Conditional kappa 0.001000220224856110: six fixed levels on #390

[rohanarun]

Conditional κ = 0.001000220224856110 (100022022485611/10^17), exactly 983291/(5*10^17) = 1.966582e-12 above #390. This is a small finite-bootstrap and arithmetic refinement of Dugongue's new supplier, with no circuit, bank, helper, fallback or physical-invoice change.

The branch builds on #390 at 0e790f2dfb64e17bdee154aee151bb0c1dddb28e, plus research/e8-prefix-bootstrap/ and its workflow. Its packaging is repaired: #390 committed a pr352.rar in place of 104 files required by its own manifest. This branch restores those exact SHA-256-pinned files from the prior supplier snapshots and removes the unlisted archive from the package. All 296 source files and the original manifest now match the intended source bytes; no supplier code or mathematical value is changed. All target-prefix, dirty-preconditioning and heterogeneous-bank gains belong to #390 and its credited contributors. This does not claim those mechanisms as new work here.

The same paid complex profile is enclosed by two independent rational moment engines between 0.001001221667017025386926 and 0.001001221667017025386927. The full positive 10^-16 fallback remains. Our #387 fixed-depth extension of the reviewed #185 mechanism uses exactly six acyclic ordinary-bootstrap levels, beta=eta=10^-18, and saving (1-beta)*b-10^-24. Every level has positive atom, borrowing, remainder and stock gaps with an explicit finite-cutoff formula for any fixed dominating constant.

All 47 strict outer inequalities, six invalid-parameter/cutoff controls, both exact moment enclosures, and the strict next-grid ceiling pass locally. Even the certified upper moment root u satisfies u/(1+u) < κ+10^-18; extra root digits or bootstrap levels alone cannot reach the next tick in this formula and paid profile.

Validation completed on Python 3.11 and 3.14: GitHub Actions run 38121315906 passes at commit ac55c57035c197f744390fe4bc9cf49df1b61816. Both saved RESULT.json artifacts report PASS_FULL_PR390_REPLAY_AND_FINITE_BOOTSTRAP: all twelve #390 stages ran afresh, the emitted profile and finite invoice matched, both exact moment engines agreed, all 47 strict outer constraints passed, and all six invalid-parameter/cutoff controls were rejected. Both runs certify the stated κ and strict next-grid ceiling. Expected records were compared only after execution; they did not replace it.

The initial source-integrity failures are resolved by restoring the 104 missing manifest-pinned supplier files described above. Every upstream byte is checked before and after execution. All 58 GitHub checks pass at this commit, including the broader repository matrix. Full CI artifacts preserve the replay outputs and logs.

Reproduce with the unchanged #390 dependencies:

python -m pip install -r research/e8-prefix-restoration/requirements.txt
python -B research/e8-prefix-bootstrap/verify.py /fresh/output

Requires C++17 and Boost headers as #390 does. The three joint-dual metadata files carry the previously verified #318 source-pin repair without changing mathematical values.

Scope: finite conditional witness. All #390 all-size local-identity, compiler, arbitrary-dirty banking, owner-route, fixed-tape, common-grid, precision/recovery, restored-row, nine-centre bit, degree-two and analytic interfaces remain assumptions. The prior #185 review covered three levels; the new six-level extension is stated here with its completed-leaf and spectator conditions. No new Lean theorem, unconditional multiplication bound, measured primitive constants or runtime improvement is claimed.

Credits: Dugongue (#390 construction); Rohan Arun (#185 stopped-leaf mechanism, #387 finite bootstrap/precision); applecrusher (#376), jacklightChen (#377), chafreaky (#378), DaysSky (#381 and bridged chronology), Dylan Crow (#370), Jacob Sussman, the #315 outer/moment lineage and all authors credited by the unchanged source notices. Prepared by Rohan Arun with OpenAI Codex assistance. Apache-2.0; original source licenses are retained.

[Mister-Meeseeks]

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

Contribution: Six fixed recurrence levels on prefix restoration.

Review and limits: Full source-bound supplier replay plus exact finite bootstrap. Additional packaged historical sources retain their individual review scopes.

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: ac55c57035c197f744390fe4bc9cf49df1b61816. Publication: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc.