[{"type":"thinking","thinking":"E-005 running in background (a few minutes). Tell the user it's running. Wait for notification.","signature":""},{"type":"text","text":"E-005 is running in the background (30 GUE samples × 8 (λ,q) configurations, each building and analyzing a Gram matrix up to 1200×1200 — a few minutes).\n\n**What it's deciding** (recap):\n- For each bandwidth λ ∈ {0.5, ⅔, 0.8, 1.0} and oversampling q ∈ {1, 2}, it measures the spectral moments μ₁..μ₄ of the sinc-Gram matrix over simulated GUE spectra.\n- Then it computes the sharp one-sided bounds: 2-moment (Christoffel), **3-moment (Markov LP)** — the new resource — and 4-moment (reference).\n- **Decision rule**: the third-moment route survives only if some configuration with λ ≤ ⅔ (the unconditional range) beats the 2-moment bound materially *and* clears the ⅔ bar after conversion.\n\nI'll report the verdict as soon as it lands."}]