K_d(x,y) = Σ_{k=0}^{d−1} φ_k(x)φ_k(y), with φ₀ = π^(−1/4)e^(−x²/2), φ₁ = √2 x φ₀ and the normalized Hermite three-term recurrence. The sum representation evaluates the diagonal directly. The Airy section uses (Ai(u)Ai′(0)−Ai′(u)Ai(0))/u and Ai′(0)² at u = 0.

These are deterministic weighted projection-kernel sections, not sampled ESDs. Float64 recurrence and SciPy Airy evaluation provide the curves; the finite-grid residual is a diagnostic, not a uniform error bound or universality proof.

The edge-CDF view uses det(I − √W K √W) with 64 Gauss–Legendre nodes on [s,10] in edge coordinates. For the reference, K is the Airy kernel, whose diagonal is Ai′(u)²−u Ai(u)²; finite ranks use the rescaled Hermite kernel. Refinement to 96 nodes and extension to cutoff 14 are checked on every stored threshold. Both are approximate half-line CDFs; tiny sensitivity differences are empirical diagnostics, not certified tail bounds. The finite-rank curve is not itself Tracy–Widom.