{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QATSMIEL7H5Z43ZHPOD4JHVZHK","short_pith_number":"pith:QATSMIEL","canonical_record":{"source":{"id":"1210.5192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-18T17:11:08Z","cross_cats_sorted":["math.GR","math.MP","quant-ph"],"title_canon_sha256":"912d4dc820baed952134e4976fde364c477d6824bfb7d1a66e8975d284a56537","abstract_canon_sha256":"17fcb513b413138ab81a7fc0c32b78eb215b9652f98aa41b55c531b33bde9278"},"schema_version":"1.0"},"canonical_sha256":"802726208bf9fb9e6f277b87c49eb93a8eb7bf8ab1a5b600573e266c22a067c8","source":{"kind":"arxiv","id":"1210.5192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5192","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5192v1","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5192","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"QATSMIEL7H5Z","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QATSMIEL7H5Z43ZH","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QATSMIEL","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QATSMIEL7H5Z43ZHPOD4JHVZHK","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-18T17:11:08Z","cross_cats_sorted":["math.GR","math.MP","quant-ph"],"title_canon_sha256":"912d4dc820baed952134e4976fde364c477d6824bfb7d1a66e8975d284a56537","abstract_canon_sha256":"17fcb513b413138ab81a7fc0c32b78eb215b9652f98aa41b55c531b33bde9278"},"schema_version":"1.0"},"canonical_sha256":"802726208bf9fb9e6f277b87c49eb93a8eb7bf8ab1a5b600573e266c22a067c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:46.443973Z","signature_b64":"pthdzCoI4nLrViuA+ABz6Jvj7MHAZEEpKcX3n6Dd8xuVTeeqFZLZY6OZAhGcZspLJCM5vCQp40qUBtChiailAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"802726208bf9fb9e6f277b87c49eb93a8eb7bf8ab1a5b600573e266c22a067c8","last_reissued_at":"2026-05-18T01:53:46.443355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:46.443355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5192","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:53:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+LblcZJ2d38BwfKr+FrbfaPd1Av2t5l4aid+HLOnc15r2NnIWRR4r0fZqhh4Yps6LuOmg9gDH2MOjd9nkshBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:42:38.469584Z"},"content_sha256":"a248c6738883cdff10b8201e1ee975de15c433030973584fb839cba6456a1aa4","schema_version":"1.0","event_id":"sha256:a248c6738883cdff10b8201e1ee975de15c433030973584fb839cba6456a1aa4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QATSMIEL7H5Z43ZHPOD4JHVZHK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic special functions and so(3,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"E. Celeghini, M.A. del Olmo","submitted_at":"2012-10-18T17:11:08Z","abstract_excerpt":"A ladder structure of operators is presented for the associated Legendre polynomials and the spherical harmonics showing that both belong to the same irreducible representation of so(3,2). As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2) is thus shown to be isomorphic to the space of linear operators acting on the L^2 functions defined on (-1,1) x Z and on the sphere S^2, respectively.\n  The presence of a ladder structure is suggested to be the general condition to obtain a Lie algebra representation defining in this way the \"algebraic special "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5192","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:53:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Gw11eeZoGIY/4rESzRvpj5LAFoI1hvSI01Kn6d69XyDf0fplrcyOxnBi5QldhqlkZlwzKU9QT5p7txOSs6KDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T14:42:38.469930Z"},"content_sha256":"31e06c0374257d873d5d61f07a3b7bc0c8bac6f9c8aed3ea66085502c3e3a20a","schema_version":"1.0","event_id":"sha256:31e06c0374257d873d5d61f07a3b7bc0c8bac6f9c8aed3ea66085502c3e3a20a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QATSMIEL7H5Z43ZHPOD4JHVZHK/bundle.json","state_url":"https://pith.science/pith/QATSMIEL7H5Z43ZHPOD4JHVZHK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QATSMIEL7H5Z43ZHPOD4JHVZHK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T14:42:38Z","links":{"resolver":"https://pith.science/pith/QATSMIEL7H5Z43ZHPOD4JHVZHK","bundle":"https://pith.science/pith/QATSMIEL7H5Z43ZHPOD4JHVZHK/bundle.json","state":"https://pith.science/pith/QATSMIEL7H5Z43ZHPOD4JHVZHK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QATSMIEL7H5Z43ZHPOD4JHVZHK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QATSMIEL7H5Z43ZHPOD4JHVZHK","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":"17fcb513b413138ab81a7fc0c32b78eb215b9652f98aa41b55c531b33bde9278","cross_cats_sorted":["math.GR","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-18T17:11:08Z","title_canon_sha256":"912d4dc820baed952134e4976fde364c477d6824bfb7d1a66e8975d284a56537"},"schema_version":"1.0","source":{"id":"1210.5192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5192","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5192v1","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5192","created_at":"2026-05-18T01:53:46Z"},{"alias_kind":"pith_short_12","alias_value":"QATSMIEL7H5Z","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QATSMIEL7H5Z43ZH","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QATSMIEL","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:31e06c0374257d873d5d61f07a3b7bc0c8bac6f9c8aed3ea66085502c3e3a20a","target":"graph","created_at":"2026-05-18T01:53:46Z","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 ladder structure of operators is presented for the associated Legendre polynomials and the spherical harmonics showing that both belong to the same irreducible representation of so(3,2). As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2) is thus shown to be isomorphic to the space of linear operators acting on the L^2 functions defined on (-1,1) x Z and on the sphere S^2, respectively.\n  The presence of a ladder structure is suggested to be the general condition to obtain a Lie algebra representation defining in this way the \"algebraic special ","authors_text":"E. Celeghini, M.A. del Olmo","cross_cats":["math.GR","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-18T17:11:08Z","title":"Algebraic special functions and so(3,2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5192","kind":"arxiv","version":1},"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:a248c6738883cdff10b8201e1ee975de15c433030973584fb839cba6456a1aa4","target":"record","created_at":"2026-05-18T01:53:46Z","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":"17fcb513b413138ab81a7fc0c32b78eb215b9652f98aa41b55c531b33bde9278","cross_cats_sorted":["math.GR","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-10-18T17:11:08Z","title_canon_sha256":"912d4dc820baed952134e4976fde364c477d6824bfb7d1a66e8975d284a56537"},"schema_version":"1.0","source":{"id":"1210.5192","kind":"arxiv","version":1}},"canonical_sha256":"802726208bf9fb9e6f277b87c49eb93a8eb7bf8ab1a5b600573e266c22a067c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"802726208bf9fb9e6f277b87c49eb93a8eb7bf8ab1a5b600573e266c22a067c8","first_computed_at":"2026-05-18T01:53:46.443355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:53:46.443355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pthdzCoI4nLrViuA+ABz6Jvj7MHAZEEpKcX3n6Dd8xuVTeeqFZLZY6OZAhGcZspLJCM5vCQp40qUBtChiailAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:53:46.443973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a248c6738883cdff10b8201e1ee975de15c433030973584fb839cba6456a1aa4","sha256:31e06c0374257d873d5d61f07a3b7bc0c8bac6f9c8aed3ea66085502c3e3a20a"],"state_sha256":"d66e410f9967e811cba32ec2b62be471374f6ef237051ec78f3bcfb2dae3298c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eN0pFVBgdi5OSkfoSPBKw8TEdOCEACf4nw7DfB3mCYJRpep/MR5JiRePgMd2scvVJu1tLcPKqGr4YnaIF/FkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T14:42:38.471794Z","bundle_sha256":"a436f7e8a57504b8ec5d5a28516dea1c795c9675a44bdd7b95ca2f08ffef8db5"}}