{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MH2XRDHMLXDQLVK655J3QFJAVN","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":"42570ddd949bca81f29dd965ac1e9306c15d878705670006a7bff4cd9e579ddb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-20T20:21:07Z","title_canon_sha256":"2c1f8016c4b2cab20bf40a876abfbaa7b7f1c546aff4fec00523d16b56f5c0f9"},"schema_version":"1.0","source":{"id":"1605.06529","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06529","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06529v2","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06529","created_at":"2026-05-18T01:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"MH2XRDHMLXDQ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MH2XRDHMLXDQLVK6","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MH2XRDHM","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:1156f03465e3fdd6c6ef76a3b946bdd96a45456151c453cc600d47b64640deef","target":"graph","created_at":"2026-05-18T01:07:56Z","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":"Each finite-dimensional algebra can be identified to the cubic matrix given by structural constants defining the multiplication between the basis elements of the algebra. In this paper we introduce the notion of flow (depending on time) of finite-dimensional algebras. This flow can be considered as a particular case of (continuous-time) dynamical system whose states are finite-dimensional algebras with matrices of structural constants satisfying an analogue of Kolmogorov-Chapman equation. These flows of algebras (FA) can also be considered as deformations of algebras with the rule (the evoluti","authors_text":"M. Ladra, U.A. Rozikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-20T20:21:07Z","title":"Flow of finite-dimensional algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06529","kind":"arxiv","version":2},"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":"sha256:48adcf7c74064ab47f53f54b0f96db5cfb488597a5f77defb430920ac1d20ef4","target":"record","created_at":"2026-05-18T01:07:56Z","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":"42570ddd949bca81f29dd965ac1e9306c15d878705670006a7bff4cd9e579ddb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-05-20T20:21:07Z","title_canon_sha256":"2c1f8016c4b2cab20bf40a876abfbaa7b7f1c546aff4fec00523d16b56f5c0f9"},"schema_version":"1.0","source":{"id":"1605.06529","kind":"arxiv","version":2}},"canonical_sha256":"61f5788cec5dc705d55eef53b81520ab6c9a7f850ccb06f79c4567efd414fb4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61f5788cec5dc705d55eef53b81520ab6c9a7f850ccb06f79c4567efd414fb4c","first_computed_at":"2026-05-18T01:07:56.593502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:56.593502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LZKtGu+ERKQ5X7YGr9SmcZVwdF4bex2P3d647tf51pjyaiNLuF+k42J9WdmDWBGAgb6tCxGg/1N8YrD1mFeNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:56.594083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06529","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48adcf7c74064ab47f53f54b0f96db5cfb488597a5f77defb430920ac1d20ef4","sha256:1156f03465e3fdd6c6ef76a3b946bdd96a45456151c453cc600d47b64640deef"],"state_sha256":"13e3a733fcc5d7b202d858e7a4d1863b6f8c7cd6a2ef95fd631455d3b053bdbb"}