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Summary

This adds research/p17-b480-check/. It independently checks the arithmetic of 1337isnot1337's #4447 (κ = 0.00300123) and zxv's #4453 (κ = 0.00300120). Both report the same phase-B contact-480 patch on #4441's p17 invoice, which changes incident ranks [2,2,1,3] → [1,1,2,4]; that is a gain for every 0 < τ < 1 by Karamata.

Claim type: an independent certified arithmetic check. No new κ. Neither PR is accepted, and the native replay is not re-run.

Results

• Invoice. It equals Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441's invoice plus exactly 19 per-call swaps: paid ranks 1 and 4 up 19 each, 2 and 3 down 19 each, targets unchanged. That gives 11,560 fields, 69,273 calls and surplus 800.
• Raw root. It lies in (0.0030012390168, 0.0030012390174), certified.
• Higher-moment strictification (main's theorem; the split bound needs u ≥ C, checked):
  • Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447 at (C, v, c, b, u) = (0.003001235, 1024, 20, 21, 1/5): α < 0.999999995876755, γ_u < 0.969136675521 and δ < 0.932537504514. The tensor bound is 0.999998976.
  • Conditional κ = 0.00300120 (71.9× smaller uniform-rank exponent) #4453 at (0.00300122, 675, 18, 22, 3/25): α < 0.999999980480395, γ_u < 0.981971727000 and δ < 0.977253011856. The tensor bound is 0.999997070.
  • All three ratios match the PRs' printed intervals to every digit.
• Polylog compiler at ambient 153^v. The θ comparisons, the shifted exit condition, θ̄^p < η and m^{1−t} < 2^p all hold; θ̄^p < η is tight for Conditional κ = 0.00300120 (71.9× smaller uniform-rank exponent) #4453 at 3.27e-5 against 3.74e-5. The stated ranks are certified, and the least passing H is slightly smaller: 64,215,171,181,937 (Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447) and 2,299,613,602,047 (Conditional κ = 0.00300120 (71.9× smaller uniform-rank exponent) #4453).

Evidence

python3.12 -B scripts/research_package.py --package research/p17-b480-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/p17-b480-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/p17-b480-check outcome=completed   (~3 s, stdlib only)

Head: bce939b6eeb7d65b8161ca0a4204267e4e1e88a0. Base: canonical main 2a13eb18.

Not covered

• The native contact, transport and phase replay.
• Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441's predecessor native work, which mihir-s-05's Independently reconstruct PR4441 helper tariffs and complete p17 invoice #4448 audits.
• The outer ledgers.

Task and overlap

• Card: independent-moment, refined.
• Claim: Handoffs and requests for independent checks #1166 (comment)

Credit

@1337isnot1337 (#4447, #4440, #4441), @zxv (#4453, #4359), the higher-moment and polylog results on main, and Jacob Alan Sussman.

Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance; no independent human review. Apache-2.0. This PR does not merge anything or change the frontier.

🤖 Generated with Claude Code

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Update (head 67b4ef8): the package now also checks the predecessors. #4441 (κ = 0.00300105): its own invoice, strictification ratios matching its intervals, and compiler (least certified H 165,312,667,114,238 against the stated 165,315,500,000,000). #4440 (κ = 0.00296): the complex and BIT query-thinned units' α, γ_u and δ match its printed endpoints to 1e-28, with tensor bounds < 0.99995 and < 0.99566. #4440's older power-majorant compiler is not re-derived.

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Update (head e02ca27): #4446 (κ = 0.003001053) is added. It uses #4441's invoice with the rank-one tail at v = 17160, c = 18, b = 19. Its α, γ and δ match the 36-digit printed intervals to 1e-30, and the tensor bound is 0.99999876. Its conservative compiler constants dominate the true ones: the exit constant 88,608 against an actual 74,093.9, and −log₂η ≤ 464.483 against an actual 418.912. H0 and H1 reproduce exactly.

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Update (head 089b597): #4440's power-majorant compiler, previously listed as not re-derived, now reproduces exactly from its PROOF.md §3 (h = 1/64, v = 1024, z0 = (t+z)/2). Complex: H0 = 75,415,467,350, H1 = 10,418,370,291,022,217, with uniform saving κ + 6d = 103609/35000000 and κ = 0.00296. BIT: H0 = 3,755,884,544, H1 = 25,986,965,159,937. The Bernoulli surpluses, c^64 < b^63 and the decay blocks also match. So every number of #4440 that this package touches now reproduces.

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Update (head 9c155a6): #4446's separate p6 BIT supplier, which supplies the ordinary BIT premise, is now checked. The rank masses are 102,419/102,932 with surplus 513. The raw root lies in (0.00314, 0.00315), above the admitted 0.00312. α < 99999/100000 at the tested saving 157/50000 (certified upper bound 0.9999882).

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Update (head 02b7e88): the #4446 BIT supplier check is now complete. Added: γ = P_1/(7^C T_t) < 999/1000 (upper bound 0.998596); the finite paid moment 1653/1696; 7^16 < 8^15; the compiler H0 = 850,090,000 and H1 = 1,066,862,950,001, reproduced; and the delayed-cover gap 1/200000.

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Update (head f848f01): the outer ledgers of all five κ PRs (#4440, #4441, #4446, #4447, #4453) are now checked. Each one's nine outer rows reproduce exactly from its printed parameters with the FINE-PRIME row formulas (εq, a, 1−ε+qβ, 1−ε+aβ, 1−ε+β, ε, ξ+1/2−ε, 79−ε−β, 3/32+ξ−ε). The binding row is always the main transform, with margins above κ of 1.3e-7, 8.6e-10, 4.3e-10, 2.1e-9 and 8.6e-9 respectively.