{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:67BGAB4YV4QLZROLES5E6BOJH7","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":"9270d4746bb238b31ad76d1b04700a47f271e4b12c8b9304bbaf75c2e6e8010a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-05-28T14:52:01Z","title_canon_sha256":"88ed37d260af57e0d4bc0e26b7a1b66c4fb346db81536805573460738d1c0715"},"schema_version":"1.0","source":{"id":"2405.18243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.18243","created_at":"2026-07-05T09:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"2405.18243v2","created_at":"2026-07-05T09:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.18243","created_at":"2026-07-05T09:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"67BGAB4YV4QL","created_at":"2026-07-05T09:44:09Z"},{"alias_kind":"pith_short_16","alias_value":"67BGAB4YV4QLZROL","created_at":"2026-07-05T09:44:09Z"},{"alias_kind":"pith_short_8","alias_value":"67BGAB4Y","created_at":"2026-07-05T09:44:09Z"}],"graph_snapshots":[{"event_id":"sha256:025961d4dc501bd1b99265b9f857320122e9b5aba17d7aadfa95984cd7b8b6f1","target":"graph","created_at":"2026-07-05T09:44:09Z","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/2405.18243/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as well as the classifications of their corresponding derivations, centroids, automorphisms, and quasi-centroids. We then characterize a selection of further invariants such as Rota-Baxter operators and second cohomology for some specific examples.","authors_text":"Ahmed Zahari, Bouzid Mosbahi, Erik Mainellis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-05-28T14:52:01Z","title":"Compatible Associative Algebras and Some Invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.18243","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:b7dba8c84f2ac6a8f3c3f926955924c2fbd2c8f8b4f638926be992e2e345179a","target":"record","created_at":"2026-07-05T09:44:09Z","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":"9270d4746bb238b31ad76d1b04700a47f271e4b12c8b9304bbaf75c2e6e8010a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2024-05-28T14:52:01Z","title_canon_sha256":"88ed37d260af57e0d4bc0e26b7a1b66c4fb346db81536805573460738d1c0715"},"schema_version":"1.0","source":{"id":"2405.18243","kind":"arxiv","version":2}},"canonical_sha256":"f7c2600798af20bcc5cb24ba4f05c93fdc665c7ea35ef641216b21213b212448","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7c2600798af20bcc5cb24ba4f05c93fdc665c7ea35ef641216b21213b212448","first_computed_at":"2026-07-05T09:44:09.571134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:44:09.571134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I6XZc2DbDZen8DngxEUSQhwnVtA2Qpo0pxG17hh/QnqROvg5VJcTJ9WyoO4TNsMYgM9XpS559Ghwx1uaMw9FCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:44:09.571598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.18243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7dba8c84f2ac6a8f3c3f926955924c2fbd2c8f8b4f638926be992e2e345179a","sha256:025961d4dc501bd1b99265b9f857320122e9b5aba17d7aadfa95984cd7b8b6f1"],"state_sha256":"685b4be8d45d4c9806a81ab7e2196fb60681f30c68215bccc864f868c513cb57"}