{"paper":{"title":"Temporal Matrix Scale Invariance and the Classification of Tipping Points","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.CD","authors_text":"Alejandro Frank, Laurence A. Jacobs","submitted_at":"2026-05-31T19:48:39Z","abstract_excerpt":"We introduce temporal matrix scale invariance (tMSI), a mathematical structure for the two-time correlation kernel of a multivariate observable. A kernel $C(t,t')$ satisfies tMSI of order $\\alpha$ if $C(kt, kt') = k^{-\\alpha}C(t,t')$ for all $k>0$; this condition holds near a tipping point, where the divergence of the coherence time produces temporal scale freedom. By a kernel factorization theorem, every tMSI kernel separates into a power-law envelope $(tt')^{-\\alpha/2}$ and a shape function $F(t/t')$ diagonalized by the Mellin transform. This reveals a decoupling of two independent exponents"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02649","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/2606.02649/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"}