{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C52XV5VB654W6HCIFJQG4WSL2S","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":"e8f417398dd1eac5529bdaa043b41c34fab6ab1c50bd62c031e3bf0b969a25e7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-04-01T23:04:59Z","title_canon_sha256":"2b179e182835bf9dcf92b32d27e5ac784d317cde0e764ad73f546447f1fc08dc"},"schema_version":"1.0","source":{"id":"1204.0278","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0278","created_at":"2026-05-18T03:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0278v2","created_at":"2026-05-18T03:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0278","created_at":"2026-05-18T03:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"C52XV5VB654W","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C52XV5VB654W6HCI","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C52XV5VB","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:03e517b0d884ebf00bd6dba8cfe6259de479fe757f207aef4ea3a2700b9b6457","target":"graph","created_at":"2026-05-18T03:20:56Z","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":"We introduce a natural generalization of marginally outer trapped surfaces, called immersed marginally outer trapped surfaces, and prove that three dimensional asymptotically flat initial data sets either contain such surfaces or are diffeomorphic to R^3. We establish a generalization of the Penrose singularity theorem which shows that the presence of an immersed marginally outer trapped surface generically implies the null geodesic incompleteness of any spacetime that satisfies the null energy condition and which admits a non-compact Cauchy surface. Taken together, these results can be viewed","authors_text":"Daniel Pollack, Gregory J. Galloway, Michael Eichmair","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-04-01T23:04:59Z","title":"Topological censorship from the initial data point of view"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0278","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":"sha256:61b02d565989c37bfd15d32266a2b91e07898c3a2682f6440fe86a4fa05caa7e","target":"record","created_at":"2026-05-18T03:20:56Z","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":"e8f417398dd1eac5529bdaa043b41c34fab6ab1c50bd62c031e3bf0b969a25e7","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-04-01T23:04:59Z","title_canon_sha256":"2b179e182835bf9dcf92b32d27e5ac784d317cde0e764ad73f546447f1fc08dc"},"schema_version":"1.0","source":{"id":"1204.0278","kind":"arxiv","version":2}},"canonical_sha256":"17757af6a1f7796f1c482a606e5a4bd48230c446ec0989e1659d2a9b73e4ffde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17757af6a1f7796f1c482a606e5a4bd48230c446ec0989e1659d2a9b73e4ffde","first_computed_at":"2026-05-18T03:20:56.950039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:56.950039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uDDa/dNSntL8EawCeDRSybZqdevteIDbwP5xky9r/1yptRUlpWb+e8sRoTmn4GS9aYiOmLKTU7pljuJsURmZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:56.950682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0278","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61b02d565989c37bfd15d32266a2b91e07898c3a2682f6440fe86a4fa05caa7e","sha256:03e517b0d884ebf00bd6dba8cfe6259de479fe757f207aef4ea3a2700b9b6457"],"state_sha256":"563c88ef2516a310d62c6c98c5245cc685349f0452f5f521fd4024a86e9ae7d5"}