{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NWN532WHXGSNFWRA5FJK7OYT3N","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":"f7d4e14b9f23be8ab1cc70bf01fdd14811e97693c0f6c57f08c8756f2fe85545","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-05-11T17:13:04Z","title_canon_sha256":"69860b389bdfaaea29e22022d305844b12b597dc2fb8fdf51efdf85dd08dddc6"},"schema_version":"1.0","source":{"id":"1405.2553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2553","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2553v1","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2553","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"NWN532WHXGSN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NWN532WHXGSNFWRA","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NWN532WH","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:14eadde4cae709ad0a1de9a498c8f9a7fa1bf1f213e7ad3a36b46a54d00049b4","target":"graph","created_at":"2026-05-18T02:52:05Z","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":"We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of matrix rank into a regular language L, the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and focus on rank-one languages: the class of languages for which the rank of minimal automaton is one. We also define the expanded canonical automaton of a rank-one language.","authors_text":"Ryoma Sin'ya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-05-11T17:13:04Z","title":"Graph Spectral Properties of Deterministic Finite Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2553","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":"sha256:08a18da5e76fb35da5f0556bc95c8f44c3ec0298acf781b6d3588d32ccb370ce","target":"record","created_at":"2026-05-18T02:52:05Z","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":"f7d4e14b9f23be8ab1cc70bf01fdd14811e97693c0f6c57f08c8756f2fe85545","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2014-05-11T17:13:04Z","title_canon_sha256":"69860b389bdfaaea29e22022d305844b12b597dc2fb8fdf51efdf85dd08dddc6"},"schema_version":"1.0","source":{"id":"1405.2553","kind":"arxiv","version":1}},"canonical_sha256":"6d9bddeac7b9a4d2da20e952afbb13db44576e74b2092fe6bfed90bcea12da58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d9bddeac7b9a4d2da20e952afbb13db44576e74b2092fe6bfed90bcea12da58","first_computed_at":"2026-05-18T02:52:05.256580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:05.256580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uZRYW1SipWOqNJZTaapQ5dDJpsEndQNkupBz5vHEcVQaSOSmi6W57ccTg+pNsmT/C50hfl5uaPZDmFWqLqgJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:05.257079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a18da5e76fb35da5f0556bc95c8f44c3ec0298acf781b6d3588d32ccb370ce","sha256:14eadde4cae709ad0a1de9a498c8f9a7fa1bf1f213e7ad3a36b46a54d00049b4"],"state_sha256":"1cf7da009864b98be008ba7d747f05013e88714723d870fe90a616af89ebd1f5"}