{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BM2Z65UWHC6YO2E5O5JLVEBVFF","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":"6c17cc1fc9f40bcc7798bcea83f1c5fa9dabca1903917b441c3e7efde86be0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-01-31T13:11:42Z","title_canon_sha256":"d4890a5e55e586216672996798e79e31587f35ad472547fae1bc79a37efbac0b"},"schema_version":"1.0","source":{"id":"1801.10436","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10436","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10436v3","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10436","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"BM2Z65UWHC6Y","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BM2Z65UWHC6YO2E5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BM2Z65UW","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:f01f4da6e95bad843332058a1b501fa7eac30f1422d950b7b0cbef0f373f043b","target":"graph","created_at":"2026-05-18T00:05:39Z","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":"It was conjectured by \\v{C}ern\\'y in 1964, that a synchronizing DFA on $n$ states always has a synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \\leq 5$, and with bounds on the number of symbols for $n \\leq 12$. Here we give the full analysis for $n \\leq 7$, without bounds on the number of symbols.\n  For PFAs (partial automata) on $\\leq 7$ states we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-","authors_text":"Hans Zantema, Henk Don, Michiel de Bondt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-01-31T13:11:42Z","title":"Lower Bounds for Synchronizing Word Lengths in Partial Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10436","kind":"arxiv","version":3},"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":"sha256:05c4cf55e6af0d91af91e3a34bccd0bb080736dc789f18eec70cea6b3590ac3e","target":"record","created_at":"2026-05-18T00:05:39Z","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":"6c17cc1fc9f40bcc7798bcea83f1c5fa9dabca1903917b441c3e7efde86be0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2018-01-31T13:11:42Z","title_canon_sha256":"d4890a5e55e586216672996798e79e31587f35ad472547fae1bc79a37efbac0b"},"schema_version":"1.0","source":{"id":"1801.10436","kind":"arxiv","version":3}},"canonical_sha256":"0b359f769638bd87689d7752ba9035294b027d1825e5c5c3d34e5a6668c607f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b359f769638bd87689d7752ba9035294b027d1825e5c5c3d34e5a6668c607f4","first_computed_at":"2026-05-18T00:05:39.394134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:39.394134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cgKV/OsPTEcD3bvh18N+/JuF/D5wzdi7SlLYNRxbsI2ZHC0qe1QKURg+8eCBCystYu4reKVv7Dhjkar5vli/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:39.394574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10436","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05c4cf55e6af0d91af91e3a34bccd0bb080736dc789f18eec70cea6b3590ac3e","sha256:f01f4da6e95bad843332058a1b501fa7eac30f1422d950b7b0cbef0f373f043b"],"state_sha256":"911f871e743e219072e091f080014e369f4e3174e7076b718196a4728ddca0fa"}