{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DRI2G4FYYOS7TKQRUAQR4YNV27","short_pith_number":"pith:DRI2G4FY","schema_version":"1.0","canonical_sha256":"1c51a370b8c3a5f9aa11a0211e61b5d7f6b252978997e0d0b4281242afa43d5d","source":{"kind":"arxiv","id":"1511.03184","version":1},"attestation_state":"computed","paper":{"title":"Between primitive and $2$-transitive: Synchronization and its friends","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Benjamin Steinberg, Jo\\~ao Ara\\'ujo, Peter J. Cameron","submitted_at":"2015-11-10T17:04:56Z","abstract_excerpt":"An automaton is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by the \\v{C}ern\\'y conjecture, one of the oldest and most famous problems in automata theory, according to which a synchronizing $n$-state automaton has a reset word of length at most $(n-1)^2$. The transitions of an automaton generate a transformation monoid on the set of states, and so an automaton can be regarded as a transformation monoid with a prescribed set of generators. In this setting, an automaton is synchron"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.03184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-11-10T17:04:56Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1e7233b918cd37f6a9d67176f11fb01d2fe783f241e5b487441d8767e30ec0a5","abstract_canon_sha256":"d126ffa3f5274b5fbaa8dc78e1afec63de344e739cdae54502c75406596a5757"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:43.711888Z","signature_b64":"WlVAWPuZELwY2idGk4zNBi2ItnNG1JjuEvAoh0Izixm2wC+5uYLOaeqS+c7ioB/eBdIVMkomycBKiFLkGPB9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c51a370b8c3a5f9aa11a0211e61b5d7f6b252978997e0d0b4281242afa43d5d","last_reissued_at":"2026-05-17T23:44:43.711463Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:43.711463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Between primitive and $2$-transitive: Synchronization and its friends","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Benjamin Steinberg, Jo\\~ao Ara\\'ujo, Peter J. Cameron","submitted_at":"2015-11-10T17:04:56Z","abstract_excerpt":"An automaton is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by the \\v{C}ern\\'y conjecture, one of the oldest and most famous problems in automata theory, according to which a synchronizing $n$-state automaton has a reset word of length at most $(n-1)^2$. The transitions of an automaton generate a transformation monoid on the set of states, and so an automaton can be regarded as a transformation monoid with a prescribed set of generators. In this setting, an automaton is synchron"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03184","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.03184","created_at":"2026-05-17T23:44:43.711525+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03184v1","created_at":"2026-05-17T23:44:43.711525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03184","created_at":"2026-05-17T23:44:43.711525+00:00"},{"alias_kind":"pith_short_12","alias_value":"DRI2G4FYYOS7","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DRI2G4FYYOS7TKQR","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DRI2G4FY","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27","json":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27.json","graph_json":"https://pith.science/api/pith-number/DRI2G4FYYOS7TKQRUAQR4YNV27/graph.json","events_json":"https://pith.science/api/pith-number/DRI2G4FYYOS7TKQRUAQR4YNV27/events.json","paper":"https://pith.science/paper/DRI2G4FY"},"agent_actions":{"view_html":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27","download_json":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27.json","view_paper":"https://pith.science/paper/DRI2G4FY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03184&json=true","fetch_graph":"https://pith.science/api/pith-number/DRI2G4FYYOS7TKQRUAQR4YNV27/graph.json","fetch_events":"https://pith.science/api/pith-number/DRI2G4FYYOS7TKQRUAQR4YNV27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27/action/storage_attestation","attest_author":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27/action/author_attestation","sign_citation":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27/action/citation_signature","submit_replication":"https://pith.science/pith/DRI2G4FYYOS7TKQRUAQR4YNV27/action/replication_record"}},"created_at":"2026-05-17T23:44:43.711525+00:00","updated_at":"2026-05-17T23:44:43.711525+00:00"}