{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:4XBPXWBG3GVCGMKIBNVIBS7GFD","short_pith_number":"pith:4XBPXWBG","schema_version":"1.0","canonical_sha256":"e5c2fbd826d9aa2331480b6a80cbe628d24763fd2cd32be6933a02659552574c","source":{"kind":"arxiv","id":"2012.01364","version":4},"attestation_state":"computed","paper":{"title":"Local Index Theory for Lorentzian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Alexander Strohmaier, Christian Baer","submitted_at":"2020-12-02T18:05:28Z","abstract_excerpt":"Index theory for Lorentzian Dirac operators is a young subject with significant differences to elliptic index theory. It is based on microlocal analysis instead of standard elliptic theory and one of the main features is that a nontrivial index is caused by topologically nontrivial dynamics rather than nontrivial topology of the base manifold. In this paper we establish a local index formula for Lorentzian Dirac-type operators on globally hyperbolic spacetimes. This local formula implies an index theorem for general Dirac-type operators on spatially compact spacetimes with Atiyah-Patodi-Singer"},"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":"2012.01364","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-12-02T18:05:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3fbb1781a2fcfa826d4baca165c5fadd9dc0fa1673fc6fef1f5eb9c5d766ab8e","abstract_canon_sha256":"22a2e2e6beb94106f4d7c27ab0aff62bca7829487737ef0bbe612e66332da2f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:00.451398Z","signature_b64":"7wPc7WR6cg6+JjQOqwxUuEa7Ta9cCLNyjjEa9Ga7wDw/rQBMnt8jPhjHbxMTtW08xeGrF26lDX4PkKsCBeHWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5c2fbd826d9aa2331480b6a80cbe628d24763fd2cd32be6933a02659552574c","last_reissued_at":"2026-07-05T10:14:00.450873Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:00.450873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Index Theory for Lorentzian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Alexander Strohmaier, Christian Baer","submitted_at":"2020-12-02T18:05:28Z","abstract_excerpt":"Index theory for Lorentzian Dirac operators is a young subject with significant differences to elliptic index theory. It is based on microlocal analysis instead of standard elliptic theory and one of the main features is that a nontrivial index is caused by topologically nontrivial dynamics rather than nontrivial topology of the base manifold. In this paper we establish a local index formula for Lorentzian Dirac-type operators on globally hyperbolic spacetimes. This local formula implies an index theorem for general Dirac-type operators on spatially compact spacetimes with Atiyah-Patodi-Singer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.01364","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.01364/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2012.01364","created_at":"2026-07-05T10:14:00.450930+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.01364v4","created_at":"2026-07-05T10:14:00.450930+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.01364","created_at":"2026-07-05T10:14:00.450930+00:00"},{"alias_kind":"pith_short_12","alias_value":"4XBPXWBG3GVC","created_at":"2026-07-05T10:14:00.450930+00:00"},{"alias_kind":"pith_short_16","alias_value":"4XBPXWBG3GVCGMKI","created_at":"2026-07-05T10:14:00.450930+00:00"},{"alias_kind":"pith_short_8","alias_value":"4XBPXWBG","created_at":"2026-07-05T10:14:00.450930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2308.12148","citing_title":"Heat and Wave kernel expansions for stationary spacetimes","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2604.25763","citing_title":"Formulas for Hadamard coefficients in terms of Green's operators","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD","json":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD.json","graph_json":"https://pith.science/api/pith-number/4XBPXWBG3GVCGMKIBNVIBS7GFD/graph.json","events_json":"https://pith.science/api/pith-number/4XBPXWBG3GVCGMKIBNVIBS7GFD/events.json","paper":"https://pith.science/paper/4XBPXWBG"},"agent_actions":{"view_html":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD","download_json":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD.json","view_paper":"https://pith.science/paper/4XBPXWBG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.01364&json=true","fetch_graph":"https://pith.science/api/pith-number/4XBPXWBG3GVCGMKIBNVIBS7GFD/graph.json","fetch_events":"https://pith.science/api/pith-number/4XBPXWBG3GVCGMKIBNVIBS7GFD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD/action/storage_attestation","attest_author":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD/action/author_attestation","sign_citation":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD/action/citation_signature","submit_replication":"https://pith.science/pith/4XBPXWBG3GVCGMKIBNVIBS7GFD/action/replication_record"}},"created_at":"2026-07-05T10:14:00.450930+00:00","updated_at":"2026-07-05T10:14:00.450930+00:00"}