal/stdout.log new file mode 100644 index 0000000000..0900be1cf7 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_RECIPROCAL_CENTRE_RANK diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/optimized/CHECKS.json b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/optimized/CHECKS.json new file mode 100644 index 0000000000..df1ae1872e --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/rank/optimized/CHECKS.json @@ -0,0 +1,84 @@ +{ + "actual_K_row_l1": 1, + "actual_R_row_l1": 56, + "checker_sha256": "550330e2c6b5b485f531c9c1f0b633ec55d6a2200839903b4f1fc3d4da9ade1e", + "coordinate_projection_checks": 256, + "coordinate_rank_distribution": { + "0": 1, + "1": 8, + "2": 28, + "3": 56, + "4": 70, + "5": 56, + "6": 28, + "7": 8, + "8": 1 + }, + "full_inverse_cases": [ + { + "basis_columns_per_order": 112, + "label": "coordinate-0", + "rank_M": 0, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-1", + "rank_M": 1, + "rank_N": 7 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-15", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-127", + "rank_M": 7, + "rank_N": 1 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-255", + "rank_M": 8, + "rank_N": 0 + }, + { + "basis_columns_per_order": 112, + "label": "noncoordinate-rank-four", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "general-centre-unit", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "nontrivial-dyadic-full-rank", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "13-integral-rank-four-forces-full-rank-partner", + "rank_M": 4, + "rank_N": 8 + } + ], + "method": "Independent dense centre algebra and 112-column vector interpreter; no producer imports.", + "negative_controls": [ + "wrong coefficient", + "repeated response", + "arbitrary noncommuting pair" + ], + "ordered_noncommuting_identity_columns": 112, + "scope": "Exact scalar family and query ranks. 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b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/reader_producer/normal/CHECKS.json new file mode 100644 index 0000000000..a8bed7e3f3 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/reader_producer/normal/CHECKS.json @@ -0,0 +1,49 @@ +{ + "additional_coefficient_binary_height": 0, + "arbitrary_input_columns_per_local_reader": 656, + "checker_sha256": "b3c15399f56018680b93cc3254218ced032ea9f2dbcbd080814fa1a63f556d45", + "complete_supplier_claimed": false, + "extra_source_native_lines_at_these_cuts": 0, + "independent_typed_accumulators_required": 16, + "native_word_replayed_here": false, + "omitted_entry_translation_failures": 224, + "payload_decompressed_sha256": "38326f6a18e1d38556a259a47ac94d95fe2caef2c54c57fb3042f442f36eb489", + "per_reader_real_scalar_units": 1088, + "phase_counts": { + "FULL_exit": 224, + "FULL_source_entry": 224, + "hole_target_entry": 224 + }, + "prefix_row_one_norm": "11", + "reader_coefficients": { + "-1": 90, + "1": 46 + }, + "reader_nonzeros": 136, + "reader_row_lengths": { + "7": 8, + "10": 8 + }, + "reader_source_port_support": 96, + "record_retention_or_restoration_claimed": false, + "source_or_helper_fields_modified": 0, + "source_pins": { + "model": { + "path": "/private/tmp/original-j-independent-20261022-87s57kva/results/reader_producer/normal/campaign/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz", + "sha256": "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0" + }, + "native": { + "path": "/private/tmp/original-j-independent-20261022-87s57kva/results/reader_producer/normal/campaign/lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/native-normal/NATIVE.json.gz", + "sha256": "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e" + }, + "scalar_tariff": { + "path": "/private/tmp/original-j-independent-20261022-87s57kva/results/reader_producer/normal/campaign/lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py", + "sha256": "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8" + }, + "views": { + "path": "/private/tmp/original-j-independent-20261022-87s57kva/results/reader_producer/normal/campaign/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + } + }, + "status": "PASS_EXACT_CURRENT_READER_CUTS" +} diff --git a/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/reader_producer/normal/READERS.json.gz b/research/publication-reviews/reciprocal-native-responses/original-j-rank-readers-review/cold-replay/reader_producer/normal/READERS.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..d2fd3a1057ef5ff4e30d7fbfd232c075f7906fd1 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z6=|+eoaLbU4^-xdcsEx!{^-Kn_P%PzX`n{p{Cd84`fGsdw9MjGetI>(9NY6t^T(m~ zUHCA%<%WjXk5hZ=7QbJP<9?Xh>$a!Sei6@Js}{7)MkY#$+|Js*yLJ1?&!=vg_vcwl zvY|dze%cS?(jMDieZ8;TadhoPFSnF|Ue(e%6PyqHudi zQz>iPq_SxW;~Q^PW12!~+Y|*AaFtKeq-nCWPIk1pXAA$AcIdIkd5iY1zxm@|KkZXD+=;rK$Iey$_-wjlzrGJ&(p=-v&;G@D|9n#_Qx`;- zGM}ZH&ZY6Wp@7zyO4i<~tU1)h!T91pQMYMo= 3 * 1024**3, "At least 3 GiB free disk space is required") + out.mkdir(exist_ok=False) + sources = check_sources() + checks = [] + for job, relative, script, has_out, expected_relative, names in JOBS: + previous = None + expected = comparable(job, FROZEN / expected_relative, HISTORICAL_ROOT, names) + for mode in ("normal", "optimized"): + result = out / job / mode + result.mkdir(parents=True) + work = result / "campaign" + shutil.copytree(FROZEN, work) + command = [sys.executable, "-I", "-B"] + (["-O"] if mode == "optimized" else []) + command.append(str(work / relative / script)) + produced = result / "generated" if has_out else work / relative + if has_out: + command += ["--out", str(produced)] + start = time.monotonic() + with (result / "stdout.log").open("w") as log: + run = subprocess.run(command, cwd=work, stdout=log, stderr=subprocess.STDOUT, check=False) + need(run.returncode == 0, "Failed " + job + " " + mode + "; read " + str(result / "stdout.log")) + actual = comparable(job, produced, work, names) + need(actual == expected, "Frozen result comparison: " + job + " " + mode) + need(previous is None or actual == previous, "Normal and optimized comparison: " + job) + previous = actual + files = {} + for name in names: + data = (produced / name).read_bytes() + shutil.copyfile(produced / name, result / name) + files[name] = {"raw_sha256": digest(data), "comparison_sha256": digest(actual[name])} + if name.endswith(".gz"): + files[name]["decompressed_sha256"] = digest(gzip.decompress(data)) + check = {"check": job, "mode": mode, "status": "PASS", "seconds": round(time.monotonic() - start, 3), + "files": files, "all_result_fields_compared": True} + checks.append(check) + shutil.rmtree(work) + if has_out: + shutil.rmtree(produced) + print(job + " " + mode + " PASS", flush=True) + check_sources() + report = {"status": "PASS_ORIGINAL_J_RANK_READERS_ANNEX", "checks": checks, + "source_files": len(sources["files"]), "frozen_sources_unchanged": True, + "source_manifest_sha256": digest((HERE / "SOURCES.json").read_bytes()), + "runner_sha256": digest(Path(__file__).read_bytes()), "python": platform.python_version(), + "platform": platform.platform(), "child_processes_run_concurrently": 1, + "comparison": "Exact bytes except the four reader source paths and SOURCE-MANIFEST keys. The raw decompressed reader payload is first bound to its raw receipt; its canonical hash then replaces that receipt field. All other fields are compared.", + "omitted": ["Producer native re-emission", "Original 3036-class phase sweep", "Reader native-event replay", "Accumulator supply, transport, and late erasure", "Global controller, recursive supplier, precision, and complete kappa calculation"]} + (out / "REPLAY.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/reciprocal-native-responses/signed-rank-eight-coefficients-review/COMMANDS.json b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/COMMANDS.json new file mode 100644 index 0000000000..a0ec78d8fb --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/COMMANDS.json @@ -0,0 +1,21 @@ +{ + "checks_passed": 4, + "child_processes_run_concurrently": 1, + "command": [ + "python3", + "-I", + "-B", + "/tmp/signed-rank-eight-independent-20261022-ixpvbov0/annex/replay.py", + "--out", + "/tmp/signed-rank-eight-independent-20261022-ixpvbov0/results" + ], + "exit_code": 0, + "expected_status": "PASS_SIGNED_RANK_EIGHT_COEFFICIENT_ANNEX", + "observed_status": "PASS_SIGNED_RANK_EIGHT_COEFFICIENT_ANNEX", + "replay_receipt_sha256": "b0cc0cc608782b4cc2d5f45c15a8aafd2a40392acc0a08bb46565614fec0a2b9", + "runtime": { + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "python": "3.14.7" + }, + "working_directory": "/Users/aliromman/Projects/IntegerMultiplicationBounds" +} diff --git a/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/FINAL-PACKAGE-CHECKS.json b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/FINAL-PACKAGE-CHECKS.json new file mode 100644 index 0000000000..bdde8fd5c3 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/FINAL-PACKAGE-CHECKS.json @@ -0,0 +1,126 @@ +{ + "all_126_original_j_annex_files_unchanged": true, + "all_13_campaign_inputs_unchanged": true, + "all_152_prior_parent_files_unchanged": true, + "annex_file_count": 37, + "annex_manifest_sha256": "2ef0140cf4b659a0aaeacb505a3689c40ca4d3c46c9926b3dd335807bd71872e", + "annex_total_bytes": 649280, + "body_template": { + "claim_findings": [], + "final_commit_links_rendering_and_readback_pending": true, + "local_source_link_targets": [ + "reciprocal-native-responses/annexes/signed-rank-eight-coefficients/README.md", + "reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md", + "reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/REPLAY.json", + "publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.md", + "reciprocal-native-responses/annexes/signed-rank-eight-coefficients/NOTICE.md" + ], + "path": "reciprocal-signed-rank-eight-body-addendum.template.md", + "sha256": "214b03f9a587376452bea8d3b638b75296ede50781411cefce6bb955f0115e1c" + }, + "independent_replay_sha256": "b0cc0cc608782b4cc2d5f45c15a8aafd2a40392acc0a08bb46565614fec0a2b9", + "local_wrapper_links": [ + { + "document": "README.md", + "target": "frozen/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/RECIPROCAL-CENTRES.md" + }, + { + "document": "README.md", + "target": "frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md" + }, + { + "document": "README.md", + "target": "replay.py" + }, + { + "document": "README.md", + "target": "SOURCES.json" + }, + { + "document": "README.md", + "target": "evidence/REPLAY.json" + }, + { + "document": "README.md", + "target": "ANNEX-MANIFEST.json" + }, + { + "document": "README.md", + "target": "NOTICE.md" + }, + { + "document": "NOTICE.md", + "target": "SOURCES.json" + }, + { + "document": "NOTICE.md", + "target": "frozen/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/RECIPROCAL-CENTRES.md" + }, + { + "document": "NOTICE.md", + "target": "frozen/lanes/controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT.md" + }, + { + "document": "NOTICE.md", + "target": "frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md" + }, + { + "document": "NOTICE.md", + "target": "notices/PR3133-NOTICE" + }, + { + "document": "NOTICE.md", + "target": "notices/PR3133-CREDITS.md" + }, + { + "document": "NOTICE.md", + "target": "notices/PR2588-NOTICE" + }, + { + "document": "NOTICE.md", + "target": "notices/PR2588-NOTICE-PR2226.md" + }, + { + "document": "NOTICE.md", + "target": "notices/PR2226-NOTICE.md" + }, + { + "document": "NOTICE.md", + "target": "EXTERNAL-NOTICES.json" + }, + { 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The source gzip file is immutable; its decompressed payload hash is also checked.", + "frozen_sources_unchanged": true, + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "python": "3.14.7", + "runner_sha256": "a0750e44d47d6fd6c49d13b054d8186726b5d9029e36fac6d3c8406e5d3d62ea", + "scope": "The signed48 full-unit and two-principal-unit coefficient classification, its six-step ordinary gauge, and its fixed64 complement. No new native schedule, native phase replay, all-stage composition, precision, supplier invoice, or complete kappa claim.", + "source_files": 13, + "source_manifest_sha256": "74bc60f989a872e9d63181268e56805c48fee2c86a99d388df62887f89527d3e", + "status": "PASS_SIGNED_RANK_EIGHT_COEFFICIENT_ANNEX" +} diff --git a/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.json b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.json new file mode 100644 index 0000000000..e4063fe778 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.json @@ -0,0 +1,93 @@ +{ + "annex": "packages/reciprocal-native-responses/annexes/signed-rank-eight-coefficients", + "annex_file_count": 37, + "annex_manifest_sha256": "2ef0140cf4b659a0aaeacb505a3689c40ca4d3c46c9926b3dd335807bd71872e", + "annex_total_bytes": 649280, + "blocking_findings": [], + 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an additional component-projector assumption.", + "Verified complete all-integer exponent classification using units in Z[1/2] and reduction modulo 3.", + "Verified both principal determinant identities, four-value intersection, injectivity of the coefficient parameterization, and closure of the 48-port family under inversion.", + "Expanded the six-step gauge on arbitrary ordinary data and verified each factor has a dyadic inverse under the stated unit condition.", + "Verified determinant 1 on 48 ports versus 2^-64 on 112 ports and the one-quarter inverse of the fixed 64-port complement.", + "Verified the fixed-family orthogonality equation and retained both principal-only and full-only counterexamples." + ], + "not_claimed": [ + "All dyadic reciprocal response matrices are classified.", + "Principal-unit conditions alone give the 65,536 count.", + "Bounded exponent tests prove the infinite classification.", + "Rank-eight correction gives eight native children or a native-cost lower bound.", + "All coefficient choices have a supplied, restored, phased native word or a uniform scalar invoice.", + "The 112-port interface has determinant one.", + "Inversion leaves the fixed 64-port response complement unchanged.", + "Orthogonality is excluded for other response families.", + "Current selected supplier admission or complete kappa improvement." + ], + "omitted": [ + "Older bipartite native emitter and native-event replay", + "New coefficient native implementation, phase and helper-restoration replay", + "All-stage routed controller and terminal decoding", + "Recursive hosting, precision, complete supplier invoice and kappa calculation", + "Independent remote source-object verification", + "Final GitHub commit links, rendering, and published-body readback" + ], + "original_j_annex_files_unchanged": 126, + "previous_parent_files_unchanged": 152, + "proof_files_read": { + "lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md": 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interface determinant, fixed 64-port complement, and family-specific orthogonality limit.", + "source_manifest_sha256": "74bc60f989a872e9d63181268e56805c48fee2c86a99d388df62887f89527d3e", + "status": "PASS_INDEPENDENT_SIGNED_RANK_EIGHT_COEFFICIENT_REVIEW" +} diff --git a/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.md b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.md new file mode 100644 index 0000000000..333b70b834 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.md @@ -0,0 +1,138 @@ +# Independent review of the signed coefficient annex + +The coefficient theorem and its stated gauge pass this bounded review. +The result is complete for the fixed signed 48-port family and the +specified selected set. It does not supply a native schedule or a +complete supplier price. It gives no complete kappa improvement. + +The reviewed annex is +`packages/reciprocal-native-responses/annexes/signed-rank-eight-coefficients`. +`REVIEW.json` binds its final manifest and proposed body. All 13 frozen +inputs match the campaign originals. Both unchanged checkers passed in +normal and optimized Python from a new temporary copy. The producer +proof, historical independent proof, matrix-source note, and both +executed checkers were read. This review includes the mathematical +argument below, rather than only the historical status or fresh receipts. + +## Full-unit classification + +The actual matrices satisfy KK^T=12I8, G^T=G, G^2=I48, det G=1, and +GK^T=K^T Lambda, with the fixed alternating signs in Lambda. For +D=diag(beta_v), these identities give + + E=G-K^T Lambda D K = G(I-K^T D K), + det E=product_v (1-12 beta_v), + E^-1=G+K^T Lambda diag(beta_v/(1-12 beta_v)) K. + +These formulas follow directly from the matrix identities and retain +factor order. They need no additional component-projector assumption. +For a dyadic beta, 1-12 beta cannot vanish, since 1/12 is not dyadic. + +Put R=Z[1/2] and s_v=1-12 beta_v. A product in R can be a unit only +when each factor is a unit. The determinant and inverse formulas prove +that E is a unit over R exactly when every s_v is a unit. The units of +R are the signed integer powers of two. Reduction modulo three is +defined on R and gives s_v=1 modulo three. It selects precisely + + s_v=(-2)^n_v, + beta_v=(1-(-2)^n_v)/12, n_v in Z. + +Conversely, these coefficients are dyadic for every integer exponent. +Inversion sends n_v to -n_v. This proves the infinite classification; +the finite exponent ranges in the checkers are controls only. + +## Principal blocks and the count + +The selected physical set is S=[0,7,15,36,42,46,79,89]. The actual +minor has det K_S=-4 and G_SS=0. Thus the selected block L has +det L=16 product beta_v. Jacobi's complementary principal-minor +identity, applied to the displayed inverse, gives the same determinant +for H on the other 40 centre ports. This remains valid when a beta +is zero, because the full dyadic response is still invertible over Q. + +Consequently the two principal blocks are units over R exactly when +each beta_v is a unit. Intersect this condition with the full-unit +classification. For positive n, the odd numerator 1-(-2)^n must have +absolute value three. For negative n=-m, clearing 2^m gives the same +test for 2^m-(-1)^m. These equations give only n=-2,-1,1,2. At n=0, +beta is zero. The four coefficients are 1/16,1/8,1/4,-1/4. + +Different parameter vectors give different matrices: multiplication +of K^T Lambda diag(delta) K=0 by K on the left and K^T on the right +gives 144 Lambda diag(delta)=0. There are therefore exactly 4^8=65536 +distinct 48-port responses under the full-unit and both-principal-unit +conditions. This finite 48-port family is closed under inversion. + +The conditions cannot be dropped. Uniform beta=1/2 has both principal +units but full determinant 5^8, which is not a dyadic unit. Uniform +beta=3/4 gives a full unit but nonunit principal blocks. Both cases +are checked. The eight centre rows and the rank of the correction +do not give a native-child count or native-cost lower bound. + +## Gauge, interface, and orthogonality + +In the stated order, the six factors on existing ordinary data give + + t_final=-K_T^T B(K_T t_initial+K_R0 r_initial), + r_final=G_R0 r_initial-K_R0^T B(K_T t_initial+K_R0 r_initial), + B=diag(alpha_v beta_v). + +These expressions equal H on all inputs. The two additions are shears; +K_T, G_R0, and B are dyadic units under the stated condition. Reversing +the six factors therefore gives H^-1. No initial zero or extra centre +field is used. This proves an existing-data factorization, not a +concrete elementary-word price for every coefficient vector. + +The ordered interface factors give det A=det L/det H=1 on the 48-port +part. The fixed 64-port complement has square 4I and determinant 2^64. +Its inverse belongs to the ordinary part of the full interface, which +therefore has determinant 2^-64. The full 112-port response inverse +uses one quarter of the fixed complement. Closure under inversion of +the 48-port coefficient family does not keep that complement unchanged. + +Finally, E is symmetric and + + E^2=I+K^T diag(12 beta_v^2-2 beta_v) K. + +Multiplication by K and K^T makes E^2=I equivalent to beta_v=0 or 1/6 +for every v. Only zero is dyadic. Thus G is the only dyadic orthogonal +member of this fixed family. This statement does not exclude another +matching or reciprocal family, including the later E=P R family. + +## Checks and publication boundary + +The producer checks six full 112-port inverse examples and enumerates +all 65536 coefficient tuples through the proved determinant formulas. +The historical independent checker imports no producer code. It uses +integer Bareiss elimination after row-denominator clearing, nine +matrix cases, and a separate eight-step recurrence for the full +determinant distribution. It checks the six-step gauge and reverse +on all 40 columns in eight cases, both ordered interface inverse +products, and the fixed 64-port complement. It also checks the +distinction between full and principal units. These finite tests +support the source matrices; the written proof establishes completeness. + +`COMMANDS.json` records the actual command. `REPLAY.json` and +`cold-replay/` retain all four receipts and logs. The runner used one +child process at a time, with `-I -B` and then also `-O`. All four +receipts match their exact frozen bytes. No normalization was used. +The runner and source manifest match the final annex. The scripts +use only the standard library and input paths derived from their +copied locations. No runtime compiler or producer module is imported. + +The final package check covers every manifest entry, the exact file +inventory, new wrapper links, the proposed body, and preservation of +the earlier parent and original-J annex files. The predecessor notices +match the already reviewed parent copies. No new remote notice +verification is claimed. The older bipartite native packet is retained +as matrix source and historical context; its emitter and native word +were not rerun or adopted for the new coefficients. + +Native query access, scatter placement, all native phases and helper +returns, routed composition, terminal decoding, recursive hosting, +precision, and a complete supplier invoice remain open. No result is +admitted to the current selected construction by this review. Final +commit-pinned GitHub links, rendered Markdown, and published readback +remain the coordinator's checks. This review makes no Git or publication +change. 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"a0750e44d47d6fd6c49d13b054d8186726b5d9029e36fac6d3c8406e5d3d62ea" + } + ], + "scope": "Additive coefficient classification for the fixed signed48 rank-eight family. No new native schedule. All prior package and original-J annex files are unchanged." +} diff --git a/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEWED-BODY-ADDENDUM.template.md b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEWED-BODY-ADDENDUM.template.md new file mode 100644 index 0000000000..396e600c8f --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEWED-BODY-ADDENDUM.template.md @@ -0,0 +1,19 @@ +The [signed rank-eight coefficient annex](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/README.md) adds a complete classification for the fixed signed 48-port family `E=G-K^T Lambda diag(beta_v)K`. The [proof and independent review](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md) show that the full response is a dyadic unit exactly when `beta_v=(1-(-2)^n_v)/12` for integers n_v. Requiring **the full response and both specified principal blocks** to be dyadic units restricts each beta to `1/4`, `1/8`, `-1/4`, or `1/16`. This gives exactly **65,536 distinct responses**, closed under inversion. Principal units alone permit more choices: beta=1/2 has both principal units but full determinant 5^8. The later `E=P R` family is outside this fixed-family classification. + +The six-step ordinary gauge acts on existing arbitrary data without an initial zero or additional centre field. Its reverse gives the ordinary inverse under the principal-unit condition. This proves a representation, not a scalar invoice for every coefficient choice. The ordered interface has determinant one on the 48-port part; including the fixed 64-port complement gives full 112-port determinant 2^-64. No new native schedule, phase replay, helper-restoration word, routed composition, terminal, precision bound, or complete supplier invoice is supplied. **No complete kappa improvement follows.** + +The [fresh replay](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/REPLAY.json) runs both unchanged checkers in normal and optimized Python. All four receipts match their frozen bytes. The producer checks six full inverse cases and all 65,536 coefficient tuples through the proved formulas. The independent checker uses Bareiss determinants, nine matrix cases, all-column gauge and interface checks, and a separate count recurrence. The infinite classification rests on its proof, not the bounded exponent controls. A [fresh separate agent review](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/REVIEW.md) records the final scope and independent replay. + +With Python 3.11+, the standard library, at least 3 GiB free space, and a new output directory: + +```sh +python3 -I -B research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/replay.py --out /tmp/signed-rank-eight-coefficients +``` + +Expected final line: + +```text +PASS_SIGNED_RANK_EIGHT_COEFFICIENT_ANNEX +``` + +The [notice](https://github.com/aliromman/integer-mult-bounds/blob/COMMIT/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/NOTICE.md) credits the coordinating, controller, bridge-review, oblique-native, and budget-geometry contributions and retains the parent native source lineage. All thirteen frozen inputs, accepted parent files, historical source pins, and Apache-2.0 notices remain unchanged. Substantial OpenAI Codex assistance was used. diff --git a/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/cold-replay/REPLAY.json b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/cold-replay/REPLAY.json new file mode 100644 index 0000000000..e9e9690660 --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/cold-replay/REPLAY.json @@ -0,0 +1,46 @@ +{ + "checks": [ + { + "check": "producer", + "equal_frozen_bytes": true, + "mode": "normal", + "receipt_sha256": "5360e919a80d48330df4eadd18b23744f3501d4fdcbf64b68f21e9530643385c", + "seconds": 5.061, + "status": "PASS_RECIPROCAL_SIGNED_CENTRE_FAMILY" + }, + { + "check": "producer", + "equal_frozen_bytes": true, + "mode": "optimized", + "receipt_sha256": "5360e919a80d48330df4eadd18b23744f3501d4fdcbf64b68f21e9530643385c", + "seconds": 6.142, + "status": "PASS_RECIPROCAL_SIGNED_CENTRE_FAMILY" + }, + { + "check": "independent", + "equal_frozen_bytes": true, + "mode": "normal", + "receipt_sha256": "4ae2a2b13b183d78ac7f2b39bf6b6fabfd631b283fc81faf2aeece9befce8dff", + "seconds": 3.79, + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_CLASSIFICATION" + }, + { + "check": "independent", + "equal_frozen_bytes": true, + "mode": "optimized", + "receipt_sha256": "4ae2a2b13b183d78ac7f2b39bf6b6fabfd631b283fc81faf2aeece9befce8dff", + "seconds": 3.725, + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_CLASSIFICATION" + } + ], + "child_processes_run_concurrently": 1, + "comparison": "All four JSON receipts match exact frozen bytes. The source gzip file is immutable; its decompressed payload hash is also checked.", + "frozen_sources_unchanged": true, + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "python": "3.14.7", + "runner_sha256": "a0750e44d47d6fd6c49d13b054d8186726b5d9029e36fac6d3c8406e5d3d62ea", + "scope": "The signed48 full-unit and two-principal-unit coefficient classification, its six-step ordinary gauge, and its fixed64 complement. No new native schedule, native phase replay, all-stage composition, precision, supplier invoice, or complete kappa claim.", + "source_files": 13, + "source_manifest_sha256": "74bc60f989a872e9d63181268e56805c48fee2c86a99d388df62887f89527d3e", + "status": "PASS_SIGNED_RANK_EIGHT_COEFFICIENT_ANNEX" +} diff --git a/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/cold-replay/independent/normal/REVIEW.json b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/cold-replay/independent/normal/REVIEW.json new file mode 100644 index 0000000000..666bcf768c --- /dev/null +++ b/research/publication-reviews/reciprocal-native-responses/signed-rank-eight-coefficients-review/cold-replay/independent/normal/REVIEW.json @@ -0,0 +1,246 @@ +{ + "centre_interface_determinant": "1", + "checker_sha256": "502fa6b230ce35f89b233ff9c32cd825cfd42b63e83ad900186888c1984fa3da", + "determinant_distribution": { + "-1/1048576": 3696, 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The first five entries retain the parent package verified source pins. The historical root notice and stopped-product source were also checked against exact local Git objects." +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/LICENSE b/research/reciprocal-native-responses/annexes/original-j-rank-readers/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/NOTICE.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/NOTICE.md new file mode 100644 index 0000000000..0857ed7eed --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/NOTICE.md @@ -0,0 +1,59 @@ +# Sources, credit, and scope + +This annex extracts completed October 2026 campaign results. Its +[source manifest](SOURCES.json) records the original paths and exact +bytes. No historical source pin or frozen proof was changed. The +existing parent package and its earlier review remain separate. + +The root lane supplied the original-J rank classification. The +independent-review lane supplied the separate scalar interpreter, the +explicit reversed-kernel argument, the one-sided denominator consequence, +the conditional grid proof, and the reverse-column native review. The +oblique-native lane supplied the capture and helper-correction plan. +The new-native-recipes lane supplied the literal coordinate rank-four +words. The new-core-transfer lane supplied the clean J and actual R. + +For the later reader result, the oblique-native lane supplied the +signed-metric model and native contracts. The cover-algebra lane supplied +the ordered caller variables. The bridge-access lane supplied the literal +D25 views. The native-escape lane supplied the source-cut construction, +and its owner-review lane supplied the separate model, ordered-operator, +phase, and reader-binding checks. No record supplier is credited as +completed by these results. + +The retained [native source notice](frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md) +and [source pins](frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json) +identify the historical native predecessors: + +- [PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), + at `51eb9c4ee9e4722010d308aa3309e039d3940cc2`, supplied the core. +- [PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), + at `f2927a4b8afcf0701a6b945e14f30de1d94f5176`, supplied the retained + byte-equal base and extra provider words. +- [PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), + at `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`, supplied recipe tools + in the inherited native lineage. This annex does not rerun that compiler. + +The unchanged [provider notice](notices/PR3133-NOTICE), +[provider credits](notices/PR3133-CREDITS.md), +[PR #2588 notice](notices/PR2588-NOTICE), +[port notice](notices/PR2588-NOTICE-PR2226.md), and +[earlier notice](notices/PR2226-NOTICE.md) retain the full predecessor +credit. [EXTERNAL-NOTICES.json](EXTERNAL-NOTICES.json) records their +source commits and hashes. No individual compiler authorship is inferred +from a PR submitter account. + +The common-grid argument inherits the +[stopped-product source](frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex) +at `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. The unchanged +[historical root notice](notices/HISTORICAL-ROOT-NOTICE) credits +@icekylinx for the stopped-product and exact denominator-grid work. +The local odd-grid review and its predecessor remain pinned in the +source manifest. The new proof applies that method to unfinished +rational parent operations under explicit endpoint and precision premises. + +The repository [Apache-2.0 license](LICENSE) applies. All retained notices +are unchanged. OpenAI Codex gave substantial assistance in the proofs, +code, checks, independent agent reviews, and extraction. An independent +agent review is not a human review, maintainer acceptance, or formal +verification of the complete multiplication theorem. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/README.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/README.md new file mode 100644 index 0000000000..e160e800ca --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/README.md @@ -0,0 +1,182 @@ +# Original-J correction ranks and reciprocal reader cuts + +This additive annex retains two completed results about reciprocal +responses. The first classifies the correction ranks for extensions of +the original clean response `J`. It includes the native implementation +of its coordinate rank-four split. The second identifies three exact +reader cuts for the later signed-metric response `E=P R`. These are +different response families. The annex does not combine them into a +controller or improve the complete kappa calculation. + +## Original-J correction rank + +The [root proof](frozen/root/RECIPROCAL-CENTRE-RANK-20261018.md) and its +[independent review](frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/REVIEW.md) +use the actual eight-row matrix `R`, with `K=R^T/4` and `RK=14I_8`: + +```text +J = I_112-KR, E = J+KMR, G = J+KNR. +EG = I iff 12I-13(M+N)+14MN = 0. +``` + +For dyadic scalar matrices `M,N`, reciprocity forces both correction +ranks to be eight. Over the rationals, the minimum rank sum is eight. +All equality cases are + +```text +M = (12/13)P, N = (12/13)(I-P), P^2=P. +``` + +The projection need not be orthogonal. The proof derives `MN=NM` from +reciprocity; it does not assume commutation. It also proves that if one +correction has no denominator divisible by 13, its reciprocal partner +has full rank eight. A rank-four/rank-four split therefore requires a +13-denominator on both sides. + +This theorem measures the two specified correction terms. It is not a +query or native-cost lower bound for arbitrary implementations of the +full response. For example, `M=N=I` gives `E=G=I`, although both specified +corrections have rank eight. The later `E=P R` family in the +parent package is outside this original-J extension theorem. + +The independent scalar check covers all 256 coordinate projections, +nine pairs on all 112 input columns in both inverse orders, and +noncommuting and incorrect-weight controls. The written argument proves +the universal rank bound and all equality cases. + +## Literal coordinate rank-four words + +The [native proof](frozen/lanes/reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md) +and [independent word review](frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/REVIEW.md) +cover `P=diag(1,1,1,1,0,0,0,0)`. They retain four original rank-eight +centre calls per word. Both responses, both orientations, and both +historical providers give eight local words. + +| Per local word | Dyadic real primitives | Real /13 scans | Native children | Native rank mass | +| --- | ---: | ---: | ---: | ---: | +| Forward E or G | 165,594 | 16 | 3,511 | 5,105 | +| Backward E or G | 165,618 | 16 | 3,511 | 5,105 | + +The scans are separate from the dyadic bill. These are local component +counts, not a complete bit-machine supplier price. Every word has 23,500 +events. The fresh reverse-column check covers all 640 arbitrary inputs, +all 408 logical helper returns, all 91 private-buffer returns, frames, +source bindings, and the division queries. `C0` ends at zero at I. +`C1` through `C7` retain their arbitrary input values at I. Requiring all +eight owned outputs to be zero needs seven extra CLEARs, or 14 primitives. + +The scalar maps are `(x,y,h)->(x,y+T x,h)` and +`(x,y,h)->(x-T^T y,y,h)`. The backward map uses the transpose of its own +response. The reciprocal is the other response. After the common FULL +output is removed, the physical matrices remain ordered: + +```text +C_F(T) = [[q,0],[q T q,q]], +C_B(T) = [[q,-T^T],[0,q]]. +``` + +Thus `EG=I` in one scalar chart does not cancel the physical port-line +operators. The new centre occurrences are bound to exact recipes from +the retained 3,036-class native phase review. This replay does not repeat +that earlier phase sweep or re-emit the native program. + +Each completed pre-division query has no new 13-denominator. The local +word adds at most one 13-denominator level at its operation boundaries. +The [conditional grid proof](frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/ODD-GRID-COMPOSITION.md) +requires exact dyadic endpoints for completed recursive children, root +conversion of every numeric field, and a separate binary and magnitude +guard. The individual rational E and G words are not completed dyadic +recursive providers. The grid check includes signed scans at widths +1 through 14, five nested trees, and failed-premise controls. + +## Reader cuts for the later signed-metric response + +The [source-cut proof](frozen/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/SOURCE-CUTS.md) +and [independent review](frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/REVIEW.md) +use the later 112-port model `E=P R`, `R=I+U ell`, and `ell U=-2I_16`. +Here `R` is a reflection, not the eight-row matrix above. Physical `P` +is a dyadic scalar matrix, not a monomial field permutation. + +Put `t=y+R0 x` and `w=x-(P0^-1 R1 P0)t`. Under the pinned F/B/F native +contracts and the literal D25 entry and exit views, the exact records are: + +| Cut | Current source | Ordered reader | Returned frame | +| --- | --- | --- | --- | +| After raw F0, before post-P0 | X | `c0=ell0 x` | `F9` | +| Before pre-P1 and raw B1 | Y | `c1=ell1 P0 t` | `F9 q_anchor` | +| After raw F2, before post-P2 | X | `c2=ell2 P1 P0 w` | `F25` | + +The middle record is a hole record, not FULL. The ordered P factors are +already in the current source values. No old-chart read is needed at +these cuts. This does not supply an accumulator in the required frame. + +Each conditional reader requires 16 separate typed accumulators and +applies 136 signed complex ADDs, at 1,088 inherited real scalar units. +Three formations cost 3,264 units if those accumulators are supplied. +The operation preserves the source and adds to each accumulator's +arbitrary baseline. It does not create a clean query from a dirty one. +The row one-norm is at most 11 at every local prefix, and this is attained. +There is no new coefficient denominator or source-line native transform. + +The independent check reconstructs the model, verifies the ordered +formulas, checks 1,792 complete Z4 phase identities, and checks all 128 +source and accumulator columns. The producer additionally checks all +656 local columns. The binding check compares 272 formation and 272 +immediate inverse instructions. An immediate inverse needs an unchanged +source; it is not a later erase for the complete controller. + +These reader costs exclude record supply, a zero baseline, accumulator +views, preparation, transport, leases, a recursive host, and final +restoration. The native contract remains a pinned premise. No reader +native-event replay or complete native invoice is claimed here. + +## Reproduction + +Use Python 3.11 or later, the standard library, at least 3 GiB free space, +and a new output directory. From the repository root: + +```sh +python3 -I -B research/reciprocal-native-responses/annexes/original-j-rank-readers/replay.py --out /tmp/original-j-rank-readers +``` + +Expected final line: + +```text +PASS_ORIGINAL_J_RANK_READERS_ANNEX +``` + +The [runner](replay.py) executes six unchanged checkers in normal Python +and with `-O`, one process at a time. It checks every frozen source before +and after execution. It writes logs, all compared results, and +`REPLAY.json` to the output directory. The retained +[publication replay](evidence/REPLAY.json) records the fresh relocated run. + +Results without source paths must match exact bytes. For the reader +payload and its receipt, the runner first binds the raw decompressed +payload to its recorded raw hash. It then canonicalizes complete JSON, +changes only the four declared source-path strings, and uses the canonical +payload hash in the canonical receipt. Source-manifest JSON has only its +absolute keys changed to campaign-relative keys. Every other field is +compared. Gzip headers are not mathematical equality tests. + +[SOURCES.json](SOURCES.json) records the 73 unchanged campaign files. +The package contains the full input closure for this runner. It does not +claim a complete runtime closure for the older producer and phase-sweep +scripts retained as source evidence. Historical freeze text remains +unchanged. Final package integrity is recorded in +[ANNEX-MANIFEST.json](ANNEX-MANIFEST.json). + +## Open next questions + +The original-J pair still needs an ordered controller with legal chart +transitions, restored arbitrary fields, a completed dyadic recursive +endpoint, and a full hosting, precision, and cost proof. The source-cut +result still needs safe typed records, their baseline contract, retention, +transport, and late erase. This annex does not solve these obligations. + +The publication context is main commit +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`, whose selected result names +[PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470). +The annex preserves historical source pins and proves no transfer to that +construction. [NOTICE.md](NOTICE.md) gives source credit, license terms, +and the AI-assistance disclosure. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/SOURCES.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/SOURCES.json new file mode 100644 index 0000000000..b4ff7f18a9 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/SOURCES.json @@ -0,0 +1,619 @@ +{ + "comparison": "Exact bytes for frozen inputs. replay.py defines complete output comparisons, including the explicit path normalization for reader JSON and source manifests.", + "files": [ + { + "bytes": 202201, + "path": "lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "roles": [ + "reader replay or binding input" + ], + "sha256": "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473" + }, + { + "bytes": 2562, + "path": "lanes/bridge-review-20261017/odd-grid-a8-review-20261017/FREEZE.json", + 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Complete canonical JSON comparison for reader CHECKS, decompressed READERS, and SOURCE-MANIFEST: normalize only the four source paths or manifest keys. Bind the raw reader payload to its raw receipt first, then use the canonical payload hash in the canonical receipt. Compare every other field.", + "frozen_sources_unchanged": true, + "omitted": [ + "Producer native re-emission", + "Original 3036-class phase sweep", + "Reader native-event replay", + "Accumulator supply, transport, and late erasure", + "Global controller, recursive supplier, precision, and complete kappa calculation" + ], + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "python": "3.14.7", + "runner_sha256": "16578a52cb555ce18db1447ac2025c265b1de305f07bf5cbb336548d4dfc2338", + "source_files": 73, + "source_manifest_sha256": "5f94525a446f86ca6e52c3187e042f90b69f389a40fb2f6b22298d3614880d63", + "status": "PASS_ORIGINAL_J_RANK_READERS_ANNEX" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/normal/GRID-CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/normal/GRID-CHECKS.json new file mode 100644 index 0000000000..50cbc391f9 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/normal/GRID-CHECKS.json @@ -0,0 +1,67 @@ +{ + "checker_sha256": "e257f0a984b9e7f4f86f25a9e2991f03e3ff0c93888be9ff75a717186af85641", + "negative_controls": [ + "unscaled finest-grid numerator", + "three rational completed children with a two-level budget", + "final unscaling before a dyadic root endpoint" + ], + "nested_integer_basis_cases": [ + { + "active_levels": 1, + "binary_budget": 8, + "completed_calls": 1, + "divisions": 0, + "events": 1, + "max_active_levels": 1, + "max_height": 0, + "odd_budget": 8 + }, + { + "active_levels": 2, + "binary_budget": 16, + "completed_calls": 3, + "divisions": 8, + "events": 19, + "max_active_levels": 2, + "max_height": 1, + "odd_budget": 16 + }, + { + "active_levels": 3, + "binary_budget": 24, + "completed_calls": 7, + "divisions": 24, + "events": 55, + "max_active_levels": 3, + "max_height": 2, + "odd_budget": 24 + }, + { + "active_levels": 4, + "binary_budget": 32, + "completed_calls": 15, + "divisions": 56, + "events": 127, + "max_active_levels": 4, + "max_height": 3, + "odd_budget": 32 + }, + { + "active_levels": 5, + "binary_budget": 40, + "completed_calls": 31, + "divisions": 120, + "events": 271, + "max_active_levels": 5, + "max_height": 4, + "odd_budget": 40 + } + ], + "scope": "Exact signed scans and test trees. The general active-path bound is proved in ODD-GRID-COMPOSITION.md. These trees are not an emitted supplier controller.", + "signed_inputs_checked_for_each_scan": 32766, + "signed_scan_widths": [ + 1, + 14 + ], + "status": "PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/normal/stdout.log b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/normal/stdout.log new file mode 100644 index 0000000000..b4f6e13eb2 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/optimized/GRID-CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/optimized/GRID-CHECKS.json new file mode 100644 index 0000000000..50cbc391f9 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/optimized/GRID-CHECKS.json @@ -0,0 +1,67 @@ +{ + "checker_sha256": "e257f0a984b9e7f4f86f25a9e2991f03e3ff0c93888be9ff75a717186af85641", + "negative_controls": [ + "unscaled finest-grid numerator", + "three rational completed children with a two-level budget", + "final unscaling before a dyadic root endpoint" + ], + "nested_integer_basis_cases": [ + { + "active_levels": 1, + "binary_budget": 8, + "completed_calls": 1, + "divisions": 0, + "events": 1, + "max_active_levels": 1, + "max_height": 0, + "odd_budget": 8 + }, + { + "active_levels": 2, + "binary_budget": 16, + "completed_calls": 3, + "divisions": 8, + "events": 19, + "max_active_levels": 2, + "max_height": 1, + "odd_budget": 16 + }, + { + "active_levels": 3, + "binary_budget": 24, + "completed_calls": 7, + "divisions": 24, + "events": 55, + "max_active_levels": 3, + "max_height": 2, + "odd_budget": 24 + }, + { + "active_levels": 4, + "binary_budget": 32, + "completed_calls": 15, + "divisions": 56, + "events": 127, + "max_active_levels": 4, + "max_height": 3, + "odd_budget": 32 + }, + { + "active_levels": 5, + "binary_budget": 40, + "completed_calls": 31, + "divisions": 120, + "events": 271, + "max_active_levels": 5, + "max_height": 4, + "odd_budget": 40 + } + ], + "scope": "Exact signed scans and test trees. The general active-path bound is proved in ODD-GRID-COMPOSITION.md. These trees are not an emitted supplier controller.", + "signed_inputs_checked_for_each_scan": 32766, + "signed_scan_widths": [ + 1, + 14 + ], + "status": "PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/optimized/stdout.log b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/optimized/stdout.log new file mode 100644 index 0000000000..b4f6e13eb2 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/grid/optimized/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/normal/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/normal/CHECKS.json new file mode 100644 index 0000000000..35105851d5 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/normal/CHECKS.json @@ -0,0 +1,550 @@ +{ + "checker_sha256": "8a9023adc5ebe5ce1f9ff09b5ce02c00ef58cd0bb695c9a26b1b8cee606cf913", + "clean_payload_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "negative_controls": { + "changed_centre_input_frame": true, + "changed_centre_scatter_sign": true, + "erased_untouched_arbitrary_owned_input": true, + "omitted_weighted_entrance_division": true + }, + "payload_decompressed_sha256": "8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013", + "phase_scope": "Exact byte binding to the prior independent all-3036-edge review, including all 32 centre directions and literal backward dual warps. No second compiler or phase interpreter is claimed in this run.", + "providers": { + "base": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + }, + "extra": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + } + }, + "scope": "Complete local rational maps, arbitrary logical helper restoration, typed native occurrences, scalar and native invoices, and one new 13-denominator level. No global controller, new recursive provider, owner layout, or kappa claim.", + "source_pins": { + "independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json": "924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d", + "independent-review-20261017/check_new_native.py": "937543157459e5c0eee788feefcf2107acf6bdf660a1209cdecece1ca1f26d01", + "new-native-recipes-20261017/base/CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "reciprocal-centre-20261018/FREEZE.json": "b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd", + "reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md": "322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737", + "reciprocal-centre-20261018/emit_reciprocal_centres.py": "cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc", + "reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-RECEIPT.json": "aafaa8b17be476d521fe4c8eb3cf3af59c72351c3aba60a9413cd2aa0baafdfc" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/normal/stdout.log b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/normal/stdout.log new file mode 100644 index 0000000000..a15817dbaa --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/normal/stdout.log @@ -0,0 +1,9 @@ +base E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/optimized/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/optimized/CHECKS.json new file mode 100644 index 0000000000..35105851d5 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/optimized/CHECKS.json @@ -0,0 +1,550 @@ +{ + "checker_sha256": "8a9023adc5ebe5ce1f9ff09b5ce02c00ef58cd0bb695c9a26b1b8cee606cf913", + "clean_payload_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "negative_controls": { + "changed_centre_input_frame": true, + "changed_centre_scatter_sign": true, + "erased_untouched_arbitrary_owned_input": true, + "omitted_weighted_entrance_division": true + }, + "payload_decompressed_sha256": "8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013", + "phase_scope": "Exact byte binding to the prior independent all-3036-edge review, including all 32 centre directions and literal backward dual warps. No second compiler or phase interpreter is claimed in this run.", + "providers": { + "base": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + }, + "extra": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + } + }, + "scope": "Complete local rational maps, arbitrary logical helper restoration, typed native occurrences, scalar and native invoices, and one new 13-denominator level. No global controller, new recursive provider, owner layout, or kappa claim.", + "source_pins": { + "independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json": "924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d", + "independent-review-20261017/check_new_native.py": "937543157459e5c0eee788feefcf2107acf6bdf660a1209cdecece1ca1f26d01", + "new-native-recipes-20261017/base/CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "reciprocal-centre-20261018/FREEZE.json": "b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd", + "reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md": "322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737", + "reciprocal-centre-20261018/emit_reciprocal_centres.py": "cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc", + "reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-RECEIPT.json": "aafaa8b17be476d521fe4c8eb3cf3af59c72351c3aba60a9413cd2aa0baafdfc" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/optimized/stdout.log b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/optimized/stdout.log new file mode 100644 index 0000000000..a15817dbaa --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/original_j_words/optimized/stdout.log @@ -0,0 +1,9 @@ +base E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +base G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra E_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_forward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +extra G_backward PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES +PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/normal/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/normal/CHECKS.json new file mode 100644 index 0000000000..df1ae1872e --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/normal/CHECKS.json @@ -0,0 +1,84 @@ +{ + "actual_K_row_l1": 1, + "actual_R_row_l1": 56, + "checker_sha256": "550330e2c6b5b485f531c9c1f0b633ec55d6a2200839903b4f1fc3d4da9ade1e", + "coordinate_projection_checks": 256, + "coordinate_rank_distribution": { + "0": 1, + "1": 8, + "2": 28, + "3": 56, + "4": 70, + "5": 56, + "6": 28, + "7": 8, + "8": 1 + }, + "full_inverse_cases": [ + { + "basis_columns_per_order": 112, + "label": "coordinate-0", + "rank_M": 0, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-1", + "rank_M": 1, + "rank_N": 7 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-15", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-127", + "rank_M": 7, + "rank_N": 1 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-255", + "rank_M": 8, + "rank_N": 0 + }, + { + "basis_columns_per_order": 112, + "label": "noncoordinate-rank-four", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "general-centre-unit", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "nontrivial-dyadic-full-rank", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "13-integral-rank-four-forces-full-rank-partner", + "rank_M": 4, + "rank_N": 8 + } + ], + "method": "Independent dense centre algebra and 112-column vector interpreter; no producer imports.", + "negative_controls": [ + "wrong coefficient", + "repeated response", + "arbitrary noncommuting pair" + ], + "ordered_noncommuting_identity_columns": 112, + "scope": "Exact scalar family and query ranks. No full native word, phase terminal, controller, or complete supplier price is certified here.", + "source_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "source_proof_sha256": "d2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9", + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_RANK" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/normal/stdout.log b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/normal/stdout.log new file mode 100644 index 0000000000..0900be1cf7 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/normal/stdout.log @@ -0,0 +1 @@ +PASS_INDEPENDENT_RECIPROCAL_CENTRE_RANK diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/optimized/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/optimized/CHECKS.json new file mode 100644 index 0000000000..df1ae1872e --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/evidence/replay/rank/optimized/CHECKS.json @@ -0,0 +1,84 @@ +{ + "actual_K_row_l1": 1, + "actual_R_row_l1": 56, + "checker_sha256": "550330e2c6b5b485f531c9c1f0b633ec55d6a2200839903b4f1fc3d4da9ade1e", + "coordinate_projection_checks": 256, + "coordinate_rank_distribution": { + "0": 1, + "1": 8, + "2": 28, + "3": 56, + "4": 70, + "5": 56, + "6": 28, + "7": 8, + "8": 1 + }, + "full_inverse_cases": [ + { + "basis_columns_per_order": 112, + "label": "coordinate-0", + "rank_M": 0, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-1", + "rank_M": 1, + "rank_N": 7 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-15", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-127", + "rank_M": 7, + "rank_N": 1 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-255", + "rank_M": 8, + "rank_N": 0 + }, + { + "basis_columns_per_order": 112, + "label": "noncoordinate-rank-four", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "general-centre-unit", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "nontrivial-dyadic-full-rank", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "13-integral-rank-four-forces-full-rank-partner", + "rank_M": 4, + "rank_N": 8 + } + ], + "method": "Independent dense centre algebra and 112-column vector interpreter; no producer imports.", + "negative_controls": [ + "wrong coefficient", + "repeated response", + "arbitrary noncommuting pair" + ], + "ordered_noncommuting_identity_columns": 112, + "scope": "Exact scalar family and query ranks. 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Complete each data-only local cover sweep before the next stage.", + "recursive_hosting_claimed": false, + "schema": "matched-dimension25-views-v1", + "source_pins": { + "matching": [ + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json", + "plain", + "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902" + ], + "permutation64": [ + "history-encoding/permutation64-native-20261018/PERMUTATION64-PROGRAMS.json.gz", + "gzip", + "87c76a500f8e22e4b500a5f5a64f23ef8cecadd0036785d7f54b2415972f1ff9" + ], + "phase": [ + "bridge-access-20261017/cycle-cover-response-20261018/check_cycle_cover.py", + "python", + "cf39b15752fcb96cc22b9013dce38e13a4399d99b30dc9f53eef788d5ded2bf4" + ], + "scalar_price": [ + "new-core-transfer-20261017/emit_raw_selected.py", + "source", + "a07cf4894a2599993006c7b99e6cb62146ece82f2ae6df72a28100ccb3a689bc" + ], + "views": [ + "bridge-access-20261017/BRIDGE-PROGRAMS.json.gz", + "compressed", + "1da2f6a6058661f19e971bb31f1823585f01c2494dca813e208af45aea7a582f" + ] + }, + "stages": [ + 0, + 1, + 2 + ] +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/FREEZE.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/FREEZE.json new file mode 100644 index 0000000000..06344d7802 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/FREEZE.json @@ -0,0 +1,41 @@ +{ + "accepted": [ + "Actual A8 ordinary inverse and fused upper factor", + "All complete-minor scalar-factor formulas and prefix denominators", + "Serial owned C0 and arbitrary data semantics", + "Exact signed fixed-odd-divisor scans and their separate costs", + "Source-backed common root-grid active-chain theorem" + ], + "contract": { + "completed_child": "Exact Gaussian-dyadic endpoint on every data and arbitrary helper column.", + "cost": "Odd scans, outer conversion, extra width, descriptors, complete binary guard and all unchanged native operations must be charged.", + "final_return": "Proved Gaussian-dyadic semantic endpoint before exact unscaling.", + "input": "Arbitrary Gaussian-dyadic root values; convert every numeric stream once, including borrowed data and helpers.", + "local_cut": "One legal common frame for data and C0; clear the owned C0 before frame assignment.", + "root_grid": "2^-P/L^K, K=M(D+1), with L=3 for A8 or L=45045 for the complete family." + }, + "date": "2026-10-17", + "files": { + "PRODUCER-REPLAY.json": "9dced005ccd264f95cce4193bbe45e0a00028669717cdf4ca7bf18640c50a349", + "REVIEW.json": "4dc2c2aaf6dd85c3b32d9508ca8dc89a7a9b0b470fe31cfcf0cf1810c36b8d41", + "REVIEW.md": "0eee1c869ba6c1c5e75075bc9dbae3324468a27a6b0dd45cd16e4f7973f9eb05", + "check_review.py": "b18eafaef07c03c0a692c7f7539aa83226e0ccabc135d00fc4705d7954277f0b", + "producer-replay/A8-ODD-GRID-WORDS.json": "525822746e2d760a81c5a4c8847c25974d0a419a2c5abbaa0472d13bde1c6aa9", + "producer-replay/A8-ODD-GRID.json": "0c1dc7cc08de30a14b42c744e73d3963a68acd83bc381f884867b85bfeaee96a", + "producer-replay/MINOR-FACTOR-WORDS.json": "8d106f08b5094a0ce15008bf3d5c3a904be62e04995438830b72a1e44047b9b3", + "producer-replay/MINOR-FACTORS.json": "daf9ef5e88b8dd0243eec4ffe0303115bbde57fbb3a12a908583e9fd74b05140" + }, + "limits": [ + "A8 content map still has rank 104 and nullity eight over Q", + "k13 ordinary block remains singular", + "Native local-word transfer is a separate review", + "No complete controller, owner schedule, hosting, precision invoice, supplier moment or kappa claim" + ], + "pr_standard": "/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md", + "publication": "No PR, commit, push or publication authorized or performed.", + "source_freezes": { + "A8": "97f00c72bc3baeb4ce3ca91b91d9e46d7978d7ec502bee77845f5484731bb086", + "family": "de05cc545581deadbe855e6ae214c9cda79a6b20add92948d066a95756ed4219" + }, + "status": "FROZEN_INDEPENDENT_COMPONENT_REVIEW" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md new file mode 100644 index 0000000000..555f0dd6b9 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/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/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/FREEZE.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/FREEZE.json new file mode 100644 index 0000000000..32359ce078 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/FREEZE.json @@ -0,0 +1,20 @@ +{ + "files": { + "CHECKS-OPTIMIZED.json": "c418cfbbf92f423cd2e5bcd8639c7d5b523376dad4a1d09c9a531157fed06fee", + "CHECKS.json": "c418cfbbf92f423cd2e5bcd8639c7d5b523376dad4a1d09c9a531157fed06fee", + "RECIPROCAL-CALLER.md": "1c54d18b4a0601dae03064cc03029bc5f2c7e53c3befbc978f163d009f24d99b", + "check_reciprocal_caller.py": "8c107239cbc9f7d491a8ef455a53826aeccd2e8c33eccfb43e9625101ceb87fc" + }, + "schema": "reciprocal-selected-baseline-freeze-v1", + "scope": { + "actual112_matrix": true, + "complete_decoder": false, + "complete_supplier": false, + "new_native_word": false, + "ordered_caller": true, + "publication": false, + "rank48_array_residual": true, + "stored_records": false + }, + "status": "PASS" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/RECIPROCAL-CALLER.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/RECIPROCAL-CALLER.md new file mode 100644 index 0000000000..748901f33b --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/cover-algebra/reciprocal-selected-baseline-20261020/RECIPROCAL-CALLER.md @@ -0,0 +1,306 @@ +# A reciprocal caller with a 48-row residual + +The actual 112-port response has a factorization E=P R. The matrix P +is an involution on 32 ports. The matrix R is an involution with +rank(R-I)=16. A three-call caller can keep P as a common bank code +and leave only three rank-16 shear corrections. + +This is an ordered caller theorem. The actual matrix is checked +independently. A new native word, stored query records, and a complete +terminal decoder are separate obligations. Rank 48 is not a native +cost of 48. + +## Source and metric + +The matrix source is + +```text +oblique-native-20261017/signed-metric-reciprocal-20261020/ +model-normal-v2/RESPONSE.json.gz +``` + +Its decompressed SHA256 is +`df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0`. +The root construction is in +`root/RECIPROCAL-RANK-TWO-20261020.md`. + +Write the physical row and column factors as L and U. They satisfy + +```text +R=I+U L, L U=-2I16, P^2=R^2=I, +E=P R, E^-1=R P. +``` + +The source also supplies a real diagonal matrix J with + +```text +P* J P=J, R* J R=J, E* J E=J. +``` + +Its diagonal entries are 1 on 80 ports, -1/2 on 16 ports, and -1/4 +on 16 ports. Thus all metric scales and inverse scales are dyadic. +The order of the inverse formulas is + +```text +E^-*=J E J^-1, E^-1=J^-1 E* J. +``` + +Do not replace E by an involution. In general E^2 is not I. + +Every nonidentity row or column of P lies in the same 32-port set S. +The physical P has 160 nonzero entries. It is not a monomial matrix. +Its accepted common-frame scalar word costs 728 real primitives. +This cost does not include global address views. + +## A local P wrapper + +Let D(A)=diag(A,A), and define + +```text +L_A=[[I,0],[A,I]], U_A=[[I,A],[0,I]]. +``` + +Assume a raw forward service has response E. Apply P to the +current-I Y input. Apply P to the completed-FULL X output. The +result is + +```text +F^P = [[P,0],[E,P]] = D(P) L_R. +``` + +For a raw backward response E^-1, the same input and output +wrappers give + +```text +B^P = [[P,-P R],[0,P]] = D(P) U_-R. +``` + +There is also an exact conversion from the chronological +inverse-adjoint of the whole wrapped forward word: + +```text +D(J^-1) (F^P)^-* D(J) = B^P. +``` + +This conversion uses only physical diagonal scales. It does not +commute a port-mixing code through a hole phase. The complete +inverse-adjoint must retain the complete helper and phase contract. + +The current-I pre-Y and completed-FULL post-X placements use the +standard stage-view contract. Its source is +`bridge-access-20261017/general-stage-views-20261020/GENERAL-VIEWS.md`, +SHA256 `5da866eb2802e8a30ea77d2f88877b5005a2eb04632514c897a426e76277db2e`. +No wrapper is granted on a retired ordinary Y hole. + +## Three different stages + +Keep all stage labels. Set + +```text +H=P1 P0, Ptot=P2 P1 P0, +Rhat0=R0, +Rhat1=P0^-1 R1 P0, +Rhat2=H^-1 R2 H. +``` + +Then + +```text +F2^P B1^P F0^P + =D(Ptot) L_Rhat2 U_-Rhat1 L_Rhat0. +``` + +This identity holds over an ordered operator ring. It uses no +commutation between stages. + +Write K_i=Rhat_i-I. Each K_i has at most 16 array columns. Let + +```text +W=L_I U_-I L_I=[[0,-I],[I,0]]. +``` + +The normalized defect is + +```text +T=W^-1 L_Rhat2 U_-Rhat1 L_Rhat0=A2 A1 A0, + +A0=[[I,0],[K0,I]], +A1=[[I-K1,-K1],[K1,I+K1]], +A2=[[I,-K2],[0,I]]. +``` + +Each A_i-I has square zero. For A1 this follows from the ordered +factorization + +```text +A1-I=[-I;I] K1 [I,I], +``` + +because [I,I][-I;I]=0. Therefore + +```text +rank(T-I) <= rank(K0)+rank(K1)+rank(K2) <=48. +``` + +For a payload field of dimension d, the bound is 48d. It is an +array-rank bound, not a count of scalar coordinates. + +An exact inverse applies these operations in this order: + +```text +X += K2 Y +q = K1(X+Y); X += q; Y -= q +Y -= K0 X. +``` + +The middle sum X+Y is unchanged by its two writes. A serial +implementation must use the complete query before either write +changes its required source. + +## Three queries at actual source cuts + +Factor the transported K_i as Uhat_i Lhat_i, where + +```text +Uhat0=U0, Lhat0=L0, +Uhat1=P0^-1 U1, Lhat1=L1 P0, +Uhat2=H^-1 U2, Lhat2=L2 H. +``` + +For arbitrary initial logical data x,y, define + +```text +c0=L0 x, +t=y+R0 x, +c1=Lhat1 t, +w=x-Rhat1 t, +c2=Lhat2 w. +``` + +Direct substitution gives the output before Ptot: + +```text +X=-y-U0 c0-Uhat1 c1, +Y= x-Uhat1 c1+Uhat2 c2. +``` + +Thus the normalized defect is also + +```text +T(x,y)=(x-Uhat1 c1+Uhat2 c2, + y+U0 c0+Uhat1 c1). +``` + +These records have three different literal read cuts: + +| Record | Actual stored argument | Read cut | +| --- | --- | --- | +| c0 | native F0 source X=x | completed X, before post-P0 | +| c1 | B1 input Y=P0 t | current-I Y, before pre-P1 | +| c2 | native F2 source X=H w | completed X, before post-P2 | + +The local rows at these cuts are L0,L1,L2. In particular, c1 is +L1 applied to the stored B1 input. It is not L1 applied to the +uncoded t. This distinction accounts for P0 without an extra old +query. + +No read discards an arbitrary baseline. To retain these records, +one must specify either owned fields or a joint invertible code +with a decoder for every displaced baseline. The c1 record starts +at the current-I cut. Its later frame progress is not free. + +## Physical endpoint and the 32-port code + +Use the all-hole raw service contract. Let Q be the diagonal +positive input line operator and q=Q^-1. For arbitrary physical +inputs X0,Y0, the first logical source is x=q X0 and y=Y0. +This is a coordinate definition; it needs no formation gate. + +Let F be the complete native Fourier progress and +Qhat=diag(Q,I). The retained signed terminal, including its +old Y Q^2 maps, gives + +```text +output = diag(F,F) Qhat D(Ptot) T Qhat^-1 input. +``` + +Do not commute F with the routed code. A logical code A at this +boundary is implemented physically as F A F^-1. + +Because each stage route is port-diagonal, it does not enlarge +the 32-port support of P. Hence Ptot is the identity outside S. +The conjugated Ptot code can be removed with the following +conditional complete-FULL recipe: + +1. Apply q to the 32 affected X fields. +2. Apply Ptot^-1 to both banks through the completed stage views. +3. Apply Q to the same 32 X fields. + +The line subtotal is 64 rank-one children. The scalar subtotal +for the six P words is 6*728=4,368 real primitives. The stage views, +helper host, precision, and line-child admission remain separate. +The operations do not remove T. + +After this code removal, a saved-record decoder would add +Q(Uhat1 c1-Uhat2 c2) to X and subtract U0 c0+Uhat1 c1 from Y, +in the complete F frame. The X scatter still contains Q on its +output ports. The availability of three 16-row records alone +does not implement those scatters. + +In particular, 3*1792+64 is only a native subtotal under a +compatible raw-service premise. No 96-child residual decoder is +claimed, and no supplier or kappa gain follows from this note. + +## A separate signed clean interface + +Suppose a completion C satisfies C J^-1 C*=G, with physical +diagonal dyadic units J,G. Suppose its ordinary rows have a legal +zero-diagonal native response and a clean selected exchange. +For x=(a,u), y=(z,v), its clean map is + +```text +F_C(x,y)=(-z,(Cx)_R,(Cx)_P,v+(Cx)_R). +``` + +Since C^-*=G^-1 C J^-1, its exact metric conversion is + +```text +D(G) F_C^-* diag(J,G^-1) + =(-z,(Cx)_R-v,(Cx)_P,v). +``` + +Selected input/output exchange then gives + +```text +w=C(z,u), +Bswap_C=(w_P,w_R-v,-a,v). +``` + +All added metric operations are diagonal field scales. This local +identity does not identify C_s and C_t at different stages. +The selected FULL and ordinary hole types must still be kept. +It does not change the all-hole reciprocal theorem above. + +## Validation and limits + +The checker independently reads the actual 112-port model. It +checks both inverse orders, the metric identities, the exact P +support, the U L factor, and the scalar P word. A regression uses +three different signed conjugations of these actual matrices. It +checks all 224 two-bank columns, the ordered factorization, both +inverse orders, and the three source-record formulas. These +signed conjugations test order; they are not the actual D25 routes. + +The proof covers general routed operator coefficients. The native +stage-view theorem is an inherited premise. This checker does not +emit a raw service, allocate records, restore dirty record fields, +or certify a complete decoder. + +The root lane supplied E=P R and its signed metric. The oblique +lane supplied the actual 112-port model and its scalar words. +The bridge lanes supply the stage-view contract and study native +record access. 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/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-LOGICAL-REVIEW.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-LOGICAL-REVIEW.md new file mode 100644 index 0000000000..2af6de29f2 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-LOGICAL-REVIEW.md @@ -0,0 +1,122 @@ +# Independent logical review of the new clean-J core + +All four local programs pass the independent exact operator check. Both +PR3133 providers give the forward map `(x,y,h)->(x,y+Jx,h)` and the +backward map `(x,y,h)->(x-Jy,y,h)`, where `J=I-R^T R/4` for the actual +112-port source matrix R. Each word costs 164,514 real scalar primitives +and has native rank mass 5,073. + +This file accepts the logical map, arbitrary-helper restoration, frame +bindings, zero-buffer contract, and local counts. Fresh verification of +the physical native recipes is a separate pending step. This file does +not accept a new global controller, owner allocation, private hosting +bound, precision bound, or complete kappa calculation. + +## Pinned input and method + +The reviewed proof is `../new-core-transfer-20261017/CLEAN-J-TRANSFER.md`, +SHA-256 `d12fca8b1abf95b20b9561334fb3d879d28ce880f6793a461ede0223fce1e2a0`. +The complete decompressed program payload has SHA-256 +`a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa`. +The producer receipt has SHA-256 +`c173491679101d121a0fb43156c73ab62d9031e62b6a969a8ab80912bc36630e`. +The source and canonical pins are in the independent receipt. + +The review imports no producer or source interpreter. It checks the +published PR3148 source bytes and their object equality with the local +PR3133 words. It checks the complete compact role inventory against the +source's removed-helper list. It compares every retained native record +and the complete retained scalar suffix against the source program. + +The independent operator method propagates output coefficients backward. +Coefficients belong to the rational group algebra of free invertible +warp generators. A scalar ADD propagates the target output coefficients +into the source column. A warp prepends its signed generator to each +operator word, with adjacent inverse cancellation. The producer instead +propagates input rows forward and appends generators. The two methods +give the same complete matrix. + +Each program has 632 arbitrary live inputs and eight arbitrary C inputs. +The check also observes all 91 zero-buffer output rows. An allocation +sets only that buffer's input to zero. The logical check does not erase +a buffer at its free event. A separate lifetime pass proves that no +buffer has a later use. Thus a zero observed output proves that the +buffer is zero at its actual free event. + +## Findings + +Every one of the 408 helper input columns is the corresponding unit +column, with an empty operator word. All helper input effects cancel +from the data outputs. C0 ends at zero. C1 through C7 retain their +arbitrary physical inputs because no event uses them. All 91 buffer +output rows are zero. The zero buffers have a clean-input contract; +they are not counted as arbitrary borrowed fields. + +The new H has 367 coefficients on 106 helper roles. Every such role +has input frame I and output frame FULL. The new source H differs +from the old campaign H. The correction uses the new H, with one +serial C0 query per centre row. It preserves its source in both +directions. It clears no borrowed helper. + +For the forward centre-deleted word, the helper debt is `-K H h` in +Y. The prefix adds `K H h` before that word. For the backward word, +the debt is `H^T R y/4` in the helpers. The prefix subtracts this +quantity before that word. The independent full-word calculation +verifies these cancellations on arbitrary inputs, including every +warp path and all cleanup gates. + +Each complete word contains 23,388 events. The input correction has +832 events and costs 8,526 real primitives. Deletion removes exactly +eight rank-eight private centre children. All 5,115 other native +records remain unchanged: 3,507 climbs, 240 warps, 978 ordinary +adapters, and 390 residual adapters. The child profile is +`{1:2433,2:724,3:228,4:102,5:20}`. + +The forward invoice is `158148-2160+8526=164514`. The backward invoice +is `158196-2208+8526=164514`. A separate count of every scalar event +agrees. Every scalar frame and retained native entry frame matches. +All live endpoint frames match the canonical source. + +Controls remove the input correction or change one of its coefficients. +Each control gives a different complete operator. The checks do not +rely on random inputs or a finite specialization of a warp matrix. + +## Warp convention and phase boundary + +The source emitter describes backward warps as conjugates of forward +warps. The source phase table uses the forward K_G convention. This +distinction must be explicit in the physical review. + +The checked backward word is an identity over free invertible warp +generators. Therefore its endpoint map holds under either consistent +substitution: K_G or conjugate(K_G), with inverse occurrences assigned +the corresponding inverse. No relation between the forward and backward +generator substitutions is used in this proof. This observation permits +a choice of physical warp convention; it does not replace a check of +the exact chart transport, monomial rank, and global phase for that +choice. + +The retained phase evidence alone is not treated as a fresh physical +replay. The new canonical providers have 1,130 frames, and their proper +helper terminal spaces must be used in the residual wrappers. The +physical review must check those actual instances, including width-six +helpers and the exact target adapters. It must not substitute the older +T74 frame set or silently use FULL for a proper terminal space. + +## Reproduction + +Run with a new output path: + +```text +python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/check_new_core.py --out work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-CORE-LOGICAL-REVIEW-FINAL.json +``` + +The checker prints one `PASS_640_ARBITRARY_COLUMNS_AND_91_ZERO_OUTPUTS` +line for each of the four programs, followed by +`PASS_INDEPENDENT_NEW_CORE_LOGICAL_TRANSFER`. It ran with exact rational +arithmetic and optimization enabled. The source interpreter was not +imported or run by this independent checker. + +OpenAI Codex assisted the review under the user's direction. No PR, +commit, or push is authorized. Before any future PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json new file mode 100644 index 0000000000..3cfc26d8f9 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json @@ -0,0 +1,105 @@ +{ + "backward_binding": "Both a consistent K choice and the literal inverse-transpose choice conjugate(K) have exact rank-zero recipes. The literal dual differs in 172 of 180 physical classes per provider.", + "clean_payload_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "interpreter_sha256": "087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b", + "max_rss_bytes": 150323200, + "method": "Independent Pauli conjugation and exact 512-entry Gaussian zero-state vectors; no generator or Clifford compiler import", + "providers": { + "base": { + "child_classes": 3036, + "endpoint_classes": 224, + "frames": 1130, + "helper_width_profile": { + "4": 26, + "5": 2, + "6": 18, + "7": 50, + "8": 99, + "9": 213 + }, + "literal_dual_classes": 180, + "literal_dual_recipes_different_from_forward": 172, + "native_occurrences": { + "backward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + }, + "forward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + } + }, + "negative_controls": [ + "wrong global phase with equal Pauli action", + "wrong FULL terminal", + "literal conjugate K can differ from K" + ], + "physical_warp_classes": 180, + "pins": { + "CANONICAL-WORD.json.gz": "bd6f84f6e7be075064f04e6141568d295631a3feab1efa75ff0326e6efa4f472", + "CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "LITERAL-DUAL-WARP-RECIPES.json": "e880f4e6ff6308675b766bfa63d472c1050b01f17fac78f8810b04eedc6e0a6e", + "LOCAL-PROGRAMS.json.gz": "4048b4494793f31c6c9ce85a7de584c53cafae0cd5c119eb1084b221cfe04ad9", + "RESIDUAL-ADAPTERS.json": "8a6130051284adf76ec932bc2a190058cc99efbed5d862bee819e3bc8c29a31b" + }, + "raw_warps": 72, + "residual_classes": 56, + "seconds": 63.83301916599157, + "status": "PASS_INDEPENDENT_NATIVE_CORE_LIFT", + "wrapped_helpers": 195 + }, + "extra": { + "child_classes": 3036, + "endpoint_classes": 224, + "frames": 1130, + "helper_width_profile": { + "4": 26, + "5": 2, + "6": 18, + "7": 50, + "8": 99, + "9": 213 + }, + "literal_dual_classes": 180, + "literal_dual_recipes_different_from_forward": 172, + "native_occurrences": { + "backward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + }, + "forward": { + "adapter": 978, + "climb": 3507, + "residual_adapter": 390, + "warp": 240 + } + }, + "negative_controls": [ + "wrong global phase with equal Pauli action", + "wrong FULL terminal", + "literal conjugate K can differ from K" + ], + "physical_warp_classes": 180, + "pins": { + "CANONICAL-WORD.json.gz": "1cf1714fc2a26c18b2b380827054246550c1402fde379745f626ff61f4ee6224", + "CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "LITERAL-DUAL-WARP-RECIPES.json": "0bafa16eea7a49af963346117cf61ca638859748752d5f0ed47a18fe6c4594ff", + "LOCAL-PROGRAMS.json.gz": "4048b4494793f31c6c9ce85a7de584c53cafae0cd5c119eb1084b221cfe04ad9", + "RESIDUAL-ADAPTERS.json": "dd8d70e07ae6ecc028d7691611966fcaee946279964736997af0aa78c61c2282" + }, + "raw_warps": 72, + "residual_classes": 56, + "seconds": 37.52593279199209, + "status": "PASS_INDEPENDENT_NATIVE_CORE_LIFT", + "wrapped_helpers": 195 + } + }, + "scope": "Local phase-aware native lift. The whole scalar map is in the separate logical review. Global hosting, owner, controller, and recursive supplier admission remain separate.", + "status": "PASS_INDEPENDENT_NEW_CORE_NATIVE_RECIPES" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.md new file mode 100644 index 0000000000..16fcf2d026 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.md @@ -0,0 +1,146 @@ +# Independent review of the new-core native implementation + +The local native implementation passes. This review closes the native +phase dependency of `NEW-CORE-LOGICAL-REVIEW.md` for both new provider +words. Together, the two reviews establish the clean-J local maps on all +632 live fields, with 408 arbitrary borrowed helpers and 91 private zero +buffers. The local bill is 164514 real scalar primitives and native rank +mass 5073. The native profile is +`{1:2433, 2:724, 3:228, 4:102, 5:20}`. + +The review does not establish a complete supplier. The global controller, +owner assignment, private storage, recursive child hosting, precision, +and complete kappa calculation remain separate obligations. + +## Evidence and independence + +`check_new_native.py` reads the fresh recipes in +`../new-native-recipes-20261017`. Its constants pin the decompressed +canonical words and local programs, the serialized standard recipes, +the residual recipes, and the new literal dual recipes. The words come +from PR3133 and the byte-equal provider objects in PR3148. This review +uses their new frames and new warps. It does not substitute an earlier +provider's geometry. + +The checker imports the pinned independent interpreter +`../interface-proof/verify_native_lift.py`. It does not import the recipe +generator, `clifford_exact.py`, or the producer's proof checker. The +interpreter computes the action on all 18 Pauli generators and the exact +512-entry Gaussian dyadic image of the zero basis vector. It uses exact +integer arithmetic. It does not use a floating point tolerance. + +These checks prove operator equality, including global phase. If two +unitary operators have the same action on the Pauli generators, their +quotient commutes with every coordinate X and Z. Commutation with all Z +makes the quotient diagonal. Commutation with all X makes every diagonal +entry equal. Equality on the nonzero image of the zero basis vector fixes +that scalar as one. Thus one checked state and all Pauli generators prove +the equality on every input. This is not a claim that the checker tests +512 separate basis inputs for every recipe. + +For each provider the checker verifies: + +- All 1130 frame bases and all 3036 directed child classes. +- All 224 source and target endpoint adapters. +- All 72 raw logical warp operators. +- All 180 standard physical warp classes. +- All 180 literal dual physical warp classes. +- All 56 residual wrapper classes, on 195 helpers. +- Every native occurrence in both clean-J words: 3507 children, 240 + warps, 978 ordinary adapters, and 390 residual adapters. + +## Frames, wrappers, and composition + +Let Gamma_U be the canonical frame of a binary subspace U. The checker +constructs it from U by an independent basis extension and the defining +permutation, quadratic phase, and coordinate Fourier gates. Each child +recipe is compared with `Gamma_V Gamma_U^-1`. The checker also verifies +that its frames are nested and that its paid rank is the absolute +difference of their dimensions. + +The source endpoint reference is the port-line operator C_q. The target +endpoint reference is `F C_q^-1`. The corresponding adapters are checked +against these operators, not only against their recorded frame numbers. +The other data endpoints are I at input and FULL at output. + +For a borrowed helper with entry E and terminal V, the raw residual is +`S = Gamma_V Gamma_E^-1`. A serialized recipe gives +`S = L C_[w] R`, where `w = dim(V)-dim(E)`. The checker proves both this +factorization and + + L^-1 S R^-1 = C_[w]. + +This is the required native action on w coordinate factors. It restores +the other `9-w` factors exactly, including phase. The helper width profile +is `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}`. The proper terminal frames are +used as recorded; they are not replaced with FULL. + +The placement of these wrappers is also checked. No wrapped helper is +used by the added correction, the zero-frame precondition, or its +compensation before the entry wrapper. In particular, this check covers +the 61 helpers with entry I and a proper terminal. No proper-terminal +helper is used in the FULL-frame cleanup. These facts let the wrapper +factorization compose with the previously checked whole logical map. +All remaining scalar operations have equal operand frames, as proved in +the separate logical review. Every native record is bound to the exact +source record that the clean-J word retains. + +## Backward warp convention + +The literal inverse transpose of a unitary logical warp K is its +entrywise conjugate. The original serialized event labels are the same +for the two orientations. The orientation must therefore select the +correct physical recipe when it uses the literal dual convention. + +The new dual tables pass the independent test against + + Gamma_V conjugate(K)^sign Gamma_U^-1. + +Every such recipe has rank zero. The distinction is real: 172 of the 180 +dual physical recipes differ from the standard table for each provider. +The review does not treat the two tables as byte-equal. + +There is a general closure theorem behind this result. Let K be a +monomial Clifford operator whose nonzero entries are fourth roots of +unity. In a standard basis, write K as an affine permutation with phase +`i^(c + alpha.x + 2q(x))`, where q is a binary quadratic form. The quotient +`conjugate(K) K^-1` has phase `2(c+alpha.x)` modulo four, after an affine +change of coordinates. It is a signed Z Pauli. If +`W = Gamma_V K Gamma_U^-1` is monomial, then + + Gamma_V conjugate(K) Gamma_U^-1 + = (Gamma_V P Gamma_V^-1) W + +for that Pauli P. Clifford conjugation preserves the Pauli group, and a +Pauli is monomial. The dual product is therefore monomial. Apply the same +argument to `K^-1` for a negative occurrence. The fourth-root hypothesis +holds for every source K. With an arbitrary global phase, the quotient +is instead a scalar times a Pauli; monomial closure still follows, but +the serialized phase contract needs the stated hypothesis. + +The whole backward scalar map was proved over free invertible warp +generators. Thus it also permits a consistent same-K implementation. The +literal dual tables give the direct inverse-transpose implementation +without the need to use that alternative interpretation. + +## Checks, limits, and reproduction + +The run used Python isolation and optimization: + + python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/check_new_native.py --providers base extra --out work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json + +It returned `PASS_INDEPENDENT_NEW_CORE_NATIVE_RECIPES`. Checks remain +active under `-O`. The receipt records all input pins and both providers. +Negative controls reject a wrong global phase that has the correct Pauli +action and a wrong FULL terminal. A further check confirms that literal +conjugation changes some source warp operators. + +Exact base operator identities imply the same identities for every +positive tensor power. This implication does not supply a caller's +exterior phases, legal source access, owner schedule, or recursive cost. +Those remain obligations of the complete construction. + +The fresh source generation, source attribution, and commit-pinned links +are in `../new-native-recipes-20261017/NATIVE-LIFT.md`. OpenAI Codex +assisted this independent review. This is a separate agent calculation, +not a maintainer review. No PR, push, or publication commit was made. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/check_new_native.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/check_new_native.py new file mode 100644 index 0000000000..471b3150a2 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/check_new_native.py @@ -0,0 +1,246 @@ +"""Check new-core native recipes with a separate exact interpreter.""" + +import argparse +from collections import Counter +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import resource +import time + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +SOURCE = LANES / 'new-native-recipes-20261017' +INTERPRETER = LANES / 'interface-proof/verify_native_lift.py' +INTERPRETER_PIN = '087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b' +CLEAN = LANES / 'new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz' +CLEAN_PIN = 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa' +PINS = { + 'base': { + 'CANONICAL-WORD.json.gz': 'bd6f84f6e7be075064f04e6141568d295631a3feab1efa75ff0326e6efa4f472', + 'LOCAL-PROGRAMS.json.gz': '4048b4494793f31c6c9ce85a7de584c53cafae0cd5c119eb1084b221cfe04ad9', + 'CLIFFORD-RECIPES.json': '580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0', + 'RESIDUAL-ADAPTERS.json': '8a6130051284adf76ec932bc2a190058cc99efbed5d862bee819e3bc8c29a31b', + 'LITERAL-DUAL-WARP-RECIPES.json': 'e880f4e6ff6308675b766bfa63d472c1050b01f17fac78f8810b04eedc6e0a6e', + }, + 'extra': { + 'CANONICAL-WORD.json.gz': '1cf1714fc2a26c18b2b380827054246550c1402fde379745f626ff61f4ee6224', + 'LOCAL-PROGRAMS.json.gz': '4048b4494793f31c6c9ce85a7de584c53cafae0cd5c119eb1084b221cfe04ad9', + 'CLIFFORD-RECIPES.json': 'f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e', + 'RESIDUAL-ADAPTERS.json': 'dd8d70e07ae6ecc028d7691611966fcaee946279964736997af0aa78c61c2282', + 'LITERAL-DUAL-WARP-RECIPES.json': '0bafa16eea7a49af963346117cf61ca638859748752d5f0ed47a18fe6c4594ff', + }, +} + + +def need(ok, label): + if not ok: + raise ValueError(label) + + +def pinned(path, pin): + raw = path.read_bytes() + if path.suffix == '.gz': + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == pin, 'Input pin: ' + str(path)) + return json.loads(raw) + + +def rank(vectors): + pivots = {} + for value in vectors: + while value: + p = value.bit_length() - 1 + if p not in pivots: + pivots[p] = value + break + value ^= pivots[p] + return len(pivots) + + +def raw_k(columns, native, dual=False): + matrix = native.transpose(tuple(columns)) + columns_inverse = native.transpose(native.inverse(matrix)) + quadratic = tuple((1 << i) ^ sum(native.parity(a & b) << j + for j, b in enumerate(columns_inverse)) + for i, a in enumerate(columns_inverse)) + linear = tuple(((-1 if dual else 1) * ((row >> i) & 1)) % 4 + for i, row in enumerate(quadratic)) + return (('P', matrix), ('D', quadratic, linear)) + + +def fields(event): + if event[0] == 'warp': + return [tuple(event[1])] + if event[0] == 'scalar': + return [tuple(x) for x in event[1][1:] if isinstance(x, list)] + return [] + + +def review(provider, native, clean): + started = time.monotonic() + data = {name: pinned(SOURCE / provider / name, pin) for name, pin in PINS[provider].items()} + c = data['CANONICAL-WORD.json.gz'] + original = data['LOCAL-PROGRAMS.json.gz'] + phase = data['CLIFFORD-RECIPES.json'] + residual = data['RESIDUAL-ADAPTERS.json'] + frames = [native.frame(tuple(v), 9) for v in c['frames']] + need(len(frames) == 1130 and c['h'] == 9 and c['v'] == 112 and c['R'] == 408, 'Canonical dimensions') + need(all(rank(v) == len(v) for v in c['frames']), 'Every frame is a basis') + edges = set(map(tuple, c['edges'])) | {(a, b) for f in c['center_frames'] for a, b in ((f, 0), (0, f))} + children = {(r['old'], r['new']): r for r in phase['children']} + need(len(children) == len(phase['children']) == 3036 and set(children) == edges, 'Exact child coverage') + for i, ((a, b), record) in enumerate(sorted(children.items())): + va, vb = c['frames'][a], c['frames'][b] + need(rank(va + vb) == max(len(va), len(vb)), 'Nested child spaces') + need(record['rank'] == abs(len(vb) - len(va)), 'Child rank') + native.equal(native.recipe(record), native.adjoint(frames[a]) + frames[b], 'Child ' + str((a, b))) + if i % 200 == 0: + print(provider, 'independent phase edges', i, '/', len(children), flush=True) + + endpoints = {(r['role'], r['port']): r for r in phase['endpoint_adapters']} + need(len(endpoints) == len(phase['endpoint_adapters']) == 224, 'Unique endpoint recipes') + need(set(endpoints) == {(role, p) for role in ('source', 'target') for p in range(112)}, 'All data endpoints') + for (role, p), record in endpoints.items(): + conventional = (('C', c['ports'][p], 1),) if role == 'source' else (('C', c['ports'][p], -1),) + native.fourier(9) + f = c['start'][p] if role == 'source' else c['final'][112 + p] + need(record['frame'] == f and record['rank'] == 0, 'Endpoint frame and rank') + native.equal(native.recipe(record), native.adjoint(conventional) + frames[f], 'Endpoint ' + str((role, p))) + need(set(c['start'][112:224]) == {0} and set(c['final'][:112]) == {1}, 'Other data endpoints') + native.equal(frames[0], (), 'Identity frame') + native.equal(frames[1], native.fourier(9), 'FULL frame') + + warps = {r['op']: r for r in c['warps']} + need(len(warps) == len(c['warps']) == 72, 'Unique logical warps') + need(set(residual['warps']) == set(map(str, warps)), 'Raw warp coverage') + logical = {} + for op, w in warps.items(): + record = residual['warps'][str(op)] + need(all(record[k] == w[k] for k in ('op', 'from_frame', 'to_frame', 'G_columns')), 'Raw warp metadata') + logical[op] = raw_k(w['G_columns'], native) + native.equal(native.monomial(record['K']), logical[op], 'Raw K ' + str(op)) + physical = {(r['sign'], r['op'], r['old'], r['new']): r for r in phase['warps']} + need(len(physical) == len(phase['warps']) == 180 and set(physical) == set(map(tuple, c['warp_edges'])), 'Physical warp coverage') + for (sign, op, a, b), record in physical.items(): + need(sign in (-1, 1) and record['rank'] == 0 and record['G_columns'] == warps[op]['G_columns'], 'Warp metadata') + operator = logical[op] if sign > 0 else native.adjoint(logical[op]) + native.equal(native.recipe(record), native.adjoint(frames[a]) + operator + frames[b], 'Physical K ' + str((sign, op, a, b))) + + dual_list = data['LITERAL-DUAL-WARP-RECIPES.json']['warps'] + dual = {(r['sign'], r['op'], r['old'], r['new']): r for r in dual_list} + need(len(dual) == len(dual_list) == 180 and set(dual) == set(physical), 'Literal dual coverage') + different_dual = 0 + for (sign, op, a, b), record in dual.items(): + need(record['orientation'] == 'backward_literal_dual' and record['rank'] == 0 and record['G_columns'] == warps[op]['G_columns'], 'Literal dual metadata') + operator = raw_k(warps[op]['G_columns'], native, True) + if sign < 0: + operator = native.adjoint(operator) + native.equal(native.recipe(record), native.adjoint(frames[a]) + operator + frames[b], 'Literal dual K ' + str((sign, op, a, b))) + different_dual += record['left'] != physical[sign, op, a, b]['left'] + need(different_dual == 172, 'Literal dual differs from source K in 172 classes') + + wrappers = residual['recipes'] + wrapped = {r for r in range(224, 632) if c['start'][r] != 0 or c['final'][r] != 1} + needed_wrappers = {str(c['start'][r]) + (':' + str(c['final'][r]) if c['final'][r] != 1 else '') for r in wrapped} + need(set(wrappers) == needed_wrappers and len(wrappers) == 56 and len(wrapped) == 195, 'Wrapper class and helper coverage') + for key, record in wrappers.items(): + a, b = record['frame'], record.get('terminal', 1) + va, vb = c['frames'][a], c['frames'][b] + width = len(vb) - len(va) + need(rank(va + vb) == len(vb) and 0 < width <= 9, 'Residual nested frames') + need(record['rank'] == width and record['entrance_rank'] == len(va) and record['vectors'] == va, 'Residual entry metadata') + if b != 1: + need(record['terminal_rank'] == len(vb) and record['terminal_vectors'] == vb, 'Proper residual terminal metadata') + product = native.adjoint(frames[a]) + frames[b] + native.equal(native.recipe(record), product, 'Residual ' + key) + wrapped_product = native.adjoint(native.monomial(record['right'])) + product + native.adjoint(native.monomial(record['left'])) + native.equal(wrapped_product, native.fourier(width), 'Coordinate wrapper ' + key) + + invoices = {} + for orientation, events in clean['providers'][provider]['programs'].items(): + need(clean['providers'][provider]['canonical'] == c, 'Clean word canonical binding') + native_tags = {'climb', 'warp', 'adapter', 'residual_adapter'} + need([e for e in events if e[0] in native_tags] == [e for e in original[orientation] if e[0] in native_tags], 'Every retained native record') + entry = events.index(['phase', 'entry_adapters']) + cleanup = events.index(['phase', 'full_frame_cleanup']) + need(not {f[1] for e in events[:entry] for f in fields(e) if f[0] == 'L'} & wrapped, 'No wrapper helper access before entry wrapper') + post = {r for r in range(224, 632) if c['final'][r] != 1} + need(not {f[1] for e in events[cleanup:] for f in fields(e) if f[0] == 'L'} & post, 'No proper-terminal helper access after its core') + counts = Counter() + adapter_records = [] + wrapper_records = [] + for e in events: + if e[0] == 'climb': + _, _, _, a, b, width = e + need((a, b) in children and children[a, b]['rank'] == width, 'Paid child occurrence binding') + counts['climb'] += 1 + elif e[0] == 'warp': + op, a, b = e[2:] + need((1 if op > 0 else -1, abs(op), a, b) in physical, 'Physical warp occurrence binding') + counts['warp'] += 1 + elif e[0] == 'adapter': + _, direction, r, f = e + need(direction in ('old_to_new', 'new_to_old'), 'Adapter direction') + need(f == (c['start'][r] if direction == 'old_to_new' else c['final'][r]), 'Adapter boundary binding') + if direction == 'old_to_new': + need(r not in wrapped, 'No duplicate helper entry wrapper') + need(r < 112 or f == 0, 'Only source ports need ordinary entry adapters') + else: + need(r not in post, 'No wrong FULL adapter on a proper terminal helper') + need(112 <= r < 224 or f == 1, 'Only target ports need ordinary exit adapters') + adapter_records.append((direction, r)) + counts['adapter'] += 1 + elif e[0] == 'residual_adapter': + _, position, r, a, *tail = e + b = tail[0] if tail else 1 + need(position in ('pre', 'post') and r in wrapped and a == c['start'][r] and b == c['final'][r], 'Residual occurrence binding') + wrapper_records.append((position, r)) + counts['residual_adapter'] += 1 + need(set(adapter_records) == {('old_to_new', r) for r in range(632) if r not in wrapped} | {('new_to_old', r) for r in range(632) if r not in post}, 'All ordinary adapter occurrences') + need(len(adapter_records) == len(set(adapter_records)), 'No repeated ordinary adapter') + need(set(wrapper_records) == {(position, r) for position in ('pre', 'post') for r in wrapped} and len(wrapper_records) == 390, 'All wrapper occurrences') + need(counts == Counter(climb=3507, warp=240, adapter=978, residual_adapter=390), 'Native occurrence inventory') + invoices[orientation] = dict(counts) + + child = native.recipe(next(iter(children.values()))) + corrupt = child + (('phase', 1),) + need(native.tableau(corrupt) == native.tableau(child) and native.state(corrupt) != native.state(child), 'Global phase negative control') + proper = next(r for r in wrappers.values() if r.get('terminal', 1) != 1) + correct = native.adjoint(frames[proper['frame']]) + frames[proper['terminal']] + wrong = native.adjoint(frames[proper['frame']]) + frames[1] + need(native.tableau(correct) != native.tableau(wrong), 'Wrong FULL terminal negative control') + need(any(native.tableau(logical[op]) != native.tableau(raw_k(warps[op]['G_columns'], native, True)) for op in logical), 'Conjugation changes some warp operators') + return {'status': 'PASS_INDEPENDENT_NATIVE_CORE_LIFT', 'pins': PINS[provider], + 'frames': len(frames), 'child_classes': len(children), 'endpoint_classes': len(endpoints), + 'raw_warps': len(warps), 'physical_warp_classes': len(physical), 'residual_classes': len(wrappers), + 'literal_dual_classes': len(dual), 'literal_dual_recipes_different_from_forward': different_dual, + 'wrapped_helpers': len(wrapped), 'native_occurrences': invoices, + 'helper_width_profile': dict(sorted(Counter(len(c['frames'][c['final'][r]]) - len(c['frames'][c['start'][r]]) for r in range(224, 632)).items())), + 'negative_controls': ['wrong global phase with equal Pauli action', 'wrong FULL terminal', 'literal conjugate K can differ from K'], + 'seconds': time.monotonic() - started} + + +def main(args): + need(sha256(INTERPRETER.read_bytes()).hexdigest() == INTERPRETER_PIN, 'Independent interpreter pin') + spec = importlib.util.spec_from_file_location('independent_native_interpreter', INTERPRETER) + native = importlib.util.module_from_spec(spec) + spec.loader.exec_module(native) + clean = pinned(CLEAN, CLEAN_PIN) + result = {'status': 'PASS_INDEPENDENT_NEW_CORE_NATIVE_RECIPES', 'interpreter_sha256': INTERPRETER_PIN, + 'clean_payload_sha256': CLEAN_PIN, 'method': 'Independent Pauli conjugation and exact 512-entry Gaussian zero-state vectors; no generator or Clifford compiler import', + 'scope': 'Local phase-aware native lift. The whole scalar map is in the separate logical review. Global hosting, owner, controller, and recursive supplier admission remain separate.', + 'backward_binding': 'Both a consistent K choice and the literal inverse-transpose choice conjugate(K) have exact rank-zero recipes. The literal dual differs in 172 of 180 physical classes per provider.', + 'providers': {name: review(name, native, clean) for name in args.providers}} + result['max_rss_bytes'] = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss + args.out.write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + print(result['status'], flush=True) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser() + parser.add_argument('--providers', nargs='+', choices=['base', 'extra'], default=['base']) + parser.add_argument('--out', type=Path, required=True) + main(parser.parse_args()) diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md new file mode 100644 index 0000000000..953df4352a --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md @@ -0,0 +1,389 @@ +# Exact division by three for the actual A8 borrowed block + +The one-minor borrowed block is invertible in the retained machine model. +Its inverse needs exact division by three. 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/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/CHECKS.json new file mode 100644 index 0000000000..df1ae1872e --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/CHECKS.json @@ -0,0 +1,84 @@ +{ + "actual_K_row_l1": 1, + "actual_R_row_l1": 56, + "checker_sha256": "550330e2c6b5b485f531c9c1f0b633ec55d6a2200839903b4f1fc3d4da9ade1e", + "coordinate_projection_checks": 256, + "coordinate_rank_distribution": { + "0": 1, + "1": 8, + "2": 28, + "3": 56, + "4": 70, + "5": 56, + "6": 28, + "7": 8, + "8": 1 + }, + "full_inverse_cases": [ + { + "basis_columns_per_order": 112, + "label": "coordinate-0", + "rank_M": 0, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-1", + "rank_M": 1, + "rank_N": 7 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-15", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-127", + "rank_M": 7, + "rank_N": 1 + }, + { + "basis_columns_per_order": 112, + "label": "coordinate-255", + "rank_M": 8, + "rank_N": 0 + }, + { + "basis_columns_per_order": 112, + "label": "noncoordinate-rank-four", + "rank_M": 4, + "rank_N": 4 + }, + { + "basis_columns_per_order": 112, + "label": "general-centre-unit", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "nontrivial-dyadic-full-rank", + "rank_M": 8, + "rank_N": 8 + }, + { + "basis_columns_per_order": 112, + "label": "13-integral-rank-four-forces-full-rank-partner", + "rank_M": 4, + "rank_N": 8 + } + ], + "method": "Independent dense centre algebra and 112-column vector interpreter; no producer imports.", + "negative_controls": [ + "wrong coefficient", + "repeated response", + "arbitrary noncommuting pair" + ], + "ordered_noncommuting_identity_columns": 112, + "scope": "Exact scalar family and query ranks. No full native word, phase terminal, controller, or complete supplier price is certified here.", + "source_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "source_proof_sha256": "d2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9", + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_RANK" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/FREEZE.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/FREEZE.json new file mode 100644 index 0000000000..2e50726cd4 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/FREEZE.json @@ -0,0 +1,26 @@ +{ + "clean_core_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "files": { + "CHECKS.json": "4cbe8ca3e0af51192fb113a2879467b30af19fc68b0f9713991e1f0bef2b2e7c", + "GRID-CHECKS.json": "4f12b6f0ed60343ad03be226e162df6a918caf813ab46ad88105c85a28fae412", + "ODD-GRID-COMPOSITION.md": "80f26788f706b5c3a3dbb3cd6bf9e0609e49d7f6384145e03daa9cbe9d3d4547", + "REVIEW.md": "410803aab5eaceca73412b960802d5eccbc45c4b4fef4bad2aae82a52d7792c4", + "check_grid.py": "e257f0a984b9e7f4f86f25a9e2991f03e3ff0c93888be9ff75a717186af85641", + "check_reciprocal.py": "550330e2c6b5b485f531c9c1f0b633ec55d6a2200839903b4f1fc3d4da9ade1e" + }, + "publication": "No PR, push, publication commit, or external mutation.", + "scope": "Scalar correction-rank theorem and conditional active-path odd-grid theorem. No native reciprocal word, complete controller, recursive supplier price, or kappa improvement is certified here.", + "source_files_relative_to_campaign": { + "lanes/bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md": "0eee1c869ba6c1c5e75075bc9dbae3324468a27a6b0dd45cd16e4f7973f9eb05", + "lanes/independent-review-20261017/NEW-CORE-LOGICAL-REVIEW.md": "dc7a2a8f8cb3e7f872266d406af157f4dcf7caa0dc74c5ceefcaa016a2fe2c7e", + "lanes/independent-review-20261017/odd-grid-a8-20261017/A8-ODD-GRID.md": "e0210105ba6c6246f1f84c8ce2d92cfd07aa6cc8a161ca27d7fcc8e0183cfb01", + "lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a", + "lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz": "53f397311592cdb1f8b786ab500ec06f0f26c35117a28da721189ce10beef079", + "root/RECIPROCAL-CENTRE-RANK-20261018.json": "6d42a30f888f78b486fdb70cdf150d80562588404e94beec4839061505f806eb", + "root/RECIPROCAL-CENTRE-RANK-20261018.md": "d2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9", + "root/RECIPROCAL-CENTRE-RANK-FREEZE-20261018.json": "c8eff152a353492c41fd783429723adebddebdca93db20e3eeaf837594ba6dab", + "root/check_reciprocal_centre_rank_20261018.py": "e01ad5199c14319e904e7f56d3e675a50722a6d7df2a366efd0273cb19bf71aa" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_RANK_AND_CONDITIONAL_GRID", + "validation": "Both peer checkers passed normal and -O runs with byte-identical receipts. No producer replay was used as the decisive peer check." +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/GRID-CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/GRID-CHECKS.json new file mode 100644 index 0000000000..50cbc391f9 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/GRID-CHECKS.json @@ -0,0 +1,67 @@ +{ + "checker_sha256": "e257f0a984b9e7f4f86f25a9e2991f03e3ff0c93888be9ff75a717186af85641", + "negative_controls": [ + "unscaled finest-grid numerator", + "three rational completed children with a two-level budget", + "final unscaling before a dyadic root endpoint" + ], + "nested_integer_basis_cases": [ + { + "active_levels": 1, + "binary_budget": 8, + "completed_calls": 1, + "divisions": 0, + "events": 1, + "max_active_levels": 1, + "max_height": 0, + "odd_budget": 8 + }, + { + "active_levels": 2, + "binary_budget": 16, + "completed_calls": 3, + "divisions": 8, + "events": 19, + "max_active_levels": 2, + "max_height": 1, + "odd_budget": 16 + }, + { + "active_levels": 3, + "binary_budget": 24, + "completed_calls": 7, + "divisions": 24, + "events": 55, + "max_active_levels": 3, + "max_height": 2, + "odd_budget": 24 + }, + { + "active_levels": 4, + "binary_budget": 32, + "completed_calls": 15, + "divisions": 56, + "events": 127, + "max_active_levels": 4, + "max_height": 3, + "odd_budget": 32 + }, + { + "active_levels": 5, + "binary_budget": 40, + "completed_calls": 31, + "divisions": 120, + "events": 271, + "max_active_levels": 5, + "max_height": 4, + "odd_budget": 40 + } + ], + "scope": "Exact signed scans and test trees. The general active-path bound is proved in ODD-GRID-COMPOSITION.md. These trees are not an emitted supplier controller.", + "signed_inputs_checked_for_each_scan": 32766, + "signed_scan_widths": [ + 1, + 14 + ], + "status": "PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/ODD-GRID-COMPOSITION.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/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/reciprocal-native-responses/annexes/original-j-rank-readers/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/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/REVIEW.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/REVIEW.md new file mode 100644 index 0000000000..e496540f5e --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/REVIEW.md @@ -0,0 +1,151 @@ +# Independent review of reciprocal centre rank + +The scalar theorem passes independent proof review. It applies to the +specified extensions of the actual clean response, + + J=I-KR, E=J+KMR, G=J+KNR, K=R^T/4, RK=14I_8. + +For this family, dyadic M and N in a reciprocal pair each have rank eight. +Over the rationals, their least total rank is eight. The stated projection +formula gives every pair at that minimum. A coordinate projection of rank +four uses four actual R rows in each added correction. + +This is a rank theorem for the two specified correction terms. It is not +a query or native-cost lower bound for every implementation of E and G. +For example, M=N=I has two rank-eight correction terms but E=G=I. A new +implementation of the identity need not form either term. The native +capture, frame, phase, and helper obligations need their own word review. +This packet does not establish a complete controller or a kappa change. + +## Pinned input and method + +The reviewed root proof is +`../../../root/RECIPROCAL-CENTRE-RANK-20261018.md`, SHA256 +`d2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9`. +The root freeze is SHA256 +`c8eff152a353492c41fd783429723adebddebdca93db20e3eeaf837594ba6dab`. +The source R is read from +`../../new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz`. +Its decompressed SHA256 is +`a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa`. +These source files were not changed. + +The new checker does not import a producer checker. It uses dense centre +matrices and a separate vector interpreter for the 112-field maps. It +checks RK=14I directly from the source entries. It also checks that every +R row has norm 56 and every K row has norm one in the row-sum norm. +The prior clean-core review binds this R to the literal native J. That +complete native replay was not repeated for this scalar theorem. + +## Ordered proof + +For a vector x, the new interpreter applies a response as + + E x = x + K(M-I)R x. + +Apply G first and then E. The coefficient between K and R is + + (M-I)+(N-I)+14(M-I)(N-I) + = 12I-13(M+N)+14MN. + +This computation retains the order MN. Since RK=14I over the rationals, +K is injective and R is onto. Thus K C R=0 is equivalent to C=0. +One can also multiply on the left by R/14 and on the right by K/14. +There is no unstated loss of a centre equation. + +The equation for reciprocity is equivalent to + + (14M-13I)(14N-13I)=I. + +For square matrices over a field, a one-sided inverse is a two-sided +inverse. Subtract the reversed product equation. It gives MN=NM. Thus +commutation is a consequence, and GE=I follows. The checker also tests +the ordered identity for a pair with MN different from NM. Reversing +that test pair changes its residual, as it must. + +Reduction modulo 13 is defined on Z[1/2]. The centre equation reduces +to MN=I over F_13. Both determinants are nonzero after reduction. They +were therefore nonzero before reduction. This proves each rank is eight. +The same proof works on a rational subring whose denominators are coprime +to 13. No rank statement for a noncommutative operator ring follows from +this argument without a separate module and reduction theorem. + +Over the rationals, rewrite the equation as + + 12I=13M+(13I-14M)N. + +The rank of the right side is at most rank(M)+rank(N). For equality in +that bound, v in ker(N) satisfies Mv=(12/13)v. Hence ker(N) is contained +in im(M), and equality of dimensions gives ker(N)=im(M). To obtain the +other equality, use the reversed reciprocal equation proved above. It +gives ker(M)=im(N). This use of the reversed equation makes the phrase +"In the same way" in the source proof explicit. + +The two kernels meet only at zero and their dimensions sum to eight. +Let P project onto ker(N) along ker(M). On these two summands M acts as +12/13 and zero, respectively. N acts as zero and 12/13. Therefore + + M=(12/13)P, N=(12/13)(I-P). + +This proves all equality cases. It does not require P to be orthogonal +or self-adjoint. The converse follows from P^2=P. The same proof, with +12,13,14 replaced by rho-2,rho-1,rho, proves the stated characteristic-zero +field result when rho is not 0, 1, or 2. In that version the coefficient +ring must contain the coefficients in use before a reduction is applied. + +## A stronger denominator consequence + +Call a rational matrix 13-integral if every entry has denominator coprime +to 13. Suppose M is 13-integral and E,G are reciprocal. The equation gives + + N=(14M-13I)^-1(13M-12I). + +The first factor exists by the reciprocal equation. The second factor is +invertible: its reduction modulo 13 is I. Thus N has full rank eight, +even if N itself has a denominator divisible by 13. Interchanging M and +N proves the corresponding statement on the other side. + +Consequently, a rank-four/rank-four reciprocal pair has a denominator +divisible by 13 in at least one entry of M and in at least one entry of N. +Allowing this denominator on only one side cannot give that split. This +is a coefficient statement, not a lower bound on scans or native calls. + +## Exact checks and limits + +The independent checker covers all 256 coordinate projections. It checks +both inverse orders on all 112 input basis vectors for nine pairs: five +coordinate ranks, one noncoordinate rank-four projection, one general +centre unit, one nontrivial dyadic reciprocal pair, and one 13-integral +rank-four correction with a full-rank partner. It also checks that +rank(MR)=rank(M) and rank(NR)=rank(N) in these cases. + +The noncoordinate example is not self-adjoint. The dyadic example uses +M=I+S and N=I-S with S^2=0. These cases test assumptions that the proof +does not make. The noncommuting residual test covers all 112 columns. +Wrong weights, a repeated response, and an arbitrary noncommuting pair +are rejected as reciprocal pairs. The proof, not these finite examples, +establishes the universal rank bounds and equality classification. + +The companion `ODD-GRID-COMPOSITION.md` proves a conditional representation +theorem. It permits these rational maps as finite parent operations while +completed recursive children retain exact Gaussian-dyadic endpoints. +It does not supply those endpoints for a changed global controller. It +does not replace the existing binary and magnitude guard by a count of +odd denominators. + +Run from the workspace root: + + python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_reciprocal.py + python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_grid.py + +Expected statuses are `PASS_INDEPENDENT_RECIPROCAL_CENTRE_RANK` and +`PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS`. Both commands also pass +with Python assertions disabled. The source pins and output hashes are +recorded in `FREEZE.json`. + +The root lane supplied the rank theorem. Earlier clean-core and +odd-grid work supplied the actual J and the representation method. +This review supplied a separate interpreter, the explicit reversed-kernel +step, the one-sided denominator consequence, and the stated composition +conditions. This work used OpenAI Codex under the user's direction. +No publication is authorized. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_grid.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_grid.py new file mode 100644 index 0000000000..ac0bb2d93b --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_grid.py @@ -0,0 +1,147 @@ +#!/usr/bin/env python3 +"""Check the signed scan and nested words on a common integer grid.""" +from hashlib import sha256 +from pathlib import Path +import json + +HERE = Path(__file__).resolve().parent + + +def need(test, label): + if not test: + raise ValueError(label) + + +def signed(value, width): + return value-(1 << width) if value >> (width-1) else value + + +def divide13(value, width): + source = value % (1 << width) + carry, output = 0, 0 + for pos in range(width): + bit = (source >> pos) & 1 + out = (bit-carry) % 2 + output |= out << pos + carry = (carry+13*out-bit)//2 + need(0 <= carry < 13, 'Division carry range') + result = signed(output, width) + accepted = carry == 13*(result < 0)-(value < 0) + return accepted, result + + +def multiply13(value, width): + source = value % (1 << width) + carry, output = 0, 0 + for pos in range(width): + bit = (source >> pos) & 1 + total = 13*bit+carry + output |= (total % 2) << pos + carry = total//2 + need(0 <= carry < 13, 'Multiplication carry range') + result = signed(output, width) + accepted = carry == 13*(value < 0)-(result < 0) + return accepted, result + + +scan_inputs = 0 +for width in range(1, 15): + limit = 1 << (width-1) + for value in range(-limit, limit): + good, quotient = divide13(value, width) + need(good == (value % 13 == 0), 'Exact signed division acceptance') + if good: + need(13*quotient == value, 'Exact signed quotient') + good, product = multiply13(value, width) + need(good == (-limit <= 13*value < limit), 'Signed multiplication overflow') + if good: + need(product == 13*value, 'Exact signed product') + scan_inputs += 1 + + +def valuation13(value): + if value == 0: + return None + value = abs(value) + exponent = 0 + while value % 13 == 0: + value //= 13 + exponent += 1 + return exponent + + +grid_cases = [] +for remaining in range(5): + levels = remaining+1 + odd_budget = 8*levels + binary_budget = 8*levels + root_scale = 13**odd_budget * 2**binary_budget + state = [[root_scale*int(i == j) for j in range(8)] for i in range(8)] + observations = {'events': 0, 'divisions': 0, 'max_height': 0, + 'completed_calls': 0, 'max_active_levels': 0} + + def observe(active): + height = max([0]+[max(0, odd_budget-v) + for row in state for value in row + if (v := valuation13(value)) is not None]) + need(height <= 8*active, 'Active-path height bound') + observations['max_height'] = max(observations['max_height'], height) + observations['max_active_levels'] = max(observations['max_active_levels'], active) + observations['events'] += 1 + + def scale_row(row, numerator, divisor, active): + need(all(value % divisor == 0 for value in state[row]), 'Exact grid division') + state[row] = [numerator*(value//divisor) for value in state[row]] + observations['divisions'] += int(divisor == 13) + observe(active) + + def shear(row, source, sign, active): + need(all(value % 2 == 0 for value in state[source]), 'Binary guard') + state[row] = [x+sign*(y//2) for x, y in zip(state[row], state[source])] + observe(active) + + def run(depth, target, sign, active): + entry = [row[:] for row in state] + if depth: + for row in range(8): + scale_row(row, -1 if row < 4 else -13, 13 if row < 4 else 1, active) + child_target = depth % 8 + run(depth-1, child_target, 1, active+1) + run(depth-1, child_target, -1, active+1) + for row in range(8): + scale_row(row, -13 if row < 4 else -1, 1 if row < 4 else 13, active) + source = (target+4) % 8 + shear(target, source, sign, active) + expected = [row[:] for row in entry] + need(all(value % 2 == 0 for value in entry[source]), 'Endpoint binary guard') + expected[target] = [x+sign*(y//2) for x, y in zip(entry[target], entry[source])] + need(state == expected, 'Every completed child has its dyadic endpoint') + observations['completed_calls'] += 1 + + run(remaining, 0, 1, 1) + need(all(value % 13**odd_budget == 0 for row in state for value in row), + 'Exact final root unscaling') + grid_cases.append({'active_levels': levels, 'odd_budget': odd_budget, + 'binary_budget': binary_budget, **observations}) + +need(1 % 13 != 0, 'Unscaled finest-grid input is rejected') +value = 13**2 +for _ in range(2): + need(value % 13 == 0, 'First rational child calls') + value //= 13 +need(value % 13 != 0, 'Rational completed children invalidate the depth-only budget') +need((-13**7) % 13**8 != 0, 'Unfinished rational root cannot be unscaled') + +out = { + 'status': 'PASS_INDEPENDENT_ODD_GRID_COMPOSITION_CHECKS', + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'signed_scan_widths': [1, 14], + 'signed_inputs_checked_for_each_scan': scan_inputs, + 'nested_integer_basis_cases': grid_cases, + 'negative_controls': ['unscaled finest-grid numerator', + 'three rational completed children with a two-level budget', + 'final unscaling before a dyadic root endpoint'], + 'scope': 'Exact signed scans and test trees. The general active-path bound is proved in ODD-GRID-COMPOSITION.md. These trees are not an emitted supplier controller.' +} +(HERE / 'GRID-CHECKS.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') +print(out['status']) diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_reciprocal.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_reciprocal.py new file mode 100644 index 0000000000..0ad51a3569 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018/check_reciprocal.py @@ -0,0 +1,208 @@ +#!/usr/bin/env python3 +"""Check the reciprocal family with an independent vector interpreter.""" +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +HERE = Path(__file__).resolve().parent +CAMPAIGN = HERE.parents[2] +SOURCE = CAMPAIGN / 'lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz' +PIN = 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa' +PROOF_PIN = 'd2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9' + + +def need(test, label): + if not test: + raise ValueError(label) + + +def eye(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def add(a, b, factor=F(1)): + return [[x + factor*y for x, y in zip(u, v)] for u, v in zip(a, b)] + + +def scale(a, factor): + return [[factor*x for x in row] for row in a] + + +def vector(a, x): + return [sum((value*x[j] for j, value in enumerate(row) if value), F(0)) + for row in a] + + +def product(a, b): + columns = list(zip(*b)) + return [[sum((u*v for u, v in zip(row, col)), F(0)) + for col in columns] for row in a] + + +def rank(a): + work = [list(row) for row in a] + pivot = 0 + for col in range(len(work[0])): + hit = next((i for i in range(pivot, len(work)) if work[i][col]), None) + if hit is None: + continue + work[pivot], work[hit] = work[hit], work[pivot] + divisor = work[pivot][col] + work[pivot] = [x/divisor for x in work[pivot]] + for i in range(len(work)): + if i != pivot and work[i][col]: + amount = work[i][col] + work[i] = [x-amount*y for x, y in zip(work[i], work[pivot])] + pivot += 1 + if pivot == len(work): + break + return pivot + + +def inverse(a): + n = len(a) + work = [list(row)+unit for row, unit in zip(a, eye(n))] + for col in range(n): + hit = next(i for i in range(col, n) if work[i][col]) + work[col], work[hit] = work[hit], work[col] + divisor = work[col][col] + work[col] = [x/divisor for x in work[col]] + for i in range(n): + if i != col: + amount = work[i][col] + work[i] = [x-amount*y for x, y in zip(work[i], work[col])] + return [row[n:] for row in work] + + +def reduction13(a): + return [[int(x.numerator)*pow(int(x.denominator), -1, 13) % 13 + for x in row] for row in a] + + +raw = gzip.decompress(SOURCE.read_bytes()) +need(sha256(raw).hexdigest() == PIN, 'Actual source pin') +proof = CAMPAIGN / 'root/RECIPROCAL-CENTRE-RANK-20261018.md' +need(sha256(proof.read_bytes()).hexdigest() == PROOF_PIN, 'Reviewed proof pin') +source = json.loads(raw) +R = [[F(row.get(str(i), 0)) for i in range(112)] for row in source['R']] +need(len(R) == 8, 'Eight actual centre rows') +K = [[R[j][i]/4 for j in range(8)] for i in range(112)] +I8 = eye(8) +need(product(R, K) == scale(I8, 14), 'Actual RK=14I') +need(rank(R) == rank(K) == 8, 'Actual two full ranks') +need(all(sum(abs(x) for x in row) == 56 for row in R), 'R row norm') +need(all(sum(abs(x) for x in row) == 1 for row in K), 'K row norm') + + +def response(m, x): + centre = vector(R, x) + correction = [a-b for a, b in zip(vector(m, centre), centre)] + return [a+b for a, b in zip(x, vector(K, correction))] + + +def bracket(m, n): + return add(add(scale(I8, 12), add(m, n), F(-13)), product(m, n), F(14)) + + +def zero(a): + return all(not x for row in a for x in row) + + +full_cases = [] + + +def check_pair(m, n, label): + need(zero(bracket(m, n)), label+' ordered bracket') + need(zero(bracket(n, m)), label+' reverse bracket') + need(product(m, n) == product(n, m), label+' consequent commutation') + for col in range(112): + x = [F(i == col) for i in range(112)] + need(response(m, response(n, x)) == x, label+' EG column '+str(col)) + need(response(n, response(m, x)) == x, label+' GE column '+str(col)) + need(rank(product(m, R)) == rank(m), label+' query rank M') + need(rank(product(n, R)) == rank(n), label+' query rank N') + full_cases.append({'label': label, 'rank_M': rank(m), 'rank_N': rank(n), + 'basis_columns_per_order': 112}) + + +coefficient = F(12, 13) +rank_counts = {} +for mask in range(256): + p = [[F(i == j and (mask >> i) & 1) for j in range(8)] for i in range(8)] + m, n = scale(p, coefficient), scale(add(I8, p, F(-1)), coefficient) + need(zero(bracket(m, n)), 'Coordinate bracket '+str(mask)) + rm, rn = rank(m), rank(n) + need(rm+rn == 8, 'Coordinate sharp rank sum') + rank_counts[str(rm)] = rank_counts.get(str(rm), 0)+1 + if mask in (0, 1, 15, 127, 255): + check_pair(m, n, 'coordinate-'+str(mask)) + +p = [[F(i == j and i < 4) for j in range(8)] for i in range(8)] +for i in range(4): + for j in range(4, 8): + p[i][j] = F((i+1)*(j-3)-3, 2**(i+j-3)) +need(product(p, p) == p, 'Noncoordinate projection') +need(p != list(map(list, zip(*p))), 'Projection need not be self-adjoint') +m, n = scale(p, coefficient), scale(add(I8, p, F(-1)), coefficient) +check_pair(m, n, 'noncoordinate-rank-four') + +unit = eye(8) +unit[0][0], unit[0][1], unit[1][1] = F(2), F(3), F(5) +m = scale(add(unit, scale(I8, 13)), F(1, 14)) +n = scale(add(inverse(unit), scale(I8, 13)), F(1, 14)) +check_pair(m, n, 'general-centre-unit') + +nilpotent = [[F(0) for _ in range(8)] for _ in range(8)] +nilpotent[0][1] = F(3, 8) +need(zero(product(nilpotent, nilpotent)), 'Square-zero example') +m, n = add(I8, nilpotent), add(I8, nilpotent, F(-1)) +check_pair(m, n, 'nontrivial-dyadic-full-rank') +reduced_product = product(reduction13(m), reduction13(n)) +need([[x % 13 for x in row] for row in reduced_product] == eye(8), + 'Reduction gives two units') + +m = [[F(i == j and i < 4) for j in range(8)] for i in range(8)] +t = add(scale(m, 14), scale(I8, 13), F(-1)) +n = product(inverse(t), add(scale(m, 13), scale(I8, 12), F(-1))) +check_pair(m, n, '13-integral-rank-four-forces-full-rank-partner') +need(rank(m) == 4 and rank(n) == 8, 'Integral-side consequence') + +left = scale(I8, F(1, 2)) +right = eye(8) +left[0][1], right[1][0] = F(3, 2), F(2) +need(product(left, right) != product(right, left), 'Noncommuting test input') +ordered = bracket(left, right) +reverse = bracket(right, left) +need(ordered != reverse, 'Order affects the centre residual') +for col in range(112): + x = [F(i == col) for i in range(112)] + lhs = [a-b for a, b in zip(response(left, response(right, x)), x)] + rhs = vector(K, vector(ordered, vector(R, x))) + need(lhs == rhs, 'Ordered identity on actual column '+str(col)) + +p = [[F(i == j and i < 4) for j in range(8)] for i in range(8)] +m = scale(p, coefficient) +n = scale(add(I8, p, F(-1)), coefficient) +need(not zero(bracket(scale(p, F(11, 13)), n)), 'Wrong coefficient rejected') +need(not zero(bracket(m, m)), 'Repeated response rejected') +need(not zero(bracket(left, right)), 'Arbitrary pair is not reciprocal') + +out = { + 'status': 'PASS_INDEPENDENT_RECIPROCAL_CENTRE_RANK', + 'source_decompressed_sha256': PIN, + 'source_proof_sha256': PROOF_PIN, + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'method': 'Independent dense centre algebra and 112-column vector interpreter; no producer imports.', + 'actual_R_row_l1': 56, + 'actual_K_row_l1': 1, + 'coordinate_projection_checks': 256, + 'coordinate_rank_distribution': rank_counts, + 'full_inverse_cases': full_cases, + 'ordered_noncommuting_identity_columns': 112, + 'negative_controls': ['wrong coefficient', 'repeated response', 'arbitrary noncommuting pair'], + 'scope': 'Exact scalar family and query ranks. No full native word, phase terminal, controller, or complete supplier price is certified here.' +} +(HERE / 'CHECKS.json').write_text(json.dumps(out, indent=2, sort_keys=True)+'\n') +print(out['status']) diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/CHECKS.json new file mode 100644 index 0000000000..35105851d5 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/CHECKS.json @@ -0,0 +1,550 @@ +{ + "checker_sha256": "8a9023adc5ebe5ce1f9ff09b5ce02c00ef58cd0bb695c9a26b1b8cee606cf913", + "clean_payload_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "negative_controls": { + "changed_centre_input_frame": true, + "changed_centre_scatter_sign": true, + "erased_untouched_arbitrary_owned_input": true, + "omitted_weighted_entrance_division": true + }, + "payload_decompressed_sha256": "8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013", + "phase_scope": "Exact byte binding to the prior independent all-3036-edge review, including all 32 centre directions and literal backward dual warps. No second compiler or phase interpreter is claimed in this run.", + "providers": { + "base": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + }, + "extra": { + "E_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 58 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 162 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 267 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 370 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "E_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 45, + "new_13_height": 0, + "position": 47 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 152 + }, + { + "formal_terms": 44, + "new_13_height": 0, + "position": 255 + }, + { + "formal_terms": 45, + "new_13_height": 0, + "position": 359 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 100, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 101, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_backward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 56, + "new_13_height": 0, + "position": 470 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 575 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 682 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 787 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12630 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12657 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12684 + }, + { + "formal_terms": 56, + "new_13_height": 0, + "position": 12711 + } + ], + "dyadic_real_primitives": 165618, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + }, + "G_forward": { + "C0_exit": "zero at I", + "C1_to_C7": "arbitrary identity at I", + "arbitrary_inputs": 640, + "complex_odd_divisions": 8, + "division_queries": [ + { + "formal_terms": 46, + "new_13_height": 0, + "position": 460 + }, + { + "formal_terms": 48, + "new_13_height": 0, + "position": 567 + }, + { + "formal_terms": 46, + "new_13_height": 0, + "position": 672 + }, + { + "formal_terms": 47, + "new_13_height": 0, + "position": 778 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12610 + }, + { + "formal_terms": 104, + "new_13_height": 0, + "position": 12637 + }, + { + "formal_terms": 102, + "new_13_height": 0, + "position": 12664 + }, + { + "formal_terms": 103, + "new_13_height": 0, + "position": 12691 + } + ], + "dyadic_real_primitives": 165594, + "events": 23500, + "local_prefix_13_height_bound": 1, + "logical_helpers": 408, + "native_children": 3511, + "native_mass": 5105, + "native_profile": { + "1": 2433, + "2": 724, + "3": 228, + "4": 102, + "5": 20, + "8": 4 + }, + "ordered_warp_algebra": "free K or dual_K words; adjacent inverse cancellation only", + "private_zero_returns": 91, + "real_odd_scans": 16 + } + } + }, + "scope": "Complete local rational maps, arbitrary logical helper restoration, typed native occurrences, scalar and native invoices, and one new 13-denominator level. No global controller, new recursive provider, owner layout, or kappa claim.", + "source_pins": { + "independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json": "924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d", + "independent-review-20261017/check_new_native.py": "937543157459e5c0eee788feefcf2107acf6bdf660a1209cdecece1ca1f26d01", + "new-native-recipes-20261017/base/CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "reciprocal-centre-20261018/FREEZE.json": "b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd", + "reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md": "322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737", + "reciprocal-centre-20261018/emit_reciprocal_centres.py": "cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc", + "reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-RECEIPT.json": "aafaa8b17be476d521fe4c8eb3cf3af59c72351c3aba60a9413cd2aa0baafdfc" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/FREEZE.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/FREEZE.json new file mode 100644 index 0000000000..205d679039 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/FREEZE.json @@ -0,0 +1,25 @@ +{ + "clean_payload_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "files": { + "CHECKS.json": "3e2238c8e94c8b20c12c68564e4e9b929d78f485bda66b5835a3e0960dffa63e", + "REVIEW.md": "0215d0865ff90fb166411e3896b8c119720a9d5e8034e70411b554517e8bafb8", + "check_words.py": "8a9023adc5ebe5ce1f9ff09b5ce02c00ef58cd0bb695c9a26b1b8cee606cf913" + }, + "payload_decompressed_sha256": "8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013", + "phase_scope": "Exact byte binding to the prior independent all-3036-edge review, including all 32 centre directions and literal backward dual warps. No second compiler or phase interpreter is claimed in this run.", + "publication": "No PR, push, commit, or publication.", + "scalar_and_grid_review_freeze_sha256": "d2432a6da3ee4f1dd7506c44be43adba173b1214a15b0eb7bc4bc69927b471bd", + "scope": "Complete local rational maps, arbitrary logical helper restoration, typed native occurrences, scalar and native invoices, and one new 13-denominator level. No global controller, new recursive provider, owner layout, or kappa claim.", + "sources": { + "independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json": "924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d", + "independent-review-20261017/check_new_native.py": "937543157459e5c0eee788feefcf2107acf6bdf660a1209cdecece1ca1f26d01", + "new-native-recipes-20261017/base/CLIFFORD-RECIPES.json": "580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0", + "new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json": "f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e", + "reciprocal-centre-20261018/FREEZE.json": "b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd", + "reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md": "322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737", + "reciprocal-centre-20261018/emit_reciprocal_centres.py": "cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc", + "reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-RECEIPT.json": "aafaa8b17be476d521fe4c8eb3cf3af59c72351c3aba60a9413cd2aa0baafdfc" + }, + "status": "PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS", + "validation": "Normal and -O checks passed with byte-identical receipts. No producer code is imported." +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/REVIEW.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/REVIEW.md new file mode 100644 index 0000000000..db09de1729 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/REVIEW.md @@ -0,0 +1,190 @@ +# Independent review of the four-centre reciprocal words + +All eight local words pass the independent review. These are E and G in +both orientations on both current providers. The review establishes the +stated logical maps on all 640 arbitrary inputs, all 91 private returns, +the frame conditions, the source bindings, and the local invoice. + +| Orientation | Dyadic scalar primitives | Real /13 scans | Native children | Rank mass | +| --- | ---: | ---: | ---: | ---: | +| Forward | 165594 | 16 | 3511 | 5105 | +| Backward | 165618 | 16 | 3511 | 5105 | + +The scalar count is the bill for the emitted scalar records. The new odd +scans are separate. This table is not a complete bit-machine supplier +price. Global hosting, record and descriptor work, precision, the routed +controller, and recursive use remain separate obligations. The selected +kappa value does not change. + +C0 ends at zero at I. C1 through C7 retain their arbitrary input values +at I. A caller that requires all eight owned outputs to be zero must add +seven CLEARs, at a cost of fourteen scalar primitives. None of the 408 +logical helper inputs must be zero. Their restoration has the inherited +native wrapper convention. + +## Sources and separate method + +The source packet is +`../../reciprocal-centre-20261018/FREEZE.json`, SHA256 +`b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd`. +The proof SHA256 is +`322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737`. +The literal payload has decompressed SHA256 +`8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013`. +The source clean core has decompressed SHA256 +`a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa`. +The producer files were not changed. + +The producer used forward propagation of symbolic rows. This review uses +a new reverse-column interpreter. It imports no producer code. Each +column records every output and its ordered word in the warp operators. +Forward K and backward dual_K letters have distinct types. Only adjacent +inverse letters cancel. In particular, the replay assumes no commutation +between different warps or between port operators and R. + +The new interpreter also inserts an observable for C0 immediately before +each division. It pulls these observables back through the complete +earlier prefix. This checks the division queries by a method different +from the producer's check of every changed forward row. + +## Complete map and source changes + +The source R and H in the new payload match the pinned clean packet. +Every canonical field, frame, warp, and helper label also matches. For +each word, removing its four centre blocks leaves the complete source +core unchanged, including every scalar and native record. + +The entrance has the same scalar records as the clean source. It adds +one division after each complete query for the selected four rows. The +other four rows keep their old weight. The check verifies the query, +division, and scatter order in all eight entrance rows. + +Every inserted centre block comes from its own original 26-event block. +It changes its owned field from C_j to C0. Each quarter ADD at I changes +from its old coefficient to twelve times that coefficient. There is one +new division on the I side of the original rank-eight child. The final +backward CLEAR resets the empty C0 field to I. All other source events +retain their exact values and order. There is no change of frame on a +nonzero value without its native operation. + +For the selected set S, the expected response is + + T=I - sum(j in S) R_j^T R_j/52 + - sum(j not in S) R_j^T R_j/4. + +The reverse-column replay proves + + forward: (x,y,h) -> (x, y+T x, h), + backward: (x,y,h) -> (x-T^T y, y, h). + +It checks these maps on all 632 live and all eight arbitrary owned input +columns. It also treats the state at each private buffer's release as an +output observable. Each such observable is zero on all permitted inputs. +The 91 buffers are each allocated once, accessed only while live, and +returned at FULL. No arbitrary helper or data field is cleared or copied +over. The only such target is the owned C0 field. + +For E, S={0,1,2,3}. For G, S={4,5,6,7}. The independent scalar review in +`../reciprocal-centre-rank-review-20261018/REVIEW.md` proves EG=GE=I on +the same actual R and classifies the correction ranks. That rank theorem +is about the specified added terms. It is not a lower bound on all ways +to implement the resulting full response. + +## Frames and phase dependency + +The frame check covers every scalar, division, climb, centre call, warp, +ordinary adapter, residual wrapper, and private lifetime. Each new divide +uses C0 at I. Each forward capture copies the actual source field at the +same rank-eight frame. Each centre call has exactly its original old and +new frames and rank. Every live and owned exit frame matches the contract. + +The new occurrences use the exact recipes already covered by +`../NEW-CORE-NATIVE-REVIEW.json`, SHA256 +`924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d`. +That independent source sweep checked all 3036 child classes per provider, +including both directions of all eight centre frames. It checked Pauli +action and an exact 512-entry Gaussian state to fix global phase. It also +checked the literal backward dual warp recipes and the helper wrappers. + +This run binds all 32 new centre occurrences across the eight words to +those exact source recipe bytes. The payload's sixteen centre recipes +per provider match the old complete phase source. All non-centre native +records are unchanged. No new non-dyadic frame map is introduced. A real +scalar division commutes with the linear frame map on that same field. +These facts make the inherited phase review applicable. This run does +not claim a second independent phase-interpreter sweep. + +Let q denote the diagonal inverse-line operator and remove the common +output F. The physical data maps are + + C_F(T) = [[q, 0], [q T q, q]], + C_B(T) = [[q, -T^T], [0, q]]. + +Indeed, the logical X input is q times its conventional physical input. +The X output is at FULL and the Y output is at its port-hole frame. These +facts put q on both sides of T in the forward lower block. They do not +put q beside T in the backward upper block. This derivation uses no +commutation of q and T. The scalar identity EG=I does not remove these +physical boundary conditions. + +## Denominator proof from independent observables + +For every word, the eight C0 queries immediately before /13 pull back +to Gaussian-dyadic coefficients on all formal inputs. In the free-word +representation checked here the scalar coefficients are rational dyadic, +and every warp letter has a Gaussian-dyadic physical endpoint. Thus these +completed queries have no new factor 13 in their denominator. + +All other scalar and native operation endpoints are Gaussian dyadic. +Start with denominator height zero relative to the word input. A dyadic +operation cannot increase the largest 13-denominator height. Each odd +division acts on one of the proved height-zero queries and gives height +at most one. Induction over all literal events proves height at most one +at every operation boundary. This proof includes arbitrary helper payloads +and the private lifetimes; it is not a test on chosen numeric values. + +The result also applies relative to an incoming odd height h: all local +prefixes have height at most h+1. It does not apply to arbitrary unscaled +numerators on a finest grid. The separate common-grid theorem must provide +divisibility. The internals of recursively implemented children need that +theorem's exact endpoint and precision conditions. + +Consequently a future parent may charge one new 13-denominator level per +complete occurrence of one of these local words. This is stronger than +charging all eight complex division events separately. It remains +necessary to prove that each completed recursive provider and the outer +endpoint have the required dyadic full-state maps. E and G individually +are not such providers. + +## Invoice and controls + +Each retained forward centre block costs 270 scalar primitives. Each +backward block costs 276. The coefficient change from a quarter to three +has the same ADD price in the source accounting. The weighted entrance +keeps its old scalar bill. Thus four blocks add 1080 or 1104 to the clean +164514 bill. The four rank-eight calls add 32 to the clean rank mass 5073. +The full profile is {1:2433,2:724,3:228,4:102,5:20,8:4}. + +There are eight complex /13 operations, hence sixteen real scans. Their +linear scan and root conversion cost is separate from the table. A full +supplier must also pay for its phase and layout implementation under its +retained machine model; a native rank count alone does not pay that cost. + +The independent checks reject omission of an entrance division, a wrong +centre scatter sign, a wrong centre input frame, and erasure of an +untouched arbitrary owned input. All checks pass with Python assertions +disabled, with byte-identical receipts. + +Run from the workspace root: + + python3 work/centre-encoding-campaign-20261014/lanes/independent-review-20261017/reciprocal-native-review-20261018/check_words.py + +Expected status: `PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS`. +`CHECKS.json` records each pre-division observable and local invoice. +`FREEZE.json` pins this review and its sources. + +The new-native-recipes lane supplied the emitted words. The root lane +supplied the reciprocal split. The oblique-native lane supplied the +capture and helper-correction plan. The earlier native and grid reviews +supplied the stated source dependencies. This review used OpenAI Codex +under the user's direction. No publication is authorized. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/check_words.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/check_words.py new file mode 100644 index 0000000000..bb8bb04877 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/independent-review-20261017/reciprocal-native-review-20261018/check_words.py @@ -0,0 +1,368 @@ +#!/usr/bin/env python3 +"""Review reciprocal words by reverse columns and division observables.""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as F +from hashlib import sha256 +from pathlib import Path +import gzip +import json + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES / 'reciprocal-centre-20261018' +PINS = { + 'reciprocal-centre-20261018/FREEZE.json': + 'b0a396e5582d723dbf99e0199792031b47562d62039d6a2983b3aff2f9e772fd', + 'reciprocal-centre-20261018/RECIPROCAL-CENTRE-NATIVE.md': + '322026cad321521b10f8a6d0626a6c3191943971be7f9eba186bb60d2dc83737', + 'reciprocal-centre-20261018/emit_reciprocal_centres.py': + 'cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc', + 'reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-RECEIPT.json': + 'aafaa8b17be476d521fe4c8eb3cf3af59c72351c3aba60a9413cd2aa0baafdfc', + 'independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json': + '924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d', + 'independent-review-20261017/check_new_native.py': + '937543157459e5c0eee788feefcf2107acf6bdf660a1209cdecece1ca1f26d01', + 'new-native-recipes-20261017/base/CLIFFORD-RECIPES.json': + '580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0', + 'new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json': + 'f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e', +} +PAYLOAD_PIN = '8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013' +CLEAN_PIN = 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa' + + +def need(test, label): + if not test: + raise ValueError(label) + + +def read_gzip(path, pin): + raw = gzip.decompress(path.read_bytes()) + need(sha256(raw).hexdigest() == pin, 'Compressed source pin '+str(path)) + return json.loads(raw) + + +def accumulate(target, source, scale=F(1)): + for key, value in source.items(): + updated = target.get(key, F(0))+scale*value + if updated: + target[key] = updated + else: + target.pop(key, None) + + +def parse(op): + tag, target = op[0], tuple(op[1]) + need(tag in ('add', 'copy', 'clear', 'scale'), 'Scalar grammar') + source = tuple(op[2]) if tag in ('add', 'copy') else None + value = F(*op[-2:]) if tag in ('add', 'scale') else F(1) + need(source is None or source != target, 'Distinct scalar operands') + return tag, target, source, value + + +def price(op): + tag, _, _, value = parse(op) + if tag in ('clear', 'copy'): + return 2 + a, b = abs(value.numerator), value.denominator + need(a > 0 and b & (b-1) == 0, 'Dyadic old primitive') + if tag == 'scale': + need(a & (a-1) == 0, 'Power-of-two SCALE') + return 2*(abs(a.bit_length()-b.bit_length())+int(value < 0)) + return 2*(1+a.bit_length()+a.bit_count()+b.bit_length()) + + +def pullback(events, fields, backward=False): + columns = {field: {(field, ()): F(1)} for field in fields} + division_positions = [] + for position in range(len(events)-1, -1, -1): + event = events[position] + tag = event[0] + if tag == 'scalar': + kind, target, source, value = parse(event[1]) + if kind == 'add': + accumulate(columns[source], columns[target], value) + elif kind == 'scale': + columns[target] = {key: value*x for key, x in columns[target].items()} + elif kind == 'copy': + accumulate(columns[source], columns[target]) + columns[target] = {} + else: + columns[target] = {} + elif tag == 'divide_odd': + field = tuple(event[1]) + columns[field] = {key: x/F(event[2]) for key, x in columns[field].items()} + accumulate(columns[field], {(('D', position), ()): F(1)}) + division_positions.append(position) + elif tag == 'warp': + field = tuple(event[1]) + letter = ('dual_K' if backward else 'K', event[2]) + inverse = (letter[0], -letter[1]) + columns[field] = {(output, word[:-1] if word and word[-1] == inverse else word+(letter,)): value + for (output, word), value in columns[field].items()} + elif tag == 'zero_buffer': + if event[1] == 'alloc': + columns['Z', event[2]] = {} + else: + need(event[1] == 'free', 'Zero-buffer grammar') + else: + need(tag in ('center', 'climb', 'phase', 'adapter', 'residual_adapter'), + 'Complete native grammar') + queries = {pos: {} for pos in sorted(division_positions)} + complete = {field: {} for field in fields} + for field, column in columns.items(): + for (output, word), value in column.items(): + if output[0] == 'D': + queries[output[1]][field, word] = value + else: + complete[field][output, word] = value + return complete, queries + + +def expected(fields, R, selected, backward): + result = {f: {} if f[0] == 'Z' or f == ('C', 0) else {(f, ()): F(1)} for f in fields} + sign = F(-1 if backward else 1) + for p in range(112): + source = ('L', 112+p if backward else p) + target = ('L', p if backward else 112+p) + accumulate(result[source], {(target, ()): sign}) + for j, row in enumerate(R): + weight = -F(1, 52) if j in selected else -F(1, 4) + for q, value in row.items(): + target = ('L', q if backward else 112+q) + accumulate(result[source], {(target, ()): sign*weight*value*row.get(p, F(0))}) + return result + + +def types(events, c): + frames = {('L', i): f for i, f in enumerate(c['start'])} + frames.update({('C', i): 0 for i in range(8)}) + active, allocated, released = set(), set(), set() + bill, divisions = 0, 0 + profile, native = Counter(), Counter() + warp_edges = set(map(tuple, c['warp_edges'])) + for pos, event in enumerate(events): + tag = event[0] + if tag == 'scalar': + kind, target, source, value = parse(event[1]) + need(target in frames and (source is None or source in frames), 'Live scalar access') + need(all(f[0] != 'C' or f[1] == 0 for f in (target, source) if f is not None), + 'Only C0 is used') + if kind == 'clear': + need(target == ('C', 0), 'No borrowed clear') + frames[target] = event[2] + else: + need(frames[target] == event[2] and (source is None or frames[source] == event[2]), + 'Scalar common frame at '+str(pos)) + need(kind != 'copy' or target == ('C', 0), 'Only an owned copy target') + bill += price(event[1]) + elif tag == 'divide_odd': + need(event == ['divide_odd', ['C', 0], 13, 0] and frames['C', 0] == 0, + 'Odd division has a legal I-frame query') + divisions += 1 + elif tag in ('climb', 'center'): + if tag == 'climb': + field, old, new, width = ('L', event[2]), *event[3:] + else: + field, old, new, width = ('C', event[1]), *event[2:] + need(field == ('C', 0) and width == 8, 'Serial C0 centre child') + need(frames[field] == old, 'Native frame at '+str(pos)) + need(abs(len(c['frames'][new])-len(c['frames'][old])) == width, 'Native rank') + frames[field] = new + profile[width] += 1 + native[tag] += 1 + elif tag == 'warp': + field, symbol, old, new = tuple(event[1]), *event[2:] + need(field in frames and frames[field] == old, 'Warp input frame') + need((1 if symbol > 0 else -1, abs(symbol), old, new) in warp_edges, 'Warp class') + frames[field] = new + native[tag] += 1 + elif tag == 'zero_buffer': + field = ('Z', event[2]) + if event[1] == 'alloc': + need(field not in frames and field not in allocated, 'Unique private allocation') + frames[field] = 1 + allocated.add(field) + active.add(field) + else: + need(event[1] == 'free' and field in active and frames[field] == 1, + 'Private release at FULL') + active.remove(field) + released.add(field) + del frames[field] + elif tag == 'adapter': + _, side, field, frame = event + need(side in ('old_to_new', 'new_to_old'), 'Adapter direction') + need(frame == c['start' if side == 'old_to_new' else 'final'][field], 'Adapter endpoint') + native[tag] += 1 + elif tag == 'residual_adapter': + _, side, field, old, *tail = event + need(side in ('pre', 'post') and old == c['start'][field] + and (tail[0] if tail else 1) == c['final'][field], 'Residual wrapper endpoints') + native[tag] += 1 + else: + need(tag == 'phase', 'Event grammar') + need(not active and allocated == released == {('Z', x) for x in c['zero_buffers']}, + 'All private lifetimes') + need([frames['L', i] for i in range(632)] == c['final'], 'All live exit frames') + need(all(frames['C', i] == 0 for i in range(8)), 'All owned exit frames') + need(profile == Counter({1: 2433, 2: 724, 3: 228, 4: 102, 5: 20, 8: 4}), 'Child profile') + need(native == Counter(climb=3507, center=4, warp=240, adapter=978, residual_adapter=390), + 'Complete native inventory') + need(divisions == 8, 'Eight complex odd divisions') + return {'dyadic_real_primitives': bill, 'complex_odd_divisions': divisions, + 'real_odd_scans': 2*divisions, 'native_profile': dict(sorted(profile.items())), + 'native_mass': sum(k*v for k, v in profile.items()), 'native_children': sum(profile.values())} + + +def source_binding(word, clean, canonical, selected, backward, recipes): + events = word['program'] + split = events.index(['phase', 'zero_frame_precondition']) + need(split == 836 and word['weighted_prefix_events'] == split, 'Weighted prefix size') + old_split = clean['programs'][backward].index(['phase', 'zero_frame_precondition']) + prefix = [deepcopy(e) for e in events[:split] if e[0] != 'divide_odd'] + prefix[0] = clean['programs'][backward][0] + need(prefix == clean['programs'][backward][:old_split], 'No other entrance edits') + row, active, divided, divisions = -1, False, False, [] + for event in events[1:split]: + if event[0] == 'scalar' and event[1][0] == 'clear': + if not active: + row, active, divided = row+1, True, False + else: + need(divided == (row in selected), 'Exactly the selected entrance rows divide') + active = False + elif event[0] == 'divide_odd': + need(active and not divided, 'One division per selected query') + divided = True + divisions.append(row) + else: + target, source = tuple(event[1][1]), tuple(event[1][2]) + if target == ('C', 0): + need(not divided, 'Query finishes before division') + else: + need(source == ('C', 0) and divided == (row in selected), 'Scatter follows selected division') + need(row == 7 and not active and divisions == sorted(selected), 'All eight entrance rows') + start = events.index(['phase', 'centers'])+1 + end = events.index(['phase', 'B'], start) + need(end-start == 108 and word['centre_block_events'] == 108, 'Four complete centre blocks') + stripped = events[split:start]+events[end:] + need(stripped == clean['programs'][backward][old_split:], 'Every retained core event is unchanged') + original = clean['removed_centre_blocks'][backward] + need(len(original) == 208 and len(word['centre_bindings']) == 4, 'Source centre inventory') + for i, j in enumerate(sorted(selected)): + block = events[start+27*i:start+27*(i+1)] + source = original[26*j:26*(j+1)] + actual = [deepcopy(e) for e in block if e[0] != 'divide_odd'] + need(len(actual) == 26, 'One added division in each centre block') + for k, event in enumerate(actual): + old = source[k] + if event[0] == 'center': + need(event == ['center', 0, *old[2:]], 'Only the owned child target changes') + event[1] = j + else: + op = event[1] + for entry in op: + if isinstance(entry, list) and entry[0] == 'C': + need(entry == ['C', 0], 'Serial owned field') + entry[1] = j + if op[0] == 'add' and event[2] == 0: + need(F(*op[-2:]) == 12*F(*old[1][-2:]), 'Weighted original quarter ADD') + op[-2:] = old[1][-2:] + if backward == 'backward' and k == 25: + need(event[2] == 0, 'Final empty C0 resets to I') + event[2] = old[2] + need(event == old, 'Every retained centre scalar has its source') + binding = word['centre_bindings'][i] + pos = binding['position'] + call = events[pos] + need(binding['centre'] == j and binding['event'] == call, 'Occurrence centre label') + need(binding['source_event'] == next(e for e in source if e[0] == 'center'), 'Original centre binding') + pair = tuple(call[2:4]) + need(tuple(binding['recipe_key']) == pair and recipes[pair]['rank'] == 8, 'Exact child class') + digest = sha256((json.dumps(recipes[pair], sort_keys=True, separators=(',', ':'))+'\n').encode()).hexdigest() + need(binding['recipe_sha256'] == digest, 'Exact source recipe hash') + division_pos = pos-1 if backward == 'backward' else pos+1 + need(events[division_pos] == ['divide_odd', ['C', 0], 13, 0], 'Division is on the I side of the child') + + +for path, pin in PINS.items(): + need(sha256((LANES/path).read_bytes()).hexdigest() == pin, 'Source pin '+path) +payload = read_gzip(SOURCE/'producer-final/RECIPROCAL-CENTRE-PROGRAMS.json.gz', PAYLOAD_PIN) +clean = read_gzip(LANES/'new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz', CLEAN_PIN) +need(payload['R'] == clean['R'] and payload['H'] == clean['H'], 'Actual centre and helper matrices') +R = [{int(k): F(v) for k, v in row.items()} for row in clean['R']] +report = {'status': 'PASS_INDEPENDENT_RECIPROCAL_NATIVE_WORDS', 'providers': {}, + 'source_pins': PINS, 'payload_decompressed_sha256': PAYLOAD_PIN, + 'clean_payload_decompressed_sha256': CLEAN_PIN} +for name in ('base', 'extra'): + provider = payload['providers'][name] + c = provider['canonical'] + need(c == clean['providers'][name]['canonical'], 'Complete canonical source binding') + phases = json.loads((LANES/'new-native-recipes-20261017'/name/'CLIFFORD-RECIPES.json').read_bytes()) + recipes = {(r['old'], r['new']): r for r in phases['children']} + centre_pairs = {(a, b) for f in c['center_frames'] for a, b in ((f, 0), (0, f))} + need(len(centre_pairs) == 16, 'Sixteen source centre directions') + carried = {(r['old'], r['new']): r for r in provider['centre_recipes']} + need(set(carried) == centre_pairs and all(carried[key] == recipes[key] for key in carried), + 'Every carried centre recipe was covered by the prior complete independent phase review') + fields = [('L', i) for i in range(632)]+[('C', i) for i in range(8)]+[('Z', z) for z in c['zero_buffers']] + report['providers'][name] = {} + for response, selected in (('E', set(range(4))), ('G', set(range(4, 8)))): + for orientation in ('forward', 'backward'): + key = response+'_'+orientation + word = provider['words'][key] + need(word['selected_centres'] == sorted(selected), 'Chosen four actual rows') + source_binding(word, clean['providers'][name], c, selected, orientation, recipes) + bill = types(word['program'], c) + need(bill['dyadic_real_primitives'] == (165618 if orientation == 'backward' else 165594), + 'Complete dyadic scalar price') + actual, queries = pullback(word['program'], fields, orientation == 'backward') + want = expected(fields, R, selected, orientation == 'backward') + need(actual == want, 'Complete reverse-column response '+name+' '+key) + need(all(output[0] != 'Z' for col in actual.values() for output, _ in col), 'All private return outputs are zero') + query_report = [] + for pos, row in queries.items(): + need(row, 'Nonzero completed query') + need(all(value.denominator & (value.denominator-1) == 0 for value in row.values()), + 'Every completed division query is dyadic on every formal input') + query_report.append({'position': pos, 'formal_terms': len(row), 'new_13_height': 0}) + need(len(query_report) == 8, 'All eight pre-division observables') + bill.update(events=len(word['program']), arbitrary_inputs=640, logical_helpers=408, + private_zero_returns=91, C0_exit='zero at I', C1_to_C7='arbitrary identity at I', + division_queries=query_report, local_prefix_13_height_bound=1, + ordered_warp_algebra='free K or dual_K words; adjacent inverse cancellation only') + report['providers'][name][key] = bill + print(name, key, 'PASS_640_COLUMNS_AND_8_QUERY_OBSERVABLES', flush=True) + +provider = payload['providers']['base'] +word = provider['words']['E_forward'] +c = provider['canonical'] +fields = [('L', i) for i in range(632)]+[('C', i) for i in range(8)]+[('Z', z) for z in c['zero_buffers']] +want = expected(fields, R, set(range(4)), False) +controls = {} +changed = deepcopy(word['program']) +changed.pop(next(i for i, e in enumerate(changed) if e[0] == 'divide_odd')) +controls['omitted_weighted_entrance_division'] = pullback(changed, fields)[0] != want +changed = deepcopy(word['program']) +changed[word['centre_bindings'][0]['position']+2][1][3] *= -1 +controls['changed_centre_scatter_sign'] = pullback(changed, fields)[0] != want +changed = deepcopy(word['program']) +changed.append(['scalar', ['clear', ['C', 1]], 0]) +controls['erased_untouched_arbitrary_owned_input'] = pullback(changed, fields)[0] != want +changed = deepcopy(word['program']) +changed[word['centre_bindings'][0]['position']][2] = 0 +try: + types(changed, c) +except ValueError as error: + controls['changed_centre_input_frame'] = 'Native frame' in str(error) +else: + controls['changed_centre_input_frame'] = False +need(all(controls.values()), 'Every negative control fails the intended contract') +report['negative_controls'] = controls +report['checker_sha256'] = sha256(Path(__file__).read_bytes()).hexdigest() +report['phase_scope'] = 'Exact byte binding to the prior independent all-3036-edge review, including all 32 centre directions and literal backward dual warps. No second compiler or phase interpreter is claimed in this run.' +report['scope'] = 'Complete local rational maps, arbitrary logical helper restoration, typed native occurrences, scalar and native invoices, and one new 13-denominator level. No global controller, new recursive provider, owner layout, or kappa claim.' +(HERE/'CHECKS.json').write_text(json.dumps(report, indent=2, sort_keys=True)+'\n') +print(report['status']) diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/interface-proof/rational-decoder/sources/notes/stopped-product-complex.tex new file mode 100644 index 0000000000..4a9037137c --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/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> j) & 1) for v, c in terms) % 4 for j in range(25)) + quadratic = [] + for i in range(25): + for j in range(i + 1, 25): + sample = (1 << i) | (1 << j) + value = (sum(c * ((v & sample).bit_count() & 1) for v, c in terms) - + linear[i] - linear[j]) % 4 + if value: + need(value == 2, "Even quadratic coefficient") + quadratic.append((i, j, value)) + return matrix, linear, tuple(quadratic) + + +def route(columns): + return [("R", tuple(columns), 0)] + + +def line(vector, power): + return [("P", vector, power)] + + +def fourier(start, stop, power=1): + return [("P", 1 << j, power) for j in range(start, stop)] + + +def plus(*terms): + result = {} + for coefficient, row in terms: + for key, value in row.items(): + total = result.get(key, F(0)) + coefficient * value + if total: + result[key] = total + else: + result.pop(key, None) + return result + + +def linear(matrix, rows): + return [plus(*((c, rows[j]) for j, c in row.items())) for row in matrix] + + +def sparse(rows): + return [{int(j): F(c) for j, c in row.items() if F(c)} for row in rows] + + +def transpose(matrix, columns): + result = [{} for _ in range(columns)] + for i, row in enumerate(matrix): + for j, value in row.items(): + result[j][i] = value + return result + + +def eye(size): + return [{j: F(1)} for j in range(size)] + + +def add_price(value): + a, b = abs(value.numerator), value.denominator + need(a and b & (b - 1) == 0, "Nonzero dyadic ADD") + return 2 * (3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1) + + +def local_invoice(item): + profile = Counter() + scalar = 0 + for event in item["events"]: + if event[0] == "native": + profile[event[4]] += 1 + else: + need(event[0] == "scalar", "Known native word event") + gate = event[1] + value = F(gate[3]) + if gate[0] == "add": + scalar += add_price(value) + else: + need(gate[0] == "scale", "Known native scalar event") + a, b = abs(value.numerator), value.denominator + need(a & (a - 1) == b & (b - 1) == 0, "Signed dyadic unit scale") + scalar += 2 * (abs(a.bit_length() - b.bit_length()) + (value < 0)) + return {"profile": dict(sorted(profile.items())), "native_mass": sum(r * n for r, n in profile.items()), + "native_children": sum(profile.values()), "real_scalar_primitives": scalar} + + +def source_matrix_checks(source, selected, ordinary, h, d): + basis = eye(224) + a, u = [basis[p] for p in selected], [basis[p] for p in ordinary] + z, v = [basis[112 + p] for p in selected], [basis[112 + p] for p in ordinary] + + def joined(ap, ur, zp, vr): + result = [None] * 224 + for ports, rows, offset in ((selected, ap, 0), (ordinary, ur, 0), + (selected, zp, 112), (ordinary, vr, 112)): + for p, row in zip(ports, rows): + result[offset + p] = row + return result + + alpha = [plus((1, x), (1, y)) for x, y in zip(a, linear(h, u))] + lower = [plus((1, x), (1, y), (1, z0)) for x, y, z0 in zip(v, u, linear(d, alpha))] + forward = joined([plus((-1, row)) for row in z], u, alpha, lower) + need(forward == sparse(source["forward"]["content_map"]), "All 224 forward content columns") + inverse = joined([plus((1, x), (-1, y)) for x, y in zip(z, linear(h, u))], u, + [plus((-1, row)) for row in a], + [plus((1, x), (-1, y), (-1, z0)) for x, y, z0 in zip(v, u, linear(d, z))]) + need(inverse == sparse(source["forward"]["inverse_content_map"]), "Stored forward inverse") + need(linear(forward, inverse) == basis and linear(inverse, forward) == basis, "Forward inverse both orders") + inverse_adjoint = transpose(inverse, 224) + need(inverse_adjoint == sparse(source["dual"]["content_maps"]["inverse_adjoint"]), "Actual inverse transpose") + permutation = list(range(224)) + for p in selected: + permutation[p], permutation[112 + p] = 112 + p, p + conjugate = [{permutation[j]: value for j, value in inverse_adjoint[permutation[i]].items()} + for i in range(224)] + beta = [plus((1, x), (1, y)) for x, y in zip(z, linear(h, v))] + middle = [plus((1, x), (1, y), (-1, z0)) for x, y, z0 in zip(u, linear(d, z), v)] + backward = joined(beta, middle, [plus((-1, row)) for row in a], v) + need(backward == conjugate == sparse(source["dual"]["content_maps"]["selected_swap_conjugate"]), + "All 224 selected-swap inverse-adjoint columns") + return forward, backward + + +def abstract_check(): + """Keep H0,H1,H2,D0,D1,D2 free and preserve every product order.""" + a, u, z, v = [{(i, ()): F(1)} for i in range(4)] + + def op(name, row): + return {(source, (name,) + word): coefficient for (source, word), coefficient in row.items()} + + def forward(s, state): + ap, ur, zp, vr = state + alpha = plus((1, ap), (1, op("H" + str(s), ur))) + return [plus((-1, zp)), ur, alpha, + plus((1, vr), (1, ur), (1, op("D" + str(s), alpha)))] + + def backward(s, state): + ap, ur, zp, vr = state + return [plus((1, zp), (1, op("H" + str(s), vr))), + plus((1, ur), (1, op("D" + str(s), zp)), (-1, vr)), plus((-1, ap)), vr] + + first = forward(0, [a, u, z, v]) + second = backward(1, first) + endpoint = forward(2, second) + alpha = plus((1, a), (1, op("H0", u))) + k = plus((1, v), (1, u), (1, op("D0", alpha))) + w = plus((-1, v), (1, op("D1", alpha)), (-1, op("D0", alpha))) + beta = plus((1, alpha), (1, op("H1", k)), (1, op("H2", w))) + r = plus((1, u), (1, op("D1", alpha)), (1, op("D2", beta))) + need(first == [plus((-1, z)), u, alpha, k], "First stage endpoint") + need(second == [plus((1, alpha), (1, op("H1", k))), w, z, k], "Second stage endpoint") + need(endpoint == [plus((-1, z)), w, beta, r], "Third stage endpoint") + recovered_k = plus((1, r), (-1, op("D2", beta)), (-1, w)) + recovered_alpha = plus((1, beta), (-1, op("H1", recovered_k)), (-1, op("H2", w))) + recovered_u = plus((1, r), (-1, op("D1", recovered_alpha)), (-1, op("D2", beta))) + recovered_a = plus((1, recovered_alpha), (-1, op("H0", recovered_u))) + recovered_v = plus((-1, w), (1, op("D1", recovered_alpha)), (-1, op("D0", recovered_alpha))) + need([recovered_alpha, recovered_a, recovered_u, recovered_v] == [alpha, a, u, v], "Ordered content inverse") + state = list(endpoint) + trace = [list(state)] + # The first 96 positive lines change the ordinary Y frame to FULL. + state[3] = plus((1, state[3]), (-1, op("D2", state[2]))) + trace.append(list(state)) + state[2] = plus((1, state[2]), (-1, op("H1", state[3]))) + trace.append(list(state)) + state[2] = plus((1, state[2]), (1, op("H1", state[1])), (-1, op("H2", state[1]))) + trace.append(list(state)) + state[1] = plus((-1, state[1]), (1, op("D1", state[2])), (-1, op("D0", state[2]))) + trace.append(list(state)) + state[3] = plus((1, state[3]), (-1, op("D1", state[2]))) + trace.append(list(state)) + state[2] = plus((1, state[2]), (-1, op("H0", state[3]))) + trace.append(list(state)) + state[0] = plus((-1, state[0])) + trace.append(list(state)) + need(state == [z, v, a, u], "In-place terminal content and bank order") + # The final 112 positive lines restore Q(a,u) on Y. + def encode(rows): + return [[{"source_group": source, "word": list(word), "coefficient": str(value)} + for (source, word), value in sorted(row.items())] for row in rows] + return {"initial_groups": ["a", "u", "z", "v"], "first": encode(first), + "second": encode(second), "endpoint": encode(endpoint), + "terminal_trace_after_ordinary_Q": [encode(rows) for rows in trace], + "endpoint_holes": "Only Y_R has the exterior q_R.", + "operator_relations_used": "None between H_s and D_t; no inverse of I+H1 D2."} + + +def affine_product(left, right): + matrix, shift = left + other, translation = right + return compose(matrix, other), shift ^ act(matrix, translation) + + +def terminal_shear(matrix, source_fields, target_fields, stage, sign, views): + events = [] + if stage: + for field in source_fields + target_fields: + rho, shift = views[stage, field % 112] + events.append(["MAP", field, list(rho), shift]) + for i, row in enumerate(matrix): + for j, coefficient in sorted(row.items()): + events.append(["ADD", target_fields[i], source_fields[j], str(sign * coefficient)]) + if stage: + for field in target_fields + source_fields: + rho, shift = views[stage, field % 112] + events.append(["MAP", field, list(rho), shift]) + state = [{(j, UNIT, 0): F(1)} for j in range(224)] + invoice = Counter() + for event in events: + invoice[event[0]] += 1 + if event[0] == "MAP": + target, view = event[1], (tuple(event[2]), event[3]) + state[target] = {(source, new[0], new[1]): value + for (source, old, translation), value in state[target].items() + for new in [affine_product(view, (old, translation))]} + else: + target, source, coefficient = event[1], event[2], F(event[3]) + state[target] = plus((1, state[target]), (coefficient, state[source])) + invoice["scalar_units"] += add_price(coefficient) + expected = [{(j, UNIT, 0): F(1)} for j in range(224)] + for i, row in enumerate(matrix): + target = target_fields[i] + left = views[stage, target % 112] if stage else ID + for j, coefficient in row.items(): + source = source_fields[j] + right = views[stage, source % 112] if stage else ID + product = affine_product(left, right) + expected[target][source, product[0], product[1]] = sign * coefficient + need(state == expected, "Literal FULL shear on all 224 columns") + return events, dict(sorted(invoice.items())) + + +def write_json(path, value): + raw = (json.dumps(value, indent=2, sort_keys=True) + "\n").encode() + path.write_bytes(raw) + return digest(raw) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + parser.add_argument("--producer-run", default="run-terminal-normal") + args = parser.parse_args() + need(shutil.disk_usage(HERE).free >= 3 * 1024**3, "At least 3 GiB free") + args.out.mkdir(parents=True, exist_ok=False) + source, manifest = {}, {} + for name, (path, pin) in SOURCES.items(): + raw = path.read_bytes() + decoded = gzip.decompress(raw) if path.suffix == ".gz" else raw + need(digest(decoded) == pin, "Pinned source " + name) + manifest[name] = {"path": str(path), "sha256": digest(raw), "payload_sha256": pin} + source[name] = json.loads(decoded) + extra = { + "forward_proof": NATIVE / "clean-late-exchange-20261020/CLEAN-LATE-EXCHANGE.md", + "dual_proof": NATIVE / "clean-late-exchange-20261020/CLEAN-DUAL.md", + "producer_proof": PRODUCER / "NO-RESET.md", + "producer_checker": PRODUCER / "check_no_reset.py", + "producer_phase_library": LANE / "coupled-data-split-20261020/check_typed_split.py", + "producer_checks": PRODUCER / args.producer_run / "CHECKS.json", + "producer_freeze": PRODUCER / "FREEZE.json", + } + for name, path in extra.items(): + pin = digest(path.read_bytes()) + if name in PRODUCER_PINS: + need(pin == PRODUCER_PINS[name], "Pinned " + name) + manifest[name] = {"path": str(path), "sha256": pin} + producer = json.loads(extra["producer_checks"].read_bytes()) + records = {(x["stage"], x["port"]): x for x in source["views"]["entries"]} + need(len(source["views"]["entries"]) == 336 and + set(records) == {(s, p) for s in range(3) for p in range(112)}, "Complete D25 view set") + p, r = source["row_code"]["selected_ports"], source["row_code"]["ordinary_ports"] + need(len(p) == 16 and len(r) == 96 and sorted(p + r) == list(range(112)), "Actual partition") + for name in ("forward", "dual"): + need(source[name]["selected_ports"] == p and source[name]["ports"] == source["row_code"]["ports"], + "Native selected set and port order") + need(source[name]["code"] == source["row_code"]["code"] and + source[name]["response"] == source["row_code"]["response"], "Native response and row-code equality") + q = [records[0, a]["q"] for a in range(112)] + need(q == source["row_code"]["ports"], "Actual route port labels") + c, e = sparse(source["row_code"]["code"]), sparse(source["row_code"]["response"]) + h = [{j: c[a][b] for j, b in enumerate(r) if b in c[a]} for a in p] + d = [{j: e[a][b] for j, b in enumerate(p) if b in e[a]} for a in r] + expected_c = eye(112) + for i, a in enumerate(p): + expected_c[a].update({r[j]: value for j, value in h[i].items()}) + need(c == expected_c, "C has the exact row-only form") + need(d == [{i: -value for i, value in row.items()} for row in transpose(h, 96)], "D=-H transpose") + dh = linear(d, h) + for i, a in enumerate(r): + expected = {p[j]: value for j, value in d[i].items()} + for j, value in dh[i].items(): + expected[r[j]] = value + expected = plus((1, expected), (1, {a: F(1)})) + need(expected == e[a], "Actual ordinary response row is u+D(a+Hu)") + source_matrix_checks(source, p, r, h, d) + invoices = {} + for name in ("forward", "dual"): + for provider, variants in source[name]["providers"].items(): + for variant, item in variants.items(): + bill = local_invoice(item) + need(bill["real_scalar_primitives"] == 8600 and bill["native_children"] == 1520, + "Native scalar and child counts") + expected_profile = {1: 1392, 2: 64, 3: 48, 9 if variant == "I" else 8: 16} + need(bill["profile"] == expected_profile, "Native profile") + invoices[name + ":" + provider + ":" + variant] = bill + views, counts, certificates = {}, Counter(), [] + identity_normal = normal([]) + for s in range(3): + for a in range(112): + row = records[s, a] + matrix = tuple(row["route_columns"]) + need(row["q"] == q[a] and act(matrix, q[a]) == q[a], "Route fixes the matching line") + need(compose(matrix, matrix) == UNIT and + all(transposed(matrix, matrix[j]) == (1 << j) for j in range(25)), + "Orthogonal involution") + if s == 0: + need(matrix == UNIT, "Stage zero route") + continue + alignment = row["literal_stage_alignment"] + need(alignment["entry_X"] == alignment["entry_Y"] and + alignment["exit_X"] == alignment["exit_Y"], "Matched physical bank views") + delta = act(matrix, alignment["entry_X"]) + entry = line(delta, 2) + route(matrix) + exit_view = line(alignment["exit_X"], 2) + route(matrix) + fprev = fourier(0, 9 + 8 * (s - 1)) + fnext = fourier(0, 9 + 8 * s) + fext = fourier(9, 9 + 8 * s) + checks = [ + (entry + fprev, fext + line(q[a], 1) + route(matrix)), + (entry + fprev + line(q[a], -1), fext + route(matrix)), + (exit_view + fnext, fnext + route(matrix)), + (exit_view + fnext + line(q[a], -1), fnext + line(q[a], -1) + route(matrix)), + ] + for left, right in checks: + need(normal(left) == normal(right), "Natural mixed frame identity") + counts["natural_frame_identities"] += 1 + full_result = normal(exit_view + fourier(0, 25)) + need(full_result == normal(fourier(0, 25) + route(matrix)), "Past FULL view") + need(normal(exit_view + exit_view) == identity_normal, "Physical FULL view is an involution") + need(normal(exit_view + line(q[a], 1)) == normal(line(q[a], 1) + exit_view), "View commutes with its own Q") + counts["past_FULL_views"] += 1 + counts["physical_view_inverse_orders"] += 1 + counts["omitted_entry_translation_rejected"] += normal(route(matrix) + fprev) != normal(checks[0][1]) + if a in r: + counts["ordinary_Y_wrong_FULL_type_rejected"] += normal(entry + fprev) != normal(fext + route(matrix)) + view = matrix, alignment["exit_X"] + views[s, a] = view + certificates.append({"stage": s, "port": a, "entry_translation_after_route": delta, + "FULL_translation_after_route": alignment["exit_X"], + "route_columns": list(matrix), "FULL_input_character_normal": full_result}) + full = fourier(0, 25) + for a in range(112): + need(normal(line(q[a], 1) + full) == normal(full + line(q[a], 1)), + "Positive final line preserves the common FULL exterior") + counts["terminal_positive_line_frame_checks"] += 1 + if a in r: + need(normal(line(q[a], 1) + full + line(q[a], -1)) == normal(full), + "Positive ordinary line removes its hole") + counts["terminal_positive_line_frame_checks"] += 1 + counts["negative_ordinary_line_rejected"] += ( + normal(line(q[a], -1) + full + line(q[a], -1)) != normal(full)) + abstract = abstract_check() + xp, xr = p, r + yp, yr = [112 + a for a in p], [112 + a for a in r] + specs = [ + ("minus_D2", d, yp, yr, 2, -1), + ("minus_H1", h, yr, yp, 1, -1), + ("plus_H1_W", h, xr, yp, 1, 1), + ("minus_H2_W", h, xr, yp, 2, -1), + ("plus_D1_alpha", d, yp, xr, 1, 1), + ("minus_D0_alpha", d, yp, xr, 0, -1), + ("minus_D1_alpha", d, yp, yr, 1, -1), + ("minus_H0", h, yr, yp, 0, -1), + ] + word = [["LINE", field, q[field % 112], 1] for field in yr] + shear_invoices = {} + for index, (name, matrix, sources, targets, stage, sign) in enumerate(specs): + if index == 4: + word.extend([["NEG", field] for field in xr]) + events, bill = terminal_shear(matrix, sources, targets, stage, F(sign), views) + word.extend(events) + shear_invoices[name] = bill + word.extend([["NEG", field] for field in xp]) + word.extend([["LINE", 112 + a, q[a], 1] for a in range(112)]) + word_counts = Counter(event[0] for event in word) + need(word_counts == {"LINE": 208, "MAP": 1344, "ADD": 1728, "NEG": 112}, "Literal terminal counts") + scalar = sum(bill["scalar_units"] for bill in shear_invoices.values()) + 2 * word_counts["NEG"] + need(scalar == 16608 and all(bill["scalar_units"] == 2048 for bill in shear_invoices.values()), + "Actual terminal scalar count") + need(producer["status"] == "PASS_ACTUAL_D25_NATURAL_CLEAN_TRIPLE", "Completed producer receipt") + need(producer["literal_route_phase_identities"] == counts["natural_frame_identities"] == 896, + "Producer route count") + need(producer["terminal_operator_word"]["positive_line_operations"] == 208 and + producer["terminal_operator_word"]["direct_scalar_upper_bound"] == scalar and + producer["terminal_operator_word"]["routed_shear_affine_map_calls"] == 1344, + "Producer terminal invoice") + for variant in ("I", "Q"): + need(producer["variants"][variant]["content_inverse"] == "PASS" and + producer["variants"][variant]["checked_arbitrary_columns"] == 224, "Completed producer variants") + need(producer["variants"]["I"]["208_line_terminal_checked"], "Producer terminal passed") + need(producer["local_native_mass_initial_I"] == 1808 + 2 * 1792 == 5392 and + producer["local_scalar_initial_I"] == 3 * 8600 == 25800, "Producer local sum") + need(all(digest(Path(item["path"]).read_bytes()) == item["sha256"] for item in manifest.values()), + "Every source remains unchanged") + pins = { + "SOURCE-MANIFEST.json": write_json(args.out / "SOURCE-MANIFEST.json", manifest), + "FRAME-CERTIFICATE.json": write_json(args.out / "FRAME-CERTIFICATE.json", certificates), + "BLOCK-PROOF.json": write_json(args.out / "BLOCK-PROOF.json", abstract), + "TERMINAL-WORD.json": write_json(args.out / "TERMINAL-WORD.json", word), + } + receipt = { + "status": "PASS_INDEPENDENT_NATURAL_TRIPLE_REVIEW", + "output_sha256": pins, + "phase_checks": dict(sorted(counts.items())), + "local_content_columns": 224, + "local_inverse_both_orders": True, + "inverse_adjoint_and_selected_swap_verified": True, + "global_operator_proof": "Four-block free-operator composition plus exact natural-frame conjugation.", + "expanded_global_column_replay_repeated": False, + "H_coefficient_histogram": dict(sorted(Counter(str(x) for row in h for x in row.values()).items())), + "local_invoices_from_literal_events": invoices, + "terminal_counts": dict(sorted(word_counts.items())), + "terminal_scalar_units": scalar, + "terminal_shear_invoices": shear_invoices, + "terminal_local_shear_columns": 224, + "terminal_output": "X=F25 Y0, Y=F25 X0 for initial selected I entry.", + "extra_selected_Q_entry_restoration_lines": 16, + "new_fields": 0, + "odd_divisions": 0, + "native_line_recipes_or_global_host_supplied": False, + "complete_supplier_or_kappa_claim": False, + } + write_json(args.out / "CHECKS.json", receipt) + print(receipt["status"]) + print(json.dumps({"phase_checks": receipt["phase_checks"], "terminal_counts": receipt["terminal_counts"], + "scalar_units": scalar}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/ANCHOR-TYPES.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/ANCHOR-TYPES.json new file mode 100644 index 0000000000..da94403e43 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/ANCHOR-TYPES.json @@ -0,0 +1,1186 @@ +[ + { + "anchor": 0, + "current_I_return_type": "Fprev q_anchor", + "entry_translation_after_route": 3595, + "entry_translation_before_route": 15, + "exit_translation_after_route": 3588, + "q": 11, + "raw_FULL_return_type": "Fnext", + "rho_columns": [ + 2571, + 3083, + 3584, + 1547, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 14, + 7, + 16, + 32, + 64, + 128, + 256, + 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Conditional additive reader only; no accumulator supply, retention, late erase, native replay, recursive host, or kappa claim.", + "status": "FROZEN_INDEPENDENT_RECIPROCAL_SOURCE_CUT_REVIEW" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/ORDERED-CONTENTS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/ORDERED-CONTENTS.json new file mode 100644 index 0000000000..b3887e848f --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/ORDERED-CONTENTS.json @@ -0,0 +1,327 @@ +{ + "B1_raw_X": [ + { + "coefficient": "1", + "input": "x", + "operators_left_to_right": [ + "P0" + ] + }, + { + "coefficient": "-1", + "input": "x", + 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"P0" + ] + } + ] + ], + "relations_used": "Only adjacent equal P_s factors cancel.", + "t": [ + { + "coefficient": "1", + "input": "x", + "operators_left_to_right": [ + "R0" + ] + }, + { + "coefficient": "1", + "input": "y", + "operators_left_to_right": [] + } + ], + "w": [ + { + "coefficient": "1", + "input": "x", + "operators_left_to_right": [] + }, + { + "coefficient": "-1", + "input": "x", + "operators_left_to_right": [ + "P0", + "R1", + "P0", + "R0" + ] + }, + { + "coefficient": "-1", + "input": "y", + "operators_left_to_right": [ + "P0", + "R1", + "P0" + ] + } + ], + "wrong_P_R_commutation_rejected": true +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/REVIEW.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/REVIEW.md new file mode 100644 index 0000000000..a290087524 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/REVIEW.md @@ -0,0 +1,190 @@ +# Independent review of the reciprocal source cuts + +The source-cut formulas and their frame types are correct under the +pinned native contracts. No material error remains in the reviewed +producer proof. Each reader is an additive operation on sixteen +separately supplied accumulators. This review does not supply those +fields or prove their later transport and restoration. + +## Sources and independent method + +The review reads the actual reciprocal model, native contract payload, +and literal D25 views. It reconstructs the mode matrices from the sixteen +blocks, then applies the stored pair code in both directions. It does +not import a producer checker or replay a native event word. + +The source manifest gives exact file and decompressed hashes. The +native payload contains the same model as the separate model payload. +Both provider tables have the required current-I Y entry frames and +raw FULL X exit frames. The native operator contracts remain explicit +premises. Their native recipes and arbitrary-helper claims are not +proved again here. + +The phase checker is the separate, frozen phase engine from the earlier +independent natural-triple review. It normalizes ordered maps on Fourier +characters. It checks the complete linear and quadratic Z4 polynomial, +not a set of sampled characters. Each exact one-copy identity extends +to every positive tensor width. + +## Ordered local and routed operators + +The independent reconstruction gives + +```text +E=P R, E^-1=R P, P^2=R^2=I, +R=I+U ell, ell U=-2 I16. +``` + +Physical P has 160 nonzero entries and is not monomial. Its selected +anchor rows are identity rows. These facts do not permit P to commute +through the port-dependent Q. + +Use the pinned native contracts + +```text +(Qx,y) -> (F x,F q(y+E x)), +(Qx,y) -> (F(x-E^-1 y),F q y). +``` + +Pre-multiply current-I Y by P. Post-multiply raw FULL X by P. The first +contract then gives logical outputs `P x,P(y+R x)`. The second gives +`P(x-R y),P y`, because `E^-1 P=R`. Thus the common-P forward and +backward shears have the stated order. Each P acts where all fields +have a common body frame. No q factor crosses P, R, U, or ell. + +Define the routed reader by + +```text +ell_s = Gamma_c,s ell Gamma_s, +``` + +where Gamma_c,s uses the actual sixteen anchor routes. Let + +```text +t=y+R0 x, +w=x-(P0^-1 R1 P0)t. +``` + +After F0, the logical banks are `P0 x,P0 t`. After B1, they are +`P1 P0 w,P1 P0 t`. The raw X argument at F2 is therefore `P1 P0 w`. +The independent free-operator calculation obtains + +```text +c0=ell0 x, +c1=ell1 P0 t, +c2=ell2 P1 P0 w. +``` + +Only adjacent equal P_s factors cancel in this calculation. A check +rejects the replacement of `P0^-1 R1 P0` by R1. This is an ordered +operator proof on arbitrary x and y, not a numerical matrix sample. + +## Literal frame return at each cut + +The D25 record stores the entry shift before rho and the exit shift +after rho. Thus + +```text +V_in=P_rho T_delta0=T_(rho delta0) P_rho. +``` + +The checker uses this convention. It verifies 1,792 exact phase +identities: eight identities for each of 112 ports at each fresh stage. +These include both entry types, both exit types, the inverse entry, +and the literal inverse orders. All 336 routes also have the required +port labels, orthogonality, involution, and fixed own line. + +The identities that determine the records are + +```text +V_in,s Fprev = Fext,s Q Gamma_s, +V_in,s Fprev q = Fext,s Gamma_s, +V_out,s Fnext = Fnext Gamma_s, +V_in,s^-1 Fext,s = Fprev q Gamma_s. +``` + +At F0, read raw FULL X after the complete native service and before +post-P0. The source is F9 x. A same-frame accumulator receives F9 c0. + +At B1, read current-I Y before pre-P1 and before the native service. +The incoming global source is F9 q P0 t. The entry view gives the body +source `Fext,1 Gamma_1 P0 t`. A same-frame accumulator receives +`Fext,1 ell Gamma_1 P0 t`. Its inverse entry view returns + +```text +F9 q_anchor Gamma_c,1 ell Gamma_1 P0 t = F9 q_anchor c1. +``` + +This is a hole record. It is not FULL. The independent checker rejects +the proposed FULL return at all sixteen anchors of both fresh stages. + +At F2, read raw FULL X after the complete native service and before +post-P2. Its body value is `F25 Gamma_2 P1 P0 w`. The centre FULL exit +returns `F25 Gamma_c,2 ell Gamma_2 P1 P0 w=F25 c2`. + +The accumulated P factors are in the current source values. None of +these three reads requires a separate old-chart query. This fact does +not give an accumulator its required frame or owner lease. + +## Conditional scalar operation and price + +The physical ell has eight rows of length ten and eight rows of length +seven. It has 90 negative and 46 positive unit entries on 96 source +ports. The conditional reader applies 136 complex ADDs. + +The independent body replay uses all 112 arbitrary source columns and +all sixteen arbitrary accumulator columns. It proves + +```text +(source,acc) -> (source,acc+ell source). +``` + +Every source value is unchanged. Every accumulator retains its old +value. The local prefix row one-norm is at most eleven, and this bound +is attained. The word has integer coefficients and introduces no +binary or odd coefficient denominator. + +The pinned scalar tariff prices a complex signed-unit ADD at eight +real units. One reader therefore costs 136*8=1,088 units. Three reader +formations cost 3,264 units if all required typed accumulators are +supplied. These prices exclude accumulator views, preparation, storage, +transport, leases, and a later erase. An immediate inverse ADD word +works only while its source is unchanged; it does not prove late erase. + +## Verification and scope + +The normal and optimized independent runs must have identical output +bytes. The separate producer binding checks the final source proof, +checker, receipts, and serialized reader words. It does not import or +execute the producer checker. + +The completed normal and optimized runs pass with identical bytes. +Use new output directories to repeat the checks: + +```text +python3 -I -B check_review.py --out +python3 -O -I -B check_review.py --out +python3 -I -B check_binding.py --out +python3 -O -I -B check_binding.py --out +``` + +The binding checker reads the retained final-normal and final-optimized +independent outputs. It matches all 272 producer formation instructions +and all 272 immediate inverse instructions to the reconstructed reader. +It also matches the three ordered queries and accumulator types. + +This result establishes the source types and conditional reader costs. +It does not establish a native caller, safe record fields, a clean +baseline, record retention, productive helper progress, a recursive +host, complete precision, or a kappa improvement. The separate native +contract proof remains a dependency. + +The oblique lane supplied the response and native contracts. The bridge +lane supplied the literal views. The parent lane supplied the source-cut +packet. This review supplies the separate ordered proof, model +reconstruction, phase return checks, and source binding. 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/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/SOURCE-MANIFEST.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..41d098c810 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/SOURCE-MANIFEST.json @@ -0,0 +1,22 @@ +{ + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json": { + "content_sha256": 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"file_sha256": "b3c15399f56018680b93cc3254218ced032ea9f2dbcbd080814fa1a63f556d45" + } +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/binding-optimized/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/binding-optimized/CHECKS.json new file mode 100644 index 0000000000..162f69fcde --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/binding-optimized/CHECKS.json @@ -0,0 +1,12 @@ +{ + "accumulator_types_checked": 3, + "exact_immediate_inverse_instructions_checked": 272, + "exact_reader_instructions_checked": 272, + "independent_normal_optimized_byte_identical": true, + "material_findings": [], + "native_word_or_record_retention_replayed": false, + "ordered_queries_checked": 3, + "producer_checker_imported_or_executed": false, + "producer_normal_optimized_byte_identical": true, + "status": "PASS_FINAL_RECIPROCAL_READER_BINDING" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/binding-optimized/SOURCE-MANIFEST.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/binding-optimized/SOURCE-MANIFEST.json new file mode 100644 index 0000000000..5f53be6742 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/binding-optimized/SOURCE-MANIFEST.json @@ -0,0 +1,66 @@ +{ + 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"/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/SOURCE-CUTS.md": { + "content_sha256": "0da0fb811c2c2841ac63b77ea678fa973000b79408cc2d4d825167d721bf5c02", + "file_sha256": "0da0fb811c2c2841ac63b77ea678fa973000b79408cc2d4d825167d721bf5c02" + }, + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/bound-normal/CHECKS.json": { + "content_sha256": "bf1722a6ee21a5c14f50db6b848972a4bbc9fc56ec69c301357103cdc02e6c9b", + "file_sha256": "bf1722a6ee21a5c14f50db6b848972a4bbc9fc56ec69c301357103cdc02e6c9b" + }, + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/bound-normal/READERS.json.gz": { + "content_sha256": "f0a3eb19e09f425fc87e3563af72a7879f9cf64799fee0dcbd059bd297bc8045", + "file_sha256": "a788b2df709853ea516077843cb7309d37f8a190c59a119091af32e0f801e3a9" + }, + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/bound-optimized/CHECKS.json": { + "content_sha256": "bf1722a6ee21a5c14f50db6b848972a4bbc9fc56ec69c301357103cdc02e6c9b", + "file_sha256": "bf1722a6ee21a5c14f50db6b848972a4bbc9fc56ec69c301357103cdc02e6c9b" + }, + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/bound-optimized/READERS.json.gz": { + "content_sha256": "f0a3eb19e09f425fc87e3563af72a7879f9cf64799fee0dcbd059bd297bc8045", + "file_sha256": "a788b2df709853ea516077843cb7309d37f8a190c59a119091af32e0f801e3a9" + }, + "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/check_cuts.py": { + "content_sha256": "b3c15399f56018680b93cc3254218ced032ea9f2dbcbd080814fa1a63f556d45", + "file_sha256": "b3c15399f56018680b93cc3254218ced032ea9f2dbcbd080814fa1a63f556d45" + } +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/check_binding.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/check_binding.py new file mode 100644 index 0000000000..80686220f4 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/check_binding.py @@ -0,0 +1,92 @@ +"""Bind the final reader packet to the independent source-cut check.""" + +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 +PRODUCER = HERE.parents[1] / "reciprocal-reader-cuts-20261020" +PINS = { + "SOURCE-CUTS.md": "0da0fb811c2c2841ac63b77ea678fa973000b79408cc2d4d825167d721bf5c02", + "check_cuts.py": "b3c15399f56018680b93cc3254218ced032ea9f2dbcbd080814fa1a63f556d45", + "bound-normal/CHECKS.json": "bf1722a6ee21a5c14f50db6b848972a4bbc9fc56ec69c301357103cdc02e6c9b", + "bound-normal/READERS.json.gz": "f0a3eb19e09f425fc87e3563af72a7879f9cf64799fee0dcbd059bd297bc8045", +} + + +def need(test, name): + if not test: + raise ValueError(name) + + +def digest(data): + return sha256(data).hexdigest() + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + manifest, objects = {}, {} + for rel, expected in PINS.items(): + path = PRODUCER / rel + stored = path.read_bytes() + raw = gzip.decompress(stored) if path.suffix == ".gz" else stored + need(digest(raw) == expected, "Final producer source " + rel) + manifest[str(path)] = {"file_sha256": digest(stored), "content_sha256": expected} + if ".json" in rel.lower(): + objects[path.name] = json.loads(raw) + for name in ("CHECKS.json", "READERS.json.gz"): + normal, optimized = [(PRODUCER / folder / name).read_bytes() + for folder in ("bound-normal", "bound-optimized")] + need(normal == optimized, "Producer normal and optimized bytes " + name) + manifest[str(PRODUCER / "bound-optimized" / name)] = manifest[str(PRODUCER / "bound-normal" / name)] + for path in sorted((HERE / "final-normal").glob("*.json")): + raw = path.read_bytes() + other = HERE / "final-optimized" / path.name + need(raw == other.read_bytes(), "Independent normal and optimized bytes " + path.name) + manifest[str(path)] = manifest[str(other)] = {"file_sha256": digest(raw), "content_sha256": digest(raw)} + independent = json.loads((HERE / "final-normal/CHECKS.json").read_text()) + need(independent["checker_sha256"] == digest((HERE / "check_review.py").read_bytes()), + "Final independent checker bytes") + body = json.loads((HERE / "final-normal/CONDITIONAL-READER.json").read_text())["events"] + payload, receipt = objects["READERS.json.gz"], objects["CHECKS.json"] + need(receipt["checker_sha256"] == PINS["check_cuts.py"], "Final producer checker binding") + need(receipt["payload_decompressed_sha256"] == PINS["bound-normal/READERS.json.gz"], "Producer payload binding") + for name, offset in (("FULL_X", 0), ("current_I_Y", 112)): + expected = [[op, 640 + target - 112, source + offset, c] for op, target, source, c in body] + program = payload["programs"][name] + need(program["events"] == expected, "Every actual signed reader instruction " + name) + inverse = [[op, target, source, str(-F(c))] for op, target, source, c in reversed(expected)] + need(program["inverse_events"] == inverse, "Immediate inverse instruction order " + name) + need(program["complex_ADDs"] == 136 and program["real_scalar_units"] == 1088, + "Producer scalar invoice " + name) + need([row["global_accumulator_frame"] for row in payload["cut_types"]] == ["F9", "F9 q_anchor", "F25"], + "All three serialized accumulator types") + need([row["reader"] for row in payload["cut_types"]] == + ["c0=ell0 x", "c1=ell1 P0 t", "c2=ell2 (P1 P0) w"], "All three serialized ordered queries") + need(receipt["reader_nonzeros"] == 136 and receipt["reader_source_port_support"] == 96 and + receipt["reader_coefficients"] == {"-1": 90, "1": 46}, "Exact serialized reader counts") + need(not receipt["native_word_replayed_here"] and not receipt["record_retention_or_restoration_claimed"] + and not receipt["complete_supplier_claimed"], "Explicit scope boundaries") + need(receipt["phase_counts"] == {"FULL_exit": 224, "FULL_source_entry": 224, "hole_target_entry": 224}, + "Producer phase coverage") + report = {"status": "PASS_FINAL_RECIPROCAL_READER_BINDING", "material_findings": [], + "producer_normal_optimized_byte_identical": True, + "independent_normal_optimized_byte_identical": True, + "exact_reader_instructions_checked": 272, "exact_immediate_inverse_instructions_checked": 272, + "ordered_queries_checked": 3, "accumulator_types_checked": 3, + "producer_checker_imported_or_executed": False, + "native_word_or_record_retention_replayed": False} + for name, value in (("SOURCE-MANIFEST.json", manifest), ("CHECKS.json", report)): + (args.out / name).write_text(json.dumps(value, indent=2, sort_keys=True) + "\n") + print(report["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/check_review.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/check_review.py new file mode 100644 index 0000000000..e2ee45b46f --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/check_review.py @@ -0,0 +1,281 @@ +"""Check the reciprocal reader types from the fixed source data.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from functools import lru_cache +import gzip +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANE = HERE.parents[1] +LANES = LANE.parent +ENGINE = HERE.parent / "no-reset-triple-review-20261020/check_review.py" +ENGINE_PIN = "daef106365651360926f41e82cfa5bac291433ea87ba154c1d75e6fe4ce04186" +ARITHMETIC = LANES / "new-core-transfer-20261017/low-displacement-20261020/check_response.py" +ARITHMETIC_PIN = "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8" +PINS = { + "model": (LANES / "oblique-native-20261017/signed-metric-reciprocal-20261020/" + "model-normal-v2/RESPONSE.json.gz", + "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0"), + "native": (LANES / "oblique-native-20261017/signed-metric-reciprocal-20261020/" + "native-normal/NATIVE.json.gz", + "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e"), + "views": (LANES / "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473"), +} + + +def need(test, name): + if not test: + raise ValueError(name) + + +def digest(data): + return sha256(data).hexdigest() + + +need(digest(ENGINE.read_bytes()) == ENGINE_PIN, "Fixed independent phase engine") +spec = importlib.util.spec_from_file_location("independent_phase", ENGINE) +engine = importlib.util.module_from_spec(spec) +spec.loader.exec_module(engine) +eye, plus, product, sparse = engine.eye, engine.plus, engine.linear, engine.sparse +route, line, fourier = engine.route, engine.line, engine.fourier + + +@lru_cache(maxsize=None) +def normalized(word): + return engine.normal(word) + + +def same(left, right): + return normalized(tuple(left)) == normalized(tuple(right)) + + +def write_json(path, value): + data = (json.dumps(value, indent=2, sort_keys=True) + "\n").encode() + path.write_bytes(data) + return digest(data) + + +def model_check(model, native): + need(native["model"] == model, "The native payload uses the exact model") + blocks = model["blocks"] + need(Counter(len(b["ports"]) for b in blocks) == {6: 8, 8: 8}, "Actual block sizes") + need(sorted(p for b in blocks for p in b["ports"]) == list(range(112)), "Complete block partition") + h, hi = sparse(model["pair_code"]), sparse(model["pair_code_inverse"]) + need(product(h, hi) == product(hi, h) == eye(112), "Actual pair code in both orders") + u, ell, p_mode = [{} for _ in range(112)], [], eye(112) + for k, block in enumerate(blocks): + ports = block["ports"] + m = len(ports) - 4 + u_values, ell_values = [1] * (len(ports) - 2) + [m, 0], [-1] * (len(ports) - 2) + [1, 0] + need(list(map(F, block["u"])) == u_values and list(map(F, block["ell"])) == ell_values, + "The serialized block uses the declared rank-one factors") + ell.append({a: F(c) for a, c in zip(ports, ell_values) if c}) + for a, c in zip(ports, u_values): + if c: + u[a][k] = F(c) + b, c = ports[-2:] + need((b, c) == (block["b"], block["c"]), "Actual swap roles") + p_mode[b], p_mode[c] = {c: F(1)}, {b: F(1)} + r_mode = [plus((1, a), (1, b)) for a, b in zip(eye(112), product(u, ell))] + modes = {"P": p_mode, "R": r_mode, "E": product(p_mode, r_mode), + "inverse_E": product(r_mode, p_mode)} + physical = {} + for name, matrix in modes.items(): + need(matrix == sparse(model["mode"][name]), "Reconstructed mode matrix " + name) + physical[name] = product(hi, product(matrix, h)) + need(physical[name] == sparse(model["physical"][name]), "Physical pair conjugation " + name) + p, r, e, ei = [physical[name] for name in ("P", "R", "E", "inverse_E")] + L, U = product(ell, h), product(hi, u) + need(L == sparse(model["reflection_L"]) and U == sparse(model["reflection_U"]), + "Exact physical reader and column factors") + need(product(L, U) == [{j: F(-2)} for j in range(16)], "Centre reflection identity") + need(product(p, p) == product(r, r) == product(e, ei) == product(ei, e) == eye(112), + "Physical inverse identities") + need(product(ei, p) == r, "Backward pre-P gives R without a commutation") + need(any(len(row) != 1 for row in p), "Physical P is not monomial") + need(sum(map(len, p)) == 160, "Exact support of physical P") + need(all(p[a] == {a: F(1)} for a in model["centre_ports"]), "P fixes every chosen anchor row") + for word_name in ("forward_E", "backward_inverse_E"): + for provider in native["providers"].values(): + word = provider[word_name] + need(len(word["start"]) == len(word["final"]) == 640, "Complete native role table") + need(all(word["frames"][word["start"][a + 112]] == [] for a in range(112)), + "Every borrowed native entry field has the current-I body frame") + need(all(word["frames"][word["final"][a]] == list(reversed([1 << j for j in range(9)])) + for a in range(112)), "Every raw native X output has the common FULL frame") + need(native["contracts"]["input"] == "Physical X=Qx, Y=y. The native adapters are explicit.", + "Pinned native input contract") + need(native["contracts"]["forward_E"] == "Physical X=F x, Y=F q(y+E x).", "Pinned F contract") + need(native["contracts"]["backward_inverse_E"] == "Physical X=F(x-E^-1 y), Y=F q y.", + "Pinned reciprocal B contract") + return L, {"reconstructed_mode_and_physical_matrices": list(modes), + "physical_P_is_monomial": False, "physical_P_nonzeros": 160, + "native_word_replayed": False, "native_contract_is_an_explicit_premise": True} + + +def ordered_proof(): + def reduce(word): + result = [] + for symbol in word: + if result and result[-1] == symbol and symbol.startswith("P"): + result.pop() + else: + result.append(symbol) + return tuple(result) + + def op(symbol, row): + result = {} + for (source, word), coefficient in row.items(): + result = plus((1, result), (coefficient, {(source, reduce((symbol,) + word)): F(1)})) + return result + + x, y = [{(s, ()): F(1)} for s in ("x", "y")] + t = plus((1, y), (1, op("R0", x))) + f0 = op("P0", x), op("P0", t) + b1_raw_x = plus((1, f0[0]), (-1, op("R1", f0[1]))) + b1 = op("P1", b1_raw_x), op("P1", f0[1]) + w = plus((1, x), (-1, op("P0", op("R1", op("P0", t))))) + need(b1[0] == op("P1", op("P0", w)), "Ordered w formula") + f2_raw_x = b1[0] + f2 = op("P2", f2_raw_x), op("P2", plus((1, b1[1]), (1, op("R2", b1[0])))) + queries = [op("ell0", x), op("ell1", f0[1]), op("ell2", f2_raw_x)] + expected = [op("ell0", x), op("ell1", op("P0", t)), + op("ell2", op("P1", op("P0", w)))] + need(queries == expected, "All three exact source-cut readers") + need(w != plus((1, x), (-1, op("R1", t))), "P0 and R1 are not commuted") + + def encode(row): + return [{"input": s, "operators_left_to_right": list(wd), "coefficient": str(c)} + for (s, wd), c in sorted(row.items())] + + return {"relations_used": "Only adjacent equal P_s factors cancel.", + "t": encode(t), "w": encode(w), "after_F0": list(map(encode, f0)), + "B1_raw_X": encode(b1_raw_x), "after_B1": list(map(encode, b1)), + "F2_raw_X": encode(f2_raw_x), "after_F2": list(map(encode, f2)), + "queries": list(map(encode, queries)), "wrong_P_R_commutation_rejected": True} + + +def phase_check(views, model): + records = {(r["stage"], r["port"]): r for r in views["entries"]} + need(len(records) == len(views["entries"]) == 336 and + set(records) == {(s, p) for s in range(3) for p in range(112)}, "Complete literal D25 views") + need(len(set(model["centre_ports"])) == 16, "Sixteen actual centre anchors") + counts, output = Counter(), [] + for (s, p), row in sorted(records.items()): + rho, q = tuple(row["route_columns"]), model["ports"][p] + alignment = row["literal_stage_alignment"] + need(row["q"] == q and engine.act(rho, q) == q, "Exact label and fixed own line") + need(engine.compose(rho, rho) == engine.UNIT and + all(engine.transposed(rho, rho[j]) == 1 << j for j in range(25)), "Orthogonal involution") + need(alignment["entry_X"] == alignment["entry_Y"] and + alignment["exit_X"] == alignment["exit_Y"], "Same literal bank alignment") + if s == 0: + need(rho == engine.UNIT and set(alignment.values()) == {0}, "Identity initial view") + continue + delta_before, epsilon = alignment["entry_X"], alignment["exit_X"] + delta_after = engine.act(rho, delta_before) + entry = line(delta_after, 2) + route(rho) + inverse_entry = route(rho) + line(delta_after, 2) + exit_view = line(epsilon, 2) + route(rho) + previous, exterior, nex = fourier(0, 9 + 8 * (s - 1)), fourier(9, 9 + 8 * s), fourier(0, 9 + 8 * s) + identities = { + "before_after_entry_translation": (entry, route(rho) + line(delta_before, 2)), + "FULL_entry": (entry + previous, exterior + line(q, 1) + route(rho)), + "hole_entry": (entry + previous + line(q, -1), exterior + route(rho)), + "FULL_exit": (exit_view + nex, nex + route(rho)), + "hole_exit": (exit_view + nex + line(q, -1), nex + line(q, -1) + route(rho)), + "inverse_entry_return": (inverse_entry + exterior, previous + line(q, -1) + route(rho)), + "entry_inverse": (inverse_entry + entry, []), + "exit_involution": (exit_view + exit_view, []), + } + for name, (left, right) in identities.items(): + need(same(left, right), name) + counts[name] += 1 + counts["missing_entry_translation_rejected"] += not same(route(rho) + previous, + exterior + line(q, 1) + route(rho)) + if p in model["centre_ports"]: + need(not same(inverse_entry + exterior, previous + route(rho)), + "A current-I accumulator does not return to global FULL") + counts["false_FULL_accumulator_return_rejected"] += 1 + output.append({"stage": s, "anchor": p, "q": q, "rho_columns": list(rho), + "entry_translation_before_route": delta_before, + "entry_translation_after_route": delta_after, + "exit_translation_after_route": epsilon, + "current_I_return_type": "Fprev q_anchor", + "raw_FULL_return_type": "Fnext"}) + return dict(counts), output + + +def reader_check(L): + counts = Counter(c for row in L for c in row.values()) + need(counts == {F(-1): 90, F(1): 46}, "Exact signed reader coefficients") + need(Counter(map(len, L)) == {10: 8, 7: 8}, "Exact reader row lengths") + state = eye(128) + instructions = [] + maximum = F(1) + for i, row in enumerate(L): + for p, c in sorted(row.items()): + state[112 + i] = plus((1, state[112 + i]), (c, state[p])) + instructions.append(["add", 112 + i, p, str(c)]) + maximum = max(maximum, sum(abs(value) for value in state[112 + i].values())) + need(state[:112] == eye(112), "Every arbitrary source input is unchanged") + need(state[112:] == [plus((1, {112 + i: F(1)}), (1, row)) for i, row in enumerate(L)], + "Every arbitrary accumulator baseline is retained") + scalar = sum(engine.add_price(F(g[3])) for g in instructions) + need(scalar == 1088 and len(instructions) == 136, "Exact conditional body invoice") + need(maximum == 11 and all(c.denominator == 1 for row in state for c in row.values()), + "Exact local prefix norm and integer coefficients") + return {"complex_ADDs": 136, "real_scalar_units": scalar, "source_fields": 112, + "reader_source_port_support": len({p for row in L for p in row}), + "independent_accumulators_required": 16, "arbitrary_columns_checked": 128, + "source_fields_changed": 0, "accumulator_baseline_retained": True, + "prefix_row_one_norm": str(maximum), "binary_denominator_height": 0, + "map_stream_cost_included": False, "storage_or_retention_supplied": False}, instructions + + +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) + data, manifest = {}, {} + for name, (path, expected) in PINS.items(): + stored = path.read_bytes() + raw = gzip.decompress(stored) if path.suffix == ".gz" else stored + need(digest(raw) == expected, "Fixed source " + name) + data[name] = json.loads(raw) + manifest[str(path)] = {"file_sha256": digest(stored), "content_sha256": expected} + manifest[str(ENGINE)] = {"file_sha256": ENGINE_PIN, "content_sha256": ENGINE_PIN} + need(digest(ARITHMETIC.read_bytes()) == ARITHMETIC_PIN, "Fixed scalar tariff source") + manifest[str(ARITHMETIC)] = {"file_sha256": ARITHMETIC_PIN, "content_sha256": ARITHMETIC_PIN} + L, model_report = model_check(data["model"], data["native"]) + ordered = ordered_proof() + phase_report, anchor_types = phase_check(data["views"], data["model"]) + reader_report, instructions = reader_check(L) + write_json(args.out / "SOURCE-MANIFEST.json", manifest) + write_json(args.out / "ORDERED-CONTENTS.json", ordered) + write_json(args.out / "ANCHOR-TYPES.json", anchor_types) + write_json(args.out / "CONDITIONAL-READER.json", {"scope": "A body reader on supplied typed accumulators.", + "events": instructions, "report": reader_report}) + report = {"status": "PASS_INDEPENDENT_RECIPROCAL_SOURCE_CUT_TYPES", + "checker_sha256": digest(Path(__file__).read_bytes()), "model": model_report, + "phase_checks": phase_report, "reader": reader_report, + "ordered_contents_verified": True, + "cut_types": ["F9 ell0 x", "F9 q_anchor ell1 P0 t", "F25 ell2 P1 P0 w"], + "tensor_extension": "The exact one-copy identities tensor over every positive width.", + "native_word_replayed": False, "record_retention_claimed": False, + "complete_supplier_claimed": False} + write_json(args.out / "CHECKS.json", report) + print(json.dumps({"status": report["status"], "phase_identities": sum(v for k, v in phase_report.items() + if not k.endswith("rejected")), "reader_scalar": reader_report["real_scalar_units"]})) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/final-normal/ANCHOR-TYPES.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/final-normal/ANCHOR-TYPES.json new file mode 100644 index 0000000000..da94403e43 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020/final-normal/ANCHOR-TYPES.json @@ -0,0 +1,1186 @@ +[ + { + "anchor": 0, + "current_I_return_type": "Fprev q_anchor", + "entry_translation_after_route": 3595, + "entry_translation_before_route": 15, + "exit_translation_after_route": 3588, + "q": 11, + "raw_FULL_return_type": "Fnext", + "rho_columns": [ + 2571, + 3083, + 3584, + 1547, + 4096, + 8192, + 16384, + 32768, + 65536, + 13, + 14, + 7, + 16, + 32, + 64, + 128, + 256, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "stage": 1 + }, + { + "anchor": 1, + "current_I_return_type": "Fprev q_anchor", + "entry_translation_after_route": 5651, + "entry_translation_before_route": 23, + "exit_translation_after_route": 5636, + "q": 19, + "raw_FULL_return_type": "Fnext", + "rho_columns": [ + 4627, + 5139, + 5632, + 2048, + 1555, + 8192, + 16384, + 32768, + 65536, + 21, + 22, + 8, + 7, + 32, + 64, + 128, + 256, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "stage": 1 + }, + { + "anchor": 3, + "current_I_return_type": "Fprev q_anchor", + "entry_translation_after_route": 17987, + "entry_translation_before_route": 71, + "exit_translation_after_route": 17924, + "q": 67, + "raw_FULL_return_type": "Fnext", + "rho_columns": [ + 16963, + 17475, + 17920, + 2048, + 4096, + 8192, + 1603, + 32768, + 65536, + 69, + 70, + 8, + 16, + 32, + 7, + 128, + 256, + 131072, + 262144, + 524288, + 1048576, + 2097152, + 4194304, + 8388608, + 16777216 + ], + "stage": 1 + }, + { + "anchor": 6, + "current_I_return_type": "Fprev q_anchor", + "entry_translation_after_route": 3597, + "entry_translation_before_route": 15, + "exit_translation_after_route": 3586, + "q": 13, + "raw_FULL_return_type": "Fnext", + "rho_columns": [ + 3085, + 3584, + 2573, + 1549, + 4096, + 8192, + 16384, + 32768, + 65536, + 14, + 11, + 7, 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"final-optimized" + ] +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/SOURCE-CUTS.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/SOURCE-CUTS.md new file mode 100644 index 0000000000..f1f0059f32 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/SOURCE-CUTS.md @@ -0,0 +1,269 @@ +# Actual source cuts for the reciprocal centre readers + +The three centre readers in the reciprocal F/B/F controller can be +formed from current data at their stated cuts. The accumulated P codes +do not require a separate old-chart read. They are already present in +the stored source values. + +The middle reader is not a FULL record. In global coordinates, its +natural accumulator frame is `F9 q_anchor`. The first and last reader +frames are FULL, at F9 and F25. A complete construction must supply, +carry, and restore these accumulator fields. This packet does not +supply that storage or restoration. + +At each cut, the conditional operation that adds the reader to a +separate accumulator has 136 complex signed ADDs, or 1,088 inherited +real scalar units. It uses no additional native source-line transform. +That count requires the accumulator to be present in the stated body +frame. It excludes accumulator views, preparation, transport, leases, +and a later erase. + +## Actual response and local contracts + +The pinned physical response has + +```text +E = P R, R = I+U ell, +P^2=R^2=I, ell U=-2 I16. +``` + +The model is the actual 112-port response from +`oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz`, +with decompressed SHA256 +`df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0`. +The checker uses its physical matrices and its `reflection_L` and +`reflection_U`. P changes 32 physical fields and fixes the 16 specified +centre anchors. P is a dyadic scalar matrix, not a physical monomial. + +The emitted native contracts are + +```text +F_E: (Qx,y) -> (F x, F q(y+E x)), +B_(E^-1):(Qx,y) -> (F(x-E^-1 y), F q y). +``` + +Here F is the local nine-dimensional FULL transform and `q=Q^-1`. +Every target uses the hole output. The native source is +`oblique-native-20261017/signed-metric-reciprocal-20261020/native-normal/NATIVE.json.gz`, +with decompressed SHA256 +`f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e`. +Both providers contain both required literal words. Their native +transcripts and arbitrary-helper restoration are inherited. This +checker pins them and checks the cut metadata; it does not replay +their native events. + +Apply P to current-I Y before the raw service. Apply P to raw FULL X +after the service. These wrappers give + +```text +F_s = diag(P_s,P_s) [[I,0],[R_s,I]], +B_s = diag(P_s,P_s) [[I,-R_s],[0,I]]. +``` + +For B, the exact cross identity is `P E^-1 P=P R`. The backward +cross is E^-1. It is not E or E^-T. No P is commuted through Q. + +## Global routed maps and centre coordinates + +Let Gamma_s be the diagonal data route with port-p entry rho_(s,p). +Let Gamma_c,s use the same routes at the 16 declared centre anchors. +Both are involutions. Define + +```text +P_s = Gamma_s P Gamma_s, +R_s = Gamma_s R Gamma_s, +U_s = Gamma_s U Gamma_c,s, +ell_s = Gamma_c,s ell Gamma_s. +``` + +Then `R_s=I+U_s ell_s` exactly. The centre coordinates have a declared +anchor route. They are not an unspecified scalar output space. + +For the three-call word, put + +```text +t = y+R0 x, +w = x-(P0^-1 R1 P0)t. +``` + +Immediately after F0, the logical data banks are `P0 x,P0 t`. +Immediately after B1, they are `(P1 P0)w,(P1 P0)t`. Consequently the +three effective readers are + +```text +c0 = ell0 x, +c1 = ell1 P0 t, +c2 = ell2 (P1 P0)w. +``` + +The corresponding reflection factors in the stripped coordinates are + +```text +U0 ell0, +(P0^-1 U1)(ell1 P0), +((P1 P0)^-1 U2)(ell2 P1 P0). +``` + +These are ordered products. In particular, the second and third +readers are not ell1 t and ell2 w. + +## Exact view convention + +Let F_s be FULL on the root block and fresh blocks 1 through s. +Let F_ext,s be FULL only on those fresh blocks. The current literal +entry and exit views obey + +```text +V_in,s F_(s-1) = F_ext,s Q Gamma_s, +V_in,s F_(s-1) q = F_ext,s Gamma_s, +V_out,s F_s = F_s Gamma_s. +``` + +The same identities hold on the declared centre anchors. + +The D25 source stores the entry translation BEFORE the route: + +```text +V_in,s = P_rho T_delta0 + = T_(rho delta0) P_rho. +``` + +It stores the exit translation AFTER the route. The checker uses +these literal conventions and verifies all 672 full Z4 identities +for both fresh stages and all 112 ports. Omitting the entry +translation fails the negative control. + +## The three source cuts + +For c0, wait until the raw F0 source word is complete, and read X +before its added post-P0. This body source is `F9 x`. A same-frame +accumulator ADD forms `F9 ell0 x`. No entry map is needed at stage +zero. The returned global record has frame F9. + +For c1, read Y at the stage-1 current-I entrance, before pre-P1 and +before the raw native word. The incoming physical Y bank is + +```text +F9 q P0 t. +``` + +Its literal entry view gives + +```text +F_ext,1 Gamma_1 P0 t. +``` + +Thus the local physical row ell reads the required argument without +removing P0. It adds +`F_ext,1 ell Gamma_1 P0 t` to a same-frame body accumulator. + +To express that accumulator at its global centre anchor, use the +inverse entry view. The exact identity is + +```text +V_in,c,1^-1 F_ext,1 = F9 q_anchor Gamma_c,1. +``` + +The returned reader term is therefore + +```text +F9 q_anchor Gamma_c,1 ell Gamma_1 P0 t + = F9 q_anchor c1. +``` + +Calling this term FULL would omit one centre line. A later native +progression or another proved transport must account for that line. + +For c2, wait until the raw F2 source word is complete and read X +before post-P2. Its body source is + +```text +F25 Gamma_2 (P1 P0)w. +``` + +The current scalar row ell gives +`F25 ell Gamma_2 (P1 P0)w`. The centre FULL exit gives + +```text +F25 Gamma_c,2 ell Gamma_2 (P1 P0)w = F25 c2. +``` + +The accumulated P1P0 code stays in its ordered position. The query +does not read a retired ordinary hole. It reads the completed current +source before its postcode. + +## Conditional reader word and full local invoice + +The physical ell has eight rows of length ten and eight rows of length +seven. All 136 entries are +1 or -1, and their source support contains +96 distinct data ports. + +The emitted local interface has 16 independent accumulator fields. +For each nonzero ell_(i,p), it applies + +```text +acc_i += ell_(i,p) source_p. +``` + +The first and third cuts use X. The second cut uses Y. The source +and accumulator must have the same current body frame. These ADDs +have no source address maps because the data is already in that body +view. Any accumulator maps remain a separate cost. + +The complete operation on arbitrary inputs is + +```text +(data, helpers, acc) -> (data, helpers, acc+ell source). +``` + +The supplied accumulator can be dirty. Its old value remains present. +A clean query is obtained only if the caller supplies a zero +accumulator or proves a joint use of that old value. + +The checker replays all 656 independent input columns: 224 data, +416 other local roles, and 16 accumulator fields. Data and helper +values are unchanged. Reversing the ADDs restores every input if the +source is unchanged. This last condition holds for a local read/erase +test; it is not a late-erasure proof for the complete controller. + +A complex signed-unit ADD costs eight real scalar units under the +inherited tariff. Each reader formation costs 136*8=1,088 units. +All three formations cost 3,264 units if their required accumulators +are supplied. An immediate local erase costs another 1,088 per reader. +No claim is made about the cost of the required later erase. + +At each prefix of this word, an accumulator row contains its own +baseline and at most ten distinct signed source terms. Its row one-norm +is at most eleven, and the bound is attained. The word introduces no +coefficient denominator. These are local reader bounds; a complete +precision proof must also include the input frames and record lifetime. + +## Reproduction and remaining work + +Run with new output directories: + +```text +python3 -B check_cuts.py --out +python3 -O -B check_cuts.py --out +``` + +Both commands return `PASS_EXACT_CURRENT_READER_CUTS`. Their two output +files must match byte for byte. The checks bind the response and native +source pins, physical factorization, 672 phase identities, actual cut +metadata, and both complete local reader words. + +The oblique lane supplied E/P/R and the native words. The cover lane +supplied the ordered reciprocal-controller variables. The bridge lane +supplied the exact current-stage views and is investigating record +retention. This work used AI assistance. + +This result resolves the source-access question at these three cuts. +It does not supply 16 safe record fields, a zero baseline, their +recursive host, their phase transport, or their final restoration. +Those obligations determine whether these available readers become +a complete centre service. No complete supplier or kappa gain is +claimed. + +No PR, commit, push, or publication is authorized. Before any future +PR description, read +`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/bound-normal/CHECKS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/bound-normal/CHECKS.json new file mode 100644 index 0000000000..ea91170041 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/native-escape-20261017/reciprocal-reader-cuts-20261020/bound-normal/CHECKS.json @@ -0,0 +1,49 @@ +{ + "additional_coefficient_binary_height": 0, + "arbitrary_input_columns_per_local_reader": 656, + "checker_sha256": "b3c15399f56018680b93cc3254218ced032ea9f2dbcbd080814fa1a63f556d45", + "complete_supplier_claimed": false, + "extra_source_native_lines_at_these_cuts": 0, + 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Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "model": ( + "oblique-native-20261017/signed-metric-reciprocal-20261020/" + "model-normal-v2/RESPONSE.json.gz", + "df2d2028c99028db3c645b3311d7f31ff96efe72f6f9257f99157ce030ff43d0", + ), + "native": ( + "oblique-native-20261017/signed-metric-reciprocal-20261020/" + "native-normal/NATIVE.json.gz", + "f528752be6222da2b64522f9a124622acab4413e79d403d58b592d2533307d1e", + ), + "views": ( + "bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "125e74660e99d824f8699eed72c1facb59287976bf2c47fda533d654b8344473", + ), + "scalar_tariff": ( + "new-core-transfer-20261017/low-displacement-20261020/check_response.py", + "c6d92104e4345816e86163f6c1dea24fbd9b6e9b133ffd2e0c646dca17ca00a8", + ), +} + + +def need(test, message): + if not test: + raise ValueError(message) + + +def rows(raw): + return [{int(k): F(v) for k, v in row.items()} for row in raw] + + +def identity(n): + return [{i: F(1)} for i in range(n)] + + +def add(target, source, coefficient): + for k, v in source.items(): + value = target.get(k, F(0)) + coefficient * v + if value: + target[k] = value + else: + target.pop(k, None) + + +def product(a, b): + out = [] + for row in a: + target = {} + for k, v in row.items(): + add(target, b[k], v) + out.append(target) + return out + + +def act(columns, vector): + out = 0 + while vector: + low = vector & -vector + out ^= columns[low.bit_length() - 1] + vector ^= low + return out + + +def phase(terms): + """Return the complete degree-two Z4 phase polynomial.""" + out = {} + for vector, coefficient in terms: + bits = [i for i in range(25) if vector >> i & 1] + for i in bits: + out[i, i] = (out.get((i, i), 0) + coefficient) % 4 + for a, i in enumerate(bits): + for j in bits[a + 1:]: + out[i, j] = (out.get((i, j), 0) - 2 * coefficient) % 4 + return {k: v for k, v in out.items() if v} + + +def query_word(reader, source_offset): + return [["add", 640 + i, source_offset + p, str(c)] + for i, row in enumerate(reader) for p, c in sorted(row.items())] + + +def replay(word): + state = identity(656) + for op, target, source, coefficient in word: + need(op == "add" and target >= 640 and source < 224, + "Only the supplied reader bank is written") + add(state[target], state[source], F(coefficient)) + return state + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", required=True, type=Path) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + sources, pins = {}, {} + for name, (relative, expected) in PINS.items(): + path = LANES / relative + raw = path.read_bytes() + if path.suffix == ".gz": + raw = gzip.decompress(raw) + need(sha256(raw).hexdigest() == expected, "Exact source " + name) + sources[name] = None if path.suffix == ".py" else json.loads(raw) + pins[name] = {"path": str(path), "sha256": expected} + model, native = sources["model"], sources["native"] + view = {(r["stage"], r["port"]): r for r in sources["views"]["entries"]} + q, anchors = model["ports"], model["centre_ports"] + need(len(q) == 112 and len(anchors) == len(set(anchors)) == 16, "Port dimensions") + need(all(view[s, p]["q"] == q[p] for s in range(3) for p in range(112)), + "Exact physical port order") + E, Ei, R, P = [rows(model["physical"][name]) for name in ("E", "inverse_E", "R", "P")] + U, L = rows(model["reflection_U"]), rows(model["reflection_L"]) + I = identity(112) + difference = [dict(row) for row in R] + for i in range(112): + add(difference[i], I[i], F(-1)) + need(product(U, L) == difference and product(L, U) == [{i: F(-2)} for i in range(16)], + "Actual physical reflection factor") + need(product(P, R) == E and product(P, P) == product(R, R) == I, + "Exact local response factors") + need(product(P, product(Ei, P)) == product(P, R), + "The wrapped reciprocal backward map has cross P R") + need(all(P[p] == I[p] for p in anchors), "P fixes all chosen centre anchors") + need(native["contracts"]["input"] == + "Physical X=Qx, Y=y. The native adapters are explicit.", "Native input type") + need(native["contracts"]["forward_E"] == "Physical X=F x, Y=F q(y+E x).", + "Native forward contract") + need(native["contracts"]["backward_inverse_E"] == + "Physical X=F(x-E^-1 y), Y=F q y.", "Native reciprocal contract") + cuts = {} + for provider, words in native["providers"].items(): + need(set(("forward_E", "backward_inverse_E")) <= set(words), "Required literal words") + cuts[provider] = {} + for name in ("forward_E", "backward_inverse_E"): + word = words[name] + need(len(word["start"]) == len(word["final"]) == 640, "Complete local role set") + need(all(word["frames"][word["final"][p]] == list(reversed([1 << i for i in range(9)])) + for p in range(112)), "Every raw source output is FULL") + cuts[provider][name] = {"literal_events": len(word["events"]), + "entry_before_endpoint_adapters": True, + "exit_after_complete_raw_word": True} + + unit = [1 << i for i in range(25)] + counts = Counter() + negative_controls = 0 + for s in (1, 2): + for p in range(112): + record = view[s, p] + rho = record["route_columns"] + delta = record["literal_stage_alignment"] + need(act(rho, q[p]) == q[p], "The route fixes its own intrinsic line") + previous = [(a, 1) for a in unit[:9 + 8 * (s - 1)]] + exterior = [(act(rho, a), 1) for a in unit[9:9 + 8 * s]] + # The source record stores the entry translation before the route. + correction = [(delta["entry_X"], 2)] + need(phase(previous + correction) == phase(exterior + [(q[p], 1)]), + "FULL source entry has exactly one current Q") + counts["FULL_source_entry"] += 1 + need(phase(previous + [(q[p], -1)] + correction) == phase(exterior), + "Current Y entry has a common I body frame") + counts["hole_target_entry"] += 1 + full = [(a, 1) for a in unit[:9 + 8 * s]] + need(phase(full + [(act(rho, delta["exit_X"]), 2)]) == + phase([(act(rho, a), 1) for a in unit[:9 + 8 * s]]), + "FULL reader exit has the exact anchor route") + counts["FULL_exit"] += 1 + negative_controls += phase(previous) != phase(exterior + [(q[p], 1)]) + need(negative_controls > 0, "Omitting the actual entry translations is rejected") + + coefficient_counts = Counter(c for row in L for c in row.values()) + need(set(coefficient_counts) == {F(-1), F(1)}, "Signed-unit reader coefficients") + programs = {} + for name, offset in (("FULL_X", 0), ("current_I_Y", 112)): + word = query_word(L, offset) + state = replay(word) + need(state[:640] == identity(640), "All data and helper values remain unchanged") + for i, row in enumerate(L): + expected = {640 + i: F(1)} + add(expected, {offset + p: c for p, c in row.items()}, F(1)) + need(state[640 + i] == expected, "The arbitrary accumulator baseline is retained") + inverse = [[op, t, s, str(-F(c))] for op, t, s, c in reversed(word)] + need(replay(word + inverse) == identity(656), "Exact local read and erase order") + programs[name] = {"events": word, "inverse_events": inverse, + "complex_ADDs": len(word), "real_scalar_units": 8 * len(word), + "prefix_row_one_norm": str(max(sum(abs(c) for c in row.values()) + for row in state)), + "additional_coefficient_binary_height": 0} + output = { + "schema": "reciprocal-reader-current-cuts-v1", + "source_pins": pins, + "centre_anchors": anchors, + "literal_native_cut_locations": cuts, + "programs": programs, + "cut_types": [ + {"stage": 0, "source": "raw FULL X before post-P0", "stored_logical_source": "x", + "reader": "c0=ell0 x", "global_accumulator_frame": "F9"}, + {"stage": 1, "source": "current-I Y before pre-P1", "stored_logical_source": "P0 t", + "reader": "c1=ell1 P0 t", "global_accumulator_frame": "F9 q_anchor"}, + {"stage": 2, "source": "raw FULL X before post-P2", "stored_logical_source": "(P1 P0) w", + "reader": "c2=ell2 (P1 P0) w", "global_accumulator_frame": "F25"}, + ], + "obligations": [ + "Each ADD word requires16 independent accumulator fields in the declared body frame.", + "The accumulator may be dirty; the output retains its arbitrary baseline.", + "No storage, owner lease, record transport, or late erase is supplied.", + "The native transcript and its helper contract are inherited; this checker does not replay them.", + ], + } + payload = (json.dumps(output, sort_keys=True, separators=(",", ":")) + "\n").encode() + (args.out / "READERS.json.gz").write_bytes(gzip.compress(payload, mtime=0)) + receipt = { + "status": "PASS_EXACT_CURRENT_READER_CUTS", + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "payload_decompressed_sha256": sha256(payload).hexdigest(), + "source_pins": pins, + "phase_counts": dict(counts), + "omitted_entry_translation_failures": negative_controls, + "reader_nonzeros": sum(map(len, L)), + "reader_source_port_support": len({p for row in L for p in row}), + "reader_row_lengths": dict(Counter(map(len, L))), + "reader_coefficients": {str(c): n for c, n in coefficient_counts.items()}, + "per_reader_real_scalar_units": 8 * sum(map(len, L)), + "prefix_row_one_norm": programs["FULL_X"]["prefix_row_one_norm"], + "additional_coefficient_binary_height": 0, + "arbitrary_input_columns_per_local_reader": 656, + "source_or_helper_fields_modified": 0, + "independent_typed_accumulators_required": 16, + "extra_source_native_lines_at_these_cuts": 0, + "record_retention_or_restoration_claimed": False, + "native_word_replayed_here": False, + "complete_supplier_claimed": False, + } + (args.out / "CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps({"status": receipt["status"], "phases": sum(counts.values()), + "reader_ADDs": sum(map(len, L)), "scalar": receipt["per_reader_real_scalar_units"]})) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz new file mode 100644 index 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+#!/usr/bin/env python3 +"""Bind the rank-two response and the small clique cover to actual ports.""" + +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha256 +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +PINS = { + "independent-review-20261017/cyclic-pair-flags-20261018/CYCLIC-FLAGS.json": + "3034e1df3670f64e5b79a51a435d7903f3be7cef10d6b486a8bd4d420c989585", + "controller-followthrough-20261017/matched-involution-20261018/MATCHED-INVOLUTION-PROGRAM.json": + "e2443eee2a7081ce3b57b9b7afcf4f1b061b9d8ddf0fbbeb5f7b29ce0d148902", +} +CLIQUES = [ + [5, 34, 40, 85, 97], [3, 32, 38, 50, 95], [24, 48, 67, 80, 82], + [23, 35, 55, 65, 68], [1, 17, 66, 75, 83], [8, 12, 45, 107, 109], + [29, 49, 54, 56, 108], [26, 30, 64, 73, 96], [4, 33, 69, 74, 88], + [18, 22, 84], [19, 28, 77], [39, 58, 86], [6, 98, 100, 101, 102], + [31, 59, 60, 93, 103], +] + + +def need(test, message): + if not test: + raise ValueError(message) + + +def read(relative): + raw = (LANES / relative).read_bytes() + need(sha256(raw).hexdigest() == PINS[relative], "Source pin " + relative) + return json.loads(raw) + + +def identity(n): + return [{i: F(1)} for i in range(n)] + + +def add(target, source, coefficient=F(1)): + for key, value in source.items(): + target[key] = target.get(key, F(0)) + coefficient * value + if not target[key]: + del target[key] + + +def product(a, b): + result = [] + for row in a: + value = {} + for j, coefficient in row.items(): + add(value, b[j], coefficient) + result.append(value) + return result + + +def transpose(a, n): + result = [{} for _ in range(n)] + for i, row in enumerate(a): + for j, value in row.items(): + result[j][i] = value + return result + + +def restrict(a, ports): + index = {p: i for i, p in enumerate(ports)} + return [{index[p]: value for p, value in a[row].items() if p in index} + for row in ports] + + +def rank(rows, columns): + rows = [dict(row) for row in rows] + pivot = 0 + for column in range(columns): + found = next((i for i in range(pivot, len(rows)) if rows[i].get(column)), None) + if found is None: + continue + rows[pivot], rows[found] = rows[found], rows[pivot] + c = rows[pivot][column] + rows[pivot] = {p: v / c for p, v in rows[pivot].items()} + for i in range(pivot + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[pivot], -rows[i][column]) + pivot += 1 + return pivot + + +def determinant(rows): + rows = [dict(row) for row in rows] + result = F(1) + for column in range(len(rows)): + found = next((i for i in range(column, len(rows)) if rows[i].get(column)), None) + if found is None: + return F(0) + if found != column: + rows[column], rows[found] = rows[found], rows[column] + result = -result + c = rows[column][column] + result *= c + for i in range(column + 1, len(rows)): + if rows[i].get(column): + add(rows[i], rows[column], -rows[i][column] / c) + return result + + +def inverse_word(word): + return [[op, target, origin, str(1 / F(c) if op == "scale" else -F(c))] + for op, target, origin, c in reversed(word)] + + +def transpose_word(word): + return [[op, target if op == "scale" else origin, + origin if op == "scale" else target, c] + for op, target, origin, c in reversed(word)] + + +def replay(word): + state = identity(112) + maximum = F(1) + for op, target, origin, coefficient in word: + c = F(coefficient) + if op == "scale": + state[target] = {p: c * v for p, v in state[target].items() if c * v} + else: + need(op == "add" and target != origin, "Scalar word grammar") + add(state[target], state[origin], c) + maximum = max(maximum, sum(abs(c) for c in state[target].values())) + return state, maximum + + +def price(word): + result = 0 + for op, _, _, coefficient in word: + c = F(coefficient) + a, b = abs(c.numerator), c.denominator + need(a and not b & (b - 1), "Dyadic coefficient") + if op == "scale": + need(not a & (a - 1), "Dyadic unit scale") + result += 2 * (abs(a.bit_length() - b.bit_length()) + (c < 0)) + else: + result += 2 * (1 + a.bit_length() + a.bit_count() + b.bit_length()) + return result + + +def maximal_cliques(ports, q): + n = len(ports) + adjacent = [sum(1 << j for j, r in enumerate(ports) + if i != j and not (q[p] & q[r]).bit_count() % 2) + for i, p in enumerate(ports)] + result = [] + + def visit(chosen, possible, excluded): + if not possible and not excluded: + result.append(chosen) + return + options = possible | excluded + pivot = max((i for i in range(n) if options >> i & 1), + key=lambda i: (adjacent[i] & possible).bit_count(), default=0) + todo = possible & ~adjacent[pivot] + while todo: + bit = todo & -todo + i = bit.bit_length() - 1 + todo -= bit + visit(chosen | bit, possible & adjacent[i], excluded & adjacent[i]) + possible -= bit + excluded |= bit + + visit(0, (1 << n) - 1, 0) + return [[ports[i] for i in range(n) if mask >> i & 1] for mask in sorted(result)] + + +def encoded(rows): + return [{str(p): str(c) for p, c in sorted(row.items())} for row in rows] + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + args.out.mkdir(parents=True, exist_ok=False) + cyclic = read(next(name for name in PINS if "CYCLIC" in name)) + matching = read(next(name for name in PINS if "MATCHED" in name)) + selected, small = matching["selected_ports"], matching["small_ports"] + selected_set = set(selected) + q = cyclic["ports"] + h = identity(112) + codes = [] + for pair in cyclic["pair_codes"]: + a, b = pair["ports"] + aa, ab = pair["matrix"][0] + ba, bb = pair["matrix"][1] + h[a], h[b] = {a: F(aa), b: F(ab)}, {a: F(ba), b: F(bb)} + if aa != 1: + codes.append(["scale", a, None, str(aa)]) + codes.extend([["add", a, b, str(ab)], ["scale", b, None, str(2 * bb)], + ["add", b, a, str(ba * aa)]]) + hi = transpose(h, 112) + for p in cyclic["affected_ports"]: + hi[p] = {k: v / 2 for k, v in hi[p].items()} + need(product(h, hi) == identity(112), "Actual pair inverse") + mode = identity(112) + mode_inverse = identity(112) + mode_u, mode_v = [{} for _ in range(112)], [] + mode_word, assignments = [], [] + for vertex, group in enumerate(cyclic["cyclic_carriers"]): + chosen = [p for p in group if selected_set.intersection(map(int, cyclic["mode_rows"][str(p)]))] + rest = [p for p in group if p not in chosen] + need(len(chosen) == 2 and len(rest) == 4, "Two selected modes per vertex") + order = chosen + rest + signs = [1, 1 if vertex % 2 == 0 else -1, 1, 1, 1, 1] + e = [{j: F((i == j) - 1) for j in range(4) if i != j} | {4: F(1)} + for i in range(4)] + e += [{5: F(1)}, {0: F(-2), 1: F(-2), 2: F(-2), 3: F(-2), 4: F(3)}] + swap = [0, 1, 2, 3, 5, 4] + ei = [{swap[j]: c for j, c in e[swap[i]].items()} for i in range(6)] + need(product(e, ei) == product(ei, e) == identity(6), "Six-mode reciprocal pair") + for i, p in enumerate(order): + mode[p] = {order[j]: c * signs[i] * signs[j] for j, c in e[i].items()} + mode_inverse[p] = {order[j]: c * signs[i] * signs[j] for j, c in ei[i].items()} + offset = len(mode_v) + local_u = [[1, 0]] * 4 + [[0, 1], [2, -1]] + local_v = [[-1, -1, -1, -1, 1, 0], [0, 0, 0, 0, -1, 1]] + for i, p in enumerate(order): + mode_u[p].update({offset + j: F(value * signs[i]) + for j, value in enumerate(local_u[i]) if value}) + mode_v.extend([{order[j]: F(value * signs[j]) for j, value in enumerate(row) if value} + for row in local_v]) + a, b, c = order[:4], order[4], order[5] + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(-signs[i])]) + for i, p in enumerate(a): + mode_word.append(["add", p, b, str(signs[i])]) + mode_word.append(["scale", b, None, "-1"]) + for i, p in enumerate(a): + mode_word.append(["add", b, p, str(signs[i])]) + mode_word.extend([["add", b, c, "1"], ["add", c, b, "-1"], + ["add", b, c, "1"], ["scale", c, None, "-1"]]) + assignments.append({"vertex": vertex, "ordered_carriers_a_b_c": order, "signs": signs}) + need(replay(mode_word)[0] == mode, "In-place rank-two mode code") + response, response_inverse = product(hi, product(mode, h)), product(hi, product(mode_inverse, h)) + u, v = product(hi, mode_u), product(mode_v, h) + small_word = [] + need(sorted(p for group in CLIQUES for p in group) == sorted(small), "Exact disjoint64 cover") + for group in CLIQUES: + k = len(group) + need(k in (3, 5), "Dyadic clique size") + need(all((q[p] & q[r]).bit_count() % 2 == int(p == r) + for p in group for r in group), "Actual orthonormal clique") + for p in group: + response[p] = {r: F(-1) for r in group if r != p} + response_inverse[p] = {r: F(int(p == r)) - F(1, k - 1) for r in group} + u[p] = {len(v): F(-1)} + v.append({p: F(1) for p in group}) + a, rest = group[0], group[1:] + small_word.extend([["add", a, p, "1"] for p in rest]) + small_word.extend([["add", p, a, "-1"] for p in rest]) + small_word.append(["scale", a, None, str(1 - k)]) + small_word.extend([["add", a, p, "-1"] for p in rest]) + word = codes + mode_word + inverse_word(codes) + small_word + common_words = {"E": word, "inverse_E": inverse_word(word), + "transpose_E": transpose_word(word), + "inverse_transpose_E": transpose_word(inverse_word(word))} + expected = {"E": response, "inverse_E": response_inverse, + "transpose_E": transpose(response, 112), + "inverse_transpose_E": transpose(response_inverse, 112)} + word_receipts = {} + for name, gates in common_words.items(): + actual, maximum = replay(gates) + need(actual == expected[name], "Full112 scalar code " + name) + need(replay(gates + inverse_word(gates))[0] == identity(112), "Both code orders " + name) + word_receipts[name] = {"real_scalar_primitives": price(gates), + "prefix_row_l1_bound": str(maximum), "owned_fields": 0} + need(product(response, response_inverse) == product(response_inverse, response) == identity(112), + "Full112 reciprocal products") + correction = [dict(row) for row in response] + for i in range(112): + add(correction[i], {i: F(-1)}) + need(product(u, v) == correction and rank(u, 30) == rank(v, 112) == 30, + "Exact full rank30 correction factor") + l = restrict(response, selected) + li = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_inverse"]] + old_l = [{int(p): F(c) for p, c in row.items()} for row in matching["selected_block"]] + need(l == restrict(response_inverse, selected) == old_l, "Both selected blocks retain L") + need(product(l, li) == identity(8), "Selected inverse") + ordinary = sorted(set(range(112)) - selected_set) + p = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(selected) + if response_inverse[r].get(s)} for r in ordinary] + n = [{j: response_inverse[r].get(s, F(0)) for j, s in enumerate(ordinary) + if response_inverse[r].get(s)} for r in selected] + ordinary_inverse = restrict(response_inverse, ordinary) + for row, update in zip(ordinary_inverse, product(product(p, li), n)): + add(row, update, -1) + ordinary_block = restrict(response, ordinary) + need(product(ordinary_block, ordinary_inverse) == product(ordinary_inverse, ordinary_block) + == identity(104), "Both ordinary104 inverse orders") + need(all(not c.denominator & (c.denominator - 1) + for row in ordinary_inverse for c in row.values()), "Dyadic ordinary inverse") + maxima = maximal_cliques(small, q) + histogram = Counter(map(len, maxima)) + need(histogram == {4: 896, 8: 64}, "Exhaustive maximal clique census") + # A separate exhaustive extension pass checks the absence of a ninth vertex. + need(all(not any(p not in clique and all(not (q[p] & q[r]).bit_count() % 2 for r in clique) + for p in small) for clique in maxima), "Each reported clique is maximal") + receipt = { + "status": "PASS_LOW_DISPLACEMENT_RESPONSE", + "source_pins": PINS, "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest(), + "correction_rank_large48": 16, "correction_rank_small64": 14, "correction_rank_full112": 30, + "selected_determinant": str(determinant(l)), + "full_determinant": str(determinant(response)), + "ordinary104_determinant": str(determinant(ordinary_block)), + "small_clique_sizes": dict(sorted(Counter(map(len, CLIQUES)).items())), + "all_maximal_small_clique_sizes": dict(sorted(histogram.items())), + "common_frame_scalar_codes": word_receipts, + "scope": "Exact port matrices, principal units, scalar codes and geometry. Native phases and terminal access are separate.", + } + payload = { + "source_pins": PINS, "ports": q, "selected_ports": selected, "ordinary_ports": ordinary, + "large_ports": cyclic["affected_ports"], "small_ports": small, + "vertex_assignments": assignments, "mode_response": encoded(mode), + "mode_inverse": encoded(mode_inverse), "small_cliques": CLIQUES, + "response": encoded(response), "response_inverse": encoded(response_inverse), + "correction_U": encoded(u), "correction_V": encoded(v), + "selected_block": encoded(l), "selected_inverse": encoded(li), + "ordinary_inverse": encoded(ordinary_inverse), "common_frame_words": common_words, + "maximal_small_cliques": maxima, + } + raw = (json.dumps(payload, indent=2, sort_keys=True) + "\n").encode() + (args.out / "RESPONSE-PROGRAM.json").write_bytes(raw) + receipt["payload_sha256"] = sha256(raw).hexdigest() + (args.out / "RESPONSE-CHECKS.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(json.dumps(receipt, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md new file mode 100644 index 0000000000..a1fc7101cb --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/NATIVE-LIFT.md @@ -0,0 +1,140 @@ +# Native recipes for the new centre-deleted core + +This lane checks the native operators for both PR3133 provider words. +The words are the byte-equal copies in PR3148. It uses the new frame and +warp data. It does not use the earlier T74 frame data. + +Fresh generation passed for both providers. Each run checked 1130 frames, +3036 directed child edges, 224 endpoint adapters, 180 signed physical warp +classes, 72 logical warp operators, and 56 residual wrapper classes. The +residual classes include 32 proper terminal pairs, of which 24 are cold. +Each source run rejected 25 wrapper mutations and 13 warp mutations. + +The fresh child and residual recipe files have the same hashes as the +authenticated PR3133 native receipt. Both literal dual runs also passed: +each checked all 180 signed classes on all 512 columns. In each provider, +172 literal dual recipes differ from the forward recipes. All literal +dual recipes have rank zero. Thus the choice of logical warp orientation +does affect the phase tables, but it does not add native children. + +The independent interpreter review is a separate calculation. The scalar +map, stock, controller, precision, and complete kappa calculation are also +separate checks. `RESULT.json` gives the generation result; `FREEZE.json` +pins its inputs, scripts, proofs, and outputs. + +## Exact operator test + +For a binary subspace U, let T_U be the canonical Clifford frame in the +pinned source. A child from U to V must implement T_V T_U^{-1}. The +generator derives its recipe from this product. It checks the full Pauli +table and the exact Gaussian dyadic image of the zero basis vector. These +two checks include the global phase. + +To see this, let A and B be unitary operators with the same action on all +Pauli generators. Then B^{-1} A commutes with every X and Z generator. An +operator that commutes with every Z generator is diagonal in the standard +basis. If it also commutes with every X generator, all diagonal entries +are equal. Thus A is a scalar multiple of B. Equality on the zero basis +vector fixes that scalar as one. The argument applies to each generated +Clifford product. It also proves equality of all positive tensor powers. + +Each child recipe has the form L C_[r] R, with R applied first. The +serialized L and R are monomial Clifford operators. For a nested frame +change, the checked r is the difference of the frame dimensions. The +physical warp product is T_V K_G^{sign} T_U^{-1}. Its checked r is zero. +The separate Gaussian matrix implementation checks every one of its 512 +columns. + +A helper that enters at E and leaves at V has residual T_V T_E^{-1}. +The recipes include the proper terminal subspaces of the new words. They +also include the cold pairs with E equal to zero. The exact wrapper test +checks R^{-1}, then the residual, then L^{-1}; the result is C_[r]. It does +not replace a proper terminal frame by FULL. + +## Literal dual warps + +The backward scalar proof uses the inverse transpose of each logical +warp. For a unitary warp K this is the entrywise conjugate of K. The +source emitter stores the same signed warp labels for both orientations. +The orientation must therefore select a physical implementation. + +There are two valid routes. The free-operator proof can establish the +endpoint identity for an arbitrary consistent choice of invertible warp +generators. The physical implementation can then use the forward K in +both orientations. Alternatively, the literal dual implementation can +use conjugate(K) in the backward orientation. This lane supplies exact +recipes for the second route as well. + +The literal dual route has a general rank-zero closure property. Let K +be a monomial Clifford operator whose nonzero entries are fourth roots of +unity. Every source K_G has this property. In a standard basis, K is an affine +permutation with a phase of the form + + i^(c + alpha.x + 2 q(x)), + +where q is a binary quadratic form. Conjugation changes this phase by +2(c + alpha.x) modulo 4. The quadratic term vanishes. After the affine +permutation, this phase is a signed Z Pauli. Thus + + conjugate(K) K^{-1} = P + +for a Pauli P. Suppose the accepted physical warp is + + W = T_V K T_U^{-1} + +and W is monomial. Then its literal dual counterpart is + + T_V conjugate(K) T_U^{-1} = (T_V P T_V^{-1}) W. + +A Clifford frame maps a Pauli to a Pauli. A Pauli is monomial. Hence the +literal dual counterpart is monomial and needs no native child. Apply the +same argument to K^{-1} for a negative signed occurrence. This proof does +not require U and V to be FULL, or require the Pauli to be diagonal after +frame conjugation. + +`generate_dual_warps.py` also checks this conclusion directly for each +signed class of each new provider. It uses the physical product +T_V conjugate(K_G)^{sign} T_U^{-1}. A separate Gaussian matrix calculation +compares all 512 columns. A wrong global phase must fail. + +## Source and credit + +The core comes from +[PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), at +commit `51eb9c4ee9e4722010d308aa3309e039d3940cc2`. The byte-equal provider +words are in +[PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), at +commit `f2927a4b8afcf0701a6b945e14f30de1d94f5176`: + +- [Base word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/base.json.gz). +- [Extra word](https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/words/extra.json.gz). + +The unchanged recipe sources come from +[PR2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588), at +commit `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb`: + +- [Phase compiler](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_phases.py). +- [Residual wrappers](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_adapters.py). +- [Gaussian matrix implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_gauss.py). +- [Serialized warp checker](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/bw_check_recipes.py). +- [Exact Clifford implementation](https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py). + +The source files retain their original author and AI-assistance notices. +The wrapper source credits the PR458 construction. The warp source credits +Cinna Davis and PR2226. OpenAI Codex assisted this lane's driver, literal +dual calculation, proof, and local checks. The independent review is a +separate agent calculation. It is not a maintainer review. + +## Reproduction + +Use one process and the workspace Python that has NumPy: + + work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_recipes.py + OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 work/verification-venv/bin/python -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/generate_dual_warps.py + python3 -I -B work/centre-encoding-campaign-20261014/lanes/new-native-recipes-20261017/freeze_results.py + +The first command checks every source and input pin before generation. +It runs the wrapper, phase, and serialized warp checks for each provider. +The second command checks the source and first-stage output pins before +it generates the literal dual recipes. The scripts write results only +inside this lane. No PR, push, or publication commit is part of this work. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json new file mode 100644 index 0000000000..c3df9a69e7 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/SOURCE-PINS.json @@ -0,0 +1,10 @@ +{ + "source_commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "source_sha256": { + "bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce", + "bw_check_recipes.py": "d600b959a0ac462dc28deb8c0d5d8f9e0c76d7f7d7b6f92a296c5ef9e0a1de19", + "bw_gauss.py": "0884b14d6d77cde419a3c773ad9b21d0d18de1e6e20e6b6d5add458ed32ba4cb", + "bw_phases.py": "9d1a620e26715f4c42fd0347ecc14ef5a4a9031867869b64e8bae4d8526a821e", + "vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/base/CLIFFORD-RECIPES.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/base/CLIFFORD-RECIPES.json new file mode 100644 index 0000000000..fed4d40157 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/new-native-recipes-20261017/base/CLIFFORD-RECIPES.json @@ -0,0 +1 @@ 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zyDkTPh;iwYmOI}NnIzi;iUwu9Fd6bGi15|z&Vd3Aq9EW#Cq_2KjyUxyin}?WZ0HwP ztwVb>hkuFvVw~E6#g~9g)?GS> zikz)oapsxAs-?PBOnqwpv)*Ug0sL$Mf0k2Ahk7|u9b5nml9@D#T?7eyWGofFo6{n; z?|jd+fbrAt70IT$&JSMVFMzkFt62R|Y5PMXaUhgd0Z&akQZiuo zeM?XjT2I&aY%0PCxklf8u6D!7a&TI1&?2HbmX!i+W*?|^*jgLvZNlD3-^a2*z=gyS zD!|=+7pyy%0s`VVugpB+fmL=vE5C>QgOSkz1x?ADoz{Ov`;&7Af*~jW#p>-fpLDlc z>w2RxI#?cqs=rN&Pa5}Iw^_$yKaN;Z_~uZlC#*8%9IvGg8pULzEdc*EJMBN;pkl+1 zUE%&(ajD8${@*3F;v$r-^b^-21_7$m&5@2{mNot7tp(Y=0Ptwr4RgH};i4G(ce{m&`X8cuUV6aq=Ij!;jYT?zr(+yI^-h znztj{*{Vs8#gL&H^<^-OTAvAhwB4}}6YDQRli$(^4NY|QR_vPh5QbGvS_FjQ;-VOO zdnHB{!98=jpRZn{0?v(+ZCD>yNViM`i4t3Ujc_F?ul*cT`dd6ww}oBMRLj-5?fV1SZIQ=^J=#~ zvbFn{pI0OeAZm=cS5mpDpR^l{xGw!ZXzpDtFUDpfs_5-1@5K-PwV>p?{^ZV-rr{4p zZPQGvLh-%!TTMqWwj(URb`$Gu{Ri6H@-!SYj#dTyG*2BH*k`Yp{w(j`lc`jU=FKNh zVC9`bNO5^BM-n=|C-JZ5W7pUZthl9I>S2&6hs#G~LNx^dd7R+R%_o|J8p6(lvja#f ziy%q2j86^_ql7X{h%rJwruN7BbY0bk3jd1>@~?{E{{d|R>QpbhdnNw@;u31e*95wa0|FE_>9;+{ z-)G6r0{KA~;aUs$L$Oef**2}4e0145?|R~SbY)e^fn|r50j>&9|NQ&An^h?sWDoA+ z5N^JkIy>KtBSsQ2cHjM8-|PeAUP}htZEe$lBNS~wDS@2FEu8Vj6u&Oaj8hC2g+A|p zm|&ugL|*y{JhM2_eajfjfdItgya?okW=^PQiaQs#(hUIIDB4v&i>mP*y#NZaH%;~f zf`+|xPBbq(Q+AIE2_hhcyoQWcoGS^Yzh%00S{a+n17RzJNX|Cr;!Dx@$kBv;lD8MJ zDFbM%;{U&XR(5VfEXwPyBqkO3t4~t~?zk9o2bCOJ2Eu-n_%Xt5uP-8c>4wuQ6Zj~g zs-I`UI;}iS<{+SYl_Q%~gC1PS33X%_B|PB&e~>ke?!^)ws%P#TR(!JUIy}q6innQ| z(^}p3#g`8C(D{8Fvogwf-6^mRk3^y0t$fwNH^Ehcrh-y)pnEx`=I(!$+k^iZNfkBB ziy|%8W6{=)u^Umce%fcW4(kZKJE}S01*}d`{8~wNNs|pKfr@gC$(iU1D(;atJa4`W zhUE9yzD#__7%TdRKZEZ<^K*fF-StJ()+gn-h~A*U6=@6DRkV-mvsR9eR8E-RQZPF4 zKDOO)7Wt8m*j}JHV8L}@RZ8jg1s3Z)LImoO=3+DCHMl8gWoa@F=poYYQP-jRk0X{L z^=OX#^w55WfZ+QUeLzL_(w7fxVQ%GMK$Tws7$Yd$1*~{wy0!cg#D}10ww4dD51^@C zh(?-D+wq|v`lvAtzFTDf=$8z)MHAZAFI^m1LvALJuY6lg-q$hq@ix+yr+sW7Hew_f zJsRZNJv{AeV4n(v3P^pzKpuy;sG{q!;OJCWyFqt=_&wYII>3qV9cvn|L&1NPvx5Cc zxj0Z1u~oqIe{@W6xc$%q9z8!<>n&jQOn)ua=CEKs3IC6MiNVV0_%+fYiisqOjImcG zR|lCknHG^9x~{r&OjA)?Cddf27&*pRhiibox1S{YM|(wwu>y@q>p9ZFO6|1K$*HIr z=&rI+?DqFLPdIvTS?GFrM$_!Z7<*q5Fs`=i&W(UDPNnu9Yv=iEf9`zz(Drbkwpl%A z3%^K3$J_>SO954XwZKSS|KLJ9p?W4hegX12Sl9RKgZ~fmlZzQ)^z62T>Nw$yYbD#1 zS5{$!?JmpBYbH=@`*d##TzU@j`iq8~iCX=Z?bh?__^+IFglIN@I^#d2OV;>smY0MX znq#_+LB;2D!?wujR5G6Sf_G(u`Y!+LsyYoIQw`dlx~n|h}PwOtd0tVE(G z*bsdH3=m5YMjqwa1|kFv zu?A7fa$c!UX)h!`6g;(lFF zSUcJ~SupAn-FT0Ov-=QP@j@D_t7~o9$D6_PGBErKrM9k1ZP$pn+&!gS>wZ9=y?xGT ziEU?=4) R_jt R_js/4. +``` + +The formula for G exchanges the two groups. Direct multiplication gives + +```text +EG-I = K[12I-13(M+N)+14MN]R = 0. +GE-I = K[12I-13(M+N)+14NM]R = 0. +``` + +Here M+N=(12/13)I and MN=NM=0. The checker verifies RK=14I and both +full 112 by 112 inverse products with exact rational arithmetic. E and +G are symmetric for this coordinate P. + +The separate +[rank theorem](../../root/RECIPROCAL-CENTRE-RANK-20261018.md) states the +optimal rank sum and the coefficient-ring obstruction for this response +family. This construction does not use a finite test as a proof of that +rank theorem. It implements the coordinate rank-four case directly. + +## Centre and helper operations + +At the centre cut, the source computes eight values + +```text +c_j = R_j x + H_j h. +``` + +The actual centre fields are `[92,57,81,224,11,240,9,256]`. Their frames +are `[250,264,597,267,599,268,602,269]`, each of rank eight. The source +already has a native transition from each such frame to I and its +reverse. No new frame or native compiler is required. + +With all centre blocks deleted, the forward core has the data response +Jx and helper term -KHh. Keeping the centre correction M gives +`Jx+KMRx-K(I-M)Hh`. The entrance correction is therefore +`Y += K(I-M)Hh`. All H helper roles and all Y roles are at I at this +entrance. The selected centre rows have weight 1/13; the other rows have +weight one. The backward entrance is its negative transpose, +`h -= H^T(I-M)^T K^T y`. Replace M by N for G. + +The literal entrance uses C0 for each of the eight rows. In the forward +word it queries H_j h, divides C0 by 13 for a selected row, and scatters +through R_j^T/4. In the backward word it queries R_j y/4, divides for a +selected row, and scatters through -H_j^T. A CLEAR starts and ends each +row. No helper or data field is cleared. + +For each selected forward centre, copy the actual centre field into C0 +at its rank-eight frame. Use the exact original rank-eight transition to +I. Divide C0 by 13, multiply each original scatter coefficient by 12, +and clear C0 at I. Each original scatter coefficient is +1/4 or -1/4, +so the new dyadic scatter coefficient is +3 or -3. + +For each selected backward centre, accumulate the original query in C0 +at I with its coefficients multiplied by 12. Divide C0 by 13. Use the +exact original transition from I to the rank-eight frame. Apply the +original final ADD to the centre field, then clear C0 at I. An owned +CLEAR may set the empty field's frame; no nonzero value is relabelled. + +The centre event's owned target changes from C_j to C0. Its old frame, +new frame, and rank do not change. Every occurrence has a binding to the +original event and the exact recipe for that frame pair. No centre +values need to persist between blocks. + +## Complete local maps and frames + +For T equal to E or G, the literal words have the maps + +```text +forward: (x,y,h) -> (x, y+T x, h), +backward: (x,y,h) -> (x-T^T y, y, h). +``` + +The backward word uses T^T. It does not use T^-1. Although T is symmetric +in this coordinate example, its reciprocal is the other response. + +The producer propagates exact rational rows through every literal event. +Each row contains formal input fields and free words in the warp +operators. Only adjacent inverse letters cancel. Backward warp symbols +are separate from forward symbols. Thus the check assumes no extra +commutation between port operators or warps. + +Each check covers all 632 live input fields and all eight arbitrary +owned input fields. All 408 helper outputs have their original logical +values, and no helper term remains in a data output. C0 ends at zero at +I. C1 through C7 retain their exact arbitrary input values at I, because +the word does not access them. If a caller requires all eight owned +outputs to be zero, seven further CLEARs cost fourteen dyadic real +primitives. + +All 91 private buffers are allocated once and are zero at their actual +return. The checker checks every scalar frame, signed warp class, +ordinary adapter endpoint, residual adapter endpoint, private lifetime, +and final live and owned frame. Every ordinary native record has the +same value and order as in the clean source. The complete retained core, +including its scalar events, is copied without change. + +The data roles also retain the source convention. Each X input has its +intrinsic port-line frame, each Y input has frame I, each X output has +FULL, and each Y output has its intrinsic port-hole frame. Let q be the +diagonal inverse-line operator. After removal of the common output F, +the physical data maps are + +```text +C_F(T) = [[q, 0], [q T q, q]], +C_B(T) = [[q, -T^T], [0, q]]. +``` + +These formulas keep the written order of q and T. The identity EG=I +holds in the shared logical chart. It does not by itself cancel q +factors between differently typed physical calls. That use needs a +controller and a legal chart transition. + +## Exact native phases + +The unchanged native records use the frozen current-core phase review. +That review covers the current geometry, the literal backward dual warp +recipes, endpoint adapters, and proper helper wrappers. Its receipt is +`../independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json`, SHA256 +`924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d`. +This packet does not repeat that full sweep. + +The producer does repeat all sixteen centre directions for each of the +two providers. It reads the pinned recipe and compares it with +`T_new T_old^-1` from the source frame vectors. The separate exact +interpreter checks all eighteen Pauli images and one complete Gaussian +state of dimension 512. The state check fixes the global phase. Every +new centre occurrence is bound to one of these thirty-two checks. + +Multiplication by a real rational scalar commutes with a linear frame +operator on the same field. All new scalar operations occur at their +declared common frame. This justifies the divide and scatter placement; +it does not commute an index-dependent q through R, K, E, or G. + +## Denominators and division scans + +The literal replay checks the denominator of every coefficient in every +changed row at every prefix. All coefficients have denominator +`2^a 13^b` with b at most one. At each of the eight divisions, all +coefficients in the completed C0 query have b=0 before division. This +is an exact finite-circuit statement on all formal input columns. It +applies to arbitrary values, not to selected numerical test inputs. + +Consequently one word adds at most one factor 13 relative to its input +grid. This includes arbitrary helper payloads. Exact physical frame +operators are Gaussian dyadic and do not add a factor 13 at their ideal +endpoints. The statement is about the emitted operation boundaries; +it does not supply a bound for the internals of recursively implemented +children or for roundoff error. + +The fixed-odd-grid dependency is the frozen +[independent grid review](../bridge-review-20261017/odd-grid-a8-review-20261017/REVIEW.md). +Its freeze SHA256 is +`81ebbea971c0902a80479f9af4c82e72c660093c9f712b537690293aaaf21d60`. +That family includes division by 13. Each real scan uses the signed +carry recurrence + +```text +a = (b-c) mod 2, c' = (c+13a-b)/2, 0 <= c < 13. +``` + +The scan requires an exact divisible grid numerator and its signed end +condition. A common grid must supply the required factor 13 at each +complete query. Arbitrary finest-grid numerators are not an admissible +replacement for root inputs that were converted to that grid. + +There are sixteen real scans per word. The inherited arithmetic-head +bound is at most `64(w_g+1)` for those scans, with descriptor work +separate. Here w_g is the full root-grid binary record width. Root +conversion must include every numeric stream, including arbitrary +borrowed fields. + +A depth-only recursive odd-height bound requires every completed child +to have its exact Gaussian-dyadic endpoint on all arbitrary input +columns. E and G do not satisfy that condition individually. They can +be rational prefixes inside a future parent whose completed endpoint +is proved dyadic. The number of unfinished such prefixes per level, +root conversion, binary guard, descriptor work, and roundoff analysis +remain part of that future construction. + +## Price and checks + +| Word | Dyadic real primitives | Complex /13 | Real scans | Children | Rank mass | +| --- | ---: | ---: | ---: | ---: | ---: | +| E forward | 165594 | 8 | 16 | 3511 | 5105 | +| E backward | 165618 | 8 | 16 | 3511 | 5105 | +| G forward | 165594 | 8 | 16 | 3511 | 5105 | +| G backward | 165618 | 8 | 16 | 3511 | 5105 | + +These counts hold for both providers. Every word has 23500 events. Its +native profile is `{1:2433,2:724,3:228,4:102,5:20,8:4}`. The original +clean profile has rank mass 5073; four retained centre calls add 32. +Each forward centre block costs 270 dyadic real primitives. Each +backward block costs 276. The weighted entrance has the same dyadic +bill as the old entrance and adds four of the eight divisions. + +The checker rejects four changed constructions: omission of an entrance +division, a changed centre scatter sign, a wrong centre input frame, and +use of the same projection for both reciprocal responses. For each +provider it also rejects a changed centre global phase with the exact +state interpreter. The receipt records the failures. + +The program is in +[RECIPROCAL-CENTRE-PROGRAMS.json.gz](producer-final/RECIPROCAL-CENTRE-PROGRAMS.json.gz). +Its decompressed SHA256 is +`8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013`. +The [receipt](producer-final/RECIPROCAL-CENTRE-RECEIPT.json) gives the +input pins, every division position, the per-word checks, and the native +recipe checks. `FREEZE.json` pins the final local packet. The earlier +`producer/` run is a development result, not the frozen receipt. + +Run from the workspace root with a new output directory: + +```sh +python3 -I -B work/centre-encoding-campaign-20261014/lanes/reciprocal-centre-20261018/emit_reciprocal_centres.py --out /tmp/reciprocal-centre-reproduction +``` + +The final status is `PASS_RECIPROCAL_CENTRE_NATIVE_PRODUCER`. The output +program bytes are deterministic. The receipt also records elapsed time. +The script requires at least 3 GiB free disk space and uses one process. + +The current supplier and clean-core work supply the source R, H, native +chains, and endpoint conventions. The root lane derived the reciprocal +split and its rank classification. The oblique-native lane supplied the +centre-capture and weighted helper-correction plan. The new-native-recipes +lane implemented this packet. The earlier native and grid review lanes +supply the stated dependencies. This work used OpenAI Codex under the +user's direction. No PR, push, commit, or publication is authorized. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/reciprocal-centre-20261018/emit_reciprocal_centres.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/reciprocal-centre-20261018/emit_reciprocal_centres.py new file mode 100644 index 0000000000..4d0e1d2c9a --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/reciprocal-centre-20261018/emit_reciprocal_centres.py @@ -0,0 +1,480 @@ +#!/usr/bin/env python3 +"""Emit and check the two reciprocal centre extensions. + +Use a new output directory. Keep odd division separate from scalar gates. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import shutil +import time + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parent +PINS = { + 'new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz': + ('gzip', 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa'), + 'new-native-recipes-20261017/base/CLIFFORD-RECIPES.json': + ('plain', '580dee1ca6d0a2971bc1dbe93558b8331bfa61662ce1736b24d944a55127b4f0'), + 'new-native-recipes-20261017/extra/CLIFFORD-RECIPES.json': + ('plain', 'f3c678f44ac8c116376d707b088516b0c17744a8508f2863843b912738d2024e'), + 'interface-proof/verify_native_lift.py': + ('plain', '087ad4cc683e5caf1f2a8cd62d5f65c9b4dde2636593b417f8f5099a29875c8b'), + 'independent-review-20261017/NEW-CORE-NATIVE-REVIEW.json': + ('plain', '924b898621dd25ea9d3330563fdf7acf6c3b63dc99526e15faaee682f4bdd94d'), + 'bridge-review-20261017/odd-grid-a8-review-20261017/FREEZE.json': + ('plain', '81ebbea971c0902a80479f9af4c82e72c660093c9f712b537690293aaaf21d60'), +} + + +def require(condition, label): + if not condition: + raise ValueError(label) + + +def digest(raw): + return sha256(raw).hexdigest() + + +def encode(value): + return (json.dumps(value, sort_keys=True, separators=(',', ':')) + '\n').encode() + + +def load_inputs(): + values, pins = {}, {} + for name, (mode, pin) in PINS.items(): + disk = (LANES / name).read_bytes() + raw = gzip.decompress(disk) if mode == 'gzip' else disk + require(digest(raw) == pin, 'Input pin: ' + name) + pins[name] = {'content_sha256': pin, 'file_sha256': digest(disk), 'mode': mode} + if name.endswith(('.json', '.json.gz')): + values[name] = json.loads(raw) + return values, pins + + +def scalar_cost(op): + if op[0] in ('clear', 'copy'): + return 2 + q = Q(*op[-2:]) + a, b = abs(q.numerator), q.denominator + require(a and b & (b - 1) == 0, 'Nonzero dyadic scalar') + if op[0] == 'scale': + require(a & (a - 1) == 0, 'Power-of-two SCALE') + return 2 * (abs(a.bit_length() - b.bit_length()) + int(q < 0)) + require(op[0] == 'add', 'Scalar opcode') + return 2 * (3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1) + + +def native(event): + return event[0] in ('climb', 'warp', 'adapter', 'residual_adapter', 'center') + + +def add_scalar(events, target, source, coefficient, frame=0): + q = Q(coefficient) + require(q, 'Nonzero ADD') + events.append(['scalar', ['add', target, source, q.numerator, q.denominator], frame]) + + +def weighted_prefix(R, H, mapping, selected, backward): + events = [['phase', 'weighted_centre_helper_correction']] + C = ['C', 0] + for j in range(8): + events.append(['scalar', ['clear', C], 0]) + query = R[j] if backward else H[j] + for field, value in sorted(query.items()): + source = ['L', 112 + field if backward else mapping[field]] + add_scalar(events, C, source, value / 4 if backward else value) + if j in selected: + events.append(['divide_odd', C, 13, 0]) + scatter = H[j] if backward else R[j] + for field, value in sorted(scatter.items()): + target = ['L', mapping[field] if backward else 112 + field] + add_scalar(events, target, C, -value if backward else value / 4) + events.append(['scalar', ['clear', C], 0]) + return events + + +def selected_blocks(source, selected, backward): + require(len(source) == 208, 'Eight source centre blocks') + result, bindings = [], [] + for j in range(8): + block = deepcopy(source[26*j:26*(j+1)]) + calls = [e for e in block if e[0] == 'center'] + require(len(calls) == 1 and calls[0][1] == j and calls[0][4] == 8, + 'Source centre block shape') + if j not in selected: + continue + require(block[0][0:2] == ['scalar', ['clear', ['C', j]]], 'Centre starts with CLEAR') + require(block[-1][0:2] == ['scalar', ['clear', ['C', j]]], 'Centre ends with CLEAR') + old_call = deepcopy(calls[0]) + start = len(result) + for e in block: + if e[0] == 'center': + if backward: + result.append(['divide_odd', ['C', 0], 13, 0]) + e[1] = 0 + bindings.append({'centre': j, 'local_position': len(result), + 'source_event': old_call, 'event': deepcopy(e)}) + result.append(e) + if not backward: + result.append(['divide_odd', ['C', 0], 13, 0]) + continue + require(e[0] == 'scalar', 'Centre scalar event') + op = e[1] + for k, value in enumerate(op): + if isinstance(value, list) and value[0] == 'C': + require(value == ['C', j], 'One owned field in each source block') + op[k] = ['C', 0] + if op[0] == 'add' and e[2] == 0: + require(Q(*op[-2:]) in (Q(1, 4), Q(-1, 4)), 'Source quarter coefficient') + q = 12 * Q(*op[-2:]) + op[-2:] = [q.numerator, q.denominator] + result.append(e) + if backward: + require(result[-1][1] == ['clear', ['C', 0]], 'Final owned CLEAR') + result[-1][2] = 0 + require(len(result) - start == 27, 'One added division per retained block') + return result, bindings + + +def make_word(provider, R, H, selected, backward): + c = provider['canonical'] + mapping = {old: i for i, old in enumerate(list(range(224)) + c['helper_origin'])} + require(len(mapping) == 632, 'Compact field namespace') + require(all(c['start'][mapping[h]] == 0 and c['final'][mapping[h]] == 1 + for row in H for h in row), 'Helper correction has I input and FULL output') + orientation = 'backward' if backward else 'forward' + clean = provider['programs'][orientation] + first = clean.index(['phase', 'zero_frame_precondition']) + require(first == 832, 'Clean correction boundary') + core = deepcopy(clean[first:]) + cut = core.index(['phase', 'centers']) + 1 + require(core[cut] == ['phase', 'B'], 'Empty centre cut') + prefix = weighted_prefix(R, H, mapping, selected, backward) + blocks, bindings = selected_blocks(provider['removed_centre_blocks'][orientation], selected, backward) + program = prefix + core[:cut] + blocks + core[cut:] + for binding in bindings: + binding['position'] = len(prefix) + cut + binding.pop('local_position') + require(program[binding['position']] == binding['event'], 'Exact centre occurrence binding') + require([e for e in program if native(e) and e[0] != 'center'] == + [e for e in clean if native(e)], 'All non-centre native records are unchanged') + return {'selected_centres': sorted(selected), 'program': program, + 'centre_bindings': bindings, 'weighted_prefix_events': len(prefix), + 'centre_block_events': len(blocks)} + + +def acc(target, source, coefficient): + for key, value in source.items(): + new = target.get(key, 0) + coefficient * value + if new: + target[key] = new + else: + target.pop(key, None) + + +def height(row): + result = 0 + for value in row.values(): + denominator, h = value.denominator, 0 + while denominator % 13 == 0: + denominator //= 13 + h += 1 + require(denominator & (denominator - 1) == 0, 'Only dyadic and 13 denominators') + result = max(result, h) + return result + + +def unit(field): + return {(field, ()): Q(1)} + + +def replay(word, c, R, backward): + fields = [('L', i) for i in range(632)] + [('C', i) for i in range(8)] + rows = {f: unit(f) for f in fields} + frames = {('L', i): f for i, f in enumerate(c['start'])} + frames.update({('C', i): 0 for i in range(8)}) + live_zero, allocated_zero = set(), set() + divisions, child_heights, peak = [], Counter(), 0 + selected = set(word['selected_centres']) + warp_classes = set(map(tuple, c['warp_edges'])) + + def access(field): + require(field in rows and (field[0] != 'Z' or field in live_zero), + ('Live field access', field)) + + for position, event in enumerate(word['program']): + tag, changed = event[0], None + if tag == 'scalar': + op, frame = event[1:] + f = tuple(op[1]) + access(f) + changed = f + if op[0] == 'clear': + require(f[0] == 'C', ('Only owned fields can be cleared', position)) + rows[f], frames[f] = {}, frame + elif op[0] in ('copy', 'add'): + source = tuple(op[2]) + access(source) + require(frames[f] == frames[source] == frame, ('Scalar frame', position)) + require(f != source, ('Distinct scalar fields', position)) + if op[0] == 'copy': + require(f[0] == 'C', ('Only owned fields can be copied over', position)) + rows[f] = dict(rows[source]) + else: + acc(rows[f], rows[source], Q(op[3], op[4])) + elif op[0] == 'scale': + require(frames[f] == frame, ('SCALE frame', position)) + rows[f] = {k: Q(*op[2:]) * v for k, v in rows[f].items()} + else: + raise ValueError(('Scalar opcode', op)) + scalar_cost(op) + elif tag == 'divide_odd': + f, divisor, frame = tuple(event[1]), event[2], event[3] + access(f) + require(f == ('C', 0) and divisor == 13 and frames[f] == frame == 0, + ('Odd-division contract', position)) + before = height(rows[f]) + rows[f] = {k: v / divisor for k, v in rows[f].items()} + divisions.append({'position': position, 'input_13_height': before, + 'output_13_height': height(rows[f])}) + changed = f + elif tag in ('climb', 'center'): + if tag == 'climb': + f, old, new, rank = ('L', event[2]), *event[3:] + else: + f, old, new, rank = ('C', event[1]), *event[2:] + require(f == ('C', 0) and rank == 8, 'Serial rank-eight centre call') + require(frames[f] == old, ('Native input frame', position, f)) + require(abs(len(c['frames'][new]) - len(c['frames'][old])) == rank, + ('Native rank', position)) + frames[f] = new + child_heights[height(rows[f])] += 1 + elif tag == 'warp': + f, symbol, old, new = tuple(event[1]), *event[2:] + access(f) + require(frames[f] == old, ('Warp input frame', position)) + require((1 if symbol > 0 else -1, abs(symbol), old, new) in warp_classes, + ('Signed warp class', position)) + frames[f] = new + if backward: + symbol = (abs(symbol) + 1000) * (1 if symbol > 0 else -1) + rows[f] = {(source, word[1:] if word and word[0] == -symbol else (symbol,) + word): value + for (source, word), value in rows[f].items()} + changed = f + elif tag == 'zero_buffer': + f = ('Z', event[2]) + if event[1] == 'alloc': + require(f not in allocated_zero, 'Private field is allocated once') + allocated_zero.add(f) + live_zero.add(f) + rows[f], frames[f] = {}, 1 + else: + require(event[1] == 'free' and f in live_zero and not rows[f], + ('Private field is returned to zero', position)) + require(frames[f] == 1, ('Private field is returned at FULL', position)) + live_zero.remove(f) + elif tag == 'adapter': + _, side, field, frame = event + require(side in ('old_to_new', 'new_to_old'), 'Adapter orientation') + endpoint = c['start'] if side == 'old_to_new' else c['final'] + require(endpoint[field] == frame, 'Adapter endpoint') + elif tag == 'residual_adapter': + _, side, field, entry, *tail = event + require(side in ('pre', 'post') and entry == c['start'][field] + and (tail[0] if tail else 1) == c['final'][field], 'Helper wrapper endpoints') + else: + require(tag == 'phase', ('Event grammar', tag)) + if changed is not None: + peak = max(peak, height(rows[changed])) + require(not live_zero and len(allocated_zero) == 91, 'All 91 private fields are released') + for f in fields: + kind, p = f + expected = unit(f) + if kind == 'C' and p == 0: + expected = {} + elif kind == 'L' and (p < 112 if backward else 112 <= p < 224): + port = p if backward else p - 112 + base = 112 if backward else 0 + sign = -1 if backward else 1 + acc(expected, unit(('L', base + port)), sign) + for j, row in enumerate(R): + coefficient = -Q(1, 52) if j in selected else -Q(1, 4) + for source, value in row.items(): + acc(expected, unit(('L', base + source)), + sign * coefficient * row.get(port, 0) * value) + require(rows[f] == expected, ('Complete response', backward, sorted(selected), f)) + require([frames['L', i] for i in range(632)] == c['final'], 'Every live output frame') + require(all(frames['C', i] == 0 for i in range(8)), 'Every owned output frame is I') + require(len(divisions) == 8 and all(d['input_13_height'] == 0 for d in divisions), + 'Eight divisions use complete queries with no new factor 13') + require(peak == 1, 'All local prefixes have at most one new factor 13') + return {'arbitrary_live_columns': 632, 'arbitrary_helper_columns': 408, + 'arbitrary_owned_columns': 8, 'C0_exit': 'zero at I', + 'C1_to_C7_exit': 'exact input value at I', 'private_fields_zero_at_release': 91, + 'all_live_endpoint_frames_checked': True, + 'max_prefix_13_height': peak, 'division_events': divisions, + 'child_input_13_height_counts': dict(sorted(child_heights.items()))} + + +def response(R, selected): + return [[Q(i == j) - sum((Q(1, 52) if k in selected else Q(1, 4)) * + row.get(i, 0) * row.get(j, 0) for k, row in enumerate(R)) + for j in range(112)] for i in range(112)] + + +def multiply(a, b): + columns = list(zip(*b)) + return [[sum(x*y for x, y in zip(row, column)) for column in columns] for row in a] + + +def check_reciprocal(R): + gram = [[sum(R[i].get(p, 0) * R[j].get(p, 0) for p in range(112)) / 4 + for j in range(8)] for i in range(8)] + require(gram == [[Q(14 * (i == j)) for j in range(8)] for i in range(8)], 'RK=14I') + e, g = response(R, set(range(4))), response(R, set(range(4, 8))) + identity = [[Q(i == j) for j in range(112)] for i in range(112)] + require(multiply(e, g) == identity and multiply(g, e) == identity, 'Both full inverse orders') + require(e == list(map(list, zip(*e))) and g == list(map(list, zip(*g))), 'Coordinate responses are symmetric') + return {'dimension': 112, 'RK': '14 I_8', 'E_G': 'I_112', 'G_E': 'I_112', + 'symmetric_coordinate_responses': True} + + +def phase_checks(values, payload): + path = LANES / 'interface-proof/verify_native_lift.py' + spec = importlib.util.spec_from_file_location('reciprocal_native_phase', path) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + result = {} + for name, provider in payload['providers'].items(): + c = provider['canonical'] + recipes = values['new-native-recipes-20261017/' + name + '/CLIFFORD-RECIPES.json']['children'] + lookup = {(r['old'], r['new']): r for r in recipes} + selected = [] + for f in c['center_frames']: + for old, new in ((f, 0), (0, f)): + r = lookup[old, new] + require(r['rank'] == 8, 'Retained centre rank') + circuit = module.adjoint(module.frame(c['frames'][old], 9)) + module.frame(c['frames'][new], 9) + module.equal(module.recipe(r), circuit, name + ' centre ' + str((old, new))) + selected.append(r) + provider['centre_recipes'] = selected + for word in provider['words'].values(): + for binding in word['centre_bindings']: + _, target, old, new, rank = binding['event'] + require(target == 0 and rank == 8 and (old, new) in lookup, + 'C0 centre occurrence has exact recipe') + binding['recipe_key'] = [old, new] + binding['recipe_sha256'] = digest(encode(lookup[old, new])) + result[name] = {'centre_recipes_checked': 16, 'Paulis_per_recipe': 18, + 'Gaussian_state_dimension_per_recipe': 512, + 'global_phase_checked': True, 'bound_centre_occurrences': 16} + changed = deepcopy(selected[0]) + changed['left']['phase'] = (changed['left']['phase'] + 1) % 4 + try: + module.equal(module.recipe(changed), module.recipe(selected[0]), 'Changed global phase') + except ValueError as error: + require('global phase' in str(error), 'Phase mutation fails the exact state check') + result[name]['global_phase_mutation_rejected'] = True + else: + raise ValueError('Global phase mutation was accepted') + return result + + +def negative_controls(payload, R): + provider = payload['providers']['base'] + original = provider['words']['E_forward'] + controls = {} + for label in ('omit_helper_division', 'change_centre_scatter_sign', 'change_centre_frame'): + changed = deepcopy(original) + events = changed['program'] + if label == 'omit_helper_division': + position = next(i for i, e in enumerate(events) if e[0] == 'divide_odd') + events.pop(position) + elif label == 'change_centre_scatter_sign': + position = changed['centre_bindings'][0]['position'] + 2 + require(events[position][0] == 'scalar' and events[position][1][0] == 'add', + 'Mutation addresses the first centre scatter') + events[position][1][3] *= -1 + else: + position = changed['centre_bindings'][0]['position'] + events[position][2] = 0 + try: + replay(changed, provider['canonical'], R, False) + except ValueError as error: + controls[label] = str(error) + else: + raise ValueError('Mutation was accepted: ' + label) + e = response(R, set(range(4))) + require(multiply(e, e) != [[Q(i == j) for j in range(112)] for i in range(112)], + 'Using the same centre projection twice must fail') + controls['same_projection_for_both_responses'] = 'E E is not I' + return controls + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('--out', type=Path, required=True) + args = parser.parse_args() + require(not args.out.exists(), 'Output directory must be new') + require(shutil.disk_usage(HERE).free >= 3 * 1024**3, 'At least 3 GiB free disk') + start = time.monotonic() + values, pins = load_inputs() + source = values['new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz'] + R = [{int(k): Q(v) for k, v in row.items()} for row in source['R']] + H = [{int(k): Q(v) for k, v in row.items()} for row in source['H']] + payload = {'schema': 'reciprocal-centre-native-v1', 'R': source['R'], 'H': source['H'], + 'providers': {}, 'source_pins': pins, + 'odd_division_opcode': ['divide_odd', ['C', 0], 13, 0]} + receipt = {'status': 'PASS_RECIPROCAL_CENTRE_NATIVE_PRODUCER', 'providers': {}, + 'reciprocity': check_reciprocal(R)} + for name, provider in source['providers'].items(): + payload['providers'][name] = {'canonical': provider['canonical'], 'words': {}} + checks = {} + for response_name, selected in (('E', set(range(4))), ('G', set(range(4, 8)))): + for orientation in ('forward', 'backward'): + backward = orientation == 'backward' + key = response_name + '_' + orientation + word = make_word(provider, R, H, selected, backward) + check = replay(word, provider['canonical'], R, backward) + profile = Counter(e[5] for e in word['program'] if e[0] == 'climb') + profile.update(e[4] for e in word['program'] if e[0] == 'center') + require(profile == {1: 2433, 2: 724, 3: 228, 4: 102, 5: 20, 8: 4}, 'Native profile') + scalar_bill = sum(scalar_cost(e[1]) for e in word['program'] if e[0] == 'scalar') + require(scalar_bill == (165618 if backward else 165594), 'Complete dyadic scalar invoice') + check.update(events=len(word['program']), native_profile=dict(sorted(profile.items())), + native_children=sum(profile.values()), native_mass=sum(k*v for k, v in profile.items()), + dyadic_real_primitives=scalar_bill, complex_divisions_by_13=8, + real_division_scans=16, division_head_steps_bound='64 (w_g + 1)', + all_owned_zero_exit_extra_dyadic_primitives=14, + ordinary_native_records_unchanged=True) + payload['providers'][name]['words'][key] = word + checks[key] = check + print(name, key, scalar_bill, 3511, 5105, 'PASS', flush=True) + receipt['providers'][name] = checks + receipt['centre_phase_checks'] = phase_checks(values, payload) + receipt['negative_controls'] = negative_controls(payload, R) + receipt['source_pins'] = pins + receipt['scope'] = ('Literal local rational couplers on all 640 input columns. E and G are not completed ' + 'dyadic recursive providers. All ordinary native records retain the pinned phase proof. ' + 'All 32 centre recipes receive fresh exact Pauli and Gaussian-state checks. No global ' + 'controller, child hosting, full binary precision guard, or complete kappa claim.') + raw = encode(payload) + disk = gzip.compress(raw, mtime=0) + receipt.update(payload_sha256=digest(raw), payload_file_sha256=digest(disk), + emitter_sha256=digest(Path(__file__).read_bytes()), + elapsed_seconds=round(time.monotonic() - start, 3)) + args.out.mkdir(parents=True) + (args.out / 'RECIPROCAL-CENTRE-PROGRAMS.json.gz').write_bytes(disk) + (args.out / 'RECIPROCAL-CENTRE-RECEIPT.json').write_text(json.dumps(receipt, indent=2) + '\n') + print(receipt['status'], receipt['payload_sha256'], flush=True) + + +if __name__ == '__main__': + main() diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-PROGRAMS.json.gz b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/lanes/reciprocal-centre-20261018/producer-final/RECIPROCAL-CENTRE-PROGRAMS.json.gz new file mode 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E and G are not completed dyadic recursive providers. All ordinary native records retain the pinned phase proof. All 32 centre recipes receive fresh exact Pauli and Gaussian-state checks. No global controller, child hosting, full binary precision guard, or complete kappa claim.", + "payload_sha256": "8b3d6fbba7d7221a82927475bc38d479798f776fa27c22ef9a447c7a9a1d5013", + "payload_file_sha256": "5ec7f426930f667743228f35e13bdbf356ca18f85c8183275690ad9dc2e12708", + "emitter_sha256": "cf420eb592c45823ef78fabe2bed07512b2467684589ccbec38d254103215abc", + "elapsed_seconds": 17.227 +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-20261018.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-20261018.json new file mode 100644 index 0000000000..66523e695d --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-20261018.json @@ -0,0 +1,44 @@ +{ + "checker_sha256": "e01ad5199c14319e904e7f56d3e675a50722a6d7df2a366efd0273cb19bf71aa", + "coordinate_projection_checks": 256, + "full_112_field_inverse_checks": [ + { + "E_entries": 5824, + "G_entries": 5936, + "label": "coordinate-mask-0" + }, + { + "E_entries": 7392, + "G_entries": 7448, + "label": "coordinate-mask-1" + }, + { + "E_entries": 9096, + "G_entries": 9096, + "label": "coordinate-mask-15" + }, + { + "E_entries": 7448, + "G_entries": 7392, + "label": "coordinate-mask-127" + }, + { + "E_entries": 5936, + "G_entries": 5824, + "label": "coordinate-mask-255" + }, + { + "E_entries": 10788, + "G_entries": 10788, + "label": "noncoordinate-rank-four" + } + ], + "mutation_checks": [ + "wrong coefficient", + "repeated response" + ], + "proof_sha256": "d2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9", + "scope": "Exact centre algebra. Native words, global phase transport, and supplier pricing are separate obligations.", + "source_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "status": "PASS_EXACT_RECIPROCAL_CENTRE_RANK" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-20261018.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-20261018.md new file mode 100644 index 0000000000..10411320d5 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-20261018.md @@ -0,0 +1,147 @@ +# Exact division cuts the centre rank of reciprocal responses + +The actual clean native response is J=I-KR, where R has eight rows, +K=R^T/4, and RK=14I. Consider two extensions of this same response: + + E=J+KMR, G=J+KNR. (1) + +Here M and N are scalar eight-by-eight matrices. The centre information +needed for the extra terms is MRx and NRx. This note measures their +rational ranks. Native access, capture, storage, and restoration need +separate circuit checks. + +If the coefficients of M and N are dyadic and EG=I, both M and N must +have rank eight. If exact division by 13 is allowed, the least possible +sum of the two ranks is eight. Every pair at this minimum has the form + + M=(12/13)P, N=(12/13)(I-P), (2) + +where P is a projection. A coordinate projection of rank four gives four +centre queries in each direction. Thus the coefficient representation +changes which reciprocal responses are possible in this actual family. +It cuts the minimum total query rank from sixteen to eight. + +This is not a lower bound for other native response families. In +particular, a new interior response need not have the form (1). This +result does not supply a routed controller or a complete supplier price. +The selected kappa value does not change. + +## Ordered identity + +Direct multiplication, using RK=14I, gives + + EG-I=K[12I-13(M+N)+14MN]R. (3) + +The matrices K and R have full column and row rank over the rationals. +Thus EG=I if and only if the bracket in (3) is zero. Equivalently, + + (14M-13I)(14N-13I)=I. (4) + +No commutation of M and N is assumed to derive (3). Equation (4) +implies it: the two factors are inverses of square matrices, so they +commute, and therefore MN=NM. Also GE=I. + +## Dyadic necessity + +Reduce (3) modulo 13. Reduction is defined for every dyadic coefficient +because 2 is invertible modulo 13. The result is + + MN=I over F_13. + +Both reduced matrices are invertible. Their rational determinants are +therefore nonzero, and both rational ranks are eight. The choice +M=N=I gives E=G=I, so the lower bound of sixteen is sharp within (1). + +The same proof applies to any rational coefficient ring that has a +reduction to F_13. In particular, admitting fixed odd denominators +coprime to 13 does not remove this obstruction. The proof does not cover +operator-valued coefficients unless their reduction and rank convention +are specified separately. + +## Rational optimum and all equality cases + +Equation (3) gives + + 12I=13M+(13I-14M)N. + +The rank of the right side is at most rank(M)+rank(N), so this sum is +at least eight. Suppose it equals eight. For v in ker(N), equation (3) +gives Mv=(12/13)v. Hence ker(N) is contained in im(M). Their dimensions +are equal, so im(M)=ker(N). In the same way im(N)=ker(M). + +The two kernels have zero intersection: equation (3) applied to a +vector in both kernels gives 12v=0. Their dimensions sum to eight, +so they form a direct sum. Let P be the projection onto ker(N) along +ker(M). Then M=(12/13)P and N=(12/13)(I-P), as claimed. + +Conversely, for any P with P^2=P, the matrices in (2) have MN=NM=0 +and M+N=(12/13)I. Equation (3) is zero. Their rank sum is eight. + +This proof also gives the general statement. If RK=rho I on an +r-dimensional centre space over a field of characteristic zero, and +rho is not 0, 1, or 2, then the minimum rank sum for reciprocal +extensions of J=I-KR is r. Its equality cases are + + M=((rho-2)/(rho-1))P, + N=((rho-2)/(rho-1))(I-P). + +If a coefficient ring reduces to a field where rho=1, each extension +instead has full centre rank r. For the actual supplier rho=14, so +the relevant prime is 13. + +## What the construction does + +On ker(R), both E and G act as the identity. On im(K), write a vector +as Kc and split c into Pc+(I-P)c. Then + + E Kc=K[-(1/13)Pc-13(I-P)c], + G Kc=K[-13Pc-(1/13)(I-P)c]. + +Thus each map leaves the bulk unchanged and exchanges the two centre +scales with its reciprocal. For a coordinate rank-four P, each extra +term in (1) uses four rows of the actual R. The original rank-eight +centre capture can therefore be restricted to four coordinates if its +helper correction is changed with the same weights. That literal +native implementation is a separate packet. + +The accepted odd-grid representation theorem permits exact division +by a fixed odd integer after root conversion, including arbitrary +borrowed fields. It requires the completed recursive children to have +their stated exact endpoints and charges unfinished prefixes along the +active recursion path. This note uses that theorem only to identify a +legal coefficient representation. It does not prove a precision bound +for an unspecified global controller. + +The forward and reverse scalar responses can now be reciprocal in one +chart. Their physical maps still contain ordered port operators q. +For example, the forward response is qEq in the common full chart. +Changing charts, transporting the code, and the terminal remain open. +Replacing E^T by E^-1 without a separate reverse word is not valid. + +## Verification and source evidence + +The checker reads the pinned actual R from +../lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz. +Its decompressed SHA256 is +a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa. +It checks RK=14I, every coordinate projection on the eight-dimensional +centre, and both full 112-field inverse orders for five coordinate +projections and one noncoordinate projection. It also checks two +mutations that break reciprocity. These exact calculations support the +proof; a finite list of examples is not the rank argument above. + +Run from the workspace root: + + python3 work/centre-encoding-campaign-20261014/root/check_reciprocal_centre_rank_20261018.py + +Expected status: + + PASS_EXACT_RECIPROCAL_CENTRE_RANK + +The source R, clean J, and native capture are inherited from the current +supplier and the earlier clean-core work. The root lane derived the +reciprocal split and rank classification. Oblique-native supplied the +capture and helper-correction plan. The new-native-recipes lane is +checking its literal implementation. This work used OpenAI Codex under +the user's direction. Independent proof review is still required. +No publication is authorized. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-FREEZE-20261018.json b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-FREEZE-20261018.json new file mode 100644 index 0000000000..4f4db4e9fd --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/RECIPROCAL-CENTRE-RANK-FREEZE-20261018.json @@ -0,0 +1,11 @@ +{ + "files": { + "RECIPROCAL-CENTRE-RANK-20261018.json": "6d42a30f888f78b486fdb70cdf150d80562588404e94beec4839061505f806eb", + "RECIPROCAL-CENTRE-RANK-20261018.md": "d2209a60d45d52b6b1d8fed622820acd3468330cc0af926719c3a8747a2606b9", + "check_reciprocal_centre_rank_20261018.py": "e01ad5199c14319e904e7f56d3e675a50722a6d7df2a366efd0273cb19bf71aa" + }, + "publication": "prohibited pending explicit user approval", + "schema": "reciprocal-centre-rank-freeze-v1", + "source_decompressed_sha256": "a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa", + "status": "producer_exact_pass_independent_review_pending" +} diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/check_reciprocal_centre_rank_20261018.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/check_reciprocal_centre_rank_20261018.py new file mode 100644 index 0000000000..2525ec803d --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/frozen/root/check_reciprocal_centre_rank_20261018.py @@ -0,0 +1,107 @@ +#!/usr/bin/env python3 +"""Check the reciprocal centre identity on the pinned actual supplier.""" +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parent / 'lanes/new-core-transfer-20261017/CLEAN-J-PROGRAMS.json.gz' +PIN = 'a6c5dc63a47c1fdb0a97314a3b8541035f507beccb1029762f703039465187fa' + + +def need(value, label): + if not value: + raise ValueError(label) + + +def add(a, b, scale=F(1)): + out = [dict(row) for row in a] + for i, row in enumerate(b): + for j, value in row.items(): + new = out[i].get(j, F(0)) + scale*value + if new: + out[i][j] = new + else: + out[i].pop(j, None) + return out + + +def scale(a, c): + return [{j: c*v for j, v in row.items() if c*v} for row in a] + + +def mul(a, b): + out = [{} for _ in a] + for i, row in enumerate(a): + for k, value in row.items(): + for j, other in b[k].items(): + new = out[i].get(j, F(0)) + value*other + if new: + out[i][j] = new + else: + out[i].pop(j, None) + return out + + +def identity(n): + return [{i: F(1)} for i in range(n)] + + +raw = gzip.decompress(SOURCE.read_bytes()) +need(sha256(raw).hexdigest() == PIN, 'Source pin') +data = json.loads(raw) +R = [{int(k): F(v) for k, v in row.items()} for row in data['R']] +K = [{j: R[j][i]/4 for j in range(8) if i in R[j]} for i in range(112)] +I8, I112 = identity(8), identity(112) +need(mul(R, K) == scale(I8, F(14)), 'Actual RK') +J = add(I112, mul(K, R), F(-1)) +coefficient = F(12, 13) +coordinate_count = 0 +full_cases = [] + + +def bracket(M, N): + return add(add(scale(I8, F(12)), add(M, N), F(-13)), mul(M, N), F(14)) + + +def check_full(P, label): + need(mul(P, P) == P, 'Projection '+label) + M, N = scale(P, coefficient), scale(add(I8, P, F(-1)), coefficient) + E = add(J, mul(mul(K, M), R)) + G = add(J, mul(mul(K, N), R)) + need(mul(E, G) == I112, 'EG '+label) + need(mul(G, E) == I112, 'GE '+label) + full_cases.append({'label': label, 'E_entries': sum(map(len, E)), + 'G_entries': sum(map(len, G))}) + + +for mask in range(256): + P = [{i: F(1)} if (mask >> i) & 1 else {} for i in range(8)] + M, N = scale(P, coefficient), scale(add(I8, P, F(-1)), coefficient) + need(not any(bracket(M, N)), 'Coordinate reciprocal equation') + coordinate_count += 1 + if mask in (0, 1, 15, 127, 255): + check_full(P, 'coordinate-mask-'+str(mask)) + +P = [{0: F(1), 4: F(3, 2)}, {1: F(1), 5: F(-2)}, + {2: F(1), 6: F(1, 2)}, {3: F(1), 7: F(5)}, {}, {}, {}, {}] +check_full(P, 'noncoordinate-rank-four') +M = scale(P, coefficient) +N = scale(add(I8, P, F(-1)), coefficient) +need(any(bracket(scale(P, F(11, 13)), N)), 'Wrong coefficient mutation') +need(any(bracket(M, M)), 'Repeated response mutation') +need(not any(bracket(I8, I8)), 'Sharp dyadic full-rank example') + +proof = HERE / 'RECIPROCAL-CENTRE-RANK-20261018.md' +out = {'status': 'PASS_EXACT_RECIPROCAL_CENTRE_RANK', 'source_sha256': PIN, + 'checker_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'proof_sha256': sha256(proof.read_bytes()).hexdigest(), + 'coordinate_projection_checks': coordinate_count, + 'full_112_field_inverse_checks': full_cases, + 'mutation_checks': ['wrong coefficient', 'repeated response'], + 'scope': 'Exact centre algebra. Native words, global phase transport, and supplier pricing are separate obligations.'} +(HERE / 'RECIPROCAL-CENTRE-RANK-20261018.json').write_text( + json.dumps(out, indent=2, sort_keys=True)+'\n') +print(out['status']) diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/HISTORICAL-ROOT-NOTICE b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/HISTORICAL-ROOT-NOTICE new file mode 100644 index 0000000000..59d8e0cf31 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/HISTORICAL-ROOT-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/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR2226-NOTICE.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR2226-NOTICE.md new file mode 100644 index 0000000000..5ea70357a0 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/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. diff --git a/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR2588-NOTICE b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR2588-NOTICE new file mode 100644 index 0000000000..46411b80b2 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/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/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR2588-NOTICE-PR2226.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR2588-NOTICE-PR2226.md new file mode 100644 index 0000000000..a14b299ef5 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR2588-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/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR3133-CREDITS.md b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR3133-CREDITS.md new file mode 100644 index 0000000000..24f00912d4 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/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/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR3133-NOTICE b/research/reciprocal-native-responses/annexes/original-j-rank-readers/notices/PR3133-NOTICE new file mode 100644 index 0000000000..89c20926ea --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/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/reciprocal-native-responses/annexes/original-j-rank-readers/replay.py b/research/reciprocal-native-responses/annexes/original-j-rank-readers/replay.py new file mode 100644 index 0000000000..b704f915fb --- /dev/null +++ b/research/reciprocal-native-responses/annexes/original-j-rank-readers/replay.py @@ -0,0 +1,163 @@ +#!/usr/bin/env python3 +"""Run the unchanged rank, local-word, grid, and reader checks in fresh copies.""" + +import argparse +from copy import deepcopy +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import platform +import shutil +import subprocess +import sys +import time + + +HERE = Path(__file__).resolve().parent +FROZEN = HERE / "frozen" +HISTORICAL_ROOT = "/Users/aliromman/Projects/IntegerMultiplicationBounds/work/centre-encoding-campaign-20261014" +RANK = "lanes/independent-review-20261017/reciprocal-centre-rank-review-20261018" +NATIVE = "lanes/independent-review-20261017/reciprocal-native-review-20261018" +READER = "lanes/native-escape-20261017/reciprocal-reader-cuts-20261020" +REVIEW = "lanes/native-escape-20261017/owner-review/reciprocal-source-cut-review-20261020" +READER_INPUTS = { + "model": "lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/model-normal-v2/RESPONSE.json.gz", + "native": "lanes/oblique-native-20261017/signed-metric-reciprocal-20261020/native-normal/NATIVE.json.gz", + "views": "lanes/bridge-access-20261017/matched-stage-access-20261018/DIMENSION25-VIEWS.json", + "scalar_tariff": "lanes/new-core-transfer-20261017/low-displacement-20261020/check_response.py", +} +JOBS = [ + ("rank", RANK, "check_reciprocal.py", False, RANK, ["CHECKS.json"]), + ("grid", RANK, "check_grid.py", False, RANK, ["GRID-CHECKS.json"]), + ("original_j_words", NATIVE, "check_words.py", False, NATIVE, ["CHECKS.json"]), + ("reader_producer", READER, "check_cuts.py", True, READER + "/bound-normal", ["CHECKS.json", "READERS.json.gz"]), + ("reader_independent", REVIEW, "check_review.py", True, REVIEW, ["CHECKS.json", "SOURCE-MANIFEST.json", "ORDERED-CONTENTS.json", "ANCHOR-TYPES.json", "CONDITIONAL-READER.json"]), + ("reader_binding", REVIEW, "check_binding.py", True, REVIEW + "/binding-normal", ["CHECKS.json", "SOURCE-MANIFEST.json"]), +] + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def digest(data): + return sha256(data).hexdigest() + + +def encoded(value): + return (json.dumps(value, sort_keys=True, separators=(",", ":")) + "\n").encode() + + +def check_sources(): + manifest = json.loads((HERE / "SOURCES.json").read_text()) + for row in manifest["files"]: + data = (FROZEN / row["path"]).read_bytes() + need(len(data) == row["bytes"] and digest(data) == row["sha256"], "Frozen source: " + row["path"]) + if "decompressed_sha256" in row: + need(digest(gzip.decompress(data)) == row["decompressed_sha256"], "Frozen payload: " + row["path"]) + return manifest + + +def path_manifest(data, root): + """Change only absolute manifest keys to campaign-relative keys.""" + result = {} + prefix = str(root) + "/" + for key, value in json.loads(data).items(): + need(key.startswith(prefix), "Manifest path is inside its declared campaign") + relative = key[len(prefix):] + need((FROZEN / relative).is_file(), "Manifest path has a retained source") + result["$CAMPAIGN/" + relative] = value + return encoded(result) + + +def reader_outputs(directory, root): + """Bind the raw payload, then normalize its four source-path strings.""" + payload_bytes = gzip.decompress((directory / "READERS.json.gz").read_bytes()) + payload = json.loads(payload_bytes) + receipt = json.loads((directory / "CHECKS.json").read_bytes()) + need(digest(payload_bytes) == receipt["payload_decompressed_sha256"], "Reader raw payload matches its receipt") + payload, receipt = deepcopy(payload), deepcopy(receipt) + for obj in (payload, receipt): + need(set(obj["source_pins"]) == set(READER_INPUTS), "Exactly four reader source pins") + for name, relative in READER_INPUTS.items(): + pin = obj["source_pins"][name] + need(pin["path"] == str(root) + "/" + relative, "Exact reader source path: " + name) + source = (FROZEN / relative).read_bytes() + content = gzip.decompress(source) if relative.endswith(".gz") else source + need(pin["sha256"] == digest(content), "Reader source hash: " + name) + pin["path"] = "$CAMPAIGN/" + relative + canonical_payload = encoded(payload) + receipt["payload_decompressed_sha256"] = digest(canonical_payload) + return {"READERS.json.gz": canonical_payload, "CHECKS.json": encoded(receipt)} + + +def comparable(job, directory, root, names): + if job == "reader_producer": + return reader_outputs(directory, root) + return {name: path_manifest((directory / name).read_bytes(), root) + if name == "SOURCE-MANIFEST.json" else (directory / name).read_bytes() + for name in names} + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + out = args.out.resolve() + need(not out.is_relative_to(HERE), "Output must be outside the source annex") + out.parent.mkdir(parents=True, exist_ok=True) + need(shutil.disk_usage(out.parent).free >= 3 * 1024**3, "At least 3 GiB free disk space is required") + out.mkdir(exist_ok=False) + sources = check_sources() + checks = [] + for job, relative, script, has_out, expected_relative, names in JOBS: + previous = None + expected = comparable(job, FROZEN / expected_relative, HISTORICAL_ROOT, names) + for mode in ("normal", "optimized"): + result = out / job / mode + result.mkdir(parents=True) + work = result / "campaign" + shutil.copytree(FROZEN, work) + command = [sys.executable, "-I", "-B"] + (["-O"] if mode == "optimized" else []) + command.append(str(work / relative / script)) + produced = result / "generated" if has_out else work / relative + if has_out: + command += ["--out", str(produced)] + start = time.monotonic() + with (result / "stdout.log").open("w") as log: + run = subprocess.run(command, cwd=work, stdout=log, stderr=subprocess.STDOUT, check=False) + need(run.returncode == 0, "Failed " + job + " " + mode + "; read " + str(result / "stdout.log")) + actual = comparable(job, produced, work, names) + need(actual == expected, "Frozen result comparison: " + job + " " + mode) + need(previous is None or actual == previous, "Normal and optimized comparison: " + job) + previous = actual + files = {} + for name in names: + data = (produced / name).read_bytes() + shutil.copyfile(produced / name, result / name) + files[name] = {"raw_sha256": digest(data), "comparison_sha256": digest(actual[name])} + if name.endswith(".gz"): + files[name]["decompressed_sha256"] = digest(gzip.decompress(data)) + check = {"check": job, "mode": mode, "status": "PASS", "seconds": round(time.monotonic() - start, 3), + "files": files, "all_result_fields_compared": True} + checks.append(check) + shutil.rmtree(work) + if has_out: + shutil.rmtree(produced) + print(job + " " + mode + " PASS", flush=True) + check_sources() + report = {"status": "PASS_ORIGINAL_J_RANK_READERS_ANNEX", "checks": checks, + "source_files": len(sources["files"]), "frozen_sources_unchanged": True, + "source_manifest_sha256": digest((HERE / "SOURCES.json").read_bytes()), + "runner_sha256": digest(Path(__file__).read_bytes()), "python": platform.python_version(), + "platform": platform.platform(), "child_processes_run_concurrently": 1, + "comparison": "Exact bytes for files without source paths. Complete canonical JSON comparison for reader CHECKS, decompressed READERS, and SOURCE-MANIFEST: normalize only the four source paths or manifest keys. Bind the raw reader payload to its raw receipt first, then use the canonical payload hash in the canonical receipt. Compare every other field.", + "omitted": ["Producer native re-emission", "Original 3036-class phase sweep", "Reader native-event replay", "Accumulator supply, transport, and late erasure", "Global controller, recursive supplier, precision, and complete kappa calculation"]} + (out / "REPLAY.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + print(report["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/ANNEX-MANIFEST.json b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/ANNEX-MANIFEST.json new file mode 100644 index 0000000000..2eb1088e7c --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/ANNEX-MANIFEST.json @@ -0,0 +1,185 @@ +{ + "files": [ + { + "bytes": 2319, + "path": "EXTERNAL-NOTICES.json", + "sha256": "580b28d74bb72ca158ab15599baca2bff0e4b43c7bbc43f787d16307ac975709" + }, + { + "bytes": 11357, + 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No new native schedule. All prior package and original-J annex files are unchanged." +} diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/EXTERNAL-NOTICES.json b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/EXTERNAL-NOTICES.json new file mode 100644 index 0000000000..de2d746073 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/EXTERNAL-NOTICES.json @@ -0,0 +1,40 @@ +{ + "files": [ + { + "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "file": "notices/PR2588-NOTICE", + "sha256": "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b", + "source": "research/gmx-t74-borrow43-handoff/NOTICE", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/NOTICE" + }, + { + "commit": "f2927a4b8afcf0701a6b945e14f30de1d94f5176", + "file": "notices/PR3133-NOTICE", + "sha256": "c9731c9cca25ede32c2a1b3aef6d5b249973cb2ed5fb2494407bdca598763661", + "source": "research/coupled-carrier-cap740/vendor/PR3133-NOTICE", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/f2927a4b8afcf0701a6b945e14f30de1d94f5176/research/coupled-carrier-cap740/vendor/PR3133-NOTICE" + }, + { + "commit": "f2927a4b8afcf0701a6b945e14f30de1d94f5176", + "file": "notices/PR3133-CREDITS.md", + "sha256": "1d9d8f56d8899f55878e4cb2c4e052b22506444016a51c2e678773505f5189e6", + "source": "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" + }, + { + "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "file": "notices/PR2588-NOTICE-PR2226.md", + "sha256": "6b6730303818f6edc2a253eb4d05471eee58f28b5815fb250c32ae376f774c8a", + "source": "research/gmx-t74-borrow43-handoff/new/code/borrow/NOTICE-PR2226.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/NOTICE-PR2226.md" + }, + { + "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb", + "file": "notices/PR2226-NOTICE.md", + "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422", + "source": "research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/PR2226-NOTICE.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/blob/8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb/research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/PR2226-NOTICE.md" + } + ], + "scope": "Unchanged notices from verified historical GitHub file objects." +} diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/LICENSE b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/NOTICE.md b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/NOTICE.md new file mode 100644 index 0000000000..7a53b52f11 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/NOTICE.md @@ -0,0 +1,38 @@ +# Sources and credit + +The [source manifest](SOURCES.json) retains all files used by the two +coefficient checkers byte for byte. The coordinating lane supplied the +full-unit exponent parameterization. The controller lane supplied the +actual signed family and the principal-unit classification. The earlier +bridge-review work supplied the six-step ordinary gauge. The signed +matrix source also builds on the oblique-native and budget-geometry +work. Their source credit remains in the retained +[producer proof](frozen/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/RECIPROCAL-CENTRES.md) +and [signed-source proof](frozen/lanes/controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT.md). + +The bridge-review lane supplied the +[independent review](frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md), +integer Bareiss determinant method, separate count recurrence, complete +ordinary-gauge check, and explicit 48-port versus 112-port determinant +scope. The coefficient classification does not inherit a native schedule +for all its new coefficient choices from the older source packet. + +The source data retains the parent native lineage from +[PR #3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133), +[PR #3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148), and +[PR #2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588). +The unchanged [provider notice](notices/PR3133-NOTICE), +[provider credits](notices/PR3133-CREDITS.md), +[recipe-tool notice](notices/PR2588-NOTICE), +[port notice](notices/PR2588-NOTICE-PR2226.md), and +[earlier notice](notices/PR2226-NOTICE.md) preserve that credit. +[EXTERNAL-NOTICES.json](EXTERNAL-NOTICES.json) retains their verified +historical source commits and hashes. No native compiler runs in this +annex, and no individual authorship is inferred from a PR submitter. + +The repository [Apache-2.0 license](LICENSE) applies. Historical notices, +freeze status, and source text remain unchanged. OpenAI Codex gave +substantial assistance in the construction, proofs, checkers, agent +reviews, and extraction. An independent agent review is not a human +review, maintainer acceptance, or formal verification of the complete +integer-multiplication theorem. diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/README.md b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/README.md new file mode 100644 index 0000000000..ae9810d0aa --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/README.md @@ -0,0 +1,145 @@ +# Reciprocal coefficients for the fixed signed 48-port family + +This annex classifies the dyadic coefficients of a fixed signed response +with eight centre rows. Exactly 65,536 responses have a dyadic inverse +and dyadic inverses for both specified principal blocks. This is a +coefficient theorem and a proof of an ordinary gauge on existing data. +It does not supply a native schedule, routed controller, complete +supplier invoice, or kappa improvement. + +The [producer proof](frozen/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/RECIPROCAL-CENTRES.md) +and [independent review](frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md) +use the actual matrix payload. Here a dyadic unit matrix means a matrix +and its inverse both have entries in `Z[1/2]`. + +## Complete coefficient classification + +On the 48-port part, the actual matrices satisfy + +```text +K K^T = 12I_8, G^T=G, G^2=I_48, det(G)=1, +G K^T = K^T Lambda, Lambda=diag(1,-1,1,-1,1,-1,1,-1). +``` + +For dyadic parameters `beta_v`, put `D=diag(beta_v)` and +`E=G-K^T Lambda D K`. Set `s_v=1-12 beta_v`. Then + +```text +det(E) = product_v s_v, +E^-1 = G+K^T Lambda diag(beta_v/s_v) K. +``` + +The full 48-port response is a dyadic unit exactly when + +```text +beta_v = (1-(-2)^n_v)/12, n_v in Z. +``` + +This is an infinite classification. Reduction modulo three and the +dyadic-unit equation prove completeness; a finite exponent check does +not. Inversion sends each exponent `n_v` to `-n_v`. + +The selected physical ports are `S=[0,7,15,36,42,46,79,89]`. Let +`L=E_SS` and let `H` be the principal block on the other 40 centre ports. +The actual selected minor has `det(K_S)=-4` and `G_SS=0`, which gives + +```text +det(L)=det(H)=16 product_v beta_v. +``` + +Thus both principal blocks are dyadic units exactly when every beta_v +is a dyadic unit. Impose the full-response condition as well. Each +exponent must then be one of `-2,-1,1,2`: + +| Exponent n | beta | s | Reciprocal beta | +| ---: | ---: | ---: | ---: | +| 1 | 1/4 | -2 | 1/8 | +| -1 | 1/8 | -1/2 | 1/4 | +| 2 | -1/4 | 4 | 1/16 | +| -2 | 1/16 | 1/4 | -1/4 | + +The eight choices are independent. Different coefficient vectors give +different response matrices, so `4^8=65,536` counts distinct responses. +This finite family is closed under inversion. + +All three unit conditions are necessary for this count. For example, +uniform `beta=1/2` gives two principal units but a full determinant +`5^8`, which is not a dyadic unit. Uniform `beta=3/4` gives a full unit +but does not give principal units. These are retained negative controls. + +## Ordinary gauge and dimension limits + +Let `T=G(S)` and let `R0` contain the other 32 centre ports. Put +`B=diag(alpha_v beta_v)`. The six-step factorization acts on arbitrary +ordinary data `(t,r)`: + +```text +t <- K_T t +t <- t+K_R0 r +t <- -B t +r <- G_R0 r +r <- r+K_R0^T t +t <- K_T^T t +``` + +It gives H. Reversing the steps and inverting each factor gives H^-1. +Each factor is a dyadic unit under the principal-unit condition. No +initial zero, clear, or additional centre field is used. This proves +the representation on existing data; it does not price an elementary +word for every coefficient choice. + +The ordered borrowed interface and its inverse have determinant one on +the 48-port part. The fixed 64-port complement has square `4I` and +determinant `2^64`. Including it gives full 112-port interface determinant +`2^-64`, not one. The distinction is explicit in the independent review. + +Within this fixed signed family, `E^2=I` requires each beta_v to be zero +or `1/6`. Only zero is dyadic, so G is its only dyadic orthogonal member. +This family-specific statement does not constrain the other reciprocal +families in the parent package, including the later `E=P R` construction. + +## Fresh exact checks + +The producer checks both full 112-port inverse orders for six cases and +counts all 65,536 coefficient tuples through the proved determinant +formulas. The independent checker uses integer Bareiss determinants, +nine matrix cases, and a separate eight-step count recurrence. It checks +the six-step gauge and its reverse on all 40 columns in eight cases, +both ordered interface inverse products, and the fixed complement. +Exponent ranges `[-64,64]` and `[-128,128]` are controls for the proof. + +Use Python 3.11 or later, the standard library, at least 3 GiB free space, +and a new output directory. From the repository root: + +```sh +python3 -I -B research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/replay.py --out /tmp/signed-rank-eight-coefficients +``` + +Expected final line: + +```text +PASS_SIGNED_RANK_EIGHT_COEFFICIENT_ANNEX +``` + +The [runner](replay.py) executes both unchanged checkers in normal Python +and with `-O`, one process at a time. All four receipts must match their +frozen bytes. [SOURCES.json](SOURCES.json) records the 13 unchanged source +files. The [fresh replay receipt](evidence/REPLAY.json) records the +relocated run. [ANNEX-MANIFEST.json](ANNEX-MANIFEST.json) binds the final +annex files. The older bipartite native packet is retained as matrix +source and historical context; its native emitter is not rerun here. + +## Open next questions + +A native realization still has to form the eight queries at legal cuts, +place the chosen scatter coefficients, preserve every helper, and verify +its phases. Routed stage composition, terminal decoding, child hosting, +precision, and a complete price remain separate obligations. This annex +does not perform new work on those questions. + +The publication context remains main commit +`b58ad9ef4d4e861b0eaa5dba41742bdc072dca51`, whose selected result names +[PR #4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470). +Historical source pins stay fixed, and no transfer to that construction +is proved. [NOTICE.md](NOTICE.md) records the source credit, license, +and substantial AI assistance. diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/SOURCES.json b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/SOURCES.json new file mode 100644 index 0000000000..d2a7d01274 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/SOURCES.json @@ -0,0 +1,111 @@ +{ + "files": [ + { + "bytes": 657, + "path": "lanes/bridge-review-20261017/reciprocal-centres-review-20261020/FREEZE.json", + "roles": [ + "frozen source record" + ], + "sha256": "a57f64a1ba7bb3245900f06a6e15850a5d3fae3886660eed6e4c8d542603c258" + }, + { + "bytes": 5625, + "path": "lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.json", + "roles": [ + "file bound by lanes/bridge-review-20261017/reciprocal-centres-review-20261020/FREEZE.json" + ], + "sha256": "4ae2a2b13b183d78ac7f2b39bf6b6fabfd631b283fc81faf2aeece9befce8dff" + }, + { + "bytes": 8851, + "path": "lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md", + "roles": [ + "file bound by lanes/bridge-review-20261017/reciprocal-centres-review-20261020/FREEZE.json" + ], + "sha256": "15f67cc3763e642f14101438173b4b36f1ae7d89068bfb0b49cc7e36fadb5aab" + }, + { + "bytes": 12127, + "path": "lanes/bridge-review-20261017/reciprocal-centres-review-20261020/check_review.py", + "roles": [ + "file bound by lanes/bridge-review-20261017/reciprocal-centres-review-20261020/FREEZE.json" + ], + "sha256": "502fa6b230ce35f89b233ff9c32cd825cfd42b63e83ad900186888c1984fa3da" + }, + { + "bytes": 489974, + "decompressed_sha256": "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee", + "path": "lanes/controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz", + "roles": [ + "file bound by lanes/controller-followthrough-20261017/bipartite-eight-20261018/FREEZE.json" + ], + "sha256": "b2fb08cb6325003cf1fa8eaa7bd29279a437ddfc5b9bd0d24561959cd829c01f" + }, + { + "bytes": 4441, + "path": "lanes/controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT.json", + "roles": [ + "file bound by lanes/controller-followthrough-20261017/bipartite-eight-20261018/FREEZE.json" + ], + "sha256": "da5e354b51adb14447d073fb7867902398686471d8592d1c90860ca4aec25771" + }, + { + "bytes": 7368, + "path": "lanes/controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT.md", + "roles": [ + "file bound by lanes/controller-followthrough-20261017/bipartite-eight-20261018/FREEZE.json" + ], + "sha256": "d6cf5e7b2f8adb70a0eeeace3b9528e5c759961de1d79a79c8dbe6e76f36d3dc" + }, + { + "bytes": 1023, + "path": "lanes/controller-followthrough-20261017/bipartite-eight-20261018/FREEZE.json", + "roles": [ + "frozen source record" + ], + "sha256": "c147770b253d8b33a18ba6edb766ab505d203ba8ecd16507764d9a8c1c98e1c1" + }, + { + "bytes": 18893, + "path": "lanes/controller-followthrough-20261017/bipartite-eight-20261018/check_bipartite_eight.py", + "roles": [ + "file bound by lanes/controller-followthrough-20261017/bipartite-eight-20261018/FREEZE.json" + ], + "sha256": "e552e541bf681dc411aeb987bf0903efa367f2acdd3af4d611999b7e947d0b9b" + }, + { + "bytes": 598, + "path": "lanes/controller-followthrough-20261017/reciprocal-centres-20261018/FREEZE.json", + "roles": [ + "frozen source record" + ], + "sha256": "8dbeea6d6ed538592b7f20cb651dd1ad257a1fbaa60c9b0d3c04a2a51e98c99e" + }, + { + "bytes": 5140, + "path": "lanes/controller-followthrough-20261017/reciprocal-centres-20261018/RECIPROCAL-CENTRES.json", + "roles": [ + "file bound by lanes/controller-followthrough-20261017/reciprocal-centres-20261018/FREEZE.json" + ], + "sha256": "5360e919a80d48330df4eadd18b23744f3501d4fdcbf64b68f21e9530643385c" + }, + { + "bytes": 8026, + "path": "lanes/controller-followthrough-20261017/reciprocal-centres-20261018/RECIPROCAL-CENTRES.md", + "roles": [ + "file bound by lanes/controller-followthrough-20261017/reciprocal-centres-20261018/FREEZE.json" + ], + "sha256": "59996d9be93fc257c73eb49b896fcb639ab5019d4b6471be7e04fd3a6cbe3ab3" + }, + { + "bytes": 7332, + "path": "lanes/controller-followthrough-20261017/reciprocal-centres-20261018/check_reciprocal_centres.py", + "roles": [ + "file bound by lanes/controller-followthrough-20261017/reciprocal-centres-20261018/FREEZE.json" + ], + "sha256": "477f29d4ddb16dc24922ed57dbac81bdbcdeb26d5e3490d595b4bc32944e43a1" + } + ], + "schema": "signed-rank-eight-coefficient-sources-v1", + "scope": "Exact frozen closure for the two coefficient checkers. The older bipartite packet supplies the matrix payload and historical context; its native emitter is not replayed." +} diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/PRESERVATION.json b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/PRESERVATION.json new file mode 100644 index 0000000000..bbae49d7e4 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/PRESERVATION.json @@ -0,0 +1,7 @@ +{ + "accepted_parent_files": 152, + "changed": [], + "original_j_files_including_manifest": 126, + "original_j_manifest_sha256": "8c130b4c9d634616e6b31b57a3f356b2094a6b3271d77a5f96c7f8c3c81e7854", + "status": "PASS_PARENT_AND_ORIGINAL_J_ANNEX_UNCHANGED" +} diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/REPLAY.json b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/REPLAY.json new file mode 100644 index 0000000000..7e9495c6ab --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/evidence/REPLAY.json @@ -0,0 +1,46 @@ +{ + "checks": [ + { + "check": "producer", + "equal_frozen_bytes": true, + "mode": "normal", + "receipt_sha256": "5360e919a80d48330df4eadd18b23744f3501d4fdcbf64b68f21e9530643385c", + "seconds": 2.039, + "status": "PASS_RECIPROCAL_SIGNED_CENTRE_FAMILY" + }, + { + "check": "producer", + "equal_frozen_bytes": true, + "mode": "optimized", + "receipt_sha256": "5360e919a80d48330df4eadd18b23744f3501d4fdcbf64b68f21e9530643385c", + "seconds": 2.195, + "status": "PASS_RECIPROCAL_SIGNED_CENTRE_FAMILY" + }, + { + "check": "independent", + "equal_frozen_bytes": true, + "mode": "normal", + "receipt_sha256": "4ae2a2b13b183d78ac7f2b39bf6b6fabfd631b283fc81faf2aeece9befce8dff", + "seconds": 2.196, + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_CLASSIFICATION" + }, + { + "check": "independent", + "equal_frozen_bytes": true, + "mode": "optimized", + "receipt_sha256": "4ae2a2b13b183d78ac7f2b39bf6b6fabfd631b283fc81faf2aeece9befce8dff", + "seconds": 2.166, + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_CLASSIFICATION" + } + ], + "child_processes_run_concurrently": 1, + "comparison": "All four JSON receipts match exact frozen bytes. The source gzip file is immutable; its decompressed payload hash is also checked.", + "frozen_sources_unchanged": true, + "platform": "macOS-26.6.1-arm64-arm-64bit-Mach-O", + "python": "3.14.7", + "runner_sha256": "a0750e44d47d6fd6c49d13b054d8186726b5d9029e36fac6d3c8406e5d3d62ea", + "scope": "The signed48 full-unit and two-principal-unit coefficient classification, its six-step ordinary gauge, and its fixed64 complement. 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The infinite classification is proved in REVIEW.md; the finite controls do not prove completeness. No native schedule, all-stage closure, precision, or supplier invoice is claimed.", + "selected_centre_determinant": "-4", + "six_step_gauge_cases": 8, + "small64_determinant": "18446744073709551616", + "source_payload_decompressed_sha256": "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee", + "status": "PASS_INDEPENDENT_RECIPROCAL_CENTRE_CLASSIFICATION" +} diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md new file mode 100644 index 0000000000..42bf7e5741 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/REVIEW.md @@ -0,0 +1,257 @@ +# Independent review of reciprocal signed centres + +The coefficient theorem passes. For the actual signed 48-port family, +the full response is a dyadic unit exactly when its eight parameters +have the form + +```text +beta_v = (1-(-2)^n_v)/12, with n_v an integer. +``` + +If the full response and both specified principal blocks must all be +dyadic units, each n_v must be one of -2,-1,1,2. This gives exactly +65,536 distinct responses. The family is closed under inversion. + +The four-value conclusion includes the full-unit hypothesis. Principal +units alone admit more choices. For example, the earlier coefficient +beta=1/2 makes both principal blocks dyadic units, while the full +48-port response has determinant 5^8 and is not a dyadic unit. + +The theorem makes a local reciprocal response possible without an odd +denominator in its inverse. It does not supply a native schedule or +identify responses in different stage charts. + +## Source and independent method + +The producer is +`controller-followthrough-20261017/reciprocal-centres-20261018`. +Its freeze SHA-256 is +`8dbeea6d6ed538592b7f20cb651dd1ad257a1fbaa60c9b0d3c04a2a51e98c99e`. +The signed source payload has decompressed SHA-256 +`0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee`. + +This review imports no producer. It uses the actual matrices and +selected ports from that payload. It computes determinants by +integer Bareiss elimination after clearing row denominators. +This differs from the producer's rational Gaussian elimination. +It also checks the six-step ordinary gauge on all 40 input columns, +its inverse in both orders, and the ordered interface inverse. + +The nine matrix cases include all four uniform admitted choices, +a different mixed admitted choice, the old beta=1/2 response, +a full unit with nonunit principal blocks, a singular selected +block, and mixed exponents outside the four-value range. + +## A proof from the actual matrix identities + +The independent checks establish + +```text +K K^T = 12 I_8, +G^T = G, G^2 = I_48, det(G)=1, +G K^T = K^T Lambda. +``` + +Here Lambda has the actual alternating component signs. For diagonal +D=diag(beta_v), define E=G-K^T Lambda D K. Since G K^T=K^T Lambda, + +```text +E = G (I-K^T D K). +``` + +The determinant identity det(I-AB)=det(I-BA) therefore gives + +```text +det(E) = product_v (1-12 beta_v). +``` + +Put s_v=1-12 beta_v. Direct multiplication, using K K^T=12I, +gives + +```text +E^-1 = G + K^T Lambda diag(beta_v/s_v) K. +``` + +This proof needs no unverified choice of component projectors. It +follows from the actual source identities above. It also fixes the +order of the factors and does not commute an intrinsic Q phase +through the response. + +Let R=Z[1/2], and assume every beta_v is in R. Then s_v is nonzero: +beta_v=1/12 is not in R. E is a unit over R if and only if every s_v +is a unit. Necessity follows because a product of elements of a +commutative ring can be a unit only when each factor is a unit. +Sufficiency follows from the displayed inverse. + +## Infinite coefficient classification + +The units of R are +/-2^n. Reduction modulo 3 is defined on R because +2 is invertible modulo 3. The equation s=1-12 beta implies s=1 +modulo 3. Among +/-2^n, exactly one sign has this residue: +s=(-2)^n. + +Conversely, 1-(-2)^n lies in 3R for every integer n. Dividing by 12 +therefore leaves an element of R. Inversion sends s to 1/s and +hence n to -n. + +This proves completeness over all integer exponents. The checker +uses the range -128 through 128 only as a control. That finite +range is not the reason that the classification is complete. + +## Principal blocks + +The selected set is + +```text +S=[0,7,15,36,42,46,79,89]. +``` + +The actual selected matrix K_S has determinant -4, and G_SS=0. +With L=E_SS and H=E_UU on the other 40 centre ports, + +```text +det(L) = det(-K_S^T Lambda D K_S) + = 16 product_v beta_v. +``` + +The selected block of the full inverse is +K_S^T Lambda diag(beta_v/s_v) K_S. Jacobi's complementary +principal-minor identity gives + +```text +det(H) = det(E) det((E^-1)_SS) + = 16 product_v beta_v + = det(L). +``` + +This identity holds for every dyadic coefficient vector, including +vectors with a zero beta. The full response remains invertible over +the rationals in that case, so Jacobi's identity still applies. +Both principal blocks are units over R exactly when all beta_v +are units over R. + +Now impose the full-unit classification as well. For n>0, the +integer 1-(-2)^n is odd. After its factor 3 is removed, beta is a +dyadic unit exactly when + +```text +abs(1-(-2)^n)=3. +``` + +For odd n this is 1+2^n=3, so n=1. For even n this is +2^n-1=3, so n=2. For n=-m<0, clearing 2^m gives the same two +equations with m, and hence n=-1 or n=-2. At n=0, beta=0. +There are no other integer cases. + +The four beta values are 1/4,1/8,-1/4,1/16. Reciprocity exchanges +1/4 with 1/8 and -1/4 with 1/16. + +Different coefficient vectors give different matrices. Indeed, +if K^T Lambda diag(delta_v) K=0, multiplication on the left by K +and on the right by K^T gives 144 Lambda diag(delta_v)=0. +Thus every delta_v is zero. Consequently 4^8 counts distinct +responses, not only formal parameter choices. + +The checker also reproduces the complete determinant distribution +by an eight-step count recurrence. It does not copy the producer's +enumeration of all coefficient tuples. + +## The existing-data gauge + +Let T=G(S), and let R_0 contain the other 32 centre ports. The source +checks establish that T is disjoint from S, K_T is a dyadic unit, +G maps T back to S, and G_R0 is a signed permutation. Thus on the +ordinary coordinates ordered as (T,R_0), the G term is +diag(0,G_R0). + +Put B=diag(alpha_v beta_v). Start with arbitrary data (t,r), and +apply the six steps from the producer: + +```text +t <- K_T t +t <- t+K_R0 r +t <- -B t +r <- G_R0 r +r <- r+K_R0^T t +t <- K_T^T t +``` + +After step three, t=-B(K_T t_initial+K_R0 r_initial). +The last two output expressions are therefore exactly H(t_initial, +r_initial). If every beta_v is a dyadic unit, each step is an +invertible dyadic operation. The two scatter steps are shears. +No value is cleared and no initial zero is used. + +Reversing these six steps and inverting each factor gives H^-1. +The independent checker compares that reverse factor with an +unrelated Gaussian inverse on all 40 columns. This proves the +existing-data representation claim. It does not price the +elementary scalar word for every coefficient choice. + +The ordered block formulas for A and A inverse also pass both +inverse products. On the 48-port centre part, + +```text +det(A)=det(L)/det(H)=1. +``` + +This statement must keep its dimension. The frozen 64-port +complement has square 4I and determinant 2^64. It belongs to the +ordinary block of the full interface. Therefore the corresponding +full 112-port interface has determinant 2^-64, still a dyadic unit. +It does not have determinant one. + +## Orthogonality and scope + +The same identities give + +```text +E^2 = I + K^T diag(12 beta_v^2-2 beta_v) K. +``` + +Multiplication by K and K^T shows that E^2=I exactly when every +beta_v is 0 or 1/6. The latter is not dyadic. Thus the only +orthogonal member with dyadic parameters in this fixed signed +family is G itself. + +This is a family-specific obstruction. New matching responses and +other rank-two responses can lie outside this family. They are +not ruled out by this theorem. + +The useful uniform reciprocal pair is beta=1/4 and beta=1/8. +Both use the same eight centre rows. The theorem permits a native +construction to change their scatter coefficients and keep a +dyadic inverse. It does not prove that the actual schedule can +form those queries at the required cuts. Native phase correctness, +arbitrary helper restoration, complete recursive price, routed +stage composition, and terminal decoding remain separate work. +No kappa improvement follows from this matrix packet alone. + +## Reproduction and credit + +Run from the workspace root: + +```text +python3 -I -B work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/check_review.py +python3 -I -B -O work/centre-encoding-campaign-20261014/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/check_review.py +``` + +Both runs must report: + +```text +PASS_INDEPENDENT_RECIPROCAL_CENTRE_CLASSIFICATION +``` + +The receipts must have equal bytes. FREEZE.json records the proof, +checker, receipt, and source pins. + +The coordinating agent supplied the full-unit exponent +parameterization. The controller lane supplied the principal-unit +classification and the actual coefficient family. The earlier +bridge-review signed-pivot work supplied the six-step gauge. The +signed source also uses the oblique and budget-geometry work. +This independent review used OpenAI Codex assistance. No PR, +commit, or push was made. + +Before a future PR description, read +/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md. diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/check_review.py b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/check_review.py new file mode 100644 index 0000000000..7972821196 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/bridge-review-20261017/reciprocal-centres-review-20261020/check_review.py @@ -0,0 +1,263 @@ +"""Check the actual reciprocal family with exact matrix arithmetic.""" + +from collections import defaultdict +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from math import lcm +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +LANES = HERE.parents[1] +SOURCE = LANES/"controller-followthrough-20261017/reciprocal-centres-20261018" +FREEZE_PIN = "8dbeea6d6ed538592b7f20cb651dd1ad257a1fbaa60c9b0d3c04a2a51e98c99e" +DATA_PIN = "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee" +SELF_PIN = sha256(Path(__file__).read_bytes()).hexdigest() + + +def need(test, message): + if not test: + raise ValueError(message) + + +def identity(n): + return [[F(i==j) for j in range(n)] for i in range(n)] + + +def transpose(a): + return [list(row) for row in zip(*a)] + + +def mul(a,b): + columns = transpose(b) + return [[sum((x*y for x,y in zip(row,col) if x and y), F(0)) for col in columns] for row in a] + + +def add(a,b,c=F(1)): + return [[x+c*y for x,y in zip(row,other)] for row,other in zip(a,b)] + + +def scale(a,c): + return [[c*x for x in row] for row in a] + + +def submatrix(a,rows,columns=None): + columns = rows if columns is None else columns + return [[a[i][j] for j in columns] for i in rows] + + +def diagonal(values): + return [[F(v) if i==j else F(0) for j in range(len(values))] for i,v in enumerate(values)] + + +def determinant(a): + """Clear each row denominator, then use integer Bareiss elimination.""" + n = len(a) + rows, denominator = [], 1 + for row in a: + d = lcm(*(v.denominator for v in row)) + rows.append([int(v*d) for v in row]) + denominator *= d + sign, previous = 1, 1 + for j in range(n-1): + pivot = next((k for k in range(j,n) if rows[k][j]),None) + if pivot is None: + return F(0) + if pivot != j: + rows[j],rows[pivot] = rows[pivot],rows[j] + sign = -sign + value = rows[j][j] + for r in range(j+1,n): + for c in range(j+1,n): + numerator = value*rows[r][c]-rows[r][j]*rows[j][c] + need(numerator%previous == 0, "Exact Bareiss division") + rows[r][c] = numerator//previous + rows[r][j] = 0 + previous = value + return F(sign*rows[-1][-1],denominator) + + +def inverse(a): + n = len(a) + rows = [list(row)+unit for row,unit in zip(a,identity(n))] + for j in range(n): + pivot = next(k for k in range(j,n) if rows[k][j]) + rows[j],rows[pivot] = rows[pivot],rows[j] + value = rows[j][j] + rows[j] = [x/value for x in rows[j]] + for r in range(n): + if r != j and rows[r][j]: + value = rows[r][j] + rows[r] = [x-value*y for x,y in zip(rows[r],rows[j])] + return [row[n:] for row in rows] + + +def dyadic_unit(value): + a,b = abs(value.numerator),value.denominator + return bool(a) and a&(a-1)==0 and b&(b-1)==0 + + +def product(values): + result = F(1) + for value in values: + result *= value + return result + + +def factor_h(kt,kr,gr,coefficients,reverse=False): + rows = identity(40) + if not reverse: + rows[:8] = mul(kt,rows[:8]) + rows[:8] = add(rows[:8],mul(kr,rows[8:])) + rows[:8] = mul(diagonal([-v for v in coefficients]),rows[:8]) + rows[8:] = mul(gr,rows[8:]) + rows[8:] = add(rows[8:],mul(transpose(kr),rows[:8])) + rows[:8] = mul(transpose(kt),rows[:8]) + else: + rows[:8] = mul(inverse(transpose(kt)),rows[:8]) + rows[8:] = add(rows[8:],mul(transpose(kr),rows[:8]),F(-1)) + rows[8:] = mul(gr,rows[8:]) + rows[:8] = mul(diagonal([-1/v for v in coefficients]),rows[:8]) + rows[:8] = add(rows[:8],mul(kr,rows[8:]),F(-1)) + rows[:8] = mul(inverse(kt),rows[:8]) + return rows + + +def block(a,b,c,d): + return [x+y for x,y in zip(a,b)]+[x+y for x,y in zip(c,d)] + + +def main(): + raw = (SOURCE/"FREEZE.json").read_bytes() + need(sha256(raw).hexdigest()==FREEZE_PIN,"Producer freeze pin") + for name,digest in json.loads(raw)["files"].items(): + need(sha256((SOURCE/name).read_bytes()).hexdigest()==digest,"Frozen producer file: "+name) + raw = gzip.decompress((SOURCE.parent/"bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz").read_bytes()) + need(sha256(raw).hexdigest()==DATA_PIN,"Actual signed source") + data = json.loads(raw) + sparse = lambda rows:[{int(p):F(v) for p,v in row.items()} for row in rows] + full_g,full_k,full_response = map(sparse,(data["signed_monomial"],data["centre_rows"],data["response"])) + large,small = data["large_ports"],data["small_ports"] + need(set(large).isdisjoint(small) and set(large)|set(small)==set(range(112)) and + all(set(row)<=set(large) for row in full_k) and + all(not full_g[p] for p in small) and + all(set(full_response[p])<=set(small) for p in small), + "No hidden centre or small-complement cross block") + index = {p:i for i,p in enumerate(large)} + selected = [index[p] for p in data["selected_ports"]] + partners = [index[p] for p in data["partner_ports"]] + residual = [index[p] for p in data["residual_ports"]] + ordinary = partners+residual + need(len(large)==48 and len(small)==64 and len(set(ordinary))==40 and + set(selected).isdisjoint(ordinary),"Actual port partition") + g = [[full_g[p].get(r,F(0)) for r in large] for p in large] + k = [[row.get(p,F(0)) for p in large] for row in full_k] + alpha = list(map(F,data["component_signs"])) + need(alpha==[1,-1,1,-1,1,-1,1,-1],"Actual alternating signs") + kt = transpose(k) + need(mul(k,kt)==scale(identity(8),F(12)),"Exact independent centre rows") + need(g==transpose(g) and mul(g,g)==identity(48) and determinant(g)==1,"Actual signed involution") + need(mul(g,kt)==mul(kt,diagonal(alpha)),"Actual signed centre action") + base = [[full_response[p].get(r,F(0)) for r in large] for p in large] + need(base==add(g,scale(mul(mul(kt,diagonal(alpha)),k),F(1,2)),F(-1)), + "The family contains the actual frozen beta=1/2 response") + ks = submatrix(k,list(range(8)),selected) + kpartner = submatrix(k,list(range(8)),partners) + kr = submatrix(k,list(range(8)),residual) + gr = submatrix(g,residual) + need(determinant(ks)==-4 and abs(determinant(kpartner))==4,"Both selected centre bases") + need(not any(any(row) for row in submatrix(g,selected)),"Selected G is zero") + need(all({j for j,v in enumerate(g[i]) if v} <= set(partners) for i in selected) and + all({j for j,v in enumerate(g[i]) if v} <= set(selected) for i in partners) and + mul(gr,gr)==identity(32),"Partner permutation and residual closure") + small_response = [[full_response[p].get(r,F(0)) for r in small] for p in small] + need(mul(small_response,small_response)==scale(identity(64),F(4)) and + determinant(small_response)==2**64,"Exact full64 complement") + allowed = [F(1,4),F(1,8),F(-1,4),F(1,16)] + cases = [(f"uniform_{v}",[v]*8) for v in allowed] + cases += [ + ("mixed_independent",[allowed[i] for i in (3,3,0,1,2,0,2,1)]), + ("old_principal_units_only",[F(1,2)]*8), + ("full_unit_nonprincipal",[F(3,4)]*8), + ("zero_selected_minor",[F(0)]+[F(1,4)]*7), + ("mixed_unbounded_exponents",[(1-F(-2)**n)/12 for n in (-9,-4,-3,-1,1,3,5,8)]), + ] + reports = [] + for name,beta in cases: + spectral = [1-12*b for b in beta] + need(all(spectral),"All dyadic choices have nonzero centre eigenvalues") + e = add(g,mul(mul(kt,diagonal([a*b for a,b in zip(alpha,beta)])),k),F(-1)) + ei = add(g,mul(mul(kt,diagonal([a*b/s for a,b,s in zip(alpha,beta,spectral)])),k)) + need(mul(e,ei)==mul(ei,e)==identity(48),"Both exact response inverse orders") + l,h = submatrix(e,selected),submatrix(e,ordinary) + dl,dh = determinant(l),determinant(h) + expected = 16*product(beta) + need(dl==dh==expected and determinant(e)==product(spectral),"Direct Bareiss determinants") + result = {"case":name,"beta":[str(v) for v in beta],"det48":str(product(spectral)), + "det_selected":str(dl),"det_ordinary40":str(dh), + "full_dyadic_unit":all(dyadic_unit(s) for s in spectral), + "both_principal_dyadic_units":dyadic_unit(dl)} + if all(beta): + coefficients = [a*b for a,b in zip(alpha,beta)] + literal = factor_h(kpartner,kr,gr,coefficients) + literal_inverse = factor_h(kpartner,kr,gr,coefficients,True) + reference = inverse(h) + need(literal==h and literal_inverse==reference and + mul(literal,literal_inverse)==mul(literal_inverse,literal)==identity(40), + "All40 arbitrary input columns of the six-step gauge and its reverse") + b,d = submatrix(e,selected,ordinary),submatrix(e,ordinary,selected) + li = inverse(l) + a = block(add(scale(l,F(-1)),mul(mul(b,reference),d)),scale(mul(b,reference),F(-1)), + scale(mul(reference,d),F(-1)),reference) + ai = block(scale(li,F(-1)),scale(mul(li,b),F(-1)), + scale(mul(d,li),F(-1)),add(h,mul(mul(d,li),b),F(-1))) + need(mul(a,ai)==mul(ai,a)==identity(48) and determinant(a)==1,"Both local interface inverse orders") + result["six_step_gauge_and_interface"]=True + reports.append(result) + need(reports[5]["full_dyadic_unit"] is False and reports[5]["both_principal_dyadic_units"] is True, + "Principal units alone do not imply the four-value classification") + need(reports[6]["full_dyadic_unit"] is True and reports[6]["both_principal_dyadic_units"] is False, + "Full units alone do not imply principal units") + # Count determinant values by a recurrence, without enumerating the producer's parameter tuples. + states = {(1,4):1} + for _ in range(8): + updated = defaultdict(int) + for (sign,power),count in states.items(): + for dv,dp in ((1,-2),(1,-3),(-1,-2),(1,-4)): + updated[sign*dv,power+dp] += count + states = updated + histogram = {str(F(sign)*F(2)**power):count for (sign,power),count in states.items()} + producer = json.loads((SOURCE/"RECIPROCAL-CENTRES.json").read_bytes()) + need(sum(histogram.values())==65536 and histogram==producer["principal_determinant_histogram"], + "Independent eight-component count and determinant distribution") + exponent_checks = [] + for n in range(-128,129): + s = F(-2)**n + beta = (1-s)/12 + need(beta.denominator&(beta.denominator-1)==0 and + dyadic_unit(beta)==(n in (-2,-1,1,2)),"Independent finite controls of the infinite proof") + need(-beta/s==(1-F(-2)**(-n))/12,"Reciprocity reverses the exponent") + if dyadic_unit(beta): + exponent_checks.append({"n":n,"beta":str(beta),"s":str(s)}) + need(sha256(Path(__file__).read_bytes()).hexdigest()==SELF_PIN,"Checker stayed fixed") + receipt = { + "status":"PASS_INDEPENDENT_RECIPROCAL_CENTRE_CLASSIFICATION", + "checker_sha256":SELF_PIN,"producer_freeze_sha256":FREEZE_PIN, + "source_payload_decompressed_sha256":DATA_PIN,"matrix_cases":reports, + "six_step_gauge_cases":sum("six_step_gauge_and_interface" in r for r in reports), + "parameter_count":65536,"determinant_distribution":histogram, + "finite_exponent_controls":[-128,128],"four_unit_parameters":exponent_checks, + "selected_centre_determinant":str(determinant(ks)), + "partner_centre_determinant":str(determinant(kpartner)), + "small64_determinant":str(2**64),"centre_interface_determinant":"1", + "full112_interface_determinant":str(F(1,2**64)), + "scope":"Exact signed48 family and its fixed64 complement. The infinite classification is proved in REVIEW.md; the finite controls do not prove completeness. No native schedule, all-stage closure, precision, or supplier invoice is claimed.", + } + (HERE/"REVIEW.json").write_text(json.dumps(receipt,indent=2,sort_keys=True)+"\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/controller-followthrough-20261017/bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz new file mode 100644 index 0000000000000000000000000000000000000000..aaebe41c872a3c466a461ecdda9f7e427533d657 GIT binary patch literal 489974 zcmce+g;N~O_dN{3Sv;_~CqQs_haka&WN~+w;0}ufcL?t8vbZ}0cXxMpemtM=`!~E( z)3>UtXL@e;?Q{CvnkEfHg!=FL^nTK|TEWm_P4&ch?2i5OiD~yN?f4qrPyZy&3J<>7 z+K_KGA}Gd1=xairNN8qB5l?VB``D+glcx5qXz@RJMM6imLT|V8La)!Z9dB3d7naMYkxB)G+AdTx%E)a 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z{dwW`Q|0Sd!5pQ(F-NL5mG9ncq76+eri{|iC{N~pmmg`=xc_L%AM^K4R9>|)yPUQe=B*Ug9`ug;F-1Fbt|=MH zh?pgmS9+)!yD;1WQ?q7!=MtfKuR(71tt7+Vz?x>bjS?m8L`0#d6`=PBt8}qVMvP=D{yMDKe8N?ogGc?$JdLF3)C)B*{A`)Hha_6~ z{5o(=5X$@`B5zr5ytcCOAeaS1bXMcxaVSQ1StvL$lPH$X80t|YXul(4ZJ z)A>u7)3CJk+Ag;8m`WvIc?M35A+_~yh9Ms#AUz*epN5)sSHGQ`)AU}aA=aaAQ&RL8 z@ODq?6ByaPun)7V8rd4HYZJN-8FtidA1XeO=3LnE{&J4d(+BG3y;9)w zUeEivQsC?P!&?5w>*v$jxzXoSi|~8Rmc!?%80^Q(8mMpm*2lw|@WZ_2nx41o3FCgt z@s>#d!}7F9)Mx1mSYMsHWh(rGyLEz%Um~rM{w+UySLOHKlB{jDKVTZ-hD={Y$>O%tE! zd&cIL#;y`in-j)^7WFMv-|;oQILGIA*c&}2$F}Z+2hD!HNJpx!)Emu~mcLszUKQ6> zr7fTpKmN8mRV6KHTe{w_JXoL3MelpRUxp*^;xUd$$~uJ=ogL4Ywmxe0, `1-(-2)^n` is odd and +divisible by3. The coefficient beta is a unit if and only if the absolute +value of this numerator is3. This occurs only at n=1 or n=2. For +`n=-m<0`, the same test is `abs(2^m-(-1)^m)=3`, so m=1 or m=2. At n=0, +beta is zero and L is singular. + +The four possible coefficients and their inverses are: + +| n | beta | s | reciprocal beta | +| ---: | ---: | ---: | ---: | +| 1 | 1/4 | -2 | 1/8 | +| -1 | 1/8 | -1/2 | 1/4 | +| 2 | -1/4 | 4 | 1/16 | +| -2 | 1/16 | 1/4 | -1/4 | + +Each of the eight components can use any of these four choices. There +are exactly `4^8=65,536` full-unit responses with both principal units +in this parameter family. The family is closed under inversion. + +For uniform beta, the determinants in (7) are `16 beta^8`. They are +`2^-12` for beta=1/4 or -1/4, `2^-20` for beta=1/8, and `2^-28` for +beta=1/16. These values must not be conflated with each other. + +## Existing data fields can carry the inverse gauge + +The ordinary factor does not need a separate centre bank. Let `T=G(S)` +and let R contain the other 32 centre ports. In the following word, t +and r are arbitrary data. Put `B=diag(alpha_v beta_v)`. + +```text +t <- K_T t +t <- t + K_R r +t <- -B t +r <- G_R r +r <- r + K_R^T t +t <- K_T^T t. (8) +``` + +Expansion gives H exactly. Every factor is a dyadic unit when every +beta_v is a dyadic unit. Reverse the word and invert each factor to +obtain H^-1. This is the same factor order as the frozen eight-port +ordinary gauge. Its central eight scalings have different coefficients. +No owned centre field is required. A native emitter must still price +the concrete coefficient choices and the other boundary factors. + +For `E_beta=[[L,B_s],[D_s,H]]`, the usual diagonal borrowed interface has + +```text +A = [[-L+B_s H^-1 D_s, -B_s H^-1], + [-H^-1 D_s, H^-1]], +A^-1 = [[-L^-1, -L^-1 B_s], + [-D_s L^-1, H-D_s L^-1 B_s]]. +``` + +Equations (6) and (7) give `det(A)=1`. This preserves the local data-unit +interface for all 65,536 choices. It does not make an old Y query legal +at a later cut. + +## Reciprocity is more general than orthogonality + +The real symmetric response (2) is orthogonal if and only if every +`s_v` is +1 or -1. With dyadic beta_v, (5) permits only +1 among those +two values. Hence a dyadic orthogonal response in this family must have +every beta_v=0 and equal G. The nontrivial orthogonal choice beta=1/6 +is not dyadic. It is not needed for the reciprocal pair (1). + +The separate 64-port response in the frozen source has square `4I`. +Its reciprocal is therefore one quarter of itself. Combining that +reciprocal with (3) gives an exact full 112-port inverse. The checker +checks both full inverse orders for all four uniform choices and two +mixed choices. It also checks the selected and ordinary determinants +directly from the 48-port matrices. + +## Verification and use + +Run from the workspace root: + +```text +python3 work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/check_reciprocal_centres.py +python3 -O work/centre-encoding-campaign-20261014/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/check_reciprocal_centres.py +``` + +Both commands must print `PASS_RECIPROCAL_SIGNED_CENTRE_FAMILY` and +produce an identical receipt. The checker imports no producer code. It +reads the pinned matrices, verifies K K^T, G K^T, G^2, the selected +minor, both full inverse orders, direct determinants, and all 65,536 +component combinations through the proved determinant formulas. + +The next native target is the uniform reciprocal pair beta=1/4 and +beta=1/8. A compatible source schedule can reuse all eight centre +queries and change only their scalar scatter coefficients. Full native +replay, recursive cost, routed stage composition, and the terminal +endpoint remain separate checks. No kappa claim is made here. + +This is AI-assisted research. It builds on the controller lane's signed +centre geometry, the bridge-review and budget-geometry principal-minor +proofs, and the oblique-native productive pair-code source schedule. +The coordinating agent supplied the complete exponent parameterization +in (5); this packet adds the principal-unit classification and the +independent component family. diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/check_reciprocal_centres.py b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/check_reciprocal_centres.py new file mode 100644 index 0000000000..e846d91cbf --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/frozen/lanes/controller-followthrough-20261017/reciprocal-centres-20261018/check_reciprocal_centres.py @@ -0,0 +1,171 @@ +#!/usr/bin/env python3 +"""Check the signed centre family and its exact reciprocal parameters.""" + +from collections import defaultdict +from fractions import Fraction as F +from hashlib import sha256 +from itertools import product +from pathlib import Path +import gzip +import json + + +HERE = Path(__file__).resolve().parent +SOURCE = HERE.parent / "bipartite-eight-20261018/BIPARTITE-EIGHT-PROGRAM.json.gz" +PIN = "0c832994c1d06562a8db0b9b3d940f6f6143c37beed983f874a69f2bf6ecfdee" + + +def need(value, message): + if not value: + raise RuntimeError(message) + + +def clean(row): + return {p: v for p, v in row.items() if v} + + +def mul(a, b): + result = [] + for row in a: + out = defaultdict(F) + for middle, left in row.items(): + for column, right in b[middle].items(): + out[column] += left * right + result.append(clean(out)) + return result + + +def transpose(a, columns): + out = [{} for _ in range(columns)] + for i, row in enumerate(a): + for j, value in row.items(): + out[j][i] = value + return out + + +def restrict(a, ports): + index = {p: i for i, p in enumerate(ports)} + return [{index[p]: v for p, v in a[row].items() if p in index} for row in ports] + + +def determinant(a): + n = len(a) + rows = [[a[i].get(j, F(0)) for j in range(n)] for i in range(n)] + result = F(1) + for i in range(n): + pivot = next((j for j in range(i, n) if rows[j][i]), None) + if pivot is None: + return F(0) + if pivot != i: + rows[i], rows[pivot] = rows[pivot], rows[i] + result = -result + value = rows[i][i] + result *= value + for j in range(i + 1, n): + if rows[j][i]: + ratio = rows[j][i] / value + rows[j] = [a - ratio * b for a, b in zip(rows[j], rows[i])] + return result + + +def unit(value): + numerator, denominator = abs(value.numerator), value.denominator + return bool(numerator) and numerator & (numerator - 1) == 0 and denominator & (denominator - 1) == 0 + + +def dyadic(value): + return value.denominator & (value.denominator - 1) == 0 + + +def multiply(values): + out = F(1) + for value in values: + out *= value + return out + + +def main(): + raw = gzip.decompress(SOURCE.read_bytes()) + need(sha256(raw).hexdigest() == PIN, "Pinned source changed") + source = json.loads(raw) + decode = lambda rows: [{int(p): F(v) for p, v in row.items()} for row in rows] + base, g, k = decode(source["response"]), decode(source["signed_monomial"]), decode(source["centre_rows"]) + large, small, selected = source["large_ports"], source["small_ports"], source["selected_ports"] + partners = source["partner_ports"] + ordinary = sorted(set(large) - set(selected)) + alpha = [F(v) for v in source["component_signs"]] + kt = transpose(k, 112) + need(mul(k, kt) == [{i: F(12)} for i in range(8)], "Actual K K transpose is 12I") + expected_gk = [{j: value * alpha[j] for j, value in row.items()} for row in kt] + need(mul(g, kt) == expected_gk, "Actual G K transpose is K transpose Lambda") + need(mul(g, g) == [{p: F(1)} if p in large else {} for p in range(112)], "G is an involution on48") + need(not any(restrict(g, selected)), "Selected G block is zero") + need(determinant([kt[p] for p in selected]) == F(-4), "Selected centre minor has determinant -4") + + def response(beta, reciprocal_small=False): + out = [dict(row) for row in g] + for v, centre in enumerate(k): + for p, left in centre.items(): + for q, right in centre.items(): + out[p][q] = out[p].get(q, F(0)) - beta[v] * alpha[v] * left * right + for p in small: + out[p] = {q: value / (4 if reciprocal_small else 1) for q, value in base[p].items()} + return [clean(row) for row in out] + + identity = [{p: F(1)} for p in range(112)] + allowed = [F(1, 4), F(1, 8), F(-1, 4), F(1, 16)] + cases = [(f"uniform_{value}", [value] * 8) for value in allowed] + cases += [("mixed_four_parameters", allowed * 2), + ("mixed_reverse_parameters", list(reversed(allowed)) * 2)] + reports = [] + for name, beta in cases: + spectral = [1 - 12 * value for value in beta] + reciprocal = [-value / s for value, s in zip(beta, spectral)] + e, ei = response(beta), response(reciprocal, reciprocal_small=True) + need(mul(e, ei) == identity and mul(ei, e) == identity, "Both full112 reciprocal orders") + dl = determinant(restrict(e, selected)) + dh = determinant(restrict(e, ordinary)) + expected = 16 * multiply(beta) + need(dl == dh == expected and unit(dl), "Both actual principal determinants") + need(determinant(restrict(e, large)) == multiply(spectral), "Actual48 response determinant") + reports.append({"case": name, "beta": [str(v) for v in beta], + "reciprocal_beta": [str(v) for v in reciprocal], + "selected_determinant": str(dl), "ordinary40_determinant": str(dh), + "response48_determinant": str(multiply(spectral)), + "both_full112_inverse_orders": True}) + + parameters = [] + for exponent in range(-64, 65): + spectral = F(-2) ** exponent + beta = (1 - spectral) / 12 + need(dyadic(beta), "Every sampled integral exponent gives a dyadic coefficient") + need(unit(beta) == (exponent in (-2, -1, 1, 2)), "Only the four nonzero principal-unit parameters") + parameters.append({"n": exponent, "beta": str(beta), "s": str(spectral), "beta_is_unit": unit(beta)}) + + count = 0 + determinant_histogram = defaultdict(int) + for beta in product(allowed, repeat=8): + spectral = [1 - 12 * value for value in beta] + reciprocal = [-value / s for value, s in zip(beta, spectral)] + need(all(v in allowed for v in reciprocal), "The four-parameter family is closed under inversion") + value = 16 * multiply(beta) + need(unit(value) and all(unit(s) for s in spectral), "All component choices give full and principal units") + determinant_histogram[str(value)] += 1 + count += 1 + need(count == 65536, "The independent eight-component count is4^8") + receipt = {"status": "PASS_RECIPROCAL_SIGNED_CENTRE_FAMILY", + "scope": "Exact coefficient family and actual source matrix checks; independently adjustable centre scatter and full native composition remain implementation premises", + "source_payload_decompressed_sha256": PIN, + "selected_ports": selected, "partner_ports": partners, + "full112_matrix_cases": reports, "component_choice_count": count, + "principal_determinant_histogram": dict(sorted(determinant_histogram.items())), + "exponent_spot_check_range": [-64, 64], + "exponent_classification_basis": "The proof uses reduction modulo3 and the exact dyadic-unit equations, not a bounded search", + "parameters_with_both_units": [v for v in parameters if v["beta_is_unit"]], + "checker_sha256": sha256(Path(__file__).read_bytes()).hexdigest()} + (HERE / "RECIPROCAL-CENTRES.json").write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + print(receipt["status"]) + + +if __name__ == "__main__": + main() diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR2226-NOTICE.md b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR2226-NOTICE.md new file mode 100644 index 0000000000..5ea70357a0 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/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. diff --git a/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR2588-NOTICE b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR2588-NOTICE new file mode 100644 index 0000000000..46411b80b2 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/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/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR2588-NOTICE-PR2226.md b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR2588-NOTICE-PR2226.md new file mode 100644 index 0000000000..a14b299ef5 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR2588-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/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR3133-CREDITS.md b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR3133-CREDITS.md new file mode 100644 index 0000000000..24f00912d4 --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/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/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR3133-NOTICE b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/notices/PR3133-NOTICE new file mode 100644 index 0000000000..89c20926ea --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/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/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/replay.py b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/replay.py new file mode 100644 index 0000000000..b223a7598e --- /dev/null +++ b/research/reciprocal-native-responses/annexes/signed-rank-eight-coefficients/replay.py @@ -0,0 +1,91 @@ +#!/usr/bin/env python3 +"""Run the unchanged signed-family coefficient checks in fresh copies.""" + +import argparse +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import platform +import shutil +import subprocess +import sys +import time + + +HERE = Path(__file__).resolve().parent +FROZEN = HERE / "frozen" +CHECKS = [ + ("producer", "lanes/controller-followthrough-20261017/reciprocal-centres-20261018", + "check_reciprocal_centres.py", "RECIPROCAL-CENTRES.json"), + ("independent", "lanes/bridge-review-20261017/reciprocal-centres-review-20261020", + "check_review.py", "REVIEW.json"), +] + + +def need(value, message): + if not value: + raise ValueError(message) + + +def digest(data): + return sha256(data).hexdigest() + + +def check_sources(): + manifest = json.loads((HERE / "SOURCES.json").read_text()) + for row in manifest["files"]: + data = (FROZEN / row["path"]).read_bytes() + need(len(data) == row["bytes"] and digest(data) == row["sha256"], "Frozen source: " + row["path"]) + if "decompressed_sha256" in row: + need(digest(gzip.decompress(data)) == row["decompressed_sha256"], "Frozen matrix payload") + return manifest + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument("--out", type=Path, required=True) + args = parser.parse_args() + out = args.out.resolve() + need(not out.is_relative_to(HERE), "Output must be outside the source annex") + out.parent.mkdir(parents=True, exist_ok=True) + need(shutil.disk_usage(out.parent).free >= 3 * 1024**3, "At least 3 GiB free disk space is required") + out.mkdir(exist_ok=False) + manifest = check_sources() + results = [] + for name, relative, script, receipt in CHECKS: + expected = (FROZEN / relative / receipt).read_bytes() + for mode in ("normal", "optimized"): + result = out / name / mode + result.mkdir(parents=True) + work = result / "campaign" + shutil.copytree(FROZEN, work) + command = [sys.executable, "-I", "-B"] + (["-O"] if mode == "optimized" else []) + command.append(str(work / relative / script)) + start = time.monotonic() + with (result / "stdout.log").open("w") as log: + run = subprocess.run(command, cwd=work, stdout=log, stderr=subprocess.STDOUT, check=False) + need(run.returncode == 0, "Failed " + name + " " + mode + "; read " + str(result / "stdout.log")) + actual = (work / relative / receipt).read_bytes() + need(actual == expected, "Exact frozen receipt comparison: " + name + " " + mode) + (result / receipt).write_bytes(actual) + results.append({"check": name, "mode": mode, "status": json.loads(actual)["status"], + "seconds": round(time.monotonic() - start, 3), + "receipt_sha256": digest(actual), "equal_frozen_bytes": True}) + shutil.rmtree(work) + print(name + " " + mode + " PASS", flush=True) + check_sources() + report = {"status": "PASS_SIGNED_RANK_EIGHT_COEFFICIENT_ANNEX", "checks": results, + "source_files": len(manifest["files"]), "frozen_sources_unchanged": True, + "runner_sha256": digest(Path(__file__).read_bytes()), + "source_manifest_sha256": digest((HERE / "SOURCES.json").read_bytes()), + "python": platform.python_version(), "platform": platform.platform(), + "child_processes_run_concurrently": 1, + "comparison": "All four JSON receipts match exact frozen bytes. The source gzip file is immutable; its decompressed payload hash is also checked.", + "scope": "The signed48 full-unit and two-principal-unit coefficient classification, its six-step ordinary gauge, and its fixed64 complement. No new native schedule, native phase replay, all-stage composition, precision, supplier invoice, or complete kappa claim."} + (out / "REPLAY.json").write_text(json.dumps(report, indent=2, sort_keys=True) + "\n") + print(report["status"]) + + +if __name__ == "__main__": + main()