{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:VFNXSHVQ5PPBKDBTFAIGK5FIJD","short_pith_number":"pith:VFNXSHVQ","schema_version":"1.0","canonical_sha256":"a95b791eb0ebde150c3328106574a848fe52ed572bd5515e39e9815592892f2a","source":{"kind":"arxiv","id":"math/0606197","version":1},"attestation_state":"computed","paper":{"title":"The Tetrahedron algebra and its finite-dimensional irreducible modules","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Brian Hartwig","submitted_at":"2006-06-08T17:07:03Z","abstract_excerpt":"Recently Terwilliger and the present author found a presentation for the three-point $\\mathfrak{sl}_2$ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra $\\boxtimes$ by generators and relations and displayed an isomorphism from $\\boxtimes$ to the three-point $\\mathfrak{sl}_2$ loop algebra. In this paper we classify the finite-dimensional irreducible $\\boxtimes$-modules."},"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/0606197","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2006-06-08T17:07:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e80859eb20c14fa52d1fd49f22d5e2953ae6fc689746c8ca6928599873fe934a","abstract_canon_sha256":"cc15a48abdae79cbddfbbf99a5296ed526eb4d9525fe0762f5d3be8948f1dfe9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:55:29.678463Z","signature_b64":"JyuwOp3OB4z8UiFhVSC6xHBmifCxRuB5RNDnSZAoRu0rU+aAjrvurdyKUqQJUYLQe78gyV/pQ3I4j6bL3kMfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a95b791eb0ebde150c3328106574a848fe52ed572bd5515e39e9815592892f2a","last_reissued_at":"2026-07-04T14:55:29.678062Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:55:29.678062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Tetrahedron algebra and its finite-dimensional irreducible modules","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Brian Hartwig","submitted_at":"2006-06-08T17:07:03Z","abstract_excerpt":"Recently Terwilliger and the present author found a presentation for the three-point $\\mathfrak{sl}_2$ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra $\\boxtimes$ by generators and relations and displayed an isomorphism from $\\boxtimes$ to the three-point $\\mathfrak{sl}_2$ loop algebra. In this paper we classify the finite-dimensional irreducible $\\boxtimes$-modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606197","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/0606197/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/0606197","created_at":"2026-07-04T14:55:29.678124+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0606197v1","created_at":"2026-07-04T14:55:29.678124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606197","created_at":"2026-07-04T14:55:29.678124+00:00"},{"alias_kind":"pith_short_12","alias_value":"VFNXSHVQ5PPB","created_at":"2026-07-04T14:55:29.678124+00:00"},{"alias_kind":"pith_short_16","alias_value":"VFNXSHVQ5PPBKDBT","created_at":"2026-07-04T14:55:29.678124+00:00"},{"alias_kind":"pith_short_8","alias_value":"VFNXSHVQ","created_at":"2026-07-04T14:55:29.678124+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.19400","citing_title":"Raising and lowering maps for tridiagonal pairs","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD","json":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD.json","graph_json":"https://pith.science/api/pith-number/VFNXSHVQ5PPBKDBTFAIGK5FIJD/graph.json","events_json":"https://pith.science/api/pith-number/VFNXSHVQ5PPBKDBTFAIGK5FIJD/events.json","paper":"https://pith.science/paper/VFNXSHVQ"},"agent_actions":{"view_html":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD","download_json":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD.json","view_paper":"https://pith.science/paper/VFNXSHVQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0606197&json=true","fetch_graph":"https://pith.science/api/pith-number/VFNXSHVQ5PPBKDBTFAIGK5FIJD/graph.json","fetch_events":"https://pith.science/api/pith-number/VFNXSHVQ5PPBKDBTFAIGK5FIJD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD/action/storage_attestation","attest_author":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD/action/author_attestation","sign_citation":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD/action/citation_signature","submit_replication":"https://pith.science/pith/VFNXSHVQ5PPBKDBTFAIGK5FIJD/action/replication_record"}},"created_at":"2026-07-04T14:55:29.678124+00:00","updated_at":"2026-07-04T14:55:29.678124+00:00"}