← Session 33 — ii′-3b/3c crux + F-D finding; Lagarias letter package
thinking (286 chars)
Now NGUYEN.md checklist: the ii′-3b entry. Find the exact text in NGUYEN.md §5 Phase 5B, the ii′-3 entry says "ii′-3b STARTED (session 037) — ROUTE REVISION (D-070)... §1–§4 COMPLETE... k = 1 PROVED... Remaining: §5... → §6... → root import (with LiTightR) → audit." Update to COMPLETE.
Updating NGUYEN.md's ii′-3 entry.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\NGUYEN.md",
"old_string": " **ii\u2032-3b STARTED (session 037) \u2014 ROUTE REVISION (D-070)**: the\n moments (M) come from 5e's partialFraction_identity by PURE\n ALGEBRA + series calculus (no contours \u2014 the contour work was\n 5e's): gFun := logDeriv xiL = B + seriesFun at good points (xiL\n entire via the \u039b\u2080 closed form; perimeter ZeroCountProp ONLY \u2014\n 5f's hZC2/hNLZ not needed). \u00a71\u2013\u00a74 COMPLETE (LiMoments.lean,\n ~730 lines, build green): xiL + the conj/reflect subtype equivs,\n (G) gFun_eq_momentB, evaluations gFun_zero/gFun_one/\n gFun_one_eq_neg (FE sign), the summability budget (master\n \u03a3 mult/\u2016\u03c1\u2016\u00b2 + AM-GM mixed bound), the reindex machinery\n (sigmaP_eq_unpaired k \u2265 2, 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.",
"new_string": " **ii\u2032-3b COMPLETE (sessions 037\u2013038) \u2014 ROUTE REVISION (D-070)**:\n the moments (M) came from 5e's partialFraction_identity by PURE\n ALGEBRA + series calculus (no contours \u2014 the contour work was\n 5e's): gFun := logDeriv xiL = B + seriesFun at good points (xiL\n entire via the \u039b\u2080 closed form; perimeter ZeroCountProp ONLY \u2014\n 5f's hZC2/hNLZ not needed). LiMoments.lean (~1020 lines,\n root-imported, full build GREEN 8770 jobs): xiL + the\n conj/reflect subtype equivs, (G) gFun_eq_momentB, evaluations\n gFun_zero/gFun_one/gFun_one_eq_neg (FE sign), the summability\n budget (master \u03a3 mult/\u2016\u03c1\u2016\u00b2 + AM-GM mixed bound), the reindex\n machinery (sigmaP_eq_unpaired k \u2265 2, vTerm_tsum_eq_zero), k = 1\n (sigmaP_one_eq_neg_gFun_zero), \u00a75 the termwise iterated\n derivation at 0 (iteratedDeriv_zpow_neg_one,\n iteratedDeriv_seriesTerm, the M-test\n seriesTerm_deriv_summableLocallyUniformlyOn,\n iteratedDeriv_seriesFun_zero \u2014 the LiDigamma:749\u2013785\n iteratedDerivWithin_tsum pattern), \u00a76 gFun_eventuallyEq_zero +\n **THE CAPSTONE `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC :\n ZeroCountProp)`: sigmaP k = \u2212gFun^{(k\u22121)}(0)/(k\u22121)! PROVED for\n ALL k \u2265 1** (session 038). Audit session038: 23 decls, 3\n standard axioms only. Remaining: ii\u2032-3c (the (4.10-a) assembly;\n needs the FE derivative relation gFun^{(k\u22121)}(0) =\n (\u22121)^k\u00b7gFun^{(k\u22121)}(1), small from xiL_one_sub)."
}
raw content_json (database row)
[{"type":"thinking","thinking":"Now NGUYEN.md checklist: the ii′-3b entry. Find the exact text in NGUYEN.md §5 Phase 5B, the ii′-3 entry says \"ii′-3b STARTED (session 037) — ROUTE REVISION (D-070)... §1–§4 COMPLETE... k = 1 PROVED... Remaining: §5... → §6... → root import (with LiTightR) → audit.\" Update to COMPLETE.","signature":""},{"type":"text","text":"Updating NGUYEN.md's ii′-3 entry."},{"type":"tool_use","id":"Edit_82","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\NGUYEN.md","old_string":" **ii′-3b STARTED (session 037) — ROUTE REVISION (D-070)**: the\n moments (M) come from 5e's partialFraction_identity by PURE\n ALGEBRA + series calculus (no contours — the contour work was\n 5e's): gFun := logDeriv xiL = B + seriesFun at good points (xiL\n entire via the Λ₀ closed form; perimeter ZeroCountProp ONLY —\n 5f's hZC2/hNLZ not needed). §1–§4 COMPLETE (LiMoments.lean,\n ~730 lines, build green): xiL + the conj/reflect subtype equivs,\n (G) gFun_eq_momentB, evaluations gFun_zero/gFun_one/\n gFun_one_eq_neg (FE sign), the summability budget (master\n Σ mult/‖ρ‖² + AM-GM mixed bound), the reindex machinery\n (sigmaP_eq_unpaired k ≥ 2, 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.","new_string":" **ii′-3b COMPLETE (sessions 037–038) — ROUTE REVISION (D-070)**:\n the moments (M) came from 5e's partialFraction_identity by PURE\n ALGEBRA + series calculus (no contours — the contour work was\n 5e's): gFun := logDeriv xiL = B + seriesFun at good points (xiL\n entire via the Λ₀ closed form; perimeter ZeroCountProp ONLY —\n 5f's hZC2/hNLZ not needed). LiMoments.lean (~1020 lines,\n root-imported, full build GREEN 8770 jobs): xiL + the\n conj/reflect subtype equivs, (G) gFun_eq_momentB, evaluations\n gFun_zero/gFun_one/gFun_one_eq_neg (FE sign), the summability\n budget (master Σ mult/‖ρ‖² + AM-GM mixed bound), the reindex\n machinery (sigmaP_eq_unpaired k ≥ 2, vTerm_tsum_eq_zero), k = 1\n (sigmaP_one_eq_neg_gFun_zero), §5 the termwise iterated\n derivation at 0 (iteratedDeriv_zpow_neg_one,\n iteratedDeriv_seriesTerm, the M-test\n seriesTerm_deriv_summableLocallyUniformlyOn,\n iteratedDeriv_seriesFun_zero — the LiDigamma:749–785\n iteratedDerivWithin_tsum pattern), §6 gFun_eventuallyEq_zero +\n **THE CAPSTONE `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC :\n ZeroCountProp)`: sigmaP k = −gFun^{(k−1)}(0)/(k−1)! PROVED for\n ALL k ≥ 1** (session 038). Audit session038: 23 decls, 3\n standard axioms only. Remaining: ii′-3c (the (4.10-a) assembly;\n needs the FE derivative relation gFun^{(k−1)}(0) =\n (−1)^k·gFun^{(k−1)}(1), small from xiL_one_sub)."},"extra_content":null}]