{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5CB63C4RIFGNQVTTQLYTX5UZYH","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":"0f5ba04e0eead9a34fe0f681ae3a47407a51daa5750044ae0f1b7ab31bebf13e","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2021-04-14T07:17:51Z","title_canon_sha256":"e1fc0772c3421a9a4c7e358dac22f83137d27bf25b9ac2d4f35fb442c318337d"},"schema_version":"1.0","source":{"id":"2104.06661","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.06661","created_at":"2026-07-05T03:05:49Z"},{"alias_kind":"arxiv_version","alias_value":"2104.06661v3","created_at":"2026-07-05T03:05:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.06661","created_at":"2026-07-05T03:05:49Z"},{"alias_kind":"pith_short_12","alias_value":"5CB63C4RIFGN","created_at":"2026-07-05T03:05:49Z"},{"alias_kind":"pith_short_16","alias_value":"5CB63C4RIFGNQVTT","created_at":"2026-07-05T03:05:49Z"},{"alias_kind":"pith_short_8","alias_value":"5CB63C4R","created_at":"2026-07-05T03:05:49Z"}],"graph_snapshots":[{"event_id":"sha256:d6ca251acb69081a92923704546d148d926383b6fffc566ac71b28b99ed2413c","target":"graph","created_at":"2026-07-05T03:05:49Z","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/2104.06661/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau variables, we also construct quantum \"fundamental\" polynomials $F(x,y)$ which completely control the Weyl group actions. The geometric properties of the polynomials $F(x,y)$ for the commutative case is lifted distinctively in the quantum case to certain singularity structures as the $q$-difference operators. This property is further utilized as the characterization","authors_text":"Sanefumi Moriyama, Yasuhiko Yamada","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2021-04-14T07:17:51Z","title":"Quantum Representation of Affine Weyl Groups and Associated Quantum Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.06661","kind":"arxiv","version":3},"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:e41634d8486d911fd54bb63178c7a61bd735c69a26c15735d8054270a60a445a","target":"record","created_at":"2026-07-05T03:05:49Z","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":"0f5ba04e0eead9a34fe0f681ae3a47407a51daa5750044ae0f1b7ab31bebf13e","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2021-04-14T07:17:51Z","title_canon_sha256":"e1fc0772c3421a9a4c7e358dac22f83137d27bf25b9ac2d4f35fb442c318337d"},"schema_version":"1.0","source":{"id":"2104.06661","kind":"arxiv","version":3}},"canonical_sha256":"e883ed8b91414cd8567382f13bf699c1d44a5228131068e60cac7d5090587261","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e883ed8b91414cd8567382f13bf699c1d44a5228131068e60cac7d5090587261","first_computed_at":"2026-07-05T03:05:49.206178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:05:49.206178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KH6Hngs8S9T7mKQuoXnyNHHxnq1Yx/fA9bZiKNwSswB9nVCIYZ9bHid1MHtoAzPx0HjWlhBpGvf65nIw3QklBg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:05:49.206621Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.06661","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e41634d8486d911fd54bb63178c7a61bd735c69a26c15735d8054270a60a445a","sha256:d6ca251acb69081a92923704546d148d926383b6fffc566ac71b28b99ed2413c"],"state_sha256":"4184c424d8d0a40485bdd856e7aec4b2da5e790c806ce992698e22d6804f9152"}