[{"type":"thinking","thinking":"Now STATE.md. Update:\n1. Header: session 021 complete, ii′-4 done.\n2. DONE list: add ii′-4.\n3. Remaining map: ii′-5 → ii′-3b → ii′-3c → ii′-6 → ii′-7.\n4. NEXT ACTION: ii′-5.\n5. Handoff gotchas: add the new ones.\n\nCurrent STATE.md lines 3-16:\n```\nLast updated: 2026-08-22 | Session 020 COMPLETE — ii′-3a FULLY DONE.\nTIER ii′ in progress (user decision: option (a) — close SfBoundProp\nin Lean BEFORE submission; Paper A frozen/submittable throughout).\nDONE: ii′-0 (D-064 design + liCoeff defect + crux Sf = Res₁ found),\nii′-1a (liCoeff defect REPAIRED), ii′-1b (R1 residue machinery:\nrectInt'_Jlag), ii′-2 (elementary swaps: liCoeff_eq_sum_sigma +\nsInfty_eq_sum), ii′-3-DESIGN (D-066, route β4), ii′-3a (pieces A+B:\nLiZetaCoeff — the ζ-piece coefficients; LiArchimedean + LiDigamma —\n**iteratedDeriv_logDeriv_Gammaℝ**: the archimedean Taylor coefficients\nof logDeriv Gammaℝ(1+s) at 0 are (−1)^{j+1}·j!·lagariasA(j+1) for all\nj ≥ 0; digamma partial-fraction series built from logGammaSeq).\nAll axiom-audited: 3 standard axioms only (18 key decls audited 020).\nRemaining map (D-066 §5 resequencing): ii′-4 (L3+L1) → ii′-5 (R-bound)\n→ ii′-3b (moments) → ii′-3c (assembly → crux) → ii′-6 → ii′-7.\n```\n\nAnd NEXT ACTION section (lines 73-89). And handoff gotchas (add the session-021 ones — keep compact).","signature":""},{"type":"text","text":"Now STATE.md — header, DONE list, and NEXT ACTION for ii′-5."},{"type":"tool_use","id":"Edit_145","name":"Edit","input":{"replace_all":false,"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: 2026-08-22 | Session 020 COMPLETE — ii′-3a FULLY DONE.\nTIER ii′ in progress (user decision: option (a) — close SfBoundProp\nin Lean BEFORE submission; Paper A frozen/submittable throughout).\nDONE: ii′-0 (D-064 design + liCoeff defect + crux Sf = Res₁ found),\nii′-1a (liCoeff defect REPAIRED), ii′-1b (R1 residue machinery:\nrectInt'_Jlag), ii′-2 (elementary swaps: liCoeff_eq_sum_sigma +\nsInfty_eq_sum), ii′-3-DESIGN (D-066, route β4), ii′-3a (pieces A+B:\nLiZetaCoeff — the ζ-piece coefficients; LiArchimedean + LiDigamma —\n**iteratedDeriv_logDeriv_Gammaℝ**: the archimedean Taylor coefficients\nof logDeriv Gammaℝ(1+s) at 0 are (−1)^{j+1}·j!·lagariasA(j+1) for all\nj ≥ 0; digamma partial-fraction series built from logGammaSeq).\nAll axiom-audited: 3 standard axioms only (18 key decls audited 020).\nRemaining map (D-066 §5 resequencing): ii′-4 (L3+L1) → ii′-5 (R-bound)\n→ ii′-3b (moments) → ii′-3c (assembly → crux) → ii′-6 → ii′-7.","new_string":"# STATE.md — NGUYEN-RH-1 RESUME POINT\n# ⭐ READ THIS FIRST at the start of every session.\nLast updated: 2026-08-22 | Session 021 COMPLETE — ii′-4 FULLY DONE.\nTIER ii′ in progress (user decision: option (a) — close SfBoundProp\nin Lean BEFORE submission; Paper A frozen/submittable throughout).\nDONE: ii′-0 (D-064 design + liCoeff defect + crux Sf = Res₁ found),\nii′-1a (liCoeff defect REPAIRED), ii′-1b (R1 residue machinery:\nrectInt'_Jlag), ii′-2 (elementary swaps: liCoeff_eq_sum_sigma +\nsInfty_eq_sum), ii′-3-DESIGN (D-066, route β4), ii′-3a (pieces A+B:\nLiZetaCoeff — the ζ-piece coefficients; LiArchimedean + LiDigamma —\n**iteratedDeriv_logDeriv_Gammaℝ**: the archimedean Taylor coefficients\nof logDeriv Gammaℝ(1+s) at 0 are (−1)^{j+1}·j!·lagariasA(j+1) for all\nj ≥ 0; digamma partial-fraction series built from logGammaSeq),\nii′-4 (LiContour.lean: L3 `exists_zero_avoiding_T` midpoint pigeonhole\non perimeter `ZeroCountProp`; L1 kernel bounds `kFun_norm_le_two`,\n`kFun_shift_norm_le_exp_four_add_one`,\n`kFun_shift_norm_le_exp_sqrt_half_add_one`, `kFun_neg_two` ≤ 1;\n**zeroMult_neg_two** — trivial-zero simplicity via ζ = (s+2)·Λ/Hfun,\nHfun(−2) = −2π ≠ 0, Λ(−2) = Λ(3) ≠ 0).\nAll axiom-audited: 3 standard axioms only (17 decls audited 021).\nRemaining map (D-066 §5 resequencing): ii′-5 (R-bound)\n→ ii′-3b (moments) → ii′-3c (assembly → crux) → ii′-6 → ii′-7."},"extra_content":null}]