{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:MD3V7PZHUADS4OPUNB4S6GUDHA","short_pith_number":"pith:MD3V7PZH","schema_version":"1.0","canonical_sha256":"60f75fbf27a0072e39f468792f1a83383793e918ebe19d147238317426e2f495","source":{"kind":"arxiv","id":"math/0605356","version":1},"attestation_state":"computed","paper":{"title":"Supergroupoids, double structures, and equivariant cohomology","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Rajan Amit Mehta","submitted_at":"2006-05-14T04:41:26Z","abstract_excerpt":"Q-groupoids and Q-algebroids are, respectively, supergroupoids and superalgebroids that are equipped with compatible homological vector fields. These new objects are closely related to the double structures of Mackenzie; in particular, we show that Q-groupoids are intermediary objects between Mackenzie's LA-groupoids and double complexes, which include as a special case the simplicial model of equivariant cohomology. There is also a double complex associated to a Q-algebroid, which in the above special case is the BRST model of equivariant cohomology. Other special cases include models for the"},"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/0605356","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-05-14T04:41:26Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"3f1f15cfcf614e6c9d64e2c3f0a37b06c7e258ca43751e510c57cb829850f3c7","abstract_canon_sha256":"37c457f62a8c2d8417fcaf40e0ca16c4bbe29e3cbd716a9e694196478efb593f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:55:04.146581Z","signature_b64":"smxHoWE1dL6E1s986MFGybyy1K5/JdeGkypB7sX29iFRJTSLGyqUw24y3k+O2+02VRUR9U66fR3x7ohJB8f3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60f75fbf27a0072e39f468792f1a83383793e918ebe19d147238317426e2f495","last_reissued_at":"2026-07-04T14:55:04.146231Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:55:04.146231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Supergroupoids, double structures, and equivariant cohomology","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Rajan Amit Mehta","submitted_at":"2006-05-14T04:41:26Z","abstract_excerpt":"Q-groupoids and Q-algebroids are, respectively, supergroupoids and superalgebroids that are equipped with compatible homological vector fields. These new objects are closely related to the double structures of Mackenzie; in particular, we show that Q-groupoids are intermediary objects between Mackenzie's LA-groupoids and double complexes, which include as a special case the simplicial model of equivariant cohomology. There is also a double complex associated to a Q-algebroid, which in the above special case is the BRST model of equivariant cohomology. Other special cases include models for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605356","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/0605356/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/0605356","created_at":"2026-07-04T14:55:04.146293+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0605356v1","created_at":"2026-07-04T14:55:04.146293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605356","created_at":"2026-07-04T14:55:04.146293+00:00"},{"alias_kind":"pith_short_12","alias_value":"MD3V7PZHUADS","created_at":"2026-07-04T14:55:04.146293+00:00"},{"alias_kind":"pith_short_16","alias_value":"MD3V7PZHUADS4OPU","created_at":"2026-07-04T14:55:04.146293+00:00"},{"alias_kind":"pith_short_8","alias_value":"MD3V7PZH","created_at":"2026-07-04T14:55:04.146293+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.22910","citing_title":"Flows on Graded Manifolds","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA","json":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA.json","graph_json":"https://pith.science/api/pith-number/MD3V7PZHUADS4OPUNB4S6GUDHA/graph.json","events_json":"https://pith.science/api/pith-number/MD3V7PZHUADS4OPUNB4S6GUDHA/events.json","paper":"https://pith.science/paper/MD3V7PZH"},"agent_actions":{"view_html":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA","download_json":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA.json","view_paper":"https://pith.science/paper/MD3V7PZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0605356&json=true","fetch_graph":"https://pith.science/api/pith-number/MD3V7PZHUADS4OPUNB4S6GUDHA/graph.json","fetch_events":"https://pith.science/api/pith-number/MD3V7PZHUADS4OPUNB4S6GUDHA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA/action/storage_attestation","attest_author":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA/action/author_attestation","sign_citation":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA/action/citation_signature","submit_replication":"https://pith.science/pith/MD3V7PZHUADS4OPUNB4S6GUDHA/action/replication_record"}},"created_at":"2026-07-04T14:55:04.146293+00:00","updated_at":"2026-07-04T14:55:04.146293+00:00"}