{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:D7LDHGGXBYJW6L4KEW7JIRGNE7","short_pith_number":"pith:D7LDHGGX","schema_version":"1.0","canonical_sha256":"1fd63398d70e136f2f8a25be9444cd27cb213548d642908e0f2fad101d807135","source":{"kind":"arxiv","id":"1111.6329","version":1},"attestation_state":"computed","paper":{"title":"W-algebras at the critical level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Tomoyuki Arakawa","submitted_at":"2011-11-28T01:41:03Z","abstract_excerpt":"Let g be a complex simple Lie algebra, f a nilpotent element of g. We show that (1) the center of the W-algebra $W^{cri}(g,f)$ associated with (g,f) at the critical level coincides with the Feigin-Frenkel center of the affine Lie algebra associated with g, (2) the centerless quotient $W_{\\chi}(g,f)$ of $W^{cri}(g,f)$ corresponding to an oper $\\chi$ on the disc is simple, (3) the simple quotient $W_{\\chi}(g,f)$ is a quantization of the jet scheme of the intersection of the Slodowy slice at f with the nilpotent cone of g."},"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":"1111.6329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-11-28T01:41:03Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c98c6bff2dc282d851fa9f817064290d4c6f217fbaa311021a63f7e2b5503dd1","abstract_canon_sha256":"97e078ee937ed95656e073fe687dbb451bcb50ace172881d71efdef247bfd420"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:33.312441Z","signature_b64":"ncdVyjujC3UIEEJ2kn0t9OOiU02F6lYiV3vpiDp59nS0zWdwk/+YwmT/IQidKWz3olLbdFJwEOGVR0CwS83LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fd63398d70e136f2f8a25be9444cd27cb213548d642908e0f2fad101d807135","last_reissued_at":"2026-05-18T01:09:33.312054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:33.312054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"W-algebras at the critical level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Tomoyuki Arakawa","submitted_at":"2011-11-28T01:41:03Z","abstract_excerpt":"Let g be a complex simple Lie algebra, f a nilpotent element of g. We show that (1) the center of the W-algebra $W^{cri}(g,f)$ associated with (g,f) at the critical level coincides with the Feigin-Frenkel center of the affine Lie algebra associated with g, (2) the centerless quotient $W_{\\chi}(g,f)$ of $W^{cri}(g,f)$ corresponding to an oper $\\chi$ on the disc is simple, (3) the simple quotient $W_{\\chi}(g,f)$ is a quantization of the jet scheme of the intersection of the Slodowy slice at f with the nilpotent cone of g."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6329","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":"1111.6329","created_at":"2026-05-18T01:09:33.312113+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6329v1","created_at":"2026-05-18T01:09:33.312113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6329","created_at":"2026-05-18T01:09:33.312113+00:00"},{"alias_kind":"pith_short_12","alias_value":"D7LDHGGXBYJW","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"D7LDHGGXBYJW6L4K","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"D7LDHGGX","created_at":"2026-05-18T12:26:26.731475+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/D7LDHGGXBYJW6L4KEW7JIRGNE7","json":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7.json","graph_json":"https://pith.science/api/pith-number/D7LDHGGXBYJW6L4KEW7JIRGNE7/graph.json","events_json":"https://pith.science/api/pith-number/D7LDHGGXBYJW6L4KEW7JIRGNE7/events.json","paper":"https://pith.science/paper/D7LDHGGX"},"agent_actions":{"view_html":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7","download_json":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7.json","view_paper":"https://pith.science/paper/D7LDHGGX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6329&json=true","fetch_graph":"https://pith.science/api/pith-number/D7LDHGGXBYJW6L4KEW7JIRGNE7/graph.json","fetch_events":"https://pith.science/api/pith-number/D7LDHGGXBYJW6L4KEW7JIRGNE7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7/action/storage_attestation","attest_author":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7/action/author_attestation","sign_citation":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7/action/citation_signature","submit_replication":"https://pith.science/pith/D7LDHGGXBYJW6L4KEW7JIRGNE7/action/replication_record"}},"created_at":"2026-05-18T01:09:33.312113+00:00","updated_at":"2026-05-18T01:09:33.312113+00:00"}