{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T3A2ZPCLTKTAETREL5YK6D4XEW","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":"c50fd6b9c04d00e8f5c6f67ba9ad510c2dc20d77a5a456e97fc92543ec66ad70","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-04T13:08:08Z","title_canon_sha256":"4954d42b5269a6641b649e25d45ffdde3fbb8f2201c3c134c652c4dea99df64e"},"schema_version":"1.0","source":{"id":"1908.01337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01337","created_at":"2026-07-05T08:51:08Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01337v2","created_at":"2026-07-05T08:51:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01337","created_at":"2026-07-05T08:51:08Z"},{"alias_kind":"pith_short_12","alias_value":"T3A2ZPCLTKTA","created_at":"2026-07-05T08:51:08Z"},{"alias_kind":"pith_short_16","alias_value":"T3A2ZPCLTKTAETRE","created_at":"2026-07-05T08:51:08Z"},{"alias_kind":"pith_short_8","alias_value":"T3A2ZPCL","created_at":"2026-07-05T08:51:08Z"}],"graph_snapshots":[{"event_id":"sha256:f93ae0bb2cc5ecc18e348b0ba54479a85e223d06a728bfab34d359fbb990faf1","target":"graph","created_at":"2026-07-05T08:51:08Z","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/1908.01337/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let G be an almost simple group over an algebraically closed field k of characteristic zero, let g be its Lie algebra and let B be a Borel subgroup of G. Then B acts with finitely many orbits on the variety N_2 of the nilpotent elements in g whose height is at most 2. We provide a parametrization of the B-orbits in N_2 in terms of subsets of pairwise orthogonal roots, and we provide a complete description of the inclusion order among the B-orbit closures in terms of the Bruhat order on certain involutions in the affine Weyl group of g.","authors_text":"Jacopo Gandini, Paolo Papi, Pierluigi Moseneder Frajria","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-04T13:08:08Z","title":"Nilpotent orbits of height 2 and involutions in the affine Weyl group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01337","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:daf1423c4e5ce1024178f6db593cf0fd01e3e69b32a3167d7b1031ff5823588c","target":"record","created_at":"2026-07-05T08:51:08Z","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":"c50fd6b9c04d00e8f5c6f67ba9ad510c2dc20d77a5a456e97fc92543ec66ad70","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-08-04T13:08:08Z","title_canon_sha256":"4954d42b5269a6641b649e25d45ffdde3fbb8f2201c3c134c652c4dea99df64e"},"schema_version":"1.0","source":{"id":"1908.01337","kind":"arxiv","version":2}},"canonical_sha256":"9ec1acbc4b9aa6024e245f70af0f972594c55ae5d16e31930e431888a2fd8b66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ec1acbc4b9aa6024e245f70af0f972594c55ae5d16e31930e431888a2fd8b66","first_computed_at":"2026-07-05T08:51:08.592330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:51:08.592330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"il2aBnWdUGDvhas4FE5TlvQrDTPwvyZuZwzKzR39g6KpQaR27eQ9ihaG4X6y48C5Wj9y6RGMBBsGfwPJM3x/Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:51:08.592731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daf1423c4e5ce1024178f6db593cf0fd01e3e69b32a3167d7b1031ff5823588c","sha256:f93ae0bb2cc5ecc18e348b0ba54479a85e223d06a728bfab34d359fbb990faf1"],"state_sha256":"5d6b80c35073a6456a031e8df681c5b02cd3bdbe2ad47e6ad3974c0cab517285"}