[{"type":"thinking","thinking":"`sInfty_lower_bound` and all 8 helper lemmas: `[propext, Classical.choice, Quot.sound]` — NO sorryAx. Clean audit.\n\nCommit this milestone now (crash-safety). Per handoff: `git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit`. Stage the two Lean files. Note the untracked draft.bbl/draft.blg — leave them out (they're paper build artifacts; draft.pdf is gitignored — bbl/blg probably should be too, but not my call now; just don't stage them).\n\nThen update todos and proceed to marginTilde_convex.","signature":""},{"type":"text","text":"Clean audit — no `sorryAx` on any of the 9 new proofs. Committing this milestone immediately (crash-safety rule)."},{"type":"tool_use","id":"Bash_81","name":"Bash","input":{"command":"cd /d/Python/Quantum && git add research/lean/NguyenRH1/NguyenRH1/LiSkeleton.lean research/lean/NguyenRH1/PrintAxioms.lean && git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit -m \"$(cat <<'EOF'\nSession 011: sInfty_lower_bound PROVED (D-037 Step 1, task 5.1 tier (i) first piece) — Bernoulli truncation at K≈n/2 + γ-shifted harmonic bounds (Mathlib eulerMascheroniSeq/Seq'); parity algebra cancels γ/log2/logπ exactly, residual log defect ≤ n/(n−1) absorbed by −4; 8 support lemmas (bern_term_*, sInf_series_summable, harmonic_lower/upper, oddHarm_eq/lower, sInf_partial_lower); PrintAxioms = 3 standard axioms only, no sorryAx\nEOF\n)\" && git log --oneline -1","description":"Commit sInfty_lower_bound proof milestone"},"extra_content":null}]