Conditional kappa 0.001018766833114736: checker-clean chronological gauges and R767 reuse

[ai-nanachi]

Change and mathematical scope

Raise the pending conditional candidate from PR #389's 0.000998634658090834606116833 to 0.001018766833114735805248075, exactly
40750673324589432209923 / 40000000000000000000000000.
The complex supplier now binds; the target 0.002 has not been achieved.

Reconstruct our R779 complex word and compose the credited shared-donor, re-pivoted, enlarged and ordered entrance constructions. The resulting word has 202 entrance gauges, dimension mass 360 and 551 chronological unit shears. Both unchanged gx.check1 and gxcore.mirror pass. An incompatible target-124/125 transfer is excluded. Chronological omission controls use the literal suffix response and read-before-write invariant; they do not assume that the complete ordered entrance product has square-zero off-diagonal part.

The R767 bit word contains 55 clean-reset reuses and 54 legal frame moves. Every newly allocated helper retains an independent arbitrary dirty column. With the same new complex supplier and the old bit word, the exact fair-control candidate is 0.001016774267814750149837485; the bit changes improve the composed candidate by 199256529998565541059 / 100000000000000000000000000 and remove that bottleneck.

Update the README, proof, contributor/source credits, research record and pending candidate certificate together. The selected maintainer certificate is not promoted. Preserve the frozen PR #389 package and bind the new witnesses and original vendor bytes by manifests. Three separately scoped exact negative proofs document limits of frozen-center bases, arbitrary rank-eight completions, and fixed first-frame/full-residual bank budgets; none asserts a global impossibility for changed architectures.

This is a finite conditional witness. The all-size compiler, recursive suppliers, compressed Clifford windows, correlated dirty-bank/cover, restored-row, routing, fixed-tape, precision/recovery and analytic interfaces remain assumed. No unconditional multiplication exponent or Lean formalization is claimed.

Credits: applecrusher/Sussman E8 lineage and PR #376; prefix/signed work in #390/#395; Dugongue's response-space/shared-donor work in #401/#404; ordered/enlarged constructions in #409/#410; chafreaky's checker-clean re-pivoting and composition in #412; and the preceding bit/global/outer sources listed in SOURCE-PINS.json and the preserved notices. Prepared by ai-nanachi with substantial OpenAI Codex assistance; Apache-2.0.

Validation

The complete public replay passed locally: full frozen predecessor, reconstructed R779 intermediate, composed chronological word, 6,482 freshly recomputed old/new/reflected Gaussian phase pairs, all 1,019 complex and 1,007 bit local columns, all 1,487 bit global columns, native address phases, physical bank ownership/readback, finite invoices and reserve bridges, two exact rational moment engines, all 47 strict outer inequalities and adverse controls. The selected gen4 full replay and the affected historical joint-dual replay also passed. Independent scope review re-ran both original complex checker families and checked the candidate record.

Reproduce from a clean checkout with Python, C++17 and Boost:

python -m pip install -r research/e8-clean-reuse-extension/requirements.txt
python -B research/e8-clean-reuse-extension/verify.py /absolute/path/to/fresh/output
python -B research/e8-clean-reuse-extension/record.py
python -B research/e8-structural-frontiers/verify.py /absolute/path/to/another/fresh/output

No network, discovery search or cached phase admission is required. The committed Git blobs were checked against every package manifest, including the frozen predecessor; all 158 imported upstream blobs also matched their exact original bytes.

Linux CI passed on the current commit: full Python 3.13/3.14 replay passed both jobs, and 52 historical regression jobs passed all 52 jobs. Both runs bind commit 88d552526893cd15325948bb1487e9a4d4bf32f6. CI was running at submission; this paragraph was updated after both runs completed successfully. An earlier CI attempt correctly rejected Git-normalized witness bytes; the subsequent commit preserves those bytes and passes the complete blob/manifest checks. Maintainer review remains pending. Upstream pull-request workflows are awaiting maintainer authorization; these passing runs are on the fork and do not constitute maintainer approval.

[Mister-Meeseeks]

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

Contribution: Chronological gauges, helper reuse and structural negative results.

Review and limits: Both unchanged legacy checkers and the native construction are assessed on this exact word. The three negative results retain their fixed-basis, completion and endpoint restrictions.

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: 88d552526893cd15325948bb1487e9a4d4bf32f6. Publication: 64039f1bd3b6a523b96083fd858ad040a75e3030.