{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:S2ZDTLO5WHFWEP2EW27QYYACD7","short_pith_number":"pith:S2ZDTLO5","canonical_record":{"source":{"id":"1404.0358","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-01T19:29:23Z","cross_cats_sorted":[],"title_canon_sha256":"db3a3f665453938f9f36b04559adf0ecc875f44a88128c590f7546f10094c20e","abstract_canon_sha256":"2be2b750ea19122124b8b92bd7d406e0081d612e4edf7bea9e8a2ac1bc6ca135"},"schema_version":"1.0"},"canonical_sha256":"96b239adddb1cb623f44b6bf0c60021fce7563a242d20dfefcca0269699497f0","source":{"kind":"arxiv","id":"1404.0358","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0358","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0358v3","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0358","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"S2ZDTLO5WHFW","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"S2ZDTLO5WHFWEP2E","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"S2ZDTLO5","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:S2ZDTLO5WHFWEP2EW27QYYACD7","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0358","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-01T19:29:23Z","cross_cats_sorted":[],"title_canon_sha256":"db3a3f665453938f9f36b04559adf0ecc875f44a88128c590f7546f10094c20e","abstract_canon_sha256":"2be2b750ea19122124b8b92bd7d406e0081d612e4edf7bea9e8a2ac1bc6ca135"},"schema_version":"1.0"},"canonical_sha256":"96b239adddb1cb623f44b6bf0c60021fce7563a242d20dfefcca0269699497f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.607135Z","signature_b64":"l92WEMdOsjZ5QtZxS1MNrYJUkjOFbFsG4PV+ne72iyucYteJOjjrHlwkbkpKqJybE29oNPlcVrnVpo0fbtp0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96b239adddb1cb623f44b6bf0c60021fce7563a242d20dfefcca0269699497f0","last_reissued_at":"2026-05-18T01:12:36.606753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.606753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0358","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kIwgXki4ubs6ptSRfq4etGkgpIK1xi2a3ueE+eOaT5jfT+QuK0PzK7bZqTxFFROlnvQlW3bJnHjs7eOlc88IAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:30:48.189693Z"},"content_sha256":"70efaad340393f8c7a764dcd7cdce540e22bef220f85a3ec9df26f508c3deb5a","schema_version":"1.0","event_id":"sha256:70efaad340393f8c7a764dcd7cdce540e22bef220f85a3ec9df26f508c3deb5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:S2ZDTLO5WHFWEP2EW27QYYACD7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of stable marginally outer trapped surfaces in initial data sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alessandro Carlotto","submitted_at":"2014-04-01T19:29:23Z","abstract_excerpt":"In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \\textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem on the topology of black holes). We first prove that an unbounded, stable marginally outer trapped surface in an initial data set $(M,g,k)$ obeying the dominant energy condition is conformally diffeomorphic to either the plane $\\mathbb{C}$ or to the cylinder $\\mathbb{A}$ and in the latter case infinitesimal rigidity holds. As a corollary, when the DEC holds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0358","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qLMigJhJcILpuWlq/0UXnOpanE/pVK3VZOhN4skZlRophl/w7d0OqJDW30YFB5ltNnee+BLIN31pb8VkyH4UAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:30:48.190342Z"},"content_sha256":"f2d7e1a9d0c61752bf1a3c6a854ccf7cfa23368f89c2d6f02fc6ab41e6a5e199","schema_version":"1.0","event_id":"sha256:f2d7e1a9d0c61752bf1a3c6a854ccf7cfa23368f89c2d6f02fc6ab41e6a5e199"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2ZDTLO5WHFWEP2EW27QYYACD7/bundle.json","state_url":"https://pith.science/pith/S2ZDTLO5WHFWEP2EW27QYYACD7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2ZDTLO5WHFWEP2EW27QYYACD7/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":"2026-06-24T06:30:48Z","links":{"resolver":"https://pith.science/pith/S2ZDTLO5WHFWEP2EW27QYYACD7","bundle":"https://pith.science/pith/S2ZDTLO5WHFWEP2EW27QYYACD7/bundle.json","state":"https://pith.science/pith/S2ZDTLO5WHFWEP2EW27QYYACD7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2ZDTLO5WHFWEP2EW27QYYACD7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:S2ZDTLO5WHFWEP2EW27QYYACD7","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":"2be2b750ea19122124b8b92bd7d406e0081d612e4edf7bea9e8a2ac1bc6ca135","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-01T19:29:23Z","title_canon_sha256":"db3a3f665453938f9f36b04559adf0ecc875f44a88128c590f7546f10094c20e"},"schema_version":"1.0","source":{"id":"1404.0358","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0358","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0358v3","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0358","created_at":"2026-05-18T01:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"S2ZDTLO5WHFW","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"S2ZDTLO5WHFWEP2E","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"S2ZDTLO5","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f2d7e1a9d0c61752bf1a3c6a854ccf7cfa23368f89c2d6f02fc6ab41e6a5e199","target":"graph","created_at":"2026-05-18T01:12:36Z","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":"In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \\textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem on the topology of black holes). We first prove that an unbounded, stable marginally outer trapped surface in an initial data set $(M,g,k)$ obeying the dominant energy condition is conformally diffeomorphic to either the plane $\\mathbb{C}$ or to the cylinder $\\mathbb{A}$ and in the latter case infinitesimal rigidity holds. As a corollary, when the DEC holds","authors_text":"Alessandro Carlotto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-01T19:29:23Z","title":"Rigidity of stable marginally outer trapped surfaces in initial data sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0358","kind":"arxiv","version":3},"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":"sha256:70efaad340393f8c7a764dcd7cdce540e22bef220f85a3ec9df26f508c3deb5a","target":"record","created_at":"2026-05-18T01:12:36Z","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":"2be2b750ea19122124b8b92bd7d406e0081d612e4edf7bea9e8a2ac1bc6ca135","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-01T19:29:23Z","title_canon_sha256":"db3a3f665453938f9f36b04559adf0ecc875f44a88128c590f7546f10094c20e"},"schema_version":"1.0","source":{"id":"1404.0358","kind":"arxiv","version":3}},"canonical_sha256":"96b239adddb1cb623f44b6bf0c60021fce7563a242d20dfefcca0269699497f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96b239adddb1cb623f44b6bf0c60021fce7563a242d20dfefcca0269699497f0","first_computed_at":"2026-05-18T01:12:36.606753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:36.606753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l92WEMdOsjZ5QtZxS1MNrYJUkjOFbFsG4PV+ne72iyucYteJOjjrHlwkbkpKqJybE29oNPlcVrnVpo0fbtp0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:36.607135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0358","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70efaad340393f8c7a764dcd7cdce540e22bef220f85a3ec9df26f508c3deb5a","sha256:f2d7e1a9d0c61752bf1a3c6a854ccf7cfa23368f89c2d6f02fc6ab41e6a5e199"],"state_sha256":"08f9ef23bc3ee7e49e94b45fa6c9364d2c9c8ab880162719b077aff29123cf55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syh731iNrrZh+LKzZSYKHUSqjZSbS31S1U5An/6eM1fn5fZAntmije3lwt2Rv0aMqtEzlyq7BtHXn/IWudNoDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:30:48.193533Z","bundle_sha256":"dfecd37b223987b0bed1b2204a879955a25409b1575e3df1bd2ce8fcbc691ecc"}}