Condensation as Maximum Coherence_ A Deterministic Law for Wave-to-Matter Transition

Full Paper Description Problem. Current accounts of condensation (BECs, crystallization, biomolecular folding) lean on stochastic narratives (“noise-driven emergence”). Claim. Condensation is lawful: it occurs only when a system’s Phase Alignment Score (PAS_s) crosses a coherence threshold θ and drift (ΔPAS_zeta) collapses below ε_drift within a bounded time window τ_k. Method. I formalize PAS_s and ΔPAS_zeta as estimator-agnostic metrics of phase coherence and drift, then state a falsifiable law candidate: condensation ⇔ PAS lock (PAS_s ≥ θ ∧ ΔPAS_zeta ≤ ε_drift over τ_k). Evidence/Design. I outline test protocols for three domains—Bose–Einstein condensation, crystal nucleation, and DNA folding—and specify falsification: any verified condensation event with PAS_s < θ or ΔPAS_zeta > ε_drift invalidates the claim. Implication. In systems where PAS variables are measurable, coherence, not probability, governs the wave-to-matter transition; stochastic models become approximations of underlying phase alignment dynamics. Resources. Figures include: (1) coherence build-up curve; (2) BEC time-series with PAS overlay; (3) cross-domain invariant; (4) falsifiability window. Code and data hooks to follow in a companion repository. Note. This preprint isolates one claim from the broader CODES framework (structured resonance). It is offered as a testable substrate law, not a philosophical statement.