{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:L6UTDNBQE2IKIXL6LAKHQ3NXYJ","short_pith_number":"pith:L6UTDNBQ","schema_version":"1.0","canonical_sha256":"5fa931b4302690a45d7e5814786db7c2411b2c21536d91e7a4c05897337db24a","source":{"kind":"arxiv","id":"1409.1685","version":1},"attestation_state":"computed","paper":{"title":"Partial compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kenny De Commer, Thomas Timmermann","submitted_at":"2014-09-05T08:26:31Z","abstract_excerpt":"Compact quantum groups of face type, as introduced by Hayashi, form a class of compact quantum groupoids with a classical, finite set of objects. Using the notions of a weak multiplier bialgebra and weak multiplier Hopf algebra (resp. due to B{\\\"o}hm--G\\'{o}mez-Torrecillas--L\\'{o}pez-Centella and Van Daele-Wang), we generalize Hayashi's definition to allow for an infinite set of objects, and call the resulting objects partial compact quantum groups. We prove a Tannaka-Kre$\\breve{\\textrm{\\i}}$n-Woronowicz reconstruction result for such partial compact quantum groups using the notion of a partia"},"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":"1409.1685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-09-05T08:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"c60148007c24c800d1ac26f59a586086a576e55acc7cc488a28b61c00b56526d","abstract_canon_sha256":"51291e04ed027a76f6abfc0a5de2612a20423f46dc7529402be405473304309b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:28.903089Z","signature_b64":"iVGF//vi4oK6q4oYjlBNO106EOW54QtmtVUYwUjBbQ9w2LtkgwAiNVgXFTID2qHr+r6eZnYJ6vIrOQbLIO9KAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fa931b4302690a45d7e5814786db7c2411b2c21536d91e7a4c05897337db24a","last_reissued_at":"2026-05-18T00:48:28.902545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:28.902545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kenny De Commer, Thomas Timmermann","submitted_at":"2014-09-05T08:26:31Z","abstract_excerpt":"Compact quantum groups of face type, as introduced by Hayashi, form a class of compact quantum groupoids with a classical, finite set of objects. Using the notions of a weak multiplier bialgebra and weak multiplier Hopf algebra (resp. due to B{\\\"o}hm--G\\'{o}mez-Torrecillas--L\\'{o}pez-Centella and Van Daele-Wang), we generalize Hayashi's definition to allow for an infinite set of objects, and call the resulting objects partial compact quantum groups. We prove a Tannaka-Kre$\\breve{\\textrm{\\i}}$n-Woronowicz reconstruction result for such partial compact quantum groups using the notion of a partia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1685","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":"1409.1685","created_at":"2026-05-18T00:48:28.902620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1685v1","created_at":"2026-05-18T00:48:28.902620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1685","created_at":"2026-05-18T00:48:28.902620+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6UTDNBQE2IK","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6UTDNBQE2IKIXL6","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6UTDNBQ","created_at":"2026-05-18T12:28:35.611951+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/L6UTDNBQE2IKIXL6LAKHQ3NXYJ","json":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ.json","graph_json":"https://pith.science/api/pith-number/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/graph.json","events_json":"https://pith.science/api/pith-number/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/events.json","paper":"https://pith.science/paper/L6UTDNBQ"},"agent_actions":{"view_html":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ","download_json":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ.json","view_paper":"https://pith.science/paper/L6UTDNBQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1685&json=true","fetch_graph":"https://pith.science/api/pith-number/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/graph.json","fetch_events":"https://pith.science/api/pith-number/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/action/storage_attestation","attest_author":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/action/author_attestation","sign_citation":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/action/citation_signature","submit_replication":"https://pith.science/pith/L6UTDNBQE2IKIXL6LAKHQ3NXYJ/action/replication_record"}},"created_at":"2026-05-18T00:48:28.902620+00:00","updated_at":"2026-05-18T00:48:28.902620+00:00"}