{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XNHYOK4X3FP7O53YHPIVDPNDM2","short_pith_number":"pith:XNHYOK4X","schema_version":"1.0","canonical_sha256":"bb4f872b97d95ff777783bd151bda366b98954894a4d9f401812188f982363bc","source":{"kind":"arxiv","id":"1310.5118","version":2},"attestation_state":"computed","paper":{"title":"Geometry of non-compact minimal and marginally outer-trapped surfaces in asymptotically flat manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alessandro Carlotto","submitted_at":"2013-10-18T18:20:15Z","abstract_excerpt":"In this article we extend several foundational results of the theory of complete minimal surfaces of finite index in the Euclidean space to minimal surfaces in asymptotically flat manifolds and, more generally, to marginally outer-trapped surfaces in initial data sets of General Relativity. We show that if an asymptotically flat 3-manifold (M,g) of nonnegative scalar curvature contains a non-compact, properly embedded minimal surface which is stable and has quadratic area growth, then it is isometric to the flat R^{3}. This implies, for instance, that in presence of a positive ADM mass any seq"},"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":"1310.5118","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-18T18:20:15Z","cross_cats_sorted":[],"title_canon_sha256":"8262760be1efcd910849bfe79d621159955bd4605cbc42836f9afc0bd3fa66e2","abstract_canon_sha256":"53ce77cfb2fc75e924776e76ace2bfe3d05599da708aadf0814c39882f3fbdf7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:46.785276Z","signature_b64":"TKr5kBkDdyPcTjh9usMiMjYG3LJBZbNZKdEMe+3Lyfc3vJ7Jn22aQ38OimzoSrpSd/7DcnXJ/s/JjAjCFshCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb4f872b97d95ff777783bd151bda366b98954894a4d9f401812188f982363bc","last_reissued_at":"2026-05-18T02:54:46.784852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:46.784852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of non-compact minimal and marginally outer-trapped surfaces in asymptotically flat manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alessandro Carlotto","submitted_at":"2013-10-18T18:20:15Z","abstract_excerpt":"In this article we extend several foundational results of the theory of complete minimal surfaces of finite index in the Euclidean space to minimal surfaces in asymptotically flat manifolds and, more generally, to marginally outer-trapped surfaces in initial data sets of General Relativity. We show that if an asymptotically flat 3-manifold (M,g) of nonnegative scalar curvature contains a non-compact, properly embedded minimal surface which is stable and has quadratic area growth, then it is isometric to the flat R^{3}. This implies, for instance, that in presence of a positive ADM mass any seq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5118","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":"1310.5118","created_at":"2026-05-18T02:54:46.784924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5118v2","created_at":"2026-05-18T02:54:46.784924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5118","created_at":"2026-05-18T02:54:46.784924+00:00"},{"alias_kind":"pith_short_12","alias_value":"XNHYOK4X3FP7","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XNHYOK4X3FP7O53Y","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XNHYOK4X","created_at":"2026-05-18T12:28:06.772260+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/XNHYOK4X3FP7O53YHPIVDPNDM2","json":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2.json","graph_json":"https://pith.science/api/pith-number/XNHYOK4X3FP7O53YHPIVDPNDM2/graph.json","events_json":"https://pith.science/api/pith-number/XNHYOK4X3FP7O53YHPIVDPNDM2/events.json","paper":"https://pith.science/paper/XNHYOK4X"},"agent_actions":{"view_html":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2","download_json":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2.json","view_paper":"https://pith.science/paper/XNHYOK4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5118&json=true","fetch_graph":"https://pith.science/api/pith-number/XNHYOK4X3FP7O53YHPIVDPNDM2/graph.json","fetch_events":"https://pith.science/api/pith-number/XNHYOK4X3FP7O53YHPIVDPNDM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2/action/storage_attestation","attest_author":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2/action/author_attestation","sign_citation":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2/action/citation_signature","submit_replication":"https://pith.science/pith/XNHYOK4X3FP7O53YHPIVDPNDM2/action/replication_record"}},"created_at":"2026-05-18T02:54:46.784924+00:00","updated_at":"2026-05-18T02:54:46.784924+00:00"}