{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:UMXDDIUDITVA5MCES4WNFNF7OR","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":"10b4b8257c1971a42420978b7e2bff40531af8b434065f1b030d25ea0e2d7e35","cross_cats_sorted":["gr-qc","hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2004-06-23T00:29:43Z","title_canon_sha256":"f215b4121932cb97e09e8d0e3b25973161cdc1e25de4be8babd4bea20462c0f8"},"schema_version":"1.0","source":{"id":"quant-ph/0406167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0406167","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0406167v2","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0406167","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"UMXDDIUDITVA","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"UMXDDIUDITVA5MCE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"UMXDDIUD","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f8a950c7b112de1d40881bc876a5248b8672dd1dceb83f561cbe8d76f8a11f8f","target":"graph","created_at":"2026-05-18T03:47:09Z","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":"In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the {\\it only} other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformally-flat metrics this type of factor ordering fails, by just one term, to give the conformally invariant Laplace-Beltrami operator.","authors_text":"Alexander V. Turbiner, Jr., Michael P. Ryan","cross_cats":["gr-qc","hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-06-23T00:29:43Z","title":"The conformally invariant Laplace-Beltrami operator and factor ordering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0406167","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":"sha256:5f6e52117549b029f9c19c450c2b29b5905d11bff73d62453bdc96997ba0b2b4","target":"record","created_at":"2026-05-18T03:47:09Z","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":"10b4b8257c1971a42420978b7e2bff40531af8b434065f1b030d25ea0e2d7e35","cross_cats_sorted":["gr-qc","hep-th","math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2004-06-23T00:29:43Z","title_canon_sha256":"f215b4121932cb97e09e8d0e3b25973161cdc1e25de4be8babd4bea20462c0f8"},"schema_version":"1.0","source":{"id":"quant-ph/0406167","kind":"arxiv","version":2}},"canonical_sha256":"a32e31a28344ea0eb044972cd2b4bf747b8277b0ab22c6596862deee1094562c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a32e31a28344ea0eb044972cd2b4bf747b8277b0ab22c6596862deee1094562c","first_computed_at":"2026-05-18T03:47:09.304005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:09.304005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5zNrt90gac458ii43Xdk3TeEKl8vSxh1H2W5TdThwjMW/li0GjcWR4O0pdk4lkUdHthBwIKz/bzFlWiRrItBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:09.304441Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0406167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f6e52117549b029f9c19c450c2b29b5905d11bff73d62453bdc96997ba0b2b4","sha256:f8a950c7b112de1d40881bc876a5248b8672dd1dceb83f561cbe8d76f8a11f8f"],"state_sha256":"30179c5b1a0d850a1bae2bfe983b8c973d46affe14af42a619e045fc9dca2d4f"}