Reconstruction of Heat Geometry from a Scalar Process
Year: 2026
Type: preprint
Abstract: A smooth scalar process with one fixed Gaussian covariance kernel determines any finite graded family of symmetric Hilbert tensors up to a common orthogonal isomorphism of their minimal supports. For two heat tensors, its law determines a closed positive-dimensional Riemannian manifold, a Euclidean bundle, its connection and potential, and the unknown heat time, up to isometry and gauge. The quadratic tensor recovers the scaled generator; the quartic tensor recovers the spatial norm and volume, which fix the time scale. For compact finite-dimensional RCD spaces, the same law determines the measured space with distance divided by the square root of the heat time.
Source: arXiv (Cornell University)
Author: Assaad, Obayda Julien
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214215665