{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:T5TFHK3UGT6EBRCTYM2ONDZSR7","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":"f55304ec19589974d7f3a00234a7931606db13c1be71671aa84ae4694434a4d9","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2000-07-11T15:12:16Z","title_canon_sha256":"84c3864136e04851fe02c0d51508f9909f004b94d872ba23ef38999127438fe9"},"schema_version":"1.0","source":{"id":"gr-qc/0007021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0007021","created_at":"2026-07-04T16:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0007021v2","created_at":"2026-07-04T16:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0007021","created_at":"2026-07-04T16:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"T5TFHK3UGT6E","created_at":"2026-07-04T16:19:40Z"},{"alias_kind":"pith_short_16","alias_value":"T5TFHK3UGT6EBRCT","created_at":"2026-07-04T16:19:40Z"},{"alias_kind":"pith_short_8","alias_value":"T5TFHK3U","created_at":"2026-07-04T16:19:40Z"}],"graph_snapshots":[{"event_id":"sha256:2032e479fe1bacf01e45da2413a0571c1397efe76b5be9abd9fa0877e912e59a","target":"graph","created_at":"2026-07-04T16:19:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/gr-qc/0007021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set $K$, there exists another compact set $K'$ such that for any $p,q \\not\\in K'$, if there exists a ``fastest null geodesic'', $\\gamma$, between $p$ and $q$, then $\\gamma$ cannot enter $K$. As an application of this theorem, we show that if, in addition, the spacetime is globally hyperbolic with a compact Cauchy surface, then any ob","authors_text":"Robert M. Wald, Sijie Gao","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2000-07-11T15:12:16Z","title":"Theorems on gravitational time delay and related issues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0007021","kind":"arxiv","version":2},"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":"sha256:71b2023cbeab3876d775f2ae6171bc693dc7b48abd39c2103b7e295ce176eea0","target":"record","created_at":"2026-07-04T16:19:40Z","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":"f55304ec19589974d7f3a00234a7931606db13c1be71671aa84ae4694434a4d9","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2000-07-11T15:12:16Z","title_canon_sha256":"84c3864136e04851fe02c0d51508f9909f004b94d872ba23ef38999127438fe9"},"schema_version":"1.0","source":{"id":"gr-qc/0007021","kind":"arxiv","version":2}},"canonical_sha256":"9f6653ab7434fc40c453c334e68f328fdbf26a49a981792cb8d729967b71f95e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f6653ab7434fc40c453c334e68f328fdbf26a49a981792cb8d729967b71f95e","first_computed_at":"2026-07-04T16:19:40.244760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:19:40.244760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nRaSrZXqpyzMd0O7Ckve3f7xUkFClCuFTaXn60/h+rAEx2kvlJk/NA+TDRPc75gS31MEOtyKHnMku1ItQjFxBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:19:40.245121Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0007021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71b2023cbeab3876d775f2ae6171bc693dc7b48abd39c2103b7e295ce176eea0","sha256:2032e479fe1bacf01e45da2413a0571c1397efe76b5be9abd9fa0877e912e59a"],"state_sha256":"1e1a2d5677bf5aa0d1f47bb68c1eb9f6c2661d9de2816c7469995efaacc5ea54"}