Quantum Gradient Time Crystal Dilation: Classical Temporal-Opportunity Kernels and a Conditional Newtonian Calibration

Quantum Gradient Time Crystal Dilation (QGTCD) is the historical name of a documented proposal in which otherwise symmetric microscopic motion becomes directionally biased when neighboring states carry unequal temporal opportunity. This paper asks the narrower question that can presently be answered: what follows when that proposal is represented by explicit classical stochastic kernels? Three finite-step kernels are nonidentical but have, under matched smooth-lattice assumptions, the same leading drift-diffusion generator. On a compatible periodic lattice, the endpoint kernel's exact stationary measures converge to the invariant density of that limiting diffusion. These results identify a continuum model class while showing that the historical narrative does not select a unique microscopic rule. Directly interpreting its overdamped drift as universal free fall fails because the response scales with probe diffusivity. A separate position-velocity calibration removes that dependence only by importing u=-Phi/c ^2 and postulating a=c ^2 grad u; Newtonian acceleration then follows by substitution, not by derivation. Additive velocity noise without dissipation increases kinetic variance and supplies no equilibrium model. Setting c =c gives leading weak-field clock compatibility only after importing the standard clock map. The paper therefore proves conditional properties of a classical model family, defines an internal preparation-dependence discriminator, and states a preregistration-ready test structure. It does not derive a gravitational source law, equivalence principle, spacetime metric, light propagation, backreaction, quantum dynamics, or a prediction beyond general relativity. The current result is a bounded classical stochastic-model program and an explicit map of what a future gravity theory would still have to supply.