FRC 566.030 — Reciprocity in Action: The Entropy-Coherence Current Across a Synchronization Transition

FRC 566.030 develops an exactly solvable open-system diagnostic for entropy-coherence reciprocity in the von Mises / mean-field Kuramoto case. It computes the system-only quantity Q = S + ln C across a synchronization transition and shows that Q is non-constant, peaking near C ≈ 0.62, as expected when coherence is traded with an environment. The release includes the rendered manuscript PDF, Markdown source, regenerated figure, table, metrics JSON, and Python code that reproduces the closed-form Bessel-function calculation. No fitting, simulation, or estimator is used.