{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7DDGUIKUOJZXL4WW4MOAFGX4FJ","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":"18d557af1884df2efd9d700be74006259fd387c45ea3c12a0164ab5058bbae10","cross_cats_sorted":["hep-th","math-ph","math.MP","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-26T23:52:58Z","title_canon_sha256":"a47401b06196bb0450778743a23e85fff2a93ede614fcf98710a6f99717e0df9"},"schema_version":"1.0","source":{"id":"2412.19383","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19383","created_at":"2026-06-03T01:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19383v4","created_at":"2026-06-03T01:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19383","created_at":"2026-06-03T01:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"7DDGUIKUOJZX","created_at":"2026-06-03T01:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"7DDGUIKUOJZXL4WW","created_at":"2026-06-03T01:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"7DDGUIKU","created_at":"2026-06-03T01:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:c5b8a45112ef7bca7fb19d054b3de16117f9322e63bbed66ddaf7ce004f20cc6","target":"graph","created_at":"2026-06-03T01:05:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.19383/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Psi(\\textbf{z},\\textbf{a},q)$ a the fundamental solution matrix of the quantum difference equation of a Nakajima variety $X$. In this work, we prove that the operator $$ \\Psi(\\textbf{z},\\textbf{a},q) \\Psi\\left(\\textbf{z}^p,\\textbf{a}^p,q^{p^2}\\right)^{-1} $$ has no poles at the primitive complex $p$-th roots of unity $q=\\zeta_p$. As a byproduct, we show that the iterated product of the operators ${\\bf M}_{\\mathcal{L}}(\\textbf{z},\\textbf{a},q )$ from the $q$-difference equation on $X$: $$ {\\bf M}_{\\mathcal{L}} (\\textbf{z} q^{(p-1)\\mathcal{L}},\\textbf{a},q) \\cdots {\\bf M}_{\\mathcal{L}} (\\t","authors_text":"Andrey Smirnov, Peter Koroteev","cross_cats":["hep-th","math-ph","math.MP","math.NT","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-26T23:52:58Z","title":"On the Quantum K-theory of Quiver Varieties at Roots of Unity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19383","kind":"arxiv","version":4},"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":"sha256:6740ba8140768db70c4d22a0cfb57dd094a39f4102e08cf56e21068b2d2097d2","target":"record","created_at":"2026-06-03T01:05:03Z","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":"18d557af1884df2efd9d700be74006259fd387c45ea3c12a0164ab5058bbae10","cross_cats_sorted":["hep-th","math-ph","math.MP","math.NT","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-26T23:52:58Z","title_canon_sha256":"a47401b06196bb0450778743a23e85fff2a93ede614fcf98710a6f99717e0df9"},"schema_version":"1.0","source":{"id":"2412.19383","kind":"arxiv","version":4}},"canonical_sha256":"f8c66a2154727375f2d6e31c029afc2a40f0c58d624492a4321ed34dd83bf20c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8c66a2154727375f2d6e31c029afc2a40f0c58d624492a4321ed34dd83bf20c","first_computed_at":"2026-06-03T01:05:03.919192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:03.919192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/1oxX/5mZKk5Rgzqh52+uYuxrVHGxsCqAgyy/KhD7i8Kn+BQ876jfp196rK4nUIqDbS3QDt4JaRVotO9MVJBA==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:03.919630Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.19383","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6740ba8140768db70c4d22a0cfb57dd094a39f4102e08cf56e21068b2d2097d2","sha256:c5b8a45112ef7bca7fb19d054b3de16117f9322e63bbed66ddaf7ce004f20cc6"],"state_sha256":"d8e6e710e8a401f83541ff36a977849ab76fa296a2ddde82ba3c83a99ca15a75"}