{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NSC7V266VFOOIFWBX2YCD4ZRWL","short_pith_number":"pith:NSC7V266","schema_version":"1.0","canonical_sha256":"6c85faebdea95ce416c1beb021f331b2e619d484cc0df1bc622a83a0d92eea91","source":{"kind":"arxiv","id":"1202.0155","version":2},"attestation_state":"computed","paper":{"title":"On groupoids with involutions and their cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.KT"],"primary_cat":"math.OA","authors_text":"El-ka\\\"ioum M. Moutuou","submitted_at":"2012-02-01T11:58:01Z","abstract_excerpt":"We extend the definitions and main properties of graded extensions to the category of locally compact groupoids endowed with involutions. We introduce Real \\v{C}ech cohomology, which is an equivariant-like cohomology theory suitable for the context of groupoids with involutions. The Picard group of such a groupoid is discussed and is given a cohomological picture. Eventually, we generalize Crainic's result, about the differential cohomology of a proper Lie groupoid with coefficients in a given representation, to the topological case."},"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":"1202.0155","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-02-01T11:58:01Z","cross_cats_sorted":["math.GN","math.KT"],"title_canon_sha256":"2c9331b15d578ed5ce61b88cbbb66408c5782976b9a1aa22300aa12e3221c52f","abstract_canon_sha256":"6dc0cf622d2f1e060af2f16438fd13386bb43ec8cef449d06bb5b47bab68aae9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:06.225021Z","signature_b64":"MVWkpouOx0vfw6mj5IlzDZVFfqg57rWjEd+VFDxpTp0zOzgFzugVWsX9BWSyBN13d62IiQD3e3wppKBLusUWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c85faebdea95ce416c1beb021f331b2e619d484cc0df1bc622a83a0d92eea91","last_reissued_at":"2026-05-18T04:03:06.224070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:06.224070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On groupoids with involutions and their cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.KT"],"primary_cat":"math.OA","authors_text":"El-ka\\\"ioum M. Moutuou","submitted_at":"2012-02-01T11:58:01Z","abstract_excerpt":"We extend the definitions and main properties of graded extensions to the category of locally compact groupoids endowed with involutions. We introduce Real \\v{C}ech cohomology, which is an equivariant-like cohomology theory suitable for the context of groupoids with involutions. The Picard group of such a groupoid is discussed and is given a cohomological picture. Eventually, we generalize Crainic's result, about the differential cohomology of a proper Lie groupoid with coefficients in a given representation, to the topological case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0155","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":"1202.0155","created_at":"2026-05-18T04:03:06.224227+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.0155v2","created_at":"2026-05-18T04:03:06.224227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0155","created_at":"2026-05-18T04:03:06.224227+00:00"},{"alias_kind":"pith_short_12","alias_value":"NSC7V266VFOO","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NSC7V266VFOOIFWB","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NSC7V266","created_at":"2026-05-18T12:27:16.716162+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/NSC7V266VFOOIFWBX2YCD4ZRWL","json":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL.json","graph_json":"https://pith.science/api/pith-number/NSC7V266VFOOIFWBX2YCD4ZRWL/graph.json","events_json":"https://pith.science/api/pith-number/NSC7V266VFOOIFWBX2YCD4ZRWL/events.json","paper":"https://pith.science/paper/NSC7V266"},"agent_actions":{"view_html":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL","download_json":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL.json","view_paper":"https://pith.science/paper/NSC7V266","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.0155&json=true","fetch_graph":"https://pith.science/api/pith-number/NSC7V266VFOOIFWBX2YCD4ZRWL/graph.json","fetch_events":"https://pith.science/api/pith-number/NSC7V266VFOOIFWBX2YCD4ZRWL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL/action/storage_attestation","attest_author":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL/action/author_attestation","sign_citation":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL/action/citation_signature","submit_replication":"https://pith.science/pith/NSC7V266VFOOIFWBX2YCD4ZRWL/action/replication_record"}},"created_at":"2026-05-18T04:03:06.224227+00:00","updated_at":"2026-05-18T04:03:06.224227+00:00"}