diff --git a/research/released-operator-clifford-ceiling/.gitattributes b/research/released-operator-clifford-ceiling/.gitattributes new file mode 100644 index 0000000000..a99fce74c1 --- /dev/null +++ b/research/released-operator-clifford-ceiling/.gitattributes @@ -0,0 +1,2 @@ +# Immutable scientific captures retain original CRLF/LF bytes. +evidence/** -text whitespace=cr-at-eol diff --git a/research/released-operator-clifford-ceiling/EVIDENCE.json b/research/released-operator-clifford-ceiling/EVIDENCE.json new file mode 100644 index 0000000000..ad4f4273be --- /dev/null +++ b/research/released-operator-clifford-ceiling/EVIDENCE.json @@ -0,0 +1,59 @@ +{ + "files": { + "evidence/budget/FILES.json": "c1c7875633176583fcf5bfbaacdafa00806bf2e38bb15679fac0ed8a2f1eb720", + "evidence/budget/FREEZE.json": "862abf75a4440731d2aa8b66ad2a93f1b3fcee4e6ebca19cc1dcf665bfa782ee", + "evidence/budget/REPORT.md": "b8b785a815852069b27ee6b18337b6ecd64127c7a22985d0e4221a2fc11bd53a", + "evidence/budget/RESULT-OPTIMIZED.json": "b11a56c453c6f174780edd0cd19c638da7d1552ac9f3f0ff6f8340d8ada382ae", + "evidence/budget/RESULT.json": "b11a56c453c6f174780edd0cd19c638da7d1552ac9f3f0ff6f8340d8ada382ae", + "evidence/budget/check_budget.py": "e961496628064ac6257a1f6ae3bf660719ee563b07800c2b40cea25b9da9ed2b", + "evidence/independent-review/FILES.json": "22cdbdef8b15117c3324d5544179e5ff52e5cae72148e42beb7cfa08b5c1ba12", + "evidence/independent-review/POINT-BUDGET.json": "de9a8b784249c84587e5dfbe3e6e3cdaca5a432e9667d17e14d1d0a2f2b79f6d", + "evidence/independent-review/REVIEW-RESULT.json": "2e77399d0bdbf216b0a7a6b2345706a27d7dac1e0c5a80e8b2b62abb81ab2165", + "evidence/independent-review/REVIEW.md": "23b5aa5df049cb4a8fe3349c054e27d84ca151e29e263c658670639bad082428", + "evidence/independent-review/SOURCES.json": "249dbf14d6c43c6482ab7825f9de7251e00e79ee72261860cbc9422e954545de", + "evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json": "e2e02bb5089821f2f256b8efbb79f14172b4ab3bd9f482bc9e2de2aa14cd506e", + "evidence/independent-review/frozen/INVENTORY-REPORT.md": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "evidence/independent-review/frozen/RELEASE-PRIMARY.json": "1aa74f9b72d60a4e4357bc3ea9e70c650c870432714aed11b2cda46518f74952", + "evidence/independent-review/frozen/REVIEWED-PROOF.md": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "evidence/independent-review/frozen/research__coded-active-query-bound__PROOF.md": "495a1cd85cc45020adf2205f196b57dc4f65f1eb763fc4951facdb4ccbafc768", + "evidence/independent-review/frozen/research__coded-active-query-bound__README.md": "95269b047c19069caeb11edd36a485a0a86275b329aa44da90c8c08403e09178", + "evidence/independent-review/frozen/research__coded-active-query-bound__SOURCES.json": "afb6ca7a3b924d19b61b784266693b892722024d5a33de3e432fc6499238241e", + "evidence/independent-review/frozen/research__coded-native-caller__NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "evidence/independent-review/frozen/research__coded-native-caller__PHYSICAL.md": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "evidence/independent-review/frozen/research__coded-native-caller__clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "evidence/independent-review/frozen/research__coded-native-caller__normalizers.py": "7616b75758c1b36b6c05eb7fff1630f604e7563762701bccb18ec638a61090df", + "evidence/independent-review/frozen/research__native-center-free-code__CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "evidence/inventory/FILES.json": "8ca981b54bd1d6a8e08c80836119b0efeca236c69fff14bb601b2faba1a1f654", + "evidence/inventory/REPORT.md": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "evidence/inventory/SOURCES.json": "e19a7a22d535a438911c28aa3fc36daf7b0a3db582ccc429d986bb981dad68c7", + "evidence/inventory/source/RELEASE-MONITOR.json": "1aa74f9b72d60a4e4357bc3ea9e70c650c870432714aed11b2cda46518f74952", + "evidence/inventory/source/research__coded-active-query-bound__PROOF.md": "495a1cd85cc45020adf2205f196b57dc4f65f1eb763fc4951facdb4ccbafc768", + "evidence/inventory/source/research__coded-active-query-bound__README.md": "95269b047c19069caeb11edd36a485a0a86275b329aa44da90c8c08403e09178", + "evidence/inventory/source/research__coded-active-query-bound__SOURCES.json": "afb6ca7a3b924d19b61b784266693b892722024d5a33de3e432fc6499238241e", + "evidence/inventory/source/research__coded-native-caller__NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "evidence/inventory/source/research__coded-native-caller__PHYSICAL.md": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "evidence/inventory/source/research__coded-native-caller__clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "evidence/inventory/source/research__coded-native-caller__normalizers.py": "7616b75758c1b36b6c05eb7fff1630f604e7563762701bccb18ec638a61090df", + "evidence/inventory/source/research__native-center-free-code__CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "evidence/proof/PROOF.md": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "evidence/proof/SOURCE-CHECK.json": "e2e02bb5089821f2f256b8efbb79f14172b4ab3bd9f482bc9e2de2aa14cd506e", + "evidence/proof/SOURCE-FLAG-CHECK.json": "a6c30f6dc14c0673e6043ac6197ae460ce03e9e3b139146ebcb6766ecb1d088e", + "evidence/proof/SOURCES.json": "e810407fc34de1f3af196fc86e91e680075ff982bbc6fe19d6ebb02f2a0c0d9c", + "evidence/proof/check_source_and_flag.py": "025ba8f3f63fa4f4d7155a32f0f51de210693f6b425b047312d5f232e96fdc5f", + "evidence/proof/frozen/CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "evidence/proof/frozen/NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "evidence/proof/frozen/NOTICE": "317b1c5e040bab50ebfc3d0cdb3a47fc30e2f872a00895f563d7931749b1cc7b", + "evidence/proof/frozen/ORIGINS.json": "10cf47173ca238c32adb923daae7c1137c2e9c86c7066301d68fc74442b3f4d7", + "evidence/proof/frozen/PHYSICAL.md": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "evidence/supplements/FILES.json": "ecae9b828f080ea82b9fe3df3b9b01501a3ef0d1e251e772c031d79c151ea7d0", + "evidence/supplements/PAID-SHEAR-ADDENDUM.md": "c40812090fd1abd85ece881873c92729caf48d24a75338fd1a64457b56f1748b", + "evidence/supplements/SOURCE-FLAG-REVIEW.md": "3f7982e0ad104102847f05e6f6e544a42da84bf613de9a978e5e303ef8b8734d", + "evidence/supplements/SOURCES.json": "f5c88f371bc125e9dbb15e6ecbae68e2ce2573d81f0329b56775cc9a6f770021", + "evidence/supplements/frozen/CONTRACT.md": "a1001f481df15046cd09d647c6fd5539196664277be849d7c2a260a3290643cc", + "evidence/supplements/frozen/PAID-SHEAR-SCREEN.md": "81fefcf4a1be0be04076e7cba0e27ba4afe732d4810a13b0a76dbe827967c10c", + "evidence/supplements/frozen/SOURCE-FLAG-CHECK.json": "a6c30f6dc14c0673e6043ac6197ae460ce03e9e3b139146ebcb6766ecb1d088e", + "evidence/supplements/frozen/check_source_and_flag.py": "025ba8f3f63fa4f4d7155a32f0f51de210693f6b425b047312d5f232e96fdc5f" + }, + "schema_version": 1, + "status": "immutable original author and review bytes" +} diff --git a/research/released-operator-clifford-ceiling/HISTORY.md b/research/released-operator-clifford-ceiling/HISTORY.md new file mode 100644 index 0000000000..21df2d0a7c --- /dev/null +++ b/research/released-operator-clifford-ceiling/HISTORY.md @@ -0,0 +1,41 @@ +# Evidence and correction history + +The immutable evidence tree retains the final source inventory, final revised +proof, independent review and exact interval budget, with their original +local/pending-status text and source pins. Those status strings are historical +records, not a claim that a native caller was admitted later. + +The proof and review explicitly preserve and reject the tempting inference +`D3 H0 D3^-1 = H0`. The correct support is `Ht = D3 H0 D3^-1`. +A transported letter can shift the central X direction by a W vector; only +the quotient central class is fixed. The finite binary witness and its +negative controls support that distinction. An earlier rejected draft is +not available in the supplied packet; no reconstruction is presented as an +original historical draft. + +Raw Git snapshots under each original evidence folder retain their exact +bytes, including existing terminal LF bytes. All supplied scientific and +context captures checked against their declared Git blobs match raw Git; +none required removal or addition of an LF. The capture manifests and original +release-monitor receipt are preserved. No source was silently normalized. + +The original static SOURCE-CHECK was an inline source inspection. The later +retained check_source_and_flag.py separately regenerates the exact source +properties and one binary transported-flag witness; its receipt is not an +absolute-phase or theorem certificate. The independently reviewed written +proof remains the source of the sufficiently-large-width conclusion. + +The separate paid-shear CONTRACT.md was excluded from the original main theorem +packet. After its own independent review, its exact stopped-proposal bytes and +PAID-SHEAR-SCREEN are retained in a distinct supplementary capsule, not as an +accepted construction. All original main evidence bytes remain unchanged. +The budget's 44 H1 result is an unrealized-profile raw allowance only and is +not promoted into an actual paid control, compiler reserve or new κ. + +The first local staging attempt (commit dd5d13bf8830d96f389bf1a4599471f3ec237909) +was rejected by the working-versus-commit byte check: inherited text=auto +normalized three CODE.json copies from their original CRLF to LF. No source +or receipt was changed to accommodate it. A module-local .gitattributes marks +immutable evidence -text; the subsequent commit restores the exact original +8be7f3... source bytes. This failed staging result is retained as a packaging +control, not scientific evidence or the final export. diff --git a/research/released-operator-clifford-ceiling/LICENSE b/research/released-operator-clifford-ceiling/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/released-operator-clifford-ceiling/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. Definitions. + + "License" shall mean the terms and conditions for use, reproduction, + and distribution as defined by Sections 1 through 9 of this document. + + "Licensor" shall mean the copyright owner or entity authorized by + the copyright owner that is granting the License. + + "Legal Entity" shall mean the union of the acting entity and all + other entities that control, are controlled by, or are under common + control with that entity. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/released-operator-clifford-ceiling/NOTICE b/research/released-operator-clifford-ceiling/NOTICE new file mode 100644 index 0000000000..59d8e0cf31 --- /dev/null +++ b/research/released-operator-clifford-ceiling/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/released-operator-clifford-ceiling/README.md b/research/released-operator-clifford-ceiling/README.md new file mode 100644 index 0000000000..b87381b2dc --- /dev/null +++ b/research/released-operator-clifford-ceiling/README.md @@ -0,0 +1,155 @@ +# Released-operator Clifford ceiling and conditional complete-invoice allowance + +This package preserves a source-bound written obstruction for the released +[two-FULL/one-query construction target](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19143357). +Within **fixed finite columnwise monomial-Clifford plus scalar-owner programs**, +no all-width invertible `t0` satisfies the four declared free-membership +conditions. The proof gives zero `t0` at every sufficiently large width; it +allows exceptional small widths. It does not classify every physically FREE +program. No successful controller, complete caller or new κ is supplied. + +The independent review passes the corrected argument, including the essential +transported class `Ht = D3 H0 D3^-1`. It does not replace this class by `H0`. +See the unchanged [proof](evidence/proof/PROOF.md), +[independent review](evidence/independent-review/REVIEW.md), and +[source inventory](evidence/inventory/REPORT.md). These original local reports +retain their original pending/local status wording; packaging records their +subsequent review and makes no human or kernel acceptance claim. + +## Exact model and source binding + +On the actual 17 axes `q + U8 + W8`, the source normalizers define +`Cs[i,j] = A[i,j] Ks,i^-1 Ks,j`. Each address letter is lifted columnwise; +scalar owner sums are applied once, rather than tensoring an owner sum. +The released conditions require `t0`, `Q^-1 t0 Q`, `t = D3 t0 D3^-1`, +`E = Q^-1 C3 t C1 Q^-1`, and explicit implementations of their inverses. +The source endpoint is +`F3 J(t0) F1 = [[0,t],[-E,0]] diag(G,G)`, with `G = D1 D3 Q`. + +The scientific source is `4c0a359d88f22f05189d51f48387750b801a45d4`; +local-query context is `0e8a13c251a9be1029114cda8b4194f05f3a23ec`. +The latter's enlarged query alphabet is not adopted as an executable free +alphabet. The publication base is `a5df48c55ea806d7952b65acc9c76d878ff09b13`. +Every retained raw Git source capture is byte-exact, including its existing +line endings: no global LF normalization is performed. Original inventory, +author and reviewer source manifests are retained. Package [SOURCES.json](SOURCES.json) +binds the reachable raw Git blobs; [EVIDENCE.json](EVIDENCE.json) binds all +unchanged original science and receipts. See [HISTORY.md](HISTORY.md). + +The proof allows width-dependent scalar coefficients in a fixed finite +one-column Clifford universe. Uniform tensor separation supplies the +sufficiently-large-width conclusion. Arbitrary noncolumnwise routing, +non-Clifford phases, growing alphabets, extra axes, changed paid words, +changed codes or changed productive targets are outside it. COPY and owned +clear/reset are allowed within its resulting finite-expansion model; this +is not permission to discard arbitrary independent original inputs. + +## Conditional invoice, before completion costs + +The separate [exact arithmetic report](evidence/budget/REPORT.md) assumes the +**unrealized** complete profile +`T = 224 H17 + 816 H9` and +`P = 4608 H1 + 838 H2 + 1020 H3 + 254 H4 + 136 H5`. +It retains each of the 816 independent helper jobs exactly once. Two native +FULL profiles, the original 112-query bank, and all helper-complement costs +are charged. Owned query fields earn no new arbitrary-input reward. + +For `H_r(C) = r^(1-C)`, the signed moment is strictly decreasing on +`C ∈ [0.0030217758, 0.00339999]`. Its endpoint margins are enclosed by +`52.133114229301600459209653..654` and +`44.676959553589208855078743..744`. Thus **44 additional H1** is maximal +for strict raw positivity uniformly on this closed interval; 45 fails at +the upper endpoint, and another 112 H1 loses throughout. This is a raw +conditional allowance, before ordinary work, finite arithmetic, precision, +storage, endpoint completion, compiler reserve or outer transfer. It is not +funding for an actual control. A separate stopped paid-shear proposal is retained only in the distinct +appendix below; it is not an admitted construction or part of the FREE theorem. + +## Separate appendix: stopped scalar-owner paid shears + +The unchanged [paid-screen proof](evidence/supplements/frozen/PAID-SHEAR-SCREEN.md) +and its [independent review](evidence/supplements/PAID-SHEAR-ADDENDUM.md) +close one distinct extension before search. For +`S_k = I + u_k v_k^T tensor H_k`, with scalar owner vectors and address +words in the fixed commuting group generated by Pauli-X Gaussians, +the projective identity coefficient of `t0` must vanish for a monomial +endpoint. Scalar column-space rank then requires **m >= 112**. +Width-dependent scalar coefficients and dense owner vectors are included. +The written proof remains a sufficiently-large-width statement. + +Only the narrower explicit rank-two implementation in the retained +[stopped CONTRACT](evidence/supplements/frozen/CONTRACT.md) has the +execution bill `3m H2`: two independent middle arguments and one inverse. +This is an execution bill, not a lower bound on every implementation or +on every address word of the larger theorem group. Seven shears fit the +raw allowance; eight fail at the upper endpoint. Hence that explicit +priced subclass cannot close the endpoint. No shear search or emitter ran. +The retained CONTRACT is superseded by this stop certificate, not a +successful physical construction. Operator-valued owner/address gathers, +other noncommuting alphabets, retained native/query observations and +changed endpoints are excluded. No universal fresh-query lower bound follows. + +The original main proof/review/budget bytes remain unchanged. The separate +[source/flag inspection](evidence/supplements/SOURCE-FLAG-REVIEW.md) also +passes with its binary-only scope. The hook authenticates these written +appendices and checks their 7/8-count arithmetic support; it does not +machine-check the scalar coefficient rank argument. + +## Reproduce and interpret the checks + +From repository root: + +```sh +python3 -I -W error -B research/released-operator-clifford-ceiling/verify.py +python3 -I -O -W error -B research/released-operator-clifford-ceiling/verify.py +python3 -B scripts/research_package.py --package research/released-operator-clifford-ceiling --check-only +python3 -B scripts/research_package.py --package research/released-operator-clifford-ceiling +``` + +CPython 3.12, standard library only; both direct runs are bounded by 120 seconds. +The default verifier writes only in a private temporary directory. It authenticates +53 original evidence files and their nested manifests, then reruns the unchanged +author source/flag checker and conditional budget engine. It compares the full +regenerated receipts byte-for-byte. The budget loader mirrors the original +logical inventory path in private scratch and changes only `HERE`/`STOCK`; +`__file__`, scientific functions and all output fields remain unchanged. +No path-field canonicalization or edited receipt is used. + +The source checker verifies the exact A polynomial, zero diagonal, 112 distinct +source directions, 52 nonzeros per row/column and orthogonal G maps. Its actual +17-axis binary witness demonstrates that a transported letter may send +`e_q` to `e_q + e_w`, preserve the correct three flags, and fail the untransported +`Lq` condition. Five source/flag and five invoice controls reject. The former +is **binary symplectic support only**: it does not verify absolute phase, +all-width theorem logic, every physical source endpoint or a native supplier. +The written proof and independent review supply the mathematical argument; +the hook does not pretend to machine-check that theorem. + +Official portable export: + +```sh +python3 scripts/export_research_package.py export --package research/released-operator-clifford-ceiling --ref HEAD --output /tmp/released-operator-clifford-ceiling.tar.gz +python3 scripts/export_research_package.py check /tmp/released-operator-clifford-ceiling.tar.gz +``` + +## Open next questions + +A continuation must change an explicit hypothesis. One useful question is an +actual paid or non-Clifford control, with all four controls and inverses, +correct arbitrary-input ownership, physical source charts and a complete bill. +This package neither selects nor executes that candidate. Merely adding more +coupled Clifford owner programs does not evade this declared ceiling. + +## Credit + +Credit Dillon for the released construction equations, real normalizers and +charged recoding; Dugongue/mdumitrean for #4929 and A; Cao Yifan/intqwq for +the native word; Cinna Davis/1337isnot1337, zxv, Jacob Alan Sussman, Ryanson +Jonathan and all retained native/helper/Clifford/compiler contributors. +Astra's proof and source/flag support, the independent ceiling review, +Chris R/Clear1nsight's source inventory/packaging, and the separate p19 +compiler-contracts agent's exact interval budget are retained unchanged. +All new work has substantial OpenAI Codex assistance. Original Apache-2.0 +LICENSE/NOTICE and source-specific notices remain included. The elementary +tensor-separation argument is inherited mathematical tooling, not claimed +as a new theorem. No independent human or kernel acceptance is asserted. diff --git a/research/released-operator-clifford-ceiling/SOURCES.json b/research/released-operator-clifford-ceiling/SOURCES.json new file mode 100644 index 0000000000..78e3fd7c0f --- /dev/null +++ b/research/released-operator-clifford-ceiling/SOURCES.json @@ -0,0 +1,107 @@ +{ + "schema_version": 1, + "base_commit": "a5df48c55ea806d7952b65acc9c76d878ff09b13", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395", + "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/coded-native-caller/CODE.json", + "usage": "provenance", + "pin": 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a/research/released-operator-clifford-ceiling/TASK.json b/research/released-operator-clifford-ceiling/TASK.json new file mode 100644 index 0000000000..51b6e1da81 --- /dev/null +++ b/research/released-operator-clifford-ceiling/TASK.json @@ -0,0 +1,90 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 7, + "base_commit": "a5df48c55ea806d7952b65acc9c76d878ff09b13", + "original_card": { + "id": "joint-query-controller", + "question": "Can the installed QQ16 caller win a complete matched protocol bill, or can a changed demand eliminate actual paid work?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/qq16-caller-install/README.md" + ], + "methods": [ + "Derive the matched whole-caller physical bill for installed and baseline protocols.", + "Change the actual demanded observations and prove a cheaper legal producer/consumer contract." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.", + "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.", + "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer", + "4166", + "qq16-caller-install" + ], + "existing_checks": [ + { + "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.", + "evidence": "research/qq16-caller-install/README.md", + "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.", + "status": "author-checked", + "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Source-bound sufficiently-large-width obstruction for the released four-control intersection within fixed finite columnwise monomial-Clifford plus scalar-owner programs; separate exact optimistic complete-invoice raw moment allowance. Separate independently reviewed scalar-owner commuting-X shear screen (m>=112) against the explicit 3mH2 execution bill, without construction or universal physical query claim.", + "scope_change_reason": "The released handoff does not specify every physically free program. This package tests a declared Clifford subclass, rather than claiming a complete native controller or universal physical FREE obstruction.", + "bottleneck_link": "The two-FULL/one-query handoff would need four free controls and their inverses. The scoped proof eliminates that fixed Clifford control class; the conditional invoice leaves at most 44 additional H1 of strict raw moment allowance before finite bills, reserves and endpoint admission.", + "budget_minutes": 60, + "stop_rule": "No t0 search, native/emitter/compiler/Lean replay, or paid-control construction. Preserve exact reviewed science; stop at portable proof support and arithmetic verification.", + "outcome": "completed", + "evidence": "README.md; evidence/proof/PROOF.md; evidence/independent-review/REVIEW.md; evidence/budget/REPORT.md; verify.py; evidence/supplements/PAID-SHEAR-ADDENDUM.md (separate stopped scalar-owner commuting-X paid class)", + "author": "Chris R / Clear1nsight, with OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance for source-bound derivation, independent review, exact arithmetic and packaging; no kernel or independent human theorem acceptance.", + "open_questions": [ + { + "question": "Can one explicitly paid non-Clifford or changed-control program realize the released endpoint within the conditional allowance?", + "why_it_matters": "The written obstruction only closes the declared fixed columnwise Clifford class.", + "first_step": "Specify one actual finite program, all four controls and inverses, ownership and complete paid/finite bill before a new construction reservation.", + "blocked_by": "No physical endpoint or compiler transfer is supplied here; the 44 H1 figure is only a conditional raw allowance." + } + ] +} diff --git a/research/released-operator-clifford-ceiling/VERIFY.json b/research/released-operator-clifford-ceiling/VERIFY.json new file mode 100644 index 0000000000..5e262e712c --- /dev/null +++ b/research/released-operator-clifford-ceiling/VERIFY.json @@ -0,0 +1,34 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Authenticates immutable evidence, pinned source structure and a 17-axis transported-flag counterexample, then exactly regenerates the full conditional interval budget receipt in a private logical-path mirror. Source/flag and invoice controls reject. The scoped all-width theorem remains a written independently reviewed proof, not an executable theorem/native/compiler replay. Separately authenticates the independently reviewed scalar-owner commuting-X paid-shear stop capsule and checks only its explicit rank-two execution 7/8-count price support." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Authenticates immutable evidence, pinned source structure and a 17-axis transported-flag counterexample, then exactly regenerates the full conditional interval budget receipt in a private logical-path mirror. Source/flag and invoice controls reject. The scoped all-width theorem remains a written independently reviewed proof, not an executable theorem/native/compiler replay. Separately authenticates the independently reviewed scalar-owner commuting-X paid-shear stop capsule and checks only its explicit rank-two execution 7/8-count price support." + } + ] +} diff --git a/research/released-operator-clifford-ceiling/evidence/budget/FILES.json b/research/released-operator-clifford-ceiling/evidence/budget/FILES.json new file mode 100644 index 0000000000..bda3f26288 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/budget/FILES.json @@ -0,0 +1,6 @@ +{ + "REPORT.md": "b8b785a815852069b27ee6b18337b6ecd64127c7a22985d0e4221a2fc11bd53a", + "check_budget.py": "e961496628064ac6257a1f6ae3bf660719ee563b07800c2b40cea25b9da9ed2b", + "RESULT.json": "b11a56c453c6f174780edd0cd19c638da7d1552ac9f3f0ff6f8340d8ada382ae", + "RESULT-OPTIMIZED.json": "b11a56c453c6f174780edd0cd19c638da7d1552ac9f3f0ff6f8340d8ada382ae" +} diff --git a/research/released-operator-clifford-ceiling/evidence/budget/FREEZE.json b/research/released-operator-clifford-ceiling/evidence/budget/FREEZE.json new file mode 100644 index 0000000000..656b7ddef8 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/budget/FREEZE.json @@ -0,0 +1,14 @@ +{ + "scope": "Non-scientific immutable four-file budget-packet manifest; no scientific bytes changed or replay performed for this freeze.", + "files": { + "REPORT.md": "b8b785a815852069b27ee6b18337b6ecd64127c7a22985d0e4221a2fc11bd53a", + "check_budget.py": "e961496628064ac6257a1f6ae3bf660719ee563b07800c2b40cea25b9da9ed2b", + "RESULT.json": "b11a56c453c6f174780edd0cd19c638da7d1552ac9f3f0ff6f8340d8ada382ae", + "RESULT-OPTIMIZED.json": "b11a56c453c6f174780edd0cd19c638da7d1552ac9f3f0ff6f8340d8ada382ae" + }, + "claim": "44 maximal extra H1 calls for uniform strict raw moment positivity on [0.0030217758,0.00339999], conditional on the unrealized unchanged T/P; no actual control funding/compiler reserve or kappa.", + "source_inventory_manifest_sha256": "8ca981b54bd1d6a8e08c80836119b0efeca236c69fff14bb601b2faba1a1f654", + "normal_optimized_results_byte_identical": true, + "new_scientific_execution": false, + "publication_authorized_by_this_manifest": false +} diff --git a/research/released-operator-clifford-ceiling/evidence/budget/REPORT.md b/research/released-operator-clifford-ceiling/evidence/budget/REPORT.md new file mode 100644 index 0000000000..ddc6e82c07 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/budget/REPORT.md @@ -0,0 +1,82 @@ +# Released two-FULL invoice: optimistic additional recursive-control budget + +**Exact arithmetic result under an unproved complete operator/inventory premise:** at most **44 additional H1 calls** can be allowed while retaining strict raw moment positivity uniformly for `C in [0.0030217758,0.00339999]`. Forty-four succeeds uniformly; forty-five fails at the upper endpoint. This is an optimistic arithmetic grant for that declared invoice, not actual caller funding, compiler reserve or κ admission. + +The stock is Dillon's released [Discussion4930 comment19143357](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19143357), as authenticated in `coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023`. Its scientific source pin is `4c0a359d88f22f05189d51f48387750b801a45d4`; public scoped theorem pin is `0e8a13c251a9be1029114cda8b4194f05f3a23ec`. The checker authenticates all eleven files listed by that frozen inventory's FILES.json, records their hashes and manifest hash, and checks its release receipt's exact T/P. It imports no source/native/operator/compiler code. + +## Complete promised invoice, including every helper + +``` +T = 224 H17 + 816 H9 +P = 4608 H1 + 838 H2 + 1020 H3 + 254 H4 + 136 H5 +``` + +There are 224 original main inputs and exactly 816 original helper inputs, for 1,040 productive owners. Each of the two FULLs has native profile `P0={1:2201,2:412,3:510,4:127,5:40}` and helper profile `H={4:28,7:7,8:47,9:326}`. The accounting is + +``` +P = 2 P0 + 112 H1 + (94 H1 + 14 H2 + 56 H5). +``` + +The query bank costs 112 H1. The final bracket pays complements for the 94 rank-eight, 14 rank-seven and 56 rank-four helper jobs across both FULLs, completing each to rank nine; 652 helpers already have rank nine. All 816 original helper owners are credited once. Their old lower-rank outputs are not also retained as extra targets. The complement rank mass is 402. Total target and paid rank masses are respectively **11,152** and **11,040**, a raw rank-mass difference of **112**. That difference is not the extra-control budget at positive C. + +## Declared comparison interval and exact bounds + +Write `a=0.0030217758`, `b=0.00339999` and + +``` +M(C) = 224*17^(1-C) + 816*9^(1-C) + - 4608 - 838*2^(1-C) - 1020*3^(1-C) + - 254*4^(1-C) - 136*5^(1-C). +``` + +Exact rational outward enclosures give: + +| Quantity | Lower bound | Upper bound | +|---|---:|---:| +| M(a) | 52.133114229301600459209653 | 52.133114229301600459209654 | +| M(b) | 44.676959553589208855078743 | 44.676959553589208855078744 | +| M'(C), uniformly on [a,b] | −19728.040142366829130975258373 | −19700.174693469327002916426638 | + +The exact Fraction endpoints are retained in RESULT.json. For the derivative, define `L_T(C)=sum T_r*r^(1-C)*log r` and likewise `L_P`. Both are nonincreasing positive sums. Therefore + +``` +L_P(b)-L_T(a) <= M'(C) <= L_P(a)-L_T(b) < 0. +``` + +This proves strict decrease of M throughout the interval. Its minimum occurs at b; the endpoint enclosure proves `44 0.676959553589208855078743` uniformly on [a,b]. +* At b, `M(b)-45 < -0.323040446410791144921256`, so no integer grant of 45 or more is uniformly compatible with strict positivity. +* One **additional complete 112-query bank** gives a negative margin everywhere in the interval: its uniform upper bound is below `-59.866885770698399540790346`. This prices that fixed extra-query policy; it is not a universal query lower bound on other operator implementations. + +Thus **44 is maximal**, rather than merely a sufficient rounded allowance, for additional H1 jobs under this exact unchanged T/P and the requested uniform interval. The reported raw surplus 112 cannot be substituted for it. + +For a different finite nonnegative additional paid profile E, the relevant condition is `sum E_r*r^(1-C)=1,'positive integer rank') + k=r.bit_length()-1;x=Q(r,2**k) + a,b=logsmall((x-1)/(x+1));c,d=logsmall(Q(1,3)) + return rounded(a+k*c,b+k*d,10**50) + +def alternating(x,n): + need(0<=x0 and mb[1]-45<0,'44 succeeds uniformly;45 fails at B') + mutants={ + 'omit_one_helper':(dict(T)|{9:815},dict(P)), + 'omit_original112_queries':(dict(T),dict(P)|{1:P[1]-112}), + 'omit_paid_helper_complements':(dict(T),{r:n-complements.get(r,0) for r,n in P.items()}), + 'doublecredit_original_helpers_after_completion':(dict(Counter(T)+Counter({r:2*n for r,n in H.items()})),dict(P)), + 'credit_owned112_query_fields_as_inputs':(dict(Counter(T)+Counter({1:112})),dict(P)), + } + controls={} + for name,(tt,pp) in mutants.items(): + try:audit(tt,pp) + except ValueError as error:controls[name]={'rejected':True,'reason':str(error)} + else:raise ValueError('accepted invalid stock/control '+name) + return {'status':'PASS_OPTIMISTIC_UNREALIZED_INVOICE_ARITHMETIC_ONLY', + 'comparison_interval':[str(A),str(B)],'targets':T,'paid':P, + 'native_helper_profile_per_FULL':H,'native_paid_profile_per_FULL':P0, + 'helper_count_once':816,'main_count':224,'total_independent_owner_count':1040, + 'helper_complement_paid':complements,'original_query_H1':112, + 'target_rank_mass':11152,'paid_rank_mass':11040,'rank_mass_surplus':112, + 'point_margins':{str(A):enc(ma),str(B):enc(mb)}, + 'uniform_derivative_enclosure':enc(derivative), + 'uniform_margin_enclosure':enc((mb[0],ma[1])), + 'max_uniform_integer_extra_H1':44, + 'uniform_margin_after44_H1':enc((mb[0]-44,ma[1]-44)), + 'endpoint_margin_after45_H1':enc((mb[0]-45,mb[1]-45)), + 'uniform_margin_after_an_extra112_H1':enc((mb[0]-112,ma[1]-112)), + 'safe_sufficient_extra_profile_rule':'For a finite nonnegative extra paid profile, sum_r extra_r*r^(1-A)<=44 implies positive raw moment residual on [A,B] under unchanged realized T/P; not actual funding or compiler reserve.', + 'integer_budget_claim':'44 is maximal for strict raw moment positivity uniformly on the declared closed interval, conditional on this unrealized complete T/P and unchanged target credit.', + 'controls':controls,'release_url':release['url'],'scientific_source_pin':release['source_scientific_pin'], + 'source_inventory_files':sources, + 'source_inventory_manifest_sha256':sha256((STOCK/'FILES.json').read_bytes()).hexdigest(), + 'checker_sha256':sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope':'No t0/free implementations, physical contacts/helper complements, full operator/control word, precision/tape costs, compiler reserve, ordinary BIT or outer transfer are established. No kappa claim; no root-digit extraction.', + 'ordinary_BIT_extension_performed':False} + +def main(): + parser=argparse.ArgumentParser();parser.add_argument('--out',type=Path,required=True);args=parser.parse_args() + result=run();args.out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(result['status'],'max_uniform_extra_H1=44') + +if __name__=='__main__':main() diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/FILES.json b/research/released-operator-clifford-ceiling/evidence/independent-review/FILES.json new file mode 100644 index 0000000000..13299ab23b --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/FILES.json @@ -0,0 +1,21 @@ +{ + "status": "LOCAL_ONLY_BOUNDED_INDEPENDENT_THEOREM_REVIEW", + "files": { + "POINT-BUDGET.json": "de9a8b784249c84587e5dfbe3e6e3cdaca5a432e9667d17e14d1d0a2f2b79f6d", + "REVIEW-RESULT.json": "2e77399d0bdbf216b0a7a6b2345706a27d7dac1e0c5a80e8b2b62abb81ab2165", + "REVIEW.md": "23b5aa5df049cb4a8fe3349c054e27d84ca151e29e263c658670639bad082428", + "SOURCES.json": "249dbf14d6c43c6482ab7825f9de7251e00e79ee72261860cbc9422e954545de", + "frozen/AUTHOR-SOURCE-CHECK.json": "e2e02bb5089821f2f256b8efbb79f14172b4ab3bd9f482bc9e2de2aa14cd506e", + "frozen/INVENTORY-REPORT.md": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "frozen/RELEASE-PRIMARY.json": "1aa74f9b72d60a4e4357bc3ea9e70c650c870432714aed11b2cda46518f74952", + "frozen/REVIEWED-PROOF.md": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "frozen/research__coded-active-query-bound__PROOF.md": "495a1cd85cc45020adf2205f196b57dc4f65f1eb763fc4951facdb4ccbafc768", + "frozen/research__coded-active-query-bound__README.md": "95269b047c19069caeb11edd36a485a0a86275b329aa44da90c8c08403e09178", + "frozen/research__coded-active-query-bound__SOURCES.json": "afb6ca7a3b924d19b61b784266693b892722024d5a33de3e432fc6499238241e", + "frozen/research__coded-native-caller__NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "frozen/research__coded-native-caller__PHYSICAL.md": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "frozen/research__coded-native-caller__clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "frozen/research__coded-native-caller__normalizers.py": "7616b75758c1b36b6c05eb7fff1630f604e7563762701bccb18ec638a61090df", + "frozen/research__native-center-free-code__CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + } +} diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/POINT-BUDGET.json b/research/released-operator-clifford-ceiling/evidence/independent-review/POINT-BUDGET.json new file mode 100644 index 0000000000..76aa9a2d73 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/POINT-BUDGET.json @@ -0,0 +1,35 @@ +{ + "status": "CONDITIONAL_POINT_ARITHMETIC_ONLY_NO_OPERATOR_PRICED", + "targets": { + "9": 816, + "17": 224 + }, + "paid": { + "1": 4608, + "2": 838, + "3": 1020, + "4": 254, + "5": 136 + }, + "engine_reused_not_new": "outputs/p19-compiler-contracts-20261023/C-INVERSE-SCREEN-CHECK.py", + "engine_sha256": "d2b26aa7d0fa98adbbc76dd1e38381f8cfea193b7544f4597cf3bfef7cc3a980", + "point_enclosures": { + "0.0030217758": [ + "52.133114229301600459209653", + "52.133114229301600459209654" + ], + "0.00339999": [ + "44.676959553589208855078743", + "44.676959553589208855078744" + ] + }, + "max_additional_integer_H1_point_only": { + "0.0030217758": 52, + "0.00339999": 44 + }, + "uniform_interval_claim": false, + "compiler_reserve_or_tails_funded": false, + "finite_work_funded": false, + "t0_program_supplied": false, + "new_kappa": null +} diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/REVIEW-RESULT.json b/research/released-operator-clifford-ceiling/evidence/independent-review/REVIEW-RESULT.json new file mode 100644 index 0000000000..905796bb9f --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/REVIEW-RESULT.json @@ -0,0 +1,20 @@ +{ + "status": "PASS_SCOPED_COLUMNWISE_MONOMIAL_CLIFFORD_OBSTRUCTION", + "reviewed_proof_sha256": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "review_sha256": "23b5aa5df049cb4a8fe3349c054e27d84ca151e29e263c658670639bad082428", + "source_files_authenticated": 12, + "independent_solver_or_enumeration_run": false, + "native_factory_compiler_Lean_run": false, + "all_width_invertible_t0_excluded_in_declared_class": true, + "physical_FREE_universal_claim": false, + "width_dependent_qualification": "t0_f=0 at each sufficiently large width; finite small-width exceptions not excluded", + "rejected_inferences": [ + "Ht equals H0 after D3 transport", + "Rk fixes eq rather than quotient class", + "nonzero-vector lemma with v=0", + "abstract units have physical inverse programs", + "query-lower-bound H is an executable FREE dictionary", + "point budgets prove a uniform interval" + ], + "new_kappa": null +} diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/REVIEW.md b/research/released-operator-clifford-ceiling/evidence/independent-review/REVIEW.md new file mode 100644 index 0000000000..f06f34d333 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/REVIEW.md @@ -0,0 +1,190 @@ +# Independent review of the released t0 operator-intersection argument + +**PASS for the revised, explicitly scoped theorem.** No all-width invertible +t0 in the fixed finite columnwise monomial-Clifford/scalar-owner control class +satisfies the four declared free-membership conditions. The direct scalar-owner +subclass proof also passes. This is not a classification of physical FREE, a +universal obstruction to the released caller, or an application of the enlarged +query-lower-bound alphabet as an executable free dictionary. + +Reviewed proof SHA256: +`c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc`, +copied unchanged as `frozen/REVIEWED-PROOF.md`. Twelve source/proof/inventory +captures authenticate in SOURCES.json. The scientific source is +`4c0a359d88f22f05189d51f48387750b801a45d4`, with the actual CODE.json and +NORMALIZERS.json; the released handoff is Discussion4930 comment19143357. +Public #5126 `0e8a13c251a9be1029114cda8b4194f05f3a23ec` supplies separate +local-query context, not the constructive physical-free alphabet assumed here. + +## 1. Source and model discipline + +The fixed address space is q+U+W, with one central and two disjoint eight-axis +blocks:17 axes, lifted as the same one-column map on every f column. The owner +matrix A has zero diagonal, distinct source port directions q_i=G_i e_q, and +nonempty rows/columns. The source polynomial +`A^2+12A-13I=0` gives the exact inverse `(A+12I)/13`, hence each physical code +`C_s=diag(K_s)^-1 A diag(K_s)` is invertible at every width. These are the +authenticated source premises/static source-check results; no new all-port +operator evaluation or source native replay was performed for this review. + +The declared H is the projective group of **monomial Clifford** maps on those +17 one-column axes. It is finite projectively. Fixed finite scalar owner +programs, COPY/history and owned clear/reset yield matrices over its linear +span; coefficients may depend on width. Such a span is a mathematical +relaxation of explicit programs. Membership is necessary for a program in this +class; it is not by itself an executable tariff or an inverse program. + +The proof does not assume an arbitrary nonsingular algebra element has a free +inverse. H, its conjugates and their intersection are groups and are inverse +closed, but that abstract fact supplies no physical implementation for a unit +of their matrix algebra. The forward membership obstruction already excludes +the handoff's invertible solution; proving inverse-program sufficiency is +unnecessary for this negative result. + +## 2. Support and width separation are valid + +For pairwise nonproportional nonzero operator vectors v_i, choose, for each +j!=i, a functional annihilating v_j but not v_i. Their tensor product isolates +v_i^(tensor(m-1)); extra factors nonzero on v_i extend the argument to larger +widths. Thus any fixed finite union of projective classes has independent +literal tensor lifts for every sufficiently large f. Equal projective classes +are grouped first and their scalar phases are raised to f. This handles +width-dependent owner coefficients without tensoring an owner-space sum. + +The union must include the candidate control letters, their Q/D3 conjugates, +the terminal endpoint products and the letters of a proposed free endpoint +program. It is finite in this declared fixed-columnwise Clifford class. The +threshold is not claimed small or practical. No assertion is made at every +small width: a family supported only at finitely many small widths can evade +the nonzero-family wording, but cannot meet all-width invertibility. + +The precise conclusion is pointwise at sufficiently large width: any t0_f +satisfying all four memberships must be zero there. It excludes every fixed +nonzero t0 and every all-width invertible family, including width-dependent +scalar coefficients. It does not assert that no exceptional small-width +identity exists. + +## 3. D3 transport and the necessary quotient flag + +The first three controls put surviving t0 support in + +`H0=H intersect Q H Q^-1 intersect D3^-1 H D3`. + +For t=D3 t0 D3^-1 the correct transported support is +`Ht=D3 H0 D3^-1`. It must not be identified with H0. In particular +`Q^-1 t Q=D3(Q^-1 t0 Q)D3^-1` is not automatically monomial. The revised +proof correctly retains this failure of the tempting closure inference. + +On binary symplectic space Q and D3 are involutions, while their operator +squares remain nontrivial Pauli/phase maps. If h lies in H0, it stabilizes +L0,Lq,Lw. A transported k in Ht stabilizes L0,Lw,Lqw. Because k is monomial, +its X block R_k is invertible and preserves both W and span(e_q)+W. It fixes +the nonzero central class in the quotient by W; it need not fix e_q itself. +The allowed behavior e_q -> e_q+w is precisely why the stronger false +transport inference cannot be reused. + +For **nonzero** v in span(e_q)+U and nonzero w in span(e_q)+W, if +k L(v)=L(w), with `L(v)={(v v^T z,z)}`, X projection gives R_k v=w. +The induced invertible quotient map has the central class as a fixed point, +so the preimage of its span is that span. Therefore v=e_q, while w may be +e_q plus a W vector. This proves exactly the one-sided implication needed; +it does not establish w=e_q. + +## 4. The endpoint has no monomial support: cancellation does not rescue it + +A terminal endpoint block has terms + +`Q^-1 K_(3,i)^-1 K_(3,r) k K_(1,s)^-1 K_(1,j) Q^-1`, + +with coefficient `A[i,r] b[r,s,k] A[s,j]` and k in Ht. For such a word to be +monomial, its central Gaussian chart must be carried to the central chart. +Using the actual orthogonal source normalizers, this requires k to carry + +`L(G_(1,s)^-1 q_j)` to `L(G_(3,r)^-1 q_i)`. + +The quotient lemma forces `G_(1,s)^-1 q_j=e_q`, hence s=j by distinct source +directions. Its coefficient then contains A[j,j]=0. Thus **every term with +nonzero coefficient is outside H**. + +The corrected proof groups any equal nonmonomial projective classes. Internal +cancellation can remove such classes, but cannot create a class in H. Uniform +tensor separation makes their remaining span disjoint from the monomial span. +If the endpoint E also has a free representation in the declared class, it +must therefore be zero. But + +`E=Q^-1 C3 t C1 Q^-1=0` + +implies t=0 and then t0=0 because the source Q,C1,C3 are invertible. This closes +the wider-class argument without assuming unique intermediate products or a +free inverse for t0. Invertibility of the handoff's requested t0 makes the +contradiction immediate. + +This direct-sum argument was the useful correction during review: an initial +draft left an unnecessary cancellation gap. The reviewed version resolves it +without reintroducing the invalid claim that Ht=H0 or R_k e_q=e_q. + +## 5. Independent scalar-owner crosscheck + +For t0=B tensor I, t=t0 and the first three controls are scalar owner maps. +Each endpoint word has an orthogonal binary map + +`M=G_(3,i)^-1 G_(3,r) G_(1,s)^-1 G_(1,j)`. + +Writing `Q^-1=aI+bX_q`, both a,b are nonzero. If M e_q differs from e_q, +the four translations0,e_q,M e_q,e_q+M e_q are distinct and have nonzero +coefficients; the word is nonmonomial. If the directions agree, the actual +Pauli sign yields either a single translation or a scalar times M. Thus the +stated monomial criterion is correct, including sign choices and the two +Q^-1 factors. Q is never treated as order two. + +Returning the direction to e_q forces s=j and r=i by the disjoint stage +supports and distinct source q_i, annihilating the source diagonal factors. +For fixed i,j, equality of two remaining binary products would give + +`G_(3,r')^-1 G_(3,r)=G_(1,s')^-1 G_(1,s)`. + +Their stage-local intersection is the identity binary map: both sides fix U +and W, preserve the respective local spaces, and the only invertible map of +the single common binary bit fixes it. Distinct q_i then force r=r',s=s'. +So a nonzero B[r,s], together with a nonzero source entry in column r and row +s, gives a unique nonmonomial term. This independently confirms the scalar +subclass obstruction, with the same sufficiently-large-width qualification. + +## 6. Scope, corrections and constructive continuation + +The following draft issues were corrected before the reviewed hash was frozen: +the prematurely broad theorem claim while cancellation was open; an incorrect +sentence placing transported t support back in H0; missing nonzero-vector +quantifiers in the chart lemma; and the width-dependent coefficient wording. +The revised cancellation argument now legitimately proves the broader +**declared monomial-Clifford** class, rather than a universal FREE theorem. + +This result does not import #5126's enlarged arbitrary finite monomial H as +an actual physical dictionary. It does not exclude non-Clifford monomial +controls, noncolumnwise/growing alphabets, extra paid corrections, a changed +controller or productive endpoint, extra axes, a different code, or reuse of +nonfree native information outside the four-free-controls template. + +The primary constructive direction remains a **priced** coupled operator using +already available native information, or another explicit changed hypothesis. +For the handoff's promised T={9:816,17:224} and +P={1:4608,2:838,3:1020,4:254,5:136}, a separate source-reused exact point +calculation gives raw allowance52.133114229301600459209653..654 at +C=.0030217758 and44.676959553589208855078743..744 at C=.00339999. +These are conditional point budgets only, before compiler reserve/tails and +all finite costs. They do not price any proposed t0 or prove a uniform interval. +An additional112H1 or224H1 already exceeds either point allowance, so a useful +paid continuation must exploit actual shared nonfree access or a cheaper +complete endpoint rather than a standalone full-bank correction. + +No t0 solver, candidate enumeration, native/factory/emitter/compiler/Lean run, +publication or κ claim occurred in this review. Only source text/byte reads, +mathematical derivation and the labelled scalar moment calculation occurred. + +Credit Dillon's released equations and source interface; Astra's corrected +operator-intersection derivation; Dugongue/mdumitrean's source code; Cao Yifan, +Cinna Davis, zxv, Jacob Alan Sussman and the retained native/Clifford/compiler +lineage. The tensor-separation technique is retained predecessor mathematics. +Substantial OpenAI Codex assistance. Apache-2.0. Root owns research and +publication decisions; rejection of this control class does not end the search +for a constructive paid-profile gain. diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/SOURCES.json b/research/released-operator-clifford-ceiling/evidence/independent-review/SOURCES.json new file mode 100644 index 0000000000..652712e521 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/SOURCES.json @@ -0,0 +1,88 @@ +{ + "status": "BOUNDED_INDEPENDENT_READ_DERIVE_REVIEW", + "source_scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "public_query_theorem_head": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "reviewed_proof_sha256": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "files": [ + { + "snapshot": "frozen/research__coded-active-query-bound__README.md", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__coded-active-query-bound__README.md", + "commit": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "upstream_path": "research/coded-active-query-bound/README.md", + "sha256": "95269b047c19069caeb11edd36a485a0a86275b329aa44da90c8c08403e09178" + }, + { + "snapshot": "frozen/research__coded-active-query-bound__PROOF.md", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__coded-active-query-bound__PROOF.md", + "commit": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "upstream_path": "research/coded-active-query-bound/PROOF.md", + "sha256": "495a1cd85cc45020adf2205f196b57dc4f65f1eb763fc4951facdb4ccbafc768" + }, + { + "snapshot": "frozen/research__coded-active-query-bound__SOURCES.json", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__coded-active-query-bound__SOURCES.json", + "commit": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "upstream_path": "research/coded-active-query-bound/SOURCES.json", + "sha256": "afb6ca7a3b924d19b61b784266693b892722024d5a33de3e432fc6499238241e" + }, + { + "snapshot": "frozen/research__coded-native-caller__PHYSICAL.md", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__coded-native-caller__PHYSICAL.md", + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "upstream_path": "research/coded-native-caller/PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "snapshot": "frozen/research__coded-native-caller__NORMALIZERS.json", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__coded-native-caller__NORMALIZERS.json", + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "upstream_path": "research/coded-native-caller/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "snapshot": "frozen/research__native-center-free-code__CODE.json", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__native-center-free-code__CODE.json", + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "upstream_path": "research/native-center-free-code/CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "snapshot": "frozen/research__coded-native-caller__normalizers.py", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__coded-native-caller__normalizers.py", + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "upstream_path": "research/coded-native-caller/normalizers.py", + "sha256": "7616b75758c1b36b6c05eb7fff1630f604e7563762701bccb18ec638a61090df" + }, + { + "snapshot": "frozen/research__coded-native-caller__clifford_exact.py", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/source/research__coded-native-caller__clifford_exact.py", + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "upstream_path": "research/coded-native-caller/clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "snapshot": "frozen/REVIEWED-PROOF.md", + "origin": "outputs/released-operator-intersection-20261023/PROOF.md", + "sha256": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "scope": "Source/theorem capture read-only; no new operator enumeration or native execution" + }, + { + "snapshot": "frozen/AUTHOR-SOURCE-CHECK.json", + "origin": "outputs/released-operator-intersection-20261023/SOURCE-CHECK.json", + "sha256": "e2e02bb5089821f2f256b8efbb79f14172b4ab3bd9f482bc9e2de2aa14cd506e", + "scope": "Source/theorem capture read-only; no new operator enumeration or native execution" + }, + { + "snapshot": "frozen/INVENTORY-REPORT.md", + "origin": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/REPORT.md", + "sha256": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "scope": "Source/theorem capture read-only; no new operator enumeration or native execution" + }, + { + "snapshot": "frozen/RELEASE-PRIMARY.json", + "origin": "outputs/all-upstream-pr-monitor-20261023/released-operator-intersection-primary.json", + "sha256": "1aa74f9b72d60a4e4357bc3ea9e70c650c870432714aed11b2cda46518f74952", + "scope": "Source/theorem capture read-only; no new operator enumeration or native execution" + } + ] +} diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json new file mode 100644 index 0000000000..bafcc5aa2c --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json @@ -0,0 +1,20 @@ +{ + "scope": "Static exact source properties only; no operator solver, emitter, native, compiler, or Lean replay.", + "checks": { + "owner_count": 112, + "zero_diagonal": true, + "row_nonzero_counts": [ + 52 + ], + "column_nonzero_counts": [ + 52 + ], + "distinct_q": 112, + "q_weights": [ + 3, + 7 + ], + "orthogonal_G_all": true, + "scalar_polynomial_A2_plus12A_minus13I": true + } +} diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/INVENTORY-REPORT.md b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/INVENTORY-REPORT.md new file mode 100644 index 0000000000..8a200e2535 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/INVENTORY-REPORT.md @@ -0,0 +1,230 @@ +# Released two-FULL/one-query problem: source inventory + +Source inventory only, 2026-10-23. No t0 solver, search, native replay, compiler, +factory or external post was performed. The monitor authenticated Dillon's +release of original #4930 comment 19141406 and the new handoff at comment +19143357. Its exact local receipt is preserved as `source/RELEASE-MONITOR.json`. +The public theorem is `0e8a13c251a9be1029114cda8b4194f05f3a23ec`, +`research/coded-active-query-bound`; the actual code/normalizer scientific pin +is `4c0a359d88f22f05189d51f48387750b801a45d4`. The publication base is +`20a1e31bc6009b9b3f4d084bbaadc6350e34fcba`. Eight exact source files and their +hashes are listed in `SOURCES.json`. + +## Stock and actual operators + +There are two main banks of 112 arbitrary independent owner fields each. +Each field has the fixed 17-axis address stock: one shared central axis q, +eight stage-1 axes and eight disjoint stage-3 axes, lifted to f columns, plus +all retained external row/spectator fields. There is no new anchor or extra +address axis. Two fresh source FULLs add two disjoint banks of 408 arbitrary +helper inputs: 816 helper owners, 1040 original main-plus-helper owners total. +An owned query bank is dependent workspace, not productive input credit. + +Q is the actual central Gaussian, D1 and D3 the products on their respective +eight axes. They are invertible symmetric actual Gaussian operators; the +different axis factors commute. Q is not order two: its exact square is a +Pauli translation. Put G=D1 D3 Q, a rank-17 Gaussian on the complete stock. + +The physical code is not the scalar matrix A. The source gives + + Cs[i,j] = A[i,j] Ki,s^-1 Kj,s, + Fs = diag(Ds,Ds) L(Cs Q^-1). + +The exact local K words, G_rows, Z_mask and compiled monomial wrappers are in +`NORMALIZERS.json`. Embed their nine local coordinates as q plus the selected +stage's eight coordinates, with the other stage as identity. These are stored +matrix ROWS; replacing them by columns changes the operator. The K maps are +real signed orthogonal permutations, commuting with Ds Q but not generally +with Q or Ds separately. Their all-column lift retains the accumulated phase; +owner coefficients are applied once, not tensor-powered with the address map. + +## Released sufficient template and all four conditions + +All controls are 112-by-112 owner-operator matrices on this same field width. +They are not necessarily single Clifford operators. Seek an invertible t0 +such that each of the following has an explicit physically free program AND +an explicit program for its inverse: + +| Control | Definition | Mathematical inverse, in exact order | +|---|---|---| +| R1 | t0 | t0^-1 | +| R2 | S0=Q^-1 t0 Q | Q^-1 t0^-1 Q | +| R3 | t=D3 t0 D3^-1 | D3 t0^-1 D3^-1 | +| R4 | K=Q^-1 C3 t C1 Q^-1 | Q C1^-1 t^-1 C3^-1 Q | + +The released middle operator is + + J(t0) = [[-t0 C1, t0 Q], [0, -C3 S0]]. + +Under the source identities, the handoff states + + M = F3 J(t0) F1 + = [[0,t],[-K,0]] diag(G,G). + +The cancellation uses the actual source relations [C1,D1 Q]=0 and +[C3,D3 Q]=0, plus [C1,D3]=0 from the disjoint fresh-axis embedding. +For example the upper-left block of J F1 is +t0(-C1 D1+D1 Q C1 Q^-1)=0; the lower-right block of F3 J F1 cancels +by S0=Q^-1 t0 Q. No commutation of t0 with either Gaussian is assumed. + +Writing S=[[0,t],[-K,0]], its full main endpoint is + + Xout=t G Yin, Yout=-K G Xin. + +There is no main/helper leakage in the inherited FULL endpoint. The helpers +retain their autonomous source transformations. If the four explicit free +program/inverse requirements hold, the post-map + + S^-1 = [[0,-K^-1],[t^-1,0]] + +would return the main outputs to diag(G,G) on the 224 original inputs, with +the two banks routed back to their declared owners. Invertibility alone is +not a physical implementation of this post-map. + +The mathematical raw inverse transpose is, using transpose rather than +Hermitian adjoint, + + M^-T = S^-T diag(G^-1,G^-1), + S^-T = [[0,t^-T],[-K^-T,0]]. + +An actual reversed/transpose tape must preserve the source raw-dual convention, +all phases and owned-buffer lifecycles. For a source backward FULL the retained +normalization is X-only Q^2 conjugation, with D_s^2 output corrections; the +older Y-only convention cannot be substituted. The formulas here do not emit +that tape or automatically provide physical transpose programs for a generic +algebraic unit. Returning inverse-Gaussian jobs to positive jobs likewise +requires the actual Pauli maps, not an order-two assumption. + +## One paid query and chart contacts + +A direct conditional implementation of J first obtains QY in 112 owned query +fields, then forms -t0 C1 X+t0(QY) and -C3 S0 Y using the required free programs. +All reads of the old Y must finish before Y is overwritten. This explains the +one bank of 112 H1 queries. The query bank is cleared/reset only under the +retained owned-stream rules. A concrete safe COPY/query/use/reset route has +112 query fields; additional scratch for t0 or the free recodings must be +separately allocated and charged. No helper is scratch and no copied stream +earns independent output credit. The handoff does not publish a full emitter. + +Each FULL uses its actual stage-local normalizers. The source forward wrappers +at each port i, rightmost acting first, are + + input X: Ei Ki Q^-1, input Y: Ki, + output X: Ki^-1, output Y: Ds Ki^-1 Si^-1, + +where Ei,Si are the retained actual entrance-line/exit-hyperplane operators. +The complete products shown by the source are monomial; their factors cannot +be individually dropped or declared free solely from a frame label. The +middle J and final controls act on the normalized physical main fields over +all 17 axes. They must match those exact contact coordinates and preserve the +unused stage block as a spectator where required. + +## Promised recursive invoice and the helper complement + +The inherited center-free native price and helper outputs per FULL are + + P0 = 2201H1+412H2+510H3+127H4+40H5, + H = 28H4+7H7+47H8+326H9. + +The released promised complete target/paid census is + + T = 224H17 + 816H9, + P = 4608H1+838H2+1020H3+254H4+136H5. + +Its accounting decomposes exactly as + + P = 2P0 + 112H1 + (94H1+14H2+56H5). + +The last bracket is the complement price for the two native helper banks: +94 rank-eight jobs need rank-one complements; 14 rank-seven jobs need rank-two +complements; 56 rank-four jobs need rank-five complements. The remaining 652 +are already rank nine. Thus all 816 helper original inputs are credited once, +and no original rank-four/seven/eight reward is also retained after counting +its completed rank-nine job. The price has rank mass 11040 and the target +11152, giving the stated raw surplus 112. + +This arithmetic is consistent with the handoff, not an independent native +certificate for its unpublished construction. The actual complement words +must meet the helper's physical entrance/exit charts and retain the other +eight-stage coordinates as spectators, in both orientations. A rank difference +alone does not prove those physical contacts or their monomial adapters. The +source FULL/autonomous-helper premise is inherited; this review performs no +new 816-owner phase campaign. Nor does the positive raw surplus certify a +moment, finite compiler reserve, precision or outer transfer. + +Known ordinary source charges remain nonzero: 448 port-wrapper field maps per +FULL, up to 448 further maps per backward normalization, and 6596 dyadic +precompensation ADDs per native FULL in addition to the original native work. +C_s or C_s^-1 has a source program with 224 K maps, 896 scalar ADDs and 16 +owned CLEARs, using eight reusable owned mode fields. The inverse coefficient +is -1/52; its odd-denominator precision work is not free. Counts of these +macros in J/output decoders depend on the proposed t0 programs and cannot be +invented here. Query COPY/reset, inverse-query Paulis, routing, all buffers, +heights and full fixed-tape cost remain charged obligations. + +## Actual free dictionary versus a theorem's enlarged algebra + +The public active-query theorem deliberately grants arbitrary finite linear +owner programs over a fixed finite projective group H of one-column monomial +maps, possibly non-Clifford, to strengthen its LOWER BOUND. Each map is lifted +as the same h in all f columns. It permits width-dependent scalar coefficients +within that mathematical model and proves its obstruction at sufficiently +large f. It does not present an executable tariff for every such H map, every +element of its span, or every invertible matrix over that span. + +The construction handoff expressly asks for EXPLICIT free implementations. +Its actual known source dictionary is narrower and operational: + +* elementary scalar owner ADDs/mixing, signs and owner routing, with fixed + coefficients computed and rounded under the caller's precision rules; +* owned COPY/reset/clear with original independent fields preserved; +* the exact K_i,s and inverses, their supplied phase-correct P/D/X words, + ordinary phases/Paulis and any explicitly compiled fixed coordinate map; +* C1,C3 and their inverses through the concrete eight-mode scalar programs; +* Q^2 and Ds^2 Pauli maps with their actual finite passes. + +This dictionary is closed under concatenating actual finite programs. A unit +must have a returned inverse program; mathematical nonsingularity supplies +neither its finite word nor its cost. There is no admitted closure rule saying +that conjugation by Q or D3 preserves this dictionary. In particular a word +with an even Gaussian count can still be nonmonomial/nonfree. Generic finite-H +or full Clifford-span hypotheses from a different theorem must not be silently +installed here. Arbitrary width-dependent coefficients also need a uniform +descriptor, bit-height and runtime prescription, not a unit-cost oracle. + +There is also a general exact monomial-Clifford constructor in the retained +symbolic source, not just a table of K_i: `normalizers.py` lines 123–127 calls +`ce.monomial(op)`, checks exact tableau and phase, and emits only P/D/X/phase +letters. A specified rank-zero Clifford candidate can therefore be represented +by a literal fixed-axis word and its inverse. It still needs its 17-axis +embedding, all-column phase lift and finite indexed-movement/precision bill +under the retained monomial implementation. This is distinct from granting +every arbitrary non-Clifford permutation in the theorem's enlarged H. No new +letter was synthesized or tested in this review. + +### Smallest concrete units subclass for the design lead + +A useful source-grounded first class is t0=B tensor I_address, where B is a +fixed scalar owner matrix accompanied by a finite elementary program and its +inverse. A particularly strict finite generator alphabet is owner ADD with +coefficients +1 or -1, owner swaps and signs. Any fixed word in these generators +has an explicit inverse by reversing and inverting its gates, uses no Gaussian +call or new axis, and has a finite ordinary cost. B is then unimodular. Other +fixed rational B can be admitted only with their explicit scaling/division and +precision programs. This is a candidate subclass, not a claim of a solution. + +For such scalar B, the first three conditions reduce to B and B^-1 because +they commute with Q and D3. The remaining test is the actual ordered operator +Q^-1 C3 B C1 Q^-1 and its inverse. The source normalizers fix its phase-correct +17-axis terms. Astra owns the creative intersection derivation; no linear +system, determinant test, t0 candidate enumeration or operator solver is run +by this inventory review. Proving a cancellation in a one-column matrix alone +would not justify every width: an all-column word identity and its physical +finite program are still required. + +Credit Dillon for the released template and active local theorem, Dugongue for +#4929, the #4933 normalizers/coded ABI authors, Cinna Davis, Cao Yifan, zxv, +Jacob Sussman and all retained native/helper/compiler predecessors. Prepared +with substantial OpenAI Codex assistance; Apache-2.0. The joint #5124 mechanism, +finite-packing work and the other agents' operator-intersection design remain +separate ownership scopes. diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/RELEASE-PRIMARY.json b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/RELEASE-PRIMARY.json new file mode 100644 index 0000000000..814fd83d37 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/RELEASE-PRIMARY.json @@ -0,0 +1,42 @@ +{ + "at": "2026-10-23 10:16:02 UTC", + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19143357", + "author": "dillona", + "public_theorem_head": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "public_theorem_path": "research/coded-active-query-bound", + "source_scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "publication_base": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba", + "ownership": "Originalcanonical4930#19141406 nowDONE(scopedlocaltheorem/globalconstructionopen), ClaimRELEASED. Links19143357, completefavorableGaussiancaller unresolvedandAVAILABLEforchangedinformationboundarycontinuation. Newfinding0replies, no laterclaimvisiblein4930.", + "constructive_handoff": "Survivingtwo-FULL/one-querytemplate onfixed17axisphysicalembedding. Seekinvertiblet0 suchthatallfourexpressionsandtheirinverseshaveexplicitfreeimplementations.", + "four_expressions": [ + "t0", + "Q^-1 t0 Q", + "t = D3 t0 D3^-1", + "Q^-1 C3 t C1 Q^-1" + ], + "definitions": [ + "F_s = diag(D_s,D_s)L(C_s Q^-1)", + "G = D1 D3 Q", + "J(t0) = [[-t0 C1,t0 Q],[0,-C3 Q^-1 t0 Q]]", + "F3 J(t0) F1 = [[0,t],[-Q^-1 C3 t C1 Q^-1,0]] diag(G,G)" + ], + "qualification": "Sufficientconstructiontarget,nofoundt0. I leavesunresolvedQconjugatedcodeproduct. ArbitraryK/LbridgetransportthroughD3changescheapalgebra; parityevenNOTphysicallyfree. Earlierapparentbroadobstructionfailsatthatstep.", + "conditional_inventory": { + "T": { + "9": 816, + "17": 224 + }, + "P": { + "1": 4608, + "2": 838, + "3": 1020, + "4": 254, + "5": 136 + }, + "rankmass_surplus": 112, + "helpers": "All816independentonce", + "premise": "Ifvalidt0withoutanyextraaxes/paidwork; compilerprecisionouteradditional" + }, + "free_algebra_boundary": "CommentrequiresEXPLICITphysicalfreeimplementationsandinverses; it doesnotfullyenumerateeligiblefreealphabet. Do NOTsubstitute genericfiniteHfrom5126fresh-inputlowerboundorparityevenalgebra. Actualfreeclosure/callerimplementationneedsourceinventory.", + "unpublished_status": "Exploratoryconstructiontoolspreservedlocally; onlytheorempackageispublic. Do NOTassumecompletepublicemitter/instance." +} diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/REVIEWED-PROOF.md b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/REVIEWED-PROOF.md new file mode 100644 index 0000000000..08b35b275a --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/REVIEWED-PROOF.md @@ -0,0 +1,256 @@ +# A source-bound obstruction for the explicit Clifford control class + +Status: local derivation awaiting separate review. No public theorem, solver, +native/emitter/compiler/Lean replay, complete caller, or new kappa is claimed. + +This answers a precise part of Dillon's released two-FULL/one-query handoff, +Discussion 4930 comment 19143357. The new bounded investigation is rooted at +comment 19143614. The public handoff is a sufficient construction target; no +successful t0 was supplied. Its physical FREE class is not fully enumerated. +The theorem below explicitly restricts that class to fixed finite columnwise +monomial Clifford words and scalar owner programs. It does not silently replace +physical FREE by parity-even operators or by every unit of an abstract algebra. + +## Pinned input + +The scientific source is canonical commit +`4c0a359d88f22f05189d51f48387750b801a45d4`, package +`research/coded-native-caller`. Exact retained files and hashes are in +`SOURCES.json` and `frozen/`. Governing guidance was read at canonical +`20a1e31bc6009b9b3f4d084bbaadc6350e34fcba`. + +There are 112 owners. The real scalar code A is invertible, has zero diagonal, +and has 52 nonzero entries in every row and column. Each source normalizer is +K_i = Z_(z_i) P_(G_i), with G_i an orthogonal binary 9 by 9 matrix and +G_i e_q = q_i. The 112 vectors q_i are distinct, of weight 3 or 7. These exact +properties were checked directly from CODE.json and NORMALIZERS.json; the +check did not invoke the source operator evaluator. + +Embed one copy K_(1,i) on the central axis q and the eight first-stage axes U, +and another K_(3,i) on q and the eight third-stage axes W. The full address +space has exactly 17 axes. The sets {q}, U, W are disjoint. G rows are used as +rows, not columns. Every operator is lifted columnwise; scalar owner matrices +are applied once, rather than tensoring an owner sum. + +Let Q be the central Gaussian, D3 the product of the eight third-stage +Gaussians, and + + C_s[i,j] = A[i,j] K_(s,i)^-1 K_(s,j). + +Dillon's four required controls are + + t0, Q^-1 t0 Q, t = D3 t0 D3^-1, + E = Q^-1 C3 t C1 Q^-1, + +including their explicitly implementable inverses. The main endpoint is + + F3 J(t0) F1 = [[0,t],[-E,0]] diag(G,G), + G = D1 D3 Q. + +## Exact scope of the obstruction + +Let H be the projective group of monomial Clifford operators on the actual +17 one-column address bits. A control in the tested class is a fixed finite +scalar owner program in columnwise lifts h^(tensor f), h in H. Owned copies, +temporary fields and clears are allowed as long as the resulting main block +has such a finite linear expansion. Coefficients may depend on f; the set of +letters is fixed independently of f. Projective phases are absorbed into the +scalar coefficients, including their correct f dependence. + +This is a generous algebraic model of the source's explicit P/D/X/phase +Clifford words and owner ADD programs. It gives no automatic physical tariff +or inverse implementation to an arbitrary algebra element. The completed +obstruction needs neither tariff nor inverse sufficiency: it rules out every +nonzero t0 in this declared class satisfying the four memberships at all +sufficiently large f. Section 4 also gives a direct scalar-owner proof which +does not require the transported-class argument. + +It does not cover arbitrary nonlinear monomial address maps, general +non-Clifford phases, or a number/alphabet of letters growing with f. It also +does not cover a changed FULL controller, extra paid calls, extra axes, a +different productive endpoint, or a different source code. + +## 1. Why all-width membership becomes support membership + +For any finite collection of pairwise nonproportional nonzero operator +vectors v_1,...,v_m, their tensor powers are linearly independent for every +f >= m-1. For each i and j != i choose a linear functional ell_(i,j) that +kills v_j but not v_i. The tensor product of these m-1 functionals kills +every v_j^(tensor(m-1)) except i. Additional factors nonzero on v_i extend +the argument to any larger f. This elementary argument also allows +width-dependent scalar coefficients. + +Apply the lemma to the finite projective Clifford alphabet containing all +letters in the fixed proposed programs and their conjugates. If t0 and its +Q and D3 conjugates are all represented by monomial Clifford programs at +every positive width, then at sufficiently large width every surviving +letter of t0 lies in + + H0 = H intersect Q H Q^-1 intersect D3^-1 H D3. + +Conjugate t0 by D3. Its support is in Ht = D3 H0 D3^-1. The following +observations do not identify Ht with H0: + +* t is monomial by hypothesis; +* D3^-1 t D3 = t0 is monomial, and conjugation by D3^2 shows that + D3 t D3^-1 is monomial as well; +* Q^-1 t Q = D3 (Q^-1 t0 Q) D3^-1 is not automatically monomial from + those statements alone. + +The last bullet is an essential warning: it cannot be inferred merely from +the three displayed controls. Consequently, the proof below uses the exact +support class for t, not an unjustified assertion that t is again in H0. + +Define instead + + Ht = D3 H0 D3^-1. + +Every surviving letter of t lies in Ht. The next section derives the actual +invariants of this transported class directly. + +## 2. Lagrangian invariants, including the D3 transport + +Use binary symplectic coordinates (x,z), with the computational Lagrangian +L0 = {(0,z)}. Let Lq = Q L0 and Lw = D3 L0. Their X projections are +span(e_q) and W respectively. Q and D3 have order two on binary symplectic +space even though their operator squares retain phases/Paulis. + +A monomial Clifford h has symplectic form + + x' = R x, + z' = S x + R^-T z, + +where R is invertible. For h in H0, it preserves L0, Lq and Lw. +Therefore R e_q = e_q and R W = W. This is the source-fixed flag constraint; +it does not identify every parity-even word with a physical free operation. + +For a transported letter k = D3 h D3^-1 in Ht: + +* k preserves L0 because h preserves Lw; +* k preserves Lw because h preserves L0 and D3^2 L0 = L0; +* k preserves Lqw = D3 Q L0 because h preserves Lq. + +Thus its invertible X block R_k preserves W. The X projection of Lqw is +span(e_q) plus W. Hence R_k preserves span(e_q) plus W as well. On the +quotient by W, R_k therefore fixes the nonzero central class [e_q]. +This is weaker than R_k e_q=e_q, and is exactly the distinction required +by the released warning about transport through D3. + +For nonzero v in span(e_q) plus U and nonzero w in span(e_q) plus W, define the rank-one +Gaussian chart L(v) = {(v v^T z,z)}. If k L(v) = L(w), its X projections +give R_k v = w. Passing to the quotient by W and using invertibility and +the fixed central class implies v=e_q. It does NOT imply w=e_q: w may +equal e_q plus a vector in W. + +This one-sided conclusion is sufficient for a useful obstruction below. + +## 3. No monomial endpoint component + +Expand an endpoint block E[i,j]. Every term is a scalar multiple of + + Q^-1 K_(3,i)^-1 K_(3,r) k K_(1,s)^-1 K_(1,j) Q^-1, + k in Ht, + +with scalar A[i,r] b[r,s,k] A[s,j], where b are the coefficients of t. + +For this word to be monomial, k must carry + + L(G_(1,s)^-1 q_j) to L(G_(3,r)^-1 q_i). + +Section 2 forces G_(1,s)^-1 q_j=e_q, so s=j by distinctness of the source +q vectors. But A[j,j]=0. Every term with a nonzero source coefficient is +therefore outside H. This conclusion does not require r=i. + +No uniqueness assertion for different intermediate owners is needed. +Group together any projectively equal nonmonomial terms. Their sum still +has support outside H; cancellation can remove classes but cannot create +a class in H. At all sufficiently large widths, section 1 makes the span +of these remaining nonmonomial classes disjoint from the span of the +finite monomial alphabet in any proposed FREE implementation of E. + +Consequently, if E is also FREE, E=0 at every such width. The exact source +codes C1,C3 and Q are invertible, so E=Q^-1 C3 t C1 Q^-1=0 implies t=0, +then t0=0. In particular the handoff's required invertible t0 cannot exist +inside this fixed finite columnwise monomial-Clifford control class. + +This result does not mistake Ht for H0. In fact Ht permits R_k e_q=e_q+w +with nonzero w in W. The proof needs only the induced quotient action and +the resulting one-sided equality s=j. It also does not need a uniform +inverse bound: the source code inverses are exact, and all four requested +inverse programs are rendered moot by the forward obstruction. + +For arbitrary width-dependent scalar coefficients, the exact conclusion +is t0_f=0 at every sufficiently large width satisfying the four +memberships. A family nonzero only at finitely many small widths is not +excluded, but cannot satisfy the all-width invertibility contract. + +## 4. Completed scoped theorem: scalar owner interleavers + +For t0 = B tensor I, all first three controls equal B tensor I and t=t0. +Its inverses, when supplied by an explicit scalar program, are physically +legal in the same scalar class. Each term of E[i,j] is now + + A[i,r] B[r,s] A[s,j] + * Q^-1 K_(3,i)^-1 K_(3,r) K_(1,s)^-1 K_(1,j) Q^-1. + +The signed linear permutation between the two Q^-1 factors has binary map + + M = G_(3,i)^-1 G_(3,r) G_(1,s)^-1 G_(1,j). + +For a signed orthogonal permutation M, Q^-1 M Q^-1 is monomial exactly +when M e_q=e_q. If the directions differ, the two central Gaussian factors +produce four distinct translations, all with nonzero coefficient; if they +agree, their equal or opposite signs give a single monomial. This includes +absolute-sign choices and does not tensor a scalar sum. + +Here M e_q=e_q is equivalent to + + G_(3,r) G_(1,s)^-1 q_j = q_i. + +The first-stage component can vanish only if G_(1,s)^-1 q_j=e_q, +so s=j; then distinct third-stage q vectors force r=i. Both source diagonal +entries are zero. Thus every nonzero term is nonmonomial. + +For fixed i,j, terms indexed by distinct pairs (r,s) are projectively +distinct. Equality would imply + + G_(3,r')^-1 G_(3,r) = G_(1,s')^-1 G_(1,s). + +The left map is supported on q+W and the right on q+U. Their intersection +contains only the identity binary linear map: both must fix U and W, and +an invertible map on the single common bit fixes q. Distinct q vectors then +give r=r' and s=s'. Conjugating by the fixed outside factors preserves +projective distinctness. Signed phases cannot change this argument. + +For any nonzero B[r,s], choose i with A[i,r] nonzero and j with A[s,j] +nonzero (there are 52 choices each). The corresponding nonmonomial term has +nonzero coefficient and cannot cancel. Uniform tensor separation against +any proposed fixed finite columnwise monomial alphabet rules out a FREE +representation of E at all sufficiently large widths. + +Hence no fixed nonzero scalar owner matrix B, including a dense one, +satisfies the fourth condition uniformly in that model. If coefficients +depend on f, the precise conclusion is B_f=0 at every sufficiently large +width where the endpoint belongs to the declared monomial span. This +excludes every all-width invertible family B_f; it does not exclude a family +supported only at finitely many small widths. +This theorem does not rely on classifying the whole physical FREE algebra. + +## Credit and open next question + +Credit Dillon for the released construction equations, the real normalizers +and their charged recoding; Dugongue/mdumitrean for PR4929 and A; Cao Yifan +for the native word; Cinna Davis, zxv, Jacob Alan Sussman, Ryanson Jonathan, +and the full retained native/helper/Clifford/compiler lineage. The elementary +uniform tensor-separation device is already used in the preceding projective +operator work; it is not claimed as a new theorem. New local analysis has +substantial OpenAI Codex assistance and no independent human or kernel +acceptance. + +The useful continuation must change at least one declared hypothesis: +the fixed columnwise monomial-Clifford control class, the sufficient four +FREE conditions (replacing some with an explicitly paid and affordable +operator), the source code, the productive target, or the controller. +Merely adding more Clifford owner/address couplings cannot create a +monomial component. A test that assumes R_k e_q=e_q after D3 transport +repeats the released error and must be rejected. diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-active-query-bound__PROOF.md b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-active-query-bound__PROOF.md new file mode 100644 index 0000000000..1ebf18af5b --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-active-query-bound__PROOF.md @@ -0,0 +1,394 @@ +# An active local-query obstruction for the actual 112-port code + +Prepared for Dillon, 2026-10-23, with substantial OpenAI Codex assistance. +This is a scoped exact local theorem with finite source checks, not a +complete-controller lower bound, a multiplication algorithm or an admission +claim. Apache-2.0. + +## Statement + +Use the actual physical native code from `research/coded-native-caller`: + +\[ + C_{ij}=a_{ij}K_i^{-1}K_j,\qquad J=Q^{-1}CQ, +\] + +where there are 112 owners, Q is the one-central-axis Gaussian, each K_i is +the retained signed orthogonal permutation normalizer, and the scalar matrix +a has zero diagonal and 52 nonzero off-diagonal entries in every column. +The 112 vectors q_i=G_i e_0 are distinct. The source factorization +C=I-14P has an eight-mode projector P. + +Fix any finite projective group H of invertible one-column monomial maps on the +declared fixed ambient address space, containing the source normalizers and +all admitted free address maps. For example, H may be the full group of +one-column permutations with phases in a fixed finite root-of-unity group; +the free permutations need not be Clifford. Every address map is lifted as +the SAME one-column map h on all f columns, h^tensor(f). Independent choices +on individual columns are outside this grammar. Free operations are +arbitrary linear owner programs over the +monomial subgroup algebra, including scalar operations, every +actual C or C inverse, owned COPY/CLEAR, arbitrary clean buffers, saved +banks, and fanout. These are charged as ordinary finite work; "free" here +means no recursive Gaussian call. Allow every paid unary call to apply an +arbitrary fixed one-field linear operator, with chronological linear +feedback from all available fields. In particular its input may use all +earlier paid responses. All coefficients are data-independent, although +they may depend on width. Every counted field has the same address width as +one source owner; a wider packed channel is not counted as one field. + +**Theorem.** A standalone exact implementation of J, or of J-I, on 112 +arbitrary fresh owner fields requires at least 112 paid unary field calls. +The statement is valid for an identity at all positive tensor widths, and +allows the scalar owner coefficients to depend on width. The same conclusion +holds after adding any free owner operator to J. +More precisely, the bound holds at every sufficiently large tensor width, +so no all-width implementation uses fewer than 112 calls. It is not a bound +at every small width: at width one, +Q=((1+i)/2)I+((1-i)/2)X is in the scalar span of free monomials. + +**Sharp one-sided corollary.** Put P=(I-C)/14. Each of QP and PQ, as a +112-input/112-output owner operator, requires at least 112 paid unary field +calls. Exactly 112 H1 calls suffice: apply P for free and then Q to every +output, or apply Q to every input and then P. Thus the eight scalar code +modes do not yield an eight-call one-sided Q repair. The statement also +holds with Q replaced by Q inverse. + +**Canonical eight-mode corollary.** For the actual source mode matrix M, +let U_mode=diag(K_i^-1)M and V_mode=M^T diag(K_i)/56. Then +P=U_mode V_mode and V_mode U_mode=I_8. Each of Q U_mode (eight fresh inputs, +112 outputs) and V_mode Q (112 fresh inputs, eight outputs) also has exact +paid-field-call complexity 112, attained by 112 H1 calls. Thus the canonical +rectangular mode ABI does not avoid the one-sided obstruction. + +It does not cover receiving Gaussian-dependent saved data, absorbing the +correction into the paid native FULLs or their prefixes, recycling an existing +paid IDLE, or a direct coded consumer with a different endpoint. Nonlinear +controls, noncolumnwise address operations, approximate endpoints, and +unequal-width packing are outside the stated model. + +## 1. Phase-correct finite algebra and all-width evaluation + +This uses the finite-phase algebra and sufficiently-large-width tensor +faithfulness already proved in `coded-port-adapter-ceiling/PROOF.md`, section +3, and clarified by the passive saved-query package's uniform-alphabet +addendum. Here only the FREE group H must be finite projectively. An ambient +group generated by H and Q need not be finite or Clifford. + +Choose one invertible matrix representative for every projective element +of H. At width f its nonzero scalar multiplication cocycle is raised to +the f-th power; the scalar factors need not have modulus one. +Let B_f be the resulting finite-dimensional twisted group algebra over +k=C, with one basis element per projective element of H. Its evaluation +is the span of the literal tensor lifts h^tensor(f). Scalar factors are +retained through the cocycle; owner coefficients are applied only once. + +Besides H itself, we will need only a fixed finite union of its projective +cosets: the sets g_ij H used for J, the analogous right cosets for PQ and +V_mode Q, and the analogous left cosets for QP and Q U_mode. Take S to be +their union with H, with repeated projective elements identified. This set +is finite because H and the source owner/mode sets are finite. Closure of +S under multiplication is not needed: all free products remain in H, and +every target-times-free expression used below stays in its declared coset +set. A different fixed finite number of source stages merely enlarges S. + +For projectively distinct nonzero representatives v_1,...,v_N, individually +normalize each by its Hilbert-Schmidt norm. Their tensor-power +Gram matrix has diagonal one and off-diagonal entries +^f, whose magnitudes are at most rho^f for some rho<1. For +(N-1)rho^f<1 the Gram matrix is strictly diagonally dominant and positive +definite. Apply this to the projective representatives in S. Their literal +tensor lifts are linearly independent for every sufficiently large f. +Thus B_f and all the required coset subspaces evaluate faithfully, with +distinct cosets in direct sum, at those widths. Scalar factors remain raised +to the f-th power; owner coefficients are never raised to that power. + +We work at any one such width. The threshold is uniform over all free +coefficients, control choices, and control lengths because H and S are +fixed. Width-dependent scalar coefficients are allowed. A width-dependent +or noncolumnwise group of arbitrary payload maps is not allowed; neither +is an infinite projective phase grammar. No assumption that arbitrary +permutations together with Q generate a finite group is made. + +## 2. Actual-source right-coset separation + +Write g_ij=Q^-1 K_i^-1 K_j Q. For a fixed i, + +\[ + g_{ij}^{-1}g_{ik}=Q^{-1}K_j^{-1}K_kQ. (1) +\] + +For the signed orthogonal permutation M=K_j^-1 K_k, let G=G_j^-1 G_k be +its binary orthogonal coordinate matrix and e=e_0. Pauli signs affect only +tableau phases. The Z-to-X block of Q^-1 M Q is + +\[ + B=G e e^T+e e^T G. (2) +\] + +If G e=e, orthogonality gives e^T G=e^T, and B=0. If G e differs from e, +then both pairs (G e,e) and (e,G^T e) are independent; the two outer products +in (2) have rank two. Thus Q^-1 M Q is monomial exactly when G e=e. +Equivalently, G_j e=G_k e, or q_j=q_k. The actual 112 source vectors are +distinct, so (1) belongs to H exactly when j=k. + +Therefore the 112 g_ij lie in distinct right H-cosets for each fixed i. +The j=i coset is H itself, since g_ii=I. The scalar phase quotient does not +alter this test: multiplying by a scalar never changes monomiality. +The companion checker verifies all 112^2 ordered pairs by both formula +(2) and the retained exact tableau implementation. It separately checks +the actual code's zero diagonal and nonempty column supports. + +## 3. No nonzero free input survives modulo a free output + +Let F_0 be ANY 112-by-112 matrix over B_f. Suppose w in B_f^112 obeys + +\[ + (J-F_0)w=0. (3) +\] + +Row i of Jw is sum_j a_ij g_ij w_j. Each summand lies in the right-coset +subspace g_ij B_f. These subspaces are in direct sum. Every component of +F_0 w lies in B_f, the H coset. The diagonal source coefficient is zero. +For each off-diagonal supported pair (i,j), projecting (3) onto g_ij B_f +therefore gives a_ij g_ij w_j=0. A nonzero scalar and a group unit are +invertible, so w_j=0. Each column j has a supported off-diagonal entry, +and hence w=0. + +This is stronger than an eigenvector statement: J-F_0 has zero kernel on +B_f^112 for every free F_0. In particular the Q-conjugated eigenspaces of +C contain no nonzero free input embedding, despite the eight-mode +factorization of C-I. A cheap compression of J-F_0 through fewer than 112 +owner fields is impossible. + +### One-sided projector operators + +Write p=(I-a)/14, so P_ij=p_ij K_i^-1 K_j and p_ii=1/14. For PQ, fix row +i. Its blocks are p_ij h_ij with h_ij=K_i^-1 K_j Q. Every h_ij has Fourier +grade one and lies outside H. Further, + + h_ij^-1 h_ik = Q^-1 K_j^-1 K_k Q. + +Thus the h_ij occupy distinct right H-cosets as j varies. The same argument +proves ker_{B_f}(PQ-F_0)=0 for every free F_0; the nonzero diagonal of p +already supplies a supported entry in each column. + +For QP fix column j instead, and put t_ij=Q K_i^-1 K_j. These grade-one +words lie in distinct LEFT H-cosets as i varies, because + + t_ij t_kj^-1 = Q K_i^-1 K_k Q^-1 + +is nonmonomial for i different from k. Consequently a free row w satisfying +w(QP-F_0)=0 must vanish: project each fixed output column onto the distinct +left-coset subspaces B_f t_ij, and use p_ii different from zero. This is the +left-kernel version of the same source-specific separation. + +### Canonical rectangular eight-mode maps and free rebasing + +The retained 112-by-8 scalar mode matrix M obeys M^T M=56I_8 and +a=I-MM^T/4; each row has four nonzero entries. The checker verifies every +entry of these identities from the pinned source receipt. Define + + U_mode = diag(K_i^-1) M, shape 112 by 8, + V_mode = M^T diag(K_i)/56, shape 8 by 112. + +These maps are free, with P=U_mode V_mode and V_mode U_mode=I_8. +For Q U_mode the fixed mode-column a has entries M_ia Q K_i^-1. The words +t_i=Q K_i^-1 lie in distinct left H-cosets, since +t_i t_k^-1=Q K_i^-1 K_k Q^-1 is nonmonomial when i differs from k. +Each t_i itself is nonmonomial. Every row of M has a nonzero entry, so +the same columnwise projection proves that + + w (Q U_mode-F_0)=0, w in B_f^(1 by 112), + +forces w=0 for every free 112-by-8 F_0. Thus the no-left-kernel conclusion +holds even though there are only eight fresh inputs. + +Dually, V_mode Q has entries M_ja K_j Q/56. The words K_j Q lie in +distinct right H-cosets because their pairwise relative transports are +Q^-1 K_j^-1 K_k Q. Every source column is represented in at least one mode +row. Hence (V_mode Q-F_0)w=0, with w in B_f^112, forces w=0 for every free +8-by-112 F_0, even though there are only eight outputs. + +These conclusions cover all free changes of retraction basis. If another +free pair U',V' has P=U'V' and V'U'=I_8, then + + W=V_mode U', W^-1=V' U_mode, + U'=U_mode W, V'=W^-1 V_mode. + +The two inverse identities follow by substituting U'V'=P and +U_mode V_mode=P. Thus Q U' and V'Q differ from the canonical operators by +invertible free input or output boundaries. No cheaper implementation is +obtained by any such free eight-mode basis choice. + +## 4. Arbitrary chronological paid calls + +Normalize any finite acyclic linear implementation by retaining all paid +responses y_1,...,y_r. COPY, saves, fanout, overwrite and CLEAR are included +in this normalization: enlarging owned storage can preserve the history +without introducing another recursive call. At paid call t its input is + +\[ + b_t x+\sum_{s B_f^r. As a k-linear map its +domain has dimension 112 dim_k B_f and its codomain has dimension +r dim_k B_f. If r<112, choose a nonzero w in its kernel. Substitute the +formal input x=w z, with z one arbitrary field. Every direct term b_t w is +zero. Induction on t in (4) gives every paid response y_t=0, regardless of +T_t and regardless of the active feedback coefficients. Thus the claimed +endpoint J must satisfy Jw=F_0w. Section 3 contradicts this. + +This proves r>=112. Replacing J by J-I or J+F_free merely changes the free +matrix F_0 and gives the same result. + +The input-kernel proof applies verbatim to PQ. For QP use the dual output +cut: concatenate the free output columns in (5) into L in B_f^(112 by r). +If r<112, the k-linear map w -> wL from B_f^(1 by 112) to B_f^(1 by r) +has a nonzero kernel row w. Multiplying the endpoint by that row annihilates +every paid-response term, so w(QP-F_0)=0, contrary to the left-kernel result. +No assumption about the paid calls' chronology is needed beyond the +existence of the finite linear circuit normal form. + +For Q U_mode the same output cut has 112 rows and r paid-response columns, +although F_0 has only eight input columns. It again gives r>=112. For +V_mode Q the same input cut has 112 input columns, although F_0 has only +eight output rows, and also gives r>=112. Both bounds are attained by +112 H1 calls: expand eight fields through U_mode for free and apply Q to +all 112 results; or apply Q to the 112 inputs and contract through V_mode +for free. Invertible free retraction basis changes preserve these counts. +The same arguments apply with Q inverse throughout. + +## 5. Direct sums and local amortization + +For any fixed positive m, consider m fresh physical code blocks, embedded +in one fixed ambient address space. Each block may use its own eight fresh +axes and physical normalizers, with the same 112 distinct-direction +property. Let N=112m. The same proof gives + +* diag(J_1,...,J_m), or its free perturbation: at least N paid field calls; +* diag(P_1 Q,...,P_m Q): exactly N H1 calls are necessary and sufficient; +* diag(QP_1,...,QP_m): exactly N H1 calls are necessary and sufficient. +* diag(Q U_mode,1,...,Q U_mode,m), and its free retraction rebases: + exactly N H1 calls are necessary and sufficient; +* diag(V_mode,1 Q,...,V_mode,m Q), and its free retraction rebases: + exactly N H1 calls are necessary and sufficient. + +Free controls may mix different blocks arbitrarily. To see why this does +not change the proof, write a candidate free kernel column or row in m +blocks. Project each target block's rows or columns onto its nontrivial +cosets. The free comparison operator still contributes only the H coset, +even when it mixes all N owners. The corresponding single-block argument +forces every block of the candidate kernel to vanish. Apply the input or +output dimension cut with B_f^N and r=1 and price at least one, so the local correction costs at least 112. +Its added recursive price exceeds the removed-center saving by at least +48 per FULL. The direct-sum theorem gives a gap of at least 48m for m such +standalone local repairs, even when their free controls mix all inputs. + +Thus this isolated interface-restoration strategy cannot turn the removed +eight H8 calls into a recursive saving anywhere in 0<=c<1. Extra ordinary +work can only increase the cost. The conclusion does not price or rule out +absorption into correlated FULL, IDLE, or saved-query data in a complete +caller, nor a different direct coded endpoint. + +### Relationship to predecessor and active caller work + +The predecessor `coded-port-adapter-ceiling` (#4932) proves that one parallel +bank needs 112 grade-2 channels for its physical recovery adapter, using a +grade projection of full rank. It expressly excludes multiple chronological +banks. The argument here uses source-specific distinct right cosets and an +input-kernel cut to cover arbitrary chronological paid unary calls and +active feedback. Its conclusion is 112 calls of any grade; it does not +claim 112 grade-2 calls in this enlarged model. + +The conclusion excludes an independently implemented 16-, 32-, or 42-H1 +fresh-input correction of J, J-I, QP, or PQ through the native code's eight +modes. For J and J-I this is a lower bound, with the elementary 224-H1 +conjugation implementation as an upper bound; 112-call attainability is +not asserted. For QP and PQ the 112-H1 bound is attained. +It does not prove that p2 needs four thin banks, nor that a complete active +three-bank caller is impossible. Such a caller can already hold nonfree +data from its FULLs, queries, and IDLE. A useful construction must exploit +that shared paid access, change the endpoint, or leave this local grammar. +The particular eight-mode ABIs Q U_mode and V_mode Q, including their free +retraction rebases, are covered above. An arbitrary different eight-mode +endpoint, the middle compression V_mode Q U_mode, and the two-sided +compression PQP remain outside the claims. + +The actual #4932 entrance adapter is also covered by free equivalence. Its +physical monomial X wrapper is M_i=U_i K_i Q^-1. Therefore +U a U*=M (Q C Q^-1) M*, and Q C Q^-1=Q^2 J Q^-2. Since Q^2 and M are free, +and a^-1=(a+12I)/13, the physical U a^-1 U* differs from J by invertible +free boundaries, a nonzero scalar, and a free bypass. These operations +preserve the local paid-call lower bound. This correspondence uses the +retained exact physical wrapper identities; it does not replace U_i with +a bare Fourier along q_i. + +## Source and predecessor credit + +The source code and native producer are Dugongue's #4929. The actual signed +orthogonal normalizers and physical C formulation come from the retained +`coded-native-caller` package. The finite-phase group algebra, tensor +faithfulness, adapter scope and warning that rank-eight scalar modes are not +eight query heads come from #4932. The uniform finite-alphabet clarification +and related passive-controller limitations come from the retained passive +saved-query package. Credit also Cinna Davis/1337isnot1337's #4694/#4698, +Cao Yifan/intqwq's #4610 source, zxv's retained exact Clifford/compiler work, +and all source notices. This active local input-kernel argument was derived +in the current research session with substantial OpenAI Codex assistance. + +No independent human or formal-kernel acceptance is claimed. The source +native all-input theorem, numerical outer admission, and complete caller +endpoint are inherited or open, not replayed by this scratch result. diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-active-query-bound__README.md b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-active-query-bound__README.md new file mode 100644 index 0000000000..f8858cea6b --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-active-query-bound__README.md @@ -0,0 +1,60 @@ +# Sharp active local query cost for the physical eight-mode code + +**The physical code's one-sided correction and eight-mode extraction/expansion each require exactly 112 unary field calls in the stated local model, attained by 112 H1 calls.** The conjugated adapter `J=Q^-1 C Q` and `J-I` each require at least 112 unary paid calls. The proof permits arbitrary chronological linear feedback, saved inputs, copies, owned resets, fanout and free mixing across any fixed number of independent blocks. No new κ or complete-caller lower bound is claimed. + +Here `C_ij=a_ij K_i^-1 K_j` is the actual 112-port code from [#4933](https://github.com/CrocSwap/integer-mult-bounds/pull/4933), `P=(I-C)/14`, and Q is the central rank-one Gaussian. A field call operates on one owner-width field. Free operations are finite linear owner programs over a fixed finite projective group of one-column invertible monomial maps; they have ordinary scalar/routing/precision cost but no recursive Gaussian call. Paid unary maps may be arbitrary zero-preserving linear maps, so the lower bound also applies when those maps are Gaussian calls of any rank. + +The free permutations may be non-Clifford; no finite ambient Clifford group is assumed. The theorem concerns identities required at every positive tensor width; its obstruction holds at every sufficiently large width. Each admitted one-column map h acts by the same tensor lift `h^⊗f` in every column; independent per-column choices are not admitted. Scalar coefficients and finite control choices may depend on width. At width one, Gaussian operators can lie in the scalar span of monomials, so the lower bound is deliberately not asserted for every small width. It excludes wider packed channels, arbitrary noncolumnwise address maps, nonlinear or data-dependent controls, approximate endpoints and preexisting nonfree observations of the fresh inputs. A running native caller may already possess such observations, so this result does not exclude an active three-query p2 construction. + +Write `U=diag(K_i^-1) M` and `V=M^T diag(K_i)/56` for the actual source mode maps. Then `P=UV` and `VU=I_8`. The local endpoints have the following exact call bounds at sufficiently large width: + +| Endpoint | Fresh input fields | Output fields | Paid unary calls | +|---|---:|---:|---:| +| QP or PQ | 112 | 112 | Exactly 112 | +| QU, mode expansion followed by Q | 8 | 112 | Exactly 112 | +| VQ, Q followed by mode extraction | 112 | 8 | Exactly 112 | +| J or J-I | 112 | 112 | At least 112; 224 H1 suffice | + +The mode bounds also cover every free eight-mode retraction basis `P=U'V'`, `V'U'=I_8`, since these differ from U,V by invertible free boundaries. They do not classify arbitrary unrelated eight-output operators. + +## What changes relative to the predecessors + +[#4932](https://github.com/CrocSwap/integer-mult-bounds/pull/4932)'s [coded-port adapter ceiling](../coded-port-adapter-ceiling/README.md) treats one parallel query bank and forces 112 grade-two channels. The [passive saved-query ceiling](../passive-saved-query-ceiling/README.md) keeps its later paid inputs fixed. This package uses a different invariant: the physical port transports occupy distinct monomial cosets. An input or output kernel cut then covers **arbitrary chronological paid calls and active linear feedback** for the standalone local endpoint. Its 112-call result counts calls of any grade; it does not extend the predecessor's grade-two conclusion to the larger model. + +The core source fact is that the 112 vectors `G_i e0` are distinct. For each fixed output i, the words `Q^-1 K_i^-1 K_j Q` lie in distinct right monomial cosets. Each source column has 52 nonzero off-diagonal entries. Consequently `J-F` has no nonzero free input column for any free bypass F. A circuit with fewer than 112 unary calls has a nonzero free input direction that vanishes at every paid input, even when later calls use previous responses. These statements contradict each other. The output-cut version proves the QP bound; the input-cut version proves PQ. Applying Q to all 112 fields before or after the free P realizes each one-sided upper bound. + +For m independent copies, arbitrary cross-copy free mixing still requires 112m calls. The one-sided 112m-H1 upper constructions attain those bounds. This is a direct-sum statement about the declared local endpoints, not about amortization into already-paid FULLs, IDLEs or native internal prefixes. For J/J-I, 112-call attainability remains open; the elementary conjugation uses 224 H1 calls. + +An isolated repair that restores one backward coded FULL to the ordinary uncoded FULL is also priced sharply. Since `C=I−14P`, the exact entry patch is `X ← X−14QP Y`; it needs 112 H1 calls in the enlarged local model. The inherited producer removes only 8 H8 calls, worth at most 64 in every moment with exponent `1−c`, `0≤c<1`. Thus such an independently implemented repair increases the recursive paid bill by at least 48 per FULL, or 48m for a direct sum. The eight-H8 removal is an inherited source invoice, not replayed by this checker. Absorbing the patch into already-paid native operations is outside the corollary. + +The mathematical argument, finite phase treatment and all-width scope are in [PROOF.md](PROOF.md). [INDEPENDENT-REVIEW.md](INDEPENDENT-REVIEW.md) records a separately derived proof audit and binary census. [EXTENSION-REVIEW.md](EXTENSION-REVIEW.md) audits the finite-H extension, rectangular modes, rebasing, direct sums and isolated-patch tariff. Neither is independent human or proof-kernel acceptance. + +## Evidence and reproduction + +Python 3.12 for the registered runner, standard library only, from the repository root: + +```sh +python3 -B scripts/research_package.py --package research/coded-active-query-bound +``` + +Direct replay, including after an official package export with its declared inputs: + +```sh +python3 -I -W error -B research/coded-active-query-bound/verify.py +python3 -I -O -W error -B research/coded-active-query-bound/verify.py +python3 -I -O -W error -B research/coded-active-query-bound/independent.py +``` + +The main verifier authenticates the code, normalizers and exact Clifford implementation before executing the latter's source bytes. It checks all 12,544 ordered port pairs by both a separately written binary formula and source tableaus: 112 self pairs have grade 0; 12,432 distinct pairs have grade 2; all 5,824 supported off-diagonal code terms are grade 2. It also checks 12,544 left-coset conjugates, 12,544 one-sided grade-one transports, the 52-entry column supports, all 12,544 entries of `a=I-MM^T/4`, all 64 entries of `M^T M=56I`, and four mode contacts per owner. Four rejection controls alter a direction, a source column, the diagonal or a mode factor. The independent checker imports no Clifford implementation. Both compare exact finite receipts; checks remain active under `-O`. + +[RESULT.json](RESULT.json) and [INDEPENDENT.json](INDEPENDENT.json) are finite source receipts. They do not enumerate the monomial group algebra, test every circuit, or mechanically prove the tensor/kernel argument. [SOURCES.json](SOURCES.json) pins frozen main `4c0a359d88f22f05189d51f48387750b801a45d4`, live inputs and proof provenance. [VERIFY.json](VERIFY.json) declares every live input. The submission base is refreshed canonical main `20a1e31bc6009b9b3f4d084bbaadc6350e34fcba`; the earlier scientific pins remain unchanged. No predecessor package is copied or altered; provenance-only proof references resolve through the pinned Git history. [VALIDATION.md](VALIDATION.md) states executed checks and unrun obligations. + +## Open next questions + +Can a complete coded caller use nonfree observations that its FULLs and IDLEs already produced to recover all prescribed independent Gaussian outputs? This is the meaningful route left by the local result. The first step is one explicit changed paid input with its retained observations, followed by all terminal operator identities and a complete invoice. The current package supplies no such global endpoint. The final checkpoint also reviewed Cinna Davis's [common-code moving-stage interface](../common-code-moving-stages/README.md), whose transported Gaussian stages fail the inherited commutation relation, and JoyboyBrian's [fresh-D coherent-pair countermodel](../two-full-fresh-d-coherent-pair/README.md). Their changed interfaces and endpoint obligations remain distinct from this local query theorem. + +What is the exact complexity of J or J-I between 112 and 224 calls? A smaller explicit chronological circuit or stronger cut invariant would resolve the gap. The sharp 112 result for QP/PQ does not settle it. Structured first steps and blockers are in [TASK.json](TASK.json). + +## Credit + +Prepared for Dillon with substantial OpenAI Codex assistance from separate proof, independent-review, construction and packaging agents. Credit Dugongue's center-free producer [#4929](https://github.com/CrocSwap/integer-mult-bounds/pull/4929), the real signed normalizers/physical C in #4933, Chris R/Clear1nsight's #4932 finite phase algebra and one-bank theorem, the passive package's uniform-alphabet clarification, Cinna Davis/1337isnot1337's #4694/#4698, Cao Yifan/intqwq's #4610 native source, zxv and the retained Clifford/helper/compiler lineage. See [ATTRIBUTION.md](ATTRIBUTION.md). Standard causal/image/row-space rank cuts retain earlier method credit to eumemic's PR288 and Ali Romman's PR468, as summarized in [fixed-support unary-query bounds](../fixed-support-unary-query-bounds/README.md); that different carrier theorem does not imply the physical-code result here. New work is Apache-2.0. 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-native-caller__PHYSICAL.md b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-native-caller__PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-native-caller__PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-native-caller__clifford_exact.py b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-native-caller__clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__coded-native-caller__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<>j&1));vs=[1^(1<>j)&1)for j in range(N)))) + # Exact symbolic tableau plus an absolute-phase state; not merely ranks. + need(equal(K.then(R),R.then(K)),'Exact full-Gaussian commutator') + need(all((ce.mv(ce.transpose(G,N),x).bit_count()-x.bit_count()-2*ce.parity(z&x))%4==0 for x in range(512)),'Literal weight congruence') + if z: + need(not equal(perm.then(R),R.then(perm)),'Omitting signed phase must fail') + phase_controls+=1 + E=ce.canonical_frame(N,canonical['frames'][canonical['start'][idx]]) + S=ce.canonical_frame(N,canonical['frames'][canonical['final'][112+idx]]) + need(canonical['final'][idx]==1 and canonical['start'][112+idx]==0,'Full-X and ground-Y boundaries') + MX=Q.adjoint().then(K).then(E);MY=K;OX=K.adjoint();OY=S.adjoint().then(K.adjoint()).then(D) + need(all(monomial(op)for op in (MX,MY,OX,OY)),'Every physical wrapper is monomial') + need(equal(MX.then(E.adjoint()),Q.adjoint().then(K)),'All incoming coded columns') + need(equal(S.then(OY),K.adjoint().then(D)),'All outgoing coded rows') + need(equal(MX.then(E.adjoint()).then(R).then(OX),D),'Independent X diagonal') + need(equal(MY.then(S).then(OY),D),'Independent Y diagonal') + need(equal(MX.then(E.adjoint()).then(S).then(OY),Q.adjoint().then(D)),'Original same-port shear block') + # K is a real signed permutation. The real transpose equals its adjoint. + need(all(e[0]!='D'or all(a%2==0 for a in e[2])for e in K.circuit),'Real K phases') + # Raw inverse transpose uses conjugated endpoint frames and wrappers. + Q2=Q.then(Q);D2=D.then(D) + BX=Q2.adjoint().then(conjugate(MX)) + BO=conjugate(OX).then(D2).then(Q2) + BY=conjugate(OY).then(D2) + need(equal(BX.then(conjugate(E).adjoint()).then(conjugate(R)).then(BO),D),'Backward corrected X diagonal') + need(equal(K.then(conjugate(S)).then(BY),D),'Backward corrected Y diagonal') + need(equal(conjugate(R).then(BO),K.adjoint().then(Q).then(D)),'Backward all coded outgoing rows') + need(all(monomial(op)for op in (BX,K,BO,BY)),'Backward corrected wrappers monomial') + operations={'input_X':MX,'input_Y':MY,'output_X':OX,'output_Y':OY, + 'backward_input_X':BX,'backward_input_Y':K,'backward_output_X':BO,'backward_output_Y':BY} + compiled={} + for name,op in operations.items(): + mon,recipe=ce.monomial(op) + need(equal(mon,op),'Compiled monomial exact phase and tableau') + need(all(e[0] in ('P','D','X','phase')for e in mon.circuit),'No Gaussian in emitted wrapper') + compiled[name]={'word':mon.circuit,'recipe':recipe} + wrong=ce.Op(N,K.tab,K.circuit+[('phase',1)]) + need(not equal(wrong,K),'Absolute-phase-only mutation rejected') + records.append({'port':idx,'q':q,'orthogonal_transvections':vs,'G_rows':G,'Z_mask':z, + 'K_word':K.circuit,'compiled_wrappers':compiled}) + need(phase_controls>0,'Nonvacuous omitted-phase control') + # Independent scalar execution of A and A^-1 on every arbitrary-input basis. + for inverse,den in ((False,4),(True,52)): + for j in range(112): + x=[F(i==j)for i in range(112)] + temp=[sum(F(c[i])*x[i]for i in range(112))for c in M] + y=[x[i]-sum(F(M[k][i])*temp[k]for k in range(8))/den for i in range(112)] + target=[A[i][j]if not inverse else (A[i][j]+12*F(i==j))/13 for i in range(112)] + need(y==target,'Literal owned-mode scalar recoding') + result={'schema':'coded-native-real-normalizers/1','status':'PASS_CODED_NATIVE_REAL_NORMALIZERS', + 'source_payload_sha256':SOURCE_PAYLOAD,'code_sha256':CODE_HASH,'clifford_sha256':CLIFFORD_HASH, + 'ports':records,'mode_columns':M,'finite_checks':{'ports':112,'weight_congruence_addresses':112*512, + 'exact_endpoint_factor_identities':112*8,'monomial_wrappers':896,'omitted_phase_rejections':phase_controls, + 'scalar_basis_recodings':224,'gaussian_free_compiled_wrappers':896,'absolute_phase_mutations_rejected':112}, + 'recoding_bill':{'owned_fields':8,'signed_mode_adds':448,'output_scaled_adds':448, + 'owned_initial_clears':8,'owned_terminal_clears':8,'monomial_field_maps':224, + 'forward_update_coefficient':'-1/4','inverse_update_coefficient':'-1/52', + 'forward_prefix_component_l1_upper':57,'inverse_prefix_component_l1_upper':56,'inverse_output_prefix_component_l1_upper':'69/13'}, + 'local_gauge_bill':{'recodings':2,'added_recursive_calls':0,'owned_fields_reused':8, + 'recoding_scalar_adds':1792,'recoding_owned_clears':32,'recoding_monomial_field_maps':448, + 'main_wrapper_field_maps':448,'backward_extra_monomial_field_maps_upper':448}, + 'scope':'Exact physical central ABI and local gauges; not full-controller or multiplication admission.'} + return json.loads(json.dumps(result,sort_keys=True)) + +def render_receipt(result): + """Keep each generated port record on one line; compare parsed mathematics.""" + entries=[] + for key,value in sorted(result.items()): + if key=='ports': + body='[\n'+',\n'.join(' '+json.dumps(row,sort_keys=True,separators=(',',':')) for row in value)+'\n ]' + else: + body=json.dumps(value,sort_keys=True,separators=(',',':')) + entries.append(' '+json.dumps(key)+': '+body) + return '{\n'+',\n'.join(entries)+'\n}\n' + +def main(): + p=argparse.ArgumentParser();p.add_argument('--write',action='store_true');args=p.parse_args() + result=run();path=HERE/'NORMALIZERS.json' + if args.write:path.write_text(render_receipt(result)) + else:need(json.loads(path.read_text())==result,'Changed generated normalizer receipt') + print(result['status'],json.dumps(result['finite_checks'],sort_keys=True)) +if __name__=='__main__':main() diff --git a/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__native-center-free-code__CODE.json b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__native-center-free-code__CODE.json new file mode 100644 index 0000000000..03170f4a31 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/independent-review/frozen/research__native-center-free-code__CODE.json @@ -0,0 +1 @@ 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diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/FILES.json b/research/released-operator-clifford-ceiling/evidence/inventory/FILES.json new file mode 100644 index 0000000000..0f1e4c6771 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/FILES.json @@ -0,0 +1,13 @@ +{ + "REPORT.md": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "SOURCES.json": "e19a7a22d535a438911c28aa3fc36daf7b0a3db582ccc429d986bb981dad68c7", + "source/RELEASE-MONITOR.json": "1aa74f9b72d60a4e4357bc3ea9e70c650c870432714aed11b2cda46518f74952", + "source/research__coded-active-query-bound__PROOF.md": "495a1cd85cc45020adf2205f196b57dc4f65f1eb763fc4951facdb4ccbafc768", + "source/research__coded-active-query-bound__README.md": "95269b047c19069caeb11edd36a485a0a86275b329aa44da90c8c08403e09178", + "source/research__coded-active-query-bound__SOURCES.json": "afb6ca7a3b924d19b61b784266693b892722024d5a33de3e432fc6499238241e", + "source/research__coded-native-caller__NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "source/research__coded-native-caller__PHYSICAL.md": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "source/research__coded-native-caller__clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "source/research__coded-native-caller__normalizers.py": "7616b75758c1b36b6c05eb7fff1630f604e7563762701bccb18ec638a61090df", + "source/research__native-center-free-code__CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" +} diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/REPORT.md b/research/released-operator-clifford-ceiling/evidence/inventory/REPORT.md new file mode 100644 index 0000000000..8a200e2535 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/REPORT.md @@ -0,0 +1,230 @@ +# Released two-FULL/one-query problem: source inventory + +Source inventory only, 2026-10-23. No t0 solver, search, native replay, compiler, +factory or external post was performed. The monitor authenticated Dillon's +release of original #4930 comment 19141406 and the new handoff at comment +19143357. Its exact local receipt is preserved as `source/RELEASE-MONITOR.json`. +The public theorem is `0e8a13c251a9be1029114cda8b4194f05f3a23ec`, +`research/coded-active-query-bound`; the actual code/normalizer scientific pin +is `4c0a359d88f22f05189d51f48387750b801a45d4`. The publication base is +`20a1e31bc6009b9b3f4d084bbaadc6350e34fcba`. Eight exact source files and their +hashes are listed in `SOURCES.json`. + +## Stock and actual operators + +There are two main banks of 112 arbitrary independent owner fields each. +Each field has the fixed 17-axis address stock: one shared central axis q, +eight stage-1 axes and eight disjoint stage-3 axes, lifted to f columns, plus +all retained external row/spectator fields. There is no new anchor or extra +address axis. Two fresh source FULLs add two disjoint banks of 408 arbitrary +helper inputs: 816 helper owners, 1040 original main-plus-helper owners total. +An owned query bank is dependent workspace, not productive input credit. + +Q is the actual central Gaussian, D1 and D3 the products on their respective +eight axes. They are invertible symmetric actual Gaussian operators; the +different axis factors commute. Q is not order two: its exact square is a +Pauli translation. Put G=D1 D3 Q, a rank-17 Gaussian on the complete stock. + +The physical code is not the scalar matrix A. The source gives + + Cs[i,j] = A[i,j] Ki,s^-1 Kj,s, + Fs = diag(Ds,Ds) L(Cs Q^-1). + +The exact local K words, G_rows, Z_mask and compiled monomial wrappers are in +`NORMALIZERS.json`. Embed their nine local coordinates as q plus the selected +stage's eight coordinates, with the other stage as identity. These are stored +matrix ROWS; replacing them by columns changes the operator. The K maps are +real signed orthogonal permutations, commuting with Ds Q but not generally +with Q or Ds separately. Their all-column lift retains the accumulated phase; +owner coefficients are applied once, not tensor-powered with the address map. + +## Released sufficient template and all four conditions + +All controls are 112-by-112 owner-operator matrices on this same field width. +They are not necessarily single Clifford operators. Seek an invertible t0 +such that each of the following has an explicit physically free program AND +an explicit program for its inverse: + +| Control | Definition | Mathematical inverse, in exact order | +|---|---|---| +| R1 | t0 | t0^-1 | +| R2 | S0=Q^-1 t0 Q | Q^-1 t0^-1 Q | +| R3 | t=D3 t0 D3^-1 | D3 t0^-1 D3^-1 | +| R4 | K=Q^-1 C3 t C1 Q^-1 | Q C1^-1 t^-1 C3^-1 Q | + +The released middle operator is + + J(t0) = [[-t0 C1, t0 Q], [0, -C3 S0]]. + +Under the source identities, the handoff states + + M = F3 J(t0) F1 + = [[0,t],[-K,0]] diag(G,G). + +The cancellation uses the actual source relations [C1,D1 Q]=0 and +[C3,D3 Q]=0, plus [C1,D3]=0 from the disjoint fresh-axis embedding. +For example the upper-left block of J F1 is +t0(-C1 D1+D1 Q C1 Q^-1)=0; the lower-right block of F3 J F1 cancels +by S0=Q^-1 t0 Q. No commutation of t0 with either Gaussian is assumed. + +Writing S=[[0,t],[-K,0]], its full main endpoint is + + Xout=t G Yin, Yout=-K G Xin. + +There is no main/helper leakage in the inherited FULL endpoint. The helpers +retain their autonomous source transformations. If the four explicit free +program/inverse requirements hold, the post-map + + S^-1 = [[0,-K^-1],[t^-1,0]] + +would return the main outputs to diag(G,G) on the 224 original inputs, with +the two banks routed back to their declared owners. Invertibility alone is +not a physical implementation of this post-map. + +The mathematical raw inverse transpose is, using transpose rather than +Hermitian adjoint, + + M^-T = S^-T diag(G^-1,G^-1), + S^-T = [[0,t^-T],[-K^-T,0]]. + +An actual reversed/transpose tape must preserve the source raw-dual convention, +all phases and owned-buffer lifecycles. For a source backward FULL the retained +normalization is X-only Q^2 conjugation, with D_s^2 output corrections; the +older Y-only convention cannot be substituted. The formulas here do not emit +that tape or automatically provide physical transpose programs for a generic +algebraic unit. Returning inverse-Gaussian jobs to positive jobs likewise +requires the actual Pauli maps, not an order-two assumption. + +## One paid query and chart contacts + +A direct conditional implementation of J first obtains QY in 112 owned query +fields, then forms -t0 C1 X+t0(QY) and -C3 S0 Y using the required free programs. +All reads of the old Y must finish before Y is overwritten. This explains the +one bank of 112 H1 queries. The query bank is cleared/reset only under the +retained owned-stream rules. A concrete safe COPY/query/use/reset route has +112 query fields; additional scratch for t0 or the free recodings must be +separately allocated and charged. No helper is scratch and no copied stream +earns independent output credit. The handoff does not publish a full emitter. + +Each FULL uses its actual stage-local normalizers. The source forward wrappers +at each port i, rightmost acting first, are + + input X: Ei Ki Q^-1, input Y: Ki, + output X: Ki^-1, output Y: Ds Ki^-1 Si^-1, + +where Ei,Si are the retained actual entrance-line/exit-hyperplane operators. +The complete products shown by the source are monomial; their factors cannot +be individually dropped or declared free solely from a frame label. The +middle J and final controls act on the normalized physical main fields over +all 17 axes. They must match those exact contact coordinates and preserve the +unused stage block as a spectator where required. + +## Promised recursive invoice and the helper complement + +The inherited center-free native price and helper outputs per FULL are + + P0 = 2201H1+412H2+510H3+127H4+40H5, + H = 28H4+7H7+47H8+326H9. + +The released promised complete target/paid census is + + T = 224H17 + 816H9, + P = 4608H1+838H2+1020H3+254H4+136H5. + +Its accounting decomposes exactly as + + P = 2P0 + 112H1 + (94H1+14H2+56H5). + +The last bracket is the complement price for the two native helper banks: +94 rank-eight jobs need rank-one complements; 14 rank-seven jobs need rank-two +complements; 56 rank-four jobs need rank-five complements. The remaining 652 +are already rank nine. Thus all 816 helper original inputs are credited once, +and no original rank-four/seven/eight reward is also retained after counting +its completed rank-nine job. The price has rank mass 11040 and the target +11152, giving the stated raw surplus 112. + +This arithmetic is consistent with the handoff, not an independent native +certificate for its unpublished construction. The actual complement words +must meet the helper's physical entrance/exit charts and retain the other +eight-stage coordinates as spectators, in both orientations. A rank difference +alone does not prove those physical contacts or their monomial adapters. The +source FULL/autonomous-helper premise is inherited; this review performs no +new 816-owner phase campaign. Nor does the positive raw surplus certify a +moment, finite compiler reserve, precision or outer transfer. + +Known ordinary source charges remain nonzero: 448 port-wrapper field maps per +FULL, up to 448 further maps per backward normalization, and 6596 dyadic +precompensation ADDs per native FULL in addition to the original native work. +C_s or C_s^-1 has a source program with 224 K maps, 896 scalar ADDs and 16 +owned CLEARs, using eight reusable owned mode fields. The inverse coefficient +is -1/52; its odd-denominator precision work is not free. Counts of these +macros in J/output decoders depend on the proposed t0 programs and cannot be +invented here. Query COPY/reset, inverse-query Paulis, routing, all buffers, +heights and full fixed-tape cost remain charged obligations. + +## Actual free dictionary versus a theorem's enlarged algebra + +The public active-query theorem deliberately grants arbitrary finite linear +owner programs over a fixed finite projective group H of one-column monomial +maps, possibly non-Clifford, to strengthen its LOWER BOUND. Each map is lifted +as the same h in all f columns. It permits width-dependent scalar coefficients +within that mathematical model and proves its obstruction at sufficiently +large f. It does not present an executable tariff for every such H map, every +element of its span, or every invertible matrix over that span. + +The construction handoff expressly asks for EXPLICIT free implementations. +Its actual known source dictionary is narrower and operational: + +* elementary scalar owner ADDs/mixing, signs and owner routing, with fixed + coefficients computed and rounded under the caller's precision rules; +* owned COPY/reset/clear with original independent fields preserved; +* the exact K_i,s and inverses, their supplied phase-correct P/D/X words, + ordinary phases/Paulis and any explicitly compiled fixed coordinate map; +* C1,C3 and their inverses through the concrete eight-mode scalar programs; +* Q^2 and Ds^2 Pauli maps with their actual finite passes. + +This dictionary is closed under concatenating actual finite programs. A unit +must have a returned inverse program; mathematical nonsingularity supplies +neither its finite word nor its cost. There is no admitted closure rule saying +that conjugation by Q or D3 preserves this dictionary. In particular a word +with an even Gaussian count can still be nonmonomial/nonfree. Generic finite-H +or full Clifford-span hypotheses from a different theorem must not be silently +installed here. Arbitrary width-dependent coefficients also need a uniform +descriptor, bit-height and runtime prescription, not a unit-cost oracle. + +There is also a general exact monomial-Clifford constructor in the retained +symbolic source, not just a table of K_i: `normalizers.py` lines 123–127 calls +`ce.monomial(op)`, checks exact tableau and phase, and emits only P/D/X/phase +letters. A specified rank-zero Clifford candidate can therefore be represented +by a literal fixed-axis word and its inverse. It still needs its 17-axis +embedding, all-column phase lift and finite indexed-movement/precision bill +under the retained monomial implementation. This is distinct from granting +every arbitrary non-Clifford permutation in the theorem's enlarged H. No new +letter was synthesized or tested in this review. + +### Smallest concrete units subclass for the design lead + +A useful source-grounded first class is t0=B tensor I_address, where B is a +fixed scalar owner matrix accompanied by a finite elementary program and its +inverse. A particularly strict finite generator alphabet is owner ADD with +coefficients +1 or -1, owner swaps and signs. Any fixed word in these generators +has an explicit inverse by reversing and inverting its gates, uses no Gaussian +call or new axis, and has a finite ordinary cost. B is then unimodular. Other +fixed rational B can be admitted only with their explicit scaling/division and +precision programs. This is a candidate subclass, not a claim of a solution. + +For such scalar B, the first three conditions reduce to B and B^-1 because +they commute with Q and D3. The remaining test is the actual ordered operator +Q^-1 C3 B C1 Q^-1 and its inverse. The source normalizers fix its phase-correct +17-axis terms. Astra owns the creative intersection derivation; no linear +system, determinant test, t0 candidate enumeration or operator solver is run +by this inventory review. Proving a cancellation in a one-column matrix alone +would not justify every width: an all-column word identity and its physical +finite program are still required. + +Credit Dillon for the released template and active local theorem, Dugongue for +#4929, the #4933 normalizers/coded ABI authors, Cinna Davis, Cao Yifan, zxv, +Jacob Sussman and all retained native/helper/compiler predecessors. Prepared +with substantial OpenAI Codex assistance; Apache-2.0. The joint #5124 mechanism, +finite-packing work and the other agents' operator-intersection design remain +separate ownership scopes. diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/SOURCES.json b/research/released-operator-clifford-ceiling/evidence/inventory/SOURCES.json new file mode 100644 index 0000000000..0d139fad72 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/SOURCES.json @@ -0,0 +1,56 @@ +{ + "scope": "Source inventory only; no solver or source replay", + "publication_base": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba", + "release_comment": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19143357", + "monitor_receipt_sha256": "1aa74f9b72d60a4e4357bc3ea9e70c650c870432714aed11b2cda46518f74952", + "files": [ + { + "head": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "path": "research/coded-active-query-bound/README.md", + "local": "source/research__coded-active-query-bound__README.md", + "sha256": "95269b047c19069caeb11edd36a485a0a86275b329aa44da90c8c08403e09178" + }, + { + "head": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "path": "research/coded-active-query-bound/PROOF.md", + "local": "source/research__coded-active-query-bound__PROOF.md", + "sha256": "495a1cd85cc45020adf2205f196b57dc4f65f1eb763fc4951facdb4ccbafc768" + }, + { + "head": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "path": "research/coded-active-query-bound/SOURCES.json", + "local": "source/research__coded-active-query-bound__SOURCES.json", + "sha256": "afb6ca7a3b924d19b61b784266693b892722024d5a33de3e432fc6499238241e" + }, + { + "head": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/PHYSICAL.md", + "local": "source/research__coded-native-caller__PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "head": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/NORMALIZERS.json", + "local": "source/research__coded-native-caller__NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "head": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/native-center-free-code/CODE.json", + "local": "source/research__native-center-free-code__CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "head": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/normalizers.py", + "local": "source/research__coded-native-caller__normalizers.py", + "sha256": "7616b75758c1b36b6c05eb7fff1630f604e7563762701bccb18ec638a61090df" + }, + { + "head": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/clifford_exact.py", + "local": "source/research__coded-native-caller__clifford_exact.py", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + } + ] +} diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/source/RELEASE-MONITOR.json b/research/released-operator-clifford-ceiling/evidence/inventory/source/RELEASE-MONITOR.json new file mode 100644 index 0000000000..814fd83d37 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/source/RELEASE-MONITOR.json @@ -0,0 +1,42 @@ +{ + "at": "2026-10-23 10:16:02 UTC", + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930#discussioncomment-19143357", + "author": "dillona", + "public_theorem_head": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "public_theorem_path": "research/coded-active-query-bound", + "source_scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "publication_base": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba", + "ownership": "Originalcanonical4930#19141406 nowDONE(scopedlocaltheorem/globalconstructionopen), ClaimRELEASED. Links19143357, completefavorableGaussiancaller unresolvedandAVAILABLEforchangedinformationboundarycontinuation. Newfinding0replies, no laterclaimvisiblein4930.", + "constructive_handoff": "Survivingtwo-FULL/one-querytemplate onfixed17axisphysicalembedding. Seekinvertiblet0 suchthatallfourexpressionsandtheirinverseshaveexplicitfreeimplementations.", + "four_expressions": [ + "t0", + "Q^-1 t0 Q", + "t = D3 t0 D3^-1", + "Q^-1 C3 t C1 Q^-1" + ], + "definitions": [ + "F_s = diag(D_s,D_s)L(C_s Q^-1)", + "G = D1 D3 Q", + "J(t0) = [[-t0 C1,t0 Q],[0,-C3 Q^-1 t0 Q]]", + "F3 J(t0) F1 = [[0,t],[-Q^-1 C3 t C1 Q^-1,0]] diag(G,G)" + ], + "qualification": "Sufficientconstructiontarget,nofoundt0. I leavesunresolvedQconjugatedcodeproduct. ArbitraryK/LbridgetransportthroughD3changescheapalgebra; parityevenNOTphysicallyfree. Earlierapparentbroadobstructionfailsatthatstep.", + "conditional_inventory": { + "T": { + "9": 816, + "17": 224 + }, + "P": { + "1": 4608, + "2": 838, + "3": 1020, + "4": 254, + "5": 136 + }, + "rankmass_surplus": 112, + "helpers": "All816independentonce", + "premise": "Ifvalidt0withoutanyextraaxes/paidwork; compilerprecisionouteradditional" + }, + "free_algebra_boundary": "CommentrequiresEXPLICITphysicalfreeimplementationsandinverses; it doesnotfullyenumerateeligiblefreealphabet. Do NOTsubstitute genericfiniteHfrom5126fresh-inputlowerboundorparityevenalgebra. Actualfreeclosure/callerimplementationneedsourceinventory.", + "unpublished_status": "Exploratoryconstructiontoolspreservedlocally; onlytheorempackageispublic. Do NOTassumecompletepublicemitter/instance." +} diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-active-query-bound__PROOF.md b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-active-query-bound__PROOF.md new file mode 100644 index 0000000000..1ebf18af5b --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-active-query-bound__PROOF.md @@ -0,0 +1,394 @@ +# An active local-query obstruction for the actual 112-port code + +Prepared for Dillon, 2026-10-23, with substantial OpenAI Codex assistance. +This is a scoped exact local theorem with finite source checks, not a +complete-controller lower bound, a multiplication algorithm or an admission +claim. Apache-2.0. + +## Statement + +Use the actual physical native code from `research/coded-native-caller`: + +\[ + C_{ij}=a_{ij}K_i^{-1}K_j,\qquad J=Q^{-1}CQ, +\] + +where there are 112 owners, Q is the one-central-axis Gaussian, each K_i is +the retained signed orthogonal permutation normalizer, and the scalar matrix +a has zero diagonal and 52 nonzero off-diagonal entries in every column. +The 112 vectors q_i=G_i e_0 are distinct. The source factorization +C=I-14P has an eight-mode projector P. + +Fix any finite projective group H of invertible one-column monomial maps on the +declared fixed ambient address space, containing the source normalizers and +all admitted free address maps. For example, H may be the full group of +one-column permutations with phases in a fixed finite root-of-unity group; +the free permutations need not be Clifford. Every address map is lifted as +the SAME one-column map h on all f columns, h^tensor(f). Independent choices +on individual columns are outside this grammar. Free operations are +arbitrary linear owner programs over the +monomial subgroup algebra, including scalar operations, every +actual C or C inverse, owned COPY/CLEAR, arbitrary clean buffers, saved +banks, and fanout. These are charged as ordinary finite work; "free" here +means no recursive Gaussian call. Allow every paid unary call to apply an +arbitrary fixed one-field linear operator, with chronological linear +feedback from all available fields. In particular its input may use all +earlier paid responses. All coefficients are data-independent, although +they may depend on width. Every counted field has the same address width as +one source owner; a wider packed channel is not counted as one field. + +**Theorem.** A standalone exact implementation of J, or of J-I, on 112 +arbitrary fresh owner fields requires at least 112 paid unary field calls. +The statement is valid for an identity at all positive tensor widths, and +allows the scalar owner coefficients to depend on width. The same conclusion +holds after adding any free owner operator to J. +More precisely, the bound holds at every sufficiently large tensor width, +so no all-width implementation uses fewer than 112 calls. It is not a bound +at every small width: at width one, +Q=((1+i)/2)I+((1-i)/2)X is in the scalar span of free monomials. + +**Sharp one-sided corollary.** Put P=(I-C)/14. Each of QP and PQ, as a +112-input/112-output owner operator, requires at least 112 paid unary field +calls. Exactly 112 H1 calls suffice: apply P for free and then Q to every +output, or apply Q to every input and then P. Thus the eight scalar code +modes do not yield an eight-call one-sided Q repair. The statement also +holds with Q replaced by Q inverse. + +**Canonical eight-mode corollary.** For the actual source mode matrix M, +let U_mode=diag(K_i^-1)M and V_mode=M^T diag(K_i)/56. Then +P=U_mode V_mode and V_mode U_mode=I_8. Each of Q U_mode (eight fresh inputs, +112 outputs) and V_mode Q (112 fresh inputs, eight outputs) also has exact +paid-field-call complexity 112, attained by 112 H1 calls. Thus the canonical +rectangular mode ABI does not avoid the one-sided obstruction. + +It does not cover receiving Gaussian-dependent saved data, absorbing the +correction into the paid native FULLs or their prefixes, recycling an existing +paid IDLE, or a direct coded consumer with a different endpoint. Nonlinear +controls, noncolumnwise address operations, approximate endpoints, and +unequal-width packing are outside the stated model. + +## 1. Phase-correct finite algebra and all-width evaluation + +This uses the finite-phase algebra and sufficiently-large-width tensor +faithfulness already proved in `coded-port-adapter-ceiling/PROOF.md`, section +3, and clarified by the passive saved-query package's uniform-alphabet +addendum. Here only the FREE group H must be finite projectively. An ambient +group generated by H and Q need not be finite or Clifford. + +Choose one invertible matrix representative for every projective element +of H. At width f its nonzero scalar multiplication cocycle is raised to +the f-th power; the scalar factors need not have modulus one. +Let B_f be the resulting finite-dimensional twisted group algebra over +k=C, with one basis element per projective element of H. Its evaluation +is the span of the literal tensor lifts h^tensor(f). Scalar factors are +retained through the cocycle; owner coefficients are applied only once. + +Besides H itself, we will need only a fixed finite union of its projective +cosets: the sets g_ij H used for J, the analogous right cosets for PQ and +V_mode Q, and the analogous left cosets for QP and Q U_mode. Take S to be +their union with H, with repeated projective elements identified. This set +is finite because H and the source owner/mode sets are finite. Closure of +S under multiplication is not needed: all free products remain in H, and +every target-times-free expression used below stays in its declared coset +set. A different fixed finite number of source stages merely enlarges S. + +For projectively distinct nonzero representatives v_1,...,v_N, individually +normalize each by its Hilbert-Schmidt norm. Their tensor-power +Gram matrix has diagonal one and off-diagonal entries +^f, whose magnitudes are at most rho^f for some rho<1. For +(N-1)rho^f<1 the Gram matrix is strictly diagonally dominant and positive +definite. Apply this to the projective representatives in S. Their literal +tensor lifts are linearly independent for every sufficiently large f. +Thus B_f and all the required coset subspaces evaluate faithfully, with +distinct cosets in direct sum, at those widths. Scalar factors remain raised +to the f-th power; owner coefficients are never raised to that power. + +We work at any one such width. The threshold is uniform over all free +coefficients, control choices, and control lengths because H and S are +fixed. Width-dependent scalar coefficients are allowed. A width-dependent +or noncolumnwise group of arbitrary payload maps is not allowed; neither +is an infinite projective phase grammar. No assumption that arbitrary +permutations together with Q generate a finite group is made. + +## 2. Actual-source right-coset separation + +Write g_ij=Q^-1 K_i^-1 K_j Q. For a fixed i, + +\[ + g_{ij}^{-1}g_{ik}=Q^{-1}K_j^{-1}K_kQ. (1) +\] + +For the signed orthogonal permutation M=K_j^-1 K_k, let G=G_j^-1 G_k be +its binary orthogonal coordinate matrix and e=e_0. Pauli signs affect only +tableau phases. The Z-to-X block of Q^-1 M Q is + +\[ + B=G e e^T+e e^T G. (2) +\] + +If G e=e, orthogonality gives e^T G=e^T, and B=0. If G e differs from e, +then both pairs (G e,e) and (e,G^T e) are independent; the two outer products +in (2) have rank two. Thus Q^-1 M Q is monomial exactly when G e=e. +Equivalently, G_j e=G_k e, or q_j=q_k. The actual 112 source vectors are +distinct, so (1) belongs to H exactly when j=k. + +Therefore the 112 g_ij lie in distinct right H-cosets for each fixed i. +The j=i coset is H itself, since g_ii=I. The scalar phase quotient does not +alter this test: multiplying by a scalar never changes monomiality. +The companion checker verifies all 112^2 ordered pairs by both formula +(2) and the retained exact tableau implementation. It separately checks +the actual code's zero diagonal and nonempty column supports. + +## 3. No nonzero free input survives modulo a free output + +Let F_0 be ANY 112-by-112 matrix over B_f. Suppose w in B_f^112 obeys + +\[ + (J-F_0)w=0. (3) +\] + +Row i of Jw is sum_j a_ij g_ij w_j. Each summand lies in the right-coset +subspace g_ij B_f. These subspaces are in direct sum. Every component of +F_0 w lies in B_f, the H coset. The diagonal source coefficient is zero. +For each off-diagonal supported pair (i,j), projecting (3) onto g_ij B_f +therefore gives a_ij g_ij w_j=0. A nonzero scalar and a group unit are +invertible, so w_j=0. Each column j has a supported off-diagonal entry, +and hence w=0. + +This is stronger than an eigenvector statement: J-F_0 has zero kernel on +B_f^112 for every free F_0. In particular the Q-conjugated eigenspaces of +C contain no nonzero free input embedding, despite the eight-mode +factorization of C-I. A cheap compression of J-F_0 through fewer than 112 +owner fields is impossible. + +### One-sided projector operators + +Write p=(I-a)/14, so P_ij=p_ij K_i^-1 K_j and p_ii=1/14. For PQ, fix row +i. Its blocks are p_ij h_ij with h_ij=K_i^-1 K_j Q. Every h_ij has Fourier +grade one and lies outside H. Further, + + h_ij^-1 h_ik = Q^-1 K_j^-1 K_k Q. + +Thus the h_ij occupy distinct right H-cosets as j varies. The same argument +proves ker_{B_f}(PQ-F_0)=0 for every free F_0; the nonzero diagonal of p +already supplies a supported entry in each column. + +For QP fix column j instead, and put t_ij=Q K_i^-1 K_j. These grade-one +words lie in distinct LEFT H-cosets as i varies, because + + t_ij t_kj^-1 = Q K_i^-1 K_k Q^-1 + +is nonmonomial for i different from k. Consequently a free row w satisfying +w(QP-F_0)=0 must vanish: project each fixed output column onto the distinct +left-coset subspaces B_f t_ij, and use p_ii different from zero. This is the +left-kernel version of the same source-specific separation. + +### Canonical rectangular eight-mode maps and free rebasing + +The retained 112-by-8 scalar mode matrix M obeys M^T M=56I_8 and +a=I-MM^T/4; each row has four nonzero entries. The checker verifies every +entry of these identities from the pinned source receipt. Define + + U_mode = diag(K_i^-1) M, shape 112 by 8, + V_mode = M^T diag(K_i)/56, shape 8 by 112. + +These maps are free, with P=U_mode V_mode and V_mode U_mode=I_8. +For Q U_mode the fixed mode-column a has entries M_ia Q K_i^-1. The words +t_i=Q K_i^-1 lie in distinct left H-cosets, since +t_i t_k^-1=Q K_i^-1 K_k Q^-1 is nonmonomial when i differs from k. +Each t_i itself is nonmonomial. Every row of M has a nonzero entry, so +the same columnwise projection proves that + + w (Q U_mode-F_0)=0, w in B_f^(1 by 112), + +forces w=0 for every free 112-by-8 F_0. Thus the no-left-kernel conclusion +holds even though there are only eight fresh inputs. + +Dually, V_mode Q has entries M_ja K_j Q/56. The words K_j Q lie in +distinct right H-cosets because their pairwise relative transports are +Q^-1 K_j^-1 K_k Q. Every source column is represented in at least one mode +row. Hence (V_mode Q-F_0)w=0, with w in B_f^112, forces w=0 for every free +8-by-112 F_0, even though there are only eight outputs. + +These conclusions cover all free changes of retraction basis. If another +free pair U',V' has P=U'V' and V'U'=I_8, then + + W=V_mode U', W^-1=V' U_mode, + U'=U_mode W, V'=W^-1 V_mode. + +The two inverse identities follow by substituting U'V'=P and +U_mode V_mode=P. Thus Q U' and V'Q differ from the canonical operators by +invertible free input or output boundaries. No cheaper implementation is +obtained by any such free eight-mode basis choice. + +## 4. Arbitrary chronological paid calls + +Normalize any finite acyclic linear implementation by retaining all paid +responses y_1,...,y_r. COPY, saves, fanout, overwrite and CLEAR are included +in this normalization: enlarging owned storage can preserve the history +without introducing another recursive call. At paid call t its input is + +\[ + b_t x+\sum_{s B_f^r. As a k-linear map its +domain has dimension 112 dim_k B_f and its codomain has dimension +r dim_k B_f. If r<112, choose a nonzero w in its kernel. Substitute the +formal input x=w z, with z one arbitrary field. Every direct term b_t w is +zero. Induction on t in (4) gives every paid response y_t=0, regardless of +T_t and regardless of the active feedback coefficients. Thus the claimed +endpoint J must satisfy Jw=F_0w. Section 3 contradicts this. + +This proves r>=112. Replacing J by J-I or J+F_free merely changes the free +matrix F_0 and gives the same result. + +The input-kernel proof applies verbatim to PQ. For QP use the dual output +cut: concatenate the free output columns in (5) into L in B_f^(112 by r). +If r<112, the k-linear map w -> wL from B_f^(1 by 112) to B_f^(1 by r) +has a nonzero kernel row w. Multiplying the endpoint by that row annihilates +every paid-response term, so w(QP-F_0)=0, contrary to the left-kernel result. +No assumption about the paid calls' chronology is needed beyond the +existence of the finite linear circuit normal form. + +For Q U_mode the same output cut has 112 rows and r paid-response columns, +although F_0 has only eight input columns. It again gives r>=112. For +V_mode Q the same input cut has 112 input columns, although F_0 has only +eight output rows, and also gives r>=112. Both bounds are attained by +112 H1 calls: expand eight fields through U_mode for free and apply Q to +all 112 results; or apply Q to the 112 inputs and contract through V_mode +for free. Invertible free retraction basis changes preserve these counts. +The same arguments apply with Q inverse throughout. + +## 5. Direct sums and local amortization + +For any fixed positive m, consider m fresh physical code blocks, embedded +in one fixed ambient address space. Each block may use its own eight fresh +axes and physical normalizers, with the same 112 distinct-direction +property. Let N=112m. The same proof gives + +* diag(J_1,...,J_m), or its free perturbation: at least N paid field calls; +* diag(P_1 Q,...,P_m Q): exactly N H1 calls are necessary and sufficient; +* diag(QP_1,...,QP_m): exactly N H1 calls are necessary and sufficient. +* diag(Q U_mode,1,...,Q U_mode,m), and its free retraction rebases: + exactly N H1 calls are necessary and sufficient; +* diag(V_mode,1 Q,...,V_mode,m Q), and its free retraction rebases: + exactly N H1 calls are necessary and sufficient. + +Free controls may mix different blocks arbitrarily. To see why this does +not change the proof, write a candidate free kernel column or row in m +blocks. Project each target block's rows or columns onto its nontrivial +cosets. The free comparison operator still contributes only the H coset, +even when it mixes all N owners. The corresponding single-block argument +forces every block of the candidate kernel to vanish. Apply the input or +output dimension cut with B_f^N and r=1 and price at least one, so the local correction costs at least 112. +Its added recursive price exceeds the removed-center saving by at least +48 per FULL. The direct-sum theorem gives a gap of at least 48m for m such +standalone local repairs, even when their free controls mix all inputs. + +Thus this isolated interface-restoration strategy cannot turn the removed +eight H8 calls into a recursive saving anywhere in 0<=c<1. Extra ordinary +work can only increase the cost. The conclusion does not price or rule out +absorption into correlated FULL, IDLE, or saved-query data in a complete +caller, nor a different direct coded endpoint. + +### Relationship to predecessor and active caller work + +The predecessor `coded-port-adapter-ceiling` (#4932) proves that one parallel +bank needs 112 grade-2 channels for its physical recovery adapter, using a +grade projection of full rank. It expressly excludes multiple chronological +banks. The argument here uses source-specific distinct right cosets and an +input-kernel cut to cover arbitrary chronological paid unary calls and +active feedback. Its conclusion is 112 calls of any grade; it does not +claim 112 grade-2 calls in this enlarged model. + +The conclusion excludes an independently implemented 16-, 32-, or 42-H1 +fresh-input correction of J, J-I, QP, or PQ through the native code's eight +modes. For J and J-I this is a lower bound, with the elementary 224-H1 +conjugation implementation as an upper bound; 112-call attainability is +not asserted. For QP and PQ the 112-H1 bound is attained. +It does not prove that p2 needs four thin banks, nor that a complete active +three-bank caller is impossible. Such a caller can already hold nonfree +data from its FULLs, queries, and IDLE. A useful construction must exploit +that shared paid access, change the endpoint, or leave this local grammar. +The particular eight-mode ABIs Q U_mode and V_mode Q, including their free +retraction rebases, are covered above. An arbitrary different eight-mode +endpoint, the middle compression V_mode Q U_mode, and the two-sided +compression PQP remain outside the claims. + +The actual #4932 entrance adapter is also covered by free equivalence. Its +physical monomial X wrapper is M_i=U_i K_i Q^-1. Therefore +U a U*=M (Q C Q^-1) M*, and Q C Q^-1=Q^2 J Q^-2. Since Q^2 and M are free, +and a^-1=(a+12I)/13, the physical U a^-1 U* differs from J by invertible +free boundaries, a nonzero scalar, and a free bypass. These operations +preserve the local paid-call lower bound. This correspondence uses the +retained exact physical wrapper identities; it does not replace U_i with +a bare Fourier along q_i. + +## Source and predecessor credit + +The source code and native producer are Dugongue's #4929. The actual signed +orthogonal normalizers and physical C formulation come from the retained +`coded-native-caller` package. The finite-phase group algebra, tensor +faithfulness, adapter scope and warning that rank-eight scalar modes are not +eight query heads come from #4932. The uniform finite-alphabet clarification +and related passive-controller limitations come from the retained passive +saved-query package. Credit also Cinna Davis/1337isnot1337's #4694/#4698, +Cao Yifan/intqwq's #4610 source, zxv's retained exact Clifford/compiler work, +and all source notices. This active local input-kernel argument was derived +in the current research session with substantial OpenAI Codex assistance. + +No independent human or formal-kernel acceptance is claimed. The source +native all-input theorem, numerical outer admission, and complete caller +endpoint are inherited or open, not replayed by this scratch result. diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-active-query-bound__README.md b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-active-query-bound__README.md new file mode 100644 index 0000000000..f8858cea6b --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-active-query-bound__README.md @@ -0,0 +1,60 @@ +# Sharp active local query cost for the physical eight-mode code + +**The physical code's one-sided correction and eight-mode extraction/expansion each require exactly 112 unary field calls in the stated local model, attained by 112 H1 calls.** The conjugated adapter `J=Q^-1 C Q` and `J-I` each require at least 112 unary paid calls. The proof permits arbitrary chronological linear feedback, saved inputs, copies, owned resets, fanout and free mixing across any fixed number of independent blocks. No new κ or complete-caller lower bound is claimed. + +Here `C_ij=a_ij K_i^-1 K_j` is the actual 112-port code from [#4933](https://github.com/CrocSwap/integer-mult-bounds/pull/4933), `P=(I-C)/14`, and Q is the central rank-one Gaussian. A field call operates on one owner-width field. Free operations are finite linear owner programs over a fixed finite projective group of one-column invertible monomial maps; they have ordinary scalar/routing/precision cost but no recursive Gaussian call. Paid unary maps may be arbitrary zero-preserving linear maps, so the lower bound also applies when those maps are Gaussian calls of any rank. + +The free permutations may be non-Clifford; no finite ambient Clifford group is assumed. The theorem concerns identities required at every positive tensor width; its obstruction holds at every sufficiently large width. Each admitted one-column map h acts by the same tensor lift `h^⊗f` in every column; independent per-column choices are not admitted. Scalar coefficients and finite control choices may depend on width. At width one, Gaussian operators can lie in the scalar span of monomials, so the lower bound is deliberately not asserted for every small width. It excludes wider packed channels, arbitrary noncolumnwise address maps, nonlinear or data-dependent controls, approximate endpoints and preexisting nonfree observations of the fresh inputs. A running native caller may already possess such observations, so this result does not exclude an active three-query p2 construction. + +Write `U=diag(K_i^-1) M` and `V=M^T diag(K_i)/56` for the actual source mode maps. Then `P=UV` and `VU=I_8`. The local endpoints have the following exact call bounds at sufficiently large width: + +| Endpoint | Fresh input fields | Output fields | Paid unary calls | +|---|---:|---:|---:| +| QP or PQ | 112 | 112 | Exactly 112 | +| QU, mode expansion followed by Q | 8 | 112 | Exactly 112 | +| VQ, Q followed by mode extraction | 112 | 8 | Exactly 112 | +| J or J-I | 112 | 112 | At least 112; 224 H1 suffice | + +The mode bounds also cover every free eight-mode retraction basis `P=U'V'`, `V'U'=I_8`, since these differ from U,V by invertible free boundaries. They do not classify arbitrary unrelated eight-output operators. + +## What changes relative to the predecessors + +[#4932](https://github.com/CrocSwap/integer-mult-bounds/pull/4932)'s [coded-port adapter ceiling](../coded-port-adapter-ceiling/README.md) treats one parallel query bank and forces 112 grade-two channels. The [passive saved-query ceiling](../passive-saved-query-ceiling/README.md) keeps its later paid inputs fixed. This package uses a different invariant: the physical port transports occupy distinct monomial cosets. An input or output kernel cut then covers **arbitrary chronological paid calls and active linear feedback** for the standalone local endpoint. Its 112-call result counts calls of any grade; it does not extend the predecessor's grade-two conclusion to the larger model. + +The core source fact is that the 112 vectors `G_i e0` are distinct. For each fixed output i, the words `Q^-1 K_i^-1 K_j Q` lie in distinct right monomial cosets. Each source column has 52 nonzero off-diagonal entries. Consequently `J-F` has no nonzero free input column for any free bypass F. A circuit with fewer than 112 unary calls has a nonzero free input direction that vanishes at every paid input, even when later calls use previous responses. These statements contradict each other. The output-cut version proves the QP bound; the input-cut version proves PQ. Applying Q to all 112 fields before or after the free P realizes each one-sided upper bound. + +For m independent copies, arbitrary cross-copy free mixing still requires 112m calls. The one-sided 112m-H1 upper constructions attain those bounds. This is a direct-sum statement about the declared local endpoints, not about amortization into already-paid FULLs, IDLEs or native internal prefixes. For J/J-I, 112-call attainability remains open; the elementary conjugation uses 224 H1 calls. + +An isolated repair that restores one backward coded FULL to the ordinary uncoded FULL is also priced sharply. Since `C=I−14P`, the exact entry patch is `X ← X−14QP Y`; it needs 112 H1 calls in the enlarged local model. The inherited producer removes only 8 H8 calls, worth at most 64 in every moment with exponent `1−c`, `0≤c<1`. Thus such an independently implemented repair increases the recursive paid bill by at least 48 per FULL, or 48m for a direct sum. The eight-H8 removal is an inherited source invoice, not replayed by this checker. Absorbing the patch into already-paid native operations is outside the corollary. + +The mathematical argument, finite phase treatment and all-width scope are in [PROOF.md](PROOF.md). [INDEPENDENT-REVIEW.md](INDEPENDENT-REVIEW.md) records a separately derived proof audit and binary census. [EXTENSION-REVIEW.md](EXTENSION-REVIEW.md) audits the finite-H extension, rectangular modes, rebasing, direct sums and isolated-patch tariff. Neither is independent human or proof-kernel acceptance. + +## Evidence and reproduction + +Python 3.12 for the registered runner, standard library only, from the repository root: + +```sh +python3 -B scripts/research_package.py --package research/coded-active-query-bound +``` + +Direct replay, including after an official package export with its declared inputs: + +```sh +python3 -I -W error -B research/coded-active-query-bound/verify.py +python3 -I -O -W error -B research/coded-active-query-bound/verify.py +python3 -I -O -W error -B research/coded-active-query-bound/independent.py +``` + +The main verifier authenticates the code, normalizers and exact Clifford implementation before executing the latter's source bytes. It checks all 12,544 ordered port pairs by both a separately written binary formula and source tableaus: 112 self pairs have grade 0; 12,432 distinct pairs have grade 2; all 5,824 supported off-diagonal code terms are grade 2. It also checks 12,544 left-coset conjugates, 12,544 one-sided grade-one transports, the 52-entry column supports, all 12,544 entries of `a=I-MM^T/4`, all 64 entries of `M^T M=56I`, and four mode contacts per owner. Four rejection controls alter a direction, a source column, the diagonal or a mode factor. The independent checker imports no Clifford implementation. Both compare exact finite receipts; checks remain active under `-O`. + +[RESULT.json](RESULT.json) and [INDEPENDENT.json](INDEPENDENT.json) are finite source receipts. They do not enumerate the monomial group algebra, test every circuit, or mechanically prove the tensor/kernel argument. [SOURCES.json](SOURCES.json) pins frozen main `4c0a359d88f22f05189d51f48387750b801a45d4`, live inputs and proof provenance. [VERIFY.json](VERIFY.json) declares every live input. The submission base is refreshed canonical main `20a1e31bc6009b9b3f4d084bbaadc6350e34fcba`; the earlier scientific pins remain unchanged. No predecessor package is copied or altered; provenance-only proof references resolve through the pinned Git history. [VALIDATION.md](VALIDATION.md) states executed checks and unrun obligations. + +## Open next questions + +Can a complete coded caller use nonfree observations that its FULLs and IDLEs already produced to recover all prescribed independent Gaussian outputs? This is the meaningful route left by the local result. The first step is one explicit changed paid input with its retained observations, followed by all terminal operator identities and a complete invoice. The current package supplies no such global endpoint. The final checkpoint also reviewed Cinna Davis's [common-code moving-stage interface](../common-code-moving-stages/README.md), whose transported Gaussian stages fail the inherited commutation relation, and JoyboyBrian's [fresh-D coherent-pair countermodel](../two-full-fresh-d-coherent-pair/README.md). Their changed interfaces and endpoint obligations remain distinct from this local query theorem. + +What is the exact complexity of J or J-I between 112 and 224 calls? A smaller explicit chronological circuit or stronger cut invariant would resolve the gap. The sharp 112 result for QP/PQ does not settle it. Structured first steps and blockers are in [TASK.json](TASK.json). + +## Credit + +Prepared for Dillon with substantial OpenAI Codex assistance from separate proof, independent-review, construction and packaging agents. Credit Dugongue's center-free producer [#4929](https://github.com/CrocSwap/integer-mult-bounds/pull/4929), the real signed normalizers/physical C in #4933, Chris R/Clear1nsight's #4932 finite phase algebra and one-bank theorem, the passive package's uniform-alphabet clarification, Cinna Davis/1337isnot1337's #4694/#4698, Cao Yifan/intqwq's #4610 native source, zxv and the retained Clifford/helper/compiler lineage. See [ATTRIBUTION.md](ATTRIBUTION.md). Standard causal/image/row-space rank cuts retain earlier method credit to eumemic's PR288 and Ali Romman's PR468, as summarized in [fixed-support unary-query bounds](../fixed-support-unary-query-bounds/README.md); that different carrier theorem does not imply the physical-code result here. New work is Apache-2.0. 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+ ], + "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448}, + "schema": "coded-native-real-normalizers/1", + "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.", + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS" +} diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-native-caller__PHYSICAL.md b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-native-caller__PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-native-caller__PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-native-caller__clifford_exact.py b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-native-caller__clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__coded-native-caller__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<>j&1));vs=[1^(1<>j)&1)for j in range(N)))) + # Exact symbolic tableau plus an absolute-phase state; not merely ranks. + need(equal(K.then(R),R.then(K)),'Exact full-Gaussian commutator') + need(all((ce.mv(ce.transpose(G,N),x).bit_count()-x.bit_count()-2*ce.parity(z&x))%4==0 for x in range(512)),'Literal weight congruence') + if z: + need(not equal(perm.then(R),R.then(perm)),'Omitting signed phase must fail') + phase_controls+=1 + E=ce.canonical_frame(N,canonical['frames'][canonical['start'][idx]]) + S=ce.canonical_frame(N,canonical['frames'][canonical['final'][112+idx]]) + need(canonical['final'][idx]==1 and canonical['start'][112+idx]==0,'Full-X and ground-Y boundaries') + MX=Q.adjoint().then(K).then(E);MY=K;OX=K.adjoint();OY=S.adjoint().then(K.adjoint()).then(D) + need(all(monomial(op)for op in (MX,MY,OX,OY)),'Every physical wrapper is monomial') + need(equal(MX.then(E.adjoint()),Q.adjoint().then(K)),'All incoming coded columns') + need(equal(S.then(OY),K.adjoint().then(D)),'All outgoing coded rows') + need(equal(MX.then(E.adjoint()).then(R).then(OX),D),'Independent X diagonal') + need(equal(MY.then(S).then(OY),D),'Independent Y diagonal') + need(equal(MX.then(E.adjoint()).then(S).then(OY),Q.adjoint().then(D)),'Original same-port shear block') + # K is a real signed permutation. The real transpose equals its adjoint. + need(all(e[0]!='D'or all(a%2==0 for a in e[2])for e in K.circuit),'Real K phases') + # Raw inverse transpose uses conjugated endpoint frames and wrappers. + Q2=Q.then(Q);D2=D.then(D) + BX=Q2.adjoint().then(conjugate(MX)) + BO=conjugate(OX).then(D2).then(Q2) + BY=conjugate(OY).then(D2) + need(equal(BX.then(conjugate(E).adjoint()).then(conjugate(R)).then(BO),D),'Backward corrected X diagonal') + need(equal(K.then(conjugate(S)).then(BY),D),'Backward corrected Y diagonal') + need(equal(conjugate(R).then(BO),K.adjoint().then(Q).then(D)),'Backward all coded outgoing rows') + need(all(monomial(op)for op in (BX,K,BO,BY)),'Backward corrected wrappers monomial') + operations={'input_X':MX,'input_Y':MY,'output_X':OX,'output_Y':OY, + 'backward_input_X':BX,'backward_input_Y':K,'backward_output_X':BO,'backward_output_Y':BY} + compiled={} + for name,op in operations.items(): + mon,recipe=ce.monomial(op) + need(equal(mon,op),'Compiled monomial exact phase and tableau') + need(all(e[0] in ('P','D','X','phase')for e in mon.circuit),'No Gaussian in emitted wrapper') + compiled[name]={'word':mon.circuit,'recipe':recipe} + wrong=ce.Op(N,K.tab,K.circuit+[('phase',1)]) + need(not equal(wrong,K),'Absolute-phase-only mutation rejected') + records.append({'port':idx,'q':q,'orthogonal_transvections':vs,'G_rows':G,'Z_mask':z, + 'K_word':K.circuit,'compiled_wrappers':compiled}) + need(phase_controls>0,'Nonvacuous omitted-phase control') + # Independent scalar execution of A and A^-1 on every arbitrary-input basis. + for inverse,den in ((False,4),(True,52)): + for j in range(112): + x=[F(i==j)for i in range(112)] + temp=[sum(F(c[i])*x[i]for i in range(112))for c in M] + y=[x[i]-sum(F(M[k][i])*temp[k]for k in range(8))/den for i in range(112)] + target=[A[i][j]if not inverse else (A[i][j]+12*F(i==j))/13 for i in range(112)] + need(y==target,'Literal owned-mode scalar recoding') + result={'schema':'coded-native-real-normalizers/1','status':'PASS_CODED_NATIVE_REAL_NORMALIZERS', + 'source_payload_sha256':SOURCE_PAYLOAD,'code_sha256':CODE_HASH,'clifford_sha256':CLIFFORD_HASH, + 'ports':records,'mode_columns':M,'finite_checks':{'ports':112,'weight_congruence_addresses':112*512, + 'exact_endpoint_factor_identities':112*8,'monomial_wrappers':896,'omitted_phase_rejections':phase_controls, + 'scalar_basis_recodings':224,'gaussian_free_compiled_wrappers':896,'absolute_phase_mutations_rejected':112}, + 'recoding_bill':{'owned_fields':8,'signed_mode_adds':448,'output_scaled_adds':448, + 'owned_initial_clears':8,'owned_terminal_clears':8,'monomial_field_maps':224, + 'forward_update_coefficient':'-1/4','inverse_update_coefficient':'-1/52', + 'forward_prefix_component_l1_upper':57,'inverse_prefix_component_l1_upper':56,'inverse_output_prefix_component_l1_upper':'69/13'}, + 'local_gauge_bill':{'recodings':2,'added_recursive_calls':0,'owned_fields_reused':8, + 'recoding_scalar_adds':1792,'recoding_owned_clears':32,'recoding_monomial_field_maps':448, + 'main_wrapper_field_maps':448,'backward_extra_monomial_field_maps_upper':448}, + 'scope':'Exact physical central ABI and local gauges; not full-controller or multiplication admission.'} + return json.loads(json.dumps(result,sort_keys=True)) + +def render_receipt(result): + """Keep each generated port record on one line; compare parsed mathematics.""" + entries=[] + for key,value in sorted(result.items()): + if key=='ports': + body='[\n'+',\n'.join(' '+json.dumps(row,sort_keys=True,separators=(',',':')) for row in value)+'\n ]' + else: + body=json.dumps(value,sort_keys=True,separators=(',',':')) + entries.append(' '+json.dumps(key)+': '+body) + return '{\n'+',\n'.join(entries)+'\n}\n' + +def main(): + p=argparse.ArgumentParser();p.add_argument('--write',action='store_true');args=p.parse_args() + result=run();path=HERE/'NORMALIZERS.json' + if args.write:path.write_text(render_receipt(result)) + else:need(json.loads(path.read_text())==result,'Changed generated normalizer receipt') + print(result['status'],json.dumps(result['finite_checks'],sort_keys=True)) +if __name__=='__main__':main() diff --git a/research/released-operator-clifford-ceiling/evidence/inventory/source/research__native-center-free-code__CODE.json b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__native-center-free-code__CODE.json new file mode 100644 index 0000000000..03170f4a31 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/inventory/source/research__native-center-free-code__CODE.json @@ -0,0 +1 @@ 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diff --git a/research/released-operator-clifford-ceiling/evidence/proof/PROOF.md b/research/released-operator-clifford-ceiling/evidence/proof/PROOF.md new file mode 100644 index 0000000000..08b35b275a --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/PROOF.md @@ -0,0 +1,256 @@ +# A source-bound obstruction for the explicit Clifford control class + +Status: local derivation awaiting separate review. No public theorem, solver, +native/emitter/compiler/Lean replay, complete caller, or new kappa is claimed. + +This answers a precise part of Dillon's released two-FULL/one-query handoff, +Discussion 4930 comment 19143357. The new bounded investigation is rooted at +comment 19143614. The public handoff is a sufficient construction target; no +successful t0 was supplied. Its physical FREE class is not fully enumerated. +The theorem below explicitly restricts that class to fixed finite columnwise +monomial Clifford words and scalar owner programs. It does not silently replace +physical FREE by parity-even operators or by every unit of an abstract algebra. + +## Pinned input + +The scientific source is canonical commit +`4c0a359d88f22f05189d51f48387750b801a45d4`, package +`research/coded-native-caller`. Exact retained files and hashes are in +`SOURCES.json` and `frozen/`. Governing guidance was read at canonical +`20a1e31bc6009b9b3f4d084bbaadc6350e34fcba`. + +There are 112 owners. The real scalar code A is invertible, has zero diagonal, +and has 52 nonzero entries in every row and column. Each source normalizer is +K_i = Z_(z_i) P_(G_i), with G_i an orthogonal binary 9 by 9 matrix and +G_i e_q = q_i. The 112 vectors q_i are distinct, of weight 3 or 7. These exact +properties were checked directly from CODE.json and NORMALIZERS.json; the +check did not invoke the source operator evaluator. + +Embed one copy K_(1,i) on the central axis q and the eight first-stage axes U, +and another K_(3,i) on q and the eight third-stage axes W. The full address +space has exactly 17 axes. The sets {q}, U, W are disjoint. G rows are used as +rows, not columns. Every operator is lifted columnwise; scalar owner matrices +are applied once, rather than tensoring an owner sum. + +Let Q be the central Gaussian, D3 the product of the eight third-stage +Gaussians, and + + C_s[i,j] = A[i,j] K_(s,i)^-1 K_(s,j). + +Dillon's four required controls are + + t0, Q^-1 t0 Q, t = D3 t0 D3^-1, + E = Q^-1 C3 t C1 Q^-1, + +including their explicitly implementable inverses. The main endpoint is + + F3 J(t0) F1 = [[0,t],[-E,0]] diag(G,G), + G = D1 D3 Q. + +## Exact scope of the obstruction + +Let H be the projective group of monomial Clifford operators on the actual +17 one-column address bits. A control in the tested class is a fixed finite +scalar owner program in columnwise lifts h^(tensor f), h in H. Owned copies, +temporary fields and clears are allowed as long as the resulting main block +has such a finite linear expansion. Coefficients may depend on f; the set of +letters is fixed independently of f. Projective phases are absorbed into the +scalar coefficients, including their correct f dependence. + +This is a generous algebraic model of the source's explicit P/D/X/phase +Clifford words and owner ADD programs. It gives no automatic physical tariff +or inverse implementation to an arbitrary algebra element. The completed +obstruction needs neither tariff nor inverse sufficiency: it rules out every +nonzero t0 in this declared class satisfying the four memberships at all +sufficiently large f. Section 4 also gives a direct scalar-owner proof which +does not require the transported-class argument. + +It does not cover arbitrary nonlinear monomial address maps, general +non-Clifford phases, or a number/alphabet of letters growing with f. It also +does not cover a changed FULL controller, extra paid calls, extra axes, a +different productive endpoint, or a different source code. + +## 1. Why all-width membership becomes support membership + +For any finite collection of pairwise nonproportional nonzero operator +vectors v_1,...,v_m, their tensor powers are linearly independent for every +f >= m-1. For each i and j != i choose a linear functional ell_(i,j) that +kills v_j but not v_i. The tensor product of these m-1 functionals kills +every v_j^(tensor(m-1)) except i. Additional factors nonzero on v_i extend +the argument to any larger f. This elementary argument also allows +width-dependent scalar coefficients. + +Apply the lemma to the finite projective Clifford alphabet containing all +letters in the fixed proposed programs and their conjugates. If t0 and its +Q and D3 conjugates are all represented by monomial Clifford programs at +every positive width, then at sufficiently large width every surviving +letter of t0 lies in + + H0 = H intersect Q H Q^-1 intersect D3^-1 H D3. + +Conjugate t0 by D3. Its support is in Ht = D3 H0 D3^-1. The following +observations do not identify Ht with H0: + +* t is monomial by hypothesis; +* D3^-1 t D3 = t0 is monomial, and conjugation by D3^2 shows that + D3 t D3^-1 is monomial as well; +* Q^-1 t Q = D3 (Q^-1 t0 Q) D3^-1 is not automatically monomial from + those statements alone. + +The last bullet is an essential warning: it cannot be inferred merely from +the three displayed controls. Consequently, the proof below uses the exact +support class for t, not an unjustified assertion that t is again in H0. + +Define instead + + Ht = D3 H0 D3^-1. + +Every surviving letter of t lies in Ht. The next section derives the actual +invariants of this transported class directly. + +## 2. Lagrangian invariants, including the D3 transport + +Use binary symplectic coordinates (x,z), with the computational Lagrangian +L0 = {(0,z)}. Let Lq = Q L0 and Lw = D3 L0. Their X projections are +span(e_q) and W respectively. Q and D3 have order two on binary symplectic +space even though their operator squares retain phases/Paulis. + +A monomial Clifford h has symplectic form + + x' = R x, + z' = S x + R^-T z, + +where R is invertible. For h in H0, it preserves L0, Lq and Lw. +Therefore R e_q = e_q and R W = W. This is the source-fixed flag constraint; +it does not identify every parity-even word with a physical free operation. + +For a transported letter k = D3 h D3^-1 in Ht: + +* k preserves L0 because h preserves Lw; +* k preserves Lw because h preserves L0 and D3^2 L0 = L0; +* k preserves Lqw = D3 Q L0 because h preserves Lq. + +Thus its invertible X block R_k preserves W. The X projection of Lqw is +span(e_q) plus W. Hence R_k preserves span(e_q) plus W as well. On the +quotient by W, R_k therefore fixes the nonzero central class [e_q]. +This is weaker than R_k e_q=e_q, and is exactly the distinction required +by the released warning about transport through D3. + +For nonzero v in span(e_q) plus U and nonzero w in span(e_q) plus W, define the rank-one +Gaussian chart L(v) = {(v v^T z,z)}. If k L(v) = L(w), its X projections +give R_k v = w. Passing to the quotient by W and using invertibility and +the fixed central class implies v=e_q. It does NOT imply w=e_q: w may +equal e_q plus a vector in W. + +This one-sided conclusion is sufficient for a useful obstruction below. + +## 3. No monomial endpoint component + +Expand an endpoint block E[i,j]. Every term is a scalar multiple of + + Q^-1 K_(3,i)^-1 K_(3,r) k K_(1,s)^-1 K_(1,j) Q^-1, + k in Ht, + +with scalar A[i,r] b[r,s,k] A[s,j], where b are the coefficients of t. + +For this word to be monomial, k must carry + + L(G_(1,s)^-1 q_j) to L(G_(3,r)^-1 q_i). + +Section 2 forces G_(1,s)^-1 q_j=e_q, so s=j by distinctness of the source +q vectors. But A[j,j]=0. Every term with a nonzero source coefficient is +therefore outside H. This conclusion does not require r=i. + +No uniqueness assertion for different intermediate owners is needed. +Group together any projectively equal nonmonomial terms. Their sum still +has support outside H; cancellation can remove classes but cannot create +a class in H. At all sufficiently large widths, section 1 makes the span +of these remaining nonmonomial classes disjoint from the span of the +finite monomial alphabet in any proposed FREE implementation of E. + +Consequently, if E is also FREE, E=0 at every such width. The exact source +codes C1,C3 and Q are invertible, so E=Q^-1 C3 t C1 Q^-1=0 implies t=0, +then t0=0. In particular the handoff's required invertible t0 cannot exist +inside this fixed finite columnwise monomial-Clifford control class. + +This result does not mistake Ht for H0. In fact Ht permits R_k e_q=e_q+w +with nonzero w in W. The proof needs only the induced quotient action and +the resulting one-sided equality s=j. It also does not need a uniform +inverse bound: the source code inverses are exact, and all four requested +inverse programs are rendered moot by the forward obstruction. + +For arbitrary width-dependent scalar coefficients, the exact conclusion +is t0_f=0 at every sufficiently large width satisfying the four +memberships. A family nonzero only at finitely many small widths is not +excluded, but cannot satisfy the all-width invertibility contract. + +## 4. Completed scoped theorem: scalar owner interleavers + +For t0 = B tensor I, all first three controls equal B tensor I and t=t0. +Its inverses, when supplied by an explicit scalar program, are physically +legal in the same scalar class. Each term of E[i,j] is now + + A[i,r] B[r,s] A[s,j] + * Q^-1 K_(3,i)^-1 K_(3,r) K_(1,s)^-1 K_(1,j) Q^-1. + +The signed linear permutation between the two Q^-1 factors has binary map + + M = G_(3,i)^-1 G_(3,r) G_(1,s)^-1 G_(1,j). + +For a signed orthogonal permutation M, Q^-1 M Q^-1 is monomial exactly +when M e_q=e_q. If the directions differ, the two central Gaussian factors +produce four distinct translations, all with nonzero coefficient; if they +agree, their equal or opposite signs give a single monomial. This includes +absolute-sign choices and does not tensor a scalar sum. + +Here M e_q=e_q is equivalent to + + G_(3,r) G_(1,s)^-1 q_j = q_i. + +The first-stage component can vanish only if G_(1,s)^-1 q_j=e_q, +so s=j; then distinct third-stage q vectors force r=i. Both source diagonal +entries are zero. Thus every nonzero term is nonmonomial. + +For fixed i,j, terms indexed by distinct pairs (r,s) are projectively +distinct. Equality would imply + + G_(3,r')^-1 G_(3,r) = G_(1,s')^-1 G_(1,s). + +The left map is supported on q+W and the right on q+U. Their intersection +contains only the identity binary linear map: both must fix U and W, and +an invertible map on the single common bit fixes q. Distinct q vectors then +give r=r' and s=s'. Conjugating by the fixed outside factors preserves +projective distinctness. Signed phases cannot change this argument. + +For any nonzero B[r,s], choose i with A[i,r] nonzero and j with A[s,j] +nonzero (there are 52 choices each). The corresponding nonmonomial term has +nonzero coefficient and cannot cancel. Uniform tensor separation against +any proposed fixed finite columnwise monomial alphabet rules out a FREE +representation of E at all sufficiently large widths. + +Hence no fixed nonzero scalar owner matrix B, including a dense one, +satisfies the fourth condition uniformly in that model. If coefficients +depend on f, the precise conclusion is B_f=0 at every sufficiently large +width where the endpoint belongs to the declared monomial span. This +excludes every all-width invertible family B_f; it does not exclude a family +supported only at finitely many small widths. +This theorem does not rely on classifying the whole physical FREE algebra. + +## Credit and open next question + +Credit Dillon for the released construction equations, the real normalizers +and their charged recoding; Dugongue/mdumitrean for PR4929 and A; Cao Yifan +for the native word; Cinna Davis, zxv, Jacob Alan Sussman, Ryanson Jonathan, +and the full retained native/helper/Clifford/compiler lineage. The elementary +uniform tensor-separation device is already used in the preceding projective +operator work; it is not claimed as a new theorem. New local analysis has +substantial OpenAI Codex assistance and no independent human or kernel +acceptance. + +The useful continuation must change at least one declared hypothesis: +the fixed columnwise monomial-Clifford control class, the sufficient four +FREE conditions (replacing some with an explicitly paid and affordable +operator), the source code, the productive target, or the controller. +Merely adding more Clifford owner/address couplings cannot create a +monomial component. A test that assumes R_k e_q=e_q after D3 transport +repeats the released error and must be rejected. diff --git a/research/released-operator-clifford-ceiling/evidence/proof/SOURCE-CHECK.json b/research/released-operator-clifford-ceiling/evidence/proof/SOURCE-CHECK.json new file mode 100644 index 0000000000..bafcc5aa2c --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/SOURCE-CHECK.json @@ -0,0 +1,20 @@ +{ + "scope": "Static exact source properties only; no operator solver, emitter, native, compiler, or Lean replay.", + "checks": { + "owner_count": 112, + "zero_diagonal": true, + "row_nonzero_counts": [ + 52 + ], + "column_nonzero_counts": [ + 52 + ], + "distinct_q": 112, + "q_weights": [ + 3, + 7 + ], + "orthogonal_G_all": true, + "scalar_polynomial_A2_plus12A_minus13I": true + } +} diff --git a/research/released-operator-clifford-ceiling/evidence/proof/SOURCE-FLAG-CHECK.json b/research/released-operator-clifford-ceiling/evidence/proof/SOURCE-FLAG-CHECK.json new file mode 100644 index 0000000000..3809fe4d65 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/SOURCE-FLAG-CHECK.json @@ -0,0 +1,53 @@ +{ + "axis_embedding": { + "central": 0, + "stage1": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "stage3": [ + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16 + ] + }, + "rejection_controls": { + "reject_central_shift_erasure": true, + "reject_corrupted_orthogonal_map": true, + "reject_duplicated_port_direction": true, + "reject_nonzero_code_diagonal": true, + "reject_untransported_H0_substitution": true + }, + "scope": "Exact pinned source structure and one 17-axis binary symplectic transport witness; not an all-width theorem replay, phase checker, t0 search, native/compiler replay, or supplier admission.", + "source_checks": { + "112_distinct_q": true, + "A2_plus_12A_equals_13I": true, + "G_rows_match_literal_q": true, + "all_G_orthogonal": true, + "q_weight_3_or_7": true, + "row_and_column_nonzero_counts_52": true, + "zero_diagonal": true + }, + "status": "PASS_SOURCE_AND_TRANSPORTED_FLAG_ONLY", + "transported_flag_witness": { + "D3_h_D3inv_monomial": true, + "Qinv_h_Q_monomial": true, + "Qinv_k_Q_not_monomial": true, + "h_CZ_in_H0": true, + "k_central_X_image_is_q_plus_w": true, + "k_does_not_preserve_Lq": true, + "k_preserves_correct_transported_flags": true, + "quotient_flag_excludes_noncentral_U_vectors": true + } +} diff --git a/research/released-operator-clifford-ceiling/evidence/proof/SOURCES.json b/research/released-operator-clifford-ceiling/evidence/proof/SOURCES.json new file mode 100644 index 0000000000..ef42d1e3d1 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/SOURCES.json @@ -0,0 +1,36 @@ +{ + "canonical_gate_pin": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba", + "scientific_source_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "files": [ + { + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/CODE.json", + "git_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/NORMALIZERS.json", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/PHYSICAL.md", + "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/ORIGINS.json", + "git_blob": "e18a033d4de1d997f55e84d1535fc6cde20424c4", + "sha256": "10cf47173ca238c32adb923daae7c1137c2e9c86c7066301d68fc74442b3f4d7" + }, + { + "commit": "4c0a359d88f22f05189d51f48387750b801a45d4", + "path": "research/coded-native-caller/NOTICE", + "git_blob": "985b6b1bc76dacd54a9cbe9897f3b659ae93c3a4", + "sha256": "317b1c5e040bab50ebfc3d0cdb3a47fc30e2f872a00895f563d7931749b1cc7b" + } + ] +} diff --git a/research/released-operator-clifford-ceiling/evidence/proof/check_source_and_flag.py b/research/released-operator-clifford-ceiling/evidence/proof/check_source_and_flag.py new file mode 100644 index 0000000000..9b9f57090d --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/check_source_and_flag.py @@ -0,0 +1,159 @@ +#!/usr/bin/env python3 +"""Read-only source/flag checks, not a universal operator theorem checker.""" +import hashlib +import json +from fractions import Fraction +from pathlib import Path + +ROOT = Path(__file__).resolve().parent + + +def require(condition, message): + if not condition: + raise RuntimeError(message) + + +def linear(rows, vector): + return sum(((row & vector).bit_count() & 1) << j + for j, row in enumerate(rows)) + + +def image(columns, vector): + answer = 0 + while vector: + low = vector & -vector + answer ^= columns[low.bit_length() - 1] + vector ^= low + return answer + + +def compose(left, right): + return [image(left, column) for column in right] + + +def span_basis(vectors): + pivots = {} + for vector in vectors: + while vector: + p = vector.bit_length() - 1 + if p in pivots: + vector ^= pivots[p] + else: + pivots[p] = vector + break + return pivots + + +def belongs(vector, pivots): + while vector: + p = vector.bit_length() - 1 + if p not in pivots: + return False + vector ^= pivots[p] + return True + + +def preserves(operator, space): + pivots = span_basis(space) + return all(belongs(image(operator, vector), pivots) for vector in space) + + +def main(): + manifest = json.loads((ROOT / 'SOURCES.json').read_text()) + for item in manifest['files']: + path = ROOT / 'frozen' / Path(item['path']).name + require(hashlib.sha256(path.read_bytes()).hexdigest() == item['sha256'], + 'Frozen source hash mismatch: ' + str(path)) + code = json.loads((ROOT / 'frozen/CODE.json').read_text()) + normalizers = json.loads((ROOT / 'frozen/NORMALIZERS.json').read_text()) + matrix = [[Fraction(x) for x in row] for row in code['A']] + ports = normalizers['ports'] + require(len(matrix) == 112 and all(len(row) == 112 for row in matrix), + 'Owner matrix shape changed') + require(len(ports) == 112, 'Port inventory changed') + qs = [linear(p['G_rows'], 1) for p in ports] + checks = { + 'zero_diagonal': all(matrix[i][i] == 0 for i in range(112)), + 'row_and_column_nonzero_counts_52': all( + sum(x != 0 for x in row) == 52 for row in matrix) and all( + sum(matrix[i][j] != 0 for i in range(112)) == 52 + for j in range(112)), + '112_distinct_q': len(set(qs)) == 112, + 'G_rows_match_literal_q': all(q == p['q'] for q, p in zip(qs, ports)), + 'q_weight_3_or_7': all(q.bit_count() in (3, 7) for q in qs), + 'all_G_orthogonal': all( + ((p['G_rows'][i] & p['G_rows'][j]).bit_count() & 1) == (i == j) + for p in ports for i in range(9) for j in range(9)), + 'A2_plus_12A_equals_13I': all( + sum(matrix[i][k] * matrix[k][j] for k in range(112)) + + 12 * matrix[i][j] == (13 if i == j else 0) + for i in range(112) for j in range(112)), + } + require(all(checks.values()), 'Source structural check failed') + + # Binary symplectic witness on the actual 17 axes; global phases are + # deliberately outside this finite flag check's scope. + n = 17 + q, w = 0, 9 + xmask = (1 << n) - 1 + ident = [1 << j for j in range(2*n)] + Q = ident.copy() + Q[n + q] ^= 1 << q + D = ident.copy() + for j in range(9, 17): + D[n + j] ^= 1 << j + H = ident.copy() # CZ(q,w) + H[q] ^= 1 << (n + w) + H[w] ^= 1 << (n + q) + K = compose(D, compose(H, D)) + L0 = [1 << (n+j) for j in range(n)] + Lq = [image(Q, v) for v in L0] + Lw = [image(D, v) for v in L0] + Lqw = [image(D, v) for v in Lq] + monomial = lambda op: all((image(op, v) & xmask) == 0 for v in L0) + flag = { + 'h_CZ_in_H0': all(preserves(H, space) for space in (L0, Lq, Lw)), + 'Qinv_h_Q_monomial': monomial(compose(Q, compose(H, Q))), + 'D3_h_D3inv_monomial': monomial(K), + 'k_preserves_correct_transported_flags': all( + preserves(K, space) for space in (L0, Lw, Lqw)), + 'k_central_X_image_is_q_plus_w': + (image(K, 1 << q) & xmask) == ((1 << q) | (1 << w)), + 'k_does_not_preserve_Lq': not preserves(K, Lq), + 'Qinv_k_Q_not_monomial': not monomial(compose(Q, compose(K, Q))), + 'quotient_flag_excludes_noncentral_U_vectors': all( + (image(K, v) & ((1 << 9)-2)) != 0 + for v in range(1, 1 << 9) if v != 1), + } + require(all(flag.values()), 'Transported-flag witness failed') + corrupted_qs = qs.copy() + corrupted_qs[1] = corrupted_qs[0] + bad_G = ports[0]['G_rows'].copy() + bad_G[0] ^= 1 + controls = { + 'reject_nonzero_code_diagonal': not all( + (Fraction(1) if i == 0 else matrix[i][i]) == 0 for i in range(112)), + 'reject_duplicated_port_direction': len(set(corrupted_qs)) != 112, + 'reject_corrupted_orthogonal_map': not all( + ((bad_G[i] & bad_G[j]).bit_count() & 1) == (i == j) + for i in range(9) for j in range(9)), + 'reject_untransported_H0_substitution': not preserves(K, Lq), + 'reject_central_shift_erasure': + (image(K, 1 << q) & xmask) != (1 << q), + } + require(all(controls.values()), 'A rejection control failed') + print(json.dumps({ + 'status': 'PASS_SOURCE_AND_TRANSPORTED_FLAG_ONLY', + 'scope': 'Exact pinned source structure and one 17-axis binary symplectic ' + 'transport witness; not an all-width theorem replay, phase ' + 'checker, t0 search, native/compiler replay, or supplier admission.', + 'source_checks': checks, + 'transported_flag_witness': flag, + 'rejection_controls': controls, + 'axis_embedding': {'central': 0, 'stage1': list(range(1, 9)), + 'stage3': list(range(9, 17))}, + }, indent=2, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/released-operator-clifford-ceiling/evidence/proof/frozen/CODE.json b/research/released-operator-clifford-ceiling/evidence/proof/frozen/CODE.json new file mode 100644 index 0000000000..03170f4a31 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/frozen/CODE.json @@ -0,0 +1 @@ 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native caller research +Apache-2.0. Prepared for Dillon with substantial OpenAI Codex assistance. + +Retained sources: Cao Yifan / intqwq, joint-helper/native-map round-three word and PR4610; Dugongue / mdumitrean, PR4929 center-free coded producer; Cinna Davis / 1337isnot1337, PR4694 center-free cache, PR4698 helper basis, PR4470 controller and cumulative construction; zxv, retained exact Clifford implementation and native/compiler lineage; Jacob Alan Sussman, mixed-target recursion. Preserve all original source-specific headers. See ORIGINS.json for exact byte origins and README.md for the new result and limits. + +The new contribution is the phase-correct commuting physical port normalization, its corrected coded raw-dual convention, and scoped caller analysis. Center deletion, code A, its spectrum and helper compensation are predecessor work. diff --git a/research/released-operator-clifford-ceiling/evidence/proof/frozen/ORIGINS.json b/research/released-operator-clifford-ceiling/evidence/proof/frozen/ORIGINS.json new file mode 100644 index 0000000000..e18a033d4d --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/frozen/ORIGINS.json @@ -0,0 +1,30 @@ +[ + { + "path": "native-source.json.gz", + "source_path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz", + "commit": "624de9dc66858af0945e5f8a0942488d62280d43", + "source_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + }, + { + "path": "CODE.json", + "source_path": "research/native-center-free-code/CODE.json", + "commit": "361f5d4100640177d6a983dd2f336021c75bfd5e", + "source_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "clifford_exact.py", + "source_path": "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py", + "commit": "624de9dc66858af0945e5f8a0942488d62280d43", + "source_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "path": "CONTROLLER.json", + "source_path": "research/joint-helper-lattice/CONTROLLER.json", + "commit": "624de9dc66858af0945e5f8a0942488d62280d43", + "source_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5", + "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f" + } +] diff --git a/research/released-operator-clifford-ceiling/evidence/proof/frozen/PHYSICAL.md b/research/released-operator-clifford-ceiling/evidence/proof/frozen/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/proof/frozen/PHYSICAL.md @@ -0,0 +1,71 @@ +# Real physical normalizers for the coded producer + +This is local constructive research on canonical/pr4929, not a completed supplier or exponent claim. Source code and Gaussian conventions retain the original authors' credit. + +Let n=9 and let q be any of the source's 112 port vectors (weight 3 or 7). Let e0=1. Construct an orthogonal binary matrix G taking e0 to q. If q_0=0, use the orthogonal transvection T_(e0+q). If q_0=1, select j>0 with q_j=0 and use T_(ej+q) T_(e0+ej). Here T_v(x)=x+(v dot x)v; both v have even weight, hence T_v is orthogonal. Such j exists because q is not the all-ones vector. + +For row j of G put z_j=(wt(row_j G)-1)/2 modulo 2. Define K=Z_z P_G. It is a real signed permutation. The full Gaussian R has entries alpha*(-i)^wt(x+y), with alpha=(1+i)^9/2^9. Orthogonality gives + +wt(G^-1 d)-wt(d) = 2 z dot d (mod 4). + +Indeed the degree-two coefficients vanish modulo four because distinct columns of G^-1 have even dot product; the linear coefficient is the weight of that column minus one. Therefore K R K^-1=R exactly, including absolute phase. K also maps the central line to span(q), and its orthogonal complement to q-perp, at the canonical-frame Lagrangian level. All these statements tensor to every positive digit-column count. + +Let Q be the central C gate, D the product of the other eight C gates, so R=DQ. Let E_i and S_i be the actual retained entrance-line and exit-hyperplane frame operators. With the operator convention that rightmost applies first, use + +input X: E_i K_i Q^-1 +input Y: K_i +output X: K_i^-1 +output Y: D K_i^-1 S_i^-1. + +All four wrappers are monomial. Their Lagrangian incidences prove this for every port, and the scratch verifier checks exact tableaus and absolute phases at every one of the 112 source ports. With A from PR4929, define C_ij= A_ij K_i^-1 K_j. Then the full main endpoint is + +F = diag(D,D) [[I,0],[C Q^-1,I]]. + +C is a physically implementable fixed owner recoding: apply K_i to each owner, apply A among the owners at common physical coordinates, and apply K_i^-1. Its inverse uses A^-1=(A+12I)/13. Since each K_i is real orthogonal and A is real symmetric, C^T=C. Since K_i commutes with R, C commutes with R. The polynomial C^2+12C-13I=0 follows by similarity. The 408 independent helper jobs and every paid Gaussian child are unchanged. + +For the actual raw inverse transpose, F^-T=diag(D^-1,D^-1) [[I,-Q^-1 C],[0,I]], since Q,D are symmetric. Multiply both outputs by D^2, then conjugate the physical X bank by Q^2 (input Q^-2 and output Q^2). These are explicit monomial powers. The result is + +B = diag(D,D) [[I,-Q C],[0,I]]. + +The old source convention using Y-only Q^2 conjugation cannot simply be copied for noncommuting C. The X-only convention above is exact. + +For a prior code B0 commuting with the current D, set G(B0)=diag(B0,Q^-1 B0 Q). The following two constructive local identities hold without requiring C and Q to commute: + +(post X C) F (pre Y C) = G(C B0) F_standard G(B0)^-1, +(post X C^-1) B (pre Y C^-1) = G(C^-1 B0) B_standard G(B0)^-1. + +They use [C,DQ]=0 and [B0,D]=0. Every additional operation on the left is physically cheap fixed recoding. For disjoint fresh blocks, codes from earlier stages commute with the current D. These identities do not yet settle interstage ADD/IDLE compatibility, terminal gauges, productive jobs, or the complete moment. + +## Literal recoding and complete local bill + +The source code has an exact factorization A=I-MM^T/4 with M a 112-by-8 matrix having entries 0,+1,-1 and M^T M=56I. Each mode column has 56 nonzero entries, and each owner row has four. The mode columns are emitted in NORMALIZERS.json and all 12,544 entries are checked against the pinned CODE.json. This factorization is used here as a constructive scalar program, without relying on any common physical address chart for separate Gaussian mode transformations. + +To execute A on arbitrary independent owner fields x, allocate eight owned zero fields t. Compute t=M^T x with 448 signed ADDs; update x-=M t/4 with 448 scaled ADDs; clear the eight owned temporaries. Reading x is finished before any x is updated. Hence no input field is overwritten before its last source read. For A^-1 use the same program with coefficient -1/52, since A^-1=I-MM^T/52. Both are exact rational linear programs. The helper fields of the native producer are never used as scratch, copied as free credit, or erased. + +Conjugating this scalar program by the 112 K_i and their inverses implements C or C^-1. This pays 224 monomial field maps, 896 scalar ADDs and 16 owned CLEARs per recoding, with eight owned fields reusable sequentially. The two additional recodings in either local gauge identity therefore cost at most 448 monomial maps, 1,792 scalar ADDs and 32 CLEARs, with no recursive Gaussian child. The four actual port normalizers contribute 448 monomial maps per native invocation. The displayed backward conversion contributes at most 448 further monomial maps (112 input X powers, 112 output X powers and 224 output D-squares); fusing maps can reduce this upper bound but is not assumed. + +These are field-level operation counts. A lifted K_i is an explicit binary map on nine f-bit address blocks together with signs given by block parity. Its constants, indexed movement and phase passes use the retained native monomial implementation. It is therefore a fixed finite O(V polylog p) nonrecursive operation under that caller's precision/address ABI, not a zero-work instruction. Each fixed rational ADD is likewise charged at its actual scalar precision. In particular the inverse denominator 52 must be implemented and rounded; no free exact real-division oracle is assumed. This lemma makes no independent TM tariff or outer-budget claim. + +The maximum exact component-l1 prefix bound for the scalar A program, including its temporaries, is 57. For A^-1 it is 56 (the output-only bound is 69/13). Signed monomial maps preserve component magnitude. A fixed local sequence has a fixed suffix bound obtained by multiplying elementary bounds 1+|coefficient|; owned CLEAR has bound one. This gives a finite bound for local rounding propagation. The number of local uses, compiler precision and complete outer error allocation still belong to the caller theorem. + +The normalized producer still has its exact PR4929 paid profile + + {1:2201, 2:412, 3:510, 4:127, 5:40} + +and independent helper profile + + {4:28, 7:7, 8:47, 9:326}. + +No productive main ranks are asserted merely from the coupled central ABI. Those depend on the completed caller, its initial/final gauges and every paid correction. + +## Universal scope and reproducible evidence + +PR4929 supplies the arbitrary-input logical identity over Q[FreeGroup72] for its emitted center-free word with ground-chart helper pre-compensation. Its normalized main endpoint is L(A), its raw dual is L(A)^-T, and every one of the 408 helper endpoints is autonomous. This proof is an inherited premise with exact source pins, not a consequence of this normalizer checker. The present wrappers and owner recodings act exclusively on the 224 main fields; new scratch is explicitly owned. Thus the helper block remains autonomous and its independent inputs, requested transforms and paid profile remain unchanged. + +For every f>=1, assign the shared native letters their actual consistent invertible lifted operators. Evaluation of the source free-group algebra is a homomorphism and gives the source logical identity. Independently lift each K_i as its f-fold tensor product, retaining spectator coordinates; its signed-permutation word, the two direct frame identities and its commutation with R lift by operator composition. In every compiled monomial word, P and X act columnwise on the f-bit blocks, D sums its Z4 polynomial over the f columns, and a one-column scalar phase i^gamma becomes i^(f*gamma). Reusing the one-column global phase unchanged would be incorrect. Finally form the owner matrix C_f with entries A_ij K_i,f^-1 K_j,f. One does not tensor the whole 224-by-224 owner matrix and does not assert that tensor powers preserve sums. Instead the finite scalar owner program is evaluated directly in the algebra of these lifted address operators. This proves the central ABI and local gauge identities at every positive width. + +Run `python3 -I -B research/coded-native-caller/normalizers.py` or its optimized `-O` form. The checker authenticates the decompressed actual native payload, CODE.json and retained Clifford source before executing the latter. It verifies all 112 real signed normalizers, 57,344 explicit weight-congruence addresses, 896 forward/backward monomial wrappers and eight exact frame/block identities per port, including absolute phase. Each emitted wrapper is separately lowered to a literal P/D/X/phase-only word and checked against its defining expression by exact tableau and absolute-phase state. No C gate remains in an emitted wrapper. The independent incoming-column and outgoing-row identities imply all 5,824 nonzero off-diagonal code blocks, without sampling those pairs. It also executes the eight-mode recoding on all 112 arbitrary-input basis columns in both directions. Omitting the essential signed phase is rejected at every affected port. The default command compares a regenerated mathematical receipt and performs no writes; `--write` is the explicit authoring path. + +Source pins: canonical main 624de9dc66858af0945e5f8a0942488d62280d43, `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, decompressed SHA-256 cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd; PR4929 head 361f5d4100640177d6a983dd2f336021c75bfd5e, `research/native-center-free-code/CODE.json`, SHA-256 8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0; canonical `research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py`, SHA-256 2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962. Gzip container bytes are not substituted for decompressed source identity. + +Credit Dugongue's PR4929 for the coded producer and stable code; Cinna Davis's PR4694/4698 and the original cache/helper construction; Cao Yifan's PR4610 native word; the retained zxv, Jacob Alan Sussman, Cinna Davis and Clifford/native/compiler lineage. The exact canonical-frame implementation and phase conventions are retained source material. The constructive real centralizing normalizers, their explicit lifted words, X-only raw-dual convention and costed local code gauges are the additions here. New work is Apache-2.0 and has substantial OpenAI Codex assistance; no formal-kernel or independent human acceptance is asserted. diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/FILES.json b/research/released-operator-clifford-ceiling/evidence/supplements/FILES.json new file mode 100644 index 0000000000..c7d1991d38 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/FILES.json @@ -0,0 +1,12 @@ +{ + "scope": "Separate paid-shear and source-flag addenda; original frozen review unchanged", + "files": { + "PAID-SHEAR-ADDENDUM.md": "c40812090fd1abd85ece881873c92729caf48d24a75338fd1a64457b56f1748b", + "SOURCE-FLAG-REVIEW.md": "3f7982e0ad104102847f05e6f6e544a42da84bf613de9a978e5e303ef8b8734d", + "SOURCES.json": "f5c88f371bc125e9dbb15e6ecbae68e2ce2573d81f0329b56775cc9a6f770021", + "frozen/CONTRACT.md": "a1001f481df15046cd09d647c6fd5539196664277be849d7c2a260a3290643cc", + "frozen/PAID-SHEAR-SCREEN.md": "81fefcf4a1be0be04076e7cba0e27ba4afe732d4810a13b0a76dbe827967c10c", + "frozen/SOURCE-FLAG-CHECK.json": "a6c30f6dc14c0673e6043ac6197ae460ce03e9e3b139146ebcb6766ecb1d088e", + "frozen/check_source_and_flag.py": "025ba8f3f63fa4f4d7155a32f0f51de210693f6b425b047312d5f232e96fdc5f" + } +} diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/PAID-SHEAR-ADDENDUM.md b/research/released-operator-clifford-ceiling/evidence/supplements/PAID-SHEAR-ADDENDUM.md new file mode 100644 index 0000000000..cc12931da4 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/PAID-SHEAR-ADDENDUM.md @@ -0,0 +1,121 @@ +# Independent addendum: scalar-owner X-Gaussian paid shears + +**PASS for the separate source-bound necessary screen.** Reviewed +PAID-SHEAR-SCREEN.md SHA256 +`81fefcf4a1be0be04076e7cba0e27ba4afe732d4810a13b0a76dbe827967c10c` +and the retained CONTRACT.md. This is a separate extension; the original +reviewed Clifford theorem, its proof hash and review bytes remain unchanged. + +The mathematical conclusion is m>=112 for a product + +``` +t0=S_m ... S_1, +S_k=I+u_k v_k^T tensor H_k, +``` + +where u_k,v_k are scalar vectors on the112 owner coordinates and H_k belongs +to the fixed commuting group of Pauli-X Gaussian words on the same17 axes. +Dense vectors are allowed. Owner coefficients are applied once and can vary +with width. The theorem does not assume that owner matrices commute with +each other; only the address words have the stated commuting structure. + +## Collision, affine phases and sufficiently large width + +Every H in the address group commutes with every X translation. A monomial +operator commuting with all translations has underlying permutation +`p(x+a)=p(x)+a` and multipliers `c(x+a)=c(x)`. Hence it is a scalar times +one X translation. This statement includes phases; a nonconstant signed or +quadratic phase cannot be silently retained while commuting with every X. + +For a nonidentity H contribution to collide with an identity-address +contribution after the fixed source K factors, H would have to equal + +`phase*K_(3,r')^-1 K_(3,r) K_(1,s)^-1 K_(1,s')`. + +The right side is a zero-shift signed **linear** permutation and fixes address0. +If H were monomial, the preceding translation characterization therefore +forces its translation to vanish and H to be projectively I. Source disjoint +stage supports and distinct q_i then force r'=r and s'=s. Thus a grouped +identity coefficient B0[r,s] cannot be cancelled by a nonidentity H class or +a different intermediate owner pair. + +With B0[r,s] nonzero, nonempty source column r and row s supply output/input +i,j with A[i,r]A[s,j] nonzero. Zero source diagonal gives r!=i and s!=j. +The original scalar-owner monomial criterion then makes its endpoint word +nonmonomial. Therefore B0 contributes a unique nonzero nonmonomial class. +Uniform tensor separation from the fixed finite proposed monomial endpoint +alphabet forces B0=0 whenever the endpoint E is declared free. + +This uses the same correct projective convention as the main proof: reduce +equal one-column words first, raise their scalar cocycles/phases to f and +leave owner coefficients outside the tensor product. The X-Gaussian group on +fixed17 axes is projectively finite. Its source-product classes plus any +fixed finite free endpoint alphabet admit a uniform sufficiently-large-width +separation threshold. No all-small-width statement or practical threshold +is claimed. Width-dependent scalar coefficients do not evade the conclusion +at those widths. A growing/noncolumnwise alphabet is outside the theorem. + +## Scalar owner rank bound and inverse condition + +For T_k=S_k T_(k-1), exact telescoping gives + +``` +t0-I=sum_k u_k (v_k^T tensor H_k) T_(k-1). +``` + +Taking the grouped projective identity coefficient is linear. Since u_k is +scalar in owner space, it factors out of that extraction, yielding + +``` +B0-I=sum_k u_k w_k^T, +rank(B0-I)<=dim span{u_k}<=m. +``` + +B0=0 consequently implies112<=m. This remains true for arbitrary dense scalar +vectors and width-dependent scalar entries. It does not assert attainability +at112 shears. The explicit physical inverse S_k^-1=I-u_k v_k^T tensor H_k +requires v_k^T u_k=0; it uses H_k again, not H_k^-1. For a product, inverse +execution reverses the shear order. The rank lower bound itself does not need +nilpotence or any inverse-program sufficiency. + +This coefficient-extraction step is precisely where **operator-valued** +owner/address gathers and scatters leave the proof. If the components of u_k +contain different K maps, extracting identity classes can produce columns +outside one fixed scalar span. No m>=112 bound is transferred to that class, +or to retained correlated native/query observations, without a new argument. + +## Conditional price consequence + +The theorem's H group is broader than the **priced subset** in CONTRACT.md. +The latter chooses H_k=C_w C_v with independent Pauli-X directions and an +explicit monomial rank-two Gaussian implementation. In that specific +middle/exit execution, two independent t0 arguments and one t0^-1 use give +the added bill3mH2, conditional on legal free E/E^-1 and the unchanged complete +target invoice. This is an explicit execution bill, not a universal minimum +for every conceivable implementation or every H in the larger group. + +The independently recorded raw allowance is strictly above44 and below45 +at the included right endpoint b=.00339999, with uniform minimum there. +Seven shears cost21H2<42 throughout the positive-C interval. Eight cost +24H2(b)>45: indeed1-b>15/16 and +`15^16=6568408355712890625<9223372036854775808=2^63` +gives `2^(15/16)>15/8`, hence24H2(b)>45. Thus seven is the maximal shear +count compatible with this explicit raw price at the required endpoint. + +The necessary m>=112 contradicts that budget. Even the weaker H2>1 gives +3mH2>336, well beyond44.67695955358... at b. No finite costs, compiler +reserve/tails, stock or outer costs were funded by this calculation. The +unrealized operator/target premise remains visible. + +**Stop this scalar-owner commuting-X shear class before search.** Continue +constructively only after changing a named hypothesis, such as an actual +operator-valued gather/scatter using an already-paid native observation, +with its complete ownership, phase, inverse, source-access and paid bill. +This is not a universal fresh-query lower bound or a reason to stop the +broader paid-profile-gain objective. + +No solver, shear enumeration, checker/native/factory/emitter/compiler/Lean +execution or public action was performed by this independent reviewer. +Credit Astra's separate paid screen, Dillon's released template, Dugongue's +source code and the retained native/helper/Clifford/compiler lineage. +Substantial OpenAI Codex assistance; Apache-2.0. diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/SOURCE-FLAG-REVIEW.md b/research/released-operator-clifford-ceiling/evidence/supplements/SOURCE-FLAG-REVIEW.md new file mode 100644 index 0000000000..1d59e35fa4 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/SOURCE-FLAG-REVIEW.md @@ -0,0 +1,40 @@ +# Bounded inspection of the source/flag checker supplement + +**PASS for its stated finite scope.** Reviewed check_source_and_flag.py SHA256 +`025ba8f3f63fa4f4d7155a32f0f51de210693f6b425b047312d5f232e96fdc5f` +and its saved SOURCE-FLAG-CHECK.json. The packager separately reports exact +normal/optimized replay and receipt equality. This reviewer inspected code +and source contracts without rerunning the checker or source algorithm. + +The checker uses standard-library integer/Fraction operations and explicit +RuntimeError checks, with no assertions disabled by optimization and no dynamic +source imports, subprocesses, solver, native emitter or network access. It +authenticates the five retained source files before checking the literal112 +owner inventory, zero diagonal,52 nonzeros per row/column, distinct literal q +directions, correct G ROW convention, orthogonality and the exact A polynomial. +This is finite source-structure evidence, not an all-width theorem replay. + +Its17-axis flag example is correctly embedded: q=0, U=1..8, W=9..16, w=9. +Q and D3 are upper-right symmetric binary symplectic shears; CZ(q,w) is a +lower-left symmetric shear. Their composition K=D3 CZ D3^-1 is therefore +symplectic and invertible. The code uses column images consistently for these +maps and row matrices consistently for the source G data. Basis-inclusion +tests establish equality of the known full-dimensional Lagrangians here. + +The example correctly has CZ in H0 but transported K in Ht, with central X +image e_q+e_w. K preserves L0,Lw,Lqw and fails to preserve Lq; its Q conjugate +is nonmonomial. This is a valid concrete rejection of Ht=H0 and of replacing +the quotient-central condition by R_k e_q=e_q. The small loop over noncentral +U vectors corroborates that particular example's quotient behavior, not the +universal flag lemma for arbitrary K. + +The controls test a nonzero A diagonal, duplicated port direction, corrupted +orthogonal source row, untransported-H0 substitution and erased central shift. +No portability or source/control gap was found within this bounded scope. +The file correctly excludes absolute-phase checking, all-width theorem replay, +t0 search, native/compiler execution and supplier admission from its claim. + +This supplement may be packaged unchanged with those limits. It does not +replace the written support/separation proof. No original proof/review bytes +were edited. Credit the source author and packager; substantial OpenAI Codex +assistance. Local independent inspection only. diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/SOURCES.json b/research/released-operator-clifford-ceiling/evidence/supplements/SOURCES.json new file mode 100644 index 0000000000..cf10418969 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/SOURCES.json @@ -0,0 +1,29 @@ +{ + "scope": "Two separate bounded supplements; original reviewed proof/review unchanged", + "files": [ + { + "snapshot": "frozen/PAID-SHEAR-SCREEN.md", + "origin": "outputs/released-operator-intersection-20261023/PAID-SHEAR-SCREEN.md", + "sha256": "81fefcf4a1be0be04076e7cba0e27ba4afe732d4810a13b0a76dbe827967c10c", + "scope": "Read-only supplement inspection; no source algorithm/checker rerun by reviewer" + }, + { + "snapshot": "frozen/CONTRACT.md", + "origin": "outputs/released-operator-intersection-20261023/CONTRACT.md", + "sha256": "a1001f481df15046cd09d647c6fd5539196664277be849d7c2a260a3290643cc", + "scope": "Read-only supplement inspection; no source algorithm/checker rerun by reviewer" + }, + { + "snapshot": "frozen/check_source_and_flag.py", + "origin": "outputs/released-operator-intersection-20261023/check_source_and_flag.py", + "sha256": "025ba8f3f63fa4f4d7155a32f0f51de210693f6b425b047312d5f232e96fdc5f", + "scope": "Read-only supplement inspection; no source algorithm/checker rerun by reviewer" + }, + { + "snapshot": "frozen/SOURCE-FLAG-CHECK.json", + "origin": "outputs/released-operator-intersection-20261023/SOURCE-FLAG-CHECK.json", + "sha256": "a6c30f6dc14c0673e6043ac6197ae460ce03e9e3b139146ebcb6766ecb1d088e", + "scope": "Read-only supplement inspection; no source algorithm/checker rerun by reviewer" + } + ] +} diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/frozen/CONTRACT.md b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/CONTRACT.md new file mode 100644 index 0000000000..dc979fe409 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/CONTRACT.md @@ -0,0 +1,187 @@ +# Released operator intersection: feasibility gate and changed contract + +Local-only research handoff, 2026-10-23. Read/derive gate completed; no t0 +solver, broad operator search, emitter, native/compiler/Lean campaign or +public write was run by this worker. + +**Subsequent bounded screen:** the explicit scalar-owner X-Gaussian shear +class below is now **STOPPED**, before search. PAID-SHEAR-SCREEN.md proves +it needs m>=112, including dense scalar rank-one owner updates; its budget +allows at most seven. The construction and invoice below are retained to +show exactly what was tested and why one new monomial component was +insufficient. The prospective next test described below is superseded by +that analytic stop certificate. + +## Decision + +NARROW the original four-FREE construction: no invertible t0 exists when +all controls use fixed finite columnwise monomial Clifford words and scalar +owner programs on the actual 17 axes. The proof explicitly transports the +control algebra through D3. It does not equate that transported algebra with +the original one. See PROOF.md and the separate independent review at +`outputs/released-operator-independent-review-20261023/REVIEW.md`. + +The actual physical FREE dictionary is not fully enumerated in the released +comment, so this is not a universal exclusion of its sufficient template. +The useful constructive continuation is a changed information boundary: +retain a specific already-paid native/query observation, or allow a small +explicitly charged Gaussian control whose complete endpoint becomes legal. + +## Source and ownership + +Dillon's original 4930 comment 19141406 is DONE / RELEASED. The surviving +equations and invitation are comment 19143357, authenticated by the sole +upstream monitor. The prospective current claim is comment 19143614. The +monitor receipt is `outputs/all-upstream-pr-monitor-20261023/released-operator-intersection-primary.json`. + +The source inventory, including exact inverse order and raw-dual convention, +is `coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/REPORT.md`. +This investigation neither owns jointchart5124 nor finitepacked5095. + +## Boundary and complete conditional invoice + +The main stock is two banks of 112 independent owner fields on exactly +17 axes: central q, eight first-stage axes U and eight third-stage axes W. +The 816 native helper inputs are independent jobs, retained once each. +They are not clean scratch and cannot be reused as correlated observations +while keeping their independent productive credit. + +The intended main target is diag(G,G), G=D1 D3 Q, after explicitly undoing +the endpoint code [[0,t],[-E,0]]. The stage helper completion claims all +816 rank-nine helpers. It still needs the source-fixed constructive caller +and physical completion program identified in the independent inventory. + +| Item | Conditional Gaussian profile | Status | +|---|---:|---| +| Two unchanged native FULL calls | 2 * {1:2201, 2:412, 3:510, 4:127, 5:40} | Source-pinned inventory | +| Central query bank | 112 H1 | Required, retained | +| Helper completion | 94 H1 + 14 H2 + 56 H5 | Released conditional inventory; explicit complete caller remains open | +| Total paid P | {1:4608, 2:838, 3:1020, 4:254, 5:136} | Conditional | +| Productive T | {9:816, 17:224} | Conditional on complete caller and endpoint | +| Rank-mass difference | 112 | Arithmetic diagnostic only | +| Existing code recoding C_s or C_s^-1 | 224 monomial field maps, 896 scalar ADDs, 16 CLEARs, eight owned temporaries | Constructive field-level source bound; inverse uses /52 | +| t0 / conjugates / endpoint inverse | Must be actual words with inverse, phases and source access | Obstructed in the declared FREE class; unknown beyond it | +| Nonrecursive precision, indexed movement, storage/stock, compiler tails and outer transfer | Additional | Unknown; never zeroed | + +The independently frozen optimistic budget is +`outputs/released-operator-optimistic-budget-20261023/REPORT.md`. +It gives M(C)>=44.67695955358 for C in [.0030217758,.00339999], before +compiler reserve, finite work and other admission costs. The point values +are M(.0030217758) in [52.133114229301600459209653, +52.133114229301600459209654] and M(.00339999) in +[44.676959553589208855078743,44.676959553589208855078744]. +The raw surplus 112 is therefore not an affordable 112-H1 decoder grant. + +## Explicit paid perturbation that escapes the FREE obstruction + +This is a concrete changed test class, not a successful complete decoder. +Choose distinct owner indices a,b and i,j with A[i,a] A[b,j] nonzero. Define + + v = G_(1,b)^-1 q_j, + w = G_(3,a)^-1 q_i. + +Because A has zero diagonal, v has a nonzero U component and w a nonzero +W component. They are nonzero and independent. Let C_v and C_w be the +rank-one Gaussians along the Pauli-X translation directions v,w, with the +source's exact phase convention. Their product H=C_w C_v is one rank-two +Gaussian under a fixed invertible binary address permutation carrying two +coordinate directions to v,w. No extra address axis is introduced. + +For a fixed rational coefficient c, set + + S = I + c E_(a,b) tensor H. + +Its inverse is I-c E_(a,b) tensor H since a!=b. Both have a literal query +implementation: copy the source field b to a new owned zero field, apply +the rank-two Gaussian with its monomial pre/post address maps, add c times +the result to field a, and clear the owned temporary after its last read. +The source field is retained, and no arbitrary dirty helper is borrowed. +The inverse uses the same H query with the opposite coefficient; it does +not require H^-1. Each use costs one H2, one COPY, one scaled ADD, one +CLEAR, and the fixed monomial address maps, all at their actual precision. + +All C directions here are Pauli-X Gaussian directions. They commute with +Q and D3. Therefore S, Q^-1 S Q and D3 S D3^-1 are the same paid operator. +For a product t0=S_m ... S_1, inverse execution reverses the order and +negates each coefficient. The all-width lift preserves each product and +its phase; the owner sums are never tensor-powered. + +This changes the obstruction's premise in a visible way. At the selected +endpoint block (i,j), H sends the rank-one chart L(v) to L(w), so the +corresponding term of Q^-1 C3 t0 C1 Q^-1 is monomial. With one S, this new +monomial coefficient is nonzero and cannot be contributed by the baseline +t0=I. This is a real necessary-condition change, not a parity-only claim. + +It does not show that the remaining nonmonomial terms vanish, that E has +an explicit FREE inverse, or that a short product suffices. A single local +entry becoming monomial earns no productive target or kappa credit. + +## Full execution cost of the paid test class + +Because t0 commutes with Q and D3, its middle bridge is + + J(t0) = [[-t0 C1, t0 Q], [0, -C3 t0]]. + +Compute the original central query Q y once, form u=-C1 x+Q y, execute +t0 on u, execute t0 on y, and apply the free source C3 recoding to the +second result. The two t0 arguments are independent; they cannot be +identified or charged as one query without an explicit shared observation. +Undo t=t0 on the positive endpoint with t0^-1. If the remaining E and +E^-1 have explicit free programs, the added Gaussian bill is exactly + + 3m H2. + +The old 112-H1 query bank and all 816 helpers remain in P/T. Additional +owned query temporaries are sequential and earn no productive credit. +Finite maps, COPY/ADD/CLEAR, coefficients, precision and stock costs remain +explicit obligations. Without a successful E/E^-1 program, 3m H2 is not +a complete admissible caller bill. + +For m<=7, the additional moment is at most 42 on the comparison interval +(H2=2^(1-C)<2), leaving only an optimistic >=2.67695955358 allowance at +the right endpoint before the still-unpriced obligations. Eight shears cost +24 H2, which exceeds the right-endpoint allowance. This is a severe +necessary screen, not a prediction that seven shears can close the code. + +## Smallest discriminating test and stop rule + +No search is authorized by this document. The next reviewed test should +use one explicit (a,b,i,j), exact v,w and phase-correct literal H word to +check the claimed new monomial endpoint component. Then derive, before +enumerating words, whether at most seven such shears could cancel every +nonmonomial projective class while retaining invertibility and an actual +FREE E^-1 program. Stop this subclass if its required count exceeds the +budget, or if a source field is missing at the stated cut. Do not expand +to a larger search merely because one component passes. + +A stronger continuation may replace one of the paid observations with an +already-paid query/native intermediate. That contract must name the exact +field, last source read, chart, owner, phase, delivered operator, and final +restoration/erasure. It must prove that retaining the observation does not +remove an independent helper target or reintroduce its cost later. The +released standalone fresh-query lower bound does not settle such a changed +information boundary, but it does not provide the observation either. + +## Rejected inexpensive-looking alternatives + +* Scalar owner t0=B tensor I is excluded even for dense B, by PROOF.md. +* Additional Clifford owner/address recodings with four FREE controls are + excluded by the correctly transported proof; parity-even is insufficient. +* With t0=I, literal terminal inversion Q C1^-1 C3^-1 Q requires two fresh + 112-field H1 banks. Their added 224 H1 already loses the optimistic budget. +* Even one fresh 112-H1 bank loses the complete-moment allowance. It must + not be funded from the raw rank-mass surplus 112. +* Retaining eight scalar code-mode observations does not make their later + rank-eight D3 transformations free. Eight additional H8 cost more than + the optimistic 44.6769 allowance; reuse inside the existing native call + would require a separate literal caller contract. + +## Credit + +Retain Dillon's released equations and normalizers; Dugongue/mdumitrean's +center-free code and A; Cao Yifan's native word; Cinna Davis, zxv, Jacob +Alan Sussman, Ryanson Jonathan and all retained helper, Clifford, compiler +and precision contributors. The source-inventory and independent-proof +workers supplied deliberately separate checks. This local work has +substantial OpenAI Codex assistance; no independent human, formal-kernel +or scientific admission is claimed. diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/frozen/PAID-SHEAR-SCREEN.md b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/PAID-SHEAR-SCREEN.md new file mode 100644 index 0000000000..296523437f --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/PAID-SHEAR-SCREEN.md @@ -0,0 +1,120 @@ +# Stop certificate for scalar-owner X-Gaussian shears + +Local read/derive screen, requested after CONTRACT.md. No operator or +parameter search was run. This note is separate from the already reviewed +Clifford FREE proof and requires its own independent review. + +## Decision and scope + +The proposed affordable class cannot work: it requires at least 112 scalar +owner rank-one shears, whereas its optimistic complete query allowance +permits at most seven. This includes dense scalar owner vectors, not just +single E_(a,b) updates. A paid term creating one monomial endpoint component +does not eliminate the old nonmonomial identity component. + +The result covers + + t0 = S_m ... S_1, + S_k = I + u_k v_k^T tensor H_k, + +where u_k,v_k are scalar 112-owner vectors and H_k belongs to the group +generated by the Pauli-X Gaussians C_v used in CONTRACT.md. Coefficients +are applied once on owners. For the explicit inverse program one assumes +v_k^T u_k=0, but the necessary lower bound does not need that assumption. + +It does not cover operator-valued owner/address gather and scatter maps, +other intervening noncommuting control alphabets, retained native/query +observations, or a changed endpoint/controller. No universal fresh-query +lower bound is asserted. + +## 1. The address group has a restrictive monomial intersection + +Every C_v is a polynomial in the X-translation X_v, so every product H +commutes with every X-translation on the 17 address bits. If such an H is +monomial, write its action as a permutation p with nonzero multipliers c. +Commutation with all translations implies + + p(x+a)=p(x)+a, c(x+a)=c(x). + +Hence p(x)=x+b and c is constant: H is a scalar times X_b. This also +follows directly from the source Gaussian words. It is not an assertion +about all monomial Clifford operators. + +The C_v group is finite up to phase because these are Clifford operators +on a fixed 17-axis space. The all-width lift and projective phase convention +are the same as in PROOF.md. Let B0 be the 112 by 112 scalar coefficient of +the projective identity address word in t0 after equal classes are grouped. + +## 2. FREE terminal output forces B0=0 + +The endpoint is E=Q^-1 C3 t0 C1 Q^-1, since every H_k commutes with D3. +Fix an identity-word contribution at intermediate owner pair (r,s). +Before the fixed outer factors, its address word is + + K_(3,r) K_(1,s)^-1. + +A contribution from any H at any other pair (r',s') could coincide with +this class only if + + H = phase * K_(3,r')^-1 K_(3,r) K_(1,s)^-1 K_(1,s'). + +The right side is a signed binary linear permutation with no translation. +By section 1 the left side, if monomial at all, is a scalar X-translation. +Therefore its translation must vanish, so H is projectively the identity. +The disjoint-stage binary-map argument in PROOF.md then gives r'=r and +s'=s. Thus the identity-word contribution at (r,s) cannot cancel against +any nonidentity H or any different owner pair. + +For any nonzero B0[r,s], choose output i and input j with A[i,r] A[s,j] +nonzero, using the actual 52 nonzeros per source row/column. The associated +endpoint word + + Q^-1 K_(3,i)^-1 K_(3,r) K_(1,s)^-1 K_(1,j) Q^-1 + +is nonmonomial by the scalar theorem: it could be monomial only if r=i +and s=j, which would require zero source diagonal entries. Its coefficient +is nonzero and, by the preceding argument, cannot cancel against any +other contribution of t0. Uniform tensor-word separation therefore excludes +a fixed finite columnwise monomial implementation of E at sufficiently +large widths. Consequently a FREE E requires B0=0. + +## 3. At least 112 paid shears are necessary + +Let T_0=I and T_k=S_k T_(k-1). The exact telescoping identity is + + t0-I = sum_k u_k (v_k^T tensor H_k) T_(k-1). + +Take the coefficient of the projective identity address word. Because each +u_k is scalar in owner space, this gives + + B0-I = sum_k u_k w_k^T + +for some scalar row vectors w_k^T. In particular rank(B0-I)<=m. But section +2 requires B0=0, so + + 112 = rank(I) <= m. + +This statement holds at each sufficiently large width even if the scalar +coefficients vary with width; it excludes an all-width invertible solution +with fewer than 112 shears. It does not assert that 112 shears suffice. + +## Invoice consequence and reopening boundary + +The explicit middle/exit execution in CONTRACT.md costs 3m H2 in addition +to the released base profile. Since m>=112, even using H2>1 for C<1 gives +an added moment greater than 336, against the proven optimistic allowance +44.67695955358 at the comparison interval's right endpoint. The class is +decisively unaffordable before finite work, compiler or stock costs. + +Stop this class; do not enumerate seven-shear words or tune coefficients. +A continuation must change a mathematical premise, for example literal +operator-valued owner/address gather/scatter with a paid mixed sandwich, +or a named already-paid native/query observation. Such a changed program +needs its own source access, ownership, phase, inverse and full cost proof. +The present rank argument cannot be transferred to it merely by calling a +whole operator-valued query a scalar rank-one shear. + +Credit the released Dillon construction, Dugongue's source code and the +full native/Clifford/helper lineage recorded in PROOF.md. This additional +screen has substantial OpenAI Codex assistance; no human, proof-kernel, +compiler or scientific admission is claimed. diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/frozen/SOURCE-FLAG-CHECK.json b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/SOURCE-FLAG-CHECK.json new file mode 100644 index 0000000000..3809fe4d65 --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/SOURCE-FLAG-CHECK.json @@ -0,0 +1,53 @@ +{ + "axis_embedding": { + "central": 0, + "stage1": [ + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8 + ], + "stage3": [ + 9, + 10, + 11, + 12, + 13, + 14, + 15, + 16 + ] + }, + "rejection_controls": { + "reject_central_shift_erasure": true, + "reject_corrupted_orthogonal_map": true, + "reject_duplicated_port_direction": true, + "reject_nonzero_code_diagonal": true, + "reject_untransported_H0_substitution": true + }, + "scope": "Exact pinned source structure and one 17-axis binary symplectic transport witness; not an all-width theorem replay, phase checker, t0 search, native/compiler replay, or supplier admission.", + "source_checks": { + "112_distinct_q": true, + "A2_plus_12A_equals_13I": true, + "G_rows_match_literal_q": true, + "all_G_orthogonal": true, + "q_weight_3_or_7": true, + "row_and_column_nonzero_counts_52": true, + "zero_diagonal": true + }, + "status": "PASS_SOURCE_AND_TRANSPORTED_FLAG_ONLY", + "transported_flag_witness": { + "D3_h_D3inv_monomial": true, + "Qinv_h_Q_monomial": true, + "Qinv_k_Q_not_monomial": true, + "h_CZ_in_H0": true, + "k_central_X_image_is_q_plus_w": true, + "k_does_not_preserve_Lq": true, + "k_preserves_correct_transported_flags": true, + "quotient_flag_excludes_noncentral_U_vectors": true + } +} diff --git a/research/released-operator-clifford-ceiling/evidence/supplements/frozen/check_source_and_flag.py b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/check_source_and_flag.py new file mode 100644 index 0000000000..9b9f57090d --- /dev/null +++ b/research/released-operator-clifford-ceiling/evidence/supplements/frozen/check_source_and_flag.py @@ -0,0 +1,159 @@ +#!/usr/bin/env python3 +"""Read-only source/flag checks, not a universal operator theorem checker.""" +import hashlib +import json +from fractions import Fraction +from pathlib import Path + +ROOT = Path(__file__).resolve().parent + + +def require(condition, message): + if not condition: + raise RuntimeError(message) + + +def linear(rows, vector): + return sum(((row & vector).bit_count() & 1) << j + for j, row in enumerate(rows)) + + +def image(columns, vector): + answer = 0 + while vector: + low = vector & -vector + answer ^= columns[low.bit_length() - 1] + vector ^= low + return answer + + +def compose(left, right): + return [image(left, column) for column in right] + + +def span_basis(vectors): + pivots = {} + for vector in vectors: + while vector: + p = vector.bit_length() - 1 + if p in pivots: + vector ^= pivots[p] + else: + pivots[p] = vector + break + return pivots + + +def belongs(vector, pivots): + while vector: + p = vector.bit_length() - 1 + if p not in pivots: + return False + vector ^= pivots[p] + return True + + +def preserves(operator, space): + pivots = span_basis(space) + return all(belongs(image(operator, vector), pivots) for vector in space) + + +def main(): + manifest = json.loads((ROOT / 'SOURCES.json').read_text()) + for item in manifest['files']: + path = ROOT / 'frozen' / Path(item['path']).name + require(hashlib.sha256(path.read_bytes()).hexdigest() == item['sha256'], + 'Frozen source hash mismatch: ' + str(path)) + code = json.loads((ROOT / 'frozen/CODE.json').read_text()) + normalizers = json.loads((ROOT / 'frozen/NORMALIZERS.json').read_text()) + matrix = [[Fraction(x) for x in row] for row in code['A']] + ports = normalizers['ports'] + require(len(matrix) == 112 and all(len(row) == 112 for row in matrix), + 'Owner matrix shape changed') + require(len(ports) == 112, 'Port inventory changed') + qs = [linear(p['G_rows'], 1) for p in ports] + checks = { + 'zero_diagonal': all(matrix[i][i] == 0 for i in range(112)), + 'row_and_column_nonzero_counts_52': all( + sum(x != 0 for x in row) == 52 for row in matrix) and all( + sum(matrix[i][j] != 0 for i in range(112)) == 52 + for j in range(112)), + '112_distinct_q': len(set(qs)) == 112, + 'G_rows_match_literal_q': all(q == p['q'] for q, p in zip(qs, ports)), + 'q_weight_3_or_7': all(q.bit_count() in (3, 7) for q in qs), + 'all_G_orthogonal': all( + ((p['G_rows'][i] & p['G_rows'][j]).bit_count() & 1) == (i == j) + for p in ports for i in range(9) for j in range(9)), + 'A2_plus_12A_equals_13I': all( + sum(matrix[i][k] * matrix[k][j] for k in range(112)) + + 12 * matrix[i][j] == (13 if i == j else 0) + for i in range(112) for j in range(112)), + } + require(all(checks.values()), 'Source structural check failed') + + # Binary symplectic witness on the actual 17 axes; global phases are + # deliberately outside this finite flag check's scope. + n = 17 + q, w = 0, 9 + xmask = (1 << n) - 1 + ident = [1 << j for j in range(2*n)] + Q = ident.copy() + Q[n + q] ^= 1 << q + D = ident.copy() + for j in range(9, 17): + D[n + j] ^= 1 << j + H = ident.copy() # CZ(q,w) + H[q] ^= 1 << (n + w) + H[w] ^= 1 << (n + q) + K = compose(D, compose(H, D)) + L0 = [1 << (n+j) for j in range(n)] + Lq = [image(Q, v) for v in L0] + Lw = [image(D, v) for v in L0] + Lqw = [image(D, v) for v in Lq] + monomial = lambda op: all((image(op, v) & xmask) == 0 for v in L0) + flag = { + 'h_CZ_in_H0': all(preserves(H, space) for space in (L0, Lq, Lw)), + 'Qinv_h_Q_monomial': monomial(compose(Q, compose(H, Q))), + 'D3_h_D3inv_monomial': monomial(K), + 'k_preserves_correct_transported_flags': all( + preserves(K, space) for space in (L0, Lw, Lqw)), + 'k_central_X_image_is_q_plus_w': + (image(K, 1 << q) & xmask) == ((1 << q) | (1 << w)), + 'k_does_not_preserve_Lq': not preserves(K, Lq), + 'Qinv_k_Q_not_monomial': not monomial(compose(Q, compose(K, Q))), + 'quotient_flag_excludes_noncentral_U_vectors': all( + (image(K, v) & ((1 << 9)-2)) != 0 + for v in range(1, 1 << 9) if v != 1), + } + require(all(flag.values()), 'Transported-flag witness failed') + corrupted_qs = qs.copy() + corrupted_qs[1] = corrupted_qs[0] + bad_G = ports[0]['G_rows'].copy() + bad_G[0] ^= 1 + controls = { + 'reject_nonzero_code_diagonal': not all( + (Fraction(1) if i == 0 else matrix[i][i]) == 0 for i in range(112)), + 'reject_duplicated_port_direction': len(set(corrupted_qs)) != 112, + 'reject_corrupted_orthogonal_map': not all( + ((bad_G[i] & bad_G[j]).bit_count() & 1) == (i == j) + for i in range(9) for j in range(9)), + 'reject_untransported_H0_substitution': not preserves(K, Lq), + 'reject_central_shift_erasure': + (image(K, 1 << q) & xmask) != (1 << q), + } + require(all(controls.values()), 'A rejection control failed') + print(json.dumps({ + 'status': 'PASS_SOURCE_AND_TRANSPORTED_FLAG_ONLY', + 'scope': 'Exact pinned source structure and one 17-axis binary symplectic ' + 'transport witness; not an all-width theorem replay, phase ' + 'checker, t0 search, native/compiler replay, or supplier admission.', + 'source_checks': checks, + 'transported_flag_witness': flag, + 'rejection_controls': controls, + 'axis_embedding': {'central': 0, 'stage1': list(range(1, 9)), + 'stage3': list(range(9, 17))}, + }, indent=2, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/released-operator-clifford-ceiling/verify.py b/research/released-operator-clifford-ceiling/verify.py new file mode 100644 index 0000000000..905e7d1286 --- /dev/null +++ b/research/released-operator-clifford-ceiling/verify.py @@ -0,0 +1,90 @@ +#!/usr/bin/env python3 +"""Portable evidence and finite-support replay; the theorem remains written proof.""" +from hashlib import sha256 +import importlib.util +import json +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile + +ROOT = Path(__file__).resolve().parent + +def need(ok, message): + if not ok: + raise ValueError(message) + +def encoded(value): + return (json.dumps(value, indent=2, sort_keys=True) + '\n').encode() + +def authenticate(): + manifest = json.loads((ROOT / 'EVIDENCE.json').read_text()) + actual = {str(p.relative_to(ROOT)) for p in (ROOT / 'evidence').rglob('*') if p.is_file()} + need(actual == set(manifest['files']), 'evidence file inventory changed') + for name, digest in manifest['files'].items(): + path = ROOT / name + need(not path.is_symlink() and sha256(path.read_bytes()).hexdigest() == digest, + 'immutable evidence mismatch: ' + name) + # The author's original nested manifests remain byte-exact and independently bind their files. + for directory in ['inventory', 'budget', 'independent-review', 'supplements']: + base = ROOT / 'evidence' / directory + original = json.loads((base / 'FILES.json').read_text()) + files = original.get('files', original) + for name, digest in files.items(): + need(sha256((base / name).read_bytes()).hexdigest() == digest, + 'original author manifest mismatch: ' + directory + '/' + name) + need((ROOT / 'evidence/proof/PROOF.md').read_bytes() == + (ROOT / 'evidence/independent-review/frozen/REVIEWED-PROOF.md').read_bytes(), + 'reviewed proof differs from the author freeze') + return manifest + +def run(): + manifest = authenticate() + proof = ROOT / 'evidence/proof' + # Execute unchanged source checker in this interpreter's optimization mode. + cmd = [sys.executable, '-I'] + if sys.flags.optimize: + cmd.append('-O') + cmd += ['-W', 'error', '-B', str(proof / 'check_source_and_flag.py')] + source = subprocess.run(cmd, check=True, capture_output=True, timeout=90).stdout + need(source == (proof / 'SOURCE-FLAG-CHECK.json').read_bytes(), + 'source/flag receipt did not regenerate byte-exactly') + check = ROOT / 'evidence/budget/check_budget.py' + spec = importlib.util.spec_from_file_location('frozen_conditional_budget', check) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + # Only private loader paths move. __file__ remains the original unchanged checker, + # retaining its exact self digest; all scientific functions and JSON fields are unchanged. + with tempfile.TemporaryDirectory(prefix='released-ceiling-') as temporary: + temp = Path(temporary) + stock = temp / 'coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023' + shutil.copytree(ROOT / 'evidence/inventory', stock) + module.HERE = temp / 'outputs/released-operator-optimistic-budget-20261023' + module.STOCK = stock + value = module.run() + budget = encoded(value) + # Price support for the separate written paid-shear screen, not its theorem. + need(21 * 2 < module.margin(module.B)[0], 'seven explicit shears fit raw allowance') + need(24 * module.power(2, module.B)[0] > 45, 'eight explicit shears fail at B') + need(3 * 112 > module.margin(module.A)[1], '112-shear bill exceeds entire raw allowance') + for name in ['RESULT.json', 'RESULT-OPTIMIZED.json']: + need(budget == (ROOT / 'evidence/budget' / name).read_bytes(), + 'full conditional budget receipt differs: ' + name) + print(json.dumps({ + 'status': 'PASS_SCOPED_SUPPORT_AND_CONDITIONAL_ARITHMETIC', + 'immutable_evidence_files': len(manifest['files']), + 'reviewed_proof_sha256': sha256((proof / 'PROOF.md').read_bytes()).hexdigest(), + 'source_flag_receipt_sha256': sha256(source).hexdigest(), + 'budget_receipt_sha256': sha256(budget).hexdigest(), + 'source_flag_controls': 5, + 'separate_paid_screen_proof_sha256': sha256((ROOT / 'evidence/supplements/frozen/PAID-SHEAR-SCREEN.md').read_bytes()).hexdigest(), + 'separate_paid_screen_review_sha256': sha256((ROOT / 'evidence/supplements/PAID-SHEAR-ADDENDUM.md').read_bytes()).hexdigest(), + 'explicit_rank_two_shear_execution_max_raw_count': 7, + 'conditional_invoice_controls': 5, + 'max_uniform_integer_extra_H1': value['max_uniform_integer_extra_H1'], + 'scope': 'Written independently reviewed sufficiently-large-width fixed columnwise Clifford obstruction; finite source/flag support and conditional invoice arithmetic only. No absolute-phase/native/compiler/caller replay, physical FREE classification or kappa.' + }, indent=2, sort_keys=True)) + +if __name__ == '__main__': + run()