{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LRYGE6752ATNRRPWFMSDWVOYME","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":"d2745142783529935a03c9635f2ab0eb61a2127992be9acbe2c43bcaf2c22c9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-19T22:28:23Z","title_canon_sha256":"c8ef7e66ed01487de61f3a140b1994b239e53cc964c04fa6fd306e5311e75248"},"schema_version":"1.0","source":{"id":"1308.4185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4185","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4185v1","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4185","created_at":"2026-05-18T03:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"LRYGE6752ATN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LRYGE6752ATNRRPW","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LRYGE675","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:4893c82a28f04866970f2763905036a367282cefe49554f7392dcf9d10869451","target":"graph","created_at":"2026-05-18T03:15:33Z","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":"The first part of this thesis deals with certain properties of the quantum symmetric and exterior algebras of Type 1 representations of $U_q(g)$ defined by Berenstein and Zwicknagl. We define a notion of a commutative algebra object in a coboundary category, and we prove that the quantum symmetric algebra of a module is the universal commutative algebra generated by that module. That is, the functor assigning to a module its quantum symmetric algebra is left adjoint to a forgetful functor. We also prove a conjecture of Berenstein and Zwicknagl, stating that the quantum symmetric and exterior c","authors_text":"Matthew Tucker-Simmons","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-19T22:28:23Z","title":"Quantum Algebras Associated to Irreducible Generalized Flag Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4185","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:b7d089d68c2ce41fb9f48d8c31b3fd35f3d4e1078379a3ff5b3b8170e988464f","target":"record","created_at":"2026-05-18T03:15:33Z","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":"d2745142783529935a03c9635f2ab0eb61a2127992be9acbe2c43bcaf2c22c9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-08-19T22:28:23Z","title_canon_sha256":"c8ef7e66ed01487de61f3a140b1994b239e53cc964c04fa6fd306e5311e75248"},"schema_version":"1.0","source":{"id":"1308.4185","kind":"arxiv","version":1}},"canonical_sha256":"5c70627bfdd026d8c5f62b243b55d86131e402927a98effffa55a99b2e908496","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c70627bfdd026d8c5f62b243b55d86131e402927a98effffa55a99b2e908496","first_computed_at":"2026-05-18T03:15:33.537557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:33.537557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C6VOjanXfNP9+e1dSBgzexEtXoWmidLSRL4rzXX98tWAT5nl0vW1Y/2B/oO5cm8qmrQUbmFUivVjSngc4CxBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:33.538300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7d089d68c2ce41fb9f48d8c31b3fd35f3d4e1078379a3ff5b3b8170e988464f","sha256:4893c82a28f04866970f2763905036a367282cefe49554f7392dcf9d10869451"],"state_sha256":"8c8fb879f53557bcdba1d5e574b4496f2e39076ebabcbbde42817d1f708b97e2"}