De Broglie Phase, Momentum, Flux, and Zero-Point Motion De Broglie Wave as O‑Field Phase in CRVD A Mathematical Note

This note states a minimal, explicitly mathematical CRVD-style phase/flux formulation in which the de Broglie wavelength arises from the phase field of an underlying substrate -field, and it explains why zero-point (ground-state) motion persists even at as a signature of a locked, non-vanishing phase/flux configuration rather than thermal agitation.