[pinterbanget]

Summary

This adds research/pr4535-arithmetic-check/. It is an independent arithmetic check, with certified intervals, of hexapode's #4535 (conditional κ = 0.003020165 via #4532's critical-root compiler on #4470's unchanged p16 supplier).

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

Results

Everything checked reproduces #4535.

• Critical exponent. [θ_lo, θ_hi] brackets T_θ = P_θ, certified, and equals exactly 1 minus Independently check #4470's arithmetic (κ = 0.00302015): invoice, local change, root bracket, tails (no new κ) #4478's raw-root bracket.
• Saving order. κ < uniform saving, and t − θ_hi = 377/10¹² exactly.
• Mirror at θ. The worst window ratio is 0.56281 ≤ 141/250, in the maximizing cell (1/48, 1/41).
• Absorption. ln A ≤ 13.6223 (matching logA_upper). The margin is 352.33 at ln N = 10¹² and 236.79 at the stated N = 2^{10¹²}, monotone beyond.
  • Labelling note: Improve conditional multiplication kappa to 0.003020165 via critical-root transfer #4535's margin_lower is computed at ln N = 10¹², not at ln 2^{10¹²}. It is still positive at the stated N.
• Outer rows. 7 of the 9 rows exceed κ, and the binding main-transform margin equals the reported 29969798347/10²⁰. The parameter schedule is κ + k·d. The ξ rows are not recomputed because ξ is not printed.

Evidence

python3.12 -B scripts/research_package.py --package research/pr4535-arithmetic-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4535-arithmetic-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4535-arithmetic-check outcome=completed   (~10 s, stdlib only)

Head: 26502792b9d46fc353fc7b092de070a675264fd8. Base: canonical main f9f85c1e.

Not covered

• Prove adaptive gate criterion and critical-root leaf bounds (no κ) #4532's critical-root theorem.
• The finite envelope.
• The native and physical premises.

Credit: hexapode (#4535), dillona (#4532) and #4470's lineage. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code

[pinterbanget]

Update (head 4617b96): #4535's finite-envelope arithmetic is now checked. The height G <= 210^11 holds at N = 2^(10^12) (M = 1024, g = 2). Since W0 = 10,928 < 2^14 and W0 + P0 + 1 = 75,549 < 2^17, the class envelope C_N < 2^(17G+31) = 2^3,400,000,000,031. The episode counts are 144 = 188 and 1,680 = 15*112. All match RESULT.json.