{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QJ7AKNRCBN6R6GO2WFEG5DGHU7","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":"9dad939c705d5d1606ef7718e8a1cd79fc1f58bb23ff80bb885d05f3625ec970","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-08-08T17:00:13Z","title_canon_sha256":"505e30a853dc217ffc3bb29156a117c2eee5db154e094881610694f8cda54ae0"},"schema_version":"1.0","source":{"id":"2608.08234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08234","created_at":"2026-08-11T01:22:04Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08234v1","created_at":"2026-08-11T01:22:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08234","created_at":"2026-08-11T01:22:04Z"},{"alias_kind":"pith_short_12","alias_value":"QJ7AKNRCBN6R","created_at":"2026-08-11T01:22:04Z"},{"alias_kind":"pith_short_16","alias_value":"QJ7AKNRCBN6R6GO2","created_at":"2026-08-11T01:22:04Z"},{"alias_kind":"pith_short_8","alias_value":"QJ7AKNRC","created_at":"2026-08-11T01:22:04Z"}],"graph_snapshots":[{"event_id":"sha256:5ccfa28d9ea592e957b4ef7a6d79669788d42be250511751af393bf4eab6cc80","target":"graph","created_at":"2026-08-11T01:22:04Z","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/2608.08234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a simply connected simple complex algebraic group. It is proved by Oya, Qin, and Yakimov \\cite{OQY} that the quantized coordinate ring $\\mathcal{O}_q(G)$ is generated by generalized quantum minors, and therefore carries a quantized cluster algebra structure, for all $G$ but type $F_4$. In this article, we settle the $F_4$ case by an argument uniform across $G_2$, $F_4$, and $E_8$. The main idea is to bootstrap the existing proof in type $E_8$, which relies on Lusztig's canonical basis of the quantum adjoint representation, and replace it with the combinatorics of the quasi-minuscule","authors_text":"Ayan Dey","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-08-08T17:00:13Z","title":"Generalized Quantum Minors Generate Quantized Coordinate Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08234","kind":"arxiv","version":1},"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:c395ad118583c33a07a8284e1cdc9bf29a9674d41585c937aa98b0391f79b7e7","target":"record","created_at":"2026-08-11T01:22:04Z","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":"9dad939c705d5d1606ef7718e8a1cd79fc1f58bb23ff80bb885d05f3625ec970","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-08-08T17:00:13Z","title_canon_sha256":"505e30a853dc217ffc3bb29156a117c2eee5db154e094881610694f8cda54ae0"},"schema_version":"1.0","source":{"id":"2608.08234","kind":"arxiv","version":1}},"canonical_sha256":"827e0536220b7d1f19dab1486e8cc7a7d6af613930d087a9fea29d47e006c606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"827e0536220b7d1f19dab1486e8cc7a7d6af613930d087a9fea29d47e006c606","first_computed_at":"2026-08-11T01:22:04.908320Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:22:04.908320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OAxuy+sCmQgKmq/GkFHkU+m+M08lac8cWhjazrsjQYFpqv9STUc7Ex+WcOuvK5SS3VQ+1f2a+rViqOVPk3/IBA==","signature_status":"signed_v1","signed_at":"2026-08-11T01:22:04.911201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.08234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c395ad118583c33a07a8284e1cdc9bf29a9674d41585c937aa98b0391f79b7e7","sha256:5ccfa28d9ea592e957b4ef7a6d79669788d42be250511751af393bf4eab6cc80"],"state_sha256":"27c6d4c728ad0979edcf1a1a6379d84fc2686160cf48efc41c73dbf0d6bbee9b"}