{"paper":{"title":"The continuous oriented chromatic number of directed Schreier graphs of \\(\\mathbb Z^2\\)-shift actions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Ruijun Wang","submitted_at":"2026-07-01T03:05:25Z","abstract_excerpt":"Let \\(\\vec F(2^{\\mathbb Z^2})\\) be the directed Schreier graph on the free part of the Bernoulli shift \\(\\mathbb Z^2\\curvearrowright 2^{\\mathbb Z^2}\\), with arcs in the two coordinate directions. We prove that the continuous oriented chromatic number of it is 7, that is, there is a tournament on 7 vertices receiving a continuous graph homomorphism from $\\vec F(2^{\\mathbb Z^2})$ and there is no continuous graph homomorphism from $\\vec F(2^{\\mathbb Z^2})$ to any tournament on 6 vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00367","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/2607.00367/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"}