{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:T5TFHK3UGT6EBRCTYM2ONDZSR7","short_pith_number":"pith:T5TFHK3U","canonical_record":{"source":{"id":"gr-qc/0007021","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-07-11T15:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"84c3864136e04851fe02c0d51508f9909f004b94d872ba23ef38999127438fe9","abstract_canon_sha256":"f55304ec19589974d7f3a00234a7931606db13c1be71671aa84ae4694434a4d9"},"schema_version":"1.0"},"canonical_sha256":"9f6653ab7434fc40c453c334e68f328fdbf26a49a981792cb8d729967b71f95e","source":{"kind":"arxiv","id":"gr-qc/0007021","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:T5TFHK3UGT6EBRCTYM2ONDZSR7","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0007021","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-07-11T15:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"84c3864136e04851fe02c0d51508f9909f004b94d872ba23ef38999127438fe9","abstract_canon_sha256":"f55304ec19589974d7f3a00234a7931606db13c1be71671aa84ae4694434a4d9"},"schema_version":"1.0"},"canonical_sha256":"9f6653ab7434fc40c453c334e68f328fdbf26a49a981792cb8d729967b71f95e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:19:40.245121Z","signature_b64":"nRaSrZXqpyzMd0O7Ckve3f7xUkFClCuFTaXn60/h+rAEx2kvlJk/NA+TDRPc75gS31MEOtyKHnMku1ItQjFxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f6653ab7434fc40c453c334e68f328fdbf26a49a981792cb8d729967b71f95e","last_reissued_at":"2026-07-04T16:19:40.244760Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:19:40.244760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0007021","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:19:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rkzsb00KJA3X2t0At7SBEvn3w6R/V0nJ4GTs8a8GShpKMx5bIriqjcAkPMnAY8sGZ+CGLz3D1iJzPLd2UrugAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:16:40.714026Z"},"content_sha256":"71b2023cbeab3876d775f2ae6171bc693dc7b48abd39c2103b7e295ce176eea0","schema_version":"1.0","event_id":"sha256:71b2023cbeab3876d775f2ae6171bc693dc7b48abd39c2103b7e295ce176eea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:T5TFHK3UGT6EBRCTYM2ONDZSR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theorems on gravitational time delay and related issues","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Robert M. Wald, Sijie Gao","submitted_at":"2000-07-11T15:12:16Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0007021","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/gr-qc/0007021/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:19:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQaLzlvz4B1BFV3TMRbtRXbWJhAgnTEkI1Y2SkLMXEe5J93PO3ZrWgREE/WCit9thhHNdW2wLT+niZQXGLtFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:16:40.714973Z"},"content_sha256":"2032e479fe1bacf01e45da2413a0571c1397efe76b5be9abd9fa0877e912e59a","schema_version":"1.0","event_id":"sha256:2032e479fe1bacf01e45da2413a0571c1397efe76b5be9abd9fa0877e912e59a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T5TFHK3UGT6EBRCTYM2ONDZSR7/bundle.json","state_url":"https://pith.science/pith/T5TFHK3UGT6EBRCTYM2ONDZSR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T5TFHK3UGT6EBRCTYM2ONDZSR7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T09:16:40Z","links":{"resolver":"https://pith.science/pith/T5TFHK3UGT6EBRCTYM2ONDZSR7","bundle":"https://pith.science/pith/T5TFHK3UGT6EBRCTYM2ONDZSR7/bundle.json","state":"https://pith.science/pith/T5TFHK3UGT6EBRCTYM2ONDZSR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T5TFHK3UGT6EBRCTYM2ONDZSR7/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6AFIAzwwrWBKMT7cykEHTmB+/Hpp6MtcGX8pxuQb4BX7ip2SHDj9OL31z2oKHAGh6ZMzxyaaUXY8CQXk86m5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:16:40.719610Z","bundle_sha256":"026ff6ea6b967bc56c9ab077a9a132159fb00f37ae04cfec626f9b997fc7fed4"}}