{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UE3VAZAK22HPWOVX5LSW6JNKQM","short_pith_number":"pith:UE3VAZAK","schema_version":"1.0","canonical_sha256":"a13750640ad68efb3ab7eae56f25aa831048d202748e1b1f6f8a04ecaed131a8","source":{"kind":"arxiv","id":"1607.07039","version":3},"attestation_state":"computed","paper":{"title":"Getzler rescaling via adiabatic deformation and a renormalized local index formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.OA","authors_text":"Elmar Schrohe, Karsten Bohlen","submitted_at":"2016-07-24T13:16:24Z","abstract_excerpt":"We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). With the help of a renormalized supertrace, defined on a suitable class of regularizing operators, the proof of the index theorem relies on a rescaling technique similar in spirit to Getzler's rescaling. With a given Lie manifold we associate an appropriate integrating Lie groupoid. We then describe the heat kernel of a geometric Dirac operator via a functional calculus with values in the convolution algebra of sections of a rescaled bundle over 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":"1607.07039","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-07-24T13:16:24Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f30746e6e194a160ade6a4dbd470bc37746cf8728cdcf875842f1893a329fe64","abstract_canon_sha256":"cc50e8f98b1eb26772c93f2be4647b5d900adab395183ebeb52c0e1285f14691"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:26.360211Z","signature_b64":"N4mb05PQgI91fyk9dheBaI6ozDl8r0CrNU5D0pspoH1qfOWnOmjs5kDRJhTkqj4frW4yNG2CKD5R8h85TI45CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a13750640ad68efb3ab7eae56f25aa831048d202748e1b1f6f8a04ecaed131a8","last_reissued_at":"2026-05-18T00:46:26.359536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:26.359536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Getzler rescaling via adiabatic deformation and a renormalized local index formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.OA","authors_text":"Elmar Schrohe, Karsten Bohlen","submitted_at":"2016-07-24T13:16:24Z","abstract_excerpt":"We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). With the help of a renormalized supertrace, defined on a suitable class of regularizing operators, the proof of the index theorem relies on a rescaling technique similar in spirit to Getzler's rescaling. With a given Lie manifold we associate an appropriate integrating Lie groupoid. We then describe the heat kernel of a geometric Dirac operator via a functional calculus with values in the convolution algebra of sections of a rescaled bundle over the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07039","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":"1607.07039","created_at":"2026-05-18T00:46:26.359651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.07039v3","created_at":"2026-05-18T00:46:26.359651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07039","created_at":"2026-05-18T00:46:26.359651+00:00"},{"alias_kind":"pith_short_12","alias_value":"UE3VAZAK22HP","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UE3VAZAK22HPWOVX","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UE3VAZAK","created_at":"2026-05-18T12:30:46.583412+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/UE3VAZAK22HPWOVX5LSW6JNKQM","json":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM.json","graph_json":"https://pith.science/api/pith-number/UE3VAZAK22HPWOVX5LSW6JNKQM/graph.json","events_json":"https://pith.science/api/pith-number/UE3VAZAK22HPWOVX5LSW6JNKQM/events.json","paper":"https://pith.science/paper/UE3VAZAK"},"agent_actions":{"view_html":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM","download_json":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM.json","view_paper":"https://pith.science/paper/UE3VAZAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.07039&json=true","fetch_graph":"https://pith.science/api/pith-number/UE3VAZAK22HPWOVX5LSW6JNKQM/graph.json","fetch_events":"https://pith.science/api/pith-number/UE3VAZAK22HPWOVX5LSW6JNKQM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM/action/storage_attestation","attest_author":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM/action/author_attestation","sign_citation":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM/action/citation_signature","submit_replication":"https://pith.science/pith/UE3VAZAK22HPWOVX5LSW6JNKQM/action/replication_record"}},"created_at":"2026-05-18T00:46:26.359651+00:00","updated_at":"2026-05-18T00:46:26.359651+00:00"}