{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RPLLYNFKEEJYSH3IJPWU5EOBZ2","short_pith_number":"pith:RPLLYNFK","canonical_record":{"source":{"id":"1110.2087","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T15:59:03Z","cross_cats_sorted":[],"title_canon_sha256":"398b1024b45acf2c7cb6a182f5f8bb2886ce921c9e5c4f83f52ef4cc350d26ff","abstract_canon_sha256":"5badae7a9be2a2d0bb747edf9d8cc3668e82af664662249b7de96520a2de0fd7"},"schema_version":"1.0"},"canonical_sha256":"8bd6bc34aa2113891f684bed4e91c1ce9526c3d4d50518850b9cbf64d8c48dd9","source":{"kind":"arxiv","id":"1110.2087","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2087","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2087v2","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2087","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"RPLLYNFKEEJY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RPLLYNFKEEJYSH3I","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RPLLYNFK","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RPLLYNFKEEJYSH3IJPWU5EOBZ2","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2087","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T15:59:03Z","cross_cats_sorted":[],"title_canon_sha256":"398b1024b45acf2c7cb6a182f5f8bb2886ce921c9e5c4f83f52ef4cc350d26ff","abstract_canon_sha256":"5badae7a9be2a2d0bb747edf9d8cc3668e82af664662249b7de96520a2de0fd7"},"schema_version":"1.0"},"canonical_sha256":"8bd6bc34aa2113891f684bed4e91c1ce9526c3d4d50518850b9cbf64d8c48dd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:52.503940Z","signature_b64":"i7MGfhHGOUg2p7YwE24ctlAxek6nE39m7YGy8OA+r2ahCD7CSN+gJd/LiyxArTWX5hynRXOqQqrH5tqaDe9RDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bd6bc34aa2113891f684bed4e91c1ce9526c3d4d50518850b9cbf64d8c48dd9","last_reissued_at":"2026-05-18T01:23:52.503251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:52.503251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2087","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":"2026-05-18T01:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jC0f1WtJL5LyCM5x84PSdp9vodMxVtka0bdRWhX/1+RrLSwHrcEdiM/xQdc6nCfS3MxBKkjPt431xpbs03KpCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:54:46.347648Z"},"content_sha256":"d0b8ab67ce2a82ddb01c331bd1611ce837d9cb2cc3b9c8d4316dd1c596bb884e","schema_version":"1.0","event_id":"sha256:d0b8ab67ce2a82ddb01c331bd1611ce837d9cb2cc3b9c8d4316dd1c596bb884e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RPLLYNFKEEJYSH3IJPWU5EOBZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spacetime positive mass theorem in dimensions less than eight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dan A. Lee, Lan-Hsuan Huang, Michael Eichmair, Richard Schoen","submitted_at":"2011-10-10T15:59:03Z","abstract_excerpt":"We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM energy-momentum vector $(E,P)$ of the initial data satisfies the inequality $E \\ge |P|$. Previously, this theorem was proven only for spin manifolds by E. Witten. Our proof is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case. Instead of minimal hypersurfaces, we use marginally outer trapped hypersurfaces (MOT"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2087","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":"2026-05-18T01:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkhLbqmeEwGix9P2zTOYMgmDklVgwJn15GJ2XHT4i5bmgP3KUAxfUl75EbvJ0MTJR4lj6SD6rohy/b4yONNPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:54:46.347996Z"},"content_sha256":"c61ef7135f1323a40172cbb6aad9b07d5dcd5f3a27c7cc43cfa48a587d5193c0","schema_version":"1.0","event_id":"sha256:c61ef7135f1323a40172cbb6aad9b07d5dcd5f3a27c7cc43cfa48a587d5193c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RPLLYNFKEEJYSH3IJPWU5EOBZ2/bundle.json","state_url":"https://pith.science/pith/RPLLYNFKEEJYSH3IJPWU5EOBZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RPLLYNFKEEJYSH3IJPWU5EOBZ2/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":"2026-05-28T01:54:46Z","links":{"resolver":"https://pith.science/pith/RPLLYNFKEEJYSH3IJPWU5EOBZ2","bundle":"https://pith.science/pith/RPLLYNFKEEJYSH3IJPWU5EOBZ2/bundle.json","state":"https://pith.science/pith/RPLLYNFKEEJYSH3IJPWU5EOBZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RPLLYNFKEEJYSH3IJPWU5EOBZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RPLLYNFKEEJYSH3IJPWU5EOBZ2","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":"5badae7a9be2a2d0bb747edf9d8cc3668e82af664662249b7de96520a2de0fd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T15:59:03Z","title_canon_sha256":"398b1024b45acf2c7cb6a182f5f8bb2886ce921c9e5c4f83f52ef4cc350d26ff"},"schema_version":"1.0","source":{"id":"1110.2087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2087","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2087v2","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2087","created_at":"2026-05-18T01:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"RPLLYNFKEEJY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RPLLYNFKEEJYSH3I","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RPLLYNFK","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:c61ef7135f1323a40172cbb6aad9b07d5dcd5f3a27c7cc43cfa48a587d5193c0","target":"graph","created_at":"2026-05-18T01:23:52Z","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 prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM energy-momentum vector $(E,P)$ of the initial data satisfies the inequality $E \\ge |P|$. Previously, this theorem was proven only for spin manifolds by E. Witten. Our proof is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case. Instead of minimal hypersurfaces, we use marginally outer trapped hypersurfaces (MOT","authors_text":"Dan A. Lee, Lan-Hsuan Huang, Michael Eichmair, Richard Schoen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T15:59:03Z","title":"The spacetime positive mass theorem in dimensions less than eight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2087","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:d0b8ab67ce2a82ddb01c331bd1611ce837d9cb2cc3b9c8d4316dd1c596bb884e","target":"record","created_at":"2026-05-18T01:23:52Z","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":"5badae7a9be2a2d0bb747edf9d8cc3668e82af664662249b7de96520a2de0fd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-10T15:59:03Z","title_canon_sha256":"398b1024b45acf2c7cb6a182f5f8bb2886ce921c9e5c4f83f52ef4cc350d26ff"},"schema_version":"1.0","source":{"id":"1110.2087","kind":"arxiv","version":2}},"canonical_sha256":"8bd6bc34aa2113891f684bed4e91c1ce9526c3d4d50518850b9cbf64d8c48dd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bd6bc34aa2113891f684bed4e91c1ce9526c3d4d50518850b9cbf64d8c48dd9","first_computed_at":"2026-05-18T01:23:52.503251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:52.503251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7MGfhHGOUg2p7YwE24ctlAxek6nE39m7YGy8OA+r2ahCD7CSN+gJd/LiyxArTWX5hynRXOqQqrH5tqaDe9RDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:52.503940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0b8ab67ce2a82ddb01c331bd1611ce837d9cb2cc3b9c8d4316dd1c596bb884e","sha256:c61ef7135f1323a40172cbb6aad9b07d5dcd5f3a27c7cc43cfa48a587d5193c0"],"state_sha256":"2db8d45a9b44e6cc0ab34a3f00a8dcc7e679cdd27f991580a5e426136668729e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dqp/V7XDT2v2zRnioKPhwE2h58wuNUtKrx+UBM7bj9N5AiMjwavmVhXSCZ7k5plfB6DG9ucWj7QEVM2uWuptCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:54:46.349971Z","bundle_sha256":"76e3133fd7c803036a3fbb5d8baaf029b77cb43e278f5fce6acd58e26a1e7c91"}}