{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XVU5RMXXMAJ3OCS773YGIPJ3HD","short_pith_number":"pith:XVU5RMXX","schema_version":"1.0","canonical_sha256":"bd69d8b2f76013b70a5ffef0643d3b38d369eeabc062e3cc60f79e28a335a164","source":{"kind":"arxiv","id":"1204.2224","version":5},"attestation_state":"computed","paper":{"title":"Dirac operators on foliations: the Lichnerowicz inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Weiping Zhang","submitted_at":"2012-04-10T17:27:43Z","abstract_excerpt":"We construct Dirac operators on foliations by applying the Bismut-Lebeau analytic localization technique to the Connes fibration over a foliation. The Laplacian of the resulting Dirac operators has better lower bound than that obtained by using the usual adiabatic limit arguments on the original foliation. As a consequence, we prove an extension of the Lichnerowicz-Hitchin vanishing theorem to the case of foliations."},"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":"1204.2224","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-10T17:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"c727f4d7696294e9e874afb1abb4c01e2b5b830969b41218e538e960a8ec0a0b","abstract_canon_sha256":"177b3ea0b35217905efd9e8b07dc43d3bc067abed5be12694ba145184e79fc0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:19.188674Z","signature_b64":"xiDbsybDQanaiz459dRakc32t8otNbasPLAYHBZjXGc8SnrSS09YvWXQX2ZNercVg4r3x+eMvo6h8W18/PTpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd69d8b2f76013b70a5ffef0643d3b38d369eeabc062e3cc60f79e28a335a164","last_reissued_at":"2026-05-18T02:27:19.187965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:19.187965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirac operators on foliations: the Lichnerowicz inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Weiping Zhang","submitted_at":"2012-04-10T17:27:43Z","abstract_excerpt":"We construct Dirac operators on foliations by applying the Bismut-Lebeau analytic localization technique to the Connes fibration over a foliation. The Laplacian of the resulting Dirac operators has better lower bound than that obtained by using the usual adiabatic limit arguments on the original foliation. As a consequence, we prove an extension of the Lichnerowicz-Hitchin vanishing theorem to the case of foliations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2224","kind":"arxiv","version":5},"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":"1204.2224","created_at":"2026-05-18T02:27:19.188068+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2224v5","created_at":"2026-05-18T02:27:19.188068+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2224","created_at":"2026-05-18T02:27:19.188068+00:00"},{"alias_kind":"pith_short_12","alias_value":"XVU5RMXXMAJ3","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XVU5RMXXMAJ3OCS7","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XVU5RMXX","created_at":"2026-05-18T12:27:27.928770+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/XVU5RMXXMAJ3OCS773YGIPJ3HD","json":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD.json","graph_json":"https://pith.science/api/pith-number/XVU5RMXXMAJ3OCS773YGIPJ3HD/graph.json","events_json":"https://pith.science/api/pith-number/XVU5RMXXMAJ3OCS773YGIPJ3HD/events.json","paper":"https://pith.science/paper/XVU5RMXX"},"agent_actions":{"view_html":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD","download_json":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD.json","view_paper":"https://pith.science/paper/XVU5RMXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2224&json=true","fetch_graph":"https://pith.science/api/pith-number/XVU5RMXXMAJ3OCS773YGIPJ3HD/graph.json","fetch_events":"https://pith.science/api/pith-number/XVU5RMXXMAJ3OCS773YGIPJ3HD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD/action/storage_attestation","attest_author":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD/action/author_attestation","sign_citation":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD/action/citation_signature","submit_replication":"https://pith.science/pith/XVU5RMXXMAJ3OCS773YGIPJ3HD/action/replication_record"}},"created_at":"2026-05-18T02:27:19.188068+00:00","updated_at":"2026-05-18T02:27:19.188068+00:00"}