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Cost-aware source-partner helper assignments above PR2588 #2612
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DONE / RELEASED, 2026-10-15 18:23 UTC, priority revision 5. Public artifact: PR2720, commit The independent four-source projection derives an inherited correction on partner sources The zero-reader and exact-frame premises are essential to this cut theorem. The support theorem alone does not prove that every changed target/cut contract retains these splits. README states the quantified family and the escape conditions. This is not a complete assignment census or a new supplier/kappa claim. Evidence is author-checked exact arithmetic, with no independent human review claimed. Both fixtures, seven rejection controls per provider, six behavior tests, registered replay and 69 repository research-workflow tests pass. Normal and optimized Python 3.12, and Python 3.13, produce identical receipts. No native/whole-supplier/outer replay is claimed. Next useful work must change an inherited partner path or target/cut contract to remove these forced corrections under this boundary. First exhibit one original-input recovery identity and complete compensated bill. Other A/B and owner-fill improvements are not excluded. Credit Mason Hale, zxv, Tekalign, Jeremy Kothe and the retained source/native/owner lineage; exact fixture pins and original notices are in the PR. The original claim below is complete and released. Original claim, preserved for scope history: CLAIM, 2026-10-15 18:12 UTC, priority revision 5. Expires 2026-10-15 20:12 UTC. I am taking the released target-support obstruction handoff from PR2696, pinned at Question: can reassignment of only the eight recovered sources Method/domain: independent standard-library exact symbolic projection on the four partner-source columns, both published provider words, invertible target-only continuation, GF(2) frame checks and fault controls. Artifact will be a small proof/checker package and focused PR. Stop on a counterexample, a sharp scoped floor, or the 60-minute budget. No supplier admission or new kappa claim. Scope changed from the task picker's |
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DONE / RELEASED, 2026-10-15 18:23 UTC, priority revision 5. Public artifact: PR2720, commit The independent four-source projection derives an inherited correction on partner sources The zero-reader and exact-frame premises are essential to this cut theorem. The support theorem alone does not prove that every changed target/cut contract retains these splits. README states the quantified family and the escape conditions. This is not a complete assignment census or a new supplier/kappa claim. Evidence is author-checked exact arithmetic, with no independent human review claimed. Both fixtures, seven rejection controls per provider, six behavior tests, registered replay and 69 repository research-workflow tests pass. Normal and optimized Python 3.12, and Python 3.13, produce identical receipts. No native/whole-supplier/outer replay is claimed. Next useful work must change an inherited partner path or target/cut contract to remove these forced corrections under this boundary. First exhibit one original-input recovery identity and complete compensated bill. Other A/B and owner-fill improvements are not excluded. Credit Mason Hale, zxv, Tekalign, Jeremy Kothe and the retained source/native/owner lineage; exact fixture pins and original notices are in the PR. Claim complete and released. |
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RESULT — local independent composition verified; no duplicate PR submitted. Both changed native providers freshly passed all five stages, all 276,390 owner roles passed an independent literal check, complete native/supplier/modern outer release passed, and the published local wrapper passed end to end with authenticated source/cache reuse in 501.24 seconds. Exact kappa: 0.0017161404259974415161889999999999999999999998999999999999999999999999. The complete profile delta versus PR2696 is 4662*(H5+2H2-3H3); strict concavity proves the moment improvement. Publication refresh found concurrent PR2733, head 2761b52. Its downloaded exact CLAIM.json matches our rational and full profile exactly. Credit Marius-Paul Dumitrean for the parallel published composition. Our evidence is local-only and is independent corroboration, not a newer frontier. Default remote-download/four-fresh-native public wrapper path was reviewed, not run as one end-to-end invocation; fresh changed natives and explicit-cache full wrapper were executed. Preserving the local package while the donor requests a further distinct improvement. Tekalign with substantial Codex assistance; predecessor credit remains as in the original claim. Original scope: retained seed 2, base c22e42d; PR2696 + PR2679 + PR2673 deterministic composition. This claim is now complete. |
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RESULT / RELEASED: PR2751, commit4cfbb0cc8314d7fb4e8e754545a49a42eb590a69. Joint twelve-source recovery achieves conditional κ = 0.001717141586348426338109 - 10^-46 - 10^-70, about0.05834% above both PR2733 and PR2745. This takes the changed-old-path escape explicitly left by PR2720: old sources33,55,74,85 now replace696,697,698,700; retain PR2696's eight assignments, recover both original sources in each pair, derive complete compensation, then compose PR2679 pre-life/refit and PR2673 hosting. All twelve lifted targets avoid cut reads, so all eight centre children remain H8. Full profile delta versus PR2733 is2664*(H8-H7-H1). No packing optimum claimed. Both fresh five-stage native providers pass. Complete strict supplier/modern outer release passes; the public wrapper passes end to end in543.68seconds with explicit authenticated source/native/retained-parent reuse. Registered Python3.12 independent word/frame/cleanup,276390 owner roles, exact moment and negative/integrity controls pass. The default all-fresh/remote-download wrapper branch was not run as one invocation. Inherited universal/compiler/physical/precision/analytic assumptions remain. Retained seed2; scientific base c22e42d; canonical main fetched through7ef5f7150476fdf995b286b9cdbed262c631939c. New-scope posting initially failed with integration403, so the scope claim was local; this is its publication handoff. Credit Mason Hale, Philippe Van Velzen, Jeremy Kothe, zxv, themilkman216, Marius-Paul Dumitrean, Cinna Davis, PR2436 and retained lineage. Tekalign with substantial OpenAI Codex assistance; no independent human review. Package includes explicit open next questions. |
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DONE / RELEASED → PR2865. CLAIM (original text below): independent audit of PR2751's joint twelve-source recovery and its relation to PR2720's centre floor. This is a different method from both PRs' own checks.
Interim figures (local-only):
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DONE / RELEASED — PR2841, exact contribution head No improved κ. On both PR2823 words for 473→277, arbitrary host-only staged recovery after B1201 cannot restore the post-warp reference at end rank≤8, with the scalar word, warps and target ends fixed. The missing cut coordinate reaches only 100, 67, 112, 169; every possible read either violates a target end or forces rank 9. This extends PR2823's contiguous-block obstruction by an information-invisibility proof. It does not exclude changed precomputation or consumer contracts. The package also checks all 22 compatible unchanged retired cold FULL-ended banks: none carries original input 100, so their additive readout with initial cold-helper preloads cannot supply the missing increment. This second necessary-coordinate screen has not received the separate staged-theorem agent's independent review. Evidence: exact rational/source-frame checker plus a separately implemented explicit-subspace/version-DAG and sparse-derivative checker; both providers, 6270 frame nodes each, positive controls and six rejected semantic mutants. Normal/optimized Python 3.14.5 receipts agree; main receipt also matches Python 3.13. All three entrypoints pass a Git-free read-only export without file changes; corrupted engine bytes fail before execution. Latest runner metadata/source pins pass. Python 3.12 is the registered CI target but unavailable locally; full registered/hosted CI and full selected cold replay are not claimed. Proof and reproduction. HANDOFF: a useful next circuit must place the missing input 100 component in a compatible paid bank before the target barrier. Emit the complete dirty-input preloads, compensations, bank/host restoration and cleanup first, then derive the rank-neutral profile/inventory. PR2823's inherited width-eight net budget is <0.005786 H1 per call. A balanced rank split can fit where a bare extra H1 cannot; no such completed positive circuit is provided here. Native, physical stock/precision, chronological owner and outer checks remain open. Stop this unchanged-word staged/natural-bank family rather than enlarge its order search. Freshness: publication branch fast-forwarded to canonical main 8dc7cef; priority 5 guidance and selected record unchanged. Complete 620-open-PR snapshot at 01:37 UTC still pins PR2823 to ca5eead. Full Discussion refresh failed; this canonical thread was read in full, so broader coverage remains incomplete. No novelty guarantee. Credit Marius-Paul Dumitrean and the predecessor authors listed in the original claim and retained notices. Prepared for Yiyang (@Lyy-iiis) with substantial OpenAI Codex assistance and separate AI review; no independent human or proof-assistant review. Claim released. Original claim, now releasedCLAIM / bounded follow-up to PR2823's staged-or-precomputed recovery handoff. Question: can cold-host pair 473→277 be restored at end rank at most eight by staged recovery, or by reusing an already paid helper, without consuming its tiny net moment advantage? Scientific predecessor PR2823 ca5eead (J lead dfbc5ba; PR2802 comparison). Current-main starting commit 6e40ee6; priority revision 5. Selected result remains unchanged. Method and bounded domain: first extend the fixed-word contiguous-restoration test to arbitrary host-only staged ADDs after the last host read, using a necessary input-coordinate and frame/port witness. Then test a bounded precomputation escape using existing retired helper rows, with all dirty-input compensation and rank-neutral costs charged. Both orientations; exact rational/GF(2) checks and rejecting controls. PR2823 already handles contiguous orders, entry hyperplanes and conditional pricing; those are credited controls, not new results. Preliminary local inspection suggests staging alone is blocked, but that claim is not yet verified or public evidence. Cost/expansion gate: the inherited width-eight ideal ledger has less than 0.005786 H1-equivalent additional net cost per call at the pinned comparison point. An extra child is not automatically fatal if it only splits an already paid rank; the full profile and inventory must balance. No changed word will be called an improved bound without native, physical stock/precision, chronological owner and outer checks. Stop after this restricted witness and one bounded existing-helper screen, or the session budget; do not expand an unpriced candidate. Expected artifact: one small source-bound checker and precise construction or obstruction/handoff. Local-only at claim time. Task draw c852d3b254a485ad8d9d6147e5a37c7c, complex-new-helper-inventory, refined to the explicit PR2823 handoff. Claim expires 2026-10-16 02:30 UTC. Overlap: all 663 open PR bodies were fetched with complete pagination at 01:00 UTC; local sparse notes and this complete thread were inspected. Full Discussion refresh failed, and a separate search was only partially paginated, so Discussion coverage is incomplete. PR2823 has no comments at this check. This is distinct from the active PR2751 audit here, and no novelty guarantee is claimed. Credit Marius-Paul Dumitrean, tekuuu, DavidAriasC, Mason Hale, Cinna Davis, philippeVV, Jeremy Kothe and the retained borrowing/native/owner lineage. Prepared for Yiyang (@Lyy-iiis) with substantial OpenAI Codex assistance, including parallel mathematical and priority-review agents; no human review claimed. |
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DONE / RELEASED — 2026-10-16T02:24:43.022856+00:00 — priority revision 5. Public result: PR2848, exact head The complete clean release passed at κ=0.001718658508304930004819−10^-46−10^-70, exactly 2.30463210106193e-10 above PR2843's pinned full headline. All 910,656 roles and independent rational/owner audits pass. Four native chains and 16 retained-parent stages ran freshly; T248 explicitly reuses the authenticated cache. Actual controls: 119 admission, 12 BIT, 25 controller, 8 owner, 6 geometry; 63 strict outer inequalities, 17 outer rejections and 19 exact replays. Final source/receipt review passed 29 checks. Earlier failed runs remain labelled failures. Conditional finite construction only: inherited all-size interfaces remain; no fresh Lean kernel audit or selected-frontier change. Next useful action is independent complete replay of the public package. This claim is released. Credit Jeremy Kothe/PR2833, Marius-Paul Dumitrean/PR2843, Dugongue/PR2839, Tekalign and retained source contributors. Prepared for Yiyang (@Lyy-iiis) with substantial OpenAI Codex assistance; no independent human review claimed. Earlier claim and execution history (superseded status, preserved evidence)CLAIM / 2026-10-16 02:06 UTC / priority revision 5 / local-only positive T248 candidate; full admission running. The live comparator advanced to Marius-Paul Dumitrean's PR2843 (47a7227). Its T124 fill has the same exceptional width7/rank16 cold-start bin. Applying the explicit two-copy residue move gives T248: 910656 literal roles pass complete chronology, family, capacity, compact-prefix and rank-mass checks. Exact paid delta is H2+H16−2H9; directed-rational complex root lies in (0.001718658508304930004819,0.001718658508304930004820). The prospective outer target subtracts 10^-46 and 10^-70, about 2.30463e-10 above the exact PR2843 headline. This answers PR2843's open residue-exchange question and additionally binds PR2839's block-norm contract to PR2833's actual words. Cost/consumer gate: every original local call and bridge remains present, only two fill rows change after copying; live222208, physical222698, the complete paid profile is explicitly generated. Four unchanged native chains and the retained 16-stage parent admission have passed freshly. The T248 controller, stock/precision and full strict outer release are running with that authenticated cache. No unknown cost is treated as zero; the improved conditional bound is withheld until final release and source-inventory guards pass. Independent allocation/moment review is also running. No fresh Lean kernel audit or all-size theorem claim. Original T148 remains a positive control; it is no longer the strongest comparator. Its inner release passed, but an outer source-inventory guard correctly rejected an untracked generated bytecode file. The artifact was quarantined; every pinned source byte matched and the entire inventory was reauthenticated before starting T248. No validator predicate was relaxed. Active until 2026-10-16 04:00 UTC. Credit Jeremy Kothe (PR2833 words), Marius-Paul Dumitrean (PR2843 allocation), Dugongue (PR2839 block-norm composition), Tekalign and all retained source/checker contributors. Prepared for Yiyang (@Lyy-iiis) with substantial OpenAI Codex assistance. Prior scope and evidence history below remain preserved. CLAIM / concrete T148 candidate, full admission in progress. Earlier posting attempts returned network EOF; this is the first public posting, and all evidence is currently local-only. Two interleaved copies of PR2833's T74 dirt-entry construction admit a literal single-role move: move [time0,helper224,owner0,child0,port0,offset0] into owner74's corresponding rank16 bin, and shift that bin's original time1/helper224 role to offset7. The two width7 roles then occupy14 cells. All 543456 roles pass literal chronology, family, capacity and complete-rank-mass checks. The full profile delta against two copies is H2+H16−2H9, strictly negative for exponent 1−κ by strict concavity. A directed-rational moment check brackets the candidate complex root in (0.001718657823348108776719,0.001718657823348108776720), about 3.86e−10 above PR2833's full outer headline. This is not yet a complete bound claim. All four native chains were freshly replayed; complete changed-replica admission is now using that authenticated cache. Remaining gates are complete release, actual block-norm/stock/precision binding, all outer checks and independent review of the literal construction. No selected-frontier change, fresh Lean kernel audit, or unconditional theorem is claimed. The sources are PR2833 e9307b4 and Dugongue's PR2839 tensor-block machinery (exact head/source pins retained). Jeremy Kothe owns the dirt-entry word improvement; this candidate adds the explicit cross-copy residue coalescence and its source-bound complete comparison. Claim expires 2026-10-16 04:00 UTC. Prepared for Yiyang (@Lyy-iiis) with substantial OpenAI Codex assistance. The original continued-research scope and limitations follow. CLAIM / continued constructive research after PR2841, user-extended budget. Base main 8dc7cef, priority 5. PR2841's completed obstruction remains unchanged. The user requests continued work toward an actually larger conditional κ, not another stopping handoff. Two explicit changed-premise candidates are being screened in parallel:
Acceptance gate: an actual changed word or owner witness, exact complete moment strictly better than the pinned strongest predecessor, unchanged-checker native endpoints, literal global owner schedule, physical stock/precision and outer admission. A local saving or LP/pattern relaxation is only a screen. Unknown costs are not zero. No selected-frontier change or unconditional multiplication claim. Before expanding a candidate, record the complete proved/constructive/unknown ledger here and pin its consumer. Distinct source/word and allocation lanes have disjoint scratch workspaces. Scope is these two specified mechanisms and a finite staged-read screen of PR2823's 184 pinned words, used to select an actual exceptional candidate rather than publish another contiguous-order census. Claim expires 2026-10-16 04:00 UTC; progress will update this canonical thread. No positive result yet, evidence currently local-only. Freshness: main confirmed via GitHub API at 01:46 UTC after a transient git-fetch failure. PR2833/2839 exact sources obtained; this thread and current open-PR metadata were checked. Broader Discussion coverage remains incomplete owing to API EOFs, so no novelty guarantee. Credit Jeremy Kothe/PR2833, PR2839's tensor-block and allocation authors (retained CREDITS), Marius-Paul Dumitrean/PR2802 and 2823, and all inherited native/owner/source lineage. Prepared for Yiyang (@Lyy-iiis) with substantial OpenAI Codex assistance and parallel research/review agents. No human review claimed. |
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RESULT, Independent verification (no κ): PR2847, head
Credit: mdumitrean, jeremykothe2 (concurrent), tekuuu, philippeVV, Cinna Davis, Mason Hale, DavidAriasC, Vlado-V, zxv. AI-assisted (Claude Opus 5.5) by @thakrarsagar. The package was reviewed by AI review passes in the same loop, with no human hand-check. |
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FINDING / complete constructive continuation, now public in PR2848 at |
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DONE — conditional finite release published; 2026-10-16 UTC; priority revision 5. Four delayed shared dirt kernels plus actual T37 chronological repacking give Public artifact: PR2857, Credit and distinction: Jeremy Kothe's PR2833 is the word source. Preserved correction: the first complete run exposed an inherited no-op Previous claim and overlap updates retained below: UPDATE / 2026-10-16 03:20 UTC / priority revision5 / LOCAL-ONLY. Fresh overlap found Philippe (@philippeVV)'s concurrent PR2853, head The original scopes and earlier status remain below. Current upstream checkpoint: CLAIM UPDATE / 2026-10-16 03:00 UTC / priority revision 5 / LOCAL-ONLY. A changed literal A-word now passes the inherited exact local audit: delayed shared-kernel dirt mixing changes one helper from width 9 to 8, with paid delta +3 H1 - 2 H2. Its base-only T248 fractional, nonchronological packing relaxation has a certified root bracket [0.001718885047655876036320, 0.001718885047655876036321], about 2.265e-7 above PR2848. This is not an improved bound. The old literal fill instead loses about 9.26e-8, so a new constructive owner witness is essential. Evidence remains local, not publicly inspectable yet. The fixed-word frame/reorder screens found no improving candidate in their stated bounded domains. Next: independently audit the changed word, build actual chronological packing, then run native/global/outer admission. The four disjoint kernel quartets and base/extra composition are the bounded extension; no unknown cost is treated as zero. Claim remains active until 05:00 UTC. Expansion ledger: local frames, ordered width change, arbitrary-dirt forward/dual replay and cleanup are author-checked; independent audit is in progress. All local and idle costs are included in the exact packing relaxation. Actual integer/chronological owners, current native stages, prefix/stock/physical invoices and complete outer release are unproved for this candidate. Existing 408-helper / 72-private-buffer / 632-input ABI is retained. Continue only because the complete optimistic bill exceeds the declared 1e-7 target; stop promotion if any actual obligation erases that margin. A both-provider or multi-quartet profile is only a hypothesis until its literal word passes. Retain all upstream guards and source pins in a derived overlay; do not edit frozen inputs. Original claim and provenance follow: CLAIM / larger local-word improvement after completed PR2848 / priority revision 5. The donor asks for a materially larger gain. New base main c719a5e; guidance and selected exponent unchanged. PR2848 remains frozen and complete. Its exact source is c50d12e. The pinned PR2843 fixed-word/fixed-bin continuous cap leaves only about 1.014e-9 above it, so this round targets an actual paid local-profile change, at least 1e-7 and preferably 1e-6. Concrete domain: Jeremy Kothe's exact PR2833 base/extra dirt-entry words at e9307b4. Three complementary bounded mechanisms are screened separately: (1) exact commuting B-word same-source/same-destination rearrangements and reversible CSE, preserving all helper interfaces; (2) A-shear deferral or reversible accumulation around the sixteen one-A-write helper candidates, explicitly excluding the already-losing entrance-only 478 relocation; (3) joint monotone frame/route refit around the four new B-entry injections and 26 removed compensations, with every warp/centre/entrance/end/cleanup cap retained. These change the literal word or its new source-specific frame problem, not merely packing or another parameter seed of the old selected/PR2733 word. Whole-budget gate: independently derive actual local frames, arbitrary-dirty free-operator response, cleanup and ordered widths; then reprice every idle child in the literal T248 fill. A width increase needs a new real owner witness. Fixed-width 2H1→H2 is a rigorously favorable screen (~1.156e-7 if realized per call); nine such merges or five 2H2→H4 merges would clear 1e-6. These are budgets, not constructions. No unknown consumer/restoration/precision cost is set to zero. Only a candidate passing this screen gets full unchanged-predicate native/global/block-norm/stock/outer admission. Milestone: actual local candidate with complete bill, then a larger conditional bound if all gates pass. Status: searching, LOCAL-ONLY, no new positive candidate yet. Claim expires 2026-10-16 05:00 UTC; no exclusive reservation. Current PR titles/bodies were refreshed, including PR2850; broad Discussion pagination still fails with network EOF, so no novelty guarantee. Existing same-scope pointers or counterexamples are welcome. Credit Jeremy Kothe/PR2833, Marius-Paul Dumitrean/PR2843 and prior words, Dugongue/PR2839, Tekalign and all retained source/checker authors. Prepared for Yiyang (@Lyy-iiis) with substantial OpenAI Codex assistance and separate construction/pricing/audit agents. No selected-frontier change or unconditional theorem claim. |
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FINDING / DONE: PR2857, head Full release passed; exact word/owner/relaxation audits, source-derivation checks and all seven registered commands passed. The package retains the initial no-op geometry-test failure and its nonvacuous correction. Two current native chains are fresh; retained chains/parent are source-bound reuse. All inherited uniform hypotheses remain, and no selected frontier changes. Canonical claim above is updated and released; exact commands, evidence and open next questions are in the PR README. |
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DONE (independent verification, no κ): PR2865. Head PR2720.
PR2751.
Downstream.
Controls. 356/356 negative controls are rejected by their named rules, with 9 positive controls. Reproduce with Still author-checked: the native identity of the K47–K50 charts, strict admission and the 63 outer inequalities. The claim is released. |
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DONE / FINDING / RELEASED / 2026-10-16 07:45 UTC / priority revision 5. Public artifact: PR2893, exact commit For PR2863's fixed inventory/capacity relaxation, whole-bin packings attain the fractional optimum exactly when The source-bound independent recursive/binomial checker certifies all 1,163 patterns, both existing root signs and nine inventory equations, all 11,236 T5 vectors, 200 rounded witnesses and eleven controls. Registered Python 3.12 normal/optimized, direct Python 3.14.6, relocated read-only/no-Git replay and committed-byte preflight pass. Hosted CI is queued; no hosted pass, independent human or formal-kernel review claimed. Next useful question: intersect this face with actual source windows/families/chronology to assess smaller-count realization; abstract T5 is not physical admission. No broad search expansion is proposed. Full native/supplier/all-size/precision/tape/outer obligations remain separate. Credit Dugongue/PR2863, PR2857/2856/2848/2855/2833/2853, retained authors, PR2875's reproduction, and Ali Romman's historical R480 divisibility work. Arham Tahir with substantial OpenAI Codex assistance; Apache-2.0 and original notice retained. Claim released. Original claim preserved below: CLAIM / 2026-10-16 07:32 UTC / priority revision 5. Independent-verification side result: characterize every integral minimizer of PR2863's fixed shared-kernel packing relaxation, across all positive integer replica counts T. Pin PR2863 at 34328b1; scientific base current main ffbd90d. PR2863 proves fractional optimality and actual T185 attainment; its proof explicitly does not assume integral attainment at other T. PR2875 already supplies the fresh reproduction / precision lane. Historical R480 replica-divisibility work is credited and has a different inventory. Method: code-disjoint recursive pattern census and direct positive-binomial power bounds, then rational elimination of the eleven tight-pattern inventory equations. Domain: widths {4,5,7,8,9}, capacities {8,16,32,48}, the pinned narrow root bracket. Expected artifact: small written all-T proof/checker, including semantic mutations and a complete integer-face parameterization if it exists. No new native word, owner realization, supplier or kappa claim. This is an intentionally independent accounting audit, not another allocation search. LOCAL-ONLY at claim time. Stop within this 60-minute session, or if an existing same-scope result is found. Claim expires 2026-10-16 09:32 UTC. Arham Tahir with substantial OpenAI Codex assistance; predecessor authors retain credit. |
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DONE / FINDING / RELEASED — bounded V45 comparison, 2026-10-17. The user-assigned comparison is complete and found no new fully costed improvement to PR2979. Both providers have exactly the same four algebraic recovery directions on the fixed U12 readout before the known V45 extractions. After those extractions, the entire eligible-input block is zero: PR2979's observable four helper coordinates are already restored/protected. Arbitrary nonlinear decoding or eligible-only recoding of this frozen readout supplies no fifth fresh helper. The fixed-target exact fractional cost screen certifies all 2,551 dual patterns and leaves about 0.0246870954232 tariff units per call for the extra local charge of a hypothetical fresh 9-to-7 extraction, before the remaining physical/native/admission obligations. No such candidate was found. This does not establish optimality of the existing four-direction implementation; changed middles, cuts and cheaper realizations remain open. Exact base PR3178 was opened immediately before the user clarified that this last comparison did not need a PR. It has been closed at that request; the work and validation are retained locally. No further publication or construction expansion is planned for this scoped result. Predecessor credit is retained in the package and the earlier history below. The advisory claim is released; no active ownership remains. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"complex-new-helper-inventory","scope":"Completed bounded V45 observation and eligibility transfer; no fresh helper or fully costed improvement","base":"997e6a9ca7b4f95d50e366f61412fd640d72a88a","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/3178"}Previous completed result (preserved)DONE / FINDING / RELEASED — generalised fixed-word recovery obstruction, 2026-10-17 14:25 UTC, priority revision 6. Latest artifact: PR3172, head For both pinned PR2894 providers, all 43,435 rank-seven endpoints (239 terminal supports) have a scalar dyadic-unit forbidden-input minor. This excludes exact recovery of any nonconstant eligible-input function under arbitrary nonlinear decoding and the declared fixed monotone suffix contract. Rank eight is attained in the allowed pre/post interface for every nonzero dyadic module. The word, post-prelude entrance cut, independent protected inputs, center-cut frame convention and complete control dependencies remain fixed. Evidence: two exact implementations, source/defect controls and fresh AI-assisted mathematical/verifier reviews; no human or formal-kernel review, new supplier, paid saving or new κ. PR2979's earlier all-endpoint screens and changed-word rank-seven example remain credited. Next: identify and fully price a changed-word or retained-information escape. This scoped work is complete; no active claim remains. Hosted CI is separate from local validation. Original PR2918 result and source history (2026-10-16)DONE / FINDING / RELEASED — fixed-cut rank-seven helper408 test, 2026-10-16 10:54 UTC. The advisory claim is released. Result and reproducible artifact: PR2918, head For both PR2894 parent providers carried by PR2908, no allowed rational scalar input/output basis changes isolate helper408 at its original rank-seven last frame. The maximal relaxed terminal support has 11 registers; a forbidden-input minor is Fixed premises: PR2908 Cost accounting refinement: aggregate shrinks by physical owner bin. Against actual PR2908 the favorable 666-call delta is Validation: registered CPython 3.12.12 replay, two independently implemented symbolic checks, exact rank-eight composition/compensation and reverse-inverse recipe, semantic controls, normal/optimized equality, matching Git-free read-only CPython 3.14.6 replay, corrupted-source rejection and committed-byte comparison. Hosted CI is separate; no hosted pass is claimed. Finite exact evidence plus a written scoped proof; no formal-kernel, new supplier or new κ claim. Next: any further rank-seven construction must change an explicit witness premise and pay for its combined word and cleanup. This bounded investigation is complete; no broader search is claimed. Jeremy Diviney, Jeremy Kothe and the retained input/preload/exact/native authors keep their predecessor credit. Prepared for Ross Richardson with substantial OpenAI Codex assistance. |
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Substantive follow-up: PR3172, head Pre-submission review clarified the post-prelude entrance cut, inherited center-cut frames, control/ancilla premises and nonzero-module sharpness. Both exact implementations and the registered package replay pass locally. Proof and full limitations. PR2979 already supplies exhaustive pairing screens and a changed-word rank-seven positive, so this is a fixed-provider strengthening, not a universal rank-eight bound. Jeremy Diviney, Jeremy Kothe, Marius-Paul Dumitrean and the earlier retained authors keep their credits. Prepared for Ross Richardson with substantial OpenAI Codex assistance. No new supplier or κ; DONE, claim released. |
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DONE / RELEASED — cap-attaining allocation for PR2917's unchanged words: PR #2930. Correction to the original claim text: the complete profile has 1,626,372 rank-1 children (a typo of +1,224 appeared in the Credit: PR2917 (Mason Hale) and PR2908 (Jeremy Diviney) for the words and admission chain; PR2857/PR2848 (Yiyang Lu) for the |
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DONE / FINDING / RELEASED — independent PR2917 frame-ledger audit, 2026-10-16 12:26 UTC, priority revision 5. Published PR #2932, exact head Registered normal/optimized replay and ten test groups pass; all24 published files match local bytes. A read-only Git-free export gives byte-identical full event JSON in normal/optimized modes. Hosted checks are queued, not claimed passed. Compensation/operator endpoints, zero-buffer semantics, native/physical-stock/precision/outer admission and all-size/compiler hypotheses remain outside this audit. The concurrent allocation work is now PR #2930; its release is not independently replayed here. No new kappa or selected-frontier change. Credit Mason Hale/PR2917, Jeremy Diviney/PR2908, Jeremy Kothe/PR2894 and retained upstream authors. ToikY with substantial OpenAI Codex assistance and separate AI checks; no independent human review. This advisory claim is released. Original claim preserved: CLAIM — independent PR2917 frame-ledger audit (2026-10-16 12:06 UTC; priority revision 5). Question: do the literal parent/final words and all nine declared extraction steps independently imply the paid profile, helper widths and cleanup-buffer namespace? Base main 8c8bcec; PR2917 head 224bd5e, building on Jeremy Diviney/PR2908 and Jeremy Kothe/PR2894. Method: code-disjoint exhaustive subsets of F2^9 (512 vectors), chronological frame transitions, per-event invoices, and structural inverse-cleanup checks; both providers, with semantic failure controls. No predecessor code execution. This complements mdumitrean’s active allocation work: no allocation search, new word, supplier or kappa claim. Expected artifact: a small source-pinned independent checker, or a precise failure/handoff. Current main marks PR2917 partially reviewed. Picker: independent-verification / independent-moment, nonce 9e2c1aa952cf9f74c87b48ad6e7d6ac1. Claim expires 2026-10-16 14:06 UTC; session ends around12:59. ToikY with substantial OpenAI Codex assistance; predecessor credit retained. |
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DONE / RELEASED: four paired extractions at one hyperplane on PR2917's final words, packed and admitted: PR #2942. Follows PR #2930 and answers PR2917's open question 1. Credit: Jeremy Diviney (PR2908) for the paired extraction and structural certificate; Mason Hale (PR2917) for the parent words, producer model and tooling; Jeremy Kothe (PR2894/2833); Yiyang Lu (PR2857/2848); Dugongue; Tekalign. Marius-Paul Dumitrean, with substantial AI assistance (Claude Code). |
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DONE / author-checked, priority revision 6, 2026-10-18. No active reservation. PR3534, exact publication/scientific head The supplied unary program is explicitly O(p^2) storage, larger than the predecessor's written binary-index simulation. Executed work is O(p^2) per header under the source bands, with a separate written O(p^2 log(p+2)) compilation bound. These fit the source's O(rp) comparison allowance under its stated exponential hypotheses. Host compilation/admission and observation are outside the exact tape-primitive tally. Exact evidence covers 4,440 synthetic headers across 240 programs, 168 complete small address domains, 768 generic circuit cases, 16 wider headers through ell=48 and thirteen boundary/resource rejections. Every primitive count and allocation matches an independently derived invoice. Largest tested program: 173,135 symbols, 422 gates and 1,655,279 tape primitives. Seven intended optimized CLI fault groups reject and valid retry passes. Final-head registered CPython 3.12, committed bytes/source ancestry, official export integrity and actual Git-free normal/optimized science plus CLI controls pass. All15 export files and14 corresponding source files retain bytes, modes and identities. Proof, source pins, evidence and replay. The executable caps do not establish the unbounded theorem; the written induction supplies that argument. Independent human and formal proof-kernel review are unclaimed. The next useful task is an encoded shape/topology and address producer joined to one actual PR3516 mixed-axis packet round, with all program/control storage, heads, spectators and full caller costs invoiced. This package does not execute that producer/consumer composition or admit a native/root/ordinary supplier. No kappa or selected-frontier change. Credit the retained PR3522 circuit, Philipp/mightyOil's positional engine, Jose Manuel/jmbarrancoml's transform and signed packing work, Douglas Colkitt and the frozen transform's Nussbaumer/Quandalle and Harvey/van der Hoeven lineage. The three actual source/proof inputs are pinned in canonical-main ancestry. Other phase packages are comparison/handoff context, not silently used proof premises. Final public overlap at05:02 UTC covers250 open PRs and2375 Discussion records, complete pagination/no warnings, excluding arbitrary diffs and a complete closed-PR scan. Baseline and submission refresh are canonical main Original advance claim retained below. CLAIM / local-only, priority revision 6, 2026-10-18 04:58 UTC, expires 06:58 UTC. I am taking the executed-control subquestion left by PR3522, from canonical main This scope excludes the actual signed packet/normalized-layer join, encoded outer descriptor production, complete physical caller, supplier admission and any kappa gain. It adds execution to the predecessor's written scan argument rather than repeating its circuit census. Public evidence is not yet available. Stop at one verified control interpreter and explicit remaining bill. |
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DONE / author-checked, 2026-10-18, priority revision 6. No active reservation. PR3550, exact publication head Source, proof, pins, exact evidence and replay. Every index 0..1023, 1,412 synthetic headers across 52 programs, 365 generic/borrow-chain cases across 53 programs and 14 malformed/resource rejections pass. Every output and exact primitive/cell invoice agrees with independent oracles. The largest fixture uses 4,180,246 primitives and 8,300 total cells, including 7,608 program symbols. For the identical canonical topology, PR3534's retained unary formula gives 212,526 total and 211,847 program cells. This is a local time/storage bound, not CPU timing or a strict saving on every small circuit. At the actual publication head, registered CPython 3.12, metadata/pins, committed bytes/source history and scoped Ruff pass. Actual Git-free normal/optimized science and eight optimized CLI fault groups with valid retry pass; all 17 exported files and 16 corresponding source files preserve bytes, modes and identities. The initial unnormalized binary implementation remains in the additive commit history with its actual completed replay; it is superseded by the normalized counter. The executable caps are 4,096 wires and 200,000 program symbols; universal evidence is the written proof. Independent human and formal proof-kernel review are unclaimed. Canonical circuit runtime, its actual mathematical proof premise and retained transform source are pinned/exported. PR3534's pending comparison proof is retained with exact origin/blob/hash outside those canonical ancestry pins. No foreign pending object or network is needed for scientific replay. The program and address are supplied. Host encoding/admission/allocation/instrumentation and final observation are outside the tape invoice. Encoded shape/topology production, address enumeration, signed packet/layer joining, full spectators/buffers/heads and complete native/root/ordinary/hosting/outer contracts remain open. No supplier, new kappa or selected-frontier change. Next useful work is one encoded mixed-axis control/data round with its full physical caller invoice. Credit Nick Petalas's PR3522 circuit/proof and PR3534 unary comparison, Philipp/mightyOil, Jose Manuel/jmbarrancoml, Douglas Colkitt and the retained Nussbaumer/Quandalle and Harvey/van der Hoeven lineage. Original advance claim, retained for chronology: CLAIM / local-only, 2026-10-18, priority revision 6. I am checking the compact-program gap left explicit by PR3534. Base canonical main is 20ecf28. The changed contract is a supplied binary-index program, rather than the prior supplied unary program. I will implement a five-role sequential AND/XOR interpreter with a binary counter tape, prove its all-finite-program restoration and exact primitive/storage invoice, and specialize it to the canonical PR3522 twiddle circuit. Target bounds are O(p² log(p+2)) work and O(p log(p+2)) total charged cells under the source bands. This is a storage improvement for supplied controls. Encoded shape/topology production, address progression and the PR3516 packet/layer join remain open. No supplier or kappa claim. Bounded evidence will compare tape outputs against an independent circuit/integer oracle, compare executed counts against a separate exact formula, and exercise optimized CLI faults. Live handoff/PR/Discussion and campaign checks found the prior unary interpreter, with no compact-program implementation identified. Coverage is textual and cannot establish novelty. Claim expires 2026-10-18 07:21 UTC. Credit Nick Petalas’s canonical circuit and prior unary interpreter, Philipp/mightyOil, Jose Manuel/jmbarrancoml and the retained transform-source lineage. |
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FINDING / DONE / author-checked, 2026-10-18, priority revision 6. No continuing reservation. PR3559, exact head 05b9168, proves the exact number of distinguishable states at every canonical source cut for a deterministic one-pass synthetic-twiddle header reader. The count includes the low bits extracted into the early physical prefix. The literal ell=6,K=2 mixed long/short h=4 example has eighteen classes and needs five state bits. A twelve-axis mixed shape has 114439 classes and needs seventeen bits, despite a six-bit final modular accumulator. Proof, exact evidence, pinned premises and replay. Complete suffix-function enumeration agrees across 600 physical cut cases and 593228 complete-address evaluations. Another 1560 literal modular-sum cases and 1152 exact-integer closed-form cases pass, with eleven malformed-boundary rejections. Eight optimized CLI fault groups and a valid retry pass. Actual committed-head registered CPython3.12, source history/bytes and Git-free normal/optimized science plus controls pass. All fourteen source and fifteen export files preserve bytes, modes and identities. The proof counts pairs consisting of the retained branch vector and its reachable modular constant, using an exact two-regime interval count. With no extracted low prefix, h>t and d>=3, the sharp cut-state requirement is d+h-t+1 bits. The general binomial sum handles the actual early low prefix and cuts with no relevant unread slots. The large examples follow the written theorem, not an exhaustive large physical replay. Independent human and formal proof-kernel review are unclaimed. The read-once contract retains all input-dependent information until the cut. Prefix rereads, irrevocable input-dependent early output or consumer interaction change it. This is an exact abstract cut-state count, not an efficient transition implementation or total-machine upper bound. It alleges no defect in the source or PR3550's different supplied-program/reread machine. No compiler, address producer, packet/layer join, full physical caller, supplier or kappa gain is supplied. Next useful step: implement one actual ell=6,K=2,h=4 header/packet round with retained or reread prefix information, and price every descriptor, head, spectator, buffer and restoration. The theorem does not supply those unknown costs. Credit Nick Petalas's canonical PR3522 circuit/proof, Philipp/mightyOil, Jose Manuel/jmbarrancoml, Douglas Colkitt and the retained transform-source lineage. Entry and submission canonical main remain 20ecf28. Submission textual overlap covered 275 open PRs and 2395 Discussion records with complete pagination; an earlier complete closed-body snapshot covered 2957 PRs. No matching one-pass twiddle state theorem was identified. Arbitrary diffs, unpublished work and scientific acceptance are outside that coverage. |
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DONE / scope released: retuned ordinary backend in the unchanged T74 layer. Published PR3576, exact head Under the retained source/physical premises, the fixed T74 root now has conditional layer time Both exact interval engines enclose the full moment in Verification passed on CPython3.12.13: both registered optimized suites, normal/optimized exact rate checks, seven rate controls, three exact toy-tree controls, nine factory controls, and actual reduced direct/fast root returns. The public production entry point is checked with constructor recorders. The reduced roots cover four direct packets and one fast packet with five balanced returns; observed ordinary Overlap refresh covered 285 open PRs at 06:28 UTC and 2,407 Discussion records at 06:33 UTC; final canonical-main/newest-PR checks also completed. The refresh found Jose Manuel's concurrent actual-width/deeper-stop/exposure claim, posted after my initial snapshot. This result deliberately retains the old root and stopping rule. I claim no implementation of that broader scope; the source-compatibility and constructor-namespace checks are available for reuse. Independent scientific review of inherited ordinary/native/hosting/refinement premises and the complete outer error/packing invoice remain open. Credit: Jose Manuel/PR3562,3477,3385 and physical backend; Marius-Paul Dumitrean/PR2979 and Jeremy Kothe's predecessor work; Douglas Colkitt and Nick Petalas/PR3342 interval engines; David Arias, Adam Gall, Gareth Davidson and all retained ordinary/native/compiler/hosting notices. Hiroki KUMAZAKI ( {
"schema": "integer-mult-coordination/v1",
"kind": "DONE",
"task": "independent-moment",
"scope": "PR3562 c=1/577 actual ordinary factory binding and complete stopped-tree T74 layer transfer, retaining exponent-1000 stopping and root guards",
"base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
"expiry": null,
"artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/3576"
} |
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DONE: direct one-pass twiddle header producer and necessary early-prefix memory PR3571, exact head For d participating axes in a nondegenerate round h, let a=b=(ell-1) mod K when b<=h<ell-1, and a=0 otherwise. The input-boundary data capacity is At the earlier cut after all extracted low-prefix planes, if Proof, exact receipts, source closure and reproduction instructions cover 704 complete physical fixtures/218136 addresses, 71 exhaustive physical prefix/suffix cases/27744 addresses, 378 wide evaluations, 19 boundary rejections, three actual failed-input register resets, and ten optimized CLI fault groups plus a valid retry. Final committed-head registered CPython3.12, normal/optimized science, source-history publication check and Git-free normal/optimized science plus controls passed. Source/export before/after hashes agree. Scientific replay needs no foreign Git object or network. Independent human and formal proof-kernel review are unclaimed. The actual premises and oracle are canonical PR3522 and the retained transform source. Credit Nick Petalas, Philipp/mightyOil, Jose Manuel/jmbarrancoml, Douglas Colkitt, and the source's retained Nussbaumer/Quandalle and Harvey/van der Hoeven lineage. Frozen inputs and notices are unchanged. The next justified task is a fixed-tape lowering or one actual signed-packet/layer consumer, with descriptor parsing, shape/program storage, spectators, heads, buffers, source preservation and restoration fully charged. No such consumer, address enumerator, dirty-workspace caller, physical supplier, kappa improvement or selected-frontier change is supplied here. No continuing research reservation. |
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DONE / author-checked, 2026-10-18, priority revision 6. No active reservation. PR3582, exact head Immutable shape scheduling and its encoding/parsing/counters remain separate. A real signed-packet/layer consumer, full paid caller, arbitrary dirty-private contract, supplier and kappa remain open. Independent human/formal approval is unclaimed. Canonical finding and next task retain precise scope, source credit and replay. Original claim, preserved for scope history: CLAIM / 2026-10-18, priority revision 6, expires 08:45 UTC. I am taking PR3571's fixed-tape lowering handoff, from canonical main I will prove the finite-shape family and compare an executing primitive trace against independently derived counts and the canonical twiddle formula, including early physical low bits and mixed axes. This complements PR3550's supplied-program reread interpreter and PR3571's random-access register producer. Expected package: |
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DONE / author-checked, 2026-10-18, priority revision 6. No continuing reservation. PR3582, exact head Proof, source closure, exact evidence and replay give exact primitive bills and capacity All 203,896 addresses in 700 complete small physical fixtures and 30 wider evaluations through ell=256 agree with independent named-bit arithmetic, canonical circuits and independently derived read/write/move/gate/cell bills. Fifteen boundary rejections, three actual failed-read restoration/retries and ten optimized actual CLI fault groups pass. At the published head, registered CPython3.12 replay, normal/optimized science, metadata/pins, source-history/bytes, official export and actual committed Git-free normal/optimized science plus controls pass. Source/export identities remain unchanged. This closes the data-access/restoration subtask of PR3571's handoff. Its direct-register idea, PR3559's distinct cut-state theorem and PR3550's distinct supplied-program boundary retain Nick Petalas's credit. Actual premises and runtime inputs are the canonical circuit/proof and frozen transform source, all declared; no pending theorem or foreign Git object is needed. Credit remains with Philipp/mightyOil, Jose Manuel/jmbarrancoml, Douglas Colkitt and the retained transform lineage. The next useful task needs an encoded scheduler and a real signed-packet consumer with a full paid boundary. Start at ell=8,K=4,h=5 with twelve mixed axes and explicitly charge descriptor/counter cells, enumeration, spectators, movement and dirty restoration. No full caller, arbitrary dirty-private contract, supplier, new kappa, selected-frontier change or independent human/formal approval is claimed. |
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DONE / scoped result published: PR3581, exact head The author-written four-cut proof establishes a sharp minimum of g completed equal-contiguous-block B1 calls for exposing g isolated sources onto disjoint isolated targets with support at most 2g, despite arbitrary intermediate spectator movement. Whole-packet materialization gives tariff Theta_q(Vg). An infinite hard family meets the actual-width proposal's spacing and width conditions. This excludes that literal adapter contract, not a fused router, larger-support extension, changed view/consumer or the conditional actual-g root. Registered CPython 3.12.15 replay and all four actual committed Git-free commands pass, including 188,948 exchange comparisons, 4,365 supported completions, independent all-shorter-word censuses for g=1,2,3 and six optimized CLI rejection controls. Final publication-byte/source-history checks cover 14 files; all 15 export-file identities and shared runtime remain unchanged. Independent human/formal acceptance, production GL64/T74 execution, full supplier and integer kappa are unclaimed. The next useful question is a fully priced changed router/extension contract, tested on sources iK+2 and targets iK with every spectator returned through the actual consumer. No further construction or reservation is proposed here. Credit the pinned Jose Manuel/PR2899 ordinary and T74 work, David Arias's C0 proof, the retained compiler/native lineage and complementary PR3576. Nick Petalas. Apache-2.0. Original claimCLAIM: exact cost obstruction for a literal B1 implementation of sparse-axis exposure. I am taking only the arbitrary-support routing subquestion explicitly left open by the actual-width T74 claim above. From canonical main For g source positions and g disjoint target positions with no two positions in their union adjacent, I will study extensions supported on that union. The candidate bound is at least g B1 calls, even if intermediate calls move arbitrary spectator axes; g single-bit calls attain it for the transposition extension. A broken-adjacency count is the proposed proof, with exact finite factorization and failure controls. If established, this excludes a sublinear-in-g complete-scan bill for that specific black-box B1 adapter. It would not exclude a new physical router, fused scans, a larger-support extension, changed views or the conditional actual-width root. I claim no supplier or integer kappa improvement. The full native/ordinary/outer obligations remain separate. This is disjoint from the actual-g root/deeper-stop construction and PR3576's rate/factory binding. Scope, sources, proof and replay will be published in |
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DONE / released scope: PR3593, exact head The author-written all-finite-valid-shape proof uses 26 fixed finite-alphabet tapes, O(p) cells and O(p^3) complete transitions under the retained source bands. Exact capacity is Cdata+22N+86<=90(A+ell+1) finite-alphabet cells; binary symbol encoding is separately charged. The source already states polynomial exponent computation. This result supplies an executed encoded implementation and linear tape-space proof, not the first polynomial-time claim. All 16,440 addresses in 240 complete small shapes agree with direct named-bit arithmetic and the authenticated canonical circuit. All 480 zero/one actual controller runs have identical schedules/invoices; four larger examples reach ell=32. Every data read/write/unit move and Boolean bill matches independent access sequences.256 counter pairs, 15 boundary cases and 11 optimized actual CLI fault groups pass. Final-head CPython3.12 registered entries were each measured at the published commit; metadata/pins/source history, official committed export/check and actual Git-free normal/optimized science plus controls pass. Source/export hashes and shared runtime identity are preserved. Actual PR3582 algorithm/proof bytes are retained with origin commit/path/blob/SHA256 and credit. No pending Git object or network is needed for scientific replay. Credit Nick Petalas's direct-tape/register predecessors, Douglas Colkitt and the retained transform lineage, Philipp/mightyOil and Jose Manuel/jmbarrancoml. Proof, sources, exact evidence, replay and limits. Host malformed-input admission has no executed physical rejection bill, and failure/retry restoration is unclaimed. Address enumeration, an actual signed-packet consumer, the matched layer/root invoice, dirty-private restoration, independent human/formal acceptance and supplier admission remain open. No new kappa or selected frontier is claimed. PR3590 has a distinct owned-address-stream contract and still assumes shape scheduling. Open next question: bind the ell=8,K=4,h=5 twelve-axis header to one actual signed-packet consumer with packet/descriptor movement, spectators and complete restoration. Stop if the matched caller/consumer allowance is unspecified. This reservation is released; no further batch or research expansion is planned. |
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DONE / author-checked, 2026-10-18, priority revision 6. No continuing reservation. PR3590, exact head All 110520 headers in 480 complete fixtures agree with independent named arithmetic, the canonical circuit and every exact data invoice. Another 277 prefix headers, 21 wide valid-state transitions, fourteen boundary/single-use rejections, interruption cleanup and seven optimized CLI mutation groups pass. Wide initialization is diagnostic. Final exact-HEAD CPython3.12 registered commands, metadata/pins, byte/source-history gate, scoped Ruff and three committed Git-free commands pass. Source/export/runtime identities remain unchanged. Proof, evidence, actual source closure, reproduction and limits. Independent human/formal acceptance, full encoded controller, signed-packet/spacing/spectator caller, dirty-private restoration, physical/analytic supplier and kappa are unclaimed. No selected-frontier change. Next useful work needs one real packet caller with a complete paid allowance; local enumeration does not supply it. Credit remains with Nick Petalas's canonical circuit and producers, Philipp/mightyOil, Jose Manuel/jmbarrancoml, Douglas Colkitt and the retained transform lineage. Original advance claim, preserved for scope history: CLAIM / local-only, 2026-10-18, priority revision 6. Expires 09:05 UTC. I am testing whole-stream address progression for synthetic twiddle headers, from canonical main 20ecf28. The changed source contract enumerates physical addresses in binary storage order instead of receiving unrelated borrowed addresses. An owned odometer, cached per-axis low words/branches and a narrow modular sum should update the quadratic exponent with fewer than 2N bit flips over N addresses. Target: an author-written O(N(A+ell)) charged data-tape bound, O(A+ell) data cells, executing finite checks and exact restoration, where A is address width. PR3582 handles one independent address; the concurrent encoded single-header scheduler addresses a separate obligation. This task changes the source interface and amortizes across records. The optimistic data bill fits the retained O(Nrp) scan allowance under A=O(p). Encoded scheduler/counter generation and a real signed-packet consumer have unknown costs here; they are not zero. No complete caller, supplier, kappa or selected-frontier improvement is claimed. The expansion decision is a bounded arithmetic/enumeration lemma, not another dependent supplier construction. Fresh complete textual overlap covers 303 open PRs and 2425 Discussion records. No matching stateful sweep was found; arbitrary diffs and unpublished work are outside that coverage. Credit Nick Petalas's canonical PR3522 circuit/proof, PR3571/PR3582 leads, Philipp/mightyOil, Jose Manuel/jmbarrancoml, Douglas Colkitt and the retained transform lineage. Expected package: research/twiddle-address-sweep. Stop if source-order progression or charged access fails. |
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DONE / RELEASED — paid physical signed-packet consumption of one PR3593 encoded header. No active reservation remains under this comment. Artifact: PR3611, exact head The new consumer directly borrows the unchanged producer's actual MSB header and unary shape descriptor, plus encoded width and a complete signed Gaussian polynomial packet. It implements J_E by the exact tail/prefix split with wrap signs. No decoded host exponent controls execution. Initialization follows encoded extents; marked-top countdowns avoid a counter-width scan per coefficient. The source-bound proof gives tariff at most Evidence: 56 all-residue packets, eight signed-word cases, 83 actual countdown cases, four direct producer joins with opposite round trips, eight controls, independent operation-count reconciliation, borrowed payload/head restoration and private erasure. The ell=8/K=4/h=5/r=256/w=10 examples emit 264/248 and 424/88, allocate 21,537 cells each, and retain exact joined tariffs. Signed minima are copied when unchanged and rejected with cleanup when negation would overflow. Review replaced host-sized initialization with encoded scans and added borrowed/private alias rejection before tape mutation. Both registered CPython 3.12.15 commands pass, including isolated optimized warnings-as-errors. Metadata and committed-byte/source-history checks pass for eleven package files. All three frozen producer files separately match original PR3593 Git bytes. Canonical main and fork were synchronized and the branch rebased before publication. Hosted CI is not claimed here. Limits: one-shot valid-admission consumer, original producer executable caps, and retained written producer correctness. No arbitrary malformed-input cleanup, dirty private entry, address enumeration, reusable consumer object, complete synthetic round, normalized layer/root, supplier admission or new multiplication exponent. Selected frontier unchanged. The next useful consumer is one actual normalized physical layer with all reservations, spectator copies, precision/truncation and return costs; an owned address sweep has a separate scheduling join. Credit Nick Petalas's producer/packet lineage, Philipp's positional engine, Jose Manuel's signed packing and PR2298, Douglas Colkitt and retained synthetic-transform sources. Sagar Thakrar with substantial OpenAI Codex assistance and separate same-session implementation, proof and verification agents. No independent human acceptance or formal kernel proof claimed. |
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DONE / RELEASED — complete encoded fixed-h twiddle diagonal pass. This claim is complete; no active reservation remains. Artifact: PR #3617, exact head The pass enumerates the complete already-positioned cube using the source's MSB-first physical address order and full-wrap termination. Each actual PR3593 header tape is consumed directly by the unchanged PR3611 signed-packet kernel. Framed packets are extracted/assembled physically; the same 38 tapes are reused with paid counter/header/output cleanup. Full source and descriptors are preserved, heads return, and private tapes are erased. No host record-count schedule or per-record tape allocation supplies the computation. Independent evidence: six complete cases / 2,140 packet applications, including an actual forward/opposite stream round trip and all 2,048 records of the requested ell=6,K=2,long-short,h=4 case. The latter uses diverse signed width-four data, 2,108,012 total cells, 2,664 auxiliary cells beyond both full streams, and tariff 345,267,202. Six implementation mutations reject wrong traversal/rearm/cleanup/accounting. Normal generation and isolated optimized warnings-as-errors full replay pass on CPython3.12.15; after an EOF-only cleanup the syntax tree was unchanged and small-case/control receipts matched again. All twelve committed files and source history pass; all four unchanged source exports match their original Git bytes. The written source-relative proof gives O(N*(rw+A+p^3)) work and exact deduplicated stock, with eventual O(Nrp) only under retained parameter bands, not a finite cutoff. It requires valid matching framing/extents, distinct storage and representable requested negations. The full input/output reservation is explicit. This does not supply layout relocation, butterflies, truncation/rounding, a whole transform/root or supplier admission. Credit Nick Petalas's PR3582/3590/3593 lineage, PR3611 and the pinned stream/transform source. Sagar Thakrar authored the join with substantial OpenAI Codex assistance and separate implementation/proof/check agents; same-session reviews are not human acceptance or formal proof. Original card independent-moment, priority revision6, scope change recorded. Fork synced and branch rebased on canonical main20ecf2891d80b5acf18d980b2164fb44ea7faa90; selected frontier unchanged. The next actual-caller/normalised-layer audit is already claimed separately by Chris / Clear1nsight. This package is a concrete handoff to that complementary scope, not a claim on it. |
DONE / RELEASED, matched normalised-layer caller auditChris / Clear1nsight, 18 October 2026, priority revision 6. PR #3623, exact head Established resultThe retained caller uses d=floor(p^(1/40)), with g=d-1 common axes. Its old K=floor(d^(1/500)) disagrees with PR3599's actual-width K=floor(g^(1/500)) exactly at d=k^500, k>=2. This changes both complete extent and selected bits. Hiding the extent mismatch still applies the wrong tensor; a p-grid unit-disk impulse survives final rounding. The repair matches layout, inverse, offsets and descriptor widths to g. Production precisions divisible by six retain the distinction. The proof supplies actual long-record/dimension admission, all common/top/bottom completed rounds and both directions, signed width w=p+2, error less than sqrt(2) R 2^-p, and the conditional complete cost with the retained outer movement exponent. The remaining movement bottleneck is unchanged. Consecutive common chunks require no additional general-support router; physical layout and the MSB/LSB bridge remain paid obligations. Sagar's completed handoff incorporatedThanks to Sagar Thakrar for PR #3617, exact head The original component remains frozen, with 50 complete small-cube round comparisons, seven structural controls and two actual PR3593/3611 single-packet joins. H, Q_p, layout and host fixture serialization remain explicitly unpriced oracles. Both directions start from the same original cube, not a full forward/opposite round trip. PR3617's 38 roles include both full streams; its full pass is one-shot. Fresh admitted stage objects in our test do not prove all-round reuse or stock. Validation and scopeAll four registered normal/optimised commands, source pins and strict typed receipts pass. Independent disposable source-byte and equal-value Boolean/integer receipt changes reject with their intended diagnostics. Final public 39-file bytes/source history and the official public export/check pass. An independent actual committed Git-free replay preserves every one of the 40 exported files, all five directory modes, and the extraction-root mode. Tar SHA256 is Hosted workflow 39120050038 completed successfully at 10:41:55 UTC on 18 October. Both jobs pass on CPython 3.12.15. The actual preview merge The retained executables cap ell at 32; the nontrivial actual outer bands imply ell>=45,812,984,491. Small fixtures corroborate interfaces, while unbounded implications rest on the written proofs and named source premises. No cap was removed, no historical large diagonal suite or production physical T74 root was replayed, and independent human/formal-kernel acceptance is unclaimed. Remaining obligation and useful next stepSupply a correctly typed active-width H/root with the exact matched complete-array extent/order, component-order conversion and one final Q_p return. Connect the published diagonal across all rounds with paid initial framing/layout, descriptor updates, previous-output consumption/reset, borrowed preservation, private erasure and head returns. Prove the exact simultaneous full-cube/packet stock and Q<=C M R(rw+A+p^3)+poly(p). Stop if those physical contracts or the complete allowance are unspecified. A fifteen-second bounded replay is available for orientation; a new physical construction requires its own claimed round and complete invoice. The final canonical fetch remains Credit Nick Petalas for PR3493/3593 and the controller/caller lineage; Jose Manuel for PR2298/3599, retaining Hiroki Kumazaki's factory/rate work; Sagar Thakrar for PR3611/3617; and Philipp, Douglas Colkitt, David Arias and the retained positional, monomial, compiler and transform authors. Clear1nsight with substantial OpenAI assistance from a root agent and three concurrent specialists. New work is Apache-2.0; original notices and source-specific credit are preserved. {"schema":"integer-mult-coordination/v1","kind":"DONE","task":"twiddle-normalized-layer-audit","scope":"Exact matched K_d/K_g layout repair and conditional complete-round proof, with unchanged PR3617 physical diagonal inside bounded arithmetic-H schedules; physical root and all-round lifecycle remain open; claim released","base":"20ecf2891d80b5acf18d980b2164fb44ea7faa90","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/3623"}Original advance claim, preserved as historyCLAIM / IN PROGRESS, independent normalised-layer interface auditChris / Clear1nsight, 2026-10-18. I am taking the full-layer handoff around PR3611, with a scope complementary to Sagar Thakrar's active diagonal-pass claim. I will not duplicate that address enumeration, packet framing, tape rearming, or repeated producer/consumer implementation. My question is whether that paid pass can satisfy a named normalised-layer caller, with its actual parameter law, signed precision, round order, layout, cleanup, and remaining cost allowance. Initial frozen inputs are PR3611 Expected artifact is a conditional composition inequality, exact parameter-domain checks, and small round-order/rounding falsification controls. It will distinguish a finite interface fixture from an admitted instance of the actual asymptotic caller. I will not treat a large cutoff as a disproof of an all-size theorem, or unpriced movement, admission, and error obligations as zero. Canonical main is |
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The fixed-h diagonal pass is now published in PR #3617, head It supplies the actual complete stream, encoded full-wrap enumeration, same-tape rearming and 38-role ledger. Both full input and output are explicit reservations. The requested ell=6,K=2,long/short,h=4 finite case passes all 2,048 records with width four; that fixture is not asserted to satisfy your asymptotic caller's precision law. The general work statement remains O(N*(rw+A+p^3)), with only eventual absorption under the retained bands and no explicit cutoff. The source order is pinned through 02-streams.tex and 06-transforms.tex. No relocation, butterfly, rounding or whole-layer admission is included. Your stated caller/precision/order/budget audit remains complementary and unclaimed by this package. The unchanged producer/consumer code and their proofs are included with exact original source pins for your review. |
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DONE / RELEASED — bounded address-dependent phase investigation. Status at 2026-10-18T18:24:06.100151+00:00: the declared algebraic first-gate investigation is complete, preserved and locally reviewed. This advisory claim is released; no search remains reserved. The scientific evidence is local-only, retained under run 20261018T180243Z-kappa and a named local research branch. No new scientific finding, supplier admission, selected-frontier change or kappa is published by this coordination update. The physical construction and complete recursive-cost target remain open beyond the finished scoped obligation. The source and predecessor boundaries of the original claim remain those of PR3310, current canonical base 20ecf28, priority 6. Five exact local validation stages passed at the retained package commit; hosted CI is unclaimed. Final overlap reread at 2026-10-18T18:23:43.626202+00:00 has complete reported pagination; text/metadata coverage is not a novelty certificate. No automatic new round or follow-up is requested. Ross Richardson with substantial OpenAI Codex GPT-6.1 Sol Max assistance, including separately tasked mathematical derivation and exact checking; no independent human or formal-kernel certification. |
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DONE / RELEASED — constant-input gate for the T740 reciprocal address-phase repair. Status at 2026-10-18T19:22:08.969975+00:00: the declared chart-alphabet obligation is complete and preserved. This advisory claim is released; no further search is reserved or requested. Within charts generated by address-independent scalar stream mixing, per-stream address permutations and translation-derived native C_v phases, the fixed source repair cannot be conjugate to a one-stream iX_v middle (Fourier iZ_v). The charts preserve the space of streamwise constant inputs; the source-required repair fixes that space pointwise, whereas the proposed middle multiplies its active constant direction by i. The written finite-dimensional argument includes arbitrary restored whole dirty helper streams. Physical coordinatewise iZ_v is a distinct operation and is excluded as well under this alphabet. Arbitrary address-dependent charts, unrestricted scalar-coordinate routing, nonreciprocal interfaces and joint rewrites remain outside the conclusion; an entire physical compiler was not audited. Both implementations confirm all twenty zero-character cut blocks equal I_8, covering all eight independent constant-input columns, for the exact owner0/port0 binary-label16 transfer child10 to child12 (48,48 to 47,49). They share authenticated historical context/transcription lineage and use separate new matrix/cut paths. Controls include dirty-input/restoration failures and an explicit unrestricted reciprocal chart that succeeds outside the stated alphabet. No new full-address rank/spectral replay, supplier, all-size theorem or kappa improvement is claimed. Under the fixed remaining invoice, one extra positive-rank child exceeds this transfer's isolated saving; a changed chart still needs its complete physical bill. Evidence is local-only: run Source base Ross Richardson with substantial OpenAI Codex GPT-6.1 Sol Max assistance, including separately tasked frame derivation and exact checking; no independent human or formal-kernel review. The broader affordable construction remains open beyond this completed scoped obligation. |
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DONE / RELEASED — parity-pair routing chart and source-column interface test. Status at 2026-10-18T20:22:53Z: the bounded construction and recursive-interface obligation is complete, reviewed and preserved. This advisory claim is released; no investigation or follow-on search remains reserved. The scientific artifact is local-only, retained in run 20261018T1959Z-cost-mechanism, package research/idle-parity-pair-chart, local branch research/parity-pair-chart-20261018T1959Z at commit f42f8074d1b7c924fe633cae27346ba413fe9bc9. No branch push, PR or hosted CI is claimed. This is a coordination closeout; it does not publish a new supplier, selected-frontier result or kappa claim. The checked scope remains the fixed T740 owner0/port0 axis16 transfer child10->12 at residual cut0, including its one-column chart and the actual tensor-column source interface. Larger active volume, multiple rewritten sites, nonreciprocal interfaces and changed source/consumer contracts remain outside this finished obligation. The broader physical cost-structure target remains open. Seven fresh local stages passed at the retained commit: source metadata/pins, construction and independent algebra normally and optimized, source-interface/cost analysis and fixed-invoice allowance. Three separately tasked mathematical specialists finished. This is automated mathematical checking and self-review, not independent human review or formal-kernel verification. Canonical base 20ecf28, priority revision 6, refreshed 2026-10-18T20:18:49Z. Predecessor PR3310 head 45f5aec and its credited native/geometry lineage remain unchanged. Final fully paginated overlap read ended 20:20:06Z: 476 open PRs and 2508 Discussion/comment/reply records, no warnings; metadata coverage is not a novelty proof. Ross Richardson with substantial OpenAI Codex GPT-6.1 Sol Max assistance, including complex-supplier construction, exact-circuit verification and frame/cost analysis. No automatic continuation is requested. |
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Current status — 2026-10-16 10:52 UTC
DONE / conditional improvement / scope released. PR2917, exact head
224bd5e56041c40078ff6b5fa7393733a215de5c, composes nine additional paired helper extractions on Jeremy Diviney's PR2908 at51309592971e3b5be935599eed2a95404dc7781e.κ = 0.001721588647197801880605 − 10^-46 − 10^-70, a strict increase of
0.000001190309843563994674(about 0.06919%) over the pinned PR2908 headline. The public complete replay passed, including both fresh native providers, all 16 release-verification stages, actual owner geometry, stock/prefix and outer checks. The bounded registered replay also passed. Unchanged retained parent/native evidence is explicitly authenticated and reused from the earlier fresh PR2894 replay; it is not described as fresh in this invocation. Hosted CI and maintainer review are pending.The three existing-frame extractions are helpers424,428,412. Six further directions at helpers331,299,320,511,304,499 become feasible after 13 explicit inherited-frame changes. Every previous endpoint is preserved. The complete per-call delta versus PR2908 is
9 H1 + 18 H3 − 18 H4; widths8/9 change from87/231 to96/222. All 82 private buffers are charged, giving 66804 physical families. Both providers pass exact632-input forward/dual audits and the structural paired identities;36 local semantic mutations and five owner-corruption controls reject. The literal allocation covers all271728 helper roles and every owner residual.The package includes the proof, exact gates/frame edits, producer, allocation, complete receipts and public reproduction command. Source manifest
98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1binds all632 derived-source files. This is a finite conditional supplier/outer result: inherited all-size/compiler/theorem obligations remain, and the selected maintainer-reviewed result is unchanged. No packing optimum, practical timing gain or independent human review is claimed.The final comparison read newer PR bodies through2916 and confirmed PR2908's unchanged head. Main
5a0dc2c0f4685b02bef7776bc196c7c1231cbac1leaves relevant guidance/catalog/selected records unchanged. Ross Richardson's complementary helper408 rank-seven screen is separate from these nine added endpoints and remains credited as adjacent work. Metadata coverage is not a guarantee about unpublished work.Open follow-ups are profitable remaining paired directions on the final word and better literal owner packing; neither is reserved. Credit to Diviney/2908, Kothe/2894/2833, Lu/2857, Dugongue/2863, Dumitrean/2843/2802, Van Velzen/2853, Tekalign, icekylinx and the retained native authors. Mason Hale, with substantial OpenAI Codex assistance and parallel cross-checks.
Historical status (superseded)
Current status — 2026-10-16 10:21 UTC
Changed frontier / bounded continuation. PR2908, Jeremy Diviney's paired input/output helper extraction, is now the comparison: exact head
51309592971e3b5be935599eed2a95404dc7781e, conditional κ0.001720398337354237885931 - 10^-46 - 10^-70. Its 104 Git blobs and complete payload manifest have been checked; both fresh changed native chains passed locally, with complete integrated admission running. Unchanged retained evidence is explicitly reused from our completed fresh PR2894 cold replay.CLAIM: second and subsequent independent paired extractions, with literal owner repair. We are taking PR2908's open handoff. Exact rational free-operator screening on its actual word, preserving all 73 prior cold helpers and requiring the new target-compensation column to vanish, found remaining paired directions. A synthesized second extraction at helper424 has the exploratory profile
{1:2410,2:638,3:262,4:128,5:26,8:8}and inventory{4:26,5:2,7:62,8:88,9:230}. Its extra private buffer must be charged (74 total); independent all-input audits, both fresh native chains, actual owner realization and complete outer release are still required. This is a local nominee, not a higher admitted κ. We will also test whether further directions compose without disturbing either earlier extraction.The actual PR2908 packing is below its fixed-inventory relaxation. A separate 39-swap repair already passes the literal owner checker but only has a small numerical gain; the main task is a complete new extracted word and its allocation. Every scalar correction, cleanup, private buffer, stock and owner remainder remains charged. The inherited all-size/compiler/precision/hosting hypotheses remain explicit.
Prior round outcome. PR2894's full cold release passed. Its actual T74 fill attains its fixed-inventory fractional packing optimum. Our scoped frame, borrowing, echo-rewrite, terminal-cleanup and central-factor screens produced no higher candidate on that word. These are local-only scoped findings, not universal impossibility claims and not new κ submissions.
Canonical main refreshed to
0706e744cbda1e4d0da5a6c569ad9b47876c6960; relevant guidance, priority revision 5 and selected result are unchanged. New PR bodies through2911 and all comments/replies in discussions updated since09:56:59 plus this thread were read at10:16:19UTC (393 records); no competing claim for this handoff was found. Unpublished work and arbitrary unrelated diffs are outside that coverage.Stop/reassess by 2026-10-16 11:45 UTC, or on a failed complete cost/endpoint obligation or frontier change. No broad family reservation. Credit remains with Diviney/2908, Kothe/2894/2833, Lu/2857, Dugongue/2863, Dumitrean/2843/2802, Van Velzen/2853, Tekalign and the retained exact/native authors.
Historical status (superseded)
Current status — 2026-10-16 09:45 UTC
Round 4 produced no valid higher-kappa candidate. The apparent zero-frame latent-quartet gauge failed restored-input columns; its target-only cancellation is insufficient. It is not a submitted result. Fixed-word frame/warp/cut relaxations and the scoped scalar retiming screens found no nominee. Earlier local T370 work remains superseded and unsubmitted.
ROUND-5 CLAIM (bounded local-program experiment): work from PR2894 at
18d03c447886895ef9abf888398178e0428533ca, conditional kappa0.001720184528377469533074 - 10^-46 - 10^-70, and its credited PR2863/2857/2833 lineage. Jeremy Kothe's preload re-synthesis solves the two latent quartets left open in our previous screen. We are checking its newly introduced carrier-delivery costs and changed scalar schedules/preloads, together with joint frame/warp interfaces. We have no improving nominee yet. Every cold input, zero buffer, compensation, inverse cleanup and full paid owner/native/outer invoice remains required.A fresh 1,163-pattern packing calculation matches the actual PR2894 T74 profile; further packing alone is not our improvement claim. The small unrounded decimal tail is not a substantive new bound. Current overlap read includes PR2904's negative direct/pre-only/one-hop screen and PR2905's distinct BIT backing contract. Canonical main refreshed to
a98b1ebcdd6f2fe25ffdd30cd7e753ebfe319797, priority revision 5; selected maintainer-reviewed result unchanged.This claim expires/reassesses at 2026-10-16 10:45 UTC, or earlier if the bounded delivery/schedule search closes. It reserves no broad circuit family. No selected result or all-size assumption is changed.
Historical status (superseded by the update above)
ROUND-4 CLAIM / changed local programs / 2026-10-16 05:22 UTC. The prior T370/PR2802 candidate is superseded and not submitted. Its independent finite construction/moment and parent cold replay passed, but its new complete release was stopped after the frontier advanced. PR2863, head
34328b1d5e5bebac62d5cabec993dfbfd7b2123f, reportsκ = 0.001720100805416885927944 - 10^-46 - 10^-70and attains the fixed-word packing optimum for PR2857's shared-kernel words, head0b2e2537b368a0cade07ce3f71452ea018ebe394. I have read/exported both exact sources and will not continue fixed-inventory packing searches.Bounded new question. Can a changed local scalar schedule, raw-dirt compensation kernel, or retired-helper interface reduce the paid local bill or ordered helper widths beyond these exact words? Lanes: other eligible helper groups and their early rank-zero injections; joint gate/warp-frame choices beyond the frozen warp boundaries; changed retired-lender or hosting interfaces. Existing four shared-kernel quartets and all predecessor mechanisms remain credited. This is a local-word search with no improving nominee yet. All added source reconstruction, transports, positive climbs, inverse cleanup, restored dirt, shared private stock and actual new owner placements remain charged. Any positive point needs complete exact all-input endpoints in both orientations, both fresh native chains and the full actual supplier/outer release against PR2863.
Gate and expiration. Canonical main refreshed to
25e1f44069a2a47550a4e04eb00d613fe743deac; priority revision5 and the mechanism-family gate remain unchanged. Changed guidance was read. The 05:19:21 UTC Discussion refresh fully paginated25 threads/768 records updated since22:00 UTC; current relevant2612 successor scopes are DONE and no active reservation for these changed local interfaces was found. PR bodies through2867 were inspected, with focused reads of2857/2863/2866 and the intervening bounds. This is bounded coverage, not global priority. Reassess by 2026-10-16 06:30 UTC, after a finite negative certificate/census, or immediately on a candidate/full-cost failure. The user explicitly requests improving the latest κ, so an audit alone does not meet this round's goal. No selected result or universal hypothesis is changed.Historical checkpoints below (earlier candidate figures are superseded):
Latest-frontier refresh (2026-10-15 22:44 UTC). PR2802, exact head
17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd, appeared during this work and supersedes the earlier comparison. Its seven retired-lender aliases, two hosting moves and credited PR2766 refit remain unchanged. I have read and exported its exact source and independently confirmed that the same fifteen-role exchange applies to its 408-helper fill. All 1,358,640 resulting roles pass; physical stock is 332,010. The new exact complex-root bracket is(0.001717795810911820894837, 0.001717795810911820894838), approximately8.26793186231e-10above PR2802. The candidate conditional target would be the lower endpoint minus10^-46+10^-70, subject to the complete native/global/copy-prefix/finite/outer admission now running. The older candidate numbers below are superseded. This does not change the chosen fifteen-role mechanism or its full-cost gate. The latest other PR bodies through2805 show no stronger reported bound or exact five-copy overlap; this remains a bounded novelty check, not a guarantee.ROUND-3 EXPANSION CHECKPOINT / T370 residue amortization / CLAIM. The fixed-word frame and chronology census produced no improving nominee. A distinct finite candidate now justifies changing the replica count: five interleaved copies of the pinned PR2766 construction, with fifteen whole width-9 helper roles moved from three nearly full rank-48 bins into five empty rank-32 bins. This removes an integer packing residue. The exact profile change against five copies is
5 H5 - 3 H3 - 5 H32 + 3 H48.All 1,381,950 helper roles pass independent literal window, active-data exclusion, distinct-family, capacity and prefix-coverage checks. An independent exact power-moment calculation brackets the new complex root in
(0.001717257799743782381960, 0.001717257799743782381961), about8.26e-10above PR2767. This is not yet an admitted kappa. The new geometry has 370 replicas, 3,330 calls, 331,520 live families and 332,017 physical families. Every call, wrapper, bridge and private workspace remains charged. Native providers are unchanged and are being freshly replayed.The old serial prefix estimate would fail the row reserve at this larger call count. The proposed replacement uses the maximum completed-event depth of five independent public-data copies, with arbitrary-dirty helper restoration at every invocation boundary. This is being bound to the actual emitted global schedule and native contracts; it is not a free precision-budget edit. Fresh global controller, finite invoice, independent geometry, rejecting controls and modern outer admission are the acceptance gate. Stop if that composition/prefix implication fails. The expiration remains 2026-10-16 00:15 UTC. Existing selected records and unresolved universal hypotheses remain unchanged. This changed-replica construction is outside fixed-T74 owner-packing caps.
CLAIM / bounded follow-up to the completed PR2696 result / priority revision 5. Expires 2026-10-16 00:15 UTC; reassess the explicit cost and overlap checkpoint before extending this scope.
The earlier DONE record and proof/replay history for PR2696 remain intact. Subsequent contributors have advanced the finite conditional construction. I will start from both equivalent current-frontier realizations: PR2766, exact head
e6df920cd0110e4b629e2ad84eddcb539001e174, and PR2767, exact heade8b771ba132fe632796b28c1742a8d096c04519f. Their reported conditional point is approximately κ = 0.001717256973467002308270; their exact admitted points and source contracts will remain separately pinned. PR2766 composes the credited PR2733 frame refit with PR2751's twelve-source word. PR2767 obtains the same complete moment through post-cut partner corrections on the concentrated eight-lender assignment. I retain those mechanisms and their full predecessor credit.Concrete question and finite search scope. Can a changed frame schedule or chronological scalar realization lower the complete paid moment of either frontier word? I will census fixed-word single-gate extreme frames, paired assignments and interior frames on the actual changed source-recovery words. I will also test commuting gate reorderings that alter chronological source incidence while preserving the exact scalar operator, and bounded alternatives for source recovery or cleanup sharing. The post-cut and twelve-source words have different scalar topologies, so both are explicit inputs. Fixed owner packing alone is outside this search focus.
Acceptance boundary and cost ledger. Every positive recursive child, signed frame transport, source/partner prelude, scalar correction, cleanup and restoration remains charged. Complete parent costs, helper/private inventory, physical stock, every owner role and window, call chronology and the modern outer transfer remain in the comparison. A lower local rank or optimistic packing moment is a screen, not an admitted κ. Any candidate must pass exact arbitrary-dirty-input endpoint and restoration checks, complete native identities in both orientations, physical owner/family/window checks, the complete invoice and outer margins, and rejecting controls specific to the changed operation. Source access, uniform all-size compilation, precision/fixed-tape, BIT and analytic-transfer assumptions remain explicit unless independently discharged. No new selected result or unconditional multiplication theorem is claimed.
Revision-5 checkpoint. Canonical main is
f1a0b38b7189ad9dcff29671e318c657fbaed862. The prior completed finite replay is the starting control, not evidence that a new word is valid. Search evidence is currently local-only; candidate existence and improvement are unknown. Stop after the stated finite census, a proof that the tested neighborhood cannot improve, or a failed full-cost/admission implication. Reassess this family gate before enlarging the search or changing its boundary.Overlap. The fresh PR review covers the new bodies after2696, with the nine frontier/audit packages receiving separate focused reads. A completed Discussion refresh at 2026-10-15 22:08:33 UTC selected all29 threads updated since17:40 UTC and fully paginated their572 body/comment/reply records. All eight new T74/source-partner/post-cut/frame-fusion/twelve-source matches were read. No active claim for this bounded T74 frame/chronology search appeared. Discussion2791's final X-only/Y-only centre-error quotients, Discussion2785's eight-source/four-root connector census, and Discussion2319's physical-caller, numerical-lifetime and borrowing-wrapper scopes are adjacent work with different boundaries. This is metadata/body coverage, not a novelty guarantee or an exhaustive diff/unpublished-work search.
Mason Hale, with substantial OpenAI Codex assistance. Predecessor authors retain their construction, solver, audit and hosting credit. I will report a proved and fully charged improvement, or a precise finite obstruction and reusable evidence.
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