{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KIV5ZERTYX4OAFS2HHWXRGKW5U","short_pith_number":"pith:KIV5ZERT","schema_version":"1.0","canonical_sha256":"522bdc9233c5f8e0165a39ed789956ed3edb7d3a2573e980eca3a37e5948036d","source":{"kind":"arxiv","id":"1609.02844","version":3},"attestation_state":"computed","paper":{"title":"Lie supergroups vs. super Harish-Chandra pairs: a new equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"Fabio Gavarini","submitted_at":"2016-09-09T15:57:33Z","abstract_excerpt":"It is known that there exists a natural functor $\\Phi$ from Lie supergroups to super Harish-Chandra pairs. A functor going backwards, that associates a Lie supergroup with each super Harish-Chandra pair, yielding an equivalence of categories, was found by Koszul [18]; this result was later extended by other authors, to different levels of generality, but always elaborating on Koszul's original idea.\n  In this paper, I provide two new backwards equivalences, i.e. two different functors $\\Psi^\\circ$ and $\\Psi^e$ that construct a Lie supergroup (thought of as a special group-valued functor) out o"},"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":"1609.02844","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-09T15:57:33Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7af3d843f29ff559e34fae2f09d68a499d754aa0969da98cf954f31a9faca290","abstract_canon_sha256":"9d2f9a5d6ea0c3cf49ef3f562f84afccecbf51204ba002f28268b180c3307f37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.346060Z","signature_b64":"bHkYgq9VegbukVhlSCl5kHyimLJoEoofwJutMCngLQOSn4A/s5bHsDWM05P8S67uJwD6GIeIi9gOTqYPY2kvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"522bdc9233c5f8e0165a39ed789956ed3edb7d3a2573e980eca3a37e5948036d","last_reissued_at":"2026-05-18T00:02:02.345445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.345445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lie supergroups vs. super Harish-Chandra pairs: a new equivalence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"Fabio Gavarini","submitted_at":"2016-09-09T15:57:33Z","abstract_excerpt":"It is known that there exists a natural functor $\\Phi$ from Lie supergroups to super Harish-Chandra pairs. A functor going backwards, that associates a Lie supergroup with each super Harish-Chandra pair, yielding an equivalence of categories, was found by Koszul [18]; this result was later extended by other authors, to different levels of generality, but always elaborating on Koszul's original idea.\n  In this paper, I provide two new backwards equivalences, i.e. two different functors $\\Psi^\\circ$ and $\\Psi^e$ that construct a Lie supergroup (thought of as a special group-valued functor) out o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02844","kind":"arxiv","version":3},"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":"1609.02844","created_at":"2026-05-18T00:02:02.345566+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.02844v3","created_at":"2026-05-18T00:02:02.345566+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02844","created_at":"2026-05-18T00:02:02.345566+00:00"},{"alias_kind":"pith_short_12","alias_value":"KIV5ZERTYX4O","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KIV5ZERTYX4OAFS2","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KIV5ZERT","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.12328","citing_title":"The disoriented skein and iquantum Brauer categories","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U","json":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U.json","graph_json":"https://pith.science/api/pith-number/KIV5ZERTYX4OAFS2HHWXRGKW5U/graph.json","events_json":"https://pith.science/api/pith-number/KIV5ZERTYX4OAFS2HHWXRGKW5U/events.json","paper":"https://pith.science/paper/KIV5ZERT"},"agent_actions":{"view_html":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U","download_json":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U.json","view_paper":"https://pith.science/paper/KIV5ZERT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.02844&json=true","fetch_graph":"https://pith.science/api/pith-number/KIV5ZERTYX4OAFS2HHWXRGKW5U/graph.json","fetch_events":"https://pith.science/api/pith-number/KIV5ZERTYX4OAFS2HHWXRGKW5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U/action/storage_attestation","attest_author":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U/action/author_attestation","sign_citation":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U/action/citation_signature","submit_replication":"https://pith.science/pith/KIV5ZERTYX4OAFS2HHWXRGKW5U/action/replication_record"}},"created_at":"2026-05-18T00:02:02.345566+00:00","updated_at":"2026-05-18T00:02:02.345566+00:00"}