{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3VS42C4ENFG6SVWLTFLNBLY5WI","short_pith_number":"pith:3VS42C4E","schema_version":"1.0","canonical_sha256":"dd65cd0b84694de956cb9956d0af1db2189c188456fea2a6bf4e153898ecbabd","source":{"kind":"arxiv","id":"1302.0399","version":1},"attestation_state":"computed","paper":{"title":"The category and operad of matching dialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.QA"],"primary_cat":"math.CT","authors_text":"Chengming Bai, Li Guo, Yong Zhang","submitted_at":"2013-02-02T16:45:14Z","abstract_excerpt":"This paper gives a systematic study of matching dialgebras corresponding to the operad $As^{(2)}$ in \\cite{Zi} as the only Koszul self dual operad there other than the operads of associative algebras and Poisson algebras. The close relationship of matching dialgebras with semi-homomorphisms and matched pairs of associative algebras are established. By anti-symmetrizing, matching dialgerbas are also shown to give compatible Lie algebras, pre-Lie algebras and PostLie algebras. By the rewriting method, the operad of matching dialgebras is shown to be Koszul and the free objects are constructed in"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.0399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-02-02T16:45:14Z","cross_cats_sorted":["math.KT","math.QA"],"title_canon_sha256":"3c50f63ecf5ffc9224d11f2d6314f063aa1445eacc9cf7f0de17402bbc656ff2","abstract_canon_sha256":"1c4e2154fe2e8fce95ffbf1139d417f72e46d6315fe70a3737b4bab66d90813c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:16.204563Z","signature_b64":"gGw/4OKUIqKuhX4yqD6p7auFfhUr1wjnXSU63PeEv3E1fu1e8gEfOO2DolWasIopxvLabTYtFC+24b86MSH6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd65cd0b84694de956cb9956d0af1db2189c188456fea2a6bf4e153898ecbabd","last_reissued_at":"2026-05-18T02:47:16.203872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:16.203872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The category and operad of matching dialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.QA"],"primary_cat":"math.CT","authors_text":"Chengming Bai, Li Guo, Yong Zhang","submitted_at":"2013-02-02T16:45:14Z","abstract_excerpt":"This paper gives a systematic study of matching dialgebras corresponding to the operad $As^{(2)}$ in \\cite{Zi} as the only Koszul self dual operad there other than the operads of associative algebras and Poisson algebras. The close relationship of matching dialgebras with semi-homomorphisms and matched pairs of associative algebras are established. By anti-symmetrizing, matching dialgerbas are also shown to give compatible Lie algebras, pre-Lie algebras and PostLie algebras. By the rewriting method, the operad of matching dialgebras is shown to be Koszul and the free objects are constructed in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0399","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.0399","created_at":"2026-05-18T02:47:16.203976+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.0399v1","created_at":"2026-05-18T02:47:16.203976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0399","created_at":"2026-05-18T02:47:16.203976+00:00"},{"alias_kind":"pith_short_12","alias_value":"3VS42C4ENFG6","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3VS42C4ENFG6SVWL","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3VS42C4E","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI","json":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI.json","graph_json":"https://pith.science/api/pith-number/3VS42C4ENFG6SVWLTFLNBLY5WI/graph.json","events_json":"https://pith.science/api/pith-number/3VS42C4ENFG6SVWLTFLNBLY5WI/events.json","paper":"https://pith.science/paper/3VS42C4E"},"agent_actions":{"view_html":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI","download_json":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI.json","view_paper":"https://pith.science/paper/3VS42C4E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.0399&json=true","fetch_graph":"https://pith.science/api/pith-number/3VS42C4ENFG6SVWLTFLNBLY5WI/graph.json","fetch_events":"https://pith.science/api/pith-number/3VS42C4ENFG6SVWLTFLNBLY5WI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI/action/storage_attestation","attest_author":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI/action/author_attestation","sign_citation":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI/action/citation_signature","submit_replication":"https://pith.science/pith/3VS42C4ENFG6SVWLTFLNBLY5WI/action/replication_record"}},"created_at":"2026-05-18T02:47:16.203976+00:00","updated_at":"2026-05-18T02:47:16.203976+00:00"}