{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NMRG4CE3TPGQI2E5OININQJVBD","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":"acb55ec9b1fc57727eeb4dd443470ae1c71388869c65b0ea86fd930a790c23cf","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-18T19:22:34Z","title_canon_sha256":"36effd53db6000b621c2326a9fa5ec62327f57c6942f7b8178e2ab5fb3afd3e5"},"schema_version":"1.0","source":{"id":"1506.06017","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06017","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06017v1","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06017","created_at":"2026-05-18T01:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"NMRG4CE3TPGQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NMRG4CE3TPGQI2E5","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NMRG4CE3","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:a3db2eba4584fbe3263d7ca1c99969dd2c7ccf6498c995c644e13d471fdd4aee","target":"graph","created_at":"2026-05-18T01:42:46Z","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":"The Krohn-Rhodes complexity theory for pure (without linearity) automata is well-known. This theory uses an operation of wreath product as a decomposition tool. The main goal of the paper is to introduce the notion of complexity of linear automata. This notion is ultimately related with decompositions of linear automata. The study of these decompositions is the second objective of the paper. In order to define complexity for linear automata, we have to use three operations, namely, triangular product of linear automata, wreath product of pure automata and wreath product of a linear automaton w","authors_text":"Boris Plotkin, Tatjana Plotkin","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-18T19:22:34Z","title":"Decompositions and complexity of linear automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06017","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":"sha256:8301b7f1e50c3fc9b92de60d333285ae8a02267a0d620b5685dfde260a1ca475","target":"record","created_at":"2026-05-18T01:42:46Z","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":"acb55ec9b1fc57727eeb4dd443470ae1c71388869c65b0ea86fd930a790c23cf","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-06-18T19:22:34Z","title_canon_sha256":"36effd53db6000b621c2326a9fa5ec62327f57c6942f7b8178e2ab5fb3afd3e5"},"schema_version":"1.0","source":{"id":"1506.06017","kind":"arxiv","version":1}},"canonical_sha256":"6b226e089b9bcd04689d721a86c13508db0d86c72eb40fb687becc3d7beb605e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b226e089b9bcd04689d721a86c13508db0d86c72eb40fb687becc3d7beb605e","first_computed_at":"2026-05-18T01:42:46.478838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:46.478838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"elB6AyyZcBjnlsJbe8cBa2vMpXLXFAImjJJZJMLVOaC4553rs6tOnIoetCyeWOKHKVnGp9WwmtIPZcwfziD5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:46.479480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06017","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8301b7f1e50c3fc9b92de60d333285ae8a02267a0d620b5685dfde260a1ca475","sha256:a3db2eba4584fbe3263d7ca1c99969dd2c7ccf6498c995c644e13d471fdd4aee"],"state_sha256":"1648a441c135b84d5f7c2f2948599d880a2464b0b7e66af90370e0e13d3426e4"}