{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FME52ELMXTKXPQPCLWWFVEPFCY","short_pith_number":"pith:FME52ELM","schema_version":"1.0","canonical_sha256":"2b09dd116cbcd577c1e25dac5a91e5160acd95f504622812eccd3b209fff0b62","source":{"kind":"arxiv","id":"1602.09007","version":2},"attestation_state":"computed","paper":{"title":"Quantum difference equation for Nakajima varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Andrei Okounkov, Andrey Smirnov","submitted_at":"2016-02-29T15:34:33Z","abstract_excerpt":"For an arbitrary Nakajima quiver variety $X$, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in $Pic(X)\\otimes {\\mathbb{C}}$. We identify the lattice part of this groupoid with the operators of quantum difference equation for $X$. The cases of quivers of finite and affine type are illustrated by explicit examples."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.09007","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-29T15:34:33Z","cross_cats_sorted":["hep-th","math.MP","math.RT"],"title_canon_sha256":"ef2911255e3f883af53cc44027e958acb32f46504a9260ecd3910ee1f6c274f7","abstract_canon_sha256":"37a73d42083c7d8492bc567b25e58adc9baa0343475a46535d00bc941a7f372f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:12.600761Z","signature_b64":"vpAvuOMr6ezIO4IzzyYpGGhzR/Rqskllt7c5iAJYifYAYiGVZNUZV/40fyW6sDd9o9PaRALJtqxPyC/lIzOVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b09dd116cbcd577c1e25dac5a91e5160acd95f504622812eccd3b209fff0b62","last_reissued_at":"2026-07-05T04:18:12.600350Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:12.600350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum difference equation for Nakajima varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Andrei Okounkov, Andrey Smirnov","submitted_at":"2016-02-29T15:34:33Z","abstract_excerpt":"For an arbitrary Nakajima quiver variety $X$, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in $Pic(X)\\otimes {\\mathbb{C}}$. We identify the lattice part of this groupoid with the operators of quantum difference equation for $X$. The cases of quivers of finite and affine type are illustrated by explicit examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09007","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1602.09007/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.09007","created_at":"2026-07-05T04:18:12.600407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.09007v2","created_at":"2026-07-05T04:18:12.600407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.09007","created_at":"2026-07-05T04:18:12.600407+00:00"},{"alias_kind":"pith_short_12","alias_value":"FME52ELMXTKX","created_at":"2026-07-05T04:18:12.600407+00:00"},{"alias_kind":"pith_short_16","alias_value":"FME52ELMXTKXPQPC","created_at":"2026-07-05T04:18:12.600407+00:00"},{"alias_kind":"pith_short_8","alias_value":"FME52ELM","created_at":"2026-07-05T04:18:12.600407+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY","json":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY.json","graph_json":"https://pith.science/api/pith-number/FME52ELMXTKXPQPCLWWFVEPFCY/graph.json","events_json":"https://pith.science/api/pith-number/FME52ELMXTKXPQPCLWWFVEPFCY/events.json","paper":"https://pith.science/paper/FME52ELM"},"agent_actions":{"view_html":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY","download_json":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY.json","view_paper":"https://pith.science/paper/FME52ELM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.09007&json=true","fetch_graph":"https://pith.science/api/pith-number/FME52ELMXTKXPQPCLWWFVEPFCY/graph.json","fetch_events":"https://pith.science/api/pith-number/FME52ELMXTKXPQPCLWWFVEPFCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY/action/storage_attestation","attest_author":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY/action/author_attestation","sign_citation":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY/action/citation_signature","submit_replication":"https://pith.science/pith/FME52ELMXTKXPQPCLWWFVEPFCY/action/replication_record"}},"created_at":"2026-07-05T04:18:12.600407+00:00","updated_at":"2026-07-05T04:18:12.600407+00:00"}