← Session 32 — ii′-3b start: capstone axiom audit + moments
thinking (199 chars)
The index.md append is clean (D-070 on its own line). Now update NGUYEN.md — the ii′-3b checklist line and the session log (§8.6). Let me find the exact current text of the ii′-3b entry in NGUYEN.md.
Index clean. Now NGUYEN.md — the ii′-3b checklist line and the session log.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\NGUYEN.md",
"old_string": " Build GREEN (8762 jobs); 18 key decls audited: 3 standard axioms.\n- [ ] ii\u2032-3b R2(iii) moments (contour \u03c3_k = \u2212g^{(k\u22121)}(0)/(k\u22121)!) \u2192\n ii\u2032-3c (assembly \u2192 crux Sf = Res\u2081).",
"new_string": " Build GREEN (8762 jobs); 18 key decls audited: 3 standard axioms.\n- [~] ii\u2032-3b R2(iii) moments (\u03c3_k = \u2212g^{(k\u22121)}(0)/(k\u22121)!) \u2192 ii\u2032-3c\n (assembly \u2192 crux Sf = Res\u2081).\n \u2192 **ROUTE REVISION (session 037, D-070)**: the moments come from 5e's\n partialFraction_identity by PURE ALGEBRA + series calculus (no\n contours \u2014 the contour work was 5e's): gFun := logDeriv xiL =\n B + seriesFun at good points (xiL entire via the \u039b\u2080 closed form;\n perimeter ZeroCountProp ONLY \u2014 5f's hZC2/hNLZ not needed).\n **\u00a71\u2013\u00a74 COMPLETE (session 037)**: LiMoments.lean (~730 lines,\n build green) \u2014 xiL + the two subtype equivs, (G) gFun_eq_momentB,\n evaluations gFun_zero/gFun_one/gFun_one_eq_neg (FE sign), the\n summability budget (master \u03a3 mult/\u2016\u03c1\u2016\u00b2 + AM-GM mixed bound), the\n conj/reflect reindex machinery (sigmaP_eq_unpaired k \u2265 2,\n vTerm_tsum_eq_zero), **k = 1 PROVED:\n sigmaP_one_eq_neg_gFun_zero**. Remaining: \u00a75 (termwise iterated\n derivation at 0, k \u2265 2 \u2014 full skeleton banked in journal-037) \u2192\n \u00a76 (capstone sigmaP_eq_neg_iteratedDeriv_gFun_div) \u2192 root import\n (with LiTightR) \u2192 audit."
}
raw content_json (database row)
[{"type":"thinking","thinking":"The index.md append is clean (D-070 on its own line). Now update NGUYEN.md — the ii′-3b checklist line and the session log (§8.6). Let me find the exact current text of the ii′-3b entry in NGUYEN.md.","signature":""},{"type":"text","text":"Index clean. Now NGUYEN.md — the ii′-3b checklist line and the session log."},{"type":"tool_use","id":"Edit_134","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\NGUYEN.md","old_string":" Build GREEN (8762 jobs); 18 key decls audited: 3 standard axioms.\n- [ ] ii′-3b R2(iii) moments (contour σ_k = −g^{(k−1)}(0)/(k−1)!) →\n ii′-3c (assembly → crux Sf = Res₁).","new_string":" Build GREEN (8762 jobs); 18 key decls audited: 3 standard axioms.\n- [~] ii′-3b R2(iii) moments (σ_k = −g^{(k−1)}(0)/(k−1)!) → ii′-3c\n (assembly → crux Sf = Res₁).\n → **ROUTE REVISION (session 037, D-070)**: the moments come from 5e's\n partialFraction_identity by PURE ALGEBRA + series calculus (no\n contours — the contour work was 5e's): gFun := logDeriv xiL =\n B + seriesFun at good points (xiL entire via the Λ₀ closed form;\n perimeter ZeroCountProp ONLY — 5f's hZC2/hNLZ not needed).\n **§1–§4 COMPLETE (session 037)**: LiMoments.lean (~730 lines,\n build green) — xiL + the two subtype equivs, (G) gFun_eq_momentB,\n evaluations gFun_zero/gFun_one/gFun_one_eq_neg (FE sign), the\n summability budget (master Σ mult/‖ρ‖² + AM-GM mixed bound), the\n conj/reflect reindex machinery (sigmaP_eq_unpaired k ≥ 2,\n vTerm_tsum_eq_zero), **k = 1 PROVED:\n sigmaP_one_eq_neg_gFun_zero**. Remaining: §5 (termwise iterated\n derivation at 0, k ≥ 2 — full skeleton banked in journal-037) →\n §6 (capstone sigmaP_eq_neg_iteratedDeriv_gFun_div) → root import\n (with LiTightR) → audit."},"extra_content":null}]