[JosieElliston]

Summary

This adds research/p104-6030-compiler-binding/, a stdlib verifier that checks the selected PR6030 record against the written statements it depends on. It imports no repository engine: not PR6030's pricing.py, not higher-moment-strictification/verify.py, not mixed_target_probe.py and not the outer ledger() code. No discrepancy was found. There is no new κ, and the selected record is unchanged.

It answers open question 1 of #6043 (my corroborating PR6030 audit): "can the outer conditions and the compiler threshold be recomputed by code that does not descend from PR5827's pricing.py?"

• Part A, compiler (complete). It covers every numerical hypothesis of the higher-moment paid-tail theorem (§2) and of the logarithmic majorant (§4) in research/higher-moment-strictification/README.md. These are instantiated with the PR6030 invoice, with m, k_min and r_max taken from the vendored FINITE-PRECOMPILATION.md definitions.
  • Premises: u = 1/7 ≥ C and σ = t+u ≥ 1, with c = 16, b = 17, m = 145 and v = 1024.
  • Tail ratios α, γ and δ, and the exact tail assembly.
  • θ < θ̄ = 63/64, the shifted exits 2·(16^1024)^64 ≤ (145^1024)^63, the η capacity and the initial range.
  • The threshold (1.4·10⁹ j + 1)^1024 < 2^j: j = 47005 passes and 47004 fails, so the claimed N = 2^65807000000000 is the first passing grid point (by convexity).
  • Real quantities use directed-rounding interval arithmetic at 90 digits. The author's 30-digit intervals contain these enclosures.
• Part B, outer (partial). The nine outer savings are recomputed from PR1673's written cost table and FINE-PADDING-COMPOSITION.md, which supplies the PR1786 halo/core powers 48/128, ξ, c = 3/32, and boundary = main + s and union = main + s + 13/32. So are 24 of the 54 strict checks. All values equal RESULT.json exactly, and main transform ε·q is the limiting row, with slack 20978119357/9.8·10¹⁸.
  • Still open: 30 strict checks (the stopped-supplier λ/leaf/internal/stop rows, the BIT/effective rows, halo radius and volume, and fixed constants) and the 4 functional checks. The verifier lists them.
• Controls.
  • Input-sensitive: dropping the 208 rank-145 targets makes α > 1.14 and the test rejects. Taking m = 512 instead of the largest target rank rejects p = 1024. p_min − 1 = 1011 and j − 1 both reject. The verifier also fails on changed pinned bytes or a missing statement fragment.
  • Fixed demonstrations: the σ < 1 counterexample, decay 127/128 and θ̄ = 45/46.

Scope and remaining obligations

This checks the numerical instantiation and source binding of written theorems. It does not re-prove them; §4 extends PR4411, whose majorant was reviewed in #4425. It does not check that the P104 controller's actual batches satisfy the §4 integer-flow, exit and complement premises; those remain under the compiler and native_all_columns assumptions. The five framework assumptions are unchanged. The Part B cost formulas share their written sources with the ledger code, so Part B is source binding and an independent evaluation, not an independent derivation.

Reproduce

python3 -I -B research/p104-6030-compiler-binding/verify.py prints PASS_P104_6030_COMPILER_BINDING in under a second on Python 3.10–3.14 with no dependencies. python3.12 scripts/research_package.py --package research/p104-6030-compiler-binding passes, and so does check_research_commit.py --check-source-history. The base is main 721c03822. CI was not monitored.

Credit

• DreamingOfClouds: PR6030 and PR5907.
• Ali Romman: PR5827 and the P104 pricing chain.
• zxv: the higher-moment strictification package and the PR4411 majorant.
• zxv and Cao Yifan: the interval and compiler bounds.
• pinterbanget: the Independently review #4411's logarithmic majorant: proof holds, arithmetic certified, least ranks slightly below stated, exact L(N) <= F(N) to N = 6000 (no new κ) #4425 review.
• Jacob Alan Sussman: finite precompilation and productive recursion.
• Vlado Vojdanovski: the PR1673 outer cost table.
• Chafik Boukhalfa: PR1758/PR1786.
• Matarener and Corroborating audit of PR6030: fresh full dense replay, itinerary delta, invoice and crossing (no new κ) #6043: the invoice recount.
• Douglas Colkitt with OpenAI Codex: the PR6030 application review.

Prepared for JosieElliston by Claude Opus 5.5 (Anthropic) via Claude Code in an unattended donated session. A read-only Codex adversarial review led to the directed-rounding intervals and the split between input-sensitive controls and fixed demonstrations. This is not human or proof-kernel acceptance.

🤖 Generated with Claude Code