{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7BORRMEUHKOQMFNNGD2YAZOPPI","short_pith_number":"pith:7BORRMEU","schema_version":"1.0","canonical_sha256":"f85d18b0943a9d0615ad30f58065cf7a1f268e0162fb4e54f1bf59ec25a1e23d","source":{"kind":"arxiv","id":"2606.08627","version":1},"attestation_state":"computed","paper":{"title":"Bialgebra theory, the Yang-Baxter equation and relative Rota-Baxter operators for diassociative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Guilai Liu, Hui Hu, Shanghua Zheng, Yizhen Li","submitted_at":"2026-06-07T13:37:36Z","abstract_excerpt":"In this paper, we develop a bialgebra theory for diassociative algebras. Inspired by the notion of a quadratic diassociative algebra, we introduce the concept of a Manin triple of diassociative algebras. We then define a diassociative bialgebra, which is shown to be equivalent to a Manin triple of diassociative algebras through a specific matched pair of diassociative algebras. We further formulate the diassociative Yang-Baxter equation (DYBE) in a diassociative algebra, and prove that symmetric solutions of the DYBE give rise to diassociative bialgebras. To construct such solutions, we also i"},"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":"2606.08627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-06-07T13:37:36Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2d67d26b1632c60fce43b47c94264d6df2bf31d24a1e4fa01dba191e0b2372b1","abstract_canon_sha256":"f2e541ef4331f468a09164d81ea0f53055dda60514e378964c8701ea9f392d28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:41.832603Z","signature_b64":"NCVI4zZu+rnPIdbvR3/UEphNqmChur4tMcpsqZX6byA2lP7QxV4ZN9yoMTF4tgvQxYsB5vxC9qH8BZPA7YNODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f85d18b0943a9d0615ad30f58065cf7a1f268e0162fb4e54f1bf59ec25a1e23d","last_reissued_at":"2026-06-09T01:05:41.832183Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:41.832183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bialgebra theory, the Yang-Baxter equation and relative Rota-Baxter operators for diassociative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Guilai Liu, Hui Hu, Shanghua Zheng, Yizhen Li","submitted_at":"2026-06-07T13:37:36Z","abstract_excerpt":"In this paper, we develop a bialgebra theory for diassociative algebras. Inspired by the notion of a quadratic diassociative algebra, we introduce the concept of a Manin triple of diassociative algebras. We then define a diassociative bialgebra, which is shown to be equivalent to a Manin triple of diassociative algebras through a specific matched pair of diassociative algebras. We further formulate the diassociative Yang-Baxter equation (DYBE) in a diassociative algebra, and prove that symmetric solutions of the DYBE give rise to diassociative bialgebras. To construct such solutions, we also i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08627","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08627/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.08627","created_at":"2026-06-09T01:05:41.832246+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.08627v1","created_at":"2026-06-09T01:05:41.832246+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08627","created_at":"2026-06-09T01:05:41.832246+00:00"},{"alias_kind":"pith_short_12","alias_value":"7BORRMEUHKOQ","created_at":"2026-06-09T01:05:41.832246+00:00"},{"alias_kind":"pith_short_16","alias_value":"7BORRMEUHKOQMFNN","created_at":"2026-06-09T01:05:41.832246+00:00"},{"alias_kind":"pith_short_8","alias_value":"7BORRMEU","created_at":"2026-06-09T01:05:41.832246+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/7BORRMEUHKOQMFNNGD2YAZOPPI","json":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI.json","graph_json":"https://pith.science/api/pith-number/7BORRMEUHKOQMFNNGD2YAZOPPI/graph.json","events_json":"https://pith.science/api/pith-number/7BORRMEUHKOQMFNNGD2YAZOPPI/events.json","paper":"https://pith.science/paper/7BORRMEU"},"agent_actions":{"view_html":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI","download_json":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI.json","view_paper":"https://pith.science/paper/7BORRMEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.08627&json=true","fetch_graph":"https://pith.science/api/pith-number/7BORRMEUHKOQMFNNGD2YAZOPPI/graph.json","fetch_events":"https://pith.science/api/pith-number/7BORRMEUHKOQMFNNGD2YAZOPPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI/action/storage_attestation","attest_author":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI/action/author_attestation","sign_citation":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI/action/citation_signature","submit_replication":"https://pith.science/pith/7BORRMEUHKOQMFNNGD2YAZOPPI/action/replication_record"}},"created_at":"2026-06-09T01:05:41.832246+00:00","updated_at":"2026-06-09T01:05:41.832246+00:00"}