{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:QC2PRC6QWAQSZEXQBZCEYJQKP6","short_pith_number":"pith:QC2PRC6Q","schema_version":"1.0","canonical_sha256":"80b4f88bd0b0212c92f00e444c260a7f87c680b3b5bbff7e954b024b93d67178","source":{"kind":"arxiv","id":"0707.2302","version":2},"attestation_state":"computed","paper":{"title":"Causality and Micro-Causality in Curved Spacetime","license":"","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Graham M. Shore, Timothy J. Hollowood","submitted_at":"2007-07-16T11:13:48Z","abstract_excerpt":"We consider how causality and micro-causality are realised in QED in curved spacetime. The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion relation and calls into question the validity of micro-causality in curved spacetime. This non-analyticity is ultimately related to the generic focusing nature of congruences of geodesics in curved spacetime, as implied by the null energy condition, and the existence of conjugate points. These results arise from a calculation of the complete non-perturbative frequ"},"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":"0707.2302","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2007-07-16T11:13:48Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"f2bff08a68a05af77041971915ca65e35cc1860389f1b49588c31caa97d1ed1b","abstract_canon_sha256":"0f67a1da3a5185cfc3f839231ca97a8a9fd30913647b0cc13b784bf1da207bd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:21:20.993052Z","signature_b64":"Aq6K5g2+/W2eA2UN4A5GtbVAQdISNeAwDtM7Glga6AAPbAq1X6vHGJmEtw99oL/Z2iQ92ANiBLIZYDEAc/LLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80b4f88bd0b0212c92f00e444c260a7f87c680b3b5bbff7e954b024b93d67178","last_reissued_at":"2026-07-04T15:21:20.992700Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:21:20.992700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Causality and Micro-Causality in Curved Spacetime","license":"","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Graham M. Shore, Timothy J. Hollowood","submitted_at":"2007-07-16T11:13:48Z","abstract_excerpt":"We consider how causality and micro-causality are realised in QED in curved spacetime. The photon propagator is found to exhibit novel non-analytic behaviour due to vacuum polarization, which invalidates the Kramers-Kronig dispersion relation and calls into question the validity of micro-causality in curved spacetime. This non-analyticity is ultimately related to the generic focusing nature of congruences of geodesics in curved spacetime, as implied by the null energy condition, and the existence of conjugate points. These results arise from a calculation of the complete non-perturbative frequ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2302","kind":"arxiv","version":2},"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/0707.2302/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":"0707.2302","created_at":"2026-07-04T15:21:20.992756+00:00"},{"alias_kind":"arxiv_version","alias_value":"0707.2302v2","created_at":"2026-07-04T15:21:20.992756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.2302","created_at":"2026-07-04T15:21:20.992756+00:00"},{"alias_kind":"pith_short_12","alias_value":"QC2PRC6QWAQS","created_at":"2026-07-04T15:21:20.992756+00:00"},{"alias_kind":"pith_short_16","alias_value":"QC2PRC6QWAQSZEXQ","created_at":"2026-07-04T15:21:20.992756+00:00"},{"alias_kind":"pith_short_8","alias_value":"QC2PRC6Q","created_at":"2026-07-04T15:21:20.992756+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.04215","citing_title":"Microcausality without Lorentz invariance","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6","json":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6.json","graph_json":"https://pith.science/api/pith-number/QC2PRC6QWAQSZEXQBZCEYJQKP6/graph.json","events_json":"https://pith.science/api/pith-number/QC2PRC6QWAQSZEXQBZCEYJQKP6/events.json","paper":"https://pith.science/paper/QC2PRC6Q"},"agent_actions":{"view_html":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6","download_json":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6.json","view_paper":"https://pith.science/paper/QC2PRC6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0707.2302&json=true","fetch_graph":"https://pith.science/api/pith-number/QC2PRC6QWAQSZEXQBZCEYJQKP6/graph.json","fetch_events":"https://pith.science/api/pith-number/QC2PRC6QWAQSZEXQBZCEYJQKP6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6/action/storage_attestation","attest_author":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6/action/author_attestation","sign_citation":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6/action/citation_signature","submit_replication":"https://pith.science/pith/QC2PRC6QWAQSZEXQBZCEYJQKP6/action/replication_record"}},"created_at":"2026-07-04T15:21:20.992756+00:00","updated_at":"2026-07-04T15:21:20.992756+00:00"}