[{"type":"thinking","thinking":"Full build GREEN (8746 jobs) and axiom audit PASSES — all 12 new declarations: 3 standard axioms only.\n\nNow commit + archive closure for session 018.","signature":""},{"type":"text","text":"Build GREEN (8746 jobs), audit clean — 12 declarations, 3 standard axioms only. Committing and closing."},{"type":"tool_use","id":"Bash_147","name":"Bash","input":{"command":"cd \"D:/Python/Quantum\" && git add research/lean/NguyenRH1/NguyenRH1/LiSwaps.lean research/lean/NguyenRH1/NguyenRH1.lean research/lean/NguyenRH1/PrintAxioms.lean && git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit -m \"$(cat <<'EOF'\nSession 018: ii'-2 — the two elementary swaps (R2(i)/(ii))\n\nLiSwaps.lean (~340 lines): \n* R2(i) liCoeff_eq_sum_sigma: liCoeff n = Σ_{j=1}^n (−1)^{j+1}C(n,j)·σ_j,\n  σ_j the paired zero power sum (sigmaSlice_summable per slice j ≥ 1:\n  j=1 via Re(1/ρ) = Re(ρ)/|ρ|² paired exactness; j ≥ 2 by |ρ|^{−j} ≤\n  |ρ|^{−2} for ‖ρ‖ ≥ 2; finite ball by compactness — ii′-1a skeleton);\n  swap via Summable.tsum_finsetSum + binomial expansion\n  one_sub_one_sub_pow (CommRing-polymorphic).\n* R2(ii) sInfty_eq_sum: SInfty n = Σ_{j=1}^n (−1)^j C(n,j)·a_j (n ≥ 1),\n  a_j = Lagarias's odd-m zeta values (encoded 1 + odd≥3 tsum); swap via\n  per-slice p-series domination (oddSlice_summable); the j=1 cancellation\n  −n/m + n/m and the alternating identity Σ_{j=2}^n (−1)^jC(n,j) = n−1.\nFull build GREEN (8746 jobs); axiom audit: 3 standard axioms only on\nall 12 new declarations.\nEOF\n)\" && git log --oneline -1","description":"Commit LiSwaps.lean work"},"extra_content":null}]