{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:KH3IQYJEAI2VS3QUGSLE3I7L7H","short_pith_number":"pith:KH3IQYJE","schema_version":"1.0","canonical_sha256":"51f68861240235596e1434964da3ebf9fdf10a09807e94bfdc9da78565c753c9","source":{"kind":"arxiv","id":"2506.20004","version":3},"attestation_state":"computed","paper":{"title":"Compact Cauchy horizons admit constant surface gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Ettore Minguzzi, Raymond A. Hounnonkpe","submitted_at":"2025-06-24T20:49:51Z","abstract_excerpt":"We prove that in any spacetime dimension and under the null energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant surface gravity. That is, we solve the open degenerate case by showing that, if there is a complete generator, then there exists a smooth future-directed geodesic lightlike tangent field. The result can be stated as an existence result for a particular cohomological equation. The proof uses elements of ergodic theory, Hodge theory and Riemannian flow 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":"2506.20004","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-06-24T20:49:51Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"124e4c2a1b6ecb97a76773ec6cdbbae06a9c7ea065a943aee1b7b502fcd27434","abstract_canon_sha256":"6ee6670cfe9b12cd03a160535d4441ae13e9d045bd7f8e0a7420688371799bb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:31.432394Z","signature_b64":"RhrtL3lmcNPcSy8SJyqD4+OWKq/hhzt46VxcTo08f807oEbDlrpJ/BGEdQRnYhEBW8hhA6kGSIfNkKBWggLdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f68861240235596e1434964da3ebf9fdf10a09807e94bfdc9da78565c753c9","last_reissued_at":"2026-06-09T02:08:31.431269Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:31.431269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compact Cauchy horizons admit constant surface gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Ettore Minguzzi, Raymond A. Hounnonkpe","submitted_at":"2025-06-24T20:49:51Z","abstract_excerpt":"We prove that in any spacetime dimension and under the null energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant surface gravity. That is, we solve the open degenerate case by showing that, if there is a complete generator, then there exists a smooth future-directed geodesic lightlike tangent field. The result can be stated as an existence result for a particular cohomological equation. The proof uses elements of ergodic theory, Hodge theory and Riemannian flow theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20004","kind":"arxiv","version":3},"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/2506.20004/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":"2506.20004","created_at":"2026-06-09T02:08:31.431434+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.20004v3","created_at":"2026-06-09T02:08:31.431434+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.20004","created_at":"2026-06-09T02:08:31.431434+00:00"},{"alias_kind":"pith_short_12","alias_value":"KH3IQYJEAI2V","created_at":"2026-06-09T02:08:31.431434+00:00"},{"alias_kind":"pith_short_16","alias_value":"KH3IQYJEAI2VS3QU","created_at":"2026-06-09T02:08:31.431434+00:00"},{"alias_kind":"pith_short_8","alias_value":"KH3IQYJE","created_at":"2026-06-09T02:08:31.431434+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.13551","citing_title":"Totally geodesic null hypersurfaces and constancy of surface gravity in Finsler spacetimes","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H","json":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H.json","graph_json":"https://pith.science/api/pith-number/KH3IQYJEAI2VS3QUGSLE3I7L7H/graph.json","events_json":"https://pith.science/api/pith-number/KH3IQYJEAI2VS3QUGSLE3I7L7H/events.json","paper":"https://pith.science/paper/KH3IQYJE"},"agent_actions":{"view_html":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H","download_json":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H.json","view_paper":"https://pith.science/paper/KH3IQYJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.20004&json=true","fetch_graph":"https://pith.science/api/pith-number/KH3IQYJEAI2VS3QUGSLE3I7L7H/graph.json","fetch_events":"https://pith.science/api/pith-number/KH3IQYJEAI2VS3QUGSLE3I7L7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H/action/storage_attestation","attest_author":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H/action/author_attestation","sign_citation":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H/action/citation_signature","submit_replication":"https://pith.science/pith/KH3IQYJEAI2VS3QUGSLE3I7L7H/action/replication_record"}},"created_at":"2026-06-09T02:08:31.431434+00:00","updated_at":"2026-06-09T02:08:31.431434+00:00"}