{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TJDO6EQLCR37IBRMKYTNKPID7X","short_pith_number":"pith:TJDO6EQL","schema_version":"1.0","canonical_sha256":"9a46ef120b1477f4062c5626d53d03fdd9bc437be263a682403d0abf05771147","source":{"kind":"arxiv","id":"1111.0757","version":1},"attestation_state":"computed","paper":{"title":"Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Gilles Regniers, Joris Van der Jeugt","submitted_at":"2011-11-03T09:00:07Z","abstract_excerpt":"In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and the Heisenberg equations are the starting point, and no further assumptions are made about how the position and momentum operators commute. Wigner quantization leads to new classes of solutions, and representations of Lie superalgebras are needed to describe them. For the n-dimensional Wigner harmonic oscillator, solutions are known in terms of the Lie superalgebras osp(1|2n) and gl(1|n). For n=3N, the question arises "},"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":"1111.0757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-03T09:00:07Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"e3fa2d2f56f8a366a9e1e9bb6008343084f00b58121823a110da111e3f4a501e","abstract_canon_sha256":"60afe596e01334307a0426dae0abcb34427bf05c01ad7e496460795fd3c3b371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:13.413280Z","signature_b64":"3+IS6p6YJQUBrEwRCOwreMLWh4UiC8VgZFE3ly6d0AT45CC2163YV5rlw4T5f3jVsoCf0D4jsRTKdDCzPQjcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a46ef120b1477f4062c5626d53d03fdd9bc437be263a682403d0abf05771147","last_reissued_at":"2026-05-18T04:02:13.412545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:13.412545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Gilles Regniers, Joris Van der Jeugt","submitted_at":"2011-11-03T09:00:07Z","abstract_excerpt":"In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and the Heisenberg equations are the starting point, and no further assumptions are made about how the position and momentum operators commute. Wigner quantization leads to new classes of solutions, and representations of Lie superalgebras are needed to describe them. For the n-dimensional Wigner harmonic oscillator, solutions are known in terms of the Lie superalgebras osp(1|2n) and gl(1|n). For n=3N, the question arises "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0757","kind":"arxiv","version":1},"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":"1111.0757","created_at":"2026-05-18T04:02:13.412666+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.0757v1","created_at":"2026-05-18T04:02:13.412666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0757","created_at":"2026-05-18T04:02:13.412666+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJDO6EQLCR37","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJDO6EQLCR37IBRM","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJDO6EQL","created_at":"2026-05-18T12:26:42.757692+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/TJDO6EQLCR37IBRMKYTNKPID7X","json":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X.json","graph_json":"https://pith.science/api/pith-number/TJDO6EQLCR37IBRMKYTNKPID7X/graph.json","events_json":"https://pith.science/api/pith-number/TJDO6EQLCR37IBRMKYTNKPID7X/events.json","paper":"https://pith.science/paper/TJDO6EQL"},"agent_actions":{"view_html":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X","download_json":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X.json","view_paper":"https://pith.science/paper/TJDO6EQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.0757&json=true","fetch_graph":"https://pith.science/api/pith-number/TJDO6EQLCR37IBRMKYTNKPID7X/graph.json","fetch_events":"https://pith.science/api/pith-number/TJDO6EQLCR37IBRMKYTNKPID7X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X/action/storage_attestation","attest_author":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X/action/author_attestation","sign_citation":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X/action/citation_signature","submit_replication":"https://pith.science/pith/TJDO6EQLCR37IBRMKYTNKPID7X/action/replication_record"}},"created_at":"2026-05-18T04:02:13.412666+00:00","updated_at":"2026-05-18T04:02:13.412666+00:00"}