{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UZB2HMRWF2HZAVVK5ENE4YQQZ2","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":"b485c8b577e98a91fe4ecd398167714d59519bc56bd4dc002a75e65eccbdbf38","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-10-24T13:18:32Z","title_canon_sha256":"597a15a47c7040a1881c986cce059dea26eef9845489e3a6bea8717156e45f9f"},"schema_version":"1.0","source":{"id":"0710.4464","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.4464","created_at":"2026-05-18T04:34:55Z"},{"alias_kind":"arxiv_version","alias_value":"0710.4464v4","created_at":"2026-05-18T04:34:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.4464","created_at":"2026-05-18T04:34:55Z"},{"alias_kind":"pith_short_12","alias_value":"UZB2HMRWF2HZ","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UZB2HMRWF2HZAVVK","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UZB2HMRW","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:6f48fb8cc9cb84400fc1af1edad515cbc7532066e128cab903e4fc6c8510653e","target":"graph","created_at":"2026-05-18T04:34:55Z","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"},"paper":{"abstract_excerpt":"Let \\theta be an involution of the semisimple Lie algebra g and g=k+p be the associated Cartan decomposition. The nilpotent commuting variety of (g,\\theta) consists in pairs of nilpotent elements (x,y) of p such that [x,y]=0. It is conjectured that this variety is equidimensional and that its irreducible components are indexed by the orbits of p-distinguished elements. This conjecture was established by A. Premet in the case (g \\times g, \\theta) where \\theta(x,y)=(y,x). In this work we prove the conjecture in a significant number of other cases.","authors_text":"Michael Bulois","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-10-24T13:18:32Z","title":"Composantes irr\\'eductibles de la vari\\'et\\'e commutante nilpotente d'une alg\\`ebre de Lie sym\\'etrique semi-simple"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4464","kind":"arxiv","version":4},"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":"sha256:9e5a44e6105ffc77a9bee6d409643a24f4139ae17894888cef61ed5756c47e91","target":"record","created_at":"2026-05-18T04:34:55Z","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":"b485c8b577e98a91fe4ecd398167714d59519bc56bd4dc002a75e65eccbdbf38","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2007-10-24T13:18:32Z","title_canon_sha256":"597a15a47c7040a1881c986cce059dea26eef9845489e3a6bea8717156e45f9f"},"schema_version":"1.0","source":{"id":"0710.4464","kind":"arxiv","version":4}},"canonical_sha256":"a643a3b2362e8f9056aae91a4e6210ce9253bcd4131e196919a8e82dfdb53486","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a643a3b2362e8f9056aae91a4e6210ce9253bcd4131e196919a8e82dfdb53486","first_computed_at":"2026-05-18T04:34:55.646961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:55.646961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JxMU/3IDxjt8qW7x/MZ2MU7c6j065BysbRbVQqawcwk4GedLCMJBiXBhC1azJ6lLzxnR8pNNSFvUmPosdGw5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:55.647347Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.4464","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e5a44e6105ffc77a9bee6d409643a24f4139ae17894888cef61ed5756c47e91","sha256:6f48fb8cc9cb84400fc1af1edad515cbc7532066e128cab903e4fc6c8510653e"],"state_sha256":"66796b9dbac242f637764bfd19372d2235ab6f1a3749bf25be3ff12fff701a0e"}