{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:QZNVEJ4DSSMNRHZ7CHTSICDDXZ","short_pith_number":"pith:QZNVEJ4D","schema_version":"1.0","canonical_sha256":"865b5227839498d89f3f11e7240863be7f3776cbb6bbda5917e526874d0c9dc1","source":{"kind":"arxiv","id":"math/9901063","version":1},"attestation_state":"computed","paper":{"title":"Weight theory for C*-algebraic quantum groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Johan Kustermans, Stefaan Vaes","submitted_at":"1999-01-15T15:49:34Z","abstract_excerpt":"In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a normal weight following S. Baaj, look into slice weights and their KSGNS-constructions and investigate the tensor product of weights together with a partial GNS-construction for such a tensor product. This paper accompanies our paper 'Locally compact quantum groups' in which we propose a relatively simple definition of a locally compact quantum group in the C*-al"},"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":"math/9901063","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"1999-01-15T15:49:34Z","cross_cats_sorted":[],"title_canon_sha256":"484955eb279ba886a7ede459bae5d03da878fead4d2af273bb10a180b80d1f51","abstract_canon_sha256":"362fddeb04cdfcf754b3e3747c95a7c58f13454285b434a68a296c68db3b9ab6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:55.858723Z","signature_b64":"9sIJ+HMkKym90flzVGidwKytmQKctcT+cb9/8/R7End2kRe/p1+N9Fw1Jce3p/wTp+Ao3uKeNymD/psurHtmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"865b5227839498d89f3f11e7240863be7f3776cbb6bbda5917e526874d0c9dc1","last_reissued_at":"2026-07-04T14:40:55.858350Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:55.858350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weight theory for C*-algebraic quantum groups","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Johan Kustermans, Stefaan Vaes","submitted_at":"1999-01-15T15:49:34Z","abstract_excerpt":"In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a normal weight following S. Baaj, look into slice weights and their KSGNS-constructions and investigate the tensor product of weights together with a partial GNS-construction for such a tensor product. This paper accompanies our paper 'Locally compact quantum groups' in which we propose a relatively simple definition of a locally compact quantum group in the C*-al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9901063","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/math/9901063/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":"math/9901063","created_at":"2026-07-04T14:40:55.858411+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9901063v1","created_at":"2026-07-04T14:40:55.858411+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9901063","created_at":"2026-07-04T14:40:55.858411+00:00"},{"alias_kind":"pith_short_12","alias_value":"QZNVEJ4DSSMN","created_at":"2026-07-04T14:40:55.858411+00:00"},{"alias_kind":"pith_short_16","alias_value":"QZNVEJ4DSSMNRHZ7","created_at":"2026-07-04T14:40:55.858411+00:00"},{"alias_kind":"pith_short_8","alias_value":"QZNVEJ4D","created_at":"2026-07-04T14:40:55.858411+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.17824","citing_title":"The reduced Hao-Ng isomorphism problem for non-degenerate product systems","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ","json":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ.json","graph_json":"https://pith.science/api/pith-number/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/graph.json","events_json":"https://pith.science/api/pith-number/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/events.json","paper":"https://pith.science/paper/QZNVEJ4D"},"agent_actions":{"view_html":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ","download_json":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ.json","view_paper":"https://pith.science/paper/QZNVEJ4D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9901063&json=true","fetch_graph":"https://pith.science/api/pith-number/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/graph.json","fetch_events":"https://pith.science/api/pith-number/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/action/storage_attestation","attest_author":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/action/author_attestation","sign_citation":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/action/citation_signature","submit_replication":"https://pith.science/pith/QZNVEJ4DSSMNRHZ7CHTSICDDXZ/action/replication_record"}},"created_at":"2026-07-04T14:40:55.858411+00:00","updated_at":"2026-07-04T14:40:55.858411+00:00"}