Fokker–Planck Dynamics, Schrödinger Evolution, and Quantum Measurement: A Consolidated Compatibility Analysis with a Multimode Common-Clock Criterion

Mathematical similarities between Fokker–Planck diffusion, Schrödinger evolution and quantum measurement do not establish physical equivalence. We identify separate requirements for stationary-density matching, a shared spectral clock, quantum-state admissibility and measurement statistics. For harmonic gradient diffusion, matching a quantum ground-state position density fixes only the ratio of spatial diffusivity to relaxation rate. A common clock across independently identified modes additionally requires equal relaxation-to-frequency ratios, equivalently equal mass-weighted diffusivities. Two independently calibratable residuals distinguish these requirements; circulating Ornstein–Uhlenbeck countermodels retain the matched stationary marginals without satisfying the common-clock condition. A laboratory test requires an independently specified carrier in the strongly overdamped regime; none is identified here. We distinguish density Fisher information from quantum Fisher information, specify the phase structure needed for local Schrödinger evolution, and state Husimi-state and quantum-channel admissibility criteria. A previously published completely positive measurement instrument provides a benchmark for finite-time records and backaction. Its Born weights and threshold preparation are supplied inputs. Selected earlier Architecture of Distinction (AoD) identifications are also clarified and corrected. Neither the Born rule nor an individual outcome is derived, and no parameter-free departure from quantum mechanics is predicted.