{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4VPTNE7Q7UZQXR4UYHTQQPYWV4","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":"b1b3e138141255820e88b041c007c5a2137c03b51ef322f369a94312ec9c6153","cross_cats_sorted":["hep-th","math.RT","nlin.SI"],"license":"","primary_cat":"math.QA","submitted_at":"2006-04-26T17:33:08Z","title_canon_sha256":"349457f7f3074ae2239a3ad07a7e335f50af8839e0d048753c52f0cd4aca2707"},"schema_version":"1.0","source":{"id":"math/0604574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604574","created_at":"2026-07-04T17:02:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604574v2","created_at":"2026-07-04T17:02:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604574","created_at":"2026-07-04T17:02:09Z"},{"alias_kind":"pith_short_12","alias_value":"4VPTNE7Q7UZQ","created_at":"2026-07-04T17:02:09Z"},{"alias_kind":"pith_short_16","alias_value":"4VPTNE7Q7UZQXR4U","created_at":"2026-07-04T17:02:09Z"},{"alias_kind":"pith_short_8","alias_value":"4VPTNE7Q","created_at":"2026-07-04T17:02:09Z"}],"graph_snapshots":[{"event_id":"sha256:d996f83f25bc569c39f6e8fc7b6076b8683752bd1ffcf7f82c030a3fa4c75f61","target":"graph","created_at":"2026-07-04T17:02:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0604574/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we investigate in details the multiplications of the A-type and integrable matrix ODEs and PDEs generated by them.","authors_text":"Alexander Odesskii, Vladimir Sokolov","cross_cats":["hep-th","math.RT","nlin.SI"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2006-04-26T17:33:08Z","title":"Integrable matrix equations related to pairs of compatible associative algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604574","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:b1d89dc028cd777e4dabed7ad0e5f008bf1b4e1ac4047cb086ee8cb33915db58","target":"record","created_at":"2026-07-04T17:02:09Z","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":"b1b3e138141255820e88b041c007c5a2137c03b51ef322f369a94312ec9c6153","cross_cats_sorted":["hep-th","math.RT","nlin.SI"],"license":"","primary_cat":"math.QA","submitted_at":"2006-04-26T17:33:08Z","title_canon_sha256":"349457f7f3074ae2239a3ad07a7e335f50af8839e0d048753c52f0cd4aca2707"},"schema_version":"1.0","source":{"id":"math/0604574","kind":"arxiv","version":2}},"canonical_sha256":"e55f3693f0fd330bc794c1e7083f16af35e4893caa4f83081499e6348dacdfd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e55f3693f0fd330bc794c1e7083f16af35e4893caa4f83081499e6348dacdfd5","first_computed_at":"2026-07-04T17:02:09.124639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:02:09.124639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QnNlwyUUlhjEg2m44fRlCr/JUAINLPC/EoNUbwgjalnbz7b21m5udYFYCQ0/Yaon21ZpxfcvyjTaoCAXggrUDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:02:09.124983Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1d89dc028cd777e4dabed7ad0e5f008bf1b4e1ac4047cb086ee8cb33915db58","sha256:d996f83f25bc569c39f6e8fc7b6076b8683752bd1ffcf7f82c030a3fa4c75f61"],"state_sha256":"5259a2e590bb6e153b02440121d6a9602aba27df1dce9310e586cb394670ea20"}