[{"type":"thinking","thinking":"Also save a memory note about the Lean toolchain (machine state, useful across sessions). Then session-end protocol: update journal (finalize Lean section), NGUYEN.md (§5 checklist 5.1/5.2, session log, maybe Phase 5 heading), STATE.md, commit.\n\nNGUYEN.md Phase 5 updates:\n- 5.1: [~] skeletons done, proofs remain → mark partial with pointer.\n- 5.2: [~] inherited verified live; NguyenRH1 criterion defined (sorryAx removal pending proofs).\n- 5.3: [x] complete (draft filled, compiles 12pp).\n- 5.4: [x] complete (D-060).\n- Add session 010 entry to §8.6.\n\nAlso fix NGUYEN.md's stale \"residual → Z/6\" language? §8.6 session 008 entry says \"linear-K law K_plateau ≈ 1.9a ⟹ residual → Z/6 ≠ 0 (critical equilibrium, margin C(a) → 0.4)\". That's historical session log — the D-042/D-043 errata + D-060 cover it. Historical logs shouldn't be rewritten; but the RESULT LEDGER #5 and §3 KEY KNOWNS don't mention Z/6. Ledger #5 mentions... no Z/6 there. OK just add session 010 entry.\n\nAlso task 2.12 line in §5 says \"residual → Z/6 ≠ 0\" — that's a task outcome line; add erratum pointer. Let me add \"[ERRATUM: residual → Z/(2π), D-045/D-060]\" to that line. Similarly session 008 log line. Keep minimal: add pointer in both places.\n\nJournal finalize: update \"5.1/5.2 — Lean (in progress...)\" section to completed with outcomes.\n\nSTATE.md update: Phase 5 items status, NEXT ACTION.\n\nMemory: save lean toolchain memory.","signature":""},{"type":"text","text":"Saving the toolchain memory, then finalizing the session-end protocol."},{"type":"tool_use","id":"Write_124","name":"Write","input":{"file_path":"C:\\Users\\lucky\\.nguyen\\projects\\D--Python-Quantum\\memory\\project_lean_toolchain.md","content":"---\nname: Lean toolchain installed and zeta-23-lean fully built\ndescription: elan + Lean v4.33.0-rc2 installed 2026-08-19; zeta-23-lean builds (9010 jobs); NguyenRH1 skeleton package uses path-requires; detached lake chains are fragile\ntype: project\n---\n\nLean toolchain state on the research machine (installed session 010, 2026-08-19):\n\n- elan 4.2.3 at `~/.elan/bin` (NOT on default PATH — every fresh shell needs\n  `export PATH=\"$HOME/.elan/bin:$PATH\"`).\n- Toolchain `leanprover/lean4:v4.33.0-rc2` (pinned by zeta-23-lean/lean-toolchain).\n- zeta-23-lean (D:\\Python\\Quantum\\zeta-23-lean, gitignored vendored clone at tag\n  v1.0): Mathlib cache fetched (8681 files, ~7 GB), `lake build` green (9010 jobs),\n  Solution/Multiplicity/XiPrime/Challenge all build; live `#print axioms` audit\n  matches AUDIT.md (three standard axioms only).\n\n**Why:** task 5.1/5.2 required a real toolchain; D-007 had deferred the rebuild.\n\n**How to apply:**\n- Our Lean work lives in `research/lean/NguyenRH1/` (tracked) with path requires to\n  `../../../zeta-23-lean` and its `.lake/packages/mathlib` — never edit the vendored\n  repo, never re-download Mathlib.\n- Long `lake build` runs: detached spawn, SINGLE command only (chained `&&` detached\n  wrappers died silently with empty logs once); short PrintAxioms runs in foreground.\n- Lean 4 gotchas hit: `end` ordering (namespace closes before anonymous section);\n  Unicode subscripts ₊/₋ invalid in identifiers; Complex sin is `Complex.sin`\n  (no `csin`).\n"},"extra_content":null}]