{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DARWWDJL56GEMXJEB66CEXMYNK","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":"8aa4340c9b4a6f50c22ce1c16b3ca25dd502b116e997ed43bffe14738c3c2b9b","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-20T10:44:09Z","title_canon_sha256":"b6585d579959d71520479a126eda139188f66107f6043b0096f459ff5b20bc3b"},"schema_version":"1.0","source":{"id":"1308.4279","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4279","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4279v3","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4279","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"DARWWDJL56GE","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"DARWWDJL56GEMXJE","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"DARWWDJL","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:0d80d2f41e87225b9c00f57011d3b4cd5d5fa622634a80bca3d3cab33f77918d","target":"graph","created_at":"2026-05-18T03:02:57Z","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":"A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary spin. The presented systems describe neutral particles with non-trivial multipole momenta. Their spectra can be found algebraically like in the case of Hydrogen atom. Solutions for the systems with spins 1/2 and 1 are presented explicitly, solutions for spin 3/2 are expressed via solutions of an ordinary differential equation of first order..","authors_text":"A. G. Nikitin","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-20T10:44:09Z","title":"Laplace-Runge-Lenz vector for arbitrary spin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4279","kind":"arxiv","version":3},"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":"sha256:4c48ce0b50add2ef385fe86deb6ff39374818a9ea8d7928ee7f39785d3cb54ff","target":"record","created_at":"2026-05-18T03:02:57Z","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":"8aa4340c9b4a6f50c22ce1c16b3ca25dd502b116e997ed43bffe14738c3c2b9b","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-08-20T10:44:09Z","title_canon_sha256":"b6585d579959d71520479a126eda139188f66107f6043b0096f459ff5b20bc3b"},"schema_version":"1.0","source":{"id":"1308.4279","kind":"arxiv","version":3}},"canonical_sha256":"18236b0d2bef8c465d240fbc225d986aa494fa6965774ee7144b575ab05e3abe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18236b0d2bef8c465d240fbc225d986aa494fa6965774ee7144b575ab05e3abe","first_computed_at":"2026-05-18T03:02:57.100358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:57.100358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AEcP8mNBkfVCim/8/T/4oBzmrS/pq79PCk9kJ50r++wzhFWHyl1OZxTJ49PdyIhXBI4kn/eaZsWeqpnuvmHJCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:57.101063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4279","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c48ce0b50add2ef385fe86deb6ff39374818a9ea8d7928ee7f39785d3cb54ff","sha256:0d80d2f41e87225b9c00f57011d3b4cd5d5fa622634a80bca3d3cab33f77918d"],"state_sha256":"19b291f393af499b7e3c241cdcd03d9323fc368a6317deedce5548e1812922c4"}