{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WRICYQA7XVH4Z3T3VPFAPGGEJE","short_pith_number":"pith:WRICYQA7","schema_version":"1.0","canonical_sha256":"b4502c401fbd4fccee7babca0798c4492fb3daf393d8d6b3482e7c2030ae8968","source":{"kind":"arxiv","id":"1702.02003","version":1},"attestation_state":"computed","paper":{"title":"Group theoretical aspects of $L^2(\\mathbb{R}^+)$, $L^2(\\mathbb{R}^2)$ and associated Laguerre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E. Celeghini, M.A. del Olmo","submitted_at":"2017-02-07T13:27:23Z","abstract_excerpt":"A ladder algebraic structure for $L^2(\\mathbb{R}^+)$ which closes the Lie algebra $h(1)\\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is presented in terms of a basis of associated Laguerre polynomials. Using the Schwinger method the quadratic generators that span the alternative Lie algebras $so(3)$, $so(2,1)$ and $so(3,2)$ are also constructed. These families of (pseudo) orthogonal algebras also allow to obtain unitary irreducible representations in $L^2(\\mathbb{R}^2)$ similar to those of the spherical harmonics."},"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":"1702.02003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-07T13:27:23Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7da7383e0e01a61a714c9104db58cf851eccba614cd0dd3711cccf4b116e99f5","abstract_canon_sha256":"a5b2b46f5e3513f6992bbb5ed61eafc297fd3150fda335b4008544024759238f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:10.624404Z","signature_b64":"Csmy69CydcNGy1Nqaj2iK556rVPkSBl9msLfySXTnXXSHFFsvSpXHePtZaw08ZCla90pMyCY/WJAPRnZuOk1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4502c401fbd4fccee7babca0798c4492fb3daf393d8d6b3482e7c2030ae8968","last_reissued_at":"2026-05-18T00:51:10.623656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:10.623656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Group theoretical aspects of $L^2(\\mathbb{R}^+)$, $L^2(\\mathbb{R}^2)$ and associated Laguerre polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E. Celeghini, M.A. del Olmo","submitted_at":"2017-02-07T13:27:23Z","abstract_excerpt":"A ladder algebraic structure for $L^2(\\mathbb{R}^+)$ which closes the Lie algebra $h(1)\\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is presented in terms of a basis of associated Laguerre polynomials. Using the Schwinger method the quadratic generators that span the alternative Lie algebras $so(3)$, $so(2,1)$ and $so(3,2)$ are also constructed. These families of (pseudo) orthogonal algebras also allow to obtain unitary irreducible representations in $L^2(\\mathbb{R}^2)$ similar to those of the spherical harmonics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02003","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":"1702.02003","created_at":"2026-05-18T00:51:10.623776+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.02003v1","created_at":"2026-05-18T00:51:10.623776+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02003","created_at":"2026-05-18T00:51:10.623776+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRICYQA7XVH4","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRICYQA7XVH4Z3T3","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRICYQA7","created_at":"2026-05-18T12:31:53.515858+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/WRICYQA7XVH4Z3T3VPFAPGGEJE","json":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE.json","graph_json":"https://pith.science/api/pith-number/WRICYQA7XVH4Z3T3VPFAPGGEJE/graph.json","events_json":"https://pith.science/api/pith-number/WRICYQA7XVH4Z3T3VPFAPGGEJE/events.json","paper":"https://pith.science/paper/WRICYQA7"},"agent_actions":{"view_html":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE","download_json":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE.json","view_paper":"https://pith.science/paper/WRICYQA7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.02003&json=true","fetch_graph":"https://pith.science/api/pith-number/WRICYQA7XVH4Z3T3VPFAPGGEJE/graph.json","fetch_events":"https://pith.science/api/pith-number/WRICYQA7XVH4Z3T3VPFAPGGEJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE/action/storage_attestation","attest_author":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE/action/author_attestation","sign_citation":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE/action/citation_signature","submit_replication":"https://pith.science/pith/WRICYQA7XVH4Z3T3VPFAPGGEJE/action/replication_record"}},"created_at":"2026-05-18T00:51:10.623776+00:00","updated_at":"2026-05-18T00:51:10.623776+00:00"}