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Conditional κ = 0.000711457853376510: 887 entrances and connected-block retiming - #270

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utcorvusvolat-dotcom wants to merge 31 commits into
CrocSwap:mainfrom
utcorvusvolat-dotcom:codex/crosscut-improvement
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utcorvusvolat-dotcom wants to merge 31 commits into
CrocSwap:mainfrom
utcorvusvolat-dotcom:codex/crosscut-improvement

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This improves the conditional exponent saving to κ = 711457853376510082124745 / 10^27 = 0.000711457853376510082124745, by composing 887 entrances with connected-block frame retiming.

Stacked dependency: this branch retains PR265 at fc00fcf07a554ff6847b2a8764ecc26f5a99542a, including its PR259/263 history. For this contribution alone, use the incremental comparison against PR265. Only research/crosscut-response-pairs/, its sibling evidence directory, and the dedicated workflow are added relative to that baseline. Inherited authorship and files are preserved.

Construction and result

Retain all 518 original kernel entrances and their 25 gate retimings. Add 369 early-cut response pairs, contributing 372 entrance dimensions, then jointly retime 29 connected blocks containing 57 ADDs. The latter changes the charged rank distribution while preserving total calls and rank mass. Every additional basis gate, inverse, chart and selector remains charged; the full composition is priced from one emitted word.

Quantity PR265 This candidate
Pivot entrances 518 887
Entrance dimension 1,344 1,716
Normalized stock 173,435 173,311
Normalized child calls 3,956,800 3,970,720
Normalized rank mass 20,777,000 20,762,120
Deficit 35,200 35,200

The exact gain over PR265 is 425611242438074456938 / 10^27 (0.05986%). At the prepublication check, PR266 head b2b2a33dc95eb2d4ad9ddfade6bb9416ab9ec38e reports 883 entrances, dimension 1710 and κ = 0.000711421336565136; this endpoint is 0.00513294% higher. That comparison uses its public claim, not an independent replay of its updated package.

Verification

The complete local source-to-certificate replay passes: regenerate the pinned source, recompile the unchanged native checkers, reproduce PR265, construct the new word, bind both retiming stages by full scalar-core alignment, and rerun the native and exact arithmetic checks. Evidence is included in research/crosscut-response-pairs-evidence/.

Checks cover local forward/inverse columns; all 23,627 global columns; chronological nesting and COPY lifetimes; 916 rational bases, annihilators and weighted Gram matrices; all 3,317,400 bank assignments; exact integer operand source spans; the full finite invoice; two rational moment engines; finite cutoffs; 47 strict outer constraints and seven margins; and adjacent-grid rejection. Separate reproducible audits reject nine arithmetic and six frame corruptions.

make entrance-bank-verify also passed. A broader inherited make verify attempt was stopped before completion; no full-repository-suite pass is claimed.

The transcript SHA-256 is 8593fa0359aa13b26ede7490f500f239c97d238df2730496a9ac29bcafd7b4ae.

python3 -m pip install -r research/crosscut-response-pairs/requirements.txt
python3 -B research/crosscut-response-pairs/verify.py --output /tmp/crosscut-replay

Requires Python 3.11+, SymPy 1.14.0, C++17, Boost headers and a fresh output directory outside the checkout. No network is needed for replay. Local testing used macOS/Apple Clang; the added workflow runs Ubuntu/Python 3.11 and 3.13. CI status is reported by the checks, not assumed from the workflow definition.

Attribution and scope

PR266 independently published closely related early-cut work; 316 of our 369 additions coincide exactly with its earlier 851-entrance snapshot a2b02af47dbaf3d1c55e7586746c30e851b68102. That overlap count is not claimed for its updated 883-entrance witness. PR267 independently develops chronological donor sharing. This contribution is the concrete larger composition and connected-block retiming, not a priority claim for those directions. Full predecessor credits and substantial OpenAI Codex assistance are disclosed in NOTICE.md.

The result retains the inherited all-size compiler, common weighted chart, restored-row, routing, prime-supply, precision/recovery, complex correctness and analytic interfaces. It is not an unconditional multiplication theorem, practical-runtime benchmark or full Lean proof. No global-optimality claim is made.

Dugongue and others added 30 commits October 9, 2026 01:32
…ondensation: kappa = 7.11032238200698e-4

Adds code/descent_retiming.py between cohort-transform and the seven native checkers: twenty-five internal forward-gate frames are reassigned by local descent on the concave paid-rank objective; one local recursive call disappears at unchanged rank mass 432833. The stage rebuilds every MOVE, checks the byte-identical scalar/COPY projection, nested chains, fixed endpoints, COPY lifetimes, nondegenerate bases and exact integer operand source spans; all native checkers re-examine the retimed transcript and their receipts are re-pinned. cohort-transform.cpp uses stable_sort so the emitted transcript is platform-independent.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
…etimed multicut word: kappa = 7.11032242134072e-4

PR261's refinement (after PR235/PR252) retargeted to PR263: pinned base candidate, profile and invoice constants updated; exact endpoint 711032242134072007667807/10^27, +3933374007667807/10^27 over PR263.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Thank you @utcorvusvolat-dotcom. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Cross-cut response pairs and connected-block retiming.

Review and limits: Source-bound own Linux full replay. The 887 entrances and connected moves are assessed as one physical construction with fresh receipts.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: 9b48fd73531eaf09ebbbd5acb0f7a3eb338d9a2a. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.

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4 participants