{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:QWWKUR3KHKIAL7HEPIPDBQEWU6","short_pith_number":"pith:QWWKUR3K","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"},"canonical_sha256":"85acaa476a3a9005fce47a1e30c096a7b0e4130ed5aff5d3ef5314dcc59a9acf","source":{"kind":"arxiv","id":"math/9803141","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9803141","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/9803141v2","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9803141","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"QWWKUR3KHKIA","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"pith_short_16","alias_value":"QWWKUR3KHKIAL7HE","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"pith_short_8","alias_value":"QWWKUR3K","created_at":"2026-07-04T14:40:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:QWWKUR3KHKIAL7HEPIPDBQEWU6","target":"record","payload":{"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"},"canonical_sha256":"85acaa476a3a9005fce47a1e30c096a7b0e4130ed5aff5d3ef5314dcc59a9acf","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"},"source_kind":"arxiv","source_id":"math/9803141","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTlV/91Ee0AR0xj3pUvSUoaX+7yWDkGM+FG4qCIZwbLcV4E4IS6cFJ1DehpR81ORQOfroFYwFz4OZptK+bUlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T00:06:42.015997Z"},"content_sha256":"8766d1a4dcf2692569df8bcd6fd5f81b05883d80aa62867f0f0c0226c61fe76a","schema_version":"1.0","event_id":"sha256:8766d1a4dcf2692569df8bcd6fd5f81b05883d80aa62867f0f0c0226c61fe76a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:QWWKUR3KHKIAL7HEPIPDBQEWU6","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gk4X8YzipZkUrSBAsjQSnsBiygaC677j/m8F/Aef/FnmvNP4YPd7S+xZijT7/epFpAB6wDHt08MUEXWe2PqlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T00:06:42.016328Z"},"content_sha256":"8b162d968130187c4084e6c6e68b316069a25997dc1fd6f4c42fa4e76d173f11","schema_version":"1.0","event_id":"sha256:8b162d968130187c4084e6c6e68b316069a25997dc1fd6f4c42fa4e76d173f11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/bundle.json","state_url":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-03T00:06:42Z","links":{"resolver":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6","bundle":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/bundle.json","state":"https://pith.science/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWWKUR3KHKIAL7HEPIPDBQEWU6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:QWWKUR3KHKIAL7HEPIPDBQEWU6","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":"3a2b50c75cb5281f536de7b98b43e0569495758a89a9182ee862686ef38d2b3c","cross_cats_sorted":["math.DG","math.RT"],"license":"","primary_cat":"math.AG","submitted_at":"1998-03-30T03:56:14Z","title_canon_sha256":"08186604ef26413779c9aee6d188737a381989678453b2f970cb5c0cdb1ce15b"},"schema_version":"1.0","source":{"id":"math/9803141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9803141","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/9803141v2","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9803141","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"QWWKUR3KHKIA","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"pith_short_16","alias_value":"QWWKUR3KHKIAL7HE","created_at":"2026-07-04T14:40:29Z"},{"alias_kind":"pith_short_8","alias_value":"QWWKUR3K","created_at":"2026-07-04T14:40:29Z"}],"graph_snapshots":[{"event_id":"sha256:8b162d968130187c4084e6c6e68b316069a25997dc1fd6f4c42fa4e76d173f11","target":"graph","created_at":"2026-07-04T14:40:29Z","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/math/9803141/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Victor Ginzburg","cross_cats":["math.DG","math.RT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"1998-03-30T03:56:14Z","title":"Loop Grassmannian cohomology, the principal nilpotent and Kostant theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9803141","kind":"arxiv","version":2},"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":"sha256:8766d1a4dcf2692569df8bcd6fd5f81b05883d80aa62867f0f0c0226c61fe76a","target":"record","created_at":"2026-07-04T14:40:29Z","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":"3a2b50c75cb5281f536de7b98b43e0569495758a89a9182ee862686ef38d2b3c","cross_cats_sorted":["math.DG","math.RT"],"license":"","primary_cat":"math.AG","submitted_at":"1998-03-30T03:56:14Z","title_canon_sha256":"08186604ef26413779c9aee6d188737a381989678453b2f970cb5c0cdb1ce15b"},"schema_version":"1.0","source":{"id":"math/9803141","kind":"arxiv","version":2}},"canonical_sha256":"85acaa476a3a9005fce47a1e30c096a7b0e4130ed5aff5d3ef5314dcc59a9acf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85acaa476a3a9005fce47a1e30c096a7b0e4130ed5aff5d3ef5314dcc59a9acf","first_computed_at":"2026-07-04T14:40:29.551236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:40:29.551236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Hj388UtkKSwKuHRl7o/uQccgwfy/axgQ25skx95Dcql7EVmH4R0to91m/dHareOERjJgcdpIIJsIf2jeKnEBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:40:29.551594Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9803141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8766d1a4dcf2692569df8bcd6fd5f81b05883d80aa62867f0f0c0226c61fe76a","sha256:8b162d968130187c4084e6c6e68b316069a25997dc1fd6f4c42fa4e76d173f11"],"state_sha256":"24337091b50e3fdaff999601d4baa3c480b9447a329ddffd22d06a0d9ba38b1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BaKDoRwsJZzRzd5cmRqK1PIjk1mSRySHJ09opGY6Ojxe5X/W5H3wxDikCMZ20Ntw+VDEPX4gnOW7h80TLlTZDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T00:06:42.019527Z","bundle_sha256":"81b6b75deea29f24a4c074dd58830c1fc2ae3a44326e551db5535e5fce64556a"}}