FRC 100. 002 v2. 5 defined the structure functional Σ = SᵥM (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 Kc ≤ 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=Kc, 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 Kc the uniform-fill assumption fails by a factor of two; above K ≈ 2 histogram-bias corrections approach or exceed the signal.
Hadi Servat (Fri,) studied this question.