[{"type":"thinking","thinking":"Committed. The git status shows the website agent's concurrent modifications (RH-WEBSITE.md, web/*) — not mine, leaving them untouched per the rule.\n\nReport the session's E-025 outcome. This is a natural pause point — long session, major findings including the correction. Summarize.","signature":""},{"type":"text","text":"Task 2.13 complete and committed (`370d918`). (The `web/` modifications in git status are the website agent's — untouched per your rule.)\n\n## E-025/D-043 — three findings, one of them a correction\n\n**1. The λ_a discretization floor.** The (Q,M) pencil bottom crosses zero at a ≈ 5.2 (h=0.01) and the negative values decay O(h) under refinement — a discretization artifact. The true λ_a is unresolvable for a ≳ 3 with this machinery, so the λ→λ_a⁻ experiment as designed is machinery-limited. Side effect: D-019 F1's cliff tail values at a ≳ 3 were already floor-limited (its upper-bound tag stands).\n\n**2. The λ-flow response is real but aims at the wrong mode.** Approaching near-singular T: valley depth Δ deepens (2.16 → 6.99 at a=4, the one clean case) and residual drops 48 → 11 — qualitatively exactly the predicted ground-state channel. But the bottom eigenvector is not ξ-like (corr(v̂, Ξ) ≈ 0), so nothing learned about the sister conjecture (1.2) yet; the true ground state lives below the floor.\n\n**3. Major correction — positional locking is real.** E-019's \"γ-proximity chance-level\" was computed in the wrong direction (median over ~10³ zeros spanning z ≤ 300 against only the first 30 γ's). The correct direction — each γ to its nearest W-zero — gives min-dist ≈ **0.65/a²**: quadratic, monotone-improving locking (15× tighter than chance at a=12). Errata filed to D-029 and D-040.\n\n**The revised consolidation picture** (cleaner than before the correction):\n- positions lock quadratically ✓ (already happening)\n- valley masses ≈ m_γ = 1 ✓ (already happening)\n- **the entire obstruction is now: excess-zero outflow + residual mass → Z/6 ≠ 0** (the linear-K equilibrium)\n\n**Next action** (queued): derive the linear-K law K_plateau ≈ (6/π)a analytically from T_a's spectral bulk and identify what breaks the equilibrium — that is now the sharpest point of the whole (★) route, since everything else is converging.\n\nSession 008 has been long and productive (R-004, D-040/41/38/42/43, E-022–E-025). State is clean and committed — a natural place to pause, or I can start the linear-K analysis."}]