{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:5LBPIJCXZRAI5KJ223NS6O43WX","short_pith_number":"pith:5LBPIJCX","schema_version":"1.0","canonical_sha256":"eac2f42457cc408ea93ad6db2f3b9bb5f22c81ab393968e658672e374300106f","source":{"kind":"arxiv","id":"2106.11356","version":1},"attestation_state":"computed","paper":{"title":"The virtual intersection theory of isotropic Quot Schemes","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shubham Sinha","submitted_at":"2021-06-21T18:39:57Z","abstract_excerpt":"Isotropic Quot schemes parameterize rank $r$ isotropic subsheaves of a vector bundle equipped with symplectic or symmetric quadratic form. We define a virtual fundamental class for isotropic Quot schemes over smooth projective curves. Using torus localization, we prescribe a way to calculate top intersection numbers of tautological classes, and obtain explicit formulas when $r=2$. These include and generalize the Vafa-Intriligator formula. In this setting, we compare the Quot scheme invariants with the invariants obtained via the stable map compactification."},"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":"2106.11356","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2021-06-21T18:39:57Z","cross_cats_sorted":[],"title_canon_sha256":"9437fdd05cdedb4e25204c9511e84478ccf1dd7d2c88108363826355a491526d","abstract_canon_sha256":"3c85401f8e1debad0cb60aa91b23cce2d59b1d9ab0dd3dfa3129acd4240f343f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:51:28.457558Z","signature_b64":"BRURJACH4wEvl28Nsmuq1+SKD0+i4rSb6uO5QGWyds7Pr0A6+f6cvtnoLWRrJb51vxka0bBzsLFF1P8b/IC+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eac2f42457cc408ea93ad6db2f3b9bb5f22c81ab393968e658672e374300106f","last_reissued_at":"2026-07-05T02:51:28.457109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:51:28.457109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The virtual intersection theory of isotropic Quot Schemes","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shubham Sinha","submitted_at":"2021-06-21T18:39:57Z","abstract_excerpt":"Isotropic Quot schemes parameterize rank $r$ isotropic subsheaves of a vector bundle equipped with symplectic or symmetric quadratic form. We define a virtual fundamental class for isotropic Quot schemes over smooth projective curves. Using torus localization, we prescribe a way to calculate top intersection numbers of tautological classes, and obtain explicit formulas when $r=2$. These include and generalize the Vafa-Intriligator formula. In this setting, we compare the Quot scheme invariants with the invariants obtained via the stable map compactification."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.11356","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/2106.11356/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":"2106.11356","created_at":"2026-07-05T02:51:28.457163+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.11356v1","created_at":"2026-07-05T02:51:28.457163+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.11356","created_at":"2026-07-05T02:51:28.457163+00:00"},{"alias_kind":"pith_short_12","alias_value":"5LBPIJCXZRAI","created_at":"2026-07-05T02:51:28.457163+00:00"},{"alias_kind":"pith_short_16","alias_value":"5LBPIJCXZRAI5KJ2","created_at":"2026-07-05T02:51:28.457163+00:00"},{"alias_kind":"pith_short_8","alias_value":"5LBPIJCX","created_at":"2026-07-05T02:51:28.457163+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/5LBPIJCXZRAI5KJ223NS6O43WX","json":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX.json","graph_json":"https://pith.science/api/pith-number/5LBPIJCXZRAI5KJ223NS6O43WX/graph.json","events_json":"https://pith.science/api/pith-number/5LBPIJCXZRAI5KJ223NS6O43WX/events.json","paper":"https://pith.science/paper/5LBPIJCX"},"agent_actions":{"view_html":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX","download_json":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX.json","view_paper":"https://pith.science/paper/5LBPIJCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.11356&json=true","fetch_graph":"https://pith.science/api/pith-number/5LBPIJCXZRAI5KJ223NS6O43WX/graph.json","fetch_events":"https://pith.science/api/pith-number/5LBPIJCXZRAI5KJ223NS6O43WX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX/action/storage_attestation","attest_author":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX/action/author_attestation","sign_citation":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX/action/citation_signature","submit_replication":"https://pith.science/pith/5LBPIJCXZRAI5KJ223NS6O43WX/action/replication_record"}},"created_at":"2026-07-05T02:51:28.457163+00:00","updated_at":"2026-07-05T02:51:28.457163+00:00"}