{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:4T6WTZRDOEDQ4MIU6A2XR55QWX","short_pith_number":"pith:4T6WTZRD","schema_version":"1.0","canonical_sha256":"e4fd69e62371070e3114f03578f7b0b5f1c08082cd16a71627b8e69e35aed259","source":{"kind":"arxiv","id":"0806.1036","version":1},"attestation_state":"computed","paper":{"title":"Wave Equations on Lorentzian Manifolds and Quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christian Baer, Frank Pfaeffle, Nicolas Ginoux","submitted_at":"2008-06-05T19:22:31Z","abstract_excerpt":"This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field "},"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":"0806.1036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-06-05T19:22:31Z","cross_cats_sorted":[],"title_canon_sha256":"76e8f93ccd7421b86e183fd48a2c19913f4389a763b65dfb3727ca8e7aeb3070","abstract_canon_sha256":"99da2f27ba99fe9213a43f47b9064c5e63c0e092e943cbd41c55ddbb46272183"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:12:01.297781Z","signature_b64":"iyKvcRObitmFMrH3wGCCRLUEvYo+N01bXYHvxwbAQy9RV3jP3MP8zjtSoSjkyXABMGx2h0Nf2GQFkhvgKvjDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4fd69e62371070e3114f03578f7b0b5f1c08082cd16a71627b8e69e35aed259","last_reissued_at":"2026-07-04T15:12:01.297403Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:12:01.297403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wave Equations on Lorentzian Manifolds and Quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christian Baer, Frank Pfaeffle, Nicolas Ginoux","submitted_at":"2008-06-05T19:22:31Z","abstract_excerpt":"This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1036","kind":"arxiv","version":1},"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/0806.1036/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":"0806.1036","created_at":"2026-07-04T15:12:01.297473+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.1036v1","created_at":"2026-07-04T15:12:01.297473+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.1036","created_at":"2026-07-04T15:12:01.297473+00:00"},{"alias_kind":"pith_short_12","alias_value":"4T6WTZRDOEDQ","created_at":"2026-07-04T15:12:01.297473+00:00"},{"alias_kind":"pith_short_16","alias_value":"4T6WTZRDOEDQ4MIU","created_at":"2026-07-04T15:12:01.297473+00:00"},{"alias_kind":"pith_short_8","alias_value":"4T6WTZRD","created_at":"2026-07-04T15:12:01.297473+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2607.07810","citing_title":"Relative entropy for $\\lambda \\phi^4$ in the Rindler wedge","ref_index":28,"is_internal_anchor":true},{"citing_arxiv_id":"2605.30199","citing_title":"The Continuum Limit Analysis of Causal Fermion Systems for Curved Spacetimes","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX","json":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX.json","graph_json":"https://pith.science/api/pith-number/4T6WTZRDOEDQ4MIU6A2XR55QWX/graph.json","events_json":"https://pith.science/api/pith-number/4T6WTZRDOEDQ4MIU6A2XR55QWX/events.json","paper":"https://pith.science/paper/4T6WTZRD"},"agent_actions":{"view_html":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX","download_json":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX.json","view_paper":"https://pith.science/paper/4T6WTZRD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.1036&json=true","fetch_graph":"https://pith.science/api/pith-number/4T6WTZRDOEDQ4MIU6A2XR55QWX/graph.json","fetch_events":"https://pith.science/api/pith-number/4T6WTZRDOEDQ4MIU6A2XR55QWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX/action/storage_attestation","attest_author":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX/action/author_attestation","sign_citation":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX/action/citation_signature","submit_replication":"https://pith.science/pith/4T6WTZRDOEDQ4MIU6A2XR55QWX/action/replication_record"}},"created_at":"2026-07-04T15:12:01.297473+00:00","updated_at":"2026-07-04T15:12:01.297473+00:00"}