{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:QWWKUR3KHKIAL7HEPIPDBQEWU6","short_pith_number":"pith:QWWKUR3K","schema_version":"1.0","canonical_sha256":"85acaa476a3a9005fce47a1e30c096a7b0e4130ed5aff5d3ef5314dcc59a9acf","source":{"kind":"arxiv","id":"math/9803141","version":2},"attestation_state":"computed","paper":{"title":"Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem","license":"","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.AG","authors_text":"Victor Ginzburg","submitted_at":"1998-03-30T03:56:14Z","abstract_excerpt":"Given a complex projective algebraic variety, write H(X) for its cohomology with complex coefficients and IH(X) for its Intersection cohomology. We first show that, under some fairly general conditions, the canonical map H(X)\\to IH(X) is injective.\n  Now let Gr = G((z))/G[[z]] be the loop Grassmannian for a complex semisimple group G, and let X be the closure of a G[[z]]-orbit in Gr. We prove, using the general result above, a conjecture of D. Peterson describing the cohomology algebra H(X) in terms of the centralizer of the principal nilpotent in the Langlands dual of Lie(G).\n  In the last se"},"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/9803141","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1998-03-30T03:56:14Z","cross_cats_sorted":["math.DG","math.RT"],"title_canon_sha256":"08186604ef26413779c9aee6d188737a381989678453b2f970cb5c0cdb1ce15b","abstract_canon_sha256":"3a2b50c75cb5281f536de7b98b43e0569495758a89a9182ee862686ef38d2b3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:40:29.551594Z","signature_b64":"5Hj388UtkKSwKuHRl7o/uQccgwfy/axgQ25skx95Dcql7EVmH4R0to91m/dHareOERjJgcdpIIJsIf2jeKnEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85acaa476a3a9005fce47a1e30c096a7b0e4130ed5aff5d3ef5314dcc59a9acf","last_reissued_at":"2026-07-04T14:40:29.551236Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:40:29.551236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem","license":"","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.AG","authors_text":"Victor Ginzburg","submitted_at":"1998-03-30T03:56:14Z","abstract_excerpt":"Given a complex projective algebraic variety, write H(X) for its cohomology with complex coefficients and IH(X) for its Intersection cohomology. We first show that, under some fairly general conditions, the canonical map H(X)\\to IH(X) is injective.\n  Now let Gr = G((z))/G[[z]] be the loop Grassmannian for a complex semisimple group G, and let X be the closure of a G[[z]]-orbit in Gr. We prove, using the general result above, a conjecture of D. Peterson describing the cohomology algebra H(X) in terms of the centralizer of the principal nilpotent in the Langlands dual of Lie(G).\n  In the last se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803141","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/math/9803141/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/9803141","created_at":"2026-07-04T14:40:29.551291+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9803141v2","created_at":"2026-07-04T14:40:29.551291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9803141","created_at":"2026-07-04T14:40:29.551291+00:00"},{"alias_kind":"pith_short_12","alias_value":"QWWKUR3KHKIA","created_at":"2026-07-04T14:40:29.551291+00:00"},{"alias_kind":"pith_short_16","alias_value":"QWWKUR3KHKIAL7HE","created_at":"2026-07-04T14:40:29.551291+00:00"},{"alias_kind":"pith_short_8","alias_value":"QWWKUR3K","created_at":"2026-07-04T14:40:29.551291+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/QWWKUR3KHKIAL7HEPIPDBQEWU6","json":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6.json","graph_json":"https://pith.science/api/pith-number/QWWKUR3KHKIAL7HEPIPDBQEWU6/graph.json","events_json":"https://pith.science/api/pith-number/QWWKUR3KHKIAL7HEPIPDBQEWU6/events.json","paper":"https://pith.science/paper/QWWKUR3K"},"agent_actions":{"view_html":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6","download_json":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6.json","view_paper":"https://pith.science/paper/QWWKUR3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9803141&json=true","fetch_graph":"https://pith.science/api/pith-number/QWWKUR3KHKIAL7HEPIPDBQEWU6/graph.json","fetch_events":"https://pith.science/api/pith-number/QWWKUR3KHKIAL7HEPIPDBQEWU6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/action/storage_attestation","attest_author":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/action/author_attestation","sign_citation":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/action/citation_signature","submit_replication":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/action/replication_record"}},"created_at":"2026-07-04T14:40:29.551291+00:00","updated_at":"2026-07-04T14:40:29.551291+00:00"}