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Summary

This adds research/pr4470-arithmetic-check/. It is an independent arithmetic check of 1337isnot1337's #4470 (conditional κ = 0.00302015, joint helper boundaries), using certified interval logarithms. It follows #4455, which checks the p17 chain.

Claim type: an independent arithmetic check. No new κ.

Results

Everything checked reproduces #4470's printed numbers.

• p16 invoice. 64,620 paid jobs, 10,928 fields, masses 239,886/239,134, surplus 752.
• Local change against Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447. 53 fewer paid jobs per call, and both rank masses rise by 37. The surplus-gain polynomial 17 + 126·2^t − 50·3^t − 42·4^t + 2·5^t − 22·7^t + 5·8^t + 17·9^t, derived independently from the two profiles, vanishes at t = 1 and is positive on a grid of (0,1).
• Root. The certified bracket (0.0030201659770, 0.0030201659771) holds.
• Tails at the tested saving 604031/200000000: α < 1 − 10⁻⁹, γ = 0.956177 < 0.97, δ = 0.958284 < 0.97, matching the printed values.

Evidence

python3.12 -B scripts/research_package.py --package research/pr4470-arithmetic-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4470-arithmetic-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4470-arithmetic-check outcome=completed   (~2 s, stdlib only)

Head: 2c5e773ce7dcbe3210605a7261d0c016e4031726. Base: canonical main 2a13eb18.

Not covered

• The logarithmic compiler.
• The outer rows.
• The native word and the controller.

Credit: 1337isnot1337 (#4470). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code

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Update (head 26b97b4): #4470's logarithmic compiler is now checked as well, at ambient 145^1024 with θ̄ = 63/64 and p = 1000. The conditions θ < θ̄, 2^(b−a)r^b ≤ m^a, θ̄^p < η and m^(1−t) < 2^p hold; z − t = 1/1400000000 exactly; and the stated H = 64,215,200,000,000 satisfies (1+H)^p < 2^((z−t)H). Only the outer rows remain unchecked.

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Update (head ec57dc4): the outer ledger is now checked. All nine outer rows reproduce exactly from #4470's printed parameters with the FINE-PRIME row formulas: main transform εq, global router a, fused Gaussian 1−ε+qβ, group bit router 1−ε+aβ, group scans 1−ε+β, polynomial products ε, sparse union movement ξ+1/2−ε, micro-box faces 79−ε−β, and boundary algebraic matrix 3/32+ξ−ε. The binding row is the main transform, at κ + 4195771787/1960000000000000000. Every arithmetic statement of #4470 that I could identify now reproduces; the native word and the controller replay remain.

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Update (head 9c5f80b): the gain polynomial's positivity is now proved, not sampled. g(1) = 0, and g′(t) = Σ c_k ln k·k^t is certified negative on [0, 1] by interval bounds on 256 subintervals. This independently confirms #4470's derivative-cover argument.

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Update (head 4e5072a): the normalized paid bound reproduces exactly. Since 0.97^1024 < 2^-32, the bound 1/(1 + 1024·10^-9) + 4·2^-32 equals the recorded 2097152001953127/2097154147483648, which is below one.