Independent native source527 audits and four finite leaf levels: conditional kappa = 7.10046193592262e-4

[Dugongue]

Conditional κ = 7.10046193592262 × 10^-4, exactly 355023096796131 / 500000000000000000.

Adds research/source527-five-stage-crossover/: pinned source527 code, independent C++ audits, and a four-level finite ordinary-leaf assembly. The main physical improvement is #210 at 298f7c112889f799e8e2040099fbc325d0ccd0f6, combined with #234's five-stage architecture and #237's completed entrance banks. Our additional refinement over that pinned #210 value is only 2.42725e-13; the complete result is approximately 0.207% above pinned #237. Separately reported gains are not added.

Actual billed quantity	Value
Reused sources / independent dirty helpers	527 / 16,587
One-invocation paid rank mass	434,502
Independent gauge entrances	2,279
Literal replicas / separate stage collections	60 / 5
Completed banks / actual assignments	882,535 / 4,976,100
Literal stock / moment-only stock	1,304,935 / 260,987
Normalized rank mass / deficit	31,265,640 / 52,800
Largest child	50
Fully charged native selector invoice	656,433,896,400 < 2^40

The canonical native charts need 310 factors, so the larger selector invoice replaces the smaller public bill before finite absorption. Every finite cost uses the literal stock and all 60 replicas.

Validation

• Pristine source527 passes all eight mandatory stages with all 121 manifested files unchanged, including both signed integer decoders, inverse restoration, 25 corruption controls and retained-prime admission.
• Native extraction checks all 2,668,360 physical records and the entire paid histogram. The five-stage checker passes all 23,627 global F2 columns, 120 fresh copied centers and six rejected bridge corruptions.
• The route audit checks 195,744 exact coordinate equalities across 93 modules.
• Two bank implementations check all 4,976,100 assignments, 231 chart inverses and 25 normalizer templates; hostile allocation controls reject.
• Two exact rational interval engines check the complete profile, four acyclic finite ordinary levels, all 47 strict outer inequalities and the adjacent excluded κ grid point.
• The packaged verifier passes against the completed source-identical public run; every added native checker is freshly rerun, with payload hashes unchanged.

Reproduction

Requires C++20, Python 3.11+ and SymPy 1.14.0. Boost/JSON headers and licenses are bundled.

python -m pip install -r research/source527-five-stage-crossover/references/source527/requirements.txt
./research/source527-five-stage-crossover/verify.ps1 -Compiler g++ -TempRoot D:/proof/replay

python3 -m pip install -r research/source527-five-stage-crossover/references/source527/requirements.txt
bash research/source527-five-stage-crossover/verify.sh

Default verification performs a new public eight-stage replay followed by every native check. Outputs are preserved. proof/ROOT-COMPOSITION.md supplies the sufficient assembly and explicit finite cutoff rule; FILES.json pins the payload.

Scope and provenance

This retains the inherited all-size compiler, weighted/common-ancestor chart, restored-row, selector/routing, ordinary-leaf, prime, precision/recovery, complex symbolic and analytic interfaces. No new Lean certificate, unconditional multiplication theorem or practical benchmark is claimed. Public contributor and license notices remain unchanged. New native audits and assembly were prepared with OpenAI assistance.

Tested producer/Kneser redesigns did not improve the complete paid construction and receive no κ credit. The newer #210 movement-fusion head b0c058ba979c is recorded but its partial follow-up is outside this frozen release. This PR does not claim to exceed that newer headline or the incomplete priced #232 target.

[Mister-Meeseeks]

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

Contribution: Independent native source527 audits and four finite leaf levels.

Review and limits: Fresh eight-stage public replay and all seven independent C++ native checkers passed in 830s. Reproduction repairs: LF launcher, 28 omitted manifest-pinned files restored byte-for-byte, and unmanifested RAR moved outside checked root. Every scientific source and check stays unchanged; separate failed decoder experiments remain research only.

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: ef47efc3256a57bacf4273c35faf4b5148be5014. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.