← Session 33 — ii′-3b/3c crux + F-D finding; Lagarias letter package
thinking (525 chars)
Now update STATE.md, NGUYEN.md (ii′-3b → complete in the checklist), register in research.db, and commit.
STATE.md updates:
- Header: Session 038 COMPLETE — ii′-3b DONE.
- Session 037 headlines → move/replace with session 038 headlines.
- CURRENT POSITION: mark ii′-3b done.
- ACTIVE PLAN: remove ii′-3b §5/§6, next is ii′-3c.
- NEXT ACTION: ii′-3c.
- Handoff notes: add the new banked gotchas.
- Lean line: LiMoments now root-imported, full build 8770 jobs.
Let me rewrite the key sections of STATE.md with targeted edits.
Updating 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 037 COMPLETE at a clean boundary (user\nlog-off) \u2014 **ii\u2032-3b STARTED: \u00a71\u2013\u00a74 DONE, k=1 moment PROVED; \u00a75/\u00a76 remain.**\n\n## SESSION 037 HEADLINES",
"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 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\n ~1020 lines): \u00a75 the termwise iterated derivation at 0 \u2014\n `iteratedDeriv_zpow_neg_one`, `iteratedDeriv_seriesTerm`,\n `seriesTerm_deriv_summableLocallyUniformlyOn` (the M-test on\n ball(0, \u03b4/2), dominator j!\u00b72^{j+1}\u00b7(1/\u03b4)^{j\u22121}\u00b7mult/\u2016\u03c1\u2016\u00b2),\n `iteratedDeriv_seriesFun_zero` (the LiDigamma:749\u2013785\n iteratedDerivWithin_tsum pattern verbatim). \u00a76:\n `gFun_eventuallyEq_zero` (\ud835\udcdd[\u2260] \u2192 \ud835\udcdd via eventually_nhdsWithin_iff) +\n **THE CAPSTONE `sigmaP_eq_neg_iteratedDeriv_gFun_div`**: sigmaP k =\n \u2212(iteratedDeriv (k\u22121) gFun 0)/(k\u22121)! for ALL k \u2265 1 (k=1 via \u00a74's\n reindex; k\u22652 via (G) + \u00a75 + the per-term sign algebra\n (\u22121)^k\u00b7(\u22121)^{k+1} = \u22121 + \u2190 sigmaP_eq_unpaired + field_simp k! \u2260 0;\n FIRST-PASS GREEN). Perimeter: **ZeroCountProp ONLY**.\n2. **Closure**: LiTightR + LiMoments root-imported; full build GREEN\n (8770 jobs); AuditSession038.lean + audit-session038-axioms.txt \u2014\n 23 declarations, [propext, Classical.choice, Quot.sound] ONLY, 0\n sorryAx.\n3. Banked gotchas (journal-038): factorial `!` needs `open scoped Nat`;\n Summable.mul_left dominators must be C * (D \u03c1) (constant FIRST \u2014\n D \u03c1 * C whnf-loops the refine); rw [seriesFun] fails on the UNAPPLIED\n constant (use `show` beta-expansion); norm_sub_norm_le has NO abs on\n the LHS in this Mathlib; don't rw-away memberships still needed as\n memberships (simpa-only a copy).\n\n## SESSION 037 HEADLINES (superseded \u2014 ii\u2032-3b now DONE)"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Now update STATE.md, NGUYEN.md (ii′-3b → complete in the checklist), register in research.db, and commit.\n\nSTATE.md updates:\n- Header: Session 038 COMPLETE — ii′-3b DONE.\n- Session 037 headlines → move/replace with session 038 headlines.\n- CURRENT POSITION: mark ii′-3b done.\n- ACTIVE PLAN: remove ii′-3b §5/§6, next is ii′-3c.\n- NEXT ACTION: ii′-3c.\n- Handoff notes: add the new banked gotchas.\n- Lean line: LiMoments now root-imported, full build 8770 jobs.\n\nLet me rewrite the key sections of STATE.md with targeted edits.","signature":""},{"type":"text","text":"Updating STATE.md."},{"type":"tool_use","id":"Edit_75","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 037 COMPLETE at a clean boundary (user\nlog-off) — **ii′-3b STARTED: §1–§4 DONE, k=1 moment PROVED; §5/§6 remain.**\n\n## SESSION 037 HEADLINES","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 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\n ~1020 lines): §5 the termwise iterated derivation at 0 —\n `iteratedDeriv_zpow_neg_one`, `iteratedDeriv_seriesTerm`,\n `seriesTerm_deriv_summableLocallyUniformlyOn` (the M-test on\n ball(0, δ/2), dominator j!·2^{j+1}·(1/δ)^{j−1}·mult/‖ρ‖²),\n `iteratedDeriv_seriesFun_zero` (the LiDigamma:749–785\n iteratedDerivWithin_tsum pattern verbatim). §6:\n `gFun_eventuallyEq_zero` (𝓝[≠] → 𝓝 via eventually_nhdsWithin_iff) +\n **THE CAPSTONE `sigmaP_eq_neg_iteratedDeriv_gFun_div`**: sigmaP k =\n −(iteratedDeriv (k−1) gFun 0)/(k−1)! for ALL k ≥ 1 (k=1 via §4's\n reindex; k≥2 via (G) + §5 + the per-term sign algebra\n (−1)^k·(−1)^{k+1} = −1 + ← sigmaP_eq_unpaired + field_simp k! ≠ 0;\n FIRST-PASS GREEN). Perimeter: **ZeroCountProp ONLY**.\n2. **Closure**: LiTightR + LiMoments root-imported; full build GREEN\n (8770 jobs); AuditSession038.lean + audit-session038-axioms.txt —\n 23 declarations, [propext, Classical.choice, Quot.sound] ONLY, 0\n sorryAx.\n3. Banked gotchas (journal-038): factorial `!` needs `open scoped Nat`;\n Summable.mul_left dominators must be C * (D ρ) (constant FIRST —\n D ρ * C whnf-loops the refine); rw [seriesFun] fails on the UNAPPLIED\n constant (use `show` beta-expansion); norm_sub_norm_le has NO abs on\n the LHS in this Mathlib; don't rw-away memberships still needed as\n memberships (simpa-only a copy).\n\n## SESSION 037 HEADLINES (superseded — ii′-3b now DONE)"},"extra_content":null}]