{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:H7YWNAUSJSJJ5YC3WXNIAH5QAZ","short_pith_number":"pith:H7YWNAUS","schema_version":"1.0","canonical_sha256":"3ff16682924c929ee05bb5da801fb0065746f8b3032484c2e5aa73deaf777fdb","source":{"kind":"arxiv","id":"1612.01048","version":1},"attestation_state":"computed","paper":{"title":"Rationality of capped descendent vertex in $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"primary_cat":"math.AG","authors_text":"Andrey Smirnov","submitted_at":"2016-12-04T02:06:13Z","abstract_excerpt":"In this paper we analyze the fundamental solution of the \\textit{quantum difference equation} (qde) for the moduli space of instantons on two-dimensional projective space. The qde is a $K$-theoretic generalization of the quantum differential equation in quantum cohomology. As in the quantum cohomology case, the fundamental solution of qde provides the capping operator in $K$-theory (the rubber part of the capped vertex). We study the dependence of the capping operator on the equivariant parameters $a_i$ of the torus acting on the instanton moduli space by changing the framing. We prove that th"},"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":"1612.01048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-04T02:06:13Z","cross_cats_sorted":["hep-th","math-ph","math.MP","math.RT"],"title_canon_sha256":"36a5f2c0769237ab3add16a1215a291c4a259f3301320693ac7438a72c55e10b","abstract_canon_sha256":"3b3e55bcc3af9857e73988e5edc5b4098b50d15c5c3dcf59810618726e9958e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:48.265158Z","signature_b64":"f0ossL5D/g2KeTGcUyZUMjNuHc9Do4fZlY82BPiJ7N5Xl+X5aun+PU9aj+xulZcv3boLlrJjrHjaSWqcvd12BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ff16682924c929ee05bb5da801fb0065746f8b3032484c2e5aa73deaf777fdb","last_reissued_at":"2026-05-18T00:55:48.264511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:48.264511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rationality of capped descendent vertex in $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"primary_cat":"math.AG","authors_text":"Andrey Smirnov","submitted_at":"2016-12-04T02:06:13Z","abstract_excerpt":"In this paper we analyze the fundamental solution of the \\textit{quantum difference equation} (qde) for the moduli space of instantons on two-dimensional projective space. The qde is a $K$-theoretic generalization of the quantum differential equation in quantum cohomology. As in the quantum cohomology case, the fundamental solution of qde provides the capping operator in $K$-theory (the rubber part of the capped vertex). We study the dependence of the capping operator on the equivariant parameters $a_i$ of the torus acting on the instanton moduli space by changing the framing. We prove that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01048","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.01048","created_at":"2026-05-18T00:55:48.264619+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.01048v1","created_at":"2026-05-18T00:55:48.264619+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01048","created_at":"2026-05-18T00:55:48.264619+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7YWNAUSJSJJ","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7YWNAUSJSJJ5YC3","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7YWNAUS","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.17665","citing_title":"Rationality of the K-theoretical capped vertex function for Nakajima quiver varieties","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ","json":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ.json","graph_json":"https://pith.science/api/pith-number/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/graph.json","events_json":"https://pith.science/api/pith-number/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/events.json","paper":"https://pith.science/paper/H7YWNAUS"},"agent_actions":{"view_html":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ","download_json":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ.json","view_paper":"https://pith.science/paper/H7YWNAUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.01048&json=true","fetch_graph":"https://pith.science/api/pith-number/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/action/storage_attestation","attest_author":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/action/author_attestation","sign_citation":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/action/citation_signature","submit_replication":"https://pith.science/pith/H7YWNAUSJSJJ5YC3WXNIAH5QAZ/action/replication_record"}},"created_at":"2026-05-18T00:55:48.264619+00:00","updated_at":"2026-05-18T00:55:48.264619+00:00"}