{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CSXWFACBDUEQWU6FLISIJU6GTQ","short_pith_number":"pith:CSXWFACB","schema_version":"1.0","canonical_sha256":"14af6280411d090b53c55a2484d3c69c18eda1599c282a731c7b24e004cc7941","source":{"kind":"arxiv","id":"1812.00926","version":5},"attestation_state":"computed","paper":{"title":"Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Albert Much (Universit\\\"at Leipzig), Robert Oeckl (CCM-UNAM)","submitted_at":"2018-12-03T17:31:16Z","abstract_excerpt":"We develop a rigorous method to parametrize complex structures for Klein-Gordon theory in globally hyperbolic spacetimes that satisfy a completeness condition. The complex structures are conserved under time-evolution and implement unitary quantizations. They can be interpreted as corresponding to global choices of vacuum. The main ingredient in our construction is a system of operator differential equations. We provide a number of theorems ensuring that all ingredients and steps in the construction are well-defined. We apply the method to exhibit natural quantizations for certain classes of g"},"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":"1812.00926","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-03T17:31:16Z","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"title_canon_sha256":"f2389ed854534cdfff4e2e007dd6b6a25f9eadc4131227817b7237d6555da706","abstract_canon_sha256":"c3b5241df90d4d2f08faaf4a06afe379b11a818b7e975ecb3d6511e1024461a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:45:22.390097Z","signature_b64":"S60zaVyLA9Am4ZEhO9ag+jmfOGMorEVITu1QvWjskPYhyf4gjPuhszAHOanyar64kb6IcGeFh7vceAJSqA7UBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14af6280411d090b53c55a2484d3c69c18eda1599c282a731c7b24e004cc7941","last_reissued_at":"2026-07-05T03:45:22.389654Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:45:22.389654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Albert Much (Universit\\\"at Leipzig), Robert Oeckl (CCM-UNAM)","submitted_at":"2018-12-03T17:31:16Z","abstract_excerpt":"We develop a rigorous method to parametrize complex structures for Klein-Gordon theory in globally hyperbolic spacetimes that satisfy a completeness condition. The complex structures are conserved under time-evolution and implement unitary quantizations. They can be interpreted as corresponding to global choices of vacuum. The main ingredient in our construction is a system of operator differential equations. We provide a number of theorems ensuring that all ingredients and steps in the construction are well-defined. We apply the method to exhibit natural quantizations for certain classes of g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00926","kind":"arxiv","version":5},"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/1812.00926/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":"1812.00926","created_at":"2026-07-05T03:45:22.389720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.00926v5","created_at":"2026-07-05T03:45:22.389720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00926","created_at":"2026-07-05T03:45:22.389720+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSXWFACBDUEQ","created_at":"2026-07-05T03:45:22.389720+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSXWFACBDUEQWU6F","created_at":"2026-07-05T03:45:22.389720+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSXWFACB","created_at":"2026-07-05T03:45:22.389720+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.13351","citing_title":"Challenges for describing unitary evolution in nontrivial geometries: pictures and representations","ref_index":43,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ","json":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ.json","graph_json":"https://pith.science/api/pith-number/CSXWFACBDUEQWU6FLISIJU6GTQ/graph.json","events_json":"https://pith.science/api/pith-number/CSXWFACBDUEQWU6FLISIJU6GTQ/events.json","paper":"https://pith.science/paper/CSXWFACB"},"agent_actions":{"view_html":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ","download_json":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ.json","view_paper":"https://pith.science/paper/CSXWFACB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.00926&json=true","fetch_graph":"https://pith.science/api/pith-number/CSXWFACBDUEQWU6FLISIJU6GTQ/graph.json","fetch_events":"https://pith.science/api/pith-number/CSXWFACBDUEQWU6FLISIJU6GTQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ/action/storage_attestation","attest_author":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ/action/author_attestation","sign_citation":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ/action/citation_signature","submit_replication":"https://pith.science/pith/CSXWFACBDUEQWU6FLISIJU6GTQ/action/replication_record"}},"created_at":"2026-07-05T03:45:22.389720+00:00","updated_at":"2026-07-05T03:45:22.389720+00:00"}