Verified construction checkpoint: conditional κ = 7.110455476244e-4

[hcg890]

Change and mathematical scope

Publish an older verified construction checkpoint with conditional κ = 7.110455476244 × 10⁻⁴, exactly 1777613869061/2500000000000000. It retains 513 of PR259's 518 multicut cohorts, replaces five conflicting rank-11 quartets with seven paid closed-target delayed-inverse intervals, and applies the same 25 PR258/PR260 gate retimings once. The exact PR249 baseline and its 21 transported entrances are retained; PR251's sixteen additional entrances are excluded.

This is a checkpoint, not a current-best claim. The inspected later PR266 snapshot b2b2a33dc95eb2d4ad9ddfade6bb9416ab9ec38e reports the stronger same-model conditional bound 0.000711421336565136. That separate result is not substituted into this checkpoint's inputs or certificate.

The resulting forty-replica physical word has stock 867,045, 19,786,600 paid children, rank mass 103,869,400 and deficit 176,000. The finite coefficient is 62,644,197,182,478,801. Scalar, movement, copied-center, selector, normalization, fallback and ordinary-cutoff charges are included. The payload contract is F₂ with separately charged chosen signed-lift prefix majorants; it does not assert equality with the old signed-integer endpoint.

The result remains conditional on the inherited all-size compiler, common-ancestor/GL-cover charts, restored rows, routing, prime supply, precision/recovery, complex-symbolic/analytic interfaces and inherited-constant cutoff. No practical runtime or global optimality claim is made.

Validation

On 10 October 2026 the frozen source archive freshly passed all eight mandatory standalone stages, exit 0 in 580.9 seconds, with Python 3.14.2, SymPy 1.14.0 and assertions enabled. All 143 source files remained unchanged. The run passed 25 scalar controls, six prime controls and eight omitted-stage controls; it checked all 770 bank chart IDs, 3,317,400 assignments and 200 full namespaces.

The reviewed public closure has exactly 137 files and preserves all 117 retained numerical pins. Its cleanup removes unused historical files and changes documentation only. The numerical execution evidence belongs to the original source freeze; this is not a second full execution of the extracted public tree. Its manifest is 0af10dcca505cbd913cf1b9220a08b6a62687650ace4e3d1efd093e828e3990e; the tested source manifest is 9f6d8637b9a119cfe4566a02ab2d704f23c502e5e4357b40c28ef85a3fd4de89. The included generated certificate has SHA256 7eb58ec449c932b7092481746390c776365f302a742836cddef5643c0351802b.

Source and reproduction instructions, proof, bank proof, and certificate.

Lineage and credits

The selected kernel witness is Dugongue's PR259, with the earlier PR254 credited as ancestry. eumemic's PR249 supplies the source527 baseline and entrances. amanforindia's PR258 and Rohan Arun's PR260 independently identify the same retiming gates and replacement subspaces; they are credited together and applied once.

Henry Grant's PR234 supplies the source-bound five-stage architecture and finite interfaces; Rohan Arun's PR237 is a prior width-120 bank extension. Jacob Sussman's pinned five-stage certificate, Avi Eisenberg's PR193 complex-helper lineage, source527 contributors and the original OpenAI framework remain credited. HERITAGE.md records full author/source boundaries, inherited notices and licenses. The seven-interval composition and checks were assisted with ChatGPT. Attribution does not imply endorsement.

Relevant negative results

NEGATIVE-RESULTS.md records reviewed bounded findings, with their evidence limits:

• Directly combining all 518 cohorts with the seven intervals violates the helpers' unchanged entry contract at five quartets. All sixteen additional PR251 entrances also conflict with the fixed PR259 selection.
• PR258 and PR260 supply one shared 25-gate retiming, rather than two increments. Applying it twice fails old-frame checks.
• The fixed high-frame inverse family loses after target paths are charged. Delaying the inverse changes the family; it does not contradict that exclusion.
• Fixed-subset and larger-cohort screens are limited to their stated cuts, witnesses and prices. They do not establish global optimality.
• Persistent transforms, lift/contraction identities and the 79-factor address router do not establish an admitted supplier or κ improvement under the present full cost model. Their separate finite checks are reported research evidence and are not rerun by this construction verifier.

[Mister-Meeseeks]

Thank you @hcg890. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: Public delayed-inverse construction checkpoint.

Review and limits: Fresh complete public-package replay passed in 587s, with unchanged source pins, scalar restoration, geometry, banks and strict assembly. This validates the public checkpoint, not merely the author's earlier private freeze; conflicting moves and shared 25 retimings remain correctly excluded.

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: c2f07d311bfdad0d89bf961e4da133ee97bb78de. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.