{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M5XQUQ5FIHO22U4BQAQREJMPJB","short_pith_number":"pith:M5XQUQ5F","canonical_record":{"source":{"id":"1204.2328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-11T03:47:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"405762cd88bb687123a7c26d0f03980700481aca6de705c496d02160be47fd4a","abstract_canon_sha256":"748d46d12dd0d327a6c103ba30439a3ab9c128e3425683f1283e4b7d6c35b6f7"},"schema_version":"1.0"},"canonical_sha256":"676f0a43a541ddad5381802112258f4856847e7c8720d738e34e628d08844c3a","source":{"kind":"arxiv","id":"1204.2328","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2328","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2328v1","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2328","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"M5XQUQ5FIHO2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M5XQUQ5FIHO22U4B","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M5XQUQ5F","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M5XQUQ5FIHO22U4BQAQREJMPJB","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-11T03:47:23Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"405762cd88bb687123a7c26d0f03980700481aca6de705c496d02160be47fd4a","abstract_canon_sha256":"748d46d12dd0d327a6c103ba30439a3ab9c128e3425683f1283e4b7d6c35b6f7"},"schema_version":"1.0"},"canonical_sha256":"676f0a43a541ddad5381802112258f4856847e7c8720d738e34e628d08844c3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:12.129061Z","signature_b64":"XK6mIY4iKm9mo9Mxbbua4EbYmnSicCmt5641WESuA7Hn6Xt1FHdPRjd7vvIMcpsswIDHKYI0ZVvD/jVL4A2nCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"676f0a43a541ddad5381802112258f4856847e7c8720d738e34e628d08844c3a","last_reissued_at":"2026-05-18T03:58:12.128462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:12.128462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2328","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":"2026-05-18T03:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YLLgywfSwWWRKCEbazjcq+2qVeWpnniauHIKbbH3ked/5/tLo9utaJD4lbD//aC+28PODEVUSd2opf5Tt4yyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:52:09.543818Z"},"content_sha256":"149cbce2a298a4ac95330133e96358ca925e36309927ae95c5251dc8ba9c5719","schema_version":"1.0","event_id":"sha256:149cbce2a298a4ac95330133e96358ca925e36309927ae95c5251dc8ba9c5719"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M5XQUQ5FIHO22U4BQAQREJMPJB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"N. S. Witte","submitted_at":"2012-04-11T03:47:23Z","abstract_excerpt":"A $\\mathbb{D}$-semi-classical weight is one which satisfies a particular linear, first order homogeneous equation in a divided-difference operator $\\mathbb{D}$. It is known that the system of polynomials, orthogonal with respect to this weight, and the associated functions satisfy a linear, first order homogeneous matrix equation in the divided-difference operator termed the spectral equation. Attached to the spectral equation is a structure which constitutes a number of relations such as those arising from compatibility with the three-term recurrence relation. Here this structure is elucidate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2328","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":"2026-05-18T03:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PySVlQMGgSGiytAEU/BPJjR+QYmk1hTsaGwwX0OMGd8d5Gl5JsepMstsxL8bGb3XHkk0EMQMbs4GgQc1nlU7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:52:09.544167Z"},"content_sha256":"a29d5288b595ca070acfc23e3f686ef034d1902e94e1ce5cbe973af9ae5498ca","schema_version":"1.0","event_id":"sha256:a29d5288b595ca070acfc23e3f686ef034d1902e94e1ce5cbe973af9ae5498ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5XQUQ5FIHO22U4BQAQREJMPJB/bundle.json","state_url":"https://pith.science/pith/M5XQUQ5FIHO22U4BQAQREJMPJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5XQUQ5FIHO22U4BQAQREJMPJB/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":"2026-06-12T09:52:09Z","links":{"resolver":"https://pith.science/pith/M5XQUQ5FIHO22U4BQAQREJMPJB","bundle":"https://pith.science/pith/M5XQUQ5FIHO22U4BQAQREJMPJB/bundle.json","state":"https://pith.science/pith/M5XQUQ5FIHO22U4BQAQREJMPJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5XQUQ5FIHO22U4BQAQREJMPJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M5XQUQ5FIHO22U4BQAQREJMPJB","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":"748d46d12dd0d327a6c103ba30439a3ab9c128e3425683f1283e4b7d6c35b6f7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-11T03:47:23Z","title_canon_sha256":"405762cd88bb687123a7c26d0f03980700481aca6de705c496d02160be47fd4a"},"schema_version":"1.0","source":{"id":"1204.2328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2328","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2328v1","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2328","created_at":"2026-05-18T03:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"M5XQUQ5FIHO2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M5XQUQ5FIHO22U4B","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M5XQUQ5F","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:a29d5288b595ca070acfc23e3f686ef034d1902e94e1ce5cbe973af9ae5498ca","target":"graph","created_at":"2026-05-18T03:58:12Z","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 $\\mathbb{D}$-semi-classical weight is one which satisfies a particular linear, first order homogeneous equation in a divided-difference operator $\\mathbb{D}$. It is known that the system of polynomials, orthogonal with respect to this weight, and the associated functions satisfy a linear, first order homogeneous matrix equation in the divided-difference operator termed the spectral equation. Attached to the spectral equation is a structure which constitutes a number of relations such as those arising from compatibility with the three-term recurrence relation. Here this structure is elucidate","authors_text":"N. S. Witte","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-11T03:47:23Z","title":"Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2328","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":"sha256:149cbce2a298a4ac95330133e96358ca925e36309927ae95c5251dc8ba9c5719","target":"record","created_at":"2026-05-18T03:58:12Z","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":"748d46d12dd0d327a6c103ba30439a3ab9c128e3425683f1283e4b7d6c35b6f7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-11T03:47:23Z","title_canon_sha256":"405762cd88bb687123a7c26d0f03980700481aca6de705c496d02160be47fd4a"},"schema_version":"1.0","source":{"id":"1204.2328","kind":"arxiv","version":1}},"canonical_sha256":"676f0a43a541ddad5381802112258f4856847e7c8720d738e34e628d08844c3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"676f0a43a541ddad5381802112258f4856847e7c8720d738e34e628d08844c3a","first_computed_at":"2026-05-18T03:58:12.128462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:12.128462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XK6mIY4iKm9mo9Mxbbua4EbYmnSicCmt5641WESuA7Hn6Xt1FHdPRjd7vvIMcpsswIDHKYI0ZVvD/jVL4A2nCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:12.129061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:149cbce2a298a4ac95330133e96358ca925e36309927ae95c5251dc8ba9c5719","sha256:a29d5288b595ca070acfc23e3f686ef034d1902e94e1ce5cbe973af9ae5498ca"],"state_sha256":"6b08f7ffb644eaf35aed0132e66e653fd14c26dcea837cb0acb190ca54b3a306"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/jzKVhoAB16L/cCEI0y7rzr7G2uZUC+AEj3CAW6iL/+5nsvD/ctNWKxux4dasmf5LfijlP2Joy5QoBTL5u3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:52:09.546216Z","bundle_sha256":"52eb6b5df01b1ed4c05e796f449e395217091431cd93a8a15a976c7e0b39b93e"}}