{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:QCKKBTGJJZ6QWR6R2JRCVRRYTB","short_pith_number":"pith:QCKKBTGJ","schema_version":"1.0","canonical_sha256":"8094a0ccc94e7d0b47d1d2622ac638986adb04432f4f413089a051738c3ceabe","source":{"kind":"arxiv","id":"math/0302204","version":1},"attestation_state":"computed","paper":{"title":"Nilpotent commuting varieties of reductive Lie algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Premet","submitted_at":"2003-02-18T11:27:24Z","abstract_excerpt":"We prove that the nilpotent commuting variety of a reductive Lie algebra over an algebraically closed field of good characteristic is equidimensional. In characteristic zero, this confirms a conjecture of Vladimir Baranovsky. As a by-product, we obtain tat the punctual (local) Hilbert scheme parametrising the ideals of colength $n$ in $k[[X,Y]]$ is irreducible over any algebraically closed field $k$."},"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/0302204","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2003-02-18T11:27:24Z","cross_cats_sorted":[],"title_canon_sha256":"8dd09af9890f4a12c94de8a8fbe38cf9847a6a0b589fce7978cb4b16d075e750","abstract_canon_sha256":"224ba5a1fe9c28393a94a23d4a6650e6338135b102c1b0bdca12800284570380"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:29.171174Z","signature_b64":"lTuudcB/Z4GxZyZr4hI/c2V78NfosU+qz+yWx14lJ8zp7bik2KlidTeUeBfEi+EhZ7fwAtgVtq34YAMYS0RCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8094a0ccc94e7d0b47d1d2622ac638986adb04432f4f413089a051738c3ceabe","last_reissued_at":"2026-05-18T01:38:29.170515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:29.170515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nilpotent commuting varieties of reductive Lie algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Premet","submitted_at":"2003-02-18T11:27:24Z","abstract_excerpt":"We prove that the nilpotent commuting variety of a reductive Lie algebra over an algebraically closed field of good characteristic is equidimensional. In characteristic zero, this confirms a conjecture of Vladimir Baranovsky. As a by-product, we obtain tat the punctual (local) Hilbert scheme parametrising the ideals of colength $n$ in $k[[X,Y]]$ is irreducible over any algebraically closed field $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0302204","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":"math/0302204","created_at":"2026-05-18T01:38:29.170642+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0302204v1","created_at":"2026-05-18T01:38:29.170642+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0302204","created_at":"2026-05-18T01:38:29.170642+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCKKBTGJJZ6Q","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCKKBTGJJZ6QWR6R","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCKKBTGJ","created_at":"2026-05-18T12:25:52.051335+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/QCKKBTGJJZ6QWR6R2JRCVRRYTB","json":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB.json","graph_json":"https://pith.science/api/pith-number/QCKKBTGJJZ6QWR6R2JRCVRRYTB/graph.json","events_json":"https://pith.science/api/pith-number/QCKKBTGJJZ6QWR6R2JRCVRRYTB/events.json","paper":"https://pith.science/paper/QCKKBTGJ"},"agent_actions":{"view_html":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB","download_json":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB.json","view_paper":"https://pith.science/paper/QCKKBTGJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0302204&json=true","fetch_graph":"https://pith.science/api/pith-number/QCKKBTGJJZ6QWR6R2JRCVRRYTB/graph.json","fetch_events":"https://pith.science/api/pith-number/QCKKBTGJJZ6QWR6R2JRCVRRYTB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB/action/storage_attestation","attest_author":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB/action/author_attestation","sign_citation":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB/action/citation_signature","submit_replication":"https://pith.science/pith/QCKKBTGJJZ6QWR6R2JRCVRRYTB/action/replication_record"}},"created_at":"2026-05-18T01:38:29.170642+00:00","updated_at":"2026-05-18T01:38:29.170642+00:00"}