{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:RTULL7Q6KA7GFIV4SO4IXEIKI2","short_pith_number":"pith:RTULL7Q6","canonical_record":{"source":{"id":"math-ph/0408025","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-08-14T10:48:31Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"7ef707260e878a6c35756324562d58563337627a939f8d770714eabaa3122f1c","abstract_canon_sha256":"4b25640ba1a547877b356c717cc99c1db321c5e25d5f0455902ff40c42fb96d5"},"schema_version":"1.0"},"canonical_sha256":"8ce8b5fe1e503e62a2bc93b88b910a46b10b40f09928350b4c900db0fdfab7b4","source":{"kind":"arxiv","id":"math-ph/0408025","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0408025","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0408025v2","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0408025","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"RTULL7Q6KA7G","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"pith_short_16","alias_value":"RTULL7Q6KA7GFIV4","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"pith_short_8","alias_value":"RTULL7Q6","created_at":"2026-07-04T16:49:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:RTULL7Q6KA7GFIV4SO4IXEIKI2","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0408025","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-08-14T10:48:31Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"7ef707260e878a6c35756324562d58563337627a939f8d770714eabaa3122f1c","abstract_canon_sha256":"4b25640ba1a547877b356c717cc99c1db321c5e25d5f0455902ff40c42fb96d5"},"schema_version":"1.0"},"canonical_sha256":"8ce8b5fe1e503e62a2bc93b88b910a46b10b40f09928350b4c900db0fdfab7b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:49:11.794018Z","signature_b64":"b+owDKFcN+J4ID1nooBACTLJDbjmjleyk3wYd7nfBqTuTNhraiJFx0XC4UeBpCozdoio8U9dLSpY8AgPETWrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ce8b5fe1e503e62a2bc93b88b910a46b10b40f09928350b4c900db0fdfab7b4","last_reissued_at":"2026-07-04T16:49:11.793664Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:49:11.793664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0408025","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":"2026-07-04T16:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2GpzfMifLN7YW0/jRUI2ve9gcQpsZSMmDb+RJEKKifw8s/VgkQ4VlHe/XttOK2g0qfhGIpZC69BY2bXxk4mCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:33:55.314192Z"},"content_sha256":"50838a0abcc64181e5d9887be136274c9e2800b5455745916f769534813fa4d5","schema_version":"1.0","event_id":"sha256:50838a0abcc64181e5d9887be136274c9e2800b5455745916f769534813fa4d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:RTULL7Q6KA7GFIV4SO4IXEIKI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An integrable structure related with tridiagonal algebras","license":"","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Pascal Baseilhac","submitted_at":"2004-08-14T10:48:31Z","abstract_excerpt":"The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on the tridiagonal algebraic structure associated with a deformation parameter $q$. Representations are shown to be generated from a class of quadratic algebras, namely the reflection equations. The spectral problem is briefly discussed. Finally, related massive quantum integrable models are shown to be superintegrable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0408025","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0408025/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":"2026-07-04T16:49:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SX+0W4bXc3CANH2z5OSiFh+edT/kO5NzVb7E4sxhkd5uolvY+XDfGuI8vnKxjWQfPzAOoKcGwdHfqMUsdtNgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:33:55.314779Z"},"content_sha256":"b32917be58a2f5155b0c846250caca78d3782b6335206b50933293c57744ffee","schema_version":"1.0","event_id":"sha256:b32917be58a2f5155b0c846250caca78d3782b6335206b50933293c57744ffee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RTULL7Q6KA7GFIV4SO4IXEIKI2/bundle.json","state_url":"https://pith.science/pith/RTULL7Q6KA7GFIV4SO4IXEIKI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RTULL7Q6KA7GFIV4SO4IXEIKI2/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":"2026-08-16T15:33:55Z","links":{"resolver":"https://pith.science/pith/RTULL7Q6KA7GFIV4SO4IXEIKI2","bundle":"https://pith.science/pith/RTULL7Q6KA7GFIV4SO4IXEIKI2/bundle.json","state":"https://pith.science/pith/RTULL7Q6KA7GFIV4SO4IXEIKI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RTULL7Q6KA7GFIV4SO4IXEIKI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:RTULL7Q6KA7GFIV4SO4IXEIKI2","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":"4b25640ba1a547877b356c717cc99c1db321c5e25d5f0455902ff40c42fb96d5","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","math.QA","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2004-08-14T10:48:31Z","title_canon_sha256":"7ef707260e878a6c35756324562d58563337627a939f8d770714eabaa3122f1c"},"schema_version":"1.0","source":{"id":"math-ph/0408025","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0408025","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0408025v2","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0408025","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"pith_short_12","alias_value":"RTULL7Q6KA7G","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"pith_short_16","alias_value":"RTULL7Q6KA7GFIV4","created_at":"2026-07-04T16:49:11Z"},{"alias_kind":"pith_short_8","alias_value":"RTULL7Q6","created_at":"2026-07-04T16:49:11Z"}],"graph_snapshots":[{"event_id":"sha256:b32917be58a2f5155b0c846250caca78d3782b6335206b50933293c57744ffee","target":"graph","created_at":"2026-07-04T16:49:11Z","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-ph/0408025/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on the tridiagonal algebraic structure associated with a deformation parameter $q$. Representations are shown to be generated from a class of quadratic algebras, namely the reflection equations. The spectral problem is briefly discussed. Finally, related massive quantum integrable models are shown to be superintegrable.","authors_text":"Pascal Baseilhac","cross_cats":["cond-mat.stat-mech","hep-th","math.MP","math.QA","nlin.SI"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-08-14T10:48:31Z","title":"An integrable structure related with tridiagonal algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0408025","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":"sha256:50838a0abcc64181e5d9887be136274c9e2800b5455745916f769534813fa4d5","target":"record","created_at":"2026-07-04T16:49:11Z","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":"4b25640ba1a547877b356c717cc99c1db321c5e25d5f0455902ff40c42fb96d5","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP","math.QA","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2004-08-14T10:48:31Z","title_canon_sha256":"7ef707260e878a6c35756324562d58563337627a939f8d770714eabaa3122f1c"},"schema_version":"1.0","source":{"id":"math-ph/0408025","kind":"arxiv","version":2}},"canonical_sha256":"8ce8b5fe1e503e62a2bc93b88b910a46b10b40f09928350b4c900db0fdfab7b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ce8b5fe1e503e62a2bc93b88b910a46b10b40f09928350b4c900db0fdfab7b4","first_computed_at":"2026-07-04T16:49:11.793664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:49:11.793664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b+owDKFcN+J4ID1nooBACTLJDbjmjleyk3wYd7nfBqTuTNhraiJFx0XC4UeBpCozdoio8U9dLSpY8AgPETWrBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:49:11.794018Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0408025","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50838a0abcc64181e5d9887be136274c9e2800b5455745916f769534813fa4d5","sha256:b32917be58a2f5155b0c846250caca78d3782b6335206b50933293c57744ffee"],"state_sha256":"c4614922baae85a7f87a734174868d3c19ba3ace63a106641ad711b3d228e970"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6Qzd4T9Fevrxk901a5sx3Un52QdDwG9Je2cMaYFCDBeCeMtPylRXqMQV6mweGCam/5IvmIcx+f464kusJEfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:33:55.319449Z","bundle_sha256":"73d52a234c0b798d54bae5935eaf973cbda1624ad22002e60abd3c95323ba4b2"}}