{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:QV3MBOLOMB5AGEWUALG7FUJKOF","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":"d8b2e5bb4e4152c7311da58c5aaad4bf1a2d6471daccf158324b3ead286af1a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"1998-05-04T12:36:33Z","title_canon_sha256":"d40a68820c5800e5f7f3b43e48fb353becb0f6e20aa1d8d65f7fab205d0699cf"},"schema_version":"1.0","source":{"id":"math/9805009","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9805009","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/9805009v4","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9805009","created_at":"2026-05-18T00:43:03Z"},{"alias_kind":"pith_short_12","alias_value":"QV3MBOLOMB5A","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"QV3MBOLOMB5AGEWU","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"QV3MBOLO","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:df92d22b0d9f987fba9e1aacbf14778823ca8716fefa0c01c6d4d4ad05d6e5bc","target":"graph","created_at":"2026-05-18T00:43:03Z","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":"Let $\\hat{\\frak g}$ be an untwisted affine Kac-Moody algebra. The quantum group $U_h(\\hat{\\frak g})$ (over $\\mathbb{C}[[h]]$) is known to be a quasitriangular Hopf algebra: in particular, it has a universal $ R $--matrix, which yields an $ R $--matrix for each pair of representations of $U_h(\\hat{\\frak g})$. On the other hand, the quantum group $U_q(\\hat{\\frak g})$ (over $\\mathbb{C}(q) $) also has an $ R $--matrix for each pair of representations, but it has not a universal $ R $--matrix so that one cannot say that it is quasitriangular. Following Reshetikin, one introduces the (weaker) notion","authors_text":"Fabio Gavarini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"1998-05-04T12:36:33Z","title":"The $ R $--matrix action of untwisted affine quantum groups at roots of 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9805009","kind":"arxiv","version":4},"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:e622723c0e9802fcf311748a3746f6e020d2b3b7c729d9e13ad9cad01e4aa6a0","target":"record","created_at":"2026-05-18T00:43:03Z","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":"d8b2e5bb4e4152c7311da58c5aaad4bf1a2d6471daccf158324b3ead286af1a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"1998-05-04T12:36:33Z","title_canon_sha256":"d40a68820c5800e5f7f3b43e48fb353becb0f6e20aa1d8d65f7fab205d0699cf"},"schema_version":"1.0","source":{"id":"math/9805009","kind":"arxiv","version":4}},"canonical_sha256":"8576c0b96e607a0312d402cdf2d12a716c39c3814f0d7f418a4c5340a81a0205","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8576c0b96e607a0312d402cdf2d12a716c39c3814f0d7f418a4c5340a81a0205","first_computed_at":"2026-05-18T00:43:03.510755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:03.510755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F9veaPooOpvZ9UwchdixCnbsyu1kB/bksIfZPDCUW/+wAFlykEbwVyygXDrD5F3N18zvFi4cH3r/rjKCF6zWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:03.511549Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9805009","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e622723c0e9802fcf311748a3746f6e020d2b3b7c729d9e13ad9cad01e4aa6a0","sha256:df92d22b0d9f987fba9e1aacbf14778823ca8716fefa0c01c6d4d4ad05d6e5bc"],"state_sha256":"fbba15cff5339b2772fe0059c77d9219afec4760d7e8b105bd88a9e728fafd06"}