[{"type":"thinking","thinking":"ii′-1b(i) is COMPLETE and axiom-clean:\n- `zetaA` analytic at 1 (removable singularity)\n- `hLi` analytic at 1, hLi 1 = 1, hLi_eq_near_one\n- `lcoeff` (operational Laurent coefficients)\n- `A_iter` (A-polynomial derivatives)\n- `ResW1_eq_sum` : ResW1 n = Σ_{j=1}^n C(n,j)·lcoeff(j−1) — the w=1 residue value, exactly as designed.\n\nSession 016 has delivered ii′-1b(i). The remaining pieces of ii′-1b: (ii) principal-part integral ∮ P = ResW1, (iii) R holomorphic at 1 + rectangle residue theorem. Given the session length already (many iterations), let me assess: continue with (ii) now or wrap the session cleanly with (i) committed?\n\nPer the pacing rules (§8.5): sub-stages should end in clean committed states. ii′-1b(i) is a clean, self-contained deliverable (the residue VALUE theorem). Committing now is sensible. But the user is engaged and said \"let's go\" — I should continue working. However, this response is getting long and the natural commit boundary is here. Let me commit ii′-1b(i) and continue with (ii) in the same session if feasible — the user is on telegram, so they'll read the summary later anyway. Let me commit first (crash-safe per §8.4 NOTE: save artifacts IMMEDIATELY).\n\nFor the commit: journal entry should note ii′-1b in progress with (i) done. Actually — per protocol, journal/STATE are session-END artifacts. Since I'm mid-session and continuing, the clean approach: commit the working file with a WIP note (crash-safety), then continue with (ii). Let me do a quick WIP commit of LiResidue.lean, then push forward with (ii).\n\nActually — better practice per §8.4: \"save artifacts IMMEDIATELY when produced (crash-safe)\". So: commit LiResidue.lean + PrintAxioms.lean now with a WIP message, then continue.","signature":""},{"type":"text","text":"ii′-1b(i) is complete and axiom-clean. Committing immediately for crash-safety, then continuing with part (ii)."},{"type":"tool_use","id":"Bash_218","name":"Bash","input":{"command":"cd /d/Python/Quantum && git add research/lean/NguyenRH1/NguyenRH1/LiResidue.lean research/lean/NguyenRH1/PrintAxioms.lean && git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit -m \"$(cat <<'EOF'\nSession 016 (WIP): ii'-1b(i) — the w=1 residue value theorem\n\nLiResidue.lean Part 1, PROVED (axiom audit: 3 standard axioms only):\n- zetaA = (w-1)*zeta(w) extended by 1 at 1: analytic (removable\n  singularity via riemannZeta_residue_one + Mathlib RemovableSingularity)\n- hLi = 1 - (w-1)*(zetaA'/zetaA): analytic at 1, hLi 1 = 1, agrees with\n  (w-1)(-zeta'/zeta) on a punctured nhd of 1 (hLi_eq_near_one)\n- lcoeff k := iteratedDeriv (k+1) hLi 1 / (k+1)! (operational Laurent\n  coefficients of -zeta'/zeta at 1)\n- A_iter: derivatives of A(w) = w^n - (w-1)^n at 1\n- ResW1_eq_sum: the w=1 residue of the Lagarias-kernel integrand equals\n  sum_{j=1}^n C(n,j)*lcoeff(j-1) — via iteratedDeriv_mul (Leibniz),\n  exactly as designed in D-064 R1 / verified numerically session 014.\nEOF\n)\" && git log --oneline -1","description":"WIP commit of ii′-1b(i)"},"extra_content":null}]