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The corresponding Tridiagonal algebra $T$ is the associative K-algebra with 1 generated by two symbols $A$, $A^*$ subject to the relations (i) \\lbrack A,A^2A^*-\\beta AA^*A + A^*A^2 -\\gamma (AA^*+A^*A)- \\varrho A^*\\rbrack = 0,\n  (ii) \\lbrack A^*,A^{*2}A-\\beta A^*AA^* + AA^{*2} -\\gamma^* (A^*A+AA^*)- \\varrho^* A\\rbrack = 0, whe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0307016","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2003-07-01T22:18:25Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RA","math.RT"],"title_canon_sha256":"2b37c3a1801d72952730cd5f5d47070e6f5f4510842ad0c208fd72e3326e2667","abstract_canon_sha256":"5483a4fd45da12e62864ad1217edd19ff479bc7bfe05bed5772f7aef95eb2a21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:34.067704Z","signature_b64":"4kPsr5E3LEUvOACsK3Y9jN1HOL57b+04GTOc2x7H9ESuXDuUB4xf3n1ufFSdyKKppxWE0THWDsZdTkJ5HPnOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25aab0aec9b082c47b2dab19fcec79538f79466fc7fe0567fd6e67e8f06ba51d","last_reissued_at":"2026-07-04T14:37:34.067286Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:34.067286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two relations that generalize the $q$-Serre relations and the Dolan-Grady relations","license":"","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Paul Terwilliger","submitted_at":"2003-07-01T22:18:25Z","abstract_excerpt":"We define an algebra on two generators which we call the Tridiagonal algebra, and we consider its irreducible modules. The algebra is defined as follows. Let K denote a field, and let $\\beta, \\gamma, \\gamma^*, \\varrho, \\varrho^*$ denote a sequence of scalars taken from K. The corresponding Tridiagonal algebra $T$ is the associative K-algebra with 1 generated by two symbols $A$, $A^*$ subject to the relations (i) \\lbrack A,A^2A^*-\\beta AA^*A + A^*A^2 -\\gamma (AA^*+A^*A)- \\varrho A^*\\rbrack = 0,\n  (ii) \\lbrack A^*,A^{*2}A-\\beta A^*AA^* + AA^{*2} -\\gamma^* (A^*A+AA^*)- \\varrho^* A\\rbrack = 0, whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307016","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0307016/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0307016","created_at":"2026-07-04T14:37:34.067358+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0307016v1","created_at":"2026-07-04T14:37:34.067358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307016","created_at":"2026-07-04T14:37:34.067358+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWVLBLWJWCBM","created_at":"2026-07-04T14:37:34.067358+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWVLBLWJWCBMI6ZN","created_at":"2026-07-04T14:37:34.067358+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWVLBLWJ","created_at":"2026-07-04T14:37:34.067358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2511.15876","citing_title":"Universal TT- and TQ-relations via centrally extended q-Onsager algebra","ref_index":71,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO","json":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO.json","graph_json":"https://pith.science/api/pith-number/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/graph.json","events_json":"https://pith.science/api/pith-number/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/events.json","paper":"https://pith.science/paper/EWVLBLWJ"},"agent_actions":{"view_html":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO","download_json":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO.json","view_paper":"https://pith.science/paper/EWVLBLWJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0307016&json=true","fetch_graph":"https://pith.science/api/pith-number/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/graph.json","fetch_events":"https://pith.science/api/pith-number/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/action/storage_attestation","attest_author":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/action/author_attestation","sign_citation":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/action/citation_signature","submit_replication":"https://pith.science/pith/EWVLBLWJWCBMI6ZNVMM7Z3DZKO/action/replication_record"}},"created_at":"2026-07-04T14:37:34.067358+00:00","updated_at":"2026-07-04T14:37:34.067358+00:00"}