The φ-Selection Conjecture: A Dynamical Selection Principle for Stationary-Action Configurations

A falsifiable dynamical conjecture: of the stationary-action configurations available to a near-integrable Hamiltonian system, the ones that persist under perturbation are those whose characteristic frequency ratios are the most irrational (φ-closest). Mechanism: KAM/Diophantine theory — the golden mean is the hardest irrational to approximate (Hurwitz), so resonant configurations break first and the system is selected down to φ. Includes explicit domain restrictions, three falsifiers (F1–F3), one supporting instance (golden mean uniquely topping the KAM-breakup threshold at 0.9717 across 16 rotation numbers, apparatus validated against Greene's 0.97163540631), and a preregistered Test P1 (two-harmonic standard map, 16 rotation numbers, Greene residue criterion) — NOT YET RUN. Companion file records the preregistered null battery (T1–T8) that exhausted the spectral/flavor forms of φ-tuning in particle masses and mixing angles. Status: conjecture, not result. Formalized with AI assistance (Melody, Muse Spark); all tests were preregistered before running and are reported as run.