{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:O4DKG7RSYP4WEG5J5DJCWBL3RJ","short_pith_number":"pith:O4DKG7RS","schema_version":"1.0","canonical_sha256":"7706a37e32c3f9621ba9e8d22b057b8a575dc3264910443333ac328f007039ed","source":{"kind":"arxiv","id":"1811.02670","version":2},"attestation_state":"computed","paper":{"title":"Hausdorff closed limits and the causal boundary of globally hyperbolic spacetimes with timelike boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Ivan P. Costa e Silva, J\\'onatan Herrera, Jos\\'e Luis Flores","submitted_at":"2018-11-06T21:44:44Z","abstract_excerpt":"We show that when a spacetime $\\mathcal{M}(=M \\cup \\partial M)$ is globally hyperbolic with (possibly empty) smooth timelike boundary $\\partial M$, a metrizable topology, the closed limit topology (CLT) introduced by F. Hausdorff himself in the 1950's in set theory, can be advantageously adopted on the Geroch-Kronheimer-Penrose causal completion of M, retaining essentially all the good properties of previous topologies in this ambient. In particular, we show that if the globally hyperbolic spacetime $M$ admits a conformal boundary, defined in such broad terms as to include all the standard exa"},"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":"1811.02670","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-11-06T21:44:44Z","cross_cats_sorted":["gr-qc","math.DG","math.MP"],"title_canon_sha256":"bccc97d393358dee5ef3cfa7b245f75cb7da1b2db16bfe25247a64e61a3b83b9","abstract_canon_sha256":"2b0dc7111edf8b31ecbfcb5b86e288f12c445fee5adf6bb8c1f4ac2bafe2d490"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:39.079881Z","signature_b64":"AE4nBw+Wlzyc4JNhAY1BOeCHYPM61GVOARVZ4C4RJvEPw33ZjFsF1dyZ28DKiZFPzNgADZ8XEpHphHXBPDI/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7706a37e32c3f9621ba9e8d22b057b8a575dc3264910443333ac328f007039ed","last_reissued_at":"2026-05-18T00:00:39.079294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:39.079294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hausdorff closed limits and the causal boundary of globally hyperbolic spacetimes with timelike boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"Ivan P. Costa e Silva, J\\'onatan Herrera, Jos\\'e Luis Flores","submitted_at":"2018-11-06T21:44:44Z","abstract_excerpt":"We show that when a spacetime $\\mathcal{M}(=M \\cup \\partial M)$ is globally hyperbolic with (possibly empty) smooth timelike boundary $\\partial M$, a metrizable topology, the closed limit topology (CLT) introduced by F. Hausdorff himself in the 1950's in set theory, can be advantageously adopted on the Geroch-Kronheimer-Penrose causal completion of M, retaining essentially all the good properties of previous topologies in this ambient. In particular, we show that if the globally hyperbolic spacetime $M$ admits a conformal boundary, defined in such broad terms as to include all the standard exa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02670","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.02670","created_at":"2026-05-18T00:00:39.079427+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.02670v2","created_at":"2026-05-18T00:00:39.079427+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02670","created_at":"2026-05-18T00:00:39.079427+00:00"},{"alias_kind":"pith_short_12","alias_value":"O4DKG7RSYP4W","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"O4DKG7RSYP4WEG5J","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"O4DKG7RS","created_at":"2026-05-18T12:32:40.477152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ","json":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ.json","graph_json":"https://pith.science/api/pith-number/O4DKG7RSYP4WEG5J5DJCWBL3RJ/graph.json","events_json":"https://pith.science/api/pith-number/O4DKG7RSYP4WEG5J5DJCWBL3RJ/events.json","paper":"https://pith.science/paper/O4DKG7RS"},"agent_actions":{"view_html":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ","download_json":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ.json","view_paper":"https://pith.science/paper/O4DKG7RS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.02670&json=true","fetch_graph":"https://pith.science/api/pith-number/O4DKG7RSYP4WEG5J5DJCWBL3RJ/graph.json","fetch_events":"https://pith.science/api/pith-number/O4DKG7RSYP4WEG5J5DJCWBL3RJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ/action/storage_attestation","attest_author":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ/action/author_attestation","sign_citation":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ/action/citation_signature","submit_replication":"https://pith.science/pith/O4DKG7RSYP4WEG5J5DJCWBL3RJ/action/replication_record"}},"created_at":"2026-05-18T00:00:39.079427+00:00","updated_at":"2026-05-18T00:00:39.079427+00:00"}