{"paper":{"title":"A Measure-Theoretic Approach to Spontaneous Stochasticity","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"nlin.CD","authors_text":"Eric Simonnet, Nicolas Valade, Wandrille Ruffenach","submitted_at":"2026-07-15T15:27:32Z","abstract_excerpt":"Spontaneous stochasticity (SpSt), originating in Richardson's picture of turbulent dispersion and Lorenz's Eulerian view of finite-time loss of predictability, was later formulated under this name by Gaw\\k{e}dzki and collaborators and developed in shell models by Mailybaev and collaborators. Whether it occurs in fully developed turbulence remains a major open question.\n  Beyond a few specific classes of systems, however, SpSt has lacked a general mathematical definition. We introduce a measure-theoretic formalism in which it is understood as a measure-selection principle. Given an inviscid pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16328","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/2607.16328/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"}