[{"type":"thinking","thinking":"6-d committed (774fec5). **ii′-6 is COMPLETE** — sfBoundProp : SfBoundProp proved from exactly the six declared perimeter hypotheses.\n\nNow — what's the state? Per the plan:\n- ii′-6 DONE (6-a through 6-d).\n- Remaining: **ii′-7** (closure: `lambda_pos_finite_height_closed` with the 3 perimeter hypotheses only — wait — the perimeter is now SIX hypotheses (RHUpTo, LiVerifiedUpTo + ZeroCountProp, ZeroCountProp2, ZeroCountGlobalProp, NoLowZeros, MZeroProp) — hmm — the \"3 perimeter hypotheses only\" refers to the ORIGINAL three (RHUpTo, LiVerifiedUpTo, SfBoundProp) — with SfBoundProp now PROVED from the 6, the final `lambda_pos_finite_height_closed` would take (hRH : RHUpTo) (hfinite : LiVerifiedUpTo) + the 6 analytic/counting Props. Let me check what lambda_pos_finite_height_verified takes: (hRH : RHUpTo 3×10¹²) (hfinite : LiVerifiedUpTo 5×10⁵) (hSf : SfBoundProp). So the closed version: (hRH) (hfinite) + the 6 = 8 hypotheses total, of which RHUpTo/LiVerifiedUpTo are the computational certificates and the other 6 are the declared analytic perimeter (Trudgian N(T)/S(T) forms + Platt-class NoLowZeros + M₀).\n- ii′-7 also: full axiom audit; paper Appendix B + tag upgrade (D-062 §4 endpoint); archive closure + D-037 line-63 erratum pointer; the paper correction note (F-A both-signs + F-B two-unit + F-D dog-leg + F-E I_I kernel footnote).\n\nThat's a substantial next stage. The user asked for \"the rest of the 6-c\" — I've now done 6-c AND 6-d (the whole ii′-6). Time to report and ask about proceeding to ii′-7. Actually — per the pacing directive and the natural milestone, I should report this milestone clearly and ask whether to continue into ii′-7. The session has been long and productive. Let me also update the todos.\n\nActually — before reporting — should I do the immediate assembly `lambda_pos_finite_height_closed`? That's small (instantiate lambda_pos_finite_height_verified with sfBoundProp) — but it's ii′-7 territory per the plan. The user's directive was \"the rest of the 6-c\" — I've completed it plus 6-d. The natural stop: report and ask.\n\nLet me update the todo list and write the summary. Also per the session protocol, I should consider whether to update STATE.md/NGUYEN.md now — those are part of the END protocol. The session isn't necessarily over (user might say continue to ii′-7). But the crash-safe protocol says commit per sub-stage — done (each sub-stage committed). STATE.md updates are part of session END. I'll report the milestone and ask about ii′-7, noting that STATE.md/journal updates will happen at session end (or when the user directs).\n\nActually — hmm — let me reconsider. The user's directive was specifically \"the rest of the 6-c\". The 6-d fold was the logical completion of the side bounds (without it, the side bounds are inert). Completing ii′-6 is the right milestone. ii′-7 is a NEW stage (closure + paper + audit + errata) that the user should green-light, especially since it touches the paper (freeze protocol lifts at ii′-7).\n\nReport:\n- 6-c complete: 6-c-ii (I_III), 6-c-iii (I_I F-E), 6-c-iv (mid-horizontal arcsinh machine), 6-c-v (horizontal assembly).\n- 6-d complete: sfBoundProp : SfBoundProp PROVED from exactly the six declared perimeter hypotheses.\n- Build green 8774 jobs; axiom audits: 3 standard axioms only, 0 sorryAx on everything.\n- Commits: 6e5a98f, 9bd8ba9, 1fed1df, 5d3dc0a, 774fec5.\n- What this means: ii′-6 (the L0 assembly) is complete — |Sf n| ≤ Bn FAlt n on [10⁵, N₁ = (3×10¹²−1)²] is now Lean-proved; the ORIGINAL N₁ ≈ 9×10²⁴ preserved (D-074 dog-leg endpoint).\n- Next: ii′-7 (closure: lambda_pos_finite_height_closed, full axiom audit, paper Appendix B + tag upgrade + the F-A/F-B/F-D/F-E correction note, archive closure + D-037 line-63 erratum pointer). Ask whether to proceed.","signature":""},{"type":"text","text":"**ii′-6 COMPLETE.** The full arc is committed. Final status:\n\n## Milestone: `sfBoundProp : SfBoundProp` PROVED\n\nAll of ii′-6 is done — five commits this session:\n\n| Commit | Sub-stage | Content |\n|--------|-----------|---------|\n| `6e5a98f` | 6-c-ii | I_III left-vertical ≤ 4T((2/3)Z₂(T) + 10.5·log(T+2) + 48) + 40·1.3352 |\n| `9bd8ba9` | 6-c-iii | I_I right-vertical ≤ e^{1/3}·IIMaj (F-E kernel, uniform in t) |\n| `1fed1df` | 6-c-iv | mid-horizontal segment machine (arcsinh-FTC from scratch) |\n| `5d3dc0a` | 6-c-v | horizontal assembly (mid + DL-5 dog-leg tails, both sides) |\n| `774fec5` | 6-d | **the fold: `sfBoundProp : SfBoundProp`** |\n\nBuild green (8774 jobs); axiom audits: **[propext, Classical.choice, Quot.sound] only, 0 sorryAx** on all 27 new declarations.\n\n**What this closes:** |Sf n| ≤ Bn FAlt n on [10⁵, N₁] is now Lean-proved from exactly the six declared perimeter hypotheses (RHUpTo, ZeroCountProp, ZeroCountProp2, ZeroCountGlobalProp, NoLowZeros, MZeroProp) — with **N₁ = (3×10¹²−1)² ≈ 9×10²⁴ PRESERVED** (the D-074 dog-leg endpoint). Notable: the pinch (NI + 5.5R ≤ 7·Ĥ) discharged by a fully elementary log-mono chain — no certified log numerics needed; the bridge needed a variant at T ≤ 3·10¹² (the public T ≤ 3·10¹²−1 hypothesis fails at the top of the range incl. n = N₁ exactly — handled).\n\n**Remaining: ii′-7** (closure) — `lambda_pos_finite_height_closed` with the perimeter assembled, full axiom audit, paper Appendix B + tag upgrade + the correction note (F-A both-signs, F-B two-unit, F-D dog-leg, F-E I_I kernel), archive closure + D-037 line-63 erratum pointer. This stage touches the paper (freeze lifts at ii′-7)."},{"type":"tool_use","id":"AskUserQuestion_201","name":"AskUserQuestion","input":{"questions":[{"question":"ii′-6 is complete (sfBoundProp proved). Proceed to ii′-7 (closure + paper) now?","header":"Next stage","options":[{"label":"Continue to ii′-7 (Recommended)","description":"Assemble lambda_pos_finite_height_closed, full axiom audit, paper Appendix B + tag upgrade + correction note, archive closure."},{"label":"Stop at this milestone","description":"Run the session-END protocol (journal, STATE.md, NGUYEN.md updates) and stop here; ii′-7 next session."},{"label":"Only the Lean closure","description":"Do just lambda_pos_finite_height_closed + axiom audit now; paper/errata later."}]}]},"extra_content":null}]