{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:TCD7P66E5IXDJIEZFDDMIYN4MZ","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":"07217c72a1967283899a7a1c2e71ec3fe047c692a222bba1512c29de6793cb75","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-08-14T18:35:19Z","title_canon_sha256":"305aa3ae04ce7cad3145f2b153dd2fcbf4070b3bc1ce8d716462520348b78b68"},"schema_version":"1.0","source":{"id":"2308.07398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.07398","created_at":"2026-07-05T07:47:04Z"},{"alias_kind":"arxiv_version","alias_value":"2308.07398v2","created_at":"2026-07-05T07:47:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.07398","created_at":"2026-07-05T07:47:04Z"},{"alias_kind":"pith_short_12","alias_value":"TCD7P66E5IXD","created_at":"2026-07-05T07:47:04Z"},{"alias_kind":"pith_short_16","alias_value":"TCD7P66E5IXDJIEZ","created_at":"2026-07-05T07:47:04Z"},{"alias_kind":"pith_short_8","alias_value":"TCD7P66E","created_at":"2026-07-05T07:47:04Z"}],"graph_snapshots":[{"event_id":"sha256:62fbce36bd92382bd6e667088ed7dd35a5218453e01ea61ea5a6c421c28454e8","target":"graph","created_at":"2026-07-05T07:47:04Z","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/2308.07398/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The nilpotent cone of a simple Lie algebra is partitioned into locally closed subvarieties called special pieces, each containing exactly one special orbit. Lusztig conjectured that each special piece is the quotient of some smooth variety by a precise finite group $H$, a result proved for the classical types by Kraft and Procesi. The present work is about exceptional types. Our main result is a local version of Lusztig's conjecture: the intersection of a special piece with a Slodowy slice transverse to the minimal orbit in the piece is isomorphic to the quotient of a vector space by $H$. Alon","authors_text":"Baohua Fu, Daniel Juteau, Eric Sommers, Paul Levy","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-08-14T18:35:19Z","title":"Local geometry of special pieces of nilpotent orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.07398","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":"sha256:137261a71c9f2cfdc7e873d9e173c48da029b56a46672929453f80ef9b798b3b","target":"record","created_at":"2026-07-05T07:47:04Z","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":"07217c72a1967283899a7a1c2e71ec3fe047c692a222bba1512c29de6793cb75","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-08-14T18:35:19Z","title_canon_sha256":"305aa3ae04ce7cad3145f2b153dd2fcbf4070b3bc1ce8d716462520348b78b68"},"schema_version":"1.0","source":{"id":"2308.07398","kind":"arxiv","version":2}},"canonical_sha256":"9887f7fbc4ea2e34a09928c6c461bc664e1af743b8790838211e0eb2f9b951bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9887f7fbc4ea2e34a09928c6c461bc664e1af743b8790838211e0eb2f9b951bd","first_computed_at":"2026-07-05T07:47:04.146498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:47:04.146498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cwyhOh5QFp0YWrF3RDwOsTjQmmJXOiuuxzwfZhkJr0T07iBOENA4BI6Tg1iHNIHP7S6GTL5dPZVrNKApzTE2Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:47:04.146919Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.07398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:137261a71c9f2cfdc7e873d9e173c48da029b56a46672929453f80ef9b798b3b","sha256:62fbce36bd92382bd6e667088ed7dd35a5218453e01ea61ea5a6c421c28454e8"],"state_sha256":"093eebd9e5a19f72920eb27be890c2baf96fc7e9826b3c4a01ff54bd757b307a"}