[{"type":"thinking","thinking":"Clean run, EXIT 0. The audit file audit-session037-axioms.txt is recorded. Now report to the user concisely.\n\nResults:\n1. **Axiom dependency**: `[propext, Classical.choice, Quot.sound]` — the 3 standard axioms only. No sorryAx, no new axioms. This matches the project rule (§5.2: only propext, Classical.choice, Quot.sound permitted).\n\n2. **Exact perimeter parameters** — the capstone takes exactly three perimeter hypotheses:\n   - `hZC : ZeroCountProp` — unit-window mult-weighted zero count: ∀ t ≥ 2, Σ_{ρ ∈ zeroWindow(t)} zeroMult(ρ) ≤ C0hat(t+1), where C0hat t = 0.433·log(t+2) + 0.886·log log(t+2) + 2.9. [Trudgian 2014 N(T)/S(T), D-062 §4; strengthened to mult-weighted in session 035]\n   - `hZC2 : ZeroCountProp2` — two-unit window: ∀ t ≥ 10, Σ_{|γ−t|≤1} zeroMult(ρ) ≤ 0.6·log(t+2) + 0.886·log log(t+2) + 2.7. [Trudgian two-unit specialization, D-069]\n   - `hNLZ : NoLowZeros` — ∀ nontrivial zero ρ, 14 ≤ |Im ρ|. [Platt-class zero-location certificate, D-069]\n\nAlso the theorem's other parameters: t ≥ 10, s with −5/2 ≤ Re s ≤ 3, Im s = t, ζ(s) ≠ 0.\n\nShould I commit this? The freeze protocol says commit at every sub-stage, but this is an audit, not a sub-stage. The session-end protocol handles commits. The user asked to \"run\" and \"record\" — the record is the txt file + the audit script. I won't commit without being asked (git protocol: only commit when user explicitly asks). I'll mention the files are written.\n\nNote the audit script AuditSession037.lean is a new file at the package root like AuditSession034/035 — consistent with the established pattern, and it's not imported by the root so it doesn't affect the build.\n\nConcise report now.","signature":""},{"type":"text","text":"Audit complete, EXIT 0, recorded to `research/lean/NguyenRH1/audit-session037-axioms.txt` (script: `AuditSession037.lean`).\n\n## 1. Axiom dependency\n\n```\n'NguyenRH1.logDeriv_riemannZeta_sub_nearZeros_le_tight' depends on axioms:\n[propext, Classical.choice, Quot.sound]\n```\n\nThe 3 standard axioms only — no `sorryAx`, nothing else. Compliant with the §5.2 rule.\n\n## 2. Exact perimeter parameters (3 hypotheses, verbatim from the audit)\n\n**`hZC : ZeroCountProp`** — Trudgian 2014 N(T)/S(T), unit window (D-062 §4; mult-weighted form, session-035 strengthening):\n```\n∀ (t : ℝ), 2 ≤ t → ∑ ρ ∈ (zeroWindow_finite t).toFinset, ↑(zeroMult ρ) ≤ C0hat (t + 1)\n```\n\n**`hZC2 : ZeroCountProp2`** — Trudgian two-unit specialization (D-069, Finding 1):\n```\n∀ (t : ℝ), 10 ≤ t → ∑ ρ ∈ (zeroAbsWindow_finite t).toFinset, ↑(zeroMult ρ)\n  ≤ 0.6 * log (t + 2) + 0.886 * log (log (t + 2)) + 2.7\n```\n\n**`hNLZ : NoLowZeros`** — Platt-class zero-location certificate (D-069, P2):\n```\n∀ (ρ : ℂ), IsNontrivialZero ρ → 14 ≤ |ρ.im|\n```\n\nSupporting constructs also recorded: `C0hat t = 0.433·log(t+2) + 0.886·log log(t+2) + 2.9`, `zeroMult ρ = (analyticOrderAt riemannZeta ρ).toNat`, `nearZerosSub t = {ρ | |Im ρ − t| < 1}`, `zeroAbsWindow t = {ρ | |Im ρ − t| ≤ 1}`.\n\n## 3. Full capstone signature\n\n```\nZeroCountProp → ZeroCountProp2 → NoLowZeros →\n  ∀ {t : ℝ}, 10 ≤ t → ∀ {s : ℂ}, -5/2 ≤ s.re → s.re ≤ 3 → s.im = t →\n    riemannZeta s ≠ 0 →\n      ‖logDeriv ζ s − ∑ ρ ∈ nearZerosSub t, m_ρ/(s − ρ)‖ ≤ 10.5 * log (|t| + 2) + 48\n```\n\nEverything checks out — the tight R-bound rests on exactly the declared perimeter and nothing else. Ready for ii′-3b on your word."}]