{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DK2DR7WAZFZGJ5QWWQN77X2W4M","short_pith_number":"pith:DK2DR7WA","schema_version":"1.0","canonical_sha256":"1ab438fec0c97264f616b41bffdf56e30f10661bb78a3dbd1da3e25d503d3896","source":{"kind":"arxiv","id":"1208.4821","version":2},"attestation_state":"computed","paper":{"title":"Extended $T$-System of Type $G_2$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Evgeny Mukhin, Jian-Rong Li","submitted_at":"2012-08-23T18:11:13Z","abstract_excerpt":"We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type $G_2$ extending the celebrated $T$-system relations of type $G_2$. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type $G_2$. We use this result to obtain explicit formulas for dimensions of all participating 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":"1208.4821","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2012-08-23T18:11:13Z","cross_cats_sorted":[],"title_canon_sha256":"db62e23ad795a720ecd0edf13abf4dda94bd630028167a3314108a139416e1a4","abstract_canon_sha256":"8ca19f91c2c8b7c994524c9e1c83cf29d6c49d4a2a782a0fee17a8858b2292ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:21.003824Z","signature_b64":"ASLYrk1LCjcQxoaE3w4d0zE2qPsTLIb1fhHIKV8kCXr1mHr/e8HpocRDawK+fSzXYSL85BMZQi5DyB5nGbx+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ab438fec0c97264f616b41bffdf56e30f10661bb78a3dbd1da3e25d503d3896","last_reissued_at":"2026-05-18T03:15:21.003065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:21.003065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extended $T$-System of Type $G_2$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Evgeny Mukhin, Jian-Rong Li","submitted_at":"2012-08-23T18:11:13Z","abstract_excerpt":"We prove a family of 3-term relations in the Grothendieck ring of the category of finite-dimensional modules over the affine quantum algebra of type $G_2$ extending the celebrated $T$-system relations of type $G_2$. We show that these relations can be used to compute classes of certain irreducible modules, including classes of all minimal affinizations of type $G_2$. We use this result to obtain explicit formulas for dimensions of all participating modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4821","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":""},"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":"1208.4821","created_at":"2026-05-18T03:15:21.003192+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4821v2","created_at":"2026-05-18T03:15:21.003192+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4821","created_at":"2026-05-18T03:15:21.003192+00:00"},{"alias_kind":"pith_short_12","alias_value":"DK2DR7WAZFZG","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"DK2DR7WAZFZGJ5QW","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"DK2DR7WA","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M","json":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M.json","graph_json":"https://pith.science/api/pith-number/DK2DR7WAZFZGJ5QWWQN77X2W4M/graph.json","events_json":"https://pith.science/api/pith-number/DK2DR7WAZFZGJ5QWWQN77X2W4M/events.json","paper":"https://pith.science/paper/DK2DR7WA"},"agent_actions":{"view_html":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M","download_json":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M.json","view_paper":"https://pith.science/paper/DK2DR7WA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4821&json=true","fetch_graph":"https://pith.science/api/pith-number/DK2DR7WAZFZGJ5QWWQN77X2W4M/graph.json","fetch_events":"https://pith.science/api/pith-number/DK2DR7WAZFZGJ5QWWQN77X2W4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M/action/storage_attestation","attest_author":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M/action/author_attestation","sign_citation":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M/action/citation_signature","submit_replication":"https://pith.science/pith/DK2DR7WAZFZGJ5QWWQN77X2W4M/action/replication_record"}},"created_at":"2026-05-18T03:15:21.003192+00:00","updated_at":"2026-05-18T03:15:21.003192+00:00"}