{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DK2DR7WAZFZGJ5QWWQN77X2W4M","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":"8ca19f91c2c8b7c994524c9e1c83cf29d6c49d4a2a782a0fee17a8858b2292ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2012-08-23T18:11:13Z","title_canon_sha256":"db62e23ad795a720ecd0edf13abf4dda94bd630028167a3314108a139416e1a4"},"schema_version":"1.0","source":{"id":"1208.4821","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4821","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4821v2","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4821","created_at":"2026-05-18T03:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"DK2DR7WAZFZG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DK2DR7WAZFZGJ5QW","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DK2DR7WA","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:e4e99d44855e59cbb2eff48ed17ba80981ac58da57a99e7cb4a36b05eefec0b1","target":"graph","created_at":"2026-05-18T03:15:21Z","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":"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.","authors_text":"Evgeny Mukhin, Jian-Rong Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2012-08-23T18:11:13Z","title":"Extended $T$-System of Type $G_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4821","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":"sha256:302409e08fbe58536055790e7f868d23f2ba6853200a9242dd116490daa3c2dc","target":"record","created_at":"2026-05-18T03:15:21Z","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":"8ca19f91c2c8b7c994524c9e1c83cf29d6c49d4a2a782a0fee17a8858b2292ef","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.QA","submitted_at":"2012-08-23T18:11:13Z","title_canon_sha256":"db62e23ad795a720ecd0edf13abf4dda94bd630028167a3314108a139416e1a4"},"schema_version":"1.0","source":{"id":"1208.4821","kind":"arxiv","version":2}},"canonical_sha256":"1ab438fec0c97264f616b41bffdf56e30f10661bb78a3dbd1da3e25d503d3896","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ab438fec0c97264f616b41bffdf56e30f10661bb78a3dbd1da3e25d503d3896","first_computed_at":"2026-05-18T03:15:21.003065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:21.003065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ASLYrk1LCjcQxoaE3w4d0zE2qPsTLIb1fhHIKV8kCXr1mHr/e8HpocRDawK+fSzXYSL85BMZQi5DyB5nGbx+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:21.003824Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4821","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:302409e08fbe58536055790e7f868d23f2ba6853200a9242dd116490daa3c2dc","sha256:e4e99d44855e59cbb2eff48ed17ba80981ac58da57a99e7cb4a36b05eefec0b1"],"state_sha256":"e464180923e45f8c231f5953fb0d442aa81ae0a115181e03aa40623e66968373"}