[{"type":"thinking","thinking":"Phase 0 complete, everything committed. Report to user. Check time — probably ~12:15pm. Good point to offer a break (user mentioned wine earlier). Summarize the whole session state.","signature":""},{"type":"text","text":"**🏁 PHASE 0 COMPLETE** — everything committed (`6feebc6`). The E-002 results are in:\n\n**E-002 — 10,000 zeros, ALL CHECKS PASS**\n- γ₁ = 14.13472514173469379045725 (verified to 20 digits), strictly monotone, Riemann–von Mangoldt agreement\n- γ₁₀₀₀₀ = 9877.7826540055…; min gap 0.0377, mean gap 0.986\n- The parallel rewrite did in one window what the serial version couldn't finish in three — and it's now crash-proof (per-row flush + atomic part-files)\n\n**E-003 — the paper's machinery, confirmed empirically**\n- tr G̃/N within 0.1% of prediction at all T ✔\n- ‖G̃‖²_HS/N converges to R(ψ) with exactly the O(1/L) decay Theorem 5.7 predicts ✔\n- G̃ positive semi-definite to machine precision (negative index = 0, as it must be when all zeros are on the line) ✔\n- The sandbox is now **calibrated** — we know the exact size of finite-size effects, so Phase 1 can't mistake noise for a breakthrough\n\n**Phase 0 ledger:** 0.1 ✔ (D-001 tool index) · 0.2 ✔ (D-002–D-006, whole paper reproduced) · 0.3 ✔ (Lemma 3.2 independently) · 0.4 ✔ (E-001, machine-verified R(ψ)) · 0.5 ✔ (D-007, Lean repo audited) · 0.6 ✔ (E-002, E-003, D-008)\n\nAlso committed today: your no-boundaries rule (§4A.5), pacing rules, compute resources (R6). Nine commits, zero lost work, everything resumable.\n\n**Next stage (Phase 1.1):** re-derive the 0.682 ceiling and map every non-tight inequality — starting with the Lean `PairCeiling` construction and a domain sweep.\n\nIt's a natural milestone — want to break here, or roll into Phase 1?"}]