{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:VU3TCS3EOUX2SYKTJELW357JMU","short_pith_number":"pith:VU3TCS3E","schema_version":"1.0","canonical_sha256":"ad37314b64752fa9615349176df7e9652717eeedb4a38fd6b79f3b725ab0498f","source":{"kind":"arxiv","id":"0805.1370","version":3},"attestation_state":"computed","paper":{"title":"Isometric embeddings into the Minkowski space and new quasi-local mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Mu-Tao Wang, Shing-Tung Yau","submitted_at":"2008-05-09T15:41:08Z","abstract_excerpt":"The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface and should be independent of whichever space-like region it bounds. An important idea which is related to the Hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi-local mass from the difference of the extrinsic geometries. This approach has been "},"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":"0805.1370","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-05-09T15:41:08Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"97ed3562b4c9c5ba5a1d02b0c959386c8df5f1a4322af94fc3cf7d7dfd38e473","abstract_canon_sha256":"997e37886b251753ee3f88f334462f2199ac607e6eb0561aebdbae77df4ee9ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:10:42.149292Z","signature_b64":"SxzMw9BPDPvWHtvJlTottvC7Z0jkjzyiDLU532hgcRdpQNMtCu9SVyawIYNycyO34E/83+ABkK0kik833KuBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad37314b64752fa9615349176df7e9652717eeedb4a38fd6b79f3b725ab0498f","last_reissued_at":"2026-07-04T17:10:42.148907Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:10:42.148907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometric embeddings into the Minkowski space and new quasi-local mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Mu-Tao Wang, Shing-Tung Yau","submitted_at":"2008-05-09T15:41:08Z","abstract_excerpt":"The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface and should be independent of whichever space-like region it bounds. An important idea which is related to the Hamiltonian formulation of general relativity is to consider a reference surface in a flat ambient space with the same first fundamental form and derive the quasi-local mass from the difference of the extrinsic geometries. This approach has been "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1370","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0805.1370/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0805.1370","created_at":"2026-07-04T17:10:42.148968+00:00"},{"alias_kind":"arxiv_version","alias_value":"0805.1370v3","created_at":"2026-07-04T17:10:42.148968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1370","created_at":"2026-07-04T17:10:42.148968+00:00"},{"alias_kind":"pith_short_12","alias_value":"VU3TCS3EOUX2","created_at":"2026-07-04T17:10:42.148968+00:00"},{"alias_kind":"pith_short_16","alias_value":"VU3TCS3EOUX2SYKT","created_at":"2026-07-04T17:10:42.148968+00:00"},{"alias_kind":"pith_short_8","alias_value":"VU3TCS3E","created_at":"2026-07-04T17:10:42.148968+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.13135","citing_title":"Classification of ten-dimensional embeddings of spherically symmetric static metrics","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU","json":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU.json","graph_json":"https://pith.science/api/pith-number/VU3TCS3EOUX2SYKTJELW357JMU/graph.json","events_json":"https://pith.science/api/pith-number/VU3TCS3EOUX2SYKTJELW357JMU/events.json","paper":"https://pith.science/paper/VU3TCS3E"},"agent_actions":{"view_html":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU","download_json":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU.json","view_paper":"https://pith.science/paper/VU3TCS3E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0805.1370&json=true","fetch_graph":"https://pith.science/api/pith-number/VU3TCS3EOUX2SYKTJELW357JMU/graph.json","fetch_events":"https://pith.science/api/pith-number/VU3TCS3EOUX2SYKTJELW357JMU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU/action/storage_attestation","attest_author":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU/action/author_attestation","sign_citation":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU/action/citation_signature","submit_replication":"https://pith.science/pith/VU3TCS3EOUX2SYKTJELW357JMU/action/replication_record"}},"created_at":"2026-07-04T17:10:42.148968+00:00","updated_at":"2026-07-04T17:10:42.148968+00:00"}