Michael Chertkov

When path integral diffusion (PID) generates a finite Ising spin glass from a point source, each trajectory first chooses one of the two mirror halves of the zero-field measure, then decides among glassy classes inside that half. Theory shows every isotropic PID is Gaussian stochastic localization seen on a different clock, so the protocol sets when decisions happen and what they cost, not what is decided; on exactly enumerable Bethe and SK glasses, nested glassy levels are often settled in one or two distinct events, and these classes appear near the glass transition, keep their identity on cooling, and are absent in a ferromagnet on the same graphs.

When path integral diffusion (PID) generates a finite Ising spin glass from a point source, each trajectory first chooses one of the two mirror halves of the zero-field measure, then decides among glassy classes inside that half. Theory shows every isotropic PID is Gaussian stochastic localization seen on a different clock, so the protocol sets when decisions happen and what they cost, not what is decided; on exactly enumerable Bethe and SK glasses, nested glassy levels are often settled in one or two distinct events, and these classes appear near the glass transition, keep their identity on cooling, and are absent in a ferromagnet on the same graphs.