{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:ENN6TY55CXNM7SOYRKKFORPSEJ","short_pith_number":"pith:ENN6TY55","schema_version":"1.0","canonical_sha256":"235be9e3bd15dacfc9d88a945745f222429dc4581ecc80f6c51ac96d8cd83efe","source":{"kind":"arxiv","id":"math/0611945","version":1},"attestation_state":"computed","paper":{"title":"K-theoretic Donaldson invariants via instanton counting","license":"","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"math.AG","authors_text":"Hiraku Nakajima, Kota Yoshioka, Lothar G\\\"ottsche","submitted_at":"2006-11-30T12:20:31Z","abstract_excerpt":"In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In particular, if X is a smooth projective toric surface, we determine these invariants and their wallcrossing in terms of the K-theoretic version of the Nekrasov partition function (called 5-dimensional supersymmetric Yang-Mills theory compactified on a circle in the physics literature). Using the results of math.AG/0606180 we give an explicit generating funct"},"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":"math/0611945","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-11-30T12:20:31Z","cross_cats_sorted":["hep-th","math.DG"],"title_canon_sha256":"6fa6d793ba3ee87e947af5779a4f1823da4fb4e3ad1b8dd7accc2ba35bab65b5","abstract_canon_sha256":"45a55e1174423fa8b20f859ee8709b428ee4eed97b823a31d2916740e228dd5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:57:42.975385Z","signature_b64":"kHcvNpOxtjSqmtYzSTLQQU3aHEyfZ+ehPpc57d1bQw5JNl9880NlaL4SIluI6uy2W7xtssw1D6EFaNrryejQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"235be9e3bd15dacfc9d88a945745f222429dc4581ecc80f6c51ac96d8cd83efe","last_reissued_at":"2026-07-04T14:57:42.975007Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:57:42.975007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"K-theoretic Donaldson invariants via instanton counting","license":"","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"math.AG","authors_text":"Hiraku Nakajima, Kota Yoshioka, Lothar G\\\"ottsche","submitted_at":"2006-11-30T12:20:31Z","abstract_excerpt":"In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In particular, if X is a smooth projective toric surface, we determine these invariants and their wallcrossing in terms of the K-theoretic version of the Nekrasov partition function (called 5-dimensional supersymmetric Yang-Mills theory compactified on a circle in the physics literature). Using the results of math.AG/0606180 we give an explicit generating funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611945","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0611945/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":"math/0611945","created_at":"2026-07-04T14:57:42.975069+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0611945v1","created_at":"2026-07-04T14:57:42.975069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611945","created_at":"2026-07-04T14:57:42.975069+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENN6TY55CXNM","created_at":"2026-07-04T14:57:42.975069+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENN6TY55CXNM7SOY","created_at":"2026-07-04T14:57:42.975069+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENN6TY55","created_at":"2026-07-04T14:57:42.975069+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06663","citing_title":"Generalised global symmetries in 5d $\\mathcal{N}=1$ theories from the blow-up equations","ref_index":34,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ","json":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ.json","graph_json":"https://pith.science/api/pith-number/ENN6TY55CXNM7SOYRKKFORPSEJ/graph.json","events_json":"https://pith.science/api/pith-number/ENN6TY55CXNM7SOYRKKFORPSEJ/events.json","paper":"https://pith.science/paper/ENN6TY55"},"agent_actions":{"view_html":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ","download_json":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ.json","view_paper":"https://pith.science/paper/ENN6TY55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0611945&json=true","fetch_graph":"https://pith.science/api/pith-number/ENN6TY55CXNM7SOYRKKFORPSEJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ENN6TY55CXNM7SOYRKKFORPSEJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ/action/storage_attestation","attest_author":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ/action/author_attestation","sign_citation":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ/action/citation_signature","submit_replication":"https://pith.science/pith/ENN6TY55CXNM7SOYRKKFORPSEJ/action/replication_record"}},"created_at":"2026-07-04T14:57:42.975069+00:00","updated_at":"2026-07-04T14:57:42.975069+00:00"}