[{"type":"thinking","thinking":"I now have all three perimeter definitions verbatim from the source. Next: write an audit script that:\n1. `#print axioms logDeriv_riemannZeta_sub_nearZeros_le_tight`\n2. `#check` the capstone (full signature)\n3. `#print` the three perimeter definitions (ZeroCountProp, ZeroCountProp2, NoLowZeros) so the output records their exact statements\n4. Also print axioms of the three perimeter props? They're defs (Props), printing axioms of them would show what they depend on — propext etc. Actually the props themselves are definitions; `#print axioms ZeroCountProp` shows axioms used in its definition. Not strictly needed but harmless. The main asks: `#print axioms logDeriv_riemannZeta_sub_nearZeros_le_tight` + record the exact perimeter parameters.\n\nAlso should I print `C0hat` since ZeroCountProp references it? The \"exact perimeter parameters\" — the user wants the exact perimeter recorded. C0hat is defined in LiSkeleton. Printing it would make the record self-contained. Let me include `#print C0hat` too, plus `zeroWindow_finite`, `zeroAbsWindow`, `zeroMult`? That could get deep. A reasonable audit record: the capstone statement, its axioms, the three perimeter def printouts, and C0hat (the majorant appearing in ZeroCountProp). Also `nearZerosSub` and `zeroMult` appear in the capstone statement — printing those makes the record fully self-contained. Let me include them.\n\nLet me check where C0hat, nearZerosSub, zeroMult are defined to make sure `#print` will resolve. They're all in the NguyenRH1 namespace presumably. `#print` with open NguyenRH1 should work.\n\nThe audit file: create AuditSession037.lean following the established pattern. Note: LiTightR is NOT root-imported, so the audit must `import NguyenRH1.LiTightR` (previous session-036 audit must have done the same — let me check what audit-session036 used. Actually there's no AuditSession036.lean file listed... The ls showed AuditSession034.lean and AuditSession035.lean only, but audit-session036-axioms.txt exists. Maybe the 036 audit was a temporary script that got deleted, or it was named differently. Let me check the head of audit-session036-axioms.txt and how it was generated — actually not critical. I'll create AuditSession037.lean importing NguyenRH1.LiTightR.\n\nWait — but is the olean for LiTightR built? STATE.md says full build GREEN 8762 jobs and LiTightR NOT root-imported; `lake build NguyenRH1.LiTightR` produces the olean. The session-036 audits ran `#print axioms` on the capstone, so the olean exists (or they used `lake env lean` on a script which builds the import). Running `lake env lean AuditSession037.lean` will compile LiTightR if the olean is stale — that could take a while in foreground. Handoff says: \"For lake: SINGLE command per detached spawn; short PrintAxioms in foreground.\" The audits were run before, so the olean should be cached. I'll run in foreground with a generous timeout (e.g., 10 min max). If it's too slow, go detached.\n\nEnvironment: Windows, shell is \"unknown (use Unix shell syntax)\". PATH: elan at ~/.elan/bin, need `export PATH=\"$HOME/.elan/bin:$PATH\"` per handoff. Working dir: research/lean/NguyenRH1.\n\nPlan:\n1. Write AuditSession037.lean.\n2. Run: `cd research/lean/NguyenRH1 && export PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean AuditSession037.lean > audit-session037-axioms.txt 2>&1` — actually better to capture output via tee so I can see it. But Bash tool returns output anyway. I'll redirect to the file and then read the file.\n\nNote: `#print` output goes to stdout (info messages) — with `lake env lean` the info diagnostics appear on stderr? In Lean 4, `#print`/`#check` outputs are info-level messages, which lean prints to stdout... Actually Lean 4 command-line prints info messages to stderr I believe. Previous audits captured them in .txt files. Safest: redirect both stdout and stderr to the file.\n\nLet me write the audit script now. Content:\n\n```lean\n/-\nAuditSession037.lean — explicit dependency audit of the ii′-5f capstone\n`logDeriv_riemannZeta_sub_nearZeros_le_tight` (user-requested, pre-ii′-3b).\nRecords: full capstone signature, #print axioms, and the exact perimeter\ndefinitions (ZeroCountProp, ZeroCountProp2, NoLowZeros) with the C0hat\nmajorant and the statement-level constructs (nearZerosSub, zeroMult).\nExpected: [propext, Classical.choice, Quot.sound] only.\n-/\nimport NguyenRH1.LiTightR\n\nopen NguyenRH1\n\n/- ## 1. The capstone statement (full signature) -/\n#check @logDeriv_riemannZeta_sub_nearZeros_le_tight\n\n/- ## 2. The dependency audit -/\n#print axioms logDeriv_riemannZeta_sub_nearZeros_le_tight\n\n/- ## 3. The exact perimeter parameters (verbatim definitions) -/\n#print ZeroCountProp\n#print ZeroCountProp2\n#print NoLowZeros\n\n/- ## 4. Statement-level constructs appearing in the capstone/perimeter -/\n#print C0hat\n#print nearZerosSub\n#print zeroMult\n#print zeroAbsWindow\n```\n\nHmm, `#print axioms` inside with `open` — previous scripts used unqualified names fine.\n\nAlso `#check @...` gives the full type with all hypotheses.\n\nOne concern: `#print zeroMult` — zeroMult is a def; fine. nearZerosSub — def in LiTightR. C0hat in LiSkeleton. All under namespace NguyenRH1 presumably; open handles it.\n\nDo I want axioms of the perimeter props too? They're just defs (Prop-valued); `#print axioms ZeroCountProp` would show axioms in its definition chain (likely propext/choice/Quot.sound). Not requested. Keep it lean but it's cheap to add. The user asked specifically: \"#print axioms logDeriv_riemannZeta_sub_nearZeros_le_tight plus the exact perimeter parameters.\" I'll stick to the request + minimal context constructs.\n\nAlso worth recording: the nearZerosSub definition since it's in the statement. And zeroWindow_finite used in ZeroCountProp. Let me add `#print zeroWindow_finite`? zeroWindow_finite is a theorem (finiteness proof), printing it prints its type. Hmm — ZeroCountProp's def body references (zeroWindow_finite t).toFinset. `#print ZeroCountProp` will print the body including that reference, which is enough.\n\nLet me write the file and run it. Foreground with timeout 600000 (10 min) max — LiTightR is ~4300 lines; if olean is cached, the script runs in seconds. The olean should exist since session-036 audits ran. Try foreground first.","signature":""},{"type":"text","text":"All three perimeter definitions located verbatim in LiContour.lean. Now I'll write the audit script following the established pattern and run it."},{"type":"tool_use","id":"Write_9","name":"Write","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\AuditSession037.lean","content":"/-\nAuditSession037.lean — explicit dependency audit of the ii′-5f capstone\n`logDeriv_riemannZeta_sub_nearZeros_le_tight` (user-requested, pre-ii′-3b).\nRecords: (1) the full capstone signature, (2) `#print axioms` on the\ncapstone, (3) the exact perimeter definitions it takes as hypotheses\n(ZeroCountProp, ZeroCountProp2, NoLowZeros), (4) the statement-level\nconstructs appearing in the capstone/perimeter (C0hat, nearZerosSub,\nzeroMult, zeroAbsWindow).\nExpected: [propext, Classical.choice, Quot.sound] only.\n-/\nimport NguyenRH1.LiTightR\n\nopen NguyenRH1\n\n/- ## 1. The capstone statement (full signature, all hypotheses explicit) -/\n#check @logDeriv_riemannZeta_sub_nearZeros_le_tight\n\n/- ## 2. The dependency audit -/\n#print axioms logDeriv_riemannZeta_sub_nearZeros_le_tight\n\n/- ## 3. The exact perimeter parameters (verbatim definitions) -/\n#print ZeroCountProp\n#print ZeroCountProp2\n#print NoLowZeros\n\n/- ## 4. Statement-level constructs in the capstone/perimeter statements -/\n#print C0hat\n#print nearZerosSub\n#print zeroMult\n#print zeroAbsWindow\n"},"extra_content":null}]