{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:EQ4K3RVLKQDMEGCJRNZTIZ4W62","short_pith_number":"pith:EQ4K3RVL","schema_version":"1.0","canonical_sha256":"2438adc6ab5406c218498b73346796f69c6d1a724f779c27524d85299879d4c8","source":{"kind":"arxiv","id":"0705.2527","version":2},"attestation_state":"computed","paper":{"title":"From multiplicative unitaries to quantum groups II","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Piotr M. So{\\l}tan, S. L. Woronowicz","submitted_at":"2007-05-17T13:34:21Z","abstract_excerpt":"It is shown that all important features of a $\\mathrm{C}^*$-algebraic quantum group $(A,\\Delta)$ defined by a modular multiplicative $W$ depend only on the pair $(A,\\Delta)$ rather than the multiplicative unitary operator $W$. The proof is based on thorough study of representations of quantum groups. As an application we present a construction and study properties of the universal dual of a quantum group defined by a modular multiplicative unitary - without assuming existence of Haar weights."},"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":"0705.2527","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2007-05-17T13:34:21Z","cross_cats_sorted":[],"title_canon_sha256":"40ee219b3729531a0fb801e570bd194f75ea8f33e5939fbe0f99afaa0c02f307","abstract_canon_sha256":"d741690897cbd28b951f1c4de6a65b09ccfe7f2cea2a101c95bde65efdfb498a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:44.160428Z","signature_b64":"xGvDqzPrAlj6WSdcZrdXMe0vrySXlKSa3EFP8zMG2osszxVNMVnP+ZtBCzKYrDcYsD+KA5lmw8LHX6reCvASBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2438adc6ab5406c218498b73346796f69c6d1a724f779c27524d85299879d4c8","last_reissued_at":"2026-05-18T04:24:44.160048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:44.160048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From multiplicative unitaries to quantum groups II","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Piotr M. So{\\l}tan, S. L. Woronowicz","submitted_at":"2007-05-17T13:34:21Z","abstract_excerpt":"It is shown that all important features of a $\\mathrm{C}^*$-algebraic quantum group $(A,\\Delta)$ defined by a modular multiplicative $W$ depend only on the pair $(A,\\Delta)$ rather than the multiplicative unitary operator $W$. The proof is based on thorough study of representations of quantum groups. As an application we present a construction and study properties of the universal dual of a quantum group defined by a modular multiplicative unitary - without assuming existence of Haar weights."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2527","kind":"arxiv","version":2},"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":"0705.2527","created_at":"2026-05-18T04:24:44.160105+00:00"},{"alias_kind":"arxiv_version","alias_value":"0705.2527v2","created_at":"2026-05-18T04:24:44.160105+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2527","created_at":"2026-05-18T04:24:44.160105+00:00"},{"alias_kind":"pith_short_12","alias_value":"EQ4K3RVLKQDM","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"EQ4K3RVLKQDMEGCJ","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"EQ4K3RVL","created_at":"2026-05-18T12:25:55.427421+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/EQ4K3RVLKQDMEGCJRNZTIZ4W62","json":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62.json","graph_json":"https://pith.science/api/pith-number/EQ4K3RVLKQDMEGCJRNZTIZ4W62/graph.json","events_json":"https://pith.science/api/pith-number/EQ4K3RVLKQDMEGCJRNZTIZ4W62/events.json","paper":"https://pith.science/paper/EQ4K3RVL"},"agent_actions":{"view_html":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62","download_json":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62.json","view_paper":"https://pith.science/paper/EQ4K3RVL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0705.2527&json=true","fetch_graph":"https://pith.science/api/pith-number/EQ4K3RVLKQDMEGCJRNZTIZ4W62/graph.json","fetch_events":"https://pith.science/api/pith-number/EQ4K3RVLKQDMEGCJRNZTIZ4W62/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62/action/storage_attestation","attest_author":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62/action/author_attestation","sign_citation":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62/action/citation_signature","submit_replication":"https://pith.science/pith/EQ4K3RVLKQDMEGCJRNZTIZ4W62/action/replication_record"}},"created_at":"2026-05-18T04:24:44.160105+00:00","updated_at":"2026-05-18T04:24:44.160105+00:00"}