Spectral origin of the topological gap exponent d + {\eta}: mechanism, kernel, decomposition, and scope

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arXiv:2609.09159v1 Announce Type: new Abstract: The topological gap $\Delta$ -- the excess $H_1$ total persistence of a critical point cloud over a density-matched null -- scales as $\Delta \sim L^{d+\eta}$. We derive this analytically: the spectral integral $I(\alpha) = \sum_{k\neq 0} S_{\mathrm{c…

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1. 2026-09-10 04:00 · arXiv cs.LG
   Spectral origin of the topological gap exponent d + {\eta}: mechanism, kernel, decomposition, and scope