[{"type":"thinking","thinking":"ii′-6-0 committed. This session has been very productive: ii′-3b, ii′-3c, ii′-6-0 — three commits. It's been a long session. Per the pacing rule (§8.5 BREAK PROMPT), I should check whether to continue to ii′-6-a or pause. The work has been running long. Let me summarize and ask the user whether to continue with ii′-6-a (the Bn redefinition + margin re-verification, ~1 session estimated) or break here.","signature":""},{"type":"text","text":"# ii′-6-0 DESIGN COMPLETE — committed (8640480)\n\n## Session 038 summary (three commits today)\n| Commit | Content |\n|---|---|\n| c0f2e78 | **ii′-3b**: moments capstone `sigmaP_eq_neg_iteratedDeriv_gFun_div (hZC)`, all k ≥ 1 |\n| ec80e64 | **ii′-3c**: `lagarias_4_10_a` + **the crux `sf_eq_resW1 (hZC)`** — Sf(n) = Res₁(n) in Lean |\n| 8640480 | **ii′-6-0**: D-071 design + E-030 validation + your 8-step protocol recorded |\n\n## The ii′-6 design, in one paragraph\nThe fold analysis found the baked Bn is unprovable beyond ~5×10⁷ (two killers growing like T·log T: the both-signs bridge factor-2 and the I_III two-unit count), while near 10⁵ the honest bound is actually *smaller*. Per your approved protocol: redefine Bn honestly (2F → 4F, (2/3)Ĉ₀ → (2/3)Z2hat) — E-030 confirms the fold then works everywhere, margins stay positive and improve near the base points, and the horizontal segment-integral uses ≤ 40% of its share. Perimeter additions recorded: `ZeroCountGlobalProp` + `MZeroProp`. Paper erratum queued for ii′-7 (step 7); old results preserved in git history + E-030 (step 8).\n\n## Remaining plan (D-071 §6)\n- **ii′-6-a** (next, ~1 session): Bn redefinition + Z2hat + marginTilde/marginExpanded/mK lockstep + convexity re-proof + base-point re-certification + endpoint margins\n- **ii′-6-b**: perimeter Props + extended pigeonhole + sides identity + bridge\n- **ii′-6-c**: four side bounds (horizontals = the segment-integral machine — the long pole)\n- **ii′-6-d**: the fold ⟹ `sfBoundProp : SfBoundProp`\n- **ii′-7**: closure + paper correction note + tag upgrade\n\nThis session has run long — good point to break (everything committed and resumable, STATE.md points at ii′-6-a). Continue to ii′-6-a now, or break?"}]