{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IM3GKAGQ3VA3CMRFPZ5QBHN6EH","short_pith_number":"pith:IM3GKAGQ","canonical_record":{"source":{"id":"1406.6719","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-25T21:43:01Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"d7a152669cd4bc79b439fec47146480abcc2bbae7510a4c9db1a37296787682f","abstract_canon_sha256":"3f0ee6c435fdf5539c8342b599785f8e8ccb4e2ae152666fa7fd65259d699121"},"schema_version":"1.0"},"canonical_sha256":"43366500d0dd41b132257e7b009dbe21f8013c966df311da912c516e0fd1f5f8","source":{"kind":"arxiv","id":"1406.6719","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6719","created_at":"2026-05-18T01:42:50Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6719v3","created_at":"2026-05-18T01:42:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6719","created_at":"2026-05-18T01:42:50Z"},{"alias_kind":"pith_short_12","alias_value":"IM3GKAGQ3VA3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IM3GKAGQ3VA3CMRF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IM3GKAGQ","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IM3GKAGQ3VA3CMRFPZ5QBHN6EH","target":"record","payload":{"canonical_record":{"source":{"id":"1406.6719","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-25T21:43:01Z","cross_cats_sorted":["math.CA","math.MP"],"title_canon_sha256":"d7a152669cd4bc79b439fec47146480abcc2bbae7510a4c9db1a37296787682f","abstract_canon_sha256":"3f0ee6c435fdf5539c8342b599785f8e8ccb4e2ae152666fa7fd65259d699121"},"schema_version":"1.0"},"canonical_sha256":"43366500d0dd41b132257e7b009dbe21f8013c966df311da912c516e0fd1f5f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:42:50.176113Z","signature_b64":"d4Es7jlAtlA+EJWxYLhPDxRE84RDfvAhs9J7OcJBtDzhrkJJlRT1/r/9gkNk9IHaG9lbT0yDqJ3kJ/ylhvGyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43366500d0dd41b132257e7b009dbe21f8013c966df311da912c516e0fd1f5f8","last_reissued_at":"2026-05-18T01:42:50.175390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:42:50.175390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.6719","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:42:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KGw94nDI+OOcqTdOBjWcTfQGUiTrOqSqyfg3mTUPU3+R+xbQ9A2ro3XDF+jOacFnE6pQ7YOj8aS70mhQENJnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:38:36.904295Z"},"content_sha256":"6120b39bb78e766979be6c49e41391a301ff35898fd858a1aeaebad4c39bd089","schema_version":"1.0","event_id":"sha256:6120b39bb78e766979be6c49e41391a301ff35898fd858a1aeaebad4c39bd089"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IM3GKAGQ3VA3CMRFPZ5QBHN6EH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The multivariate Hahn polynomials and the singular oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Luc Vinet, Vincent X. Genest","submitted_at":"2014-06-25T21:43:01Z","abstract_excerpt":"Karlin and McGregor's d-variable Hahn polynomials are shown to arise in the (d+1)-dimensional singular oscillator model as the overlap coefficients between bases associated to the separation of variables in Cartesian and hyperspherical coordinates. These polynomials in d discrete variables depend on d+1 real parameters and are orthogonal with respect to the multidimensional hypergeometric distribution. The focus is put on the d=2 case for which the connection with the three-dimensional singular oscillator is used to derive the main properties of the polynomials: forward/backward shift operator"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6719","kind":"arxiv","version":3},"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":"2026-05-18T01:42:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lsgaFohCLXdxq78AQU2pq8CHwTKnDxi+SUAsnVCUU1rigFkWakIbTVj332KzFh8JOtmw6RxI9KXo3HHU6HSxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:38:36.904658Z"},"content_sha256":"793eb9630d0004942a0bcef30741c4fe014f7e280759296eef09fda492c92873","schema_version":"1.0","event_id":"sha256:793eb9630d0004942a0bcef30741c4fe014f7e280759296eef09fda492c92873"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IM3GKAGQ3VA3CMRFPZ5QBHN6EH/bundle.json","state_url":"https://pith.science/pith/IM3GKAGQ3VA3CMRFPZ5QBHN6EH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IM3GKAGQ3VA3CMRFPZ5QBHN6EH/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":"2026-05-28T14:38:36Z","links":{"resolver":"https://pith.science/pith/IM3GKAGQ3VA3CMRFPZ5QBHN6EH","bundle":"https://pith.science/pith/IM3GKAGQ3VA3CMRFPZ5QBHN6EH/bundle.json","state":"https://pith.science/pith/IM3GKAGQ3VA3CMRFPZ5QBHN6EH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IM3GKAGQ3VA3CMRFPZ5QBHN6EH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IM3GKAGQ3VA3CMRFPZ5QBHN6EH","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":"3f0ee6c435fdf5539c8342b599785f8e8ccb4e2ae152666fa7fd65259d699121","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-25T21:43:01Z","title_canon_sha256":"d7a152669cd4bc79b439fec47146480abcc2bbae7510a4c9db1a37296787682f"},"schema_version":"1.0","source":{"id":"1406.6719","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6719","created_at":"2026-05-18T01:42:50Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6719v3","created_at":"2026-05-18T01:42:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6719","created_at":"2026-05-18T01:42:50Z"},{"alias_kind":"pith_short_12","alias_value":"IM3GKAGQ3VA3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IM3GKAGQ3VA3CMRF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IM3GKAGQ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:793eb9630d0004942a0bcef30741c4fe014f7e280759296eef09fda492c92873","target":"graph","created_at":"2026-05-18T01:42:50Z","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":"Karlin and McGregor's d-variable Hahn polynomials are shown to arise in the (d+1)-dimensional singular oscillator model as the overlap coefficients between bases associated to the separation of variables in Cartesian and hyperspherical coordinates. These polynomials in d discrete variables depend on d+1 real parameters and are orthogonal with respect to the multidimensional hypergeometric distribution. The focus is put on the d=2 case for which the connection with the three-dimensional singular oscillator is used to derive the main properties of the polynomials: forward/backward shift operator","authors_text":"Luc Vinet, Vincent X. Genest","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-25T21:43:01Z","title":"The multivariate Hahn polynomials and the singular oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6719","kind":"arxiv","version":3},"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":"sha256:6120b39bb78e766979be6c49e41391a301ff35898fd858a1aeaebad4c39bd089","target":"record","created_at":"2026-05-18T01:42:50Z","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":"3f0ee6c435fdf5539c8342b599785f8e8ccb4e2ae152666fa7fd65259d699121","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-25T21:43:01Z","title_canon_sha256":"d7a152669cd4bc79b439fec47146480abcc2bbae7510a4c9db1a37296787682f"},"schema_version":"1.0","source":{"id":"1406.6719","kind":"arxiv","version":3}},"canonical_sha256":"43366500d0dd41b132257e7b009dbe21f8013c966df311da912c516e0fd1f5f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43366500d0dd41b132257e7b009dbe21f8013c966df311da912c516e0fd1f5f8","first_computed_at":"2026-05-18T01:42:50.175390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:50.175390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d4Es7jlAtlA+EJWxYLhPDxRE84RDfvAhs9J7OcJBtDzhrkJJlRT1/r/9gkNk9IHaG9lbT0yDqJ3kJ/ylhvGyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:50.176113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6719","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6120b39bb78e766979be6c49e41391a301ff35898fd858a1aeaebad4c39bd089","sha256:793eb9630d0004942a0bcef30741c4fe014f7e280759296eef09fda492c92873"],"state_sha256":"feec79288903e44e29e943762aec6016c5c535b591d3c42a3d8484349dcb70e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxMoem+DuJAmHDn7UI8mNjZoBfRzeLIa3MNk5sxruVyumrOKTGvntZlQm90aPD0+uVvn+8Y07Y9uVmK3vVd2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:38:36.906622Z","bundle_sha256":"fff5192039e51d3ee4d5e99188b1a2cac618e263739387bcab864ebb52c5742b"}}