{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:D7KSEUZKHVFWJCVR2U2PJ2AFHC","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":"8e99684d55267a3ba97fd2a0c04ba37aa251ed4eb0bc809c317c47d055511126","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-03-02T00:12:31Z","title_canon_sha256":"01592d28ca1c11fa9f94f1d0dc91804bfb4065ea389edf28300a7e804299697e"},"schema_version":"1.0","source":{"id":"0903.0192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.0192","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"arxiv_version","alias_value":"0903.0192v1","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0192","created_at":"2026-05-18T04:29:43Z"},{"alias_kind":"pith_short_12","alias_value":"D7KSEUZKHVFW","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"D7KSEUZKHVFWJCVR","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"D7KSEUZK","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:6068d19dbb73c4abaca068992faf416a7b8f5587137f2e232f8b111d94a2a10c","target":"graph","created_at":"2026-05-18T04:29:43Z","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"},"paper":{"abstract_excerpt":"A proof of the Generalized Road Coloring Problem, independent of the recent work by Beal and Perrin, is presented, using both semigroup methods and Trakhtman's algorithm. Algebraic properties of periodic, strongly connected digraphs are studied in the semigroup context. An algebraic condition which characterizes periodic, strongly connected digraphs is determined in the context of periodic Markov chains.","authors_text":"Greg Budzban, Philip Feinsilver","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-03-02T00:12:31Z","title":"The Generalized Road Coloring Problem and periodic digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0192","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":"sha256:8cd0364049e78b7ef65f1909f580c08a40f6a4d3774f7a59f2e2c819e9c57929","target":"record","created_at":"2026-05-18T04:29:43Z","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":"8e99684d55267a3ba97fd2a0c04ba37aa251ed4eb0bc809c317c47d055511126","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-03-02T00:12:31Z","title_canon_sha256":"01592d28ca1c11fa9f94f1d0dc91804bfb4065ea389edf28300a7e804299697e"},"schema_version":"1.0","source":{"id":"0903.0192","kind":"arxiv","version":1}},"canonical_sha256":"1fd522532a3d4b648ab1d534f4e80538b9980fad199b97d977c4bc755c2ced81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fd522532a3d4b648ab1d534f4e80538b9980fad199b97d977c4bc755c2ced81","first_computed_at":"2026-05-18T04:29:43.813623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:43.813623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sMOocnG70oz/ZS7l6VCeUW8nTE28Csj/hWKGX+XTuLglAnK+TCJTsW5C7YvwbLZ93KelKChvOv0W+JjCBR2ZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:43.814261Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.0192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cd0364049e78b7ef65f1909f580c08a40f6a4d3774f7a59f2e2c819e9c57929","sha256:6068d19dbb73c4abaca068992faf416a7b8f5587137f2e232f8b111d94a2a10c"],"state_sha256":"7ea4fa9e10aa7b14344692fc088f41964540dd0e29be241d4c98bc96b17b33dc"}