Accessible Phase-Space Geometry Predicts the Structure Functional in the Mixed Standard Map

FRC 100.002 v2.5 defined the structure functional Σ = S_vM(C) − S and deferred whether persistent mixed-regime Σ(∞) tracks measured phase-space geometry. Instrument A measures Σ(∞) from evolved ensembles over 12 seeds. Instrument B independently classifies the torus by finite-time Lyapunov exponent, flood-fills the accessible chaotic component from a wrapped seed region, and predicts Σ from the component's phase marginal with no fitted amplitude. Over K_c ≤ K ≤ 2.0, the prediction has 9.7% median relative error, versus 18.9% for a fitted island-area proxy. A 1000-realization fixed-area shuffle null gives zero exceedances and corrected empirical p = 1/1001 at K=K_c, 1.4, and 2.0; the real prediction lies 33.6–198.4 standard deviations above random placement. Thus spatial arrangement of the excluded regular region, not area alone, carries the predicted signal throughout the estimator-clean window. Grid, FTLE-time, and threshold convergence are reported. Below K_c the uniform-fill assumption fails by a factor of two; above K ≈ 2 histogram-bias corrections approach or exceed the signal.