{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5EFCLWPTZ42YF3ZVV4S3ZRDORN","short_pith_number":"pith:5EFCLWPT","schema_version":"1.0","canonical_sha256":"e90a25d9f3cf3582ef35af25bcc46e8b68b7c2faf35a24739513be0932315549","source":{"kind":"arxiv","id":"1709.03911","version":4},"attestation_state":"computed","paper":{"title":"An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Daniel Siemssen, Jan Derezi\\'nski","submitted_at":"2017-09-12T15:30:02Z","abstract_excerpt":"We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the electromagnetic potential and of the scalar potential. Our main goal is a construction of various kinds of propagators needed in quantum field theory."},"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":"1709.03911","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-09-12T15:30:02Z","cross_cats_sorted":["math.AP","math.FA","math.MP"],"title_canon_sha256":"f4e95936686437122d946cdadfd3d0956d47ba2b2c26ab9e076e219f28a784b6","abstract_canon_sha256":"bda36edf8fd53ea95e60a164779788927dc0f59abb287d674215ca9eaaef3758"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:13.492111Z","signature_b64":"C59ywlB0+0Lol00lMt87szt9fOKrxslBWrdnzqkDRP1OJDZYBS6VXxO+xBwCboBB2pp6XlXaEzrmTezhH1gTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e90a25d9f3cf3582ef35af25bcc46e8b68b7c2faf35a24739513be0932315549","last_reissued_at":"2026-05-17T23:46:13.491549Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:13.491549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Daniel Siemssen, Jan Derezi\\'nski","submitted_at":"2017-09-12T15:30:02Z","abstract_excerpt":"We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the electromagnetic potential and of the scalar potential. Our main goal is a construction of various kinds of propagators needed in quantum field theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03911","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":""},"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":"1709.03911","created_at":"2026-05-17T23:46:13.491649+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.03911v4","created_at":"2026-05-17T23:46:13.491649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03911","created_at":"2026-05-17T23:46:13.491649+00:00"},{"alias_kind":"pith_short_12","alias_value":"5EFCLWPTZ42Y","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5EFCLWPTZ42YF3ZV","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5EFCLWPT","created_at":"2026-05-18T12:31:00.734936+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/5EFCLWPTZ42YF3ZVV4S3ZRDORN","json":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN.json","graph_json":"https://pith.science/api/pith-number/5EFCLWPTZ42YF3ZVV4S3ZRDORN/graph.json","events_json":"https://pith.science/api/pith-number/5EFCLWPTZ42YF3ZVV4S3ZRDORN/events.json","paper":"https://pith.science/paper/5EFCLWPT"},"agent_actions":{"view_html":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN","download_json":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN.json","view_paper":"https://pith.science/paper/5EFCLWPT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.03911&json=true","fetch_graph":"https://pith.science/api/pith-number/5EFCLWPTZ42YF3ZVV4S3ZRDORN/graph.json","fetch_events":"https://pith.science/api/pith-number/5EFCLWPTZ42YF3ZVV4S3ZRDORN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN/action/storage_attestation","attest_author":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN/action/author_attestation","sign_citation":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN/action/citation_signature","submit_replication":"https://pith.science/pith/5EFCLWPTZ42YF3ZVV4S3ZRDORN/action/replication_record"}},"created_at":"2026-05-17T23:46:13.491649+00:00","updated_at":"2026-05-17T23:46:13.491649+00:00"}