[{"type":"thinking","thinking":"ii′-6-a committed. Four commits today. The session has been very long. Per the pacing rule, I should report and check whether to continue to ii′-6-b or break. Given the session length (4 major sub-stages completed), it's a natural point to pause and ask.","signature":""},{"type":"text","text":"# ii′-6-a COMPLETE — committed (5a38d87)\n\n## Session 038 tally (four commits today)\n| Commit | Content |\n|---|---|\n| c0f2e78 | ii′-3b: moments capstone (all k ≥ 1) |\n| ec80e64 | ii′-3c: `lagarias_4_10_a` + the crux `sf_eq_resW1` |\n| 8640480 | ii′-6-0: D-071 design + E-030 + your 8-step protocol |\n| 5a38d87 | **ii′-6-a: the honest-Bn redefinition EXECUTED (steps 1–5)** |\n\n## Your protocol, executed\n1. ✓ **Bn redefined**: bridge 2F → 4F, I_III (2/3)Ĉ₀ → (2/3)Z2hat (documented corrected def, identifier retained)\n2. ✓ Correction comments with D-071 pointer; old form preserved in git history + E-030\n3. ✓ **Convexity re-proved** (not assumed): `marginTilde_convex` builds green after the ψ-row literal updates\n4. ✓ **Base points re-certified**: 329,000 / 350,000 (old bounds *fail* for the corrected Bn); margins ≥ **7,001** and ≥ **82,501**\n5. ✓ **Endpoint margins re-run**: margiñ(8×10⁴) = 14,682, margiñ(10⁵) = 90,653, margin(N₁) = 2.458×10²⁶ (unchanged)\n\n**Verification**: full build GREEN (8771 jobs); `lambda_pos_finite_height_verified` + the re-proved convexity + both base-point certificates — all 3 standard axioms, 0 sorryAx. The endpoint theorem's statement is untouched.\n\n## Remaining\n- **ii′-6-b** (next): perimeter Props (`ZeroCountGlobalProp`, `MZeroProp`) + extended pigeonhole + sides identity + bridge |λ_n(T)| ≤ 4·FAlt\n- **ii′-6-c**: four side bounds (horizontals = the segment-integral machine — the long pole)\n- **ii′-6-d**: the fold ⟹ `sfBoundProp`\n- **ii′-7**: closure + Paper A correction note (step 7)\n\nThis session has run very long (4 major sub-stages). Natural break point — everything is committed and STATE.md points at ii′-6-b. Continue, or break here?"}]