{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MV4LZAEVJL6QGFSWPQBSMTLJ4F","short_pith_number":"pith:MV4LZAEV","canonical_record":{"source":{"id":"2503.04382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-06T12:35:05Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"d3ed2e4b7e403134688f2ef34a5adcbf5cb081788cfc8713d4e2cfce237940d4","abstract_canon_sha256":"22d12f3f93dda80c6e8d1ab93b2cfd0d894118db8e600daf77c10c1eae320c4d"},"schema_version":"1.0"},"canonical_sha256":"6578bc80954afd0316567c03264d69e15c95d0986a3372a3bf2de5b1c95995b1","source":{"kind":"arxiv","id":"2503.04382","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04382","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04382v2","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04382","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"pith_short_12","alias_value":"MV4LZAEVJL6Q","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"pith_short_16","alias_value":"MV4LZAEVJL6QGFSW","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"pith_short_8","alias_value":"MV4LZAEV","created_at":"2026-06-09T02:08:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MV4LZAEVJL6QGFSWPQBSMTLJ4F","target":"record","payload":{"canonical_record":{"source":{"id":"2503.04382","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-06T12:35:05Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"d3ed2e4b7e403134688f2ef34a5adcbf5cb081788cfc8713d4e2cfce237940d4","abstract_canon_sha256":"22d12f3f93dda80c6e8d1ab93b2cfd0d894118db8e600daf77c10c1eae320c4d"},"schema_version":"1.0"},"canonical_sha256":"6578bc80954afd0316567c03264d69e15c95d0986a3372a3bf2de5b1c95995b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:29.110435Z","signature_b64":"8BWQTo/nhhhgrYSEC4Hc4rHaUfDldVuE56yBF3wK66HIbtA0bwccmtghjq3IFfcVzsGjO6k15+KPt8zxwa4+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6578bc80954afd0316567c03264d69e15c95d0986a3372a3bf2de5b1c95995b1","last_reissued_at":"2026-06-09T02:08:29.109367Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:29.109367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.04382","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":"2026-06-09T02:08:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T7+Lu08LDcUu530XXrWOAO78nIdw0fLZFB4FsJjtQyiu039DsClCkw1HnjI7omz7RHZMSyJewwSSSCqvvdHvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:27:43.280596Z"},"content_sha256":"2d788563b75fc501828ed03af897855d437200050b3f498ce4cbdd631413f8aa","schema_version":"1.0","event_id":"sha256:2d788563b75fc501828ed03af897855d437200050b3f498ce4cbdd631413f8aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MV4LZAEVJL6QGFSWPQBSMTLJ4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global hyperbolicity and manifold topology from the Lorentzian distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"A. Bykov, E. Minguzzi","submitted_at":"2025-03-06T12:35:05Z","abstract_excerpt":"In this work, we seek characterizations of global hyperbolicity in smooth Lorentzian manifolds that do not rely on the manifold topology and that are inspired by metric geometry. In particular, strong causality is not assumed, so part of the problem is precisely that of recovering the manifold topology so as to make sense of it also in rough frameworks. After verifying that known standard characterizations do not meet this requirement, we propose two possible formulations. The first is based solely on chronological diamonds and is interesting due to its analogies with the Hopf-Rinow theorem. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04382","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/2503.04382/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":"2026-06-09T02:08:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZ1VNZineAGxvUHcIqmO7fWW1hUi0g/3DxSb8u0kPfSLKFyTKNWedCwIcMD1PvQIW4KzuT04RlGbSF37wMkiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:27:43.281306Z"},"content_sha256":"7014e4cf9f2ce618c2a872cd12c4eb36861992c29ec2a8df0a8f61848f83ac92","schema_version":"1.0","event_id":"sha256:7014e4cf9f2ce618c2a872cd12c4eb36861992c29ec2a8df0a8f61848f83ac92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/bundle.json","state_url":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/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":"2026-06-10T10:27:43Z","links":{"resolver":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F","bundle":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/bundle.json","state":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MV4LZAEVJL6QGFSWPQBSMTLJ4F","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":"22d12f3f93dda80c6e8d1ab93b2cfd0d894118db8e600daf77c10c1eae320c4d","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-06T12:35:05Z","title_canon_sha256":"d3ed2e4b7e403134688f2ef34a5adcbf5cb081788cfc8713d4e2cfce237940d4"},"schema_version":"1.0","source":{"id":"2503.04382","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04382","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04382v2","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04382","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"pith_short_12","alias_value":"MV4LZAEVJL6Q","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"pith_short_16","alias_value":"MV4LZAEVJL6QGFSW","created_at":"2026-06-09T02:08:29Z"},{"alias_kind":"pith_short_8","alias_value":"MV4LZAEV","created_at":"2026-06-09T02:08:29Z"}],"graph_snapshots":[{"event_id":"sha256:7014e4cf9f2ce618c2a872cd12c4eb36861992c29ec2a8df0a8f61848f83ac92","target":"graph","created_at":"2026-06-09T02:08:29Z","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/2503.04382/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we seek characterizations of global hyperbolicity in smooth Lorentzian manifolds that do not rely on the manifold topology and that are inspired by metric geometry. In particular, strong causality is not assumed, so part of the problem is precisely that of recovering the manifold topology so as to make sense of it also in rough frameworks. After verifying that known standard characterizations do not meet this requirement, we propose two possible formulations. The first is based solely on chronological diamonds and is interesting due to its analogies with the Hopf-Rinow theorem. T","authors_text":"A. Bykov, E. Minguzzi","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-06T12:35:05Z","title":"Global hyperbolicity and manifold topology from the Lorentzian distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04382","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":"sha256:2d788563b75fc501828ed03af897855d437200050b3f498ce4cbdd631413f8aa","target":"record","created_at":"2026-06-09T02:08:29Z","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":"22d12f3f93dda80c6e8d1ab93b2cfd0d894118db8e600daf77c10c1eae320c4d","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-06T12:35:05Z","title_canon_sha256":"d3ed2e4b7e403134688f2ef34a5adcbf5cb081788cfc8713d4e2cfce237940d4"},"schema_version":"1.0","source":{"id":"2503.04382","kind":"arxiv","version":2}},"canonical_sha256":"6578bc80954afd0316567c03264d69e15c95d0986a3372a3bf2de5b1c95995b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6578bc80954afd0316567c03264d69e15c95d0986a3372a3bf2de5b1c95995b1","first_computed_at":"2026-06-09T02:08:29.109367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:29.109367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8BWQTo/nhhhgrYSEC4Hc4rHaUfDldVuE56yBF3wK66HIbtA0bwccmtghjq3IFfcVzsGjO6k15+KPt8zxwa4+CA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:29.110435Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.04382","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d788563b75fc501828ed03af897855d437200050b3f498ce4cbdd631413f8aa","sha256:7014e4cf9f2ce618c2a872cd12c4eb36861992c29ec2a8df0a8f61848f83ac92"],"state_sha256":"84a535f3e0d980873954b70b7b6973b04708817cc12bdf59f2486cb2989f9bb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0tdTAJbIuDJWhI2m3nXbhqK9xifmbNWg50V+z9UwQckb2E7rbcInLfnu04IMkxGxF6euM/9m5/ucwuDRBvfACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:27:43.285468Z","bundle_sha256":"838b1cc86d05d4597cfe6b8beaab5612f1177fce51ada713eee393ca48dfcd08"}}