FRC 100.002.001 v1.5 - Accessible Phase-Space Geometry Predicts the Structure Functional in the Mixed Standard Map

FRC 100.002 defines the structure functional Σ = S_vM(C) − S, equivalently the KL projection deficit from the measured phase marginal to the matched von Mises maximum-entropy member. 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, and predicts Σ from the component's phase marginal with no fitted amplitude. Over K_c ≤ K ≤ 2.0, the original coarse sweep retains 9.7% median relative error, versus 18.9% for a fitted island-area proxy; fixed-area shuffle nulls reject random placement. A subsequently frozen dense Gate 4 test selected the strongest geometry-curvature window automatically and evaluated ten unseen midpoint conditions with 12 new seeds each. There measured Σ has essentially no rank relation to regular area (ρ=0.030, one-sided permutation p=0.477), while negative entropy supplies a stronger monotonic rank baseline (ρ=0.964). The full geometry prediction has 8.7% median magnitude error but is beaten by the frozen area-only baseline at 6.6%. Estimator, seed, null, and convergence controls pass. The coarse magnitude correspondence remains a scoped result; the registered route to pillar-level fine geometric discrimination is not passed and is closed without window search.