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RelatedCoherenceanswer-appendixchaosEntropyfinite-time-lyapunovflood-fillFRC 100 seriesFRC 566 series

Primary research (1)

PrimaryPaperv1.32026-07-09

Reciprocity in Action v1.3: Exact System-Only Motion and a Scoped Boundary Test

FRC 566.030 applies the canonical reciprocity law dS + k* d ln C = 0 through one explicit information-unit realization. With the predeclared representation k*_{mu_nat}=1, it computes Q=S+k*_{mu_nat} ln C exactly on the von Mises/Kuramoto family. Q is non-constant and reaches its unique stationary point at kappa r=1, kappa=1.608279 and C=0.621782. The exact identity is dS/d ln C=-kappa r, hence dQ/d ln C=k*_{mu_nat}-kappa r. This stationary point is dQ=0; it is not sigma_566=0 unless an explicit environment model supplies that additional equality. The family contains no bath and therefore measures neither irreversible production nor entropy export. A companion Langevin closure tests those quantities in one model class and finds no universal erasure floor in its declared normalization.

Frontier research (1)

FrontierPaperv1.32026-07-10

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.