diff --git a/research/mixed-target-capacity-ceiling/.gitattributes b/research/mixed-target-capacity-ceiling/.gitattributes new file mode 100644 index 0000000000..5479ee48ba --- /dev/null +++ b/research/mixed-target-capacity-ceiling/.gitattributes @@ -0,0 +1,2 @@ +# Preserve original source/proof/receipt CRLF and LF bytes. +evidence/** -text whitespace=cr-at-eol diff --git a/research/mixed-target-capacity-ceiling/EVIDENCE.json b/research/mixed-target-capacity-ceiling/EVIDENCE.json new file mode 100644 index 0000000000..ac6b83a620 --- /dev/null +++ b/research/mixed-target-capacity-ceiling/EVIDENCE.json @@ -0,0 +1,31 @@ +{ + "files": { + "evidence/author/REPORT.md": "11c0e2a054ac107ad605262f0c2ed3d3ab9ff3dbfc4fc7f0eadd17d1832462cc", + "evidence/author/REVIEW-FEEDBACK.md": "67e3699d38710063f90ab24274ca7f3b657a5028fc41633e6797615102aefdc4", + "evidence/author/SOURCE-CHECK-OPTIMIZED.json": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "evidence/author/SOURCE-CHECK.json": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "evidence/author/SOURCES.json": "5d7d5d3868a4dd85891f23c6ba0019cc648e5d2208a4d08fb2ab8650b67a48f2", + "evidence/author/check_source.py": "2e3149ebcbbdd2fc45f5fc057986e88c45a3e581f1e7a5c2ef42b8fe55fd981d", + "evidence/author/history/REPORT-before-target-chart-scope.md": "d0f6c6ad55073bd084d5a577b3b8cd93515c297c47f26cc52baaeb9fe7dc4a59", + "evidence/independent-review/FILES.json": "102b6ba991afe8669f9f6f626fed302c01969303df92b8edb74d852535ae40c9", + "evidence/independent-review/FREEZE.json": "83903097a8177725e83ff8aff85482e342837e9a8df6a5bbace904dc03281395", + "evidence/independent-review/RESULT-OPTIMIZED.json": "c84597bc2caaf3d7ddd99e553ad515d84b970f6d1cc92d1e4260e7ecc0fc43be", + "evidence/independent-review/RESULT.json": "c84597bc2caaf3d7ddd99e553ad515d84b970f6d1cc92d1e4260e7ecc0fc43be", + "evidence/independent-review/REVIEW.md": "aa573b3cc5d6d05781caf4a466d9a4ce9eefefa937477a5eef04c27490edc492", + "evidence/independent-review/SOURCES.json": "4d3e8b4b988d83ad2822d969dd9583591d4cd23a6bf9cc5b5643185b88f9999e", + "evidence/independent-review/check_evidence.py": "3ab42c3f8123ed576ff54410e6ed82914a969ee3eb62c98cc3b1c1e42ab118cc", + "evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "evidence/independent-review/frozen/AUTHOR-SOURCES-AT-FREEZE.json": "5d7d5d3868a4dd85891f23c6ba0019cc648e5d2208a4d08fb2ab8650b67a48f2", + "evidence/independent-review/frozen/AUTHOR-SOURCES.json": "aec91a637b50a6f00c38917d87094f6ec129515ca5536ec66374403b59558fa6", + "evidence/independent-review/frozen/AUTHOR-check_source.py": "2e3149ebcbbdd2fc45f5fc057986e88c45a3e581f1e7a5c2ef42b8fe55fd981d", + "evidence/independent-review/frozen/CLIFFORD-PREDECESSOR.md": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "evidence/independent-review/frozen/CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "evidence/independent-review/frozen/INVENTORY-REPORT.md": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "evidence/independent-review/frozen/NONLINEAR-PREDECESSOR.md": "76bea47531ed557c0c9cb210c4324d6000c74415bf13e5747b7036567853f6ef", + "evidence/independent-review/frozen/NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "evidence/independent-review/frozen/PHYSICAL.md": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "evidence/independent-review/frozen/REVIEWED-REPORT.md": "11c0e2a054ac107ad605262f0c2ed3d3ab9ff3dbfc4fc7f0eadd17d1832462cc", + "evidence/independent-review/frozen/SCIENTIFIC-SOURCES.json": "e810407fc34de1f3af196fc86e91e680075ff982bbc6fe19d6ebb02f2a0c0d9c" + }, + "schema_version": 1 +} diff --git a/research/mixed-target-capacity-ceiling/HISTORY.md b/research/mixed-target-capacity-ceiling/HISTORY.md new file mode 100644 index 0000000000..8f538cf1b6 --- /dev/null +++ b/research/mixed-target-capacity-ceiling/HISTORY.md @@ -0,0 +1,20 @@ +# Preserved review and target-chart correction + +The author report was revised after independent review required target entry +and exit charts to satisfy the same fixed finite complete-product support +condition as controls/encoders/readouts, or use the retained native charts. +The exact previous report remains in evidence/author/history. The final report +and conceptual feedback are unchanged; the independent review is the distinct +final mathematical PASS. + +Author SOURCES metadata advanced during review. Both the original metadata +capture and at-freeze metadata capture are preserved in the independent packet. +The live author SOURCES copy matches the at-freeze bytes. No scientific source, +report or receipt was silently repaired to follow those metadata updates. + +The executable controls authenticate scalar source tables and exact census +arithmetic only. The 113th-target mutation tests rank-mass inconsistency; it +is not an executable capacity proof. The written argument projects fixed +complete-product identities before evaluation, including fixed target charts. +No finite check or archival packaging is relabelled as native/compiler or +complete theorem admission. 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Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. + +Partial-gauge extension, 9 October 2026 +Copyright 2026 icekylinx + +The pair-first cube assembly, compatible backward frame enlargement, +partial source-gauge schedule and stopped whole-projector composition are +contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834. + +The physical deferred bit word, reflected event accounting, fan-order +clarification and signed two-stage endpoint are adopted from Zhihao Chen +(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with +Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen +witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38, +with the original Claude disclosure retained. Cyclic interval and core-aware +pair primitives build on Avi Eisenberg (ikeboy), PR #62, +ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance. +Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and +precision credits remain in force. Imported source notices and licenses +are preserved under references/partial-gauge/; see SOURCES.json. + +Three-stage cover extension, 9 October 2026 +Copyright 2026 icekylinx + +The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry, +weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring +fallback, uniform batching, internal row borrowing and exact composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This +repository integration uses Codex assistance and extends +PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86. + +The selected local complex DAG and support/label replay are adopted from +Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf, +with its original Apache-2.0 terms and Claude assistance disclosure. +The unchanged bit physical word retains Zhihao Chen (jacklightChen), +PR #97, and Swapnil Jain's underlying witness and assistance notices. +The prior opposite-bank, stopped ordinary-leaf, copied-center, topology, +semantic/bulk, precision and analytic credits remain applicable. +Original source notices and license bytes are preserved in +references/three-stage-cover/pr117/ and references/partial-gauge/. + +Paired-cube and shared-core extension, 9 October 2026 +Copyright 2026 icekylinx + +The paired-coordinate triple-cube identity, signed overlap channels, +original-source involution, coordinate-star centers, concrete frame/carrier +compiler, chronological source gauges, PR97 gauge-subset selection, +orthogonal cross-stage routing and exact supplier/assembly integration +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. +Repository integration uses Codex assistance and extends PR #130 at +6a9970a530119174507904e23592fd59ede19a5d. + +The substantial completed-core workspace-sharing principle is credited to +an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported +OpenAI Codex assistance. No source code, partition or serialized witness +from that PR is imported. The new routing and paired-motif integration +are described separately and claim no exclusive priority for broad sharing, +paired-coordinate, Fourier or carrier-matching ideas. + +Selected coarse queries restrict the retained eumemic PR #117 positive DAG; +its original Apache-2.0 and Claude assistance notices remain unchanged. +The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil +Jain's frozen witness, notices and historical assistance disclosures. +Earlier generalized Clifford, three-stage, uniform weighted recursion, +ordinary-leaf, semantic/bulk, precision and analytic credits remain in force. +Source-specific license bytes are preserved under references/. + +October 9 recycled-bit integration: +DaysSky (#150), William Porter/hpst3r (#147), Thomas Marchand/Th0rgal (#146), +Rohan Gupta/gupt1156 (#148), James Chang/jamesyc (#124), SovereignSteak (#122). +The original notices and assistance disclosures are retained under research/, +including research/recycled-bit-integration/NOTICE. Andrew Barnes/Bortlesboat +(#101) repairs shared verifiers using rfu08's #64 counterexample. rfu08's +scoped finite and formal-transfer packages are included separately; they do +not establish the full multiplication theorem. Earlier and parallel credits +remain applicable. Douglas Colkitt integrated these with OpenAI Codex assistance. + +SovereignSteak PR151 independently supplies the matching gauge/recycling +composition and the selected 473/10^6 atom refinement; its original package +and assistance disclosure are retained under research/gauge-recycling/. + +October 9 coordinated-frame and completed-entrance-bank integration: +Dugongue PR186, 166a34d75e853e933855f0f7e940fe77c4bb6b8d, builds on +Chafik Boukhalfa/chafreaky's PR181, 7fb2194801e3a10f54772c7f0d5505035a4fc0ad, +and eumemic's PR168 v4, 4a3c769e5c5430e7114c4d3e099ff34664677f17. +The frozen package and prerequisite archive preserve all author, source-license +and assistance notices, including PR175's compiler optimization. DaysSky's +carrier closure, James Chang's terminal substitution and balanced assembly, +geckods' stopping refinements and all preceding framework credits remain. +Rohan Arun's PR185 bootstrap and chafreaky's PR182 bit refinement are reviewed +parallel contributions; their gains are not added to the selected witness. +Douglas Colkitt integrated the package and supplied the bank scheduling +supplement with OpenAI Codex assistance, under Apache-2.0. The all-size +interfaces remain conditional; finite verification is not full formalization. diff --git a/research/mixed-target-capacity-ceiling/README.md b/research/mixed-target-capacity-ceiling/README.md new file mode 100644 index 0000000000..bbfdfa0c6a --- /dev/null +++ b/research/mixed-target-capacity-ceiling/README.md @@ -0,0 +1,133 @@ +# Mixed-target capacity ceiling for the released source + +Allowing a FREE encoder to mix both original main banks does not rescue this +unchanged two-FULL/one-query source. The independently reviewed written report +proves **at most 112 independent rank-17 main jobs** at sufficiently large widths. +Even granting rank-16 to every remaining main input and all 816 prescribed H9 +helper returns, its optimistic complete recursive invoice loses for every +`0 q_s dot q_j = 0 over F2. + +`SOURCE-CHECK.json` checks all 5,824 nonzero entries of the 112-by-112 source A +against the actual q masks, finding zero exceptions. It also rechecks the +source eight-mode identity `M^T M=56 I`. This is an exact read of existing +scalar data, not native/operator execution or a candidate search. + +The rank-eight code decomposition `A=I-MM^T/4` admits a fixed rational scalar +eigenbasis. It does not imply eight defective Gaussian owners after transport +through Q and the actual entrance/exit charts. The following bound counts +those Gaussian defects directly and permits much more than that eigenbasis. + +## Allowed changed contract + +Retain the exact two-FULL middle word, all native paths, the 112 H1 query bank, +all 816 independent helper inputs, and their billed rank-nine complements. +Require only the first three forward memberships + + t0, Q^-1 t0 Q, t=D3 t0 D3^-1 are FREE. + +Here FREE is a fixed finite scalar owner program over columnwise lifts of +monomial Clifford matrices on the actual 17 bits. Coefficients may depend on +the column width. This is an algebraic relaxation: no inverse, tariff or +bounded-height algorithm is inferred merely from membership. The argument +does not need t0 invertible and permits rectangular readouts, owned clean +scratch, saved-original FREE bypass and arbitrary FREE mixing of the 224 main +inputs. FREE programs supply no separately available extra high-rank Gaussian +observation. The helpers retain their prescribed autonomous path and one return +each, without additional productive copies. + +The actual main endpoint before input and output controls is + + M = [[0,t G],[-E G,0]], + E=Q^-1 C3 t C1 Q^-1, G=D1 D3 Q. + +Main target jobs must be independent original-owner Gaussian jobs on this +same address stock, with monomial-Clifford entry/exit charts in the Clifford +proof and arbitrary monomial entry/exit charts in the final extension, and +ranks at most 17. **The target entry and exit charts must themselves use fixed +finite columnwise complete-product supports independent of f, or the retained +canonical native charts.** This condition covers the target side of tensor +separation just as it covers the controls, encoder, readout and bypass. Growing +or noncolumnwise target-chart families are outside the theorem. In particular +a rank-17 job is a genuine full Gaussian up to those charts; +an abstract coded mixture is not target credit. Every original input remains +present exactly once. Lower-rank target choices do not supply clean initial +fields or erase arbitrary data. + +## Every negative endpoint term has Fourier rank at most 16 + +For a one-column Clifford let its Fourier rank be the rank of its symplectic +upper-right block, equivalently `17-dim(T L0 intersect L0)`. Monomial left or +right multiplication preserves this number. A genuine H17 has rank 17. + +The reviewed first-three-control argument and finite tensor separation place +each surviving letter k of t in the transported class Ht. Its monomial binary +linear block R preserves W and `span(q)+W`. Consequently `R^-T` preserves U, +the orthogonal complement of `span(q)+W`. + +A nonzero expanded negative endpoint term has the precise order + + T = Q^-1 N3 k N1 D1 D3, + N3=K3_i^-1 K3_r, N1=K1_s^-1 K1_j, + +with source coefficient containing `A[i,r] A[s,j]`. This follows from +`Q^-1 G=D1 D3`; no Q-order-two replacement is used. + +The pure Z vector `(0,q)` belongs to `D1 D3 L0`, since those factors omit q. +The signed orthogonal N1 carries it to `(0,a)`, where + + a=G1_s^-1 q_j, + q dot a = q_s dot q_j = 0. + +Thus a is a nonzero vector entirely in U. The monomial k carries this vector +to `(0,R^-T a)`, still a nonzero pure Z vector in U. N3 acts only on q+W and +therefore fixes it. Q^-1 likewise fixes every pure Z vector in U. Hence +`T L0 intersect L0` contains a nonzero vector, and the Fourier rank of T is at +most 16. This holds for every nonzero complete term, before cancellation. + +This proof uses only the right source edge; it does not assert that transported +k fixes q. For scalar-owner t0, the stronger two-edge calculation gives rank +15: up to outer monomials the Fourier block is `I+v v^T+q q^T`, with v and q +distinct orthogonal odd vectors. The general rank-16 bound is the one used. + +## Arbitrary FREE input encoding cannot create more than 112 H17 jobs + +This is an image-dimension argument over the full FREE algebra, not scalar +coefficient rank. At sufficiently large column width f, take B to be the +complex span of the lifted projective monomial Clifford group H on 17 bits. +H is finite. Tensor separation makes its projective representatives linearly +independent; its multiplication retains the scalar cocycle raised to f. +Thus B is a finite-dimensional twisted group algebra. Write `d=dim_C B`. + +Similarly, the finite projective Clifford group gives an ambient operator +space with distinct projective classes independent at sufficiently large f. +Let pi17 retain exactly the classes of Fourier rank 17. Since left and right +monomial multiplication preserves Fourier rank, pi17 is a B-bimodule map. +Width-dependent outer coefficients do not affect this support statement. + +Let U be any FREE input encoder and L any FREE output readout. On the main +input columns the proposed output is `L M U+B0`, where B0 is any saved-input +FREE bypass. The preceding lemma kills the entire negative bank under pi17; +B0 has grade zero and also vanishes. The positive bank contribution factors +as + + B^224 --U_positive--> B^112 --diag(G)--> ambient^112 + --t and positive readout--> ambient^output. + +Its image therefore has complex dimension at most 112d, irrespective of the +number of clean buffers, copies or readout rows. No claim that the raw physical +data dimension itself is d is being made; the inputs here are the FREE algebra +module, after the justified coefficient separation. + +Suppose m original inputs receive independent H17 outputs. Select their m rows +and their matching original input columns. The desired projected map on B^m +is diagonal in their actual rank-17 Gaussian operators G_j. Each G_j is an +invertible address operator, so left multiplication by G_j is injective on B. +The image dimension of that target map is exactly md. It must factor through +the same B^112 above. Therefore + + m d <= 112 d, hence m <= 112. + +Lower-rank Gaussian outputs do not appear in this projection. The argument +allows arbitrary mixing of both main banks at entry, so it is not a transfer +of the earlier unchanged-original-feed proof. Rectangular readout and saved +arbitrary inputs do not alter the capacity bound. + +## Full optimistic invoice and exact price decision + +All 1,040 original owners remain: 224 main and 816 helpers. With at most 112 +H17 main targets, the best possible rank census for `0 No blocking mathematical issue found in the extension under the retained +> source premises. The key steps are valid: the nonzero source edge makes the +> D1D3 hyperplane a union of half the U-indexed join blocks; arbitrary weighted +> monomial k transports those blocks bijectively; N3/Q^-1 cannot fill missing +> blocks. Projection onto H G H must occur in the finite complete-product +> coefficient identity before evaluation, exactly as now written, and the +> evaluated identity gives m N_f <=112 N_f without requiring infinite-algebra +> faithfulness. The all-C rank-mass inequality follows. This is written +> mathematical feedback with source receipt read, not a source/native rerun +> or a replacement for the separate independent review. + +The separate reviewer `/root/sol_new_approach_ceilings` requested that target +entry/exit charts explicitly share the fixed finite columnwise complete-product +support condition. The report was repaired and its previous version preserved; +that separate review's final freeze outcome will be recorded by its own author. +This feedback record does not relabel conceptual review as native execution, +formal-kernel validation or full compiler admission. diff --git a/research/mixed-target-capacity-ceiling/evidence/author/SOURCE-CHECK-OPTIMIZED.json b/research/mixed-target-capacity-ceiling/evidence/author/SOURCE-CHECK-OPTIMIZED.json new file mode 100644 index 0000000000..4884effc7b --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/author/SOURCE-CHECK-OPTIMIZED.json @@ -0,0 +1,101 @@ +{ + "status": "PASS_SOURCE_ONLY_DOT_AND_MODE_FACTS", + "scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "ports": 112, + "nonzero_A_edges": 5824, + "nonorthogonal_nonzero_A_edges": 0, + "distinct_q": 112, + "mode_gram": [ + [ + 56, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 56, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 56, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 56, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 56, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 56, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 56, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 56 + ] + ], + "source_files": [ + { + "path": "outputs/released-operator-intersection-20261023/frozen/CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + } + ], + "scope": "Reads existing finite scalar A, source q masks and eight mode columns only. No operator evaluation, solver, native/emitter/compiler/Lean execution, candidate enumeration or moment numerics." +} diff --git a/research/mixed-target-capacity-ceiling/evidence/author/SOURCE-CHECK.json b/research/mixed-target-capacity-ceiling/evidence/author/SOURCE-CHECK.json new file mode 100644 index 0000000000..4884effc7b --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/author/SOURCE-CHECK.json @@ -0,0 +1,101 @@ +{ + "status": "PASS_SOURCE_ONLY_DOT_AND_MODE_FACTS", + "scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "ports": 112, + "nonzero_A_edges": 5824, + "nonorthogonal_nonzero_A_edges": 0, + "distinct_q": 112, + "mode_gram": [ + [ + 56, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 56, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 56, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 56, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 56, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 56, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 56, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 56 + ] + ], + "source_files": [ + { + "path": "outputs/released-operator-intersection-20261023/frozen/CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + } + ], + "scope": "Reads existing finite scalar A, source q masks and eight mode columns only. No operator evaluation, solver, native/emitter/compiler/Lean execution, candidate enumeration or moment numerics." +} diff --git a/research/mixed-target-capacity-ceiling/evidence/author/SOURCES.json b/research/mixed-target-capacity-ceiling/evidence/author/SOURCES.json new file mode 100644 index 0000000000..39eeae70d0 --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/author/SOURCES.json @@ -0,0 +1,150 @@ +{ + "status": "LOCAL_SOURCE_BOUND_STOP_INDEPENDENT_MATHEMATICAL_PASS", + "scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "context_pin": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "root_reported_canonical": "ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c", + "guidance_provenance": "Root reported nine governing blobs unchanged from a5df48c55ea806d7952b65acc9c76d878ff09b13; retained files read directly. Missing ec278 Git object triggered failed DNS promisor fetch, interrupted. No successful fresh local canonical fetch claimed.", + "overlap": "Sole monitor, all-author bodies through 12:10:28 UTC / cursor5191 and fresh rendered4930. No exact claim found; bounded coverage only. Dillon paid-history/augmented helper/changed paid path excluded.", + "source_files": [ + { + "path": "outputs/released-operator-intersection-20261023/frozen/CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "bytes": 65977 + }, + { + "path": "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "bytes": 281582 + }, + { + "path": "outputs/released-operator-intersection-20261023/frozen/PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "bytes": 10632 + }, + { + "path": "outputs/released-operator-intersection-20261023/PROOF.md", + "sha256": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "bytes": 12155 + }, + { + "path": "outputs/released-operator-independent-review-20261023/REVIEW.md", + "sha256": "23b5aa5df049cb4a8fe3349c054e27d84ca151e29e263c658670639bad082428", + "bytes": 10418 + }, + { + "path": "outputs/nonlinear-monomial-control-ceiling-20261023/PROOF.md", + "sha256": "76bea47531ed557c0c9cb210c4324d6000c74415bf13e5747b7036567853f6ef", + "bytes": 7820 + }, + { + "path": "outputs/nonlinear-monomial-control-review-20261023/REVIEW.md", + "sha256": "0b0fe1c33eea85ccd92a3423a705fd086c6f2669f1a47f37fba9c1ca4ae91973", + "bytes": 9223 + }, + { + "path": "outputs/partial-target-consumer-gate-20261023/REPORT.md", + "sha256": "81edffd10654a8e0d190e5119ed2aa8e5ffe93c01b6827b97c5e454b62214cfe", + "bytes": 8538 + }, + { + "path": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/REPORT.md", + "sha256": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "bytes": 12159 + }, + { + "path": "outputs/mathematics-paper-research-20261023/notes/released-finite-algebra-inverse-lemma.md", + "sha256": "6f227a4846839f1e52b974562906543519458e0bae068f785da7bec1d46dbce8", + "bytes": 8443 + }, + { + "path": "outputs/released-operator-optimistic-budget-20261023/REPORT.md", + "sha256": "b8b785a815852069b27ee6b18337b6ecd64127c7a22985d0e4221a2fc11bd53a", + "bytes": 8680 + }, + { + "path": "released-operator-clifford-ceiling-20261023/AGENTS.md", + "sha256": "eb25d8ec495b80190a4b1a634710819bb74f0fae88d5203285c2b75b6f147347", + "bytes": 5580 + }, + { + "path": "released-operator-clifford-ceiling-20261023/CONTRIBUTING.md", + "sha256": "8a49fe97e2ad088a2b2e0c5b222aaab08752783b1f9c1260790d7dd13011d215", + "bytes": 7143 + }, + { + "path": "released-operator-clifford-ceiling-20261023/autoresearch.md", + "sha256": "d16f0d3bb4d4b213d06c128db6d6460b0fe9ec1ac5a6c1ea1febf1db40e7b60d", + "bytes": 5986 + }, + { + "path": "released-operator-clifford-ceiling-20261023/docs/research/agent-procedure.md", + "sha256": "74fbdc7579d240a6b03920e71a55857f20b08dfc614d472f29bc14802c564f07", + "bytes": 28999 + }, + { + "path": "released-operator-clifford-ceiling-20261023/docs/research/current-priorities.md", + "sha256": "db049fa3f75bd5345b23b736e51b7e912b39d372040b462c3e82610c482ff0c9", + "bytes": 11695 + }, + { + "path": "released-operator-clifford-ceiling-20261023/docs/research/research-family-status.md", + "sha256": "21ea61004c0270388258c4251b1c586b65f06bc807395b281deacfb886204934", + "bytes": 18401 + }, + { + "path": "released-operator-clifford-ceiling-20261023/certificates/selected-result.json", + "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375", + "bytes": 4922 + } + ], + "local_artifacts": [ + { + "path": "outputs/mixed-target-input-encoder-20261023/REPORT.md", + "sha256": "11c0e2a054ac107ad605262f0c2ed3d3ab9ff3dbfc4fc7f0eadd17d1832462cc", + "bytes": 19422 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/check_source.py", + "sha256": "2e3149ebcbbdd2fc45f5fc057986e88c45a3e581f1e7a5c2ef42b8fe55fd981d", + "bytes": 2677 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/SOURCE-CHECK.json", + "sha256": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "bytes": 1512 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/SOURCE-CHECK-OPTIMIZED.json", + "sha256": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "bytes": 1512 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/REVIEW-FEEDBACK.md", + "sha256": "67e3699d38710063f90ab24274ca7f3b657a5028fc41633e6797615102aefdc4", + "bytes": 1634 + } + ], + "checks": [ + "source-only script normal PASS", + "source-only script optimized PASS", + "normal/optimized JSON bytes identical" + ], + "no_native_solver_compiler_lean_or_public_write": true, + "history": [ + { + "path": "outputs/mixed-target-input-encoder-20261023/history/REPORT-before-target-chart-scope.md", + "sha256": "d0f6c6ad55073bd084d5a577b3b8cd93515c297c47f26cc52baaeb9fe7dc4a59" + } + ], + "conceptual_feedback": "Existing mathematics paper worker read final report11c0e2a... and partition predecessor/review: no blocking mathematical issue; separate independent freeze review still pending.", + "independent_review": { + "agent": "/root/sol_new_approach_ceilings", + "report_sha256": "11c0e2a054ac107ad605262f0c2ed3d3ab9ff3dbfc4fc7f0eadd17d1832462cc", + "mathematical_status": "PASS returned in direct reviewer message after target-chart scope repair", + "result_path": "outputs/mixed-target-capacity-independent-review-20261023/RESULT.json", + "result_sha256": "c84597bc2caaf3d7ddd99e553ad515d84b970f6d1cc92d1e4260e7ecc0fc43be", + "result_scope": "Independent source scalar/check invoice only, plus separate written mathematical review; no native/operator/compiler/Lean replay", + "written_review_path": "outputs/mixed-target-capacity-independent-review-20261023/REVIEW.md", + "written_review_freeze": "Reviewer preparing final artifact; consult that directory for final receipt." + } +} diff --git a/research/mixed-target-capacity-ceiling/evidence/author/check_source.py b/research/mixed-target-capacity-ceiling/evidence/author/check_source.py new file mode 100644 index 0000000000..28f60ef2ce --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/author/check_source.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Only authenticate and inspect retained scalar source tables; no operators.""" +import hashlib +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +EXPECTED = { + "outputs/released-operator-intersection-20261023/frozen/CODE.json": + "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json": + "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", +} + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def main(): + files = [] + data = [] + for name, expected in EXPECTED.items(): + payload = (ROOT / name).read_bytes() + digest = hashlib.sha256(payload).hexdigest() + if expected is not None: + require(digest == expected, "Pinned source hash changed: " + name) + files.append({"path": name, "sha256": digest}) + data.append(json.loads(payload)) + a = data[0]["A"] + ports = data[1]["ports"] + modes = data[1]["mode_columns"] + require(len(a) == len(ports) == 112, "Owner count changed") + require(all(len(row) == 112 for row in a), "Code shape changed") + require(len(modes) == 8 and all(len(c) == 112 for c in modes), + "Mode shape changed") + require([p["port"] for p in ports] == list(range(112)), "Port order changed") + edges = [(i, j) for i in range(112) for j in range(112) if a[i][j] != "0"] + bad = [(i, j) for i, j in edges + if (ports[i]["q"] & ports[j]["q"]).bit_count() % 2] + require(len(edges) == 5824 and not bad, "Supported-edge orthogonality failed") + require(len({p["q"] for p in ports}) == 112, "Distinct direction property failed") + gram = [[sum(modes[i][k] * modes[j][k] for k in range(112)) + for j in range(8)] for i in range(8)] + require(gram == [[56 * int(i == j) for j in range(8)] for i in range(8)], + "Mode Gram identity failed") + result = { + "status": "PASS_SOURCE_ONLY_DOT_AND_MODE_FACTS", + "scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "ports": len(ports), "nonzero_A_edges": len(edges), + "nonorthogonal_nonzero_A_edges": len(bad), + "distinct_q": len({p["q"] for p in ports}), "mode_gram": gram, + "source_files": files, + "scope": "Reads existing finite scalar A, source q masks and eight mode columns only. " + "No operator evaluation, solver, native/emitter/compiler/Lean execution, " + "candidate enumeration or moment numerics.", + } + print(json.dumps(result, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/mixed-target-capacity-ceiling/evidence/author/history/REPORT-before-target-chart-scope.md b/research/mixed-target-capacity-ceiling/evidence/author/history/REPORT-before-target-chart-scope.md new file mode 100644 index 0000000000..e9a68ebe0d --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/author/history/REPORT-before-target-chart-scope.md @@ -0,0 +1,337 @@ +# Changed input and mixed main ranks: a source-bound capacity STOP + +Local derivation, 2026-10-23. **STOP for the released provider with fixed finite +columnwise monomial FREE encoders and readouts.** At most 112 of the +224 independently supplied main inputs can receive rank-17 Gaussian outputs. +Even granting rank 16 to every remaining main input and the unchanged 816 H9 +helper returns, the complete optimistic recursive invoice loses for every +`0 q_s dot q_j = 0 over F2. + +`SOURCE-CHECK.json` checks all 5,824 nonzero entries of the 112-by-112 source A +against the actual q masks, finding zero exceptions. It also rechecks the +source eight-mode identity `M^T M=56 I`. This is an exact read of existing +scalar data, not native/operator execution or a candidate search. + +The rank-eight code decomposition `A=I-MM^T/4` admits a fixed rational scalar +eigenbasis. It does not imply eight defective Gaussian owners after transport +through Q and the actual entrance/exit charts. The following bound counts +those Gaussian defects directly and permits much more than that eigenbasis. + +## Allowed changed contract + +Retain the exact two-FULL middle word, all native paths, the 112 H1 query bank, +all 816 independent helper inputs, and their billed rank-nine complements. +Require only the first three forward memberships + + t0, Q^-1 t0 Q, t=D3 t0 D3^-1 are FREE. + +Here FREE is a fixed finite scalar owner program over columnwise lifts of +monomial Clifford matrices on the actual 17 bits. Coefficients may depend on +the column width. This is an algebraic relaxation: no inverse, tariff or +bounded-height algorithm is inferred merely from membership. The argument +does not need t0 invertible and permits rectangular readouts, owned clean +scratch, saved-original FREE bypass and arbitrary FREE mixing of the 224 main +inputs. FREE programs supply no separately available extra high-rank Gaussian +observation. The helpers retain their prescribed autonomous path and one return +each, without additional productive copies. + +The actual main endpoint before input and output controls is + + M = [[0,t G],[-E G,0]], + E=Q^-1 C3 t C1 Q^-1, G=D1 D3 Q. + +Main target jobs must be independent original-owner Gaussian jobs on this +same address stock, with monomial-Clifford entry/exit charts in the Clifford +proof and arbitrary monomial entry/exit charts in the final extension, and +ranks at most 17. In particular a rank-17 job is a genuine full Gaussian up to those charts; +an abstract coded mixture is not target credit. Every original input remains +present exactly once. Lower-rank target choices do not supply clean initial +fields or erase arbitrary data. + +## Every negative endpoint term has Fourier rank at most 16 + +For a one-column Clifford let its Fourier rank be the rank of its symplectic +upper-right block, equivalently `17-dim(T L0 intersect L0)`. Monomial left or +right multiplication preserves this number. A genuine H17 has rank 17. + +The reviewed first-three-control argument and finite tensor separation place +each surviving letter k of t in the transported class Ht. Its monomial binary +linear block R preserves W and `span(q)+W`. Consequently `R^-T` preserves U, +the orthogonal complement of `span(q)+W`. + +A nonzero expanded negative endpoint term has the precise order + + T = Q^-1 N3 k N1 D1 D3, + N3=K3_i^-1 K3_r, N1=K1_s^-1 K1_j, + +with source coefficient containing `A[i,r] A[s,j]`. This follows from +`Q^-1 G=D1 D3`; no Q-order-two replacement is used. + +The pure Z vector `(0,q)` belongs to `D1 D3 L0`, since those factors omit q. +The signed orthogonal N1 carries it to `(0,a)`, where + + a=G1_s^-1 q_j, + q dot a = q_s dot q_j = 0. + +Thus a is a nonzero vector entirely in U. The monomial k carries this vector +to `(0,R^-T a)`, still a nonzero pure Z vector in U. N3 acts only on q+W and +therefore fixes it. Q^-1 likewise fixes every pure Z vector in U. Hence +`T L0 intersect L0` contains a nonzero vector, and the Fourier rank of T is at +most 16. This holds for every nonzero complete term, before cancellation. + +This proof uses only the right source edge; it does not assert that transported +k fixes q. For scalar-owner t0, the stronger two-edge calculation gives rank +15: up to outer monomials the Fourier block is `I+v v^T+q q^T`, with v and q +distinct orthogonal odd vectors. The general rank-16 bound is the one used. + +## Arbitrary FREE input encoding cannot create more than 112 H17 jobs + +This is an image-dimension argument over the full FREE algebra, not scalar +coefficient rank. At sufficiently large column width f, take B to be the +complex span of the lifted projective monomial Clifford group H on 17 bits. +H is finite. Tensor separation makes its projective representatives linearly +independent; its multiplication retains the scalar cocycle raised to f. +Thus B is a finite-dimensional twisted group algebra. Write `d=dim_C B`. + +Similarly, the finite projective Clifford group gives an ambient operator +space with distinct projective classes independent at sufficiently large f. +Let pi17 retain exactly the classes of Fourier rank 17. Since left and right +monomial multiplication preserves Fourier rank, pi17 is a B-bimodule map. +Width-dependent outer coefficients do not affect this support statement. + +Let U be any FREE input encoder and L any FREE output readout. On the main +input columns the proposed output is `L M U+B0`, where B0 is any saved-input +FREE bypass. The preceding lemma kills the entire negative bank under pi17; +B0 has grade zero and also vanishes. The positive bank contribution factors +as + + B^224 --U_positive--> B^112 --diag(G)--> ambient^112 + --t and positive readout--> ambient^output. + +Its image therefore has complex dimension at most 112d, irrespective of the +number of clean buffers, copies or readout rows. No claim that the raw physical +data dimension itself is d is being made; the inputs here are the FREE algebra +module, after the justified coefficient separation. + +Suppose m original inputs receive independent H17 outputs. Select their m rows +and their matching original input columns. The desired projected map on B^m +is diagonal in their actual rank-17 Gaussian operators G_j. Each G_j is an +invertible address operator, so left multiplication by G_j is injective on B. +The image dimension of that target map is exactly md. It must factor through +the same B^112 above. Therefore + + m d <= 112 d, hence m <= 112. + +Lower-rank Gaussian outputs do not appear in this projection. The argument +allows arbitrary mixing of both main banks at entry, so it is not a transfer +of the earlier unchanged-original-feed proof. Rectangular readout and saved +arbitrary inputs do not alter the capacity bound. + +## Full optimistic invoice and exact price decision + +All 1,040 original owners remain: 224 main and 816 helpers. With at most 112 +H17 main targets, the best possible rank census for `0 g^(tensor f)` as a unital homomorphism. The proof needs coefficient faithfulness only on the fixed finite collection in the proposed identity, not on this entire infinite algebra. + +At each sufficiently large f, finite tensor separation makes the proposed physical endpoint equality a coefficient identity in that formal algebra. Width-dependent owner coefficients are allowed; equal projective products are grouped with their correct f-dependent scalar factors. The finite union must include the proposed target charts, as the repaired report now says. + +Projection onto the basis classes `H G H` is a bimodule map for the monomial algebra: left or right multiplication by H preserves that double coset and its complement. Thus all negative terms, FREE bypass terms and lower-rank target terms disappear. Every positive term is a monomial product on either side of G, so survives unchanged. Selecting the m target rows and their matching original input columns gives the formal identity in the correct order: + +`diag(G_1,...,G_m) = L_positive t diag(G,...,G) U_positive`. + +There are exactly 112 copies in the middle diagonal. Evaluating this already projected identity at the same sufficiently large width is legitimate. The target block diagonal has physical rank `m N_f` because each genuine target job is invertible on its original address field. The right side factors through 112 such fields and has rank at most `112 N_f`. Therefore `m<=112`. Common spectators multiply both dimensions by the same factor. There is no inference from raw data rank before projection, or from coefficient rank alone. + +## 6. Ownership and scope of the factorization + +The factorization concerns independent original main inputs, not coded mixtures credited as new jobs. The source has no main/helper leakage; the retained 816 helper endpoints are autonomous. With their paths unchanged, they are not additional observations of main inputs. The owned query bank is dependent workspace and receives no productive credit. FREE copies, clean scratch and saved-original access only change the encoder/readout or add the grade-zero bypass. + +This requires the report's exclusion of separately available native history, extra paid observations and changed helper paths. Access to an additional paid Gaussian observation could supply another channel and would change the factorization. The result does not transfer to that model or to Dillon's separately held native-history mechanisms. Similarly, arbitrary new input encoding is allowed only within the declared FREE class and unchanged physical source endpoint; changing the source, target chart family or actual intermediate paid path is outside the theorem. + +## 7. The complete optimistic invoice loses exactly + +The retained native bill is `P0={1:2201,2:412,3:510,4:127,5:40}`. Two native bills, the 112 H1 query bank, and the rank-nine helper complements give + +`P=2P0+112H1+94H1+14H2+56H5` + +` ={1:4608,2:838,3:1020,4:254,5:136}`. + +The two native helper banks have `94 H8`, `14 H7`, `56 H4` and `652 H9` jobs. Completing them gives exactly 816 H9 outputs, credited once; the earlier H4/H7/H8 rewards are replaced rather than retained additionally. This invoice is the declared retained completed-helper contract, not a universal comparison against altered helper invoices. + +For `00`. At C=0 the optimistic masses tie and positivity still fails. No numerical root, finite-work credit, compiler reserve or inverse-transpose completion is needed to establish this necessary failure. Those additional costs cannot repair it. + +## 8. Verification and limits + +`check_evidence.py` independently reads the captured CODE.json and NORMALIZERS.json, checks the scientific SHA256 pins, reconstructs source directions and all supported-edge dot products, and reconstructs the exact invoice/mass and helper multiplicities. It imports none of the author's engines. Normal and optimized Python outputs are byte-identical. Rejection controls catch a newly nonzero diagonal edge, a duplicated direction, omission of the query bank, and granting a 113th H17 target while retaining only 111 H16 targets under the same mass budget. These controls validate scalar source/accounting premises only; they do not machine-check the symbolic capacity theorem. + +No t0 solver, group enumeration, native/emitter/compiler/Lean campaign, moment scan, external write or source change was performed. The original report and all predecessor files were preserved. This review does not independently refresh upstream overlap or canonical main; those remain the separate monitor/root records. It accepts a source-bound ceiling within the declared contract, not a universal physical FREE obstruction, a construction, or a new kappa result. diff --git a/research/mixed-target-capacity-ceiling/evidence/independent-review/SOURCES.json b/research/mixed-target-capacity-ceiling/evidence/independent-review/SOURCES.json new file mode 100644 index 0000000000..a70c821ab3 --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/SOURCES.json @@ -0,0 +1,79 @@ +{ + "scientific_source_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "captures": "Byte-exact, no newline or source normalization", + "files": [ + { + "source_path": "outputs/mixed-target-input-encoder-20261023/REPORT.md", + "capture_path": "frozen/REVIEWED-REPORT.md", + "sha256": "11c0e2a054ac107ad605262f0c2ed3d3ab9ff3dbfc4fc7f0eadd17d1832462cc", + "bytes": 19422 + }, + { + "source_path": "outputs/mixed-target-input-encoder-20261023/SOURCES.json", + "capture_path": "frozen/AUTHOR-SOURCES.json", + "sha256": "aec91a637b50a6f00c38917d87094f6ec129515ca5536ec66374403b59558fa6", + "bytes": 5682 + }, + { + "source_path": "outputs/mixed-target-input-encoder-20261023/check_source.py", + "capture_path": "frozen/AUTHOR-check_source.py", + "sha256": "2e3149ebcbbdd2fc45f5fc057986e88c45a3e581f1e7a5c2ef42b8fe55fd981d", + "bytes": 2677 + }, + { + "source_path": "outputs/mixed-target-input-encoder-20261023/SOURCE-CHECK.json", + "capture_path": "frozen/AUTHOR-SOURCE-CHECK.json", + "sha256": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "bytes": 1512 + }, + { + "source_path": "outputs/released-operator-intersection-20261023/frozen/CODE.json", + "capture_path": "frozen/CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "bytes": 65977 + }, + { + "source_path": "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json", + "capture_path": "frozen/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "bytes": 281582 + }, + { + "source_path": "outputs/released-operator-intersection-20261023/frozen/PHYSICAL.md", + "capture_path": "frozen/PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "bytes": 10632 + }, + { + "source_path": "outputs/released-operator-intersection-20261023/SOURCES.json", + "capture_path": "frozen/SCIENTIFIC-SOURCES.json", + "sha256": "e810407fc34de1f3af196fc86e91e680075ff982bbc6fe19d6ebb02f2a0c0d9c", + "bytes": 1538 + }, + { + "source_path": "outputs/released-operator-intersection-20261023/PROOF.md", + "capture_path": "frozen/CLIFFORD-PREDECESSOR.md", + "sha256": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "bytes": 12155 + }, + { + "source_path": "outputs/nonlinear-monomial-control-ceiling-20261023/PROOF.md", + "capture_path": "frozen/NONLINEAR-PREDECESSOR.md", + "sha256": "76bea47531ed557c0c9cb210c4324d6000c74415bf13e5747b7036567853f6ef", + "bytes": 7820 + }, + { + "source_path": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/REPORT.md", + "capture_path": "frozen/INVENTORY-REPORT.md", + "sha256": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "bytes": 12159 + }, + { + "source_path": "outputs/mixed-target-input-encoder-20261023/SOURCES.json", + "capture_path": "frozen/AUTHOR-SOURCES-AT-FREEZE.json", + "sha256": "5d7d5d3868a4dd85891f23c6ba0019cc648e5d2208a4d08fb2ab8650b67a48f2", + "bytes": 6894 + } + ], + "mutable_metadata_note": "Author SOURCES.json advanced during review with conceptual-feedback/history metadata; reviewed REPORT.md and all scientific inputs unchanged. Original capture retained and current metadata additionally captured." +} diff --git a/research/mixed-target-capacity-ceiling/evidence/independent-review/check_evidence.py b/research/mixed-target-capacity-ceiling/evidence/independent-review/check_evidence.py new file mode 100644 index 0000000000..36eb36201d --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/check_evidence.py @@ -0,0 +1,92 @@ +#!/usr/bin/env python3 +"""Independent scalar-data and exact invoice audit, not an operator replay.""" +from fractions import Fraction +from hashlib import sha256 +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent + + +def require(value, message): + if not value: + raise RuntimeError(message) + + +def edge_property(matrix, directions): + return all(not x or (directions[s] & directions[j]).bit_count() % 2 == 0 + for s, row in enumerate(matrix) for j, x in enumerate(row)) + + +def main(): + pins = { + 'CODE.json': '8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0', + 'NORMALIZERS.json': 'ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da', + } + for name, digest in pins.items(): + require(sha256((HERE / 'frozen' / name).read_bytes()).hexdigest() == digest, + 'Source pin mismatch: ' + name) + code = json.loads((HERE / 'frozen/CODE.json').read_text()) + ports = json.loads((HERE / 'frozen/NORMALIZERS.json').read_text())['ports'] + matrix = [[Fraction(x) for x in row] for row in code['A']] + require(len(matrix) == 112 and all(len(row) == 112 for row in matrix) + and len(ports) == 112, 'Wrong source dimensions') + # G is stored by rows. Its image of the first basis vector uses the + # first BIT of each row, not the first literal row as a column. + directions = [sum((row & 1) << bit for bit, row in enumerate(p['G_rows'])) + for p in ports] + require(all(q == p['q'] for q, p in zip(directions, ports)), + 'Rows/columns or declared source q mismatch') + require(len(set(directions)) == 112, 'Non-distinct source directions') + require(all(q.bit_count() % 2 == 1 for q in directions), 'Non-odd direction') + require(all(((p['G_rows'][i] & p['G_rows'][j]).bit_count() % 2) == (i == j) + for p in ports for i in range(9) for j in range(9)), + 'Source G lost orthogonality') + require(edge_property(matrix, directions), 'Supported source edge is not orthogonal') + edge_count = sum(bool(x) for row in matrix for x in row) + require(edge_count == 5824, 'Source edge census mismatch') + + native = {1: 2201, 2: 412, 3: 510, 4: 127, 5: 40} + paid = {r: 2 * count for r, count in native.items()} + for rank, count in {1: 112 + 94, 2: 14, 5: 56}.items(): + paid[rank] += count + target = {17: 112, 16: 112, 9: 816} + mass = lambda p: sum(rank * count for rank, count in p.items()) + require(paid == {1: 4608, 2: 838, 3: 1020, 4: 254, 5: 136}, + 'Paid decomposition mismatch') + require(mass(paid) == mass(target) == 11040, 'Mass mismatch') + require(sum(target.values()) == 1040 and min(target) > max(paid), + 'Owner census/support gap mismatch') + require(2 * 408 == 816 and 2 * (47 + 7 + 28) == 94 + 14 + 56, + 'Helper complement multiplicity mismatch') + + bad_matrix = [row.copy() for row in matrix] + bad_matrix[0][0] = Fraction(1) + duplicated = directions.copy() + duplicated[1] = duplicated[0] + bad_paid = paid.copy() + bad_paid[1] -= 112 + bad_target = {17: 113, 16: 111, 9: 816} + controls = { + 'reject_added_nonzero_diagonal': not edge_property(bad_matrix, directions), + 'reject_duplicate_direction': len(set(duplicated)) != 112, + 'reject_omitted_query_bank_mass': mass(bad_paid) != 11040, + 'reject_unfunded_113th_fullrank_target_mass': mass(bad_target) != mass(paid), + } + require(all(controls.values()), 'Mutation control failed') + print(json.dumps({ + 'status': 'PASS_INDEPENDENT_SCALAR_SOURCE_AND_INVOICE_ONLY', + 'source_edges': edge_count, + 'nonorthogonal_supported_edges': 0, + 'direction_convention': 'G rows; image of e_q formed from first bit of each row', + 'paid': paid, 'optimistic_target': target, + 'paid_mass': mass(paid), 'optimistic_target_mass': mass(target), + 'target_min_rank': min(target), 'paid_max_rank': max(paid), + 'controls': controls, + 'scope': 'Exact existing scalar source data and invoice arithmetic only; no native, ' + 'operator, group enumeration, solver, compiler, Lean or moment scan.', + }, indent=2, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json new file mode 100644 index 0000000000..4884effc7b --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCE-CHECK.json @@ -0,0 +1,101 @@ +{ + "status": "PASS_SOURCE_ONLY_DOT_AND_MODE_FACTS", + "scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "ports": 112, + "nonzero_A_edges": 5824, + "nonorthogonal_nonzero_A_edges": 0, + "distinct_q": 112, + "mode_gram": [ + [ + 56, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 56, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 56, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 56, + 0, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 56, + 0, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 56, + 0, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 56, + 0 + ], + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 56 + ] + ], + "source_files": [ + { + "path": "outputs/released-operator-intersection-20261023/frozen/CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + } + ], + "scope": "Reads existing finite scalar A, source q masks and eight mode columns only. No operator evaluation, solver, native/emitter/compiler/Lean execution, candidate enumeration or moment numerics." +} diff --git a/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCES-AT-FREEZE.json b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCES-AT-FREEZE.json new file mode 100644 index 0000000000..39eeae70d0 --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/AUTHOR-SOURCES-AT-FREEZE.json @@ -0,0 +1,150 @@ +{ + "status": "LOCAL_SOURCE_BOUND_STOP_INDEPENDENT_MATHEMATICAL_PASS", + "scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "context_pin": "0e8a13c251a9be1029114cda8b4194f05f3a23ec", + "root_reported_canonical": "ec2780e8aeb1c88acaf5e9e470ef8c68e7fbbb6c", + "guidance_provenance": "Root reported nine governing blobs unchanged from a5df48c55ea806d7952b65acc9c76d878ff09b13; retained files read directly. 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Dillon paid-history/augmented helper/changed paid path excluded.", + "source_files": [ + { + "path": "outputs/released-operator-intersection-20261023/frozen/CODE.json", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "bytes": 65977 + }, + { + "path": "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", + "bytes": 281582 + }, + { + "path": "outputs/released-operator-intersection-20261023/frozen/PHYSICAL.md", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078", + "bytes": 10632 + }, + { + "path": "outputs/released-operator-intersection-20261023/PROOF.md", + "sha256": "c20b2f13e875d9e1fb6d0743693f9deccc4f7d68dcdc55ec241324ed3d7de7bc", + "bytes": 12155 + }, + { + "path": "outputs/released-operator-independent-review-20261023/REVIEW.md", + "sha256": "23b5aa5df049cb4a8fe3349c054e27d84ca151e29e263c658670639bad082428", + "bytes": 10418 + }, + { + "path": "outputs/nonlinear-monomial-control-ceiling-20261023/PROOF.md", + "sha256": "76bea47531ed557c0c9cb210c4324d6000c74415bf13e5747b7036567853f6ef", + "bytes": 7820 + }, + { + "path": "outputs/nonlinear-monomial-control-review-20261023/REVIEW.md", + "sha256": "0b0fe1c33eea85ccd92a3423a705fd086c6f2669f1a47f37fba9c1ca4ae91973", + "bytes": 9223 + }, + { + "path": "outputs/partial-target-consumer-gate-20261023/REPORT.md", + "sha256": "81edffd10654a8e0d190e5119ed2aa8e5ffe93c01b6827b97c5e454b62214cfe", + "bytes": 8538 + }, + { + "path": "coded-port-adapter-ceiling-20261023/outputs/released-operator-inventory-20261023/REPORT.md", + "sha256": "363f66bb655dd9100438aa4ae405025baafeddcaaaad0b8d0a43eecaa43ee784", + "bytes": 12159 + }, + { + "path": "outputs/mathematics-paper-research-20261023/notes/released-finite-algebra-inverse-lemma.md", + "sha256": "6f227a4846839f1e52b974562906543519458e0bae068f785da7bec1d46dbce8", + "bytes": 8443 + }, + { + "path": "outputs/released-operator-optimistic-budget-20261023/REPORT.md", + "sha256": "b8b785a815852069b27ee6b18337b6ecd64127c7a22985d0e4221a2fc11bd53a", + "bytes": 8680 + }, + { + "path": "released-operator-clifford-ceiling-20261023/AGENTS.md", + "sha256": "eb25d8ec495b80190a4b1a634710819bb74f0fae88d5203285c2b75b6f147347", + "bytes": 5580 + }, + { + "path": "released-operator-clifford-ceiling-20261023/CONTRIBUTING.md", + "sha256": "8a49fe97e2ad088a2b2e0c5b222aaab08752783b1f9c1260790d7dd13011d215", + "bytes": 7143 + }, + { + "path": "released-operator-clifford-ceiling-20261023/autoresearch.md", + "sha256": "d16f0d3bb4d4b213d06c128db6d6460b0fe9ec1ac5a6c1ea1febf1db40e7b60d", + "bytes": 5986 + }, + { + "path": "released-operator-clifford-ceiling-20261023/docs/research/agent-procedure.md", + "sha256": "74fbdc7579d240a6b03920e71a55857f20b08dfc614d472f29bc14802c564f07", + "bytes": 28999 + }, + { + "path": "released-operator-clifford-ceiling-20261023/docs/research/current-priorities.md", + "sha256": "db049fa3f75bd5345b23b736e51b7e912b39d372040b462c3e82610c482ff0c9", + "bytes": 11695 + }, + { + "path": "released-operator-clifford-ceiling-20261023/docs/research/research-family-status.md", + "sha256": "21ea61004c0270388258c4251b1c586b65f06bc807395b281deacfb886204934", + "bytes": 18401 + }, + { + "path": "released-operator-clifford-ceiling-20261023/certificates/selected-result.json", + "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375", + "bytes": 4922 + } + ], + "local_artifacts": [ + { + "path": "outputs/mixed-target-input-encoder-20261023/REPORT.md", + "sha256": "11c0e2a054ac107ad605262f0c2ed3d3ab9ff3dbfc4fc7f0eadd17d1832462cc", + "bytes": 19422 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/check_source.py", + "sha256": "2e3149ebcbbdd2fc45f5fc057986e88c45a3e581f1e7a5c2ef42b8fe55fd981d", + "bytes": 2677 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/SOURCE-CHECK.json", + "sha256": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "bytes": 1512 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/SOURCE-CHECK-OPTIMIZED.json", + "sha256": "f0e37349f46f23626dc52de25140fc4a29e2040e051ccd8a124872ce95a711e2", + "bytes": 1512 + }, + { + "path": "outputs/mixed-target-input-encoder-20261023/REVIEW-FEEDBACK.md", + "sha256": "67e3699d38710063f90ab24274ca7f3b657a5028fc41633e6797615102aefdc4", + "bytes": 1634 + } + ], + "checks": [ + "source-only script normal PASS", + "source-only script optimized PASS", + "normal/optimized JSON bytes identical" + ], + "no_native_solver_compiler_lean_or_public_write": true, + "history": [ + { + "path": "outputs/mixed-target-input-encoder-20261023/history/REPORT-before-target-chart-scope.md", + "sha256": "d0f6c6ad55073bd084d5a577b3b8cd93515c297c47f26cc52baaeb9fe7dc4a59" + } + ], + "conceptual_feedback": "Existing mathematics paper worker read final report11c0e2a... and partition predecessor/review: no blocking mathematical issue; 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b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/AUTHOR-check_source.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Only authenticate and inspect retained scalar source tables; no operators.""" +import hashlib +import json +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +EXPECTED = { + "outputs/released-operator-intersection-20261023/frozen/CODE.json": + "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "outputs/released-operator-intersection-20261023/frozen/NORMALIZERS.json": + "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da", +} + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def main(): + files = [] + data = [] + for name, expected in EXPECTED.items(): + payload = (ROOT / name).read_bytes() + digest = hashlib.sha256(payload).hexdigest() + if expected is not None: + require(digest == expected, "Pinned source hash changed: " + name) + files.append({"path": name, "sha256": digest}) + data.append(json.loads(payload)) + a = data[0]["A"] + ports = data[1]["ports"] + modes = data[1]["mode_columns"] + require(len(a) == len(ports) == 112, "Owner count changed") + require(all(len(row) == 112 for row in a), "Code shape changed") + require(len(modes) == 8 and all(len(c) == 112 for c in modes), + "Mode shape changed") + require([p["port"] for p in ports] == list(range(112)), "Port order changed") + edges = [(i, j) for i in range(112) for j in range(112) if a[i][j] != "0"] + bad = [(i, j) for i, j in edges + if (ports[i]["q"] & ports[j]["q"]).bit_count() % 2] + require(len(edges) == 5824 and not bad, "Supported-edge orthogonality failed") + require(len({p["q"] for p in ports}) == 112, "Distinct direction property failed") + gram = [[sum(modes[i][k] * modes[j][k] for k in range(112)) + for j in range(8)] for i in range(8)] + require(gram == [[56 * int(i == j) for j in range(8)] for i in range(8)], + "Mode Gram identity failed") + result = { + "status": "PASS_SOURCE_ONLY_DOT_AND_MODE_FACTS", + "scientific_pin": "4c0a359d88f22f05189d51f48387750b801a45d4", + "ports": len(ports), "nonzero_A_edges": len(edges), + "nonorthogonal_nonzero_A_edges": len(bad), + "distinct_q": len({p["q"] for p in ports}), "mode_gram": gram, + "source_files": files, + "scope": "Reads existing finite scalar A, source q masks and eight mode columns only. " + "No operator evaluation, solver, native/emitter/compiler/Lean execution, " + "candidate enumeration or moment numerics.", + } + print(json.dumps(result, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/CLIFFORD-PREDECESSOR.md b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/CLIFFORD-PREDECESSOR.md new file mode 100644 index 0000000000..08b35b275a --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/CLIFFORD-PREDECESSOR.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/mixed-target-capacity-ceiling/evidence/independent-review/frozen/CODE.json b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/CODE.json new file mode 100644 index 0000000000..03170f4a31 --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/CODE.json @@ -0,0 +1 @@ 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diff --git a/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/INVENTORY-REPORT.md b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/INVENTORY-REPORT.md new file mode 100644 index 0000000000..8a200e2535 --- /dev/null +++ b/research/mixed-target-capacity-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/mixed-target-capacity-ceiling/evidence/independent-review/frozen/NONLINEAR-PREDECESSOR.md b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/NONLINEAR-PREDECESSOR.md new file mode 100644 index 0000000000..277a32368a --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/NONLINEAR-PREDECESSOR.md @@ -0,0 +1,48 @@ +# Support-partition extension of the released four-control obstruction + +Root derivation revised after independent review; final review pending. Local-only. No paid lower bound or kappa claim. + +## Changed scope and exact predecessor + +The published PR #5160 head 7800589ce99d932bdb063aafca1f501f1a38626d proves the obstruction for fixed finite columnwise monomial-Clifford/scalar-owner programs. This extension permits arbitrary invertible one-column monomial matrices, including nonlinear address permutations and arbitrary nonzero complex weights, in a fixed finite columnwise owner program. More generally, it suffices that the complete one-column operator products occurring in each proposed control have a fixed finite support independent of width f; only their outer scalar coefficients may depend on f. Merely fixing a finite generating alphabet is insufficient if word products or lengths vary without bound with f: weighted monomial generators can generate infinitely many projective products. That larger class is not covered. It does not cover growing alphabets, noncolumnwise or general width-dependent permutations, extra paid Gaussian calls, a changed endpoint, compressed/input-coded targets or a changed source. + +Scientific source remains 4c0a359d88f22f05189d51f48387750b801a45d4, research/coded-native-caller. Reuse the authenticated source facts and exact normalizer conventions in outputs/released-operator-intersection-20261023/PROOF.md and its source checker. There are 112 owners; A is invertible with zero diagonal. K1s/K3r are actual signed linear permutations supported on q+U / q+W, G_s e_q=q_s, and distinct source q_s make G_s^-1 q_j=e_q iff s=j. Q and D3 are supported on q and W respectively, with every entry inside their respective coset blocks nonzero. These are inherited source premises, not newly machine-checked here. + +## Lemma 1 — a monomial intertwiner preserves support partitions + +Let F be an invertible matrix whose support is exactly a disjoint union of complete square blocks indexed by a partition P of the computational basis. If h and k are invertible monomial matrices and F h = k F, then their address permutations both map every P-block bijectively to a P-block, with the same induced permutation of blocks. + +For a column y, support(F h e_y) is the entire P-block containing sigma_h(y). Support(k F e_y) is sigma_k(P(y)). These must be equal. If y,y' belong to the same P-block, the latter set is unchanged, so sigma_h sends that block into a single block. Invertibility and the equal finite block sizes force equality. The same identity supplies the assertion for sigma_k. No phase restriction is used; multiplication by a monomial matrix creates no internal cancellation. + +For a two-sided variant F_out^-1 a F_in monomial, where F_in/F_out have complete equal-size coset blocks (possibly different partitions), write a F_in=F_out m and use the same column-support argument. The address permutation of a maps input blocks to output blocks. This variant uses no Clifford/symplectic classification. + +## Lemma 2 — transported letters preserve the required partitions + +Let H be the group of all invertible monomial matrices on the actual 17 one-column bits. Let h in H satisfy Q^-1 h Q in H and k=D3 h D3^-1 in H. From h Q=Q(Q^-1 h Q), Lemma 1 says sigma_h preserves q-cosets. From D3 h=k D3, both sigma_h and sigma_k preserve W-cosets. + +The join of the q- and W-coset partitions is the (q+W)-coset partition, indexed by U coordinates. An invertible permutation preserving both component partitions preserves their join, hence sigma_h preserves (q+W)-cosets. D3 and D3^-1 act inside these join blocks. Therefore k=D3 h D3^-1 has no nonzero matrix entries between an input join block and any output join block other than h's induced image. Because k is monomial, sigma_k also preserves the join partition. + +Consequently, sigma_k cannot map a pair lying in different(q+W)-cosets to a pair in the same(q+W)-coset. + +## Lemma 3 — every nonzero terminal source term remains nonmonomial + +For the same four-control equations as PR #5160, let a=K3i^-1 K3r and b=K1s^-1 K1j. A terminal term has address operator Q^-1 a k b Q^-1, coefficient A[i,r] b[r,s,k] A[s,j]. If this operator were monomial, write a k b Q^-1=Q m. The two-sided support lemma implies a k b maps q-cosets to q-cosets. Since a,b are invertible signed linear permutations, sigma_k must map cosets of v=G1s^-1 q_j to cosets of w=G3r^-1 q_i. + +Here v belongs to span(q)+U and w belongs to span(q)+W. A w-coset consists of two points in one(q+W)-coset. If v has a nonzero U component, every v-coset has its two points in different(q+W)-cosets. This contradicts Lemma 2. Thus v=e_q, so s=j by the actual distinct source directions. But then A[s,j]=A[j,j]=0. Every terminal term with nonzero source coefficient is therefore nonmonomial. This does not require r=i and does not assume the invalid transported central equality from the old draft. + +## All-width conclusion for fixed operator support + +Use the elementary tensor-separation lemma from PR #5160: tensor powers of a finite collection of pairwise nonproportional nonzero operator vectors are independent for sufficiently large f. It applies to arbitrary matrices, not only Clifford operators. + +For any fixed finite columnwise owner program, take the finite set of complete one-column operator products in its expansion and combine projectively equal products. The same applies to all four proposed control implementations. This finite-support premise is essential. Requiring t0, Q^-1t0Q and D3t0D3^-1 to have finite monomial expansions forces every surviving one-column letter h of t0 into the exact intersections in Lemma 2 for all sufficiently large widths. Coefficients may depend on f; the complete operator support remains fixed independently of f. Lemma 3 places every surviving terminal E term outside H. Cancellation may remove outside-H classes but cannot produce an H class. Separating the finite combined set against any proposed finite monomial program for E gives E_f=0 for all sufficiently large widths. + +The actual C1,C3 and Q are invertible, so E=Q^-1 C3 t C1 Q^-1=0 implies t=0 and t0=0. Hence an all-width invertible t0 is impossible in this enlarged class of fixed finite columnwise arbitrary-monomial programs, or explicitly fixed finite complete-product supports. No paid Gaussian query lower bound follows. Programs with unbounded width-dependent products even from finite weighted generators, growing supports, or noncolumnwise FREE programs and altered four-control/target contracts remain outside this theorem. + +## Verification and credit still required + +Independent proof review must check the partition argument, the exact matrix order of every intertwiner and the source support conventions. A small exact support checker with nonaffine examples can discriminate the extension but cannot prove the all-width theorem. No operator alphabet enumeration or native/compiler replay is proposed. Primary credit: Dillon released equations, Dugongue/mdumitrean source A, real normalizer authors and Cinna Davis/1337isnot1337, Cao Yifan/intqwq, zxv and retained helper/Clifford/compiler lineage. This extension is a root support-partition derivation with substantial OpenAI Codex assistance; it is not a published-paper theorem or formal-kernel proof. + + +## Revision note + +The first draft used “fixed alphabet” too loosely outside its fixed-program paragraph. Independent review identified that finite weighted monomial generators need not have finitely many projective products. This revision explicitly requires a fixed finite program or fixed finite set of complete operator products; it excludes unbounded width-dependent word products. The first draft remains in history/PROOF-DRAFT-v1.md. No source or predecessor proof was changed. diff --git a/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/NORMALIZERS.json b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/NORMALIZERS.json new file mode 100644 index 0000000000..bca92c222c --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/NORMALIZERS.json @@ -0,0 +1,126 @@ +{ + "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0", + "finite_checks": {"absolute_phase_mutations_rejected":112,"exact_endpoint_factor_identities":896,"gaussian_free_compiled_wrappers":896,"monomial_wrappers":896,"omitted_phase_rejections":112,"ports":112,"scalar_basis_recodings":224,"weight_congruence_addresses":57344}, + "local_gauge_bill": 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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/mixed-target-capacity-ceiling/evidence/independent-review/frozen/PHYSICAL.md b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/PHYSICAL.md new file mode 100644 index 0000000000..da8837ba67 --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/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/mixed-target-capacity-ceiling/evidence/independent-review/frozen/REVIEWED-REPORT.md b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/REVIEWED-REPORT.md new file mode 100644 index 0000000000..42ff2d607a --- /dev/null +++ b/research/mixed-target-capacity-ceiling/evidence/independent-review/frozen/REVIEWED-REPORT.md @@ -0,0 +1,349 @@ +# Changed input and mixed main ranks: a source-bound capacity STOP + +Local derivation, 2026-10-23. **STOP for the released provider with fixed finite +columnwise monomial FREE encoders and readouts.** At most 112 of the +224 independently supplied main inputs can receive rank-17 Gaussian outputs. +Even granting rank 16 to every remaining main input and the unchanged 816 H9 +helper returns, the complete optimistic recursive invoice loses for every +`0 q_s dot q_j = 0 over F2. + +`SOURCE-CHECK.json` checks all 5,824 nonzero entries of the 112-by-112 source A +against the actual q masks, finding zero exceptions. It also rechecks the +source eight-mode identity `M^T M=56 I`. This is an exact read of existing +scalar data, not native/operator execution or a candidate search. + +The rank-eight code decomposition `A=I-MM^T/4` admits a fixed rational scalar +eigenbasis. It does not imply eight defective Gaussian owners after transport +through Q and the actual entrance/exit charts. The following bound counts +those Gaussian defects directly and permits much more than that eigenbasis. + +## Allowed changed contract + +Retain the exact two-FULL middle word, all native paths, the 112 H1 query bank, +all 816 independent helper inputs, and their billed rank-nine complements. +Require only the first three forward memberships + + t0, Q^-1 t0 Q, t=D3 t0 D3^-1 are FREE. + +Here FREE is a fixed finite scalar owner program over columnwise lifts of +monomial Clifford matrices on the actual 17 bits. Coefficients may depend on +the column width. This is an algebraic relaxation: no inverse, tariff or +bounded-height algorithm is inferred merely from membership. The argument +does not need t0 invertible and permits rectangular readouts, owned clean +scratch, saved-original FREE bypass and arbitrary FREE mixing of the 224 main +inputs. FREE programs supply no separately available extra high-rank Gaussian +observation. The helpers retain their prescribed autonomous path and one return +each, without additional productive copies. + +The actual main endpoint before input and output controls is + + M = [[0,t G],[-E G,0]], + E=Q^-1 C3 t C1 Q^-1, G=D1 D3 Q. + +Main target jobs must be independent original-owner Gaussian jobs on this +same address stock, with monomial-Clifford entry/exit charts in the Clifford +proof and arbitrary monomial entry/exit charts in the final extension, and +ranks at most 17. **The target entry and exit charts must themselves use fixed +finite columnwise complete-product supports independent of f, or the retained +canonical native charts.** This condition covers the target side of tensor +separation just as it covers the controls, encoder, readout and bypass. Growing +or noncolumnwise target-chart families are outside the theorem. In particular +a rank-17 job is a genuine full Gaussian up to those charts; +an abstract coded mixture is not target credit. Every original input remains +present exactly once. Lower-rank target choices do not supply clean initial +fields or erase arbitrary data. + +## Every negative endpoint term has Fourier rank at most 16 + +For a one-column Clifford let its Fourier rank be the rank of its symplectic +upper-right block, equivalently `17-dim(T L0 intersect L0)`. Monomial left or +right multiplication preserves this number. A genuine H17 has rank 17. + +The reviewed first-three-control argument and finite tensor separation place +each surviving letter k of t in the transported class Ht. Its monomial binary +linear block R preserves W and `span(q)+W`. Consequently `R^-T` preserves U, +the orthogonal complement of `span(q)+W`. + +A nonzero expanded negative endpoint term has the precise order + + T = Q^-1 N3 k N1 D1 D3, + N3=K3_i^-1 K3_r, N1=K1_s^-1 K1_j, + +with source coefficient containing `A[i,r] A[s,j]`. This follows from +`Q^-1 G=D1 D3`; no Q-order-two replacement is used. + +The pure Z vector `(0,q)` belongs to `D1 D3 L0`, since those factors omit q. +The signed orthogonal N1 carries it to `(0,a)`, where + + a=G1_s^-1 q_j, + q dot a = q_s dot q_j = 0. + +Thus a is a nonzero vector entirely in U. The monomial k carries this vector +to `(0,R^-T a)`, still a nonzero pure Z vector in U. N3 acts only on q+W and +therefore fixes it. Q^-1 likewise fixes every pure Z vector in U. Hence +`T L0 intersect L0` contains a nonzero vector, and the Fourier rank of T is at +most 16. This holds for every nonzero complete term, before cancellation. + +This proof uses only the right source edge; it does not assert that transported +k fixes q. For scalar-owner t0, the stronger two-edge calculation gives rank +15: up to outer monomials the Fourier block is `I+v v^T+q q^T`, with v and q +distinct orthogonal odd vectors. The general rank-16 bound is the one used. + +## Arbitrary FREE input encoding cannot create more than 112 H17 jobs + +This is an image-dimension argument over the full FREE algebra, not scalar +coefficient rank. At sufficiently large column width f, take B to be the +complex span of the lifted projective monomial Clifford group H on 17 bits. +H is finite. Tensor separation makes its projective representatives linearly +independent; its multiplication retains the scalar cocycle raised to f. +Thus B is a finite-dimensional twisted group algebra. Write `d=dim_C B`. + +Similarly, the finite projective Clifford group gives an ambient operator +space with distinct projective classes independent at sufficiently large f. +Let pi17 retain exactly the classes of Fourier rank 17. Since left and right +monomial multiplication preserves Fourier rank, pi17 is a B-bimodule map. +Width-dependent outer coefficients do not affect this support statement. + +Let U be any FREE input encoder and L any FREE output readout. On the main +input columns the proposed output is `L M U+B0`, where B0 is any saved-input +FREE bypass. The preceding lemma kills the entire negative bank under pi17; +B0 has grade zero and also vanishes. The positive bank contribution factors +as + + B^224 --U_positive--> B^112 --diag(G)--> ambient^112 + --t and positive readout--> ambient^output. + +Its image therefore has complex dimension at most 112d, irrespective of the +number of clean buffers, copies or readout rows. No claim that the raw physical +data dimension itself is d is being made; the inputs here are the FREE algebra +module, after the justified coefficient separation. + +Suppose m original inputs receive independent H17 outputs. Select their m rows +and their matching original input columns. The desired projected map on B^m +is diagonal in their actual rank-17 Gaussian operators G_j. Each G_j is an +invertible address operator, so left multiplication by G_j is injective on B. +The image dimension of that target map is exactly md. It must factor through +the same B^112 above. Therefore + + m d <= 112 d, hence m <= 112. + +Lower-rank Gaussian outputs do not appear in this projection. The argument +allows arbitrary mixing of both main banks at entry, so it is not a transfer +of the earlier unchanged-original-feed proof. Rectangular readout and saved +arbitrary inputs do not alter the capacity bound. + +## Full optimistic invoice and exact price decision + +All 1,040 original owners remain: 224 main and 816 helpers. With at most 112 +H17 main targets, the best possible rank census for `0