{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FDIY2RQQRC73CBFER62ILSH5HW","short_pith_number":"pith:FDIY2RQQ","canonical_record":{"source":{"id":"1212.4459","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-18T19:09:31Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"50815a0d28d5e9b93e885d7d9773f26c439f87adcd711c7ad03fa46cba6355c9","abstract_canon_sha256":"e0809f9b6f1da030ebcb2e8c698bc01d0cdaef723aa7f909adca683553804958"},"schema_version":"1.0"},"canonical_sha256":"28d18d461088bfb104a48fb485c8fd3d8d49a32cae48a9ed70529e392b86b5d4","source":{"kind":"arxiv","id":"1212.4459","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4459","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4459v2","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4459","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"FDIY2RQQRC73","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FDIY2RQQRC73CBFE","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FDIY2RQQ","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FDIY2RQQRC73CBFER62ILSH5HW","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4459","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-18T19:09:31Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"50815a0d28d5e9b93e885d7d9773f26c439f87adcd711c7ad03fa46cba6355c9","abstract_canon_sha256":"e0809f9b6f1da030ebcb2e8c698bc01d0cdaef723aa7f909adca683553804958"},"schema_version":"1.0"},"canonical_sha256":"28d18d461088bfb104a48fb485c8fd3d8d49a32cae48a9ed70529e392b86b5d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:30.843360Z","signature_b64":"F70+Uuoy5ibwDJgim5jY1Cj/O4B/Ci0L5DoU9mZOpP6I0Nxbfj9taE8WIlMuAdGJlVF+79aVTIAjwusSasjAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28d18d461088bfb104a48fb485c8fd3d8d49a32cae48a9ed70529e392b86b5d4","last_reissued_at":"2026-05-18T01:52:30.842682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:30.842682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4459","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:52:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lU15kjuNNJXsZZFnafSfvtLcbV5k2hT9K26cUM9fwdcZNPYR57z5P9Fx29BLpaPI40h5Ou+wOuPAoOADDQnVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:16:27.547510Z"},"content_sha256":"3fadd6af7fcf7305af03ea6e5a25676b1135ae61deed7d492dc2c7e6bd210f5b","schema_version":"1.0","event_id":"sha256:3fadd6af7fcf7305af03ea6e5a25676b1135ae61deed7d492dc2c7e6bd210f5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FDIY2RQQRC73CBFER62ILSH5HW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alexei Zhedanov, Luc Vinet, Mourad E.H. Ismail, Vincent X. Genest","submitted_at":"2012-12-18T19:09:31Z","abstract_excerpt":"The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators are obtained by the Schwinger construction using parabosonic creation/annihilation operators. The algebra generated by the constants of motion, which we term the Schwinger-Dunkl algebra, is an extension of the Lie algebra u(2) with involutions. The system admits separation of variables in both Cartesian and polar coordinates. The separated wavefunctions are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4459","kind":"arxiv","version":2},"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":"2026-05-18T01:52:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EY6q9EJw0wXYe4m1LHU0m531ctfBv6TAUWz4iy4XluN7PggC/7V/fjGKb3XUFqm++aU4klpwWhGPMTz9K1JZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:16:27.548129Z"},"content_sha256":"b2290db38723f4270c65e69b591b79204de18349950e2d7906bdb5d9cc11e6d1","schema_version":"1.0","event_id":"sha256:b2290db38723f4270c65e69b591b79204de18349950e2d7906bdb5d9cc11e6d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FDIY2RQQRC73CBFER62ILSH5HW/bundle.json","state_url":"https://pith.science/pith/FDIY2RQQRC73CBFER62ILSH5HW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FDIY2RQQRC73CBFER62ILSH5HW/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":"2026-05-28T14:16:27Z","links":{"resolver":"https://pith.science/pith/FDIY2RQQRC73CBFER62ILSH5HW","bundle":"https://pith.science/pith/FDIY2RQQRC73CBFER62ILSH5HW/bundle.json","state":"https://pith.science/pith/FDIY2RQQRC73CBFER62ILSH5HW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FDIY2RQQRC73CBFER62ILSH5HW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FDIY2RQQRC73CBFER62ILSH5HW","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":"e0809f9b6f1da030ebcb2e8c698bc01d0cdaef723aa7f909adca683553804958","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-18T19:09:31Z","title_canon_sha256":"50815a0d28d5e9b93e885d7d9773f26c439f87adcd711c7ad03fa46cba6355c9"},"schema_version":"1.0","source":{"id":"1212.4459","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4459","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4459v2","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4459","created_at":"2026-05-18T01:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"FDIY2RQQRC73","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FDIY2RQQRC73CBFE","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FDIY2RQQ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:b2290db38723f4270c65e69b591b79204de18349950e2d7906bdb5d9cc11e6d1","target":"graph","created_at":"2026-05-18T01:52:30Z","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":"The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators are obtained by the Schwinger construction using parabosonic creation/annihilation operators. The algebra generated by the constants of motion, which we term the Schwinger-Dunkl algebra, is an extension of the Lie algebra u(2) with involutions. The system admits separation of variables in both Cartesian and polar coordinates. The separated wavefunctions are ","authors_text":"Alexei Zhedanov, Luc Vinet, Mourad E.H. Ismail, Vincent X. Genest","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-18T19:09:31Z","title":"The Dunkl oscillator in the plane I : superintegrability, separated wavefunctions and overlap coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4459","kind":"arxiv","version":2},"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":"sha256:3fadd6af7fcf7305af03ea6e5a25676b1135ae61deed7d492dc2c7e6bd210f5b","target":"record","created_at":"2026-05-18T01:52:30Z","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":"e0809f9b6f1da030ebcb2e8c698bc01d0cdaef723aa7f909adca683553804958","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-18T19:09:31Z","title_canon_sha256":"50815a0d28d5e9b93e885d7d9773f26c439f87adcd711c7ad03fa46cba6355c9"},"schema_version":"1.0","source":{"id":"1212.4459","kind":"arxiv","version":2}},"canonical_sha256":"28d18d461088bfb104a48fb485c8fd3d8d49a32cae48a9ed70529e392b86b5d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28d18d461088bfb104a48fb485c8fd3d8d49a32cae48a9ed70529e392b86b5d4","first_computed_at":"2026-05-18T01:52:30.842682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:30.842682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F70+Uuoy5ibwDJgim5jY1Cj/O4B/Ci0L5DoU9mZOpP6I0Nxbfj9taE8WIlMuAdGJlVF+79aVTIAjwusSasjAAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:30.843360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4459","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fadd6af7fcf7305af03ea6e5a25676b1135ae61deed7d492dc2c7e6bd210f5b","sha256:b2290db38723f4270c65e69b591b79204de18349950e2d7906bdb5d9cc11e6d1"],"state_sha256":"05c2a13af1cd8fe9bd59edb27da1cb32aa16dd6f1dd390005668ef1e0d5b48c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u9u6fJeSfHh8OMDSlx3fcCU6oBKtVVheSv0ZgB0sNWw/zlLFzmhxb+u1RF/bv4F8kiMFgLZs0SpfUzn3JdeHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:16:27.551193Z","bundle_sha256":"d08932b722f90620f5eb81b9eab56c20f43a38996d917bfbbe25183773eeee13"}}