[{"type":"thinking","thinking":"Summarize where we left off.","signature":""},{"type":"text","text":"Session 009 (2026-08-19) ended with **Phase 4 (Synthesis Assault) COMPLETE** — all four repairs 4.5a–d finished, and the repo is clean (last commit: `abb2cb7`).\n\n## Where we stand\n\n**Theorem status (post-repair):**\n- **T-1 / R-004** — finite-height Li theorem, λ_n > 0 for all n ≤ N₁ ≈ 9.0×10²⁴ — **fully restored**: [PROVED-CONDITIONAL(computational RH-to-T₀; finite verification)]. R-bound traced end-to-end (D-056: A = 10.5, B₀ = 48; E-028: 26× slack, N₀ = 80 000); convexity proved (D-057/E-029).\n- **T-2** (R-003 + D-041): factorization + (★) ⟺ (1.12) [PROVED modulo Phase-5 formalities, itemized D-059]; (1.12) ⟹ spec(D) ⊂ ℝ [PROVED]; ⇐ remains [SKELETON L3/L4].\n- **T-3** (valley theorem, D-049 + D-058): upper bounds and floors B1′/B3′ [PROVED-CONDITIONAL(RH)]; detector three levels verified (E-027/D-055).\n\n**Archive hygiene**: all journal/results/db/git committed; no blockers.\n\n## NEXT ACTION (per STATE.md)\n\nSession 010 = **Phase 5 planning with you**. The fork is:\n1. **5.4 full paper honesty audit** — every claim in draft.tex tagged and justified (the natural finish of Phase 4's rigor push)\n2. **5.1 Lean skeletons** — formalize the new lemmas on zeta-23-lean\n3. **New research thread** — the symbol-space opening on the (★) route (D-046 revival condition (ii)) is the one live opening left\n\nOptional cheap cleanups available anytime: E-023b (acb box cover for M₀ — removes last grid-verified constant in R-004), E-021 n = 10⁴ rerun.\n\nWhich direction do you want for Session 010?"}]