//! Spectral decode of the learned graph atom: eigengap basis, Nyström
//! out-of-sample coordinate + analytic jet, penalty/Dirichlet-form identity, and
//! the reconstruction advantage of a `q`-dimensional spectral decode over a
//! single typed circle atom on a shape outside the typed zoo.
// (d) — eigengap q-selection recovers q = 2 for the circle, and the embedding
// dimension is deliberately NOT tied to the first Betti number.
// (1) — the decode penalty and the graph Dirichlet form are the SAME object:
// diag(λ) == Φᵀ L_W Φ, where L_W is the atom's own surviving Laplacian.
// (a) — planted noisy circle: Nyström spectral coordinates achieve
// orientation-quotiented circular correlation > 0.95 against the true angle.
// (c) — the analytic Nyström jet matches a central-difference check to 1e-5
// relative (finite differences are legal in test code, banned in src).
// (b) — planted figure-eight (outside the typed zoo): the q-dimensional spectral
// decode reconstructs the shape with EV clearly beating the best single typed
// circle atom fit, both scored through the same public closed-form REML fitter.
// The Nyström extension is a first-class basis evaluator: the trait `evaluate`
// path agrees with the batched coordinate call.