{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:GGVEHOGANZKZCVVZ7253SVM3IB","short_pith_number":"pith:GGVEHOGA","schema_version":"1.0","canonical_sha256":"31aa43b8c06e559156b9febbb9559b4061aec3dff29733516f7d19fd1bc8a242","source":{"kind":"arxiv","id":"gr-qc/0302015","version":4},"attestation_state":"computed","paper":{"title":"Application of the Campbell-Magaard theorem to higher-dimensional physics","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Paul S. Wesson, Sanjeev S. Seahra","submitted_at":"2003-02-05T18:16:32Z","abstract_excerpt":"Stated succinctly, the original version of the Campbell-Magaard theorem says that it is always possible to locally embed any solution of 4-dimensional general relativity in a 5-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our universe is a 4-dimensional hypersurface Sigma_0 within a 5-dimensional manifold, such as Space-Time-Matter (STM) theory and the Randall & Sundrum (RS) braneworld scenario. In particular, we determine whether or not arbitrary spacetimes may be embedded "},"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":"gr-qc/0302015","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2003-02-05T18:16:32Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"dd7b272d03fd8c067829c09eef72273ba2c67e3324cda568bf52c42c30e0d721","abstract_canon_sha256":"2fc4b68f8656ba112ef81039dbc2512e690f06e04e2c0b4b762a05bdbcb7b405"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:47.518426Z","signature_b64":"WGvHmxslQYjvbJp835vg2iWUFCCbRJnQN31TAQPBDHyylCXOXI7/zGj2rSJgTKMU+9g2lkbGPxx6E5SNeiX4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31aa43b8c06e559156b9febbb9559b4061aec3dff29733516f7d19fd1bc8a242","last_reissued_at":"2026-05-18T01:06:47.517738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:47.517738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Application of the Campbell-Magaard theorem to higher-dimensional physics","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Paul S. Wesson, Sanjeev S. Seahra","submitted_at":"2003-02-05T18:16:32Z","abstract_excerpt":"Stated succinctly, the original version of the Campbell-Magaard theorem says that it is always possible to locally embed any solution of 4-dimensional general relativity in a 5-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our universe is a 4-dimensional hypersurface Sigma_0 within a 5-dimensional manifold, such as Space-Time-Matter (STM) theory and the Randall & Sundrum (RS) braneworld scenario. In particular, we determine whether or not arbitrary spacetimes may be embedded "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0302015","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":"gr-qc/0302015","created_at":"2026-05-18T01:06:47.517855+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0302015v4","created_at":"2026-05-18T01:06:47.517855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0302015","created_at":"2026-05-18T01:06:47.517855+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGVEHOGANZKZ","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGVEHOGANZKZCVVZ","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGVEHOGA","created_at":"2026-05-18T12:25:52.051335+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/GGVEHOGANZKZCVVZ7253SVM3IB","json":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB.json","graph_json":"https://pith.science/api/pith-number/GGVEHOGANZKZCVVZ7253SVM3IB/graph.json","events_json":"https://pith.science/api/pith-number/GGVEHOGANZKZCVVZ7253SVM3IB/events.json","paper":"https://pith.science/paper/GGVEHOGA"},"agent_actions":{"view_html":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB","download_json":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB.json","view_paper":"https://pith.science/paper/GGVEHOGA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0302015&json=true","fetch_graph":"https://pith.science/api/pith-number/GGVEHOGANZKZCVVZ7253SVM3IB/graph.json","fetch_events":"https://pith.science/api/pith-number/GGVEHOGANZKZCVVZ7253SVM3IB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB/action/storage_attestation","attest_author":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB/action/author_attestation","sign_citation":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB/action/citation_signature","submit_replication":"https://pith.science/pith/GGVEHOGANZKZCVVZ7253SVM3IB/action/replication_record"}},"created_at":"2026-05-18T01:06:47.517855+00:00","updated_at":"2026-05-18T01:06:47.517855+00:00"}