{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:U6XJ7LI4LKOSU5Q3EVPCHNCPNM","short_pith_number":"pith:U6XJ7LI4","canonical_record":{"source":{"id":"1504.06525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-24T14:33:58Z","cross_cats_sorted":["math.AG","math.CO","math.QA"],"title_canon_sha256":"80a9f985ed5eba012f5d0a4647e38b8868a93f4a0c3c19de170b4e77d4f61693","abstract_canon_sha256":"bc8b341d7ab966b255b09f633ed68aa04ffa6b25ed4d3dc7e01fd6b5f2f0a61c"},"schema_version":"1.0"},"canonical_sha256":"a7ae9fad1c5a9d2a761b255e23b44f6b1e770ab9b0915761a45d111b1ba85b97","source":{"kind":"arxiv","id":"1504.06525","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06525","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06525v2","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06525","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"U6XJ7LI4LKOS","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U6XJ7LI4LKOSU5Q3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U6XJ7LI4","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:U6XJ7LI4LKOSU5Q3EVPCHNCPNM","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-24T14:33:58Z","cross_cats_sorted":["math.AG","math.CO","math.QA"],"title_canon_sha256":"80a9f985ed5eba012f5d0a4647e38b8868a93f4a0c3c19de170b4e77d4f61693","abstract_canon_sha256":"bc8b341d7ab966b255b09f633ed68aa04ffa6b25ed4d3dc7e01fd6b5f2f0a61c"},"schema_version":"1.0"},"canonical_sha256":"a7ae9fad1c5a9d2a761b255e23b44f6b1e770ab9b0915761a45d111b1ba85b97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:23.422831Z","signature_b64":"s0WeE6awkBhhOlaWtQbcvsiZ6cu/Fo0jTu8mo+GwaZOJlnPhfbj+ZSzm0nJvTA2z7mbIdmngPI6D/nAlNulXCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7ae9fad1c5a9d2a761b255e23b44f6b1e770ab9b0915761a45d111b1ba85b97","last_reissued_at":"2026-05-18T02:05:23.422106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:23.422106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06525","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Xprz6PpHSb6hS1L8RNCdOxfe8227dxYrL6pr0grGntVUORAIldAu3WAsPuOwsqXqE/W/NjBA3RdoTdZ9u2qDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:22:29.876722Z"},"content_sha256":"4a0537088d5ce9a0b44f1d595dd22925e904d21a2aff551620c7cbdc133b14aa","schema_version":"1.0","event_id":"sha256:4a0537088d5ce9a0b44f1d595dd22925e904d21a2aff551620c7cbdc133b14aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:U6XJ7LI4LKOSU5Q3EVPCHNCPNM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Algebras and Cyclic Quiver Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Andrei Negu\\c{t}","submitted_at":"2015-04-24T14:33:58Z","abstract_excerpt":"The purpose of this thesis is to present certain viewpoints on the geometric representation theory of Nakajima cyclic quiver varieties, in relation to the Maulik-Okounkov stable basis. Our main technical tool is the shuffle algebra, which arises as the K-theoretic Hall algebra of the double cyclic quiver. We prove the isomorphism between the shuffle algebra and the quantum toroidal algebra U_{q,t}(sl_n^^), and identify the quotients of Verma modules for the shuffle algebra with the K-theory groups of Nakajima cyclic quiver varieties, which were studied by Nakajima and Varagnolo-Vasserot.\n  The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06525","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:05:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBOlHS0kzp3M9nM69qxe7TIRH46Bz04uwHuLWd3Siv8583hL0ETSiThRGUxxUUFuL8u0Yc9rMYAw3cxssNyoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:22:29.877069Z"},"content_sha256":"bb7f62c4cf6975b045dfd737bd941774115d2c31657a41bf3ebea7801c7538a2","schema_version":"1.0","event_id":"sha256:bb7f62c4cf6975b045dfd737bd941774115d2c31657a41bf3ebea7801c7538a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U6XJ7LI4LKOSU5Q3EVPCHNCPNM/bundle.json","state_url":"https://pith.science/pith/U6XJ7LI4LKOSU5Q3EVPCHNCPNM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U6XJ7LI4LKOSU5Q3EVPCHNCPNM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T05:22:29Z","links":{"resolver":"https://pith.science/pith/U6XJ7LI4LKOSU5Q3EVPCHNCPNM","bundle":"https://pith.science/pith/U6XJ7LI4LKOSU5Q3EVPCHNCPNM/bundle.json","state":"https://pith.science/pith/U6XJ7LI4LKOSU5Q3EVPCHNCPNM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U6XJ7LI4LKOSU5Q3EVPCHNCPNM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U6XJ7LI4LKOSU5Q3EVPCHNCPNM","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":"bc8b341d7ab966b255b09f633ed68aa04ffa6b25ed4d3dc7e01fd6b5f2f0a61c","cross_cats_sorted":["math.AG","math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-24T14:33:58Z","title_canon_sha256":"80a9f985ed5eba012f5d0a4647e38b8868a93f4a0c3c19de170b4e77d4f61693"},"schema_version":"1.0","source":{"id":"1504.06525","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06525","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06525v2","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06525","created_at":"2026-05-18T02:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"U6XJ7LI4LKOS","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U6XJ7LI4LKOSU5Q3","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U6XJ7LI4","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:bb7f62c4cf6975b045dfd737bd941774115d2c31657a41bf3ebea7801c7538a2","target":"graph","created_at":"2026-05-18T02:05:23Z","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 purpose of this thesis is to present certain viewpoints on the geometric representation theory of Nakajima cyclic quiver varieties, in relation to the Maulik-Okounkov stable basis. Our main technical tool is the shuffle algebra, which arises as the K-theoretic Hall algebra of the double cyclic quiver. We prove the isomorphism between the shuffle algebra and the quantum toroidal algebra U_{q,t}(sl_n^^), and identify the quotients of Verma modules for the shuffle algebra with the K-theory groups of Nakajima cyclic quiver varieties, which were studied by Nakajima and Varagnolo-Vasserot.\n  The","authors_text":"Andrei Negu\\c{t}","cross_cats":["math.AG","math.CO","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-24T14:33:58Z","title":"Quantum Algebras and Cyclic Quiver Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06525","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":"sha256:4a0537088d5ce9a0b44f1d595dd22925e904d21a2aff551620c7cbdc133b14aa","target":"record","created_at":"2026-05-18T02:05:23Z","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":"bc8b341d7ab966b255b09f633ed68aa04ffa6b25ed4d3dc7e01fd6b5f2f0a61c","cross_cats_sorted":["math.AG","math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-24T14:33:58Z","title_canon_sha256":"80a9f985ed5eba012f5d0a4647e38b8868a93f4a0c3c19de170b4e77d4f61693"},"schema_version":"1.0","source":{"id":"1504.06525","kind":"arxiv","version":2}},"canonical_sha256":"a7ae9fad1c5a9d2a761b255e23b44f6b1e770ab9b0915761a45d111b1ba85b97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7ae9fad1c5a9d2a761b255e23b44f6b1e770ab9b0915761a45d111b1ba85b97","first_computed_at":"2026-05-18T02:05:23.422106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:23.422106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s0WeE6awkBhhOlaWtQbcvsiZ6cu/Fo0jTu8mo+GwaZOJlnPhfbj+ZSzm0nJvTA2z7mbIdmngPI6D/nAlNulXCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:23.422831Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06525","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a0537088d5ce9a0b44f1d595dd22925e904d21a2aff551620c7cbdc133b14aa","sha256:bb7f62c4cf6975b045dfd737bd941774115d2c31657a41bf3ebea7801c7538a2"],"state_sha256":"6bcd276953f09ed27d238414b22765c08fa8f1bda0bc636ebb21574776e7775a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Os98m8Uwvy9DClUV6quQnk/OLCMChYz3PsSWtE9nnNR++fxnNuU9R3Tv8ALKZ5PZFAfoDBPPbQv4EPpY+f49BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:22:29.879432Z","bundle_sha256":"fef72cde60590d4ef6ebc0c2719dd6970456ac3ef8f0b86fa473b4468d276b19"}}