arXiv:2604.01484v1 Announce Type: cross
Abstract: The topological gap $\Delta = TP_{H_1}^{real} – TP_{H_1}^{shuf}$ — the excess $H_1$ total persistence of the majority-spin alpha complex over a density-matched null — encodes critical correlations in…
arXiv:2603.29072v1 Announce Type: cross
Abstract: Point-cloud persistent homology (PH) — computing alpha or Rips complexes on spin-position point clouds — has been widely applied to detect phase transitions in classical spin models since Donato et a…
arXiv:2603.27903v1 Announce Type: cross
Abstract: We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the eigenvalues of the symm…
arXiv:2603.27885v1 Announce Type: new
Abstract: We investigate whether spectral properties of neural network weight matrices can predict test accuracy. Under controlled label noise variation, the tail index alpha of the eigenvalue distribution at the …