[pinterbanget]

Summary

This adds research/pr4580-budget-check/, an independent arithmetic check of Matarener's #4580 (head 62545a03): the p3 H-branch boundary budget at κ = 0.00302015. All checked conclusions are confirmed. No new κ. There is one small reporting note about rounded bracket endpoints.

Every moment is recomputed with this package's own certified powers r^(1−s) (atanh/exp series in exact rationals, outward on a 2^−256 grid). The sources' h_interval is never used. Only the signed profiles and H112 come from the same 16 pinned main sources.

Checks

	complex	BIT
raw surplus	616	645
budget at κ (budget + 1 certified negative)	322	397
direct bill fails at s = 0	672	666
own certified roots (bills 0 / one head / two heads)	.0063799044 / .0040422293 / .0017248833	.0079333535 / .0051761597 / .0024471106

The native H112 has rank(H − I) = 8, full row and column support, and H² = I (own exact elimination). There are 112 and 111 distinct query lines.

Reporting note. Every printed positive_at is certified positive, and every printed negative_at lies within #4580's bisection width (about 3·10^−10) of the root. But two printed negative_at values sit just below the root, where the moment is still positive:

• complex, bill 0: printed 0.0063799044, root 0.00637990443…;
• BIT, bill 222: printed 0.0051761597, root 0.00517615973….

They are 10-decimal roundings, not certified brackets. The conclusions are unaffected.

python3.12 -B scripts/research_package.py --package research/pr4580-budget-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4580-budget-check outcome=completed   (~20 s, stdlib only)

Limitations:

• Price the p3 H-branch boundary at kappa 0.00302015 (322/397 calls) and close four repair routes (no new κ) #4580 §4's decoder lower bound is a written argument; only its finite inputs are checked here.
• These are raw rank screens, as Price the p3 H-branch boundary at kappa 0.00302015 (322/397 calls) and close four repair routes (no new κ) #4580 states.

Head: fd9f28beff7d03464d5a07cbdb00c38f431a1613. Base: canonical main f626db5c.

Credit: Matarener / Mark (#4580); zxv (#4359). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code