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@philphi.bsky.social

The Gaussian isn't treated as fundamental in Gaussoherence. The Fisher heat kernel is deeper with the Gaussian appearing as its local normal-coordinate form; the short-time asymptotic of diffusion on the Fisher. Gaussian smoothing is a coordinate shadow of Fisher geometry, not the mechanism itself.

19/6/26, 3:35 pm0 reposts0 likes

PHI

@philphi.bsky.social

19 June

Fisher width reinforces this. Just as Fisher width replaces Euclidean Gaussian width with a complexity measure built from the Fisher metric, the Fisher heat kernel replaces Euclidean diffusion with dynamics governed by distinguishability. Both constructions are reparameterizationinvariant and depend

PHI

@philphi.bsky.social

19 June

on the intrinsic geometry encoded by the Fisher. The quantum-to-classical transition is controlled by Fisher spectral structure. High-distinction modes contract rapidly under the Fisher heat flow while Fisher-smooth modes survive coarse-graining; Gaussian asymptotic shadow is a classical description