Conditional κ = 7.49982571369270e-4: fixed-prime eight-level transfer on #300's gen5b-full package (+4.1e-12)

[rohanarun]

Conditional κ = 749982571369270160072237/10^27 = 7.49982571369270160072237e-4, +4.10 × 10⁻¹² over #300 (7.49982567267028e-4). A small arithmetic refinement at the same word and the same conditional interfaces, not a new coding mechanism; the bit side still binds (below #233's complex supplier).

One self-contained package, research/five-stage-gen5b-full-fixed-prime/, on #300's branch; no existing file is changed. #300's complete five-stage-gen5b-full package (150 files, commit aea3dc9, upstream-files.json) is vendored unchanged under source/.

Full replay: PASS (verify.py --output, 369 s): the vendored #300 verifier end to end (all twelve stages fresh, κ 187495641816757/250000000000000000), then prime_eight_port.py on its fresh certificate.json/finite.json/primes.json/banks.json, compared key by key with the committed certificate.json.

What it is

jacklightChen's #293 port (on #291) of the fixed-prime / eight-finite-level method (Nespoli #235, Arun #243/#261/#265, sennemmi #253), re-pinned to #300's actual costs: q = 2¹²⁷ − 1 (Lucas–Lehmer residues checked), ρ = 3,456,000/q, the entire 32m² rank-one fallback, two exact interval moment engines, eight finite acyclic ordinary levels, η = 10⁻²⁴, β = 10⁻⁹, all 47 strict outer constraints and seven margins; adjacent coarse/final 10⁻²⁷ points rejected by both engines, the old fallback density rejected at the new rate, four foreign fee vectors and a cyclic eighth level rejected.

Complete paid transfer: 60 physical replicas; literal stock 1,229,680 = 5·W (W = 245,936); literal children 28,973,400; rank mass 147,297,600 (normalized 29,459,520, deficit 52,800, max child 50); 910 charts, 4,627,800 bank assignments, normalizer bound 815, selector calls 905,935,487,400 = 2·5·60·((1,229,680 − 1) + 15,426·120·815) < 2⁴⁰; q-power coefficient 90,408,185,853,299,401 < 2⁸⁰ < q, internal row coefficient 14,401; maximum determinant 118 bits.

Verify

python3 -m pip install -r research/five-stage-gen5b-full-fixed-prime/source/requirements.txt

python3 -B research/five-stage-gen5b-full-fixed-prime/verify.py --output /tmp/gen5b-full-fixed-prime-verification

About 7 minutes; prints PASS complete gen5b-full fixed-prime eight-level reproduction with κ. --check-package checks hashes and syntax only.

Scope and credits

Exactly #300's hypotheses and conditional interfaces; no Lean build (methods/Prime.lean is #293's sketch, retained unchanged). Method: Nespoli (#235), sennemmi (#253), jacklightChen (#293, the package form reused here); the supplier is #300 (rohanarun, composing chafreaky's #296/#295, DreamingOfClouds, utcorvusvolat-dotcom, Dugongue, eumemic, hcg890/Jacob Sussman, Evan McKinney; see source/NOTICE.md). Prepared by Rohan Arun with Anthropic Claude assistance; Apache-2.0.

🤖 Generated with Claude Code

[Mister-Meeseeks]

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

Contribution: Fixed-prime eight-level transfer on PR300.

Review and limits: Fresh full twelve-stage supplier and fixed-prime arithmetic replay passed in 675s after removing one absent historical stdout-log entry from the outer manifest. No scientific source, input pin or assertion changed; both engines, finite invoice, fallback and strict-grid controls pass. No new Lean build.

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: 363134af67f7aa2e0f887e79c6c22963280682d0. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.