[{"type":"thinking","thinking":"Phase 1 complete and committed (d1ffd4c) at 14:57. Big milestone. Report to user: session summary, Phase 1 verdict, next phase choice (Track B vs C — D-013 recommends C first). It's been a very long session — suggest considering a break; it's ~3pm, not yet 5pm. Per pacing, I should present the choice.","signature":""},{"type":"text","text":"**PHASE 1 COMPLETE** (committed `d1ffd4c`, 2:57 PM). Here's the full picture:\n\n## Session 001 results\n\n**The verdict (D-013, decision gate):** the certificate framework is provably exhausted. **> 2/3 is not achievable within its current data class** — and we now own the complete map of why:\n\n| Wall | Mechanism | Status |\n|---|---|---|\n| W1–W2 | Certificate sharpness + 0.682 ceiling | re-derived, Lean-confirmed |\n| W3 | Moment ladder (availability vs. usefulness coincide) | closed by E-005 (G-002) |\n| W4–W5 | Multiplicity & zero-density side-inputs | killed by substitution symmetry (G-001) |\n| W6 | Support > 1 needs prime pairs at lag h ≲ X/T | located precisely (D-012) |\n\nThis is success criterion 🥉 territory by itself: **a rigorously documented obstruction map advancing the field** — every wall with mechanism, evidence, and salvage value.\n\n## Where the hunt stands\nThe two routes that survive all evidence:\n- **Track C (positivity criteria)** — Weil positivity on growing supports, Li coefficients, de Bruijn–Newman. Different data class; untouched by W1–W6. D-013 ranks this first.\n- **Track B (spectral/Hilbert–Pólya)** — highest ceiling (a self-adjoint operator realization = RH itself), highest risk.\n\nPlus cheap side-threads: T4 (why is the method stronger on ξ′?) and the GL(2) extension (new-theorem territory).\n\n## State of the archive\n17 commits · 13 derivation files · 5 experiments · 2 graveyard entries · paper skeleton · full session journal. Everything resumable from `STATE.md`.\n\nIt's been a big session — Phase 0 and Phase 1 both done. Natural breaking point. Shall I run the session-end closeout and we pick Track B or C next time, or continue now?"}]