{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZPYCGQO5JPR5W3TTH3MMVK55MK","short_pith_number":"pith:ZPYCGQO5","schema_version":"1.0","canonical_sha256":"cbf02341dd4be3db6e733ed8caabbd6298d70ebc24bcb0729835c0c1c6b2c422","source":{"kind":"arxiv","id":"1504.07502","version":2},"attestation_state":"computed","paper":{"title":"Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.SG","authors_text":"Mich\\`ele Vergne (IMJ), Paul-Emile Paradan (IMAG)","submitted_at":"2015-04-28T14:35:34Z","abstract_excerpt":"The purpose of the present paper is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar  in the Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of the index of ge"},"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":"1504.07502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-04-28T14:35:34Z","cross_cats_sorted":["math.KT","math.RT"],"title_canon_sha256":"c9d92cd40c4bf6805f06720875d586394bf46a133843300865c00c4a685ae452","abstract_canon_sha256":"b3a23087820a291e991e05f83c25f0a82e51ad46396485424067a3371acfd150"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:12.348000Z","signature_b64":"bS6K67CY6MnVYKUvfd+sKtQcUSN5JlIxg6Z7I+ze9BfucQ8Ysaaqll/u3LjSZXKeIgq+vbkwp7X6E8ZCN/DYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbf02341dd4be3db6e733ed8caabbd6298d70ebc24bcb0729835c0c1c6b2c422","last_reissued_at":"2026-05-18T01:23:12.347251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:12.347251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.SG","authors_text":"Mich\\`ele Vergne (IMJ), Paul-Emile Paradan (IMAG)","submitted_at":"2015-04-28T14:35:34Z","abstract_excerpt":"The purpose of the present paper is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar  in the Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the multiplicities of the index of ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07502","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":"1504.07502","created_at":"2026-05-18T01:23:12.347372+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.07502v2","created_at":"2026-05-18T01:23:12.347372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07502","created_at":"2026-05-18T01:23:12.347372+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZPYCGQO5JPR5","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZPYCGQO5JPR5W3TT","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZPYCGQO5","created_at":"2026-05-18T12:29:52.810259+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/ZPYCGQO5JPR5W3TTH3MMVK55MK","json":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK.json","graph_json":"https://pith.science/api/pith-number/ZPYCGQO5JPR5W3TTH3MMVK55MK/graph.json","events_json":"https://pith.science/api/pith-number/ZPYCGQO5JPR5W3TTH3MMVK55MK/events.json","paper":"https://pith.science/paper/ZPYCGQO5"},"agent_actions":{"view_html":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK","download_json":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK.json","view_paper":"https://pith.science/paper/ZPYCGQO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.07502&json=true","fetch_graph":"https://pith.science/api/pith-number/ZPYCGQO5JPR5W3TTH3MMVK55MK/graph.json","fetch_events":"https://pith.science/api/pith-number/ZPYCGQO5JPR5W3TTH3MMVK55MK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK/action/storage_attestation","attest_author":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK/action/author_attestation","sign_citation":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK/action/citation_signature","submit_replication":"https://pith.science/pith/ZPYCGQO5JPR5W3TTH3MMVK55MK/action/replication_record"}},"created_at":"2026-05-18T01:23:12.347372+00:00","updated_at":"2026-05-18T01:23:12.347372+00:00"}