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

This corrected preprint presents its research question, method, bounded result, and principal limitations in a standardized reader-facing format. 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. It belongs to the Super Information Theory, Super Dark Time, and QGTCD physics research program. This is a corrected preprint edition released under the Creative Commons Attribution 4.0 license.