[{"type":"thinking","thinking":"Committed (00b2955). Five commits today — a huge session: ii′-3b, ii′-3c, ii′-6-0, ii′-6-a, ii′-6-b. The session has been extremely long. Per the pacing rule, I should report and check whether to continue to ii′-6-c (the long pole: the four side bounds with the segment-integral machine) or break.","signature":""},{"type":"text","text":"# ii′-6-b COMPLETE — committed (00b2955)\n\n## Session 038 tally (five 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: honest-Bn executed (steps 1–5) |\n| 00b2955 | **ii′-6-b: assembly pieces (identity + bridge)** |\n\n## What was built\n- **Perimeter Props** (both your approved trust classes): `ZeroCountGlobalProp` (global Trudgian N(T) ≤ FAlt) + `MZeroProp` (M₀ ≤ 1.3352) — printed verbatim in the audit\n- **Wide pigeonhole** `exists_zero_avoiding_T_wide`: the Finding-2 3-unit repair (clearance 1/(9·C0hat(a+2)) against *all* zeros in (a−1, a+2))\n- **Sides identity** `sf_abs_le_rectInt_add_zeroSum`: the rectangle residue theorem instantiated on the variant-B rectangle with the border proved zero-free → |Sf n| ≤ ‖RectInt‖ + ‖Σ‖\n- **Bridge** `zeroSum_norm_le_four_FAlt_add_one`: ‖Σ‖ ≤ 4·FAlt + 1 (on-the-line |ρ/(ρ−1)| = 1 ⟹ ≤ 2·mult/term; both-signs = 2× one-sign via the conj-image reindex)\n\n**Verification**: full build GREEN (8772 jobs); 12 declarations audited — 3 standard axioms, 0 sorryAx. Notable fight: the RectangleBorder-rcases trap (singleton-Eq dependent-elimination) — banked the rw + simp only + tauto route.\n\n## Remaining\n- **ii′-6-c** (the long pole): the four side bounds — I_III (tight R-bound + M₀), the horizontals (**segment-integral machine**: per-zero ∫ dx/|w−ρ| ≤ 2·log(16.5/c) via asinh), I_I (Dirichlet stepping), triv (done)\n- **ii′-6-d**: the fold ⟹ `sfBoundProp : SfBoundProp`\n- **ii′-7**: closure + Paper A correction note (step 7)\n\nThis has been an exceptionally long session (five sub-stages). Strong natural break point — everything is committed and STATE.md points at ii′-6-c. Continue, or break here?"}]