{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:F4ESVGQS7H6AQCC4Y7VLPKWRZ5","short_pith_number":"pith:F4ESVGQS","canonical_record":{"source":{"id":"1006.4601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-23T17:50:01Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d28ff41444eaf046ed1c656dc208837425a6c2b5f413676266b4f5a3dca1ba77","abstract_canon_sha256":"3d50946be03fd11771ddc0e71fc82fc23196812c2b1eed03ac80370fa749a8f6"},"schema_version":"1.0"},"canonical_sha256":"2f092a9a12f9fc08085cc7eab7aad1cf52d0f66ae1be2a8264c37738071bc0d2","source":{"kind":"arxiv","id":"1006.4601","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4601","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4601v2","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4601","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"F4ESVGQS7H6A","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F4ESVGQS7H6AQCC4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F4ESVGQS","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:F4ESVGQS7H6AQCC4Y7VLPKWRZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1006.4601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-23T17:50:01Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d28ff41444eaf046ed1c656dc208837425a6c2b5f413676266b4f5a3dca1ba77","abstract_canon_sha256":"3d50946be03fd11771ddc0e71fc82fc23196812c2b1eed03ac80370fa749a8f6"},"schema_version":"1.0"},"canonical_sha256":"2f092a9a12f9fc08085cc7eab7aad1cf52d0f66ae1be2a8264c37738071bc0d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:14.722691Z","signature_b64":"ajgMZs6o6IZQax4i9UVI0s+vashGZRuxZUKwIies9+k2BgKBrgau5w0yjEZ3l0ypAFKWD4iPOlGaS/+DRETKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f092a9a12f9fc08085cc7eab7aad1cf52d0f66ae1be2a8264c37738071bc0d2","last_reissued_at":"2026-05-18T04:35:14.722124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:14.722124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.4601","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrgJoIZsVDpU5vTm43Ncu2E7D/kypfyd+OXBLTdm6fUbxcjiPQWiUWxgBK4kQsLHbGKj9p07wjx1j3pOyDCvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:44:00.871614Z"},"content_sha256":"f499f0397c6ad7ab2de99c4fe8abfd73eba4b59eb40bf46ef6e4402b55f90513","schema_version":"1.0","event_id":"sha256:f499f0397c6ad7ab2de99c4fe8abfd73eba4b59eb40bf46ef6e4402b55f90513"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:F4ESVGQS7H6AQCC4Y7VLPKWRZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jang's equation and its applications to marginally trapped surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Jan Metzger, Lars Andersson, Michael Eichmair","submitted_at":"2010-06-23T17:50:01Z","abstract_excerpt":"In this paper we survey some recent advances in the analysis of marginally outer trapped surfaces (MOTS). We begin with a systematic review of results by Schoen and Yau on Jang's equation and its relationship with MOTS. We then explain recent work on the existence, regularity, and properties of MOTS and discuss the consequences for the trapped region. We include an outlook with some directions for future research."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4601","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ikMDHgephHcxaEmp/vsLJpV/9D2ch3uE6g6qMDfi4fidzw8viI5GgEaqJqyNfYKtXpN6rtr5xHIs+yAhD41ZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:44:00.872039Z"},"content_sha256":"0472be123a9fb18ae512905667e2257af5a84a4fd38959a6ec9fa6c103bf17c1","schema_version":"1.0","event_id":"sha256:0472be123a9fb18ae512905667e2257af5a84a4fd38959a6ec9fa6c103bf17c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F4ESVGQS7H6AQCC4Y7VLPKWRZ5/bundle.json","state_url":"https://pith.science/pith/F4ESVGQS7H6AQCC4Y7VLPKWRZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F4ESVGQS7H6AQCC4Y7VLPKWRZ5/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":"2026-05-27T20:44:00Z","links":{"resolver":"https://pith.science/pith/F4ESVGQS7H6AQCC4Y7VLPKWRZ5","bundle":"https://pith.science/pith/F4ESVGQS7H6AQCC4Y7VLPKWRZ5/bundle.json","state":"https://pith.science/pith/F4ESVGQS7H6AQCC4Y7VLPKWRZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F4ESVGQS7H6AQCC4Y7VLPKWRZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F4ESVGQS7H6AQCC4Y7VLPKWRZ5","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":"3d50946be03fd11771ddc0e71fc82fc23196812c2b1eed03ac80370fa749a8f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-23T17:50:01Z","title_canon_sha256":"d28ff41444eaf046ed1c656dc208837425a6c2b5f413676266b4f5a3dca1ba77"},"schema_version":"1.0","source":{"id":"1006.4601","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.4601","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"1006.4601v2","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4601","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"F4ESVGQS7H6A","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F4ESVGQS7H6AQCC4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F4ESVGQS","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:0472be123a9fb18ae512905667e2257af5a84a4fd38959a6ec9fa6c103bf17c1","target":"graph","created_at":"2026-05-18T04:35:14Z","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 paper we survey some recent advances in the analysis of marginally outer trapped surfaces (MOTS). We begin with a systematic review of results by Schoen and Yau on Jang's equation and its relationship with MOTS. We then explain recent work on the existence, regularity, and properties of MOTS and discuss the consequences for the trapped region. We include an outlook with some directions for future research.","authors_text":"Jan Metzger, Lars Andersson, Michael Eichmair","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-23T17:50:01Z","title":"Jang's equation and its applications to marginally trapped surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4601","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:f499f0397c6ad7ab2de99c4fe8abfd73eba4b59eb40bf46ef6e4402b55f90513","target":"record","created_at":"2026-05-18T04:35:14Z","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":"3d50946be03fd11771ddc0e71fc82fc23196812c2b1eed03ac80370fa749a8f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-23T17:50:01Z","title_canon_sha256":"d28ff41444eaf046ed1c656dc208837425a6c2b5f413676266b4f5a3dca1ba77"},"schema_version":"1.0","source":{"id":"1006.4601","kind":"arxiv","version":2}},"canonical_sha256":"2f092a9a12f9fc08085cc7eab7aad1cf52d0f66ae1be2a8264c37738071bc0d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f092a9a12f9fc08085cc7eab7aad1cf52d0f66ae1be2a8264c37738071bc0d2","first_computed_at":"2026-05-18T04:35:14.722124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:14.722124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ajgMZs6o6IZQax4i9UVI0s+vashGZRuxZUKwIies9+k2BgKBrgau5w0yjEZ3l0ypAFKWD4iPOlGaS/+DRETKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:14.722691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.4601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f499f0397c6ad7ab2de99c4fe8abfd73eba4b59eb40bf46ef6e4402b55f90513","sha256:0472be123a9fb18ae512905667e2257af5a84a4fd38959a6ec9fa6c103bf17c1"],"state_sha256":"e8f1c3842aac9ee0c392ea78eaa90ea1046e7560e0a84a437ed1c0eff784898a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+kdV5wmTuBlQDivBO5rm4kc1DCeQ5BEVXoSVrZD4YkA4v4Qoxzp+dVFI4dFyA3cxAAuAZYxlXMNyf1gV4XaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:44:00.874126Z","bundle_sha256":"045c553513271c30db42e107482033722888a017a508ad08cb4252b76ffd2778"}}