{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N2DENMGDB5GIPHFJYR2TLKWK5N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"165d232eef8d9730094360cae13d14fbd0a4b1f443238ad02f7037539bbd8f91","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-01T15:08:04Z","title_canon_sha256":"9ae192ff4c3e9f5e067f29fc18d99539e96bd17027dc5b5461f003d0573d8b92"},"schema_version":"1.0","source":{"id":"1308.0236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0236","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0236v1","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0236","created_at":"2026-05-18T03:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"N2DENMGDB5GI","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N2DENMGDB5GIPHFJ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N2DENMGD","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:8e96c70cca9a4d2fd1559628191e9024159498a9a3583a67f359a887cc4e3909","target":"graph","created_at":"2026-05-18T03:16:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the \"topological side\" of the index theorem. This results in index formulae for Lie groupoid analogues of the familiar geometric operators on manifolds such as the signature and Dirac operator expressed in terms of the usual characteristic classes in Lie algebroid cohomology.","authors_text":"H. Posthuma, M.J. Pflaum, X. Tang","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-01T15:08:04Z","title":"The index of geometric operators on Lie groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0236","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1502169590db22edd122b085a1cb98622f15ba4529fc1c741a0074f2a55ef17a","target":"record","created_at":"2026-05-18T03:16:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"165d232eef8d9730094360cae13d14fbd0a4b1f443238ad02f7037539bbd8f91","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-01T15:08:04Z","title_canon_sha256":"9ae192ff4c3e9f5e067f29fc18d99539e96bd17027dc5b5461f003d0573d8b92"},"schema_version":"1.0","source":{"id":"1308.0236","kind":"arxiv","version":1}},"canonical_sha256":"6e8646b0c30f4c879ca9c47535aacaeb71ad2f0006830763ae1f489e4f60ca53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e8646b0c30f4c879ca9c47535aacaeb71ad2f0006830763ae1f489e4f60ca53","first_computed_at":"2026-05-18T03:16:59.504769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:59.504769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZsFUgAvcFj4nh2aAPqR6HRm8ORo+/GHrRYOhN2x3mKBpuKck5bncBqWZbel4WW3xv/V/m1Hx1050melH6PfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:59.505470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1502169590db22edd122b085a1cb98622f15ba4529fc1c741a0074f2a55ef17a","sha256:8e96c70cca9a4d2fd1559628191e9024159498a9a3583a67f359a887cc4e3909"],"state_sha256":"2c13b8ef2f95f8439ec6abdc56cb726d4e98e9c00327c4b47163d07b7babccc4"}