{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:RK6GXRGUP2COAAFD4H323K43ZF","short_pith_number":"pith:RK6GXRGU","schema_version":"1.0","canonical_sha256":"8abc6bc4d47e84e000a3e1f7adab9bc969e734256c5772b8a373db00570d8eef","source":{"kind":"arxiv","id":"2303.09997","version":4},"attestation_state":"computed","paper":{"title":"Banach algebras associated to twisted \\'etale groupoids: inverse semigroup disintegration and representations on $L^p$-spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Andrew McKee, Bartosz K. Kwa\\'sniewski, Krzysztof Bardadyn","submitted_at":"2023-03-17T14:15:55Z","abstract_excerpt":"We introduce Banach algebras associated to twisted \\'etale groupoids $(\\mathcal{G},\\mathcal{L})$ and to twisted inverse semigroup actions. This provides a unifying framework for numerous recent papers on $L^p$-operator algebras and the theory of groupoid $C^*$-algebras. We prove disintegrations theorems that allow to study Banach algebras associated to $(\\mathcal{G},\\mathcal{L})$ as universal Banach algebras generated by $C_0(X)$ and a twisted inverse semigroup $S$ of partial isometries subject to some relations. They work best when the target of a representation is a dual Banach algebra. For "},"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":"2303.09997","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2023-03-17T14:15:55Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"1612edc7d804c0cb497aad9c0772b962f4ff9b43e9d84d35c24c076ad7420e80","abstract_canon_sha256":"aa50401222716d583b4daf200b15e2627aa418073c8792c56a9c7102ff361df4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:12.370835Z","signature_b64":"ho6woM2MSB4Y5whkV7Q57jQbY/NwOgRyP1n90VP8mQYDm6WrM/z/VLcwJjhfbqtAQNrJc+6UipX7R3SYfVSRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8abc6bc4d47e84e000a3e1f7adab9bc969e734256c5772b8a373db00570d8eef","last_reissued_at":"2026-07-05T11:56:12.370452Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:12.370452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Banach algebras associated to twisted \\'etale groupoids: inverse semigroup disintegration and representations on $L^p$-spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Andrew McKee, Bartosz K. Kwa\\'sniewski, Krzysztof Bardadyn","submitted_at":"2023-03-17T14:15:55Z","abstract_excerpt":"We introduce Banach algebras associated to twisted \\'etale groupoids $(\\mathcal{G},\\mathcal{L})$ and to twisted inverse semigroup actions. This provides a unifying framework for numerous recent papers on $L^p$-operator algebras and the theory of groupoid $C^*$-algebras. We prove disintegrations theorems that allow to study Banach algebras associated to $(\\mathcal{G},\\mathcal{L})$ as universal Banach algebras generated by $C_0(X)$ and a twisted inverse semigroup $S$ of partial isometries subject to some relations. They work best when the target of a representation is a dual Banach algebra. For "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09997","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.09997/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":"2303.09997","created_at":"2026-07-05T11:56:12.370509+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.09997v4","created_at":"2026-07-05T11:56:12.370509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.09997","created_at":"2026-07-05T11:56:12.370509+00:00"},{"alias_kind":"pith_short_12","alias_value":"RK6GXRGUP2CO","created_at":"2026-07-05T11:56:12.370509+00:00"},{"alias_kind":"pith_short_16","alias_value":"RK6GXRGUP2COAAFD","created_at":"2026-07-05T11:56:12.370509+00:00"},{"alias_kind":"pith_short_8","alias_value":"RK6GXRGU","created_at":"2026-07-05T11:56:12.370509+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.09563","citing_title":"Rigidity of pseudofunction algebras of ample groupoids","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF","json":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF.json","graph_json":"https://pith.science/api/pith-number/RK6GXRGUP2COAAFD4H323K43ZF/graph.json","events_json":"https://pith.science/api/pith-number/RK6GXRGUP2COAAFD4H323K43ZF/events.json","paper":"https://pith.science/paper/RK6GXRGU"},"agent_actions":{"view_html":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF","download_json":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF.json","view_paper":"https://pith.science/paper/RK6GXRGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.09997&json=true","fetch_graph":"https://pith.science/api/pith-number/RK6GXRGUP2COAAFD4H323K43ZF/graph.json","fetch_events":"https://pith.science/api/pith-number/RK6GXRGUP2COAAFD4H323K43ZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF/action/storage_attestation","attest_author":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF/action/author_attestation","sign_citation":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF/action/citation_signature","submit_replication":"https://pith.science/pith/RK6GXRGUP2COAAFD4H323K43ZF/action/replication_record"}},"created_at":"2026-07-05T11:56:12.370509+00:00","updated_at":"2026-07-05T11:56:12.370509+00:00"}