{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RQGWUY2NIN73I4HLPGSZG2IIID","short_pith_number":"pith:RQGWUY2N","schema_version":"1.0","canonical_sha256":"8c0d6a634d437fb470eb79a593690840cc9178296c7e2588c24baa8d633c2307","source":{"kind":"arxiv","id":"1106.0093","version":1},"attestation_state":"computed","paper":{"title":"The Fourier U(2) Group and Separation of Discrete Variables","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","physics.optics"],"primary_cat":"math-ph","authors_text":"Kurt Bernardo Wolf, Luis Edgar Vicent","submitted_at":"2011-06-01T05:14:33Z","abstract_excerpt":"The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra $so(4)$. Two distinct subalgebra chains are used to model arrays of $N^2$ points placed a"},"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":"1106.0093","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-06-01T05:14:33Z","cross_cats_sorted":["math.MP","physics.optics"],"title_canon_sha256":"e3e66956e6239728068333268e58388f7e02f27d3beca740b2f89991b0e0f8ac","abstract_canon_sha256":"fa91b41407dd371621f6cb824ad310778380296ed3d20f22de767fb112b27cdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:52.124870Z","signature_b64":"b9ynwI7bQPhwfKiWlBg0qC1XpokpUpSoLkBm+9R6RrI02rn2FjxNHXW/nMO69DdjPYs/GtvDWMS7JEmZOwzFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c0d6a634d437fb470eb79a593690840cc9178296c7e2588c24baa8d633c2307","last_reissued_at":"2026-05-18T04:20:52.124390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:52.124390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fourier U(2) Group and Separation of Discrete Variables","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","physics.optics"],"primary_cat":"math-ph","authors_text":"Kurt Bernardo Wolf, Luis Edgar Vicent","submitted_at":"2011-06-01T05:14:33Z","abstract_excerpt":"The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra $so(4)$. Two distinct subalgebra chains are used to model arrays of $N^2$ points placed a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0093","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":"1106.0093","created_at":"2026-05-18T04:20:52.124463+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.0093v1","created_at":"2026-05-18T04:20:52.124463+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0093","created_at":"2026-05-18T04:20:52.124463+00:00"},{"alias_kind":"pith_short_12","alias_value":"RQGWUY2NIN73","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RQGWUY2NIN73I4HL","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RQGWUY2N","created_at":"2026-05-18T12:26:41.206345+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/RQGWUY2NIN73I4HLPGSZG2IIID","json":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID.json","graph_json":"https://pith.science/api/pith-number/RQGWUY2NIN73I4HLPGSZG2IIID/graph.json","events_json":"https://pith.science/api/pith-number/RQGWUY2NIN73I4HLPGSZG2IIID/events.json","paper":"https://pith.science/paper/RQGWUY2N"},"agent_actions":{"view_html":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID","download_json":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID.json","view_paper":"https://pith.science/paper/RQGWUY2N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.0093&json=true","fetch_graph":"https://pith.science/api/pith-number/RQGWUY2NIN73I4HLPGSZG2IIID/graph.json","fetch_events":"https://pith.science/api/pith-number/RQGWUY2NIN73I4HLPGSZG2IIID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID/action/storage_attestation","attest_author":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID/action/author_attestation","sign_citation":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID/action/citation_signature","submit_replication":"https://pith.science/pith/RQGWUY2NIN73I4HLPGSZG2IIID/action/replication_record"}},"created_at":"2026-05-18T04:20:52.124463+00:00","updated_at":"2026-05-18T04:20:52.124463+00:00"}