[{"type":"thinking","thinking":"All done. Session 010 complete, everything committed (3 commits). Summarize for the user with next-action options.","signature":""},{"type":"text","text":"Session 010 complete — all of Phase 5 advanced, fully archived and committed (3 commits: `9567ba4`, `c595dfc`, `d8a80f5`).\n\n## What was done\n\n**5.3 — paper draft completed.** All stubs written (Introduction, Background on the Weil-form certificate method, Formal verification appendix), abstract refreshed with explicit correctness tags, all 12 citations resolve, MiKTeX compiles clean at 12 pp. Caught one of my own errors mid-write: an invented R(ψ) formula, replaced with the archived D-004 definition.\n\n**5.4 — full honesty audit (D-060).** Four independent audit instances checked ~55 claims against the archive with file:line evidence. Result: **0 unsupported claims**, but 10 misstatements corrected in the draft and 7 archive errata filed. The most serious finding: the paper presented \"(1.12) ⟺ spec(D) ⊂ ℝ\" as proved — the converse is a **skeleton (L3/L4)**; now stated with the split. Also fixed: \"triangle window\" → flat window (my factual error), B(n)'s fake `o(1)` tail → explicit `I_I + 1`, the detector \"0.9%\" overclaim (worst case is 2.3%), and the D-042/D-043 \"Z/6\" residual — superseded by D-045's plateau law K/(2a) → 1, so the residual asymptotic is **Z/(2π)**. R-004 itself was updated to post-repair state (it still described the pre-repair margin).\n\n**5.1/5.2 — Lean, skeleton stage (D-061).** Installed elan + the pinned v4.33.0-rc2 toolchain (user-approved), fetched the Mathlib cache, and **built zeta-23-lean in full — 9010 jobs green**, completing D-007's deferred rebuild. Ran the live `#print axioms` audit: every comparator statement shows exactly `[propext, Classical.choice, Quot.sound]`, verbatim match with AUDIT.md. Created our own package `research/lean/NguyenRH1/` (path-requires, vendored repo untouched) with **9 skeleton theorems compiling** — the finite-height Li theorem, S_∞ lower bound, margin convexity, the R-003 factorization, and four valley-law statements — all `sorry`-marked, no new axioms, and PrintAxioms shows only the 3 standard axioms + `sorryAx` as the honest skeleton marker.\n\n## Next action (Session 011, your pick)\n- **(a)** Prove the elementary Lean tier — `sInfty_lower_bound` first (Bernoulli + harmonic bounds, tactic-friendly)\n- **(b)** E-023b: acb box cover for M₀ (removes R-004's last grid-verified constant)\n- **(c)** Paper figures/tables from the archived CSVs\n- **(d)** New research on the (★) symbol-space opening"}]