{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3KIWDGOSIQ4CB3T7E3GTD24TXB","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":"84a91a51e22ae44bd8eafe38cf938f2977797700c734fbc3fcea20dc47935c15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2012-06-25T20:06:51Z","title_canon_sha256":"da95fe65d43edad85ed229ec0d3d54b6b3df62d13836e0d0503ab0e82e0790ba"},"schema_version":"1.0","source":{"id":"1206.5818","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5818","created_at":"2026-05-18T01:56:41Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5818v2","created_at":"2026-05-18T01:56:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5818","created_at":"2026-05-18T01:56:41Z"},{"alias_kind":"pith_short_12","alias_value":"3KIWDGOSIQ4C","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3KIWDGOSIQ4CB3T7","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3KIWDGOS","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:6672c471848be6cd015d714eb13a74a1d2018292950939905fcbb1adc967af9b","target":"graph","created_at":"2026-05-18T01:56:41Z","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":"The essence of the potential algebra concept [3] is that quantum mechanical free motions of scalar particles on curved surfaces of given isometry algebras can be mapped on 1D Schroedinger equations with particular potentials. As long as the Laplace-Beltrami operator on a curved surface is proportional to one of the Casimir invariants of the isometry algebra, free motion on the surface is described by means of the eigenvalue problem of that very Casimir operator and the excitation modes are classified according to the irreps of the algebra of interest. In consequence, also the spectra of the eq","authors_text":"Mariana Kirchbach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2012-06-25T20:06:51Z","title":"Conformal symmetry algebra of the quark potential and degeneracies in the hadron spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5818","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":"sha256:1cf4d294ce24a0d85c43a8badfa0e58ef3a27986480de1796633c8babc244944","target":"record","created_at":"2026-05-18T01:56:41Z","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":"84a91a51e22ae44bd8eafe38cf938f2977797700c734fbc3fcea20dc47935c15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2012-06-25T20:06:51Z","title_canon_sha256":"da95fe65d43edad85ed229ec0d3d54b6b3df62d13836e0d0503ab0e82e0790ba"},"schema_version":"1.0","source":{"id":"1206.5818","kind":"arxiv","version":2}},"canonical_sha256":"da916199d2443820ee7f26cd31eb93b86f1b9c991f78c256a4d7e662056e9d3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da916199d2443820ee7f26cd31eb93b86f1b9c991f78c256a4d7e662056e9d3e","first_computed_at":"2026-05-18T01:56:41.972411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:41.972411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"74dOaUyHkpi/oa0YTwaV+Umz5X/pTQZb2owySevTauAL5LU/4rd9mv2dlgALAFepfncTxrWKQoWjbDmRBdvuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:41.973055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5818","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cf4d294ce24a0d85c43a8badfa0e58ef3a27986480de1796633c8babc244944","sha256:6672c471848be6cd015d714eb13a74a1d2018292950939905fcbb1adc967af9b"],"state_sha256":"f82600615a78dea28f2945df2ca42c4b668d5d9bca6b80cb0d0037e64c7181ce"}