{"paper":{"title":"Slot decomposition of continuous Box-Ball Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Davide Gabrielli, In\\'es Armend\\'ariz, Pablo A. Ferrari, Pablo Blanc","submitted_at":"2026-06-18T21:25:09Z","abstract_excerpt":"We study a piecewise constant function $\\eta:\\mathbb R\\to\\{-1,1\\}$ with a finite number of discontinuities in any interval. We assume that the associated walk $\\xi:\\mathbb R\\to\\mathbb R$ satisfying $\\xi'(x)=\\eta(x)$, pinned by $\\xi(0)=0$, has finite length excursions over past minima. This is the continuous generalization of an initial ball configuration in the discrete Box Ball System introduced by Takahashi and Satsuma, where solitons of integer sizes $k\\ge1$ are identified.\n  We extend the slot decomposition developed by Ferrari, Nguyen, Rolla and Wang in the discrete setting to the continu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20948","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/2606.20948/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"}