{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:CW4FQIRFMTM3WOHLRS4ZTOJIHO","short_pith_number":"pith:CW4FQIRF","schema_version":"1.0","canonical_sha256":"15b858222564d9bb38eb8cb999b9283bb1ba4db12e9fd20d6a7e04a93dd0a3f6","source":{"kind":"arxiv","id":"1010.5435","version":4},"attestation_state":"computed","paper":{"title":"Pseudotensor problem of gravitational energy-momentum and Noether's theorem revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Zhaoyan Wu","submitted_at":"2010-10-26T15:42:06Z","abstract_excerpt":"Based on a general variational principle, Noether's theorem is revisited. It is shown that the so called pseudotensor problem of the gravitational energy-momentum is a result of mis-reading Noether's theorem, and in fact, all the Noether's conserved quantities are scalars. It is also shown, by using a counter-example, that the non-localizability of gravitational energy-momentum can not be attributed to the equivalence principle. As a direct consequence of variational principle, a generalized Hamilton-Jacobi equation for the Hamilton's principal functional is obtained."},"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":"1010.5435","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-26T15:42:06Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"54053577485dcd565b140ef32b79aea9f96002643ac46c2b6c5f64276f3000b7","abstract_canon_sha256":"0ba2b15dcbf098e5db1f774c31e313403c9d525aa3c81dd3a52adcb024d75b8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:42.619831Z","signature_b64":"mqhGFkjSykxvMkMgpRNMaZEpqo+0q0M6GbKMFehh35ZB5t6jpJuosYhNqjF9hjOjZanyI+yo1QGi+lzj4McfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b858222564d9bb38eb8cb999b9283bb1ba4db12e9fd20d6a7e04a93dd0a3f6","last_reissued_at":"2026-05-18T03:07:42.619218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:42.619218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudotensor problem of gravitational energy-momentum and Noether's theorem revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Zhaoyan Wu","submitted_at":"2010-10-26T15:42:06Z","abstract_excerpt":"Based on a general variational principle, Noether's theorem is revisited. It is shown that the so called pseudotensor problem of the gravitational energy-momentum is a result of mis-reading Noether's theorem, and in fact, all the Noether's conserved quantities are scalars. It is also shown, by using a counter-example, that the non-localizability of gravitational energy-momentum can not be attributed to the equivalence principle. As a direct consequence of variational principle, a generalized Hamilton-Jacobi equation for the Hamilton's principal functional is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5435","kind":"arxiv","version":4},"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":"1010.5435","created_at":"2026-05-18T03:07:42.619311+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5435v4","created_at":"2026-05-18T03:07:42.619311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5435","created_at":"2026-05-18T03:07:42.619311+00:00"},{"alias_kind":"pith_short_12","alias_value":"CW4FQIRFMTM3","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"CW4FQIRFMTM3WOHL","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"CW4FQIRF","created_at":"2026-05-18T12:26:06.534383+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/CW4FQIRFMTM3WOHLRS4ZTOJIHO","json":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO.json","graph_json":"https://pith.science/api/pith-number/CW4FQIRFMTM3WOHLRS4ZTOJIHO/graph.json","events_json":"https://pith.science/api/pith-number/CW4FQIRFMTM3WOHLRS4ZTOJIHO/events.json","paper":"https://pith.science/paper/CW4FQIRF"},"agent_actions":{"view_html":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO","download_json":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO.json","view_paper":"https://pith.science/paper/CW4FQIRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5435&json=true","fetch_graph":"https://pith.science/api/pith-number/CW4FQIRFMTM3WOHLRS4ZTOJIHO/graph.json","fetch_events":"https://pith.science/api/pith-number/CW4FQIRFMTM3WOHLRS4ZTOJIHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO/action/storage_attestation","attest_author":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO/action/author_attestation","sign_citation":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO/action/citation_signature","submit_replication":"https://pith.science/pith/CW4FQIRFMTM3WOHLRS4ZTOJIHO/action/replication_record"}},"created_at":"2026-05-18T03:07:42.619311+00:00","updated_at":"2026-05-18T03:07:42.619311+00:00"}