{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GP2AJKZPHEGVWSVWI4LMIYQ7C4","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":"38bce9461f68f2bb19405991b939159c54d5834430d8b8819c926578245f8f74","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-07-25T22:57:24Z","title_canon_sha256":"4fd869375ba1cc433168891fea5f080591464c559f9b807459f1d5b4104136f2"},"schema_version":"1.0","source":{"id":"1007.4357","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4357","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4357v3","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4357","created_at":"2026-05-18T03:46:18Z"},{"alias_kind":"pith_short_12","alias_value":"GP2AJKZPHEGV","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GP2AJKZPHEGVWSVW","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GP2AJKZP","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:c35f1d4a77a55542ad60028b7454ddc8b093cf2993a4ec30d0577bcf4719d0b1","target":"graph","created_at":"2026-05-18T03:46:18Z","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":"In the present paper we introduce a quantum analogue of the classical folding of a simply-laced Lie algebra g to the non-simply-laced algebra g^sigma along a Dynkin diagram automorphism sigma of g For each quantum folding we replace g^sigma by its Langlands dual g^sigma^v and construct a nilpotent Lie algebra n which interpolates between the nilpotnent parts of g and (g^sigma)^v, together with its quantized enveloping algebra U_q(n) and a Poisson structure on S(n). Remarkably, for the pair (g, (g^sigma)^v)=(so_{2n+2},sp_{2n}), the algebra U_q(n) admits an action of the Artin braid group Br_n a","authors_text":"Arkady Berenstein, Jacob Greenstein","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-07-25T22:57:24Z","title":"Quantum folding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4357","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:b18f024b4a6ee2b0b2b29818de10964f5d290ee12265b95b6e92605d08920f01","target":"record","created_at":"2026-05-18T03:46:18Z","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":"38bce9461f68f2bb19405991b939159c54d5834430d8b8819c926578245f8f74","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-07-25T22:57:24Z","title_canon_sha256":"4fd869375ba1cc433168891fea5f080591464c559f9b807459f1d5b4104136f2"},"schema_version":"1.0","source":{"id":"1007.4357","kind":"arxiv","version":3}},"canonical_sha256":"33f404ab2f390d5b4ab64716c4621f1735c18fed70ab9123d9d1da6caf74ad5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33f404ab2f390d5b4ab64716c4621f1735c18fed70ab9123d9d1da6caf74ad5b","first_computed_at":"2026-05-18T03:46:18.738362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:18.738362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rJ7Eftepq6tBs7o3RthCl/WXfYFUfzL2DWVytuTZBhaiGO2EdvqNIBKJ/N5K53F0ZyxlSKdLucUBixZoCc37CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:18.738911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4357","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b18f024b4a6ee2b0b2b29818de10964f5d290ee12265b95b6e92605d08920f01","sha256:c35f1d4a77a55542ad60028b7454ddc8b093cf2993a4ec30d0577bcf4719d0b1"],"state_sha256":"fff7db8d03b747bd305abfd7a3e272505ac5a57325e212db2e2c01c8e775ccb1"}