{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SOT36RW27AANIE4VTTMQSIYLBW","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":"09a1e5c67ca83c7bb08714bded51d176241f4ff460cc40822972516203beb3f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-12-22T14:15:57Z","title_canon_sha256":"5fb5828c269c0be95eb8c91b90a46446091932505138c06cacde1f34a7c742cb"},"schema_version":"1.0","source":{"id":"1012.4984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4984","created_at":"2026-05-18T04:32:44Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4984v1","created_at":"2026-05-18T04:32:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4984","created_at":"2026-05-18T04:32:44Z"},{"alias_kind":"pith_short_12","alias_value":"SOT36RW27AAN","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SOT36RW27AANIE4V","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SOT36RW2","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:de89bbf459c910d0e9422e86a5ff18ef1ed8be31f00c1fd76111476ef238d7dd","target":"graph","created_at":"2026-05-18T04:32:44Z","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":"In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some \"perfection\" property (simpleness, primitiveness, primeness or semiprimeness) imply that the dialgebra comes from an associative algebra with both products identified. We also describe the class of zero-cubed algebras and apply its study to that of dialgebras. Finally we describe two-dimensional associative dialgebras.","authors_text":"Candido Martin Gonzalez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-12-22T14:15:57Z","title":"Associative Dialgebras from a structural viewpoint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4984","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":"sha256:8097b4bc2e0d8e5b5dc79a02168c340d3a4d3d65e2b1737b84cce60a257dd923","target":"record","created_at":"2026-05-18T04:32:44Z","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":"09a1e5c67ca83c7bb08714bded51d176241f4ff460cc40822972516203beb3f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-12-22T14:15:57Z","title_canon_sha256":"5fb5828c269c0be95eb8c91b90a46446091932505138c06cacde1f34a7c742cb"},"schema_version":"1.0","source":{"id":"1012.4984","kind":"arxiv","version":1}},"canonical_sha256":"93a7bf46daf800d413959cd909230b0d8b749bd238643eeda3dc155fe7634451","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93a7bf46daf800d413959cd909230b0d8b749bd238643eeda3dc155fe7634451","first_computed_at":"2026-05-18T04:32:44.749924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:44.749924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TvsuMweq80Z2BzZGchFIK5QQwewQh6XwoPUdjW8daxBpWqh5bfmUYDIhNONUe7CYX1p3rsQXczo2DHmazBsGCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:44.750860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8097b4bc2e0d8e5b5dc79a02168c340d3a4d3d65e2b1737b84cce60a257dd923","sha256:de89bbf459c910d0e9422e86a5ff18ef1ed8be31f00c1fd76111476ef238d7dd"],"state_sha256":"0e75a35e5cb7c5ed7a3cc35717f54bf5998602c776868d0270ae9343889ef8f9"}