[{"type":"thinking","thinking":"All clean: 3 standard axioms only, 0 sorryAx; the corrected Bn definition printed verbatim (4F, (2/3)Z2hat ✓). ii′-6-a is COMPLETE — all 8 user-protocol steps 1–5 done (6 is ii′-6 itself, 7–8 recorded).\n\nNow archive: journal append, STATE.md, NGUYEN.md (checklist ii′-6 entry → 6-a COMPLETE), db session summary, commit.","signature":""},{"type":"text","text":"Audit clean (3 standard axioms, 0 sorryAx; corrected Bn verbatim). **ii′-6-a COMPLETE.** Closing the archive."},{"type":"tool_use","id":"Bash_235","name":"Bash","input":{"command":"cd D:/Python/Quantum && cat >> research/journal/session-038.md << 'EOF'\n\n## ii′-6-a COMPLETE (same session, third continuation) — the honest-Bn redefinition\n\nUser protocol steps 1–5 ALL DONE (D-071 §5):\n1. **Bn redefined** (LiSkeleton.lean): bridge 2F → 4F, I_III (2/3)Ĉ₀ →\n   (2/3)Z2hat (new def Z2hat with the D-071 doc comment); marginTilde\n   in lockstep.\n2. Corrected definitions carry explicit D-071 correction comments\n   (identifier retained; audit history preserved via git + E-030).\n3. **marginTilde_convex RE-PROVED** (builds green): the block constants\n   mFblock (−2→−4), mTL1b ((8/3)·0.433→(8/3)·0.6), mIdb\n   ((8/3)·2.9→(8/3)·2.7) + the ψ-row literals (vF/vTL1/vId,\n   hnn1/hnn2/hnn4) — the sign haves' `by norm_num` handled the new\n   constants mechanically; marginTilde_eq_expanded needed Z2hat added\n   to the simp only unfold list; continuousOn_marginExpanded had a\n   hardcoded const_mul (−2) → (−4).\n4. **Base points RE-CERTIFIED** (LiBasePoints.lean): the upper bounds\n   Bn_FAlt_80000_le 328,000 → 329,000 and Bn_FAlt_100000_le\n   347,000 → 350,000 (the old ones FAIL for the corrected Bn —\n   4F + (2/3)Z2 raise the totals by ~1.1–2.2k); new Z2hat interval\n   bounds (7.6705/7.7483 upper, 6.06 lower); the _ge lower-bound\n   proofs' brackets converted to Z2hat; one 3×10⁻⁵ rounding slip\n   (114.0655 → 114.0656) caught by linarith. Downstream margins:\n   marginTilde_FAlt_80000_pos (≥ 7,001 > 0 ✓),\n   marginTilde_FAlt_80000_lt_100000 (65,001 < 82,501 ✓) — statements\n   otherwise unchanged.\n5. **Endpoint margins re-run** (dps 60): margiñ(8×10⁴) = 14,681.84\n   (was 15,763.68); margiñ(10⁵) = 90,652.75 (was 91,887.77);\n   margin(N₁) = 2.457962406×10²⁶ (unchanged to leading digits).\n\n**Closure**: full build GREEN (8771 jobs — first background attempt\nkilled by the wrapper timeout; restarted detached per the long-run\nprotocol); AuditSession038c.lean + audit-session038c-axioms.txt —\nlambda_pos_finite_height_verified + marginTilde_convex + the\neq-lemmas + both base-point certificates: ALL 3 standard axioms only,\n0 sorryAx; the corrected Bn printed verbatim (4F, (2/3)Z2hat ✓).\n\nBanked: `lake env lean FILE` type-checks against the STALE olean of\nits imports — after editing a file's dependencies, `lake build\nNguyenRH1.X` FIRST (the LiBasePoints \"clean build\" against the old\nBn was an artifact); certified-constant arithmetic must be re-checked\nby hand at 1e-4 (the (2/3)·7.7483 + 60.9 + 48 = 114.06553 vs certified\n114.0655 slip).\n\n## Files (ii′-6-a)\n\n- research/lean/NguyenRH1/NguyenRH1/LiSkeleton.lean (Z2hat + corrected\n  Bn/marginTilde + block constants + ψ-row literals)\n- research/lean/NguyenRH1/NguyenRH1/LiBasePoints.lean (base points\n  re-certified at 329,000/350,000)\n- research/lean/NguyenRH1/AuditSession038c.lean +\n  audit-session038c-axioms.txt\n\n## Next\n\nii′-6-b (D-071 §6): perimeter Props (ZeroCountGlobalProp — global\nTrudgian N(T) ≤ FAlt one-sign; MZeroProp — M₀ ≤ 1.3352), the extended\npigeonhole exists_zero_avoiding_T_wide (3-unit window, clearance\n1/(9·C0hat(a+2))), the sides identity (rectInt'_Jlag on the variant-B\nrectangle ⟹ |Sf n| ≤ ‖RectInt‖ + |λ_n(T)| + |triv|), and the bridge\n|λ_n(T)| ≤ 4·FAlt (hRH + conj symmetry + ZeroCountGlobalProp).\nEOF\necho done","description":"Append ii′-6-a to journal"},"extra_content":null}]