{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:O5LHSKOWBQA4MN74SNFZ2L4CZZ","short_pith_number":"pith:O5LHSKOW","canonical_record":{"source":{"id":"math/0408390","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2004-08-27T20:39:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"022584c0ae3d86d23e7540a78502f33140be6e3a000ba164aa39b1a1f55e3bbf","abstract_canon_sha256":"5953869453d9d394d64403a523ead542a0e248224d7ffa3798eb2f87b25ad625"},"schema_version":"1.0"},"canonical_sha256":"77567929d60c01c637fc934b9d2f82ce4544e7b31f3214b4295b872a53533e19","source":{"kind":"arxiv","id":"math/0408390","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408390","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408390v3","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408390","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"O5LHSKOWBQA4","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"pith_short_16","alias_value":"O5LHSKOWBQA4MN74","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"pith_short_8","alias_value":"O5LHSKOW","created_at":"2026-07-04T15:10:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:O5LHSKOWBQA4MN74SNFZ2L4CZZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0408390","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2004-08-27T20:39:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"022584c0ae3d86d23e7540a78502f33140be6e3a000ba164aa39b1a1f55e3bbf","abstract_canon_sha256":"5953869453d9d394d64403a523ead542a0e248224d7ffa3798eb2f87b25ad625"},"schema_version":"1.0"},"canonical_sha256":"77567929d60c01c637fc934b9d2f82ce4544e7b31f3214b4295b872a53533e19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:10:56.100781Z","signature_b64":"Rraoz75712Bfu0VpelCOWFAOadF8oIvEqJEf3zlD3SnHtb1wChgReCTm8t9qmUn/1Fexqt38jmHk5RPiTsMCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77567929d60c01c637fc934b9d2f82ce4544e7b31f3214b4295b872a53533e19","last_reissued_at":"2026-07-04T15:10:56.100332Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:10:56.100332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0408390","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":"2026-07-04T15:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YTU7Y3w2I7iUlqT3Wam774QR1s2xiE0Z+gI0GREY/0VaRB+gTFV/uQIlF5R5gPWWJZcK5H73qakHSqk5NCPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:38:46.326114Z"},"content_sha256":"cfbdf5e0acc61004c9a41bd48c1a344565d08b2e78a5282dc737c48561ab771e","schema_version":"1.0","event_id":"sha256:cfbdf5e0acc61004c9a41bd48c1a344565d08b2e78a5282dc737c48561ab771e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:O5LHSKOWBQA4MN74SNFZ2L4CZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Paul Terwilliger","submitted_at":"2004-08-27T20:39:17Z","abstract_excerpt":"Let $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V\\to V$ and $A^*:V\\to V$ that satisfy the following two conditions:\n  There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal.\n  There exists a basis for $V$ with respect to which the matrix representing $A^*$ is irreducible tridiagonal and the matrix representing $A$ is diagonal.\n  We call such a pair a Leonard pair on $V$. We give a correspondence betwe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408390","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0408390/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOISRt32XuKjHnrvdxKyTFcTjROxJNmJxdxYKa2oJ7di7iaJocdYmIcOgCH5+6REfhZF3rt4r6oQjArQIHNWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T06:38:46.327012Z"},"content_sha256":"30e0e1b5fbd57bfbde73552da601bca7d8f3273a4dcd71a9ae5e66fe5dbb0511","schema_version":"1.0","event_id":"sha256:30e0e1b5fbd57bfbde73552da601bca7d8f3273a4dcd71a9ae5e66fe5dbb0511"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O5LHSKOWBQA4MN74SNFZ2L4CZZ/bundle.json","state_url":"https://pith.science/pith/O5LHSKOWBQA4MN74SNFZ2L4CZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O5LHSKOWBQA4MN74SNFZ2L4CZZ/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":"2026-08-11T06:38:46Z","links":{"resolver":"https://pith.science/pith/O5LHSKOWBQA4MN74SNFZ2L4CZZ","bundle":"https://pith.science/pith/O5LHSKOWBQA4MN74SNFZ2L4CZZ/bundle.json","state":"https://pith.science/pith/O5LHSKOWBQA4MN74SNFZ2L4CZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O5LHSKOWBQA4MN74SNFZ2L4CZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:O5LHSKOWBQA4MN74SNFZ2L4CZZ","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":"5953869453d9d394d64403a523ead542a0e248224d7ffa3798eb2f87b25ad625","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2004-08-27T20:39:17Z","title_canon_sha256":"022584c0ae3d86d23e7540a78502f33140be6e3a000ba164aa39b1a1f55e3bbf"},"schema_version":"1.0","source":{"id":"math/0408390","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408390","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408390v3","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408390","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"O5LHSKOWBQA4","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"pith_short_16","alias_value":"O5LHSKOWBQA4MN74","created_at":"2026-07-04T15:10:56Z"},{"alias_kind":"pith_short_8","alias_value":"O5LHSKOW","created_at":"2026-07-04T15:10:56Z"}],"graph_snapshots":[{"event_id":"sha256:30e0e1b5fbd57bfbde73552da601bca7d8f3273a4dcd71a9ae5e66fe5dbb0511","target":"graph","created_at":"2026-07-04T15:10:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0408390/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $K$ denote a field, and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V\\to V$ and $A^*:V\\to V$ that satisfy the following two conditions:\n  There exists a basis for $V$ with respect to which the matrix representing $A$ is irreducible tridiagonal and the matrix representing $A^*$ is diagonal.\n  There exists a basis for $V$ with respect to which the matrix representing $A^*$ is irreducible tridiagonal and the matrix representing $A$ is diagonal.\n  We call such a pair a Leonard pair on $V$. We give a correspondence betwe","authors_text":"Paul Terwilliger","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2004-08-27T20:39:17Z","title":"Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408390","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:cfbdf5e0acc61004c9a41bd48c1a344565d08b2e78a5282dc737c48561ab771e","target":"record","created_at":"2026-07-04T15:10:56Z","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":"5953869453d9d394d64403a523ead542a0e248224d7ffa3798eb2f87b25ad625","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2004-08-27T20:39:17Z","title_canon_sha256":"022584c0ae3d86d23e7540a78502f33140be6e3a000ba164aa39b1a1f55e3bbf"},"schema_version":"1.0","source":{"id":"math/0408390","kind":"arxiv","version":3}},"canonical_sha256":"77567929d60c01c637fc934b9d2f82ce4544e7b31f3214b4295b872a53533e19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77567929d60c01c637fc934b9d2f82ce4544e7b31f3214b4295b872a53533e19","first_computed_at":"2026-07-04T15:10:56.100332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:10:56.100332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rraoz75712Bfu0VpelCOWFAOadF8oIvEqJEf3zlD3SnHtb1wChgReCTm8t9qmUn/1Fexqt38jmHk5RPiTsMCCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:10:56.100781Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0408390","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfbdf5e0acc61004c9a41bd48c1a344565d08b2e78a5282dc737c48561ab771e","sha256:30e0e1b5fbd57bfbde73552da601bca7d8f3273a4dcd71a9ae5e66fe5dbb0511"],"state_sha256":"d1743b16ca2ba8e84ff2502f17ef17614ff24b16f48e96d215e6c8984c009156"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+xnEw6sm10dmIdPuiH7G7eCaRUvisc4ewFE6NBZTUVseUO4fSBuD2iYqmjR6KfBsI8D0jBiwyunv/MuPYsKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T06:38:46.333333Z","bundle_sha256":"29aa6f6fb846541f5042ee2c344a4a9c6335044ac6a7dc1dc2152d94a05764fa"}}