Abstract
Positive Fokker–Planck dynamics can reproduce stationary quantum densities and open-system phase-space evolution, but this does not by itself establish unitary Schrödinger dynamics or an individual measurement outcome. We analyze the compatibility conditions among these levels in a drift–diffusion–circulation model motivated by the Architecture of Distinction. After fixing physical dimensions, harmonic ground-state matching yields a diffusion–frequency relation, while a multimode common-clock criterion separates spectral correspondence from a shared physical time calibration. An explicit phase–density Hamiltonian supplies the additional information required for local Schrödinger evolution, with global winding conditions stated separately. A Husimi oscillator provides an exact positive three-term quantum example. For measurement, we reconstruct a finite-time completely positive instrument from an explicit contact and registration rules and distinguish apparatus backaction from conditional state update. Numerical checks verify the analytic identities and channel properties. We formulate quantitative consistency tests for harmonic matching, timing–visibility relations, finite record retention, and a separately postulated momentum-diffusion channel. The results identify which quantum structures can be represented within a positive diffusion framework and which require additional phase, operator, apparatus, or interpretive input. No individual outcome or parameter-free departure from quantum mechanics is derived from scalar diffusion alone.