← Session 33 — ii′-3b/3c crux + F-D finding; Lagarias letter package
Now STATE.md.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\STATE.md",
"old_string": "# STATE.md \u2014 NGUYEN-RH-1 RESUME POINT\n# \u2b50 READ THIS FIRST at the start of every session.\nLast updated: 2026-08-24 | Session 038 COMPLETE \u2014 **ii\u2032-3b DONE: the\ncapstone `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC : ZeroCountProp)`\nPROVED (all k \u2265 1); LiTightR + LiMoments root-imported; build GREEN\n(8770 jobs); audit: 23 decls, 3 standard axioms only.**\n\n## SESSION 038 HEADLINES\n1. **ii\u2032-3b COMPLETE** (LiMoments.lean \u00a75/\u00a76, ~290 new lines, file now",
"new_string": "# STATE.md \u2014 NGUYEN-RH-1 RESUME POINT\n# \u2b50 READ THIS FIRST at the start of every session.\nLast updated: 2026-08-24 | Session 038 COMPLETE \u2014 **ii\u2032-3b + ii\u2032-3c BOTH\nDONE: the moments capstone AND the crux `sf_eq_resW1 (hZC)` PROVED \u2014\nSf(n) = Res\u2081(n) in Lean, perimeter ZeroCountProp only; build GREEN\n(8771 jobs); audits: 31 decls total, 3 standard axioms only.**\n\n## SESSION 038 HEADLINES (ii\u2032-3c \u2014 THIS SESSION'S ENDPOINT)\n1. **ii\u2032-3c COMPLETE** (LiCrux.lean NEW, ~430 lines, root-imported):\n `gFun_one_sub_fun` (FE as a function identity, xiL_one_sub +\n chain rule), `iteratedDeriv_gFun_zero` (g^{(m)}(0) =\n (\u22121)^{m+1}g^{(m)}(1) via the UNCONDITIONAL\n iteratedDeriv_comp_const_sub), `gFun_one_add_punctured`/\n `gFun_one_add_eventuallyEq` (the shift expansion gFun(1+s) =\n 1/(1+s) + hLiExt s + \u0393R\u2032/\u0393R(1+s)), `iteratedDeriv_gFun_one`\n (coefficient extraction (\u22121)^m\u00b7m! \u2212 m!\u00b7c_m + (\u22121)^{m+1}\u00b7m!\u00b7a_{m+1}),\n **`lagarias_4_10_a (hZC)` PROVED** (lcoeff (k\u22121) = (\u22121)^k(a_k +\n sigmaP k) + (\u22121)^{k\u22121}, all k \u2265 1 \u2014 the multiplied-out\n linear_combination + mul_left_cancel\u2080 (m! \u2260 0)), and **THE CRUX\n `sf_eq_resW1 (hZC)` PROVED**: (ResW1 n).re = Sf n for n \u2265 1\n (ResW1_eq_sum + (4.10-a) + both ii\u2032-2 swaps + the binomial sum\n \u03a3(\u22121)^{j\u22121}C(n,j) = 1). Audit session038b: 8 decls, 3 standard\n axioms only. **ii\u2032-3 (ALL of Lagarias (4.10)) \u2192 COMPLETE.**\n2. **ii\u2032-3b COMPLETE** (LiMoments.lean \u00a75/\u00a76, ~290 new lines, file now"
}
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[{"type":"text","text":"Now STATE.md."},{"type":"tool_use","id":"Edit_151","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\STATE.md","old_string":"# STATE.md — NGUYEN-RH-1 RESUME POINT\n# ⭐ READ THIS FIRST at the start of every session.\nLast updated: 2026-08-24 | Session 038 COMPLETE — **ii′-3b DONE: the\ncapstone `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC : ZeroCountProp)`\nPROVED (all k ≥ 1); LiTightR + LiMoments root-imported; build GREEN\n(8770 jobs); audit: 23 decls, 3 standard axioms only.**\n\n## SESSION 038 HEADLINES\n1. **ii′-3b COMPLETE** (LiMoments.lean §5/§6, ~290 new lines, file now","new_string":"# STATE.md — NGUYEN-RH-1 RESUME POINT\n# ⭐ READ THIS FIRST at the start of every session.\nLast updated: 2026-08-24 | Session 038 COMPLETE — **ii′-3b + ii′-3c BOTH\nDONE: the moments capstone AND the crux `sf_eq_resW1 (hZC)` PROVED —\nSf(n) = Res₁(n) in Lean, perimeter ZeroCountProp only; build GREEN\n(8771 jobs); audits: 31 decls total, 3 standard axioms only.**\n\n## SESSION 038 HEADLINES (ii′-3c — THIS SESSION'S ENDPOINT)\n1. **ii′-3c COMPLETE** (LiCrux.lean NEW, ~430 lines, root-imported):\n `gFun_one_sub_fun` (FE as a function identity, xiL_one_sub +\n chain rule), `iteratedDeriv_gFun_zero` (g^{(m)}(0) =\n (−1)^{m+1}g^{(m)}(1) via the UNCONDITIONAL\n iteratedDeriv_comp_const_sub), `gFun_one_add_punctured`/\n `gFun_one_add_eventuallyEq` (the shift expansion gFun(1+s) =\n 1/(1+s) + hLiExt s + ΓR′/ΓR(1+s)), `iteratedDeriv_gFun_one`\n (coefficient extraction (−1)^m·m! − m!·c_m + (−1)^{m+1}·m!·a_{m+1}),\n **`lagarias_4_10_a (hZC)` PROVED** (lcoeff (k−1) = (−1)^k(a_k +\n sigmaP k) + (−1)^{k−1}, all k ≥ 1 — the multiplied-out\n linear_combination + mul_left_cancel₀ (m! ≠ 0)), and **THE CRUX\n `sf_eq_resW1 (hZC)` PROVED**: (ResW1 n).re = Sf n for n ≥ 1\n (ResW1_eq_sum + (4.10-a) + both ii′-2 swaps + the binomial sum\n Σ(−1)^{j−1}C(n,j) = 1). Audit session038b: 8 decls, 3 standard\n axioms only. **ii′-3 (ALL of Lagarias (4.10)) → COMPLETE.**\n2. **ii′-3b COMPLETE** (LiMoments.lean §5/§6, ~290 new lines, file now"},"extra_content":null}]