{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UB3NGHA2IYNKRK5ZBCAKDDDL72","short_pith_number":"pith:UB3NGHA2","schema_version":"1.0","canonical_sha256":"a076d31c1a461aa8abb90880a18c6bfe9c8068997250282234c4efc9c628753c","source":{"kind":"arxiv","id":"1804.08216","version":1},"attestation_state":"computed","paper":{"title":"The Minkowski formula and the quasi-local mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mu-Tao Wang, Po-Ning Chen, Shing-Tung Yau","submitted_at":"2018-04-23T01:45:52Z","abstract_excerpt":"In this article, we estimate the quasi-local energy with reference to the Minkowski spacetime [16,17], the anti-de Sitter spacetime [4], or the Schwarzschild spacetime [3]. In each case, the reference spacetime admits a conformal Killing-Yano 2-form which facilitates the application of the Minkowski formula in [15] to estimate the quasi-local energy. As a consequence of the positive mass theorems in [9,13] and the above estimate, we obtain rigidity theorems which characterize the Minkowski spacetime and the hyperbolic space."},"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":"1804.08216","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-04-23T01:45:52Z","cross_cats_sorted":[],"title_canon_sha256":"986e18c59736e47193da6df3597028a6d219464cb34467c5a59fca1fba218930","abstract_canon_sha256":"9af717bda85437b60c875bb746f847deae00f47bf53c65560a4013774a6c7d1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:28.151901Z","signature_b64":"NCwCKRS4ebmUjYKk5rnsQ35kuWAIlBivADgi25gUpil7M4a6myupHoDWuhECOPoE6M/xjlOsZ9qfwXTgKedzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a076d31c1a461aa8abb90880a18c6bfe9c8068997250282234c4efc9c628753c","last_reissued_at":"2026-05-17T23:50:28.151382Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:28.151382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Minkowski formula and the quasi-local mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mu-Tao Wang, Po-Ning Chen, Shing-Tung Yau","submitted_at":"2018-04-23T01:45:52Z","abstract_excerpt":"In this article, we estimate the quasi-local energy with reference to the Minkowski spacetime [16,17], the anti-de Sitter spacetime [4], or the Schwarzschild spacetime [3]. In each case, the reference spacetime admits a conformal Killing-Yano 2-form which facilitates the application of the Minkowski formula in [15] to estimate the quasi-local energy. As a consequence of the positive mass theorems in [9,13] and the above estimate, we obtain rigidity theorems which characterize the Minkowski spacetime and the hyperbolic space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08216","kind":"arxiv","version":1},"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":"1804.08216","created_at":"2026-05-17T23:50:28.151465+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.08216v1","created_at":"2026-05-17T23:50:28.151465+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08216","created_at":"2026-05-17T23:50:28.151465+00:00"},{"alias_kind":"pith_short_12","alias_value":"UB3NGHA2IYNK","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UB3NGHA2IYNKRK5Z","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UB3NGHA2","created_at":"2026-05-18T12:32:56.356000+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/UB3NGHA2IYNKRK5ZBCAKDDDL72","json":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72.json","graph_json":"https://pith.science/api/pith-number/UB3NGHA2IYNKRK5ZBCAKDDDL72/graph.json","events_json":"https://pith.science/api/pith-number/UB3NGHA2IYNKRK5ZBCAKDDDL72/events.json","paper":"https://pith.science/paper/UB3NGHA2"},"agent_actions":{"view_html":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72","download_json":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72.json","view_paper":"https://pith.science/paper/UB3NGHA2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.08216&json=true","fetch_graph":"https://pith.science/api/pith-number/UB3NGHA2IYNKRK5ZBCAKDDDL72/graph.json","fetch_events":"https://pith.science/api/pith-number/UB3NGHA2IYNKRK5ZBCAKDDDL72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72/action/storage_attestation","attest_author":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72/action/author_attestation","sign_citation":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72/action/citation_signature","submit_replication":"https://pith.science/pith/UB3NGHA2IYNKRK5ZBCAKDDDL72/action/replication_record"}},"created_at":"2026-05-17T23:50:28.151465+00:00","updated_at":"2026-05-17T23:50:28.151465+00:00"}