[{"type":"thinking","thinking":"Committed at 14:44. Summarize for the user honestly: the moment route is closed, which is real research progress (documented obstruction). Remaining: 1.4 (prime pairs / support>1), 1.2 (SDP tooling), 1.5 (decision gate). Suggest the 1.5 decision gate write-up + 1.4 literature research next. Keep it brief and honest about the strategic picture: Track A is nearly exhausted; Tracks B/C become more important.","signature":""},{"type":"text","text":"Committed (`0f0d555`). Here's the honest strategic picture at 2:44 PM:\n\n**What E-005 settled:** the entire moment-ladder route is closed — not just \"the third moment is unavailable at full bandwidth,\" but something stronger and cleaner: *at every bandwidth where a higher moment IS unconditionally available, its sharp certificate cap falls below 2/3 anyway.* And the oversampling hatch I found is provably empty (n₊ is q-invariant — denser grids add no spectral information). Both sides of the wall are now documented.\n\n**Why this is progress, not failure:** Track A's escape routes are now *completely mapped*. Of the three ways out of the 2-moment framework:\n1. ~~Multiplicity/zero-density inputs~~ — G-001 (substitution symmetry)\n2. ~~Higher moments~~ — G-002 (availability/uselessness coincidence)\n3. **Support > 1 (prime-pair information) — the last one standing** (task 1.4)\n\n**Remaining in Phase 1:**\n- **1.4** — the only live Track A escape: can *any* support-(1+δ) form-factor fragment be proven unconditionally? Starts with literature research (BGSTB24/25, GS25/26, GLSS25 per §4A.3).\n- **1.5** — the decision-gate document: \"is > 2/3 achievable in this framework?\" We now have almost all inputs; 1.5 should be written after the 1.4 literature check.\n- **1.2** — SDP tooling; now mostly calibration value, can be deferred.\n\nMy recommendation: **1.4 literature research next** (it's the decisive question for Track A), then write the 1.5 gate document with everything on the table. Continue?"}]