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Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting - #1148
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tomdif
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…int-entrance word At the X=439 and X=444 triangle-hybrid slot sites, replace the two-donation slot by the slot's source-holder donation with its FULL-cleanup restore plus the full read-set exchange of the copy pair, and refit all frames exactly. Entrances, ends, widths and CrocSwap#1148's T16 owners are unchanged. Local profile {1:2358,2:504,3:408,4:134,5:80,8:8}; conditional kappa 0.001675658002271934 (+9.705e-8 over CrocSwap#1148's 0.001675560947524449). The package rebuilds the word from CrocSwap#1148's word with a checked literal patch, runs audit_local, ten fusion negative controls, the native local chain and CrocSwap#1148's unchanged strict T16 admission.
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Checked follow-up: κ = 0.001675809683500501, about 0.014845% above this PR’s 0.001675560947524449. This composes X54 and the two source-holder fusions with PR1193’s 125/208 mixed T37 allocation. Overlap: Rohan Arun posted the same construction/value in #1218, and Jeremy Diviney updated #1193 to the same composition during this run. This is an independent reproduction with bounded negative follow-up searches; no new community record or priority claim. Construction, verifier, attribution and receipts · Negative-search report Local validation completed:
Further searches found no improvement: 2,238 fusion/repair candidates (2,850 evaluations), 215 shared multi-target donations, 30 paired donations, 372 single-helper entrance changes, and 700 retained commuting-reorder trials from an interrupted 14,720-case census. Six two-helper and four three-helper subsets of the fourth demotion group tie after idle credit; the known full four-helper change is the positive control. Records include limitations and reproducible scripts. These bounded screens are not an exclusion or optimality proof. Credit: Jeremy Diviney #1193; Rohan Arun #1207/#1218; Jeremy Kothe #1130 and chafreaky #1196; Marius-Paul Dumitrean #1195/#1186; Sagar Thakrar #1049; this PR’s joint entrances and all retained supplier/owner/bit ancestry. Original notices and sources are retained. Prepared for Thomas DiFiore with substantial OpenAI Codex assistance. Conditional finite construction only; inherited compiler, common-label/mutable-source realization, whole-call hosting, precision/tape/recovery, analytic-transfer and bit H1–H5 assumptions remain. Repository-wide hosted CI and an unconditional theorem are not claimed. |
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Extreme-construction follow-up: no new κ. The previous independently reproduced conditional value remains 0.001675809683500501. Reproducible research package at b7af4fa3
The structural follow-up is joint circuit/matrix-label synthesis, using the original bit contract's arbitrary rational matrix labels and arbitrary final wire permutation. An initial 40-circuit, 2×2/3×3 integer-label probe evaluates 7,813,342 proposals without a strict rank saving. That is a limited negative experiment. Network-coding constructions are proposed seeds, not claimed multiplier constructions; the limiting complex side still needs a separately justified improvement. Fresh package replay passed scalar/dual reconstruction, compensation, both independent frame obstructions and controls, scheduling controls, two-engine ceiling brackets and all matrix-label witness checks. Full search censuses are archived rather than rerun by the default verifier. No new native supplier/global admission, repository-wide suite, hosted CI, formal multiplication theorem or record claim. Credit remains with the prior X54/k8/gauge44 and mixed-allocation contributors, PR1186's frame toolkit, PR1049's endpoint checker, PR1240's relaxation, and the original manuscript's matrix-label contract. PR1238 was inspected as related end-cap research. Full attribution and source pins are in the package. Prepared for Thomas DiFiore with substantial OpenAI Codex assistance; no independent human review claimed. |
Fourteen of the 30 open claims above the selected kappa are pinned by head and blob. All obey the coverage law, and they use nine local words. No repacking of any covered word passes kappa 0.0016873148. The leading CrocSwap#1148 line sits on words whose caps are 0.17-0.21% below the selected word's; it leads by packing closer (0.47-0.52% headroom left vs 0.77-0.86%). Sixteen claims lack the needed records and are listed. No new kappa. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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100-PR batch review at This remains open after scoped triage. Next review step: Whole-head supplier review remains open for This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations. Batch review, attribution and evidence. Thank you for the contribution. |
Answers the CrocSwap#1195 review continuation point (bind the exact native providers, physical owner allocation and admission evidence, then reconcile changed predecessor blobs): - binding.py (standard library) records, from a completed verify.py run, the rebuilt word, every native artifact and its PLAN semantic identity, the bound provider directory, the owners/PLAN/SPEC hashes and the strict run's owner/profile audit, the strict admission receipt with stage log hashes, every consumed predecessor file, and the tree ids of the five inherited CrocSwap#1148 packages. --check compares the run-independent part with a recorded receipt. - evidence/WHOLE-HEAD-BINDING.json comes from a fresh run on this head (parent geometry, native chain and strict T16 admission, kappa 0.001675658002271934); a second independent fresh run and a reuse run reproduce its stable section. It also lists the six paths CrocSwap#1148's 506ea08 changed relative to e7d0d01 (records only, none consumed). - README: whole-head binding section; the branch now merges CrocSwap#1148's head.
…e k8 word with exact T37 owners Applies jeremykothe2's width-neutral X54 triangle-hybrid slot (#1130 recipe, identical edits and frames) to tomdif's joint-entrance k8 word (#1148, groups 603/611/635). The helper width inventory is unchanged, so #1169's exact T37 owner flow, owner map, windows and parent geometry are reused as-is; only the provider identity is rebound to a fresh native replay of the new word and the SPEC is re-frozen through the unchanged discovery/freeze path. Local profile {3:+2,4:-4,5:+2}; strict T37 admission passes; the all-T fixed-family signed-dual ceiling for the new word equals the attained value. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01TGoMCHAqctZe4wTb4Qr7VV
Original authors and exact source bytes preserved. Source-only intake and all remaining scientific obligations recorded in research/community-efficient2000-audit. No selected frontier change. PRs: #259, #283, #309, #379, #455, #498, #636, #638, #639, #640, #642, #644, #646, #671, #673, #676, #686, #699, #717, #746, #758, #779, #790, #794, #1043, #1060, #1083, #1086, #1147, #1148, #1150, #1154, #1169, #1176, #1183, #1186, #1192, #1195, #1201, #1207, #1218, #1225, #1238, #1286, #1297, #1319, #1407, #1424, #1464, #1485
…n k8 word with its T16 owners Applies jeremykothe2's X54 triangle-hybrid slot (#1130 recipe, identical edits and frames) to tomdif's three-demotion k8 word (#1148). The slot is width-neutral, so #1148's T16 owner map is used unchanged; the plan identities are rebound to the new locals and the SPEC is re-frozen by the unchanged discovery/freeze path. Strict admission passes. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01TGoMCHAqctZe4wTb4Qr7VV
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Change and mathematical scope
This proposes the conditional finite witness κ = 0.001675560947524449. Joint entrance choices replace eight local rank-one recursive children with four rank-two children while preserving the helper-width inventory. An exact within-call permutation therefore transfers the preceding T16 packing without another owner search.
The final local word uses demoted entrance groups 603, 611, and 635, with local profile
{1:2364,2:498,3:412,4:130,5:82,8:8}. It improves the preceding three-demotion witness, 0.001675121647789207, by 0.0262249453%. Scalar operations, coefficients, and order are unchanged. The T16 assignment hosts 69,120 whole-helper roles in 144 calls.Start review at
research/k8-joint-entrances/README.md,PROOF.md,CLAIM.json, andverify.py. The branch also includes its four additive predecessor packages:k8-coordinated-owners,k8-eight-ends,k8-eight-ends-t16, andk8-three-demotions. These retain the construction chain, eight rank-seven endpoints, source pins, unchanged admission engines, and intermediate evidence.The new exact fixed-word, fixed-inventory all-replica grid upper bound is 0.001675568675201533. It is an upper relaxation, not an achieved construction or a bound on other circuits, mixed suppliers, or recursion geometries.
The unchanged PR589 bit supplier, PR559 recurrence correction, and bit bad-residue surcharge remain. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, analytic-transfer, and bit H1–H5 assumptions remain. This is not an unconditional multiplication theorem or full Lean certification. The selected repository certificate is unchanged.
Validation
The final package passed:
PASS_JOINT_ENTRANCES_COMPLETE_ADMISSION 0.001675560947524449. Its explicit parent/native reuse uses completed fresh replays, with all consumed parent files and semantic identities rechecked, followed by local controls and full global admission.ce7ad1b6are unchanged; the remaining pinned files are predecessor packages added on this branch.Fresh reproduction (Python 3.11+, C++ compiler, Boost; choose a new output directory outside the repository):
CPLUS_INCLUDE_PATH=/path/to/boost python -B research/k8-joint-entrances/verify.py \ --base "$BASE" --work /absolute/new/output-directoryBASEis the original R480 k8 + seven-slot word pinned inresearch/k8-eight-ends/RECIPE.json. No optimization solver runs during verification. Reproduction details and explicit replay-reuse options are in the README.All 18 repository
make verifygroups completed across the initial and resumed runs, including all 87 isolated test modules and 20 patch applicability checks. This was not one successfulmake verifyinvocation: the initial system-Python attempt stopped on missingint.bit_count, and the Python 3.11 run later stopped because Apple clang rejects-fopenmp. The failed and remaining stages then passed under Python 3.11.14 and GCC 16.2.0 (continuation exit 0). No guards, tests, or tracked upstream sources were changed.evidence/REPOSITORY-VERIFICATION.jsonand three archived logs record the complete coverage and both environment failures; this regression result is separate from the package-specific witness admission above.Research scope and attribution
The search covers all 64 subsets of six individually selected entrance reductions, followed by 354 same-dimension rotation trials, a joint fixed-dimension entrance/frame search over 68 helpers, and a joint dimension-four/five plus aggregate-packing search over 56 helpers. The latter searches found no further improvement. Follow-up joint searches allowed dimensions three through five, then all 374 subspaces of each five-dimensional ceiling, on the 56 larger helpers; neither improved the relaxed exponent. Another 145 trials removed one-dimensional entrances individually, by point cohort, or all together, again without improvement. Solver output is nomination data, not an exact optimality certificate. A broader formulation over 192 entrances and 1.8 million LP variables returned no solution before its numerical solve limit; it is recorded as inconclusive, not infeasible, and yields no stronger κ.
PR1111 by seslly/shipstuff, commit
381831ea554ea983e16224dabed8921b7d0ffdbc, supplied the group-635 entrance-demotion lead. This package does not claim to originate that idea; it composes the lead with two other groups, the eight-endpoint word, refitted frames, and the preceding T16 assignment. No code or payload from PR1111 is consumed.Retain PR664's promotion mechanism, PR1018 and Rohan Arun's PR987 word lineage, PR1030's endpoint lead, PR864's frame model, Hao Yan/FanPUYen's PR858 controller and independent checker, PR870/1074 admission work, PR942 and earlier signed duals, PR589's bit supplier, and their predecessor credits. Full attribution and pinned sources are in the package notices.
Prepared for Thomas DiFiore with substantial OpenAI Codex assistance, under Apache-2.0.