{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RWKYDTFYDCXBJXCZR7LGNKG74P","short_pith_number":"pith:RWKYDTFY","schema_version":"1.0","canonical_sha256":"8d9581ccb818ae14dc598fd666a8dfe3fb5d02d0d28cfcd02d1af1d9d2bff1b3","source":{"kind":"arxiv","id":"1403.7048","version":4},"attestation_state":"computed","paper":{"title":"Interacting Hopf Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Fabio Zanasi, Filippo Bonchi, Pawel Sobocinski","submitted_at":"2014-03-27T14:21:30Z","abstract_excerpt":"We introduce the theory IH of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs. This construction is instrumental in showing that IH is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R."},"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":"1403.7048","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-03-27T14:21:30Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"c6d325e3c67dbe207c74d7770a0ee9d0c1c46adffd79eda466b957a6be3bb0cd","abstract_canon_sha256":"a0decbaa7e49e78bd5b409ee6d9b7f9b7122fb5f16b0297de39f0dc8177656b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:12.686576Z","signature_b64":"ldqsZ/gQBM5uYNnfvgLzKm+wgv6ZAXdC4S9F2PQqh4LMbFQ0KA6eKA1DTBxnlq7A+UGNLsJxh1JbBvNBsVRzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d9581ccb818ae14dc598fd666a8dfe3fb5d02d0d28cfcd02d1af1d9d2bff1b3","last_reissued_at":"2026-05-18T00:56:12.685918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:12.685918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interacting Hopf Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Fabio Zanasi, Filippo Bonchi, Pawel Sobocinski","submitted_at":"2014-03-27T14:21:30Z","abstract_excerpt":"We introduce the theory IH of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs. This construction is instrumental in showing that IH is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7048","kind":"arxiv","version":4},"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":"1403.7048","created_at":"2026-05-18T00:56:12.686016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7048v4","created_at":"2026-05-18T00:56:12.686016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7048","created_at":"2026-05-18T00:56:12.686016+00:00"},{"alias_kind":"pith_short_12","alias_value":"RWKYDTFYDCXB","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RWKYDTFYDCXBJXCZ","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RWKYDTFY","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2309.13014","citing_title":"Completeness of qufinite ZXW calculus, a graphical language for finite-dimensional quantum theory","ref_index":14,"is_internal_anchor":true},{"citing_arxiv_id":"2605.13993","citing_title":"Graphical Algebraic Geometry: From Ideals and Varieties to Quantum Calculi","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P","json":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P.json","graph_json":"https://pith.science/api/pith-number/RWKYDTFYDCXBJXCZR7LGNKG74P/graph.json","events_json":"https://pith.science/api/pith-number/RWKYDTFYDCXBJXCZR7LGNKG74P/events.json","paper":"https://pith.science/paper/RWKYDTFY"},"agent_actions":{"view_html":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P","download_json":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P.json","view_paper":"https://pith.science/paper/RWKYDTFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7048&json=true","fetch_graph":"https://pith.science/api/pith-number/RWKYDTFYDCXBJXCZR7LGNKG74P/graph.json","fetch_events":"https://pith.science/api/pith-number/RWKYDTFYDCXBJXCZR7LGNKG74P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P/action/storage_attestation","attest_author":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P/action/author_attestation","sign_citation":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P/action/citation_signature","submit_replication":"https://pith.science/pith/RWKYDTFYDCXBJXCZR7LGNKG74P/action/replication_record"}},"created_at":"2026-05-18T00:56:12.686016+00:00","updated_at":"2026-05-18T00:56:12.686016+00:00"}