{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FBENNNETW3SZC6BIBCF6G3LFCK","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":"12745a9ed3c37db8cb8abd46a6b2e58e5692ccea2e53a9c5a3453eb16f1edcbb","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-26T14:24:59Z","title_canon_sha256":"a0beb246587481aee79bcb3b89b31a2649b33d08bd2242d5cc03bf4bcd1ed7ae"},"schema_version":"1.0","source":{"id":"2508.19066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.19066","created_at":"2026-07-01T01:17:41Z"},{"alias_kind":"arxiv_version","alias_value":"2508.19066v2","created_at":"2026-07-01T01:17:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.19066","created_at":"2026-07-01T01:17:41Z"},{"alias_kind":"pith_short_12","alias_value":"FBENNNETW3SZ","created_at":"2026-07-01T01:17:41Z"},{"alias_kind":"pith_short_16","alias_value":"FBENNNETW3SZC6BI","created_at":"2026-07-01T01:17:41Z"},{"alias_kind":"pith_short_8","alias_value":"FBENNNET","created_at":"2026-07-01T01:17:41Z"}],"graph_snapshots":[{"event_id":"sha256:5e2c68de5534ecafa865f32eafc6da9cd2713b8b3a907edbfc60fcd191f788e8","target":"graph","created_at":"2026-07-01T01:17:41Z","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/2508.19066/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an introduction to our results on cluster structures for schemes of $(G,c)$-bands emphasizing their connections with seminal works of Frenkel and Reshetikhin in the 90's. In particular we construct using $(G,c)$-bands a discrete analogue of the difference Miura transformation of the loop group $LG$, and we show that it calculates the $q$-characters of the finite-dimensional representations of the quantum affine algebra $U_q(\\widehat{\\mathfrak{g}})$ of the same $A$, $D$, $E$ type as $G$, thus verifying a conjecture of Frenkel and Reshetikhin.","authors_text":"Bernard Leclerc, Luca Francone","cross_cats":["math.QA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-26T14:24:59Z","title":"An introduction to $(G,c)$-bands"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.19066","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":"sha256:81951ec4c229b74b41bc0b2aedfe773740ac65873e8856ec7bf0d289096a0609","target":"record","created_at":"2026-07-01T01:17:41Z","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":"12745a9ed3c37db8cb8abd46a6b2e58e5692ccea2e53a9c5a3453eb16f1edcbb","cross_cats_sorted":["math.QA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-08-26T14:24:59Z","title_canon_sha256":"a0beb246587481aee79bcb3b89b31a2649b33d08bd2242d5cc03bf4bcd1ed7ae"},"schema_version":"1.0","source":{"id":"2508.19066","kind":"arxiv","version":2}},"canonical_sha256":"2848d6b493b6e5917828088be36d65129c5e03f755afa5e3b640d2ac869b1c0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2848d6b493b6e5917828088be36d65129c5e03f755afa5e3b640d2ac869b1c0d","first_computed_at":"2026-07-01T01:17:41.259175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:41.259175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FAuwB7Bce+tVH69R1oRLIEQMPxSbvYRB1T8cZNQQ/VdY55k2TddPAPAvXtRUVGcx3bzGK2qj/6rTPXq4b18dCw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:41.259687Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.19066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81951ec4c229b74b41bc0b2aedfe773740ac65873e8856ec7bf0d289096a0609","sha256:5e2c68de5534ecafa865f32eafc6da9cd2713b8b3a907edbfc60fcd191f788e8"],"state_sha256":"eefcb78cc61217262e851ef2b65bcb1d13eb5a1a937379e75bbc8cbab6a48897"}