{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:B6X3S4ZVS2YHS6NHBVHUFJKSLV","short_pith_number":"pith:B6X3S4ZV","canonical_record":{"source":{"id":"1211.1287","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T16:09:34Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"6f46db9e043c29b3b7030779f5473c11607d6da06ba10570b1d226a02c37273f","abstract_canon_sha256":"31d961e87a2c09f68ae8ca23a68048158c43daa5588732991c096219fc5a7b81"},"schema_version":"1.0"},"canonical_sha256":"0fafb9733596b07979a70d4f42a5525d7a467d17eed214a786c99857bcb81bb1","source":{"kind":"arxiv","id":"1211.1287","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1287","created_at":"2026-05-18T00:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1287v3","created_at":"2026-05-18T00:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1287","created_at":"2026-05-18T00:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"B6X3S4ZVS2YH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6X3S4ZVS2YHS6NH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6X3S4ZV","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:B6X3S4ZVS2YHS6NHBVHUFJKSLV","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1287","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T16:09:34Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"6f46db9e043c29b3b7030779f5473c11607d6da06ba10570b1d226a02c37273f","abstract_canon_sha256":"31d961e87a2c09f68ae8ca23a68048158c43daa5588732991c096219fc5a7b81"},"schema_version":"1.0"},"canonical_sha256":"0fafb9733596b07979a70d4f42a5525d7a467d17eed214a786c99857bcb81bb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:07.167512Z","signature_b64":"BKLHEHwH45NvcDyMAaRIn/nV9OaL8RXqi70ZdRKY/kMLwlrIRfOQXj2akOGazImvSZ8bwE7sKryJisCMGQ64Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fafb9733596b07979a70d4f42a5525d7a467d17eed214a786c99857bcb81bb1","last_reissued_at":"2026-05-18T00:14:07.166861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:07.166861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1287","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNs2GM+6ppPgfZox7+DlCq72iiHRLArCQJIFBQw6qhVFuvhMzpZkBNd5M5C6uOnZDP/PNj627yC7uUgWauiJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:17:19.394896Z"},"content_sha256":"119016e8faa6ff07fbecf04196bbe4478a5fa3dc40786e38c04904053553f529","schema_version":"1.0","event_id":"sha256:119016e8faa6ff07fbecf04196bbe4478a5fa3dc40786e38c04904053553f529"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:B6X3S4ZVS2YHS6NHBVHUFJKSLV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Groups and Quantum Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.AG","authors_text":"Andrei Okounkov, Davesh Maulik","submitted_at":"2012-11-06T16:09:34Z","abstract_excerpt":"In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology of these varieties, and show several results about their basic structure theory. We prove a formula for quantum multiplication by divisors in terms of this Yangian action. The quantum connection can be identified with the trigonometric Casimir connection for Y_Q; equivalently, the divisor operators correspond to certain elements of Baxter subalgebras of Y_Q."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1287","kind":"arxiv","version":3},"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":"2026-05-18T00:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJNKln9/54jNs7ETK0PcuWZjaOrkF3zuPgpbsd7uDLj4UDq+eEMu1ZJt1RBEGZCqhpn3AYYfnDpJNZgSqrQ+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:17:19.395517Z"},"content_sha256":"46eea529779348f5867d310c4ccebbb300dfa5312daabddd79a56cb4fd356bca","schema_version":"1.0","event_id":"sha256:46eea529779348f5867d310c4ccebbb300dfa5312daabddd79a56cb4fd356bca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6X3S4ZVS2YHS6NHBVHUFJKSLV/bundle.json","state_url":"https://pith.science/pith/B6X3S4ZVS2YHS6NHBVHUFJKSLV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6X3S4ZVS2YHS6NHBVHUFJKSLV/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":"2026-05-27T13:17:19Z","links":{"resolver":"https://pith.science/pith/B6X3S4ZVS2YHS6NHBVHUFJKSLV","bundle":"https://pith.science/pith/B6X3S4ZVS2YHS6NHBVHUFJKSLV/bundle.json","state":"https://pith.science/pith/B6X3S4ZVS2YHS6NHBVHUFJKSLV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6X3S4ZVS2YHS6NHBVHUFJKSLV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B6X3S4ZVS2YHS6NHBVHUFJKSLV","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":"31d961e87a2c09f68ae8ca23a68048158c43daa5588732991c096219fc5a7b81","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T16:09:34Z","title_canon_sha256":"6f46db9e043c29b3b7030779f5473c11607d6da06ba10570b1d226a02c37273f"},"schema_version":"1.0","source":{"id":"1211.1287","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1287","created_at":"2026-05-18T00:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1287v3","created_at":"2026-05-18T00:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1287","created_at":"2026-05-18T00:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"B6X3S4ZVS2YH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6X3S4ZVS2YHS6NH","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6X3S4ZV","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:46eea529779348f5867d310c4ccebbb300dfa5312daabddd79a56cb4fd356bca","target":"graph","created_at":"2026-05-18T00:14:07Z","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 this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q, the Yangian of Q, acting on the cohomology of these varieties, and show several results about their basic structure theory. We prove a formula for quantum multiplication by divisors in terms of this Yangian action. The quantum connection can be identified with the trigonometric Casimir connection for Y_Q; equivalently, the divisor operators correspond to certain elements of Baxter subalgebras of Y_Q.","authors_text":"Andrei Okounkov, Davesh Maulik","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T16:09:34Z","title":"Quantum Groups and Quantum Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1287","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":"sha256:119016e8faa6ff07fbecf04196bbe4478a5fa3dc40786e38c04904053553f529","target":"record","created_at":"2026-05-18T00:14:07Z","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":"31d961e87a2c09f68ae8ca23a68048158c43daa5588732991c096219fc5a7b81","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-06T16:09:34Z","title_canon_sha256":"6f46db9e043c29b3b7030779f5473c11607d6da06ba10570b1d226a02c37273f"},"schema_version":"1.0","source":{"id":"1211.1287","kind":"arxiv","version":3}},"canonical_sha256":"0fafb9733596b07979a70d4f42a5525d7a467d17eed214a786c99857bcb81bb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fafb9733596b07979a70d4f42a5525d7a467d17eed214a786c99857bcb81bb1","first_computed_at":"2026-05-18T00:14:07.166861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:07.166861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BKLHEHwH45NvcDyMAaRIn/nV9OaL8RXqi70ZdRKY/kMLwlrIRfOQXj2akOGazImvSZ8bwE7sKryJisCMGQ64Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:07.167512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1287","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:119016e8faa6ff07fbecf04196bbe4478a5fa3dc40786e38c04904053553f529","sha256:46eea529779348f5867d310c4ccebbb300dfa5312daabddd79a56cb4fd356bca"],"state_sha256":"3cd448eda7368c2562256e1aa865d5cba077b14833df4ae983da1a97aa6d8a78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GB0J8woPPwlleoS2UxBELUfhLmLoryeCTseEgQQ00jGaLbCC3o3CFRmM5mlNB71+u2/utL65ex087YQudrvxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:17:19.398771Z","bundle_sha256":"0aeb0261d141b13f4fd7718949c143e984b17b2369a3623ac522148d4d3aa616"}}