[pinterbanget]

Summary

This adds research/kappa0023-explicit-rank-audit/. It is an independent check of the quantitative chain in zxv's #4359 that turns the p3 mixed invoices into fixed uniform suppliers at 2^276540184361 (complex) and 2^6552928412 (BIT). The chain is FINITE-PRECOMPILATION.md §3–5 together with EXPLICIT-TEMPLATE-BOUNDS.md. #4359's open question 1 asks for review "beginning with the source/exit recurrence"; this check does that.

Claim type: an independent exact check plus a separate flow simulation. No new κ, and #4359 is not accepted. The code is separately written and imports nothing from #4359.

Results

• Certified powers.
  • The superpotential margins are 0.008726900863 (complex) and 0.067093183910 (BIT). Both match the receipt.
  • The author's mixed-root brackets straddle the balance, including the 10⁻³⁰-wide complex bracket.
  • The rank-one surpluses are 224 and 225, and η > 1/4.
• Exact chain.
  • θ < θ̄, from 5^10 < 6^9 and 7^16 < 8^15.
  • m^h < 2.
  • H0 is 60,000,040 and 10,666,731, and H1 is 276,540,184,361 and 6,552,928,412. Each reproduces from its formula, and each is minimal (one less fails).
• The induction. I wrote out the exit bound Σ x_e e^(z0) ≤ (mE/n)^δ S and the strong induction L(n) < A n^(z0), and found no gap. The exit-rank bound E(n) = r_max (n/m)^θ is derived from §3's class structure: exits occur only at d = G, a = 0.
• Flow simulation. It covers every top rank from m to 10,000, with 9,944 complex and 9,951 BIT flows, aggregated by dilation. At every rank it checks exactly:
  • sources lie in (N/m, N];
  • exits are at most r_max^(G+1);
  • the rank-one potential identity Σ S_s s − Σ X_e e = surplus · (column mass) holds;
  • the exact rational L(N) is at most N.
• Observation. At N = 10⁴ the effective saving 1 − log L/log N is 0.001193 (complex) and 0.001155 (BIT), about half the claimed limits. That fits the slow convergence implied by H1; it is not a counterexample.

Evidence

python3.12 -B scripts/research_package.py --package research/kappa0023-explicit-rank-audit --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/kappa0023-explicit-rank-audit
  PASS_REGISTERED_RESEARCH_PACKAGE research/kappa0023-explicit-rank-audit outcome=completed   (~75 s, stdlib only)

The audited files are not on main. Their SHA256 values at #4359's head da637c87 are recorded in the README, and the invoices are embedded as printed. Head: 77f20afb7c24286937c75cb65a7f19e24e7a567f. Base: canonical main 12fa8c5c, priority revision 7.

Not covered

• Hypotheses 1–4 of FINITE-PRECOMPILATION.md §1: native words, splitting, adapters and closure.
• The denominator clearing, beyond the normalized recurrence.
• Scalar and routing passes.
• The delayed BIT cover, precision and storage constants, and the outer bill.
• Whether the invoices match their native words.

Task and overlap

• Card: independent-moment, refined.
• Claim: Handoffs and requests for independent checks #1166 (comment). It named supplier-boundary-audit; independent-moment fits better.
• Overlap: no review of Conditional κ = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier #4359 had been posted.

Credit

@zxv for the construction, invoices and explicit-rank argument. Jacob Alan Sussman for Theorem 1G (#4268).

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

[pinterbanget]

Follow-up data point, local float64 run of the same flow recurrence (not in the package): the effective complex saving 1 − log L(N)/log N is 0.001285 at N = 10⁵ and 0.001311 at N = 2·10⁵, continuing the slow climb toward the claimed limit 0.002304.