{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SSWLTHA7OGPFXO4YEYHFW3FJZA","short_pith_number":"pith:SSWLTHA7","canonical_record":{"source":{"id":"1701.06089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-21T21:34:33Z","cross_cats_sorted":[],"title_canon_sha256":"9009e165ee2b0e5c9d7bc267558ef1f121e77ba675bc04092a63a846745613a9","abstract_canon_sha256":"913b7f15effade1251e294e2d88e8d613bd1a829448a232d7c2e61fcfe24803b"},"schema_version":"1.0"},"canonical_sha256":"94acb99c1f719e5bbb98260e5b6ca9c81f5abc17ca4d1582a8ef377a8440d1be","source":{"kind":"arxiv","id":"1701.06089","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06089","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06089v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06089","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"SSWLTHA7OGPF","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SSWLTHA7OGPFXO4Y","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SSWLTHA7","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SSWLTHA7OGPFXO4YEYHFW3FJZA","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-21T21:34:33Z","cross_cats_sorted":[],"title_canon_sha256":"9009e165ee2b0e5c9d7bc267558ef1f121e77ba675bc04092a63a846745613a9","abstract_canon_sha256":"913b7f15effade1251e294e2d88e8d613bd1a829448a232d7c2e61fcfe24803b"},"schema_version":"1.0"},"canonical_sha256":"94acb99c1f719e5bbb98260e5b6ca9c81f5abc17ca4d1582a8ef377a8440d1be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:19.358795Z","signature_b64":"/xOcpf+MAfzpAbCrRUy95pihzc+QVJhfOpv7wpwmeL1luej8xRKrnAXm4H7u8ZDB0x8zJqW/vIihkAv/0CKzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94acb99c1f719e5bbb98260e5b6ca9c81f5abc17ca4d1582a8ef377a8440d1be","last_reissued_at":"2026-05-18T00:52:19.358295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:19.358295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06089","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":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FYo/IWjNGlFj7hyMLfBNkjzq1zH13V37K7+4rK1v2y+qdm4ZsHki5db3An51w3AnM/iUF6HAxPLPPYw70YWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:39:53.798555Z"},"content_sha256":"59cafa6358b35df6746a7076bdd9936841fb78cce6568496ab19237144905e94","schema_version":"1.0","event_id":"sha256:59cafa6358b35df6746a7076bdd9936841fb78cce6568496ab19237144905e94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SSWLTHA7OGPFXO4YEYHFW3FJZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The universal DAHA of type $(C_1^\\vee,C_1)$ and Leonard pairs of $q$-Racah type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kazumasa Nomura, Paul Terwilliger","submitted_at":"2017-01-21T21:34:33Z","abstract_excerpt":"A Leonard pair is a pair of diagonalizable linear transformations of a finite-dimensional vector space, each of which acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. Let $\\mathbb F$ denote an algebraically closed field, and fix a nonzero $q \\in \\mathbb F$ that is not a root of unity. The universal double affine Hecke algebra (DAHA) $\\hat{H}_q$ of type $(C_1^\\vee,C_1)$ is the associative $\\mathbb F$-algebra defined by generators $\\lbrace t_i^{\\pm 1}\\rbrace_{i=0}^3$ and relations (i) $t_it_i^{-1}=t_i^{-1}t_i=1$; (ii) $t_i+t_i^{-1}$ is central; (iii) $t_0t_1t_2t_3 ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06089","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":"2026-05-18T00:52:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lSB5BCqz80+mzDpC6GzPpsNnnFLz4hKCmgMHo+umQh6s/Q6DetsEURXSHbql39qYQmCeAZSf4f69vAt3dO2gBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:39:53.799162Z"},"content_sha256":"4447bd40b802316247e3a59e298ff978d96e9d8d074cbd3535cc22ca3fb807dc","schema_version":"1.0","event_id":"sha256:4447bd40b802316247e3a59e298ff978d96e9d8d074cbd3535cc22ca3fb807dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSWLTHA7OGPFXO4YEYHFW3FJZA/bundle.json","state_url":"https://pith.science/pith/SSWLTHA7OGPFXO4YEYHFW3FJZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSWLTHA7OGPFXO4YEYHFW3FJZA/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":"2026-05-25T10:39:53Z","links":{"resolver":"https://pith.science/pith/SSWLTHA7OGPFXO4YEYHFW3FJZA","bundle":"https://pith.science/pith/SSWLTHA7OGPFXO4YEYHFW3FJZA/bundle.json","state":"https://pith.science/pith/SSWLTHA7OGPFXO4YEYHFW3FJZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSWLTHA7OGPFXO4YEYHFW3FJZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SSWLTHA7OGPFXO4YEYHFW3FJZA","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":"913b7f15effade1251e294e2d88e8d613bd1a829448a232d7c2e61fcfe24803b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-21T21:34:33Z","title_canon_sha256":"9009e165ee2b0e5c9d7bc267558ef1f121e77ba675bc04092a63a846745613a9"},"schema_version":"1.0","source":{"id":"1701.06089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06089","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06089v1","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06089","created_at":"2026-05-18T00:52:19Z"},{"alias_kind":"pith_short_12","alias_value":"SSWLTHA7OGPF","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SSWLTHA7OGPFXO4Y","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SSWLTHA7","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:4447bd40b802316247e3a59e298ff978d96e9d8d074cbd3535cc22ca3fb807dc","target":"graph","created_at":"2026-05-18T00:52:19Z","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 Leonard pair is a pair of diagonalizable linear transformations of a finite-dimensional vector space, each of which acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. Let $\\mathbb F$ denote an algebraically closed field, and fix a nonzero $q \\in \\mathbb F$ that is not a root of unity. The universal double affine Hecke algebra (DAHA) $\\hat{H}_q$ of type $(C_1^\\vee,C_1)$ is the associative $\\mathbb F$-algebra defined by generators $\\lbrace t_i^{\\pm 1}\\rbrace_{i=0}^3$ and relations (i) $t_it_i^{-1}=t_i^{-1}t_i=1$; (ii) $t_i+t_i^{-1}$ is central; (iii) $t_0t_1t_2t_3 =","authors_text":"Kazumasa Nomura, Paul Terwilliger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-21T21:34:33Z","title":"The universal DAHA of type $(C_1^\\vee,C_1)$ and Leonard pairs of $q$-Racah type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06089","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":"sha256:59cafa6358b35df6746a7076bdd9936841fb78cce6568496ab19237144905e94","target":"record","created_at":"2026-05-18T00:52:19Z","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":"913b7f15effade1251e294e2d88e8d613bd1a829448a232d7c2e61fcfe24803b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-01-21T21:34:33Z","title_canon_sha256":"9009e165ee2b0e5c9d7bc267558ef1f121e77ba675bc04092a63a846745613a9"},"schema_version":"1.0","source":{"id":"1701.06089","kind":"arxiv","version":1}},"canonical_sha256":"94acb99c1f719e5bbb98260e5b6ca9c81f5abc17ca4d1582a8ef377a8440d1be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94acb99c1f719e5bbb98260e5b6ca9c81f5abc17ca4d1582a8ef377a8440d1be","first_computed_at":"2026-05-18T00:52:19.358295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:19.358295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/xOcpf+MAfzpAbCrRUy95pihzc+QVJhfOpv7wpwmeL1luej8xRKrnAXm4H7u8ZDB0x8zJqW/vIihkAv/0CKzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:19.358795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59cafa6358b35df6746a7076bdd9936841fb78cce6568496ab19237144905e94","sha256:4447bd40b802316247e3a59e298ff978d96e9d8d074cbd3535cc22ca3fb807dc"],"state_sha256":"dad1046ffaa44e2457f1b2b3001278396f86188a60662b36ffb7f454231042cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Jx/F4iUQoBxVybi7FNnzcOt0UPZfYA+S9qAuy824+60cXuYkhmCxjxuTcK6/WmerhifmEsyUfGrPAiuOD05BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T10:39:53.802010Z","bundle_sha256":"bae0fac8f0db27d04c0df74b898a470e9691552336181958e4b319de8b27c64b"}}