D-060 — Phase 5.4: full honesty audit of draft.tex

Date: 2026-08-19 | Session: 010 | Task: 5.4 Status: complete. Method: four independent read-only audit instances (claim lists extracted from draft.tex, each verified against the archive with file:line evidence), adjudicated by hand. Draft corrected; archive errata filed; paper recompiled clean (12 pp).

1. Verdict summary

~55 claims audited across abstract, Introduction, Background (§2), Results (§3.1–3.3), Obstructions (§4), Appendices A–B.

• SUPPORTED as written: ~45.
• MISSTATED in draft (all corrected same session): 10 items (§2).
• UNSUPPORTED: 0.
• Archive-side defects found (errata filed in place): 7 items (§3).
• One suspected contradiction (profile envelope vs floor) REFUTED: sinc(0) = 1, so the envelope at z = γ evaluates to ≈ 1 − 1/(2a), matching the floor lower bound. Clarifying parenthetical added to the draft.

2. Draft corrections applied (all in draft.tex, session 010)

1. §2: "triangle window" → flat window ψ₀ = 1_[−½,½] (D-002:91, D-004:71; the triangle is the autocorrelation ψ₀∗ψ₀). [factual error]
2. §2: "verified symbolically to 60 digits" → "verified symbolically and against 60-digit reference values (E-001)" — E-001 json records dps = 50 working precision vs a 60-digit reference check.
3. §2: sanity-gate scope "on every new criterion" → "each of the three main theorems … (D-053)" (gate was applied to T-1/T-2/T-3).
4. §3.1 Step 2: B(n) tail "+ o(1)" → "+ I_I + 1" with both terms identified (D-037:99 — the archive bound has explicit remainders, not o(1)).
5. Abstract item (2) tag: now states explicitly that the reduction of the limit formula to a real-spectrum statement is proved, while recovery of the limit formula from the real-spectrum property is a proof skeleton.
6. §3.2 reduction paragraph: ⟺ split — "(1.12) only if spec(D) ⊂ ℝ" [PROVED via Suzuki Cor 1.6 + D1]; converse = SKELETON (L3/L4, D-051). Matches STATE.md tags; the draft previously presented the biconditional as proved. [most serious finding]
7. §3.2 Finding 1: depth wording — "Δ(a) ≈ log a + 0.64" was the fit for log K_plateau (D-042), not for Δ. Draft now cites the valley theorem asymptotic Δ(a) = log(2a) + o(1) and the direct five-point fit Δ(a) ≈ 3.33 − 4.76/a (D-040); plateau ratios 0.973–0.997 added.
8. §3.2 Finding 4: clarified that "< 3×10⁻¹² at a = 2" is the D-046 floor-corrected bound on the true λ_a; raw Galerkin values (7.4×10⁻¹¹ at a = 2, 1.7×10⁻¹² at a = 5) are upper bounds.
9. §3.3 detector remark + Appendix A: "measured to 0.9%" → "crossings within 0.02%–2.3% of π/(2a), three of four cases within 0.5%" (E-027 V2c data; the a=4, γ≈51.4 case deviates 2.33%). Also scoped: the stress test ran at a ∈ {4,8}; the a = 12 scale comes from the E-022/E-024 spectral-measure program.
10. Appendix A: "floors ≈ 1.04" → "floors ≈ 1 (measured 0.90–1.26, a = 4…12)" (E-022b raw); "residual spread ≤ 2.2%" → "at most 2.23%" (E-024 exact max); "λ₁ to 102 digits" → "agreeing with its closed form to better than 10⁻²⁸ relative" (the automated check threshold; 102 digits was the reference-string precision).

3. Archive errata filed (in place, dated, referencing this file)

1. R-004: updated to post-repair state — step 3 constants A = 10.5/B₀ = 48 (was A = 2.0/B₀ = 2.0); step 5 N₀ = 8×10⁴, margin 16 020, convexity PROVED (D-057/E-029); step 6 overlap 6.25× (was 10×); adversarial-review H2 digamma link now PROVED (D-056); header convexity line updated.
2. D-036 §6: sign erratum — S_∞ correction is −1/(24n), not +1/(24n) (the file's own residual list proves it: −0.2500417 at n = 1000).
3. D-056 title: stale constants "A = 6.0, B₀ = 40" → A = 10.5, B₀ = 48.
4. D-055 F-C: "deviations ≤ 0.9%" erratum — correct: 0.02%–2.3% relative (three of four ≤ 0.5%).
5. D-058 (L3): same 0.9% erratum, pointer to D-055.
6. D-042 §2: linear-K law superseded by D-045 — plateau K/(2a) → 1 (measured 0.973–0.997); the "1.9a to 0.3%" fit does not survive re-checking against the file's own raw values (K/a = 1.95–1.99); residual asymptotic Z/(2π), not Z/6.
7. D-043 §D item 3: residual "→ Z/6" erratum → Z/(2π) per D-045; qualitative conclusion (nonzero residual equilibrium = the obstruction) unchanged.

4. Residual known limitations (carried knowingly, tagged in draft)

• M₀ = 1.3352 remains grid-verified (E-023 S1 + Lipschitz); acb box cover upgrade = E-023b (optional, queued).
• Valley-theorem general floor carries the non-degeneracy condition ‖G⁻¹‖‖k‖² ≤ a (D-058:20); draft covers it as "explicit local-configuration constant".
• Appendix B claim "no model-space/RKHS infrastructure in Mathlib" is plausible-but-unverified from the archive (worded as a project assessment).
• E-027 heights quoted as 23.0/51.4 are rounded mid-gap targets (actual peaks 22.5–23.3, 50.9–51.1 depending on case).

5. Conclusion

After the §2 corrections, every claim in draft.tex is either [PROVED]/[PROVED-CONDITIONAL] with the archive chain cited, [NUMERICAL] with the experiment id cited, or explicitly tagged as skeleton/measured. Task 5.4 (final honesty audit) is COMPLETE for the current draft state; any future edit to draft.tex invalidates this audit only for the edited lines.