FRC 100. 002 defines the structure functional Σ = SᵥM (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 Kc ≤ 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.
Hadi Servat (Sun,) studied this question.