[{"type":"thinking","thinking":"Committed (f4a7321). Task 2.10 complete and archived. Report to user with the findings. Also note pacing: it's ~17:30 UTC. I don't know the user's local timezone; the timestamp in E-022 JSON was UTC 17:19. If user is in a US timezone, it's midday; if Europe, evening. The 5 PM rule — I'll mention time neutrally and let them decide. Actually the last sessions ran long at night (00:04). I'll just present results and next steps, letting the user steer.","signature":""},{"type":"text","text":"Task 2.10 complete and committed (`f4a7321`). Summary:\n\n## E-022/E-022b — spectral-measure convergence (D-035 deliverable D2)\n\n**What was built**: the Clark/de Branges spectral measures μ_a = Σ (1/K_a(z_k,z_k))·δ_{z_k} for Suzuki's D_{a,π}, a ∈ {4,6,8,10,12} — atoms at W-zeros, weights from the operator metric via a new Schur-Toeplitz bordered solve (validated to 3.6e-14 against the dense machinery; V0–V3 all pass).\n\n**The findings** (D-040):\n1. **Mass conservation**: total mass ≈ 184, independent of a.\n2. **Coarse weak metric is flat** (d_a ≈ 0.0106) — no convergence visible at smoothing scale σ=8.\n3. **The valley observable** (the real discovery): K_a(z,z) sampled continuously has **deep valleys exactly at the true zeros γ** — depth Δ(a) = 2.16 → 2.94 (K-contrast up to ~19×), corr(dist-to-γ, log K) ≈ +0.4. The valleys are at the γ's, *not* at the model's own lattice zeros.\n4. **Weights, not positions**: atoms near γ's carry e²–e²·⁸× more weight (controlled within z-bins and against shifted-γ nulls — one naive elevation signal was caught as a distributional artifact by the null test before it became a claim). Positions remain chance-level (E-019), yet 63%→72.5% of the mass sits within ±0.1 of true zeros.\n5. **Saturation**: Δ(a) ≈ 3.33 − 4.76/a — decelerating, consistent with a **fixed-θ ceiling** at Δ_∞ ≈ 3.3. Full consolidation (Δ → ∞) does not happen at fixed θ=π.\n\n**Scientific meaning**: the operator metric already \"knows\" where the zeros are, but the fixed-boundary-condition family can't finish the consolidation. Since Cor 1.6 requires a *moving* θ(a), this is exactly the expected behavior if the true resolvent convergence lives along the θ(a) flow — a new, concrete constraint on task 2.9-D1, and Δ(a) is now the project's sharp convergence probe for any candidate θ(a).\n\n**Queue**: 2.9-D1 (Krein frame, now with the Δ→∞ constraint), then 2.11 (D-038). Continuing or pausing is your call — state is clean and committed either way."}]