{"paper":{"title":"Spectral Topology and Universal Krylov Dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Hendrik J. R. Van Zyl, Jeff Murugan, Masataka Watanabe","submitted_at":"2026-08-07T14:14:49Z","abstract_excerpt":"The leading asymptotic growth of Lanczos coefficients is controlled by spectral tails and furnishes a coarse classification of Krylov dynamics. We show that the \\textit{global topology} of the spectral measure, specifically the number of connected components, the gap structure, and the behaviour at gap-closing transitions, encodes a finer hierarchy of dynamical invariants invisible to tail-based arguments. Using the Riemann-Hilbert formulation of orthogonal polynomials and Deift-Zhou steepest descent, we recover the Freud growth laws $b_n\\sim n^{1/\\beta}$ for single-cut measures and determine "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07258","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.07258/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}