{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NK4JSGYAZU73KQKZJBHQN3YHBO","short_pith_number":"pith:NK4JSGYA","canonical_record":{"source":{"id":"2608.03476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-08-04T11:14:45Z","cross_cats_sorted":[],"title_canon_sha256":"5ca71ca2b52cae13c4a2edb1468f323d06e4c38849fafd018c89c860745ca35d","abstract_canon_sha256":"4fe780ef965a25cc14e69572d2902950f75d8910c271589795ea0f49826a97e9"},"schema_version":"1.0"},"canonical_sha256":"6ab8991b00cd3fb54159484f06ef070ba1368eda2634970c307220351f2427ff","source":{"kind":"arxiv","id":"2608.03476","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03476","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03476v1","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03476","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"NK4JSGYAZU73","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"pith_short_16","alias_value":"NK4JSGYAZU73KQKZ","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"pith_short_8","alias_value":"NK4JSGYA","created_at":"2026-08-05T01:35:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NK4JSGYAZU73KQKZJBHQN3YHBO","target":"record","payload":{"canonical_record":{"source":{"id":"2608.03476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-08-04T11:14:45Z","cross_cats_sorted":[],"title_canon_sha256":"5ca71ca2b52cae13c4a2edb1468f323d06e4c38849fafd018c89c860745ca35d","abstract_canon_sha256":"4fe780ef965a25cc14e69572d2902950f75d8910c271589795ea0f49826a97e9"},"schema_version":"1.0"},"canonical_sha256":"6ab8991b00cd3fb54159484f06ef070ba1368eda2634970c307220351f2427ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-05T01:35:55.616480Z","signature_b64":"RxbGAAkGQv2Bd54JZftxQqrls876l9BnZxmi/CCg2vmnRwxw/Rf1XgKnPG/U6SFI54hlwFDTz/07T3/d27c1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ab8991b00cd3fb54159484f06ef070ba1368eda2634970c307220351f2427ff","last_reissued_at":"2026-08-05T01:35:55.615041Z","signature_status":"signed_v1","first_computed_at":"2026-08-05T01:35:55.615041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.03476","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-05T01:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KslO/MUg95Wk5u7dfpavUxwIol6XtJZgK+PuLbNBZPiuS3MlgQeKbBcs11IIjsDe0rc8BwSSI83DduEasK49CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T16:42:24.310563Z"},"content_sha256":"6a03f96d1c7b1877d7256a579c0abcf055e51aa85a515834cb749854065ca61c","schema_version":"1.0","event_id":"sha256:6a03f96d1c7b1877d7256a579c0abcf055e51aa85a515834cb749854065ca61c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NK4JSGYAZU73KQKZJBHQN3YHBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global hyperbolicity meets order completeness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"E. Minguzzi","submitted_at":"2026-08-04T11:14:45Z","abstract_excerpt":"Recently, an order completeness property has attracted attention in some low regularity spacetime geometry literature, where it was named `chronocompleteness'. In this work we prove that, in the framework of standard Lorentzian geometry, this property is equivalent to global hyperbolicity. The equivalence of global hyperbolicity with other more traditional forms of order completeness is also established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03476","kind":"arxiv","version":1},"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/2608.03476/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":"2026-08-05T01:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+QSvV5sGRDU8vg8lezVMLFS5iCPEl9zGV3phpWkJGVsh71VYDge/o/i/1Irexx1BwfZWK3kOr3CzVcs/76YAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T16:42:24.313050Z"},"content_sha256":"e832e27b7c9ee4e23b0c2e08b9d2506da25c569ee396abc989ec1f8bb008760f","schema_version":"1.0","event_id":"sha256:e832e27b7c9ee4e23b0c2e08b9d2506da25c569ee396abc989ec1f8bb008760f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NK4JSGYAZU73KQKZJBHQN3YHBO/bundle.json","state_url":"https://pith.science/pith/NK4JSGYAZU73KQKZJBHQN3YHBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NK4JSGYAZU73KQKZJBHQN3YHBO/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":"2026-08-10T16:42:24Z","links":{"resolver":"https://pith.science/pith/NK4JSGYAZU73KQKZJBHQN3YHBO","bundle":"https://pith.science/pith/NK4JSGYAZU73KQKZJBHQN3YHBO/bundle.json","state":"https://pith.science/pith/NK4JSGYAZU73KQKZJBHQN3YHBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NK4JSGYAZU73KQKZJBHQN3YHBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NK4JSGYAZU73KQKZJBHQN3YHBO","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":"4fe780ef965a25cc14e69572d2902950f75d8910c271589795ea0f49826a97e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-08-04T11:14:45Z","title_canon_sha256":"5ca71ca2b52cae13c4a2edb1468f323d06e4c38849fafd018c89c860745ca35d"},"schema_version":"1.0","source":{"id":"2608.03476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03476","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03476v1","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03476","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"NK4JSGYAZU73","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"pith_short_16","alias_value":"NK4JSGYAZU73KQKZ","created_at":"2026-08-05T01:35:55Z"},{"alias_kind":"pith_short_8","alias_value":"NK4JSGYA","created_at":"2026-08-05T01:35:55Z"}],"graph_snapshots":[{"event_id":"sha256:e832e27b7c9ee4e23b0c2e08b9d2506da25c569ee396abc989ec1f8bb008760f","target":"graph","created_at":"2026-08-05T01:35:55Z","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/2608.03476/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, an order completeness property has attracted attention in some low regularity spacetime geometry literature, where it was named `chronocompleteness'. In this work we prove that, in the framework of standard Lorentzian geometry, this property is equivalent to global hyperbolicity. The equivalence of global hyperbolicity with other more traditional forms of order completeness is also established.","authors_text":"E. Minguzzi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-08-04T11:14:45Z","title":"Global hyperbolicity meets order completeness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03476","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":"sha256:6a03f96d1c7b1877d7256a579c0abcf055e51aa85a515834cb749854065ca61c","target":"record","created_at":"2026-08-05T01:35:55Z","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":"4fe780ef965a25cc14e69572d2902950f75d8910c271589795ea0f49826a97e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-08-04T11:14:45Z","title_canon_sha256":"5ca71ca2b52cae13c4a2edb1468f323d06e4c38849fafd018c89c860745ca35d"},"schema_version":"1.0","source":{"id":"2608.03476","kind":"arxiv","version":1}},"canonical_sha256":"6ab8991b00cd3fb54159484f06ef070ba1368eda2634970c307220351f2427ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ab8991b00cd3fb54159484f06ef070ba1368eda2634970c307220351f2427ff","first_computed_at":"2026-08-05T01:35:55.615041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-05T01:35:55.615041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RxbGAAkGQv2Bd54JZftxQqrls876l9BnZxmi/CCg2vmnRwxw/Rf1XgKnPG/U6SFI54hlwFDTz/07T3/d27c1DA==","signature_status":"signed_v1","signed_at":"2026-08-05T01:35:55.616480Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.03476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a03f96d1c7b1877d7256a579c0abcf055e51aa85a515834cb749854065ca61c","sha256:e832e27b7c9ee4e23b0c2e08b9d2506da25c569ee396abc989ec1f8bb008760f"],"state_sha256":"0e2d292906ab2f6b97de918a28d2d51ddba443bd1add030d10d9abd1ddfdaca1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fMrKOPtP/qipFWJ1jJF42I4/DKA+PsCjnIq3zlosQ8QwnzL4L8qdFTegLHi34hFE0/AYkIcEJTtsgxleppO6Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T16:42:24.321630Z","bundle_sha256":"13af86005c990fc61693bac576baaca553e05dd3ab8f5b67e5b630f22d5f3b50"}}