{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:MV4LZAEVJL6QGFSWPQBSMTLJ4F","short_pith_number":"pith:MV4LZAEV","schema_version":"1.0","canonical_sha256":"6578bc80954afd0316567c03264d69e15c95d0986a3372a3bf2de5b1c95995b1","source":{"kind":"arxiv","id":"2503.04382","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2503.04382","created_at":"2026-06-09T02:08:29.109500+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.04382v2","created_at":"2026-06-09T02:08:29.109500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04382","created_at":"2026-06-09T02:08:29.109500+00:00"},{"alias_kind":"pith_short_12","alias_value":"MV4LZAEVJL6Q","created_at":"2026-06-09T02:08:29.109500+00:00"},{"alias_kind":"pith_short_16","alias_value":"MV4LZAEVJL6QGFSW","created_at":"2026-06-09T02:08:29.109500+00:00"},{"alias_kind":"pith_short_8","alias_value":"MV4LZAEV","created_at":"2026-06-09T02:08:29.109500+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.11783","citing_title":"Hausdorff-type metric geometry of the space of Cauchy hypersurfaces","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F","json":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F.json","graph_json":"https://pith.science/api/pith-number/MV4LZAEVJL6QGFSWPQBSMTLJ4F/graph.json","events_json":"https://pith.science/api/pith-number/MV4LZAEVJL6QGFSWPQBSMTLJ4F/events.json","paper":"https://pith.science/paper/MV4LZAEV"},"agent_actions":{"view_html":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F","download_json":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F.json","view_paper":"https://pith.science/paper/MV4LZAEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.04382&json=true","fetch_graph":"https://pith.science/api/pith-number/MV4LZAEVJL6QGFSWPQBSMTLJ4F/graph.json","fetch_events":"https://pith.science/api/pith-number/MV4LZAEVJL6QGFSWPQBSMTLJ4F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/action/storage_attestation","attest_author":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/action/author_attestation","sign_citation":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/action/citation_signature","submit_replication":"https://pith.science/pith/MV4LZAEVJL6QGFSWPQBSMTLJ4F/action/replication_record"}},"created_at":"2026-06-09T02:08:29.109500+00:00","updated_at":"2026-06-09T02:08:29.109500+00:00"}