{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CJE5HASHU6V7WEV7VDCFUJCZIB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"974bb6ac34ce357b3a58e3b1e3b72446a44b5e7f9eb752b87f24c8188e8b32cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-01-08T11:07:48Z","title_canon_sha256":"1673dd36f655fc75213356742cf0bb08a297d54b0d7d767ed656731f83460929"},"schema_version":"1.0","source":{"id":"1801.02382","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02382","created_at":"2026-05-18T00:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02382v1","created_at":"2026-05-18T00:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02382","created_at":"2026-05-18T00:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"CJE5HASHU6V7","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CJE5HASHU6V7WEV7","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CJE5HASH","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:e67ea9012ff57b5bd76fc50c2de365ae94ced837c6695360bc1edb164f49dd40","target":"graph","created_at":"2026-05-18T00:26:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The study of gravitational waves in the presence of a cosmological constant has led to interesting forms of the de Sitter and anti-de Sitter line elements based on families of null hypersurfaces. The forms are interesting because they focus attention on the geometry of null hypersurfaces in space-times of constant curvature. Two examples are worked out in some detail. The first originated in the study of collisions of impulsive gravitational waves in which the post-collision space-time is a solution of Einstein's field equations with a cosmological constant, and the second originated in the ge","authors_text":"P. A. Hogan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-01-08T11:07:48Z","title":"Null Hypersurfaces in de Sitter and anti-de Sitter Cosmologies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02382","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ae94b75b10c96fcc4763b73395ce98073b7e5e0a92f536a3d5219c9e2ea68bf2","target":"record","created_at":"2026-05-18T00:26:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"974bb6ac34ce357b3a58e3b1e3b72446a44b5e7f9eb752b87f24c8188e8b32cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-01-08T11:07:48Z","title_canon_sha256":"1673dd36f655fc75213356742cf0bb08a297d54b0d7d767ed656731f83460929"},"schema_version":"1.0","source":{"id":"1801.02382","kind":"arxiv","version":1}},"canonical_sha256":"1249d38247a7abfb12bfa8c45a24594077ad5d50fd40f2cf9acb588334001db3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1249d38247a7abfb12bfa8c45a24594077ad5d50fd40f2cf9acb588334001db3","first_computed_at":"2026-05-18T00:26:31.798681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:31.798681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n9PYg8VMS4Zp+epAABjWMqkAACu3mLI4wZFdDtVv4ws8LH6iv2jp+X7/hYgiBNH0whgpdFYkZvh/yrr1RFG1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:31.799378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02382","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae94b75b10c96fcc4763b73395ce98073b7e5e0a92f536a3d5219c9e2ea68bf2","sha256:e67ea9012ff57b5bd76fc50c2de365ae94ced837c6695360bc1edb164f49dd40"],"state_sha256":"fbec01ddea1be010e8857b136c80c45be3878635123905cb5c2ecd3937cb6bee"}