{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EC7SAJ6GSZTARHRZP43NBDFDME","short_pith_number":"pith:EC7SAJ6G","canonical_record":{"source":{"id":"1407.0340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-01T18:11:38Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c4ccd9f3d0fc5796e954c2386e89a61d21b4ac2249e077d22b2d9ada141bc5eb","abstract_canon_sha256":"f3823b29ca153d3ff4e5b037eb0df1728b6217e1ed55337a5b8ca20aa6863b5c"},"schema_version":"1.0"},"canonical_sha256":"20bf2027c69666089e397f36d08ca361350b4b3d63ac4a3d1fdd987edba6f083","source":{"kind":"arxiv","id":"1407.0340","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0340","created_at":"2026-05-18T01:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0340v2","created_at":"2026-05-18T01:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0340","created_at":"2026-05-18T01:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"EC7SAJ6GSZTA","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EC7SAJ6GSZTARHRZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EC7SAJ6G","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EC7SAJ6GSZTARHRZP43NBDFDME","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-01T18:11:38Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c4ccd9f3d0fc5796e954c2386e89a61d21b4ac2249e077d22b2d9ada141bc5eb","abstract_canon_sha256":"f3823b29ca153d3ff4e5b037eb0df1728b6217e1ed55337a5b8ca20aa6863b5c"},"schema_version":"1.0"},"canonical_sha256":"20bf2027c69666089e397f36d08ca361350b4b3d63ac4a3d1fdd987edba6f083","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:42.937800Z","signature_b64":"K78Ba9jcGg2c1oFUXurpBEaLRt5TWXgu2I90IpzNRJY/GSdxWairxZ1d3JtQjbPJU4Yys6inaPnaOqwbAcHCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20bf2027c69666089e397f36d08ca361350b4b3d63ac4a3d1fdd987edba6f083","last_reissued_at":"2026-05-18T01:42:42.937233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:42.937233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0340","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":"2026-05-18T01:42:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mz5k6hADWJo4p1WBk1tdqiCBPIvVZSIJTslWeLj1Y4O/HskQSI2rfBiqJFfsmzQw+mX7lqH8QIqf0PDy1le7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:26:22.610819Z"},"content_sha256":"a304c30dba767fcb1a097545aa4e3f5c698d0fb792976ba47a3e0f40aa6a5689","schema_version":"1.0","event_id":"sha256:a304c30dba767fcb1a097545aa4e3f5c698d0fb792976ba47a3e0f40aa6a5689"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EC7SAJ6GSZTARHRZP43NBDFDME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Yet another proof of Hawking and Ellis's Lemma 8.5.5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"S. Krasnikov","submitted_at":"2014-07-01T18:11:38Z","abstract_excerpt":"The fact that the null generators of a future Cauchy horizon are past complete was proved first by Hawking and Ellis [1]. Then Budzy\\'nski, Kondracki, and Kr\\'olak outlined a proof free from an error found in the original one [2]. Finally, a week ago Minguzzi published his version of proof [3] patching a previously unnoticed hole in the preceding two. I am not aware of any flaws in that last proof, but it is quite difficult. In this note I present a simpler one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0340","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":""},"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":"2026-05-18T01:42:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/pBfdInIBJrD9ADSr0Y6L5cWYPa0W1lb+wBTaHMfbqai7WufMn5Hmh4VUgZwIMwjqAj6Lo7aYqj1S5gB6PpCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T11:26:22.611161Z"},"content_sha256":"ab159641a1b332c469c28301932c5352788f89aa1157bbd218b7dc5728827606","schema_version":"1.0","event_id":"sha256:ab159641a1b332c469c28301932c5352788f89aa1157bbd218b7dc5728827606"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EC7SAJ6GSZTARHRZP43NBDFDME/bundle.json","state_url":"https://pith.science/pith/EC7SAJ6GSZTARHRZP43NBDFDME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EC7SAJ6GSZTARHRZP43NBDFDME/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":"2026-06-30T11:26:22Z","links":{"resolver":"https://pith.science/pith/EC7SAJ6GSZTARHRZP43NBDFDME","bundle":"https://pith.science/pith/EC7SAJ6GSZTARHRZP43NBDFDME/bundle.json","state":"https://pith.science/pith/EC7SAJ6GSZTARHRZP43NBDFDME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EC7SAJ6GSZTARHRZP43NBDFDME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EC7SAJ6GSZTARHRZP43NBDFDME","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":"f3823b29ca153d3ff4e5b037eb0df1728b6217e1ed55337a5b8ca20aa6863b5c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-01T18:11:38Z","title_canon_sha256":"c4ccd9f3d0fc5796e954c2386e89a61d21b4ac2249e077d22b2d9ada141bc5eb"},"schema_version":"1.0","source":{"id":"1407.0340","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0340","created_at":"2026-05-18T01:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0340v2","created_at":"2026-05-18T01:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0340","created_at":"2026-05-18T01:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"EC7SAJ6GSZTA","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EC7SAJ6GSZTARHRZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EC7SAJ6G","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:ab159641a1b332c469c28301932c5352788f89aa1157bbd218b7dc5728827606","target":"graph","created_at":"2026-05-18T01:42:42Z","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 fact that the null generators of a future Cauchy horizon are past complete was proved first by Hawking and Ellis [1]. Then Budzy\\'nski, Kondracki, and Kr\\'olak outlined a proof free from an error found in the original one [2]. Finally, a week ago Minguzzi published his version of proof [3] patching a previously unnoticed hole in the preceding two. I am not aware of any flaws in that last proof, but it is quite difficult. In this note I present a simpler one.","authors_text":"S. Krasnikov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-01T18:11:38Z","title":"Yet another proof of Hawking and Ellis's Lemma 8.5.5"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0340","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:a304c30dba767fcb1a097545aa4e3f5c698d0fb792976ba47a3e0f40aa6a5689","target":"record","created_at":"2026-05-18T01:42:42Z","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":"f3823b29ca153d3ff4e5b037eb0df1728b6217e1ed55337a5b8ca20aa6863b5c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-07-01T18:11:38Z","title_canon_sha256":"c4ccd9f3d0fc5796e954c2386e89a61d21b4ac2249e077d22b2d9ada141bc5eb"},"schema_version":"1.0","source":{"id":"1407.0340","kind":"arxiv","version":2}},"canonical_sha256":"20bf2027c69666089e397f36d08ca361350b4b3d63ac4a3d1fdd987edba6f083","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20bf2027c69666089e397f36d08ca361350b4b3d63ac4a3d1fdd987edba6f083","first_computed_at":"2026-05-18T01:42:42.937233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:42.937233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K78Ba9jcGg2c1oFUXurpBEaLRt5TWXgu2I90IpzNRJY/GSdxWairxZ1d3JtQjbPJU4Yys6inaPnaOqwbAcHCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:42.937800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0340","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a304c30dba767fcb1a097545aa4e3f5c698d0fb792976ba47a3e0f40aa6a5689","sha256:ab159641a1b332c469c28301932c5352788f89aa1157bbd218b7dc5728827606"],"state_sha256":"508a03102e063e24e34ab79dc44f1071d200e2a6a0b78069b6dbba692af5c113"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PelHqpgzAxzrzwieiULQia+GrffMJ+TzR4DBu2C0WH/PthnjYEDGjAQbdIGdaGpnP1MLLT2F4BpFMo5zxfoeDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T11:26:22.613235Z","bundle_sha256":"e1e6ef781fc9b2228099a24d3b5d525e6eb4ed2efaaec55511c34a1e320b3db6"}}