{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZJOMW5FJZPQKNSIFZIHIPA4Q7R","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dd7d10851d391ed490e5a4072827494f7fe01bc93a71206260f3e1dd95e6cdc4","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-07-01T03:05:25Z","title_canon_sha256":"197b773007ba82c2bc002e0a7f73f6120a3bbbdff8faa9945b9aff4bd62a87e7"},"schema_version":"1.0","source":{"id":"2607.00367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00367","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00367v1","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00367","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZJOMW5FJZPQK","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_16","alias_value":"ZJOMW5FJZPQKNSIF","created_at":"2026-07-02T01:17:41Z"},{"alias_kind":"pith_short_8","alias_value":"ZJOMW5FJ","created_at":"2026-07-02T01:17:41Z"}],"graph_snapshots":[{"event_id":"sha256:f3a82bc0f94f288d2934aac634638c5ffadd3c719443c5dee37f634f479be434","target":"graph","created_at":"2026-07-02T01:17:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.00367/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Ruijun Wang","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-07-01T03:05:25Z","title":"The continuous oriented chromatic number of directed Schreier graphs of \\(\\mathbb Z^2\\)-shift actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00367","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ccb1ae6a2400f34f729b2ff216678d0865d410ec4b00aa0e2c35016d6ad24b10","target":"record","created_at":"2026-07-02T01:17:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dd7d10851d391ed490e5a4072827494f7fe01bc93a71206260f3e1dd95e6cdc4","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-07-01T03:05:25Z","title_canon_sha256":"197b773007ba82c2bc002e0a7f73f6120a3bbbdff8faa9945b9aff4bd62a87e7"},"schema_version":"1.0","source":{"id":"2607.00367","kind":"arxiv","version":1}},"canonical_sha256":"ca5ccb74a9cbe0a6c905ca0e878390fc734d5d2ced72ac54ccc282ee1639189e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca5ccb74a9cbe0a6c905ca0e878390fc734d5d2ced72ac54ccc282ee1639189e","first_computed_at":"2026-07-02T01:17:41.359359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:17:41.359359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V7+h1D45VGM6VfpioQgx0KK8d4W4rIw1U7nOpZ6k9GUWxwMQUQTLjVsJvozXxqCmiX8Dab0sgMAuor+mpQkfDA==","signature_status":"signed_v1","signed_at":"2026-07-02T01:17:41.359798Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccb1ae6a2400f34f729b2ff216678d0865d410ec4b00aa0e2c35016d6ad24b10","sha256:f3a82bc0f94f288d2934aac634638c5ffadd3c719443c5dee37f634f479be434"],"state_sha256":"977e7bf9976f2d47667f9a31cb9059038ef1ee7589e11cc3711b580e2c1ac311"}