{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QMNACNKVXNJ5ZPWOE6TQARNM6S","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":"794bdc607e5a4fd21966138340ac347441a173f8b1b399cffb3cf04280f29c6f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-16T10:10:15Z","title_canon_sha256":"5abec1354a68d23773316fa3b6082ccd82a8353f6e8107b9e32a7c48a59df251"},"schema_version":"1.0","source":{"id":"1212.3772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3772","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3772v2","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3772","created_at":"2026-05-18T03:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"QMNACNKVXNJ5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QMNACNKVXNJ5ZPWO","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QMNACNKV","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:3eb17c8c0870b6b029a5955b3de5eac5f09de759f4ea9af27eccb9b694f8a8fe","target":"graph","created_at":"2026-05-18T03:37:40Z","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":"In this note we give a closed expression for the number of points over finite fields of the Lusztig nilpotent variety associated to any quiver without edge loops, in terms of Kac's A-polynomial. We conjecture a similar result for quivers in which edge loops are allowed. Finally, we give a formula for the number of points over a finite field of the various stratas of the Lusztig nilpotent variety involved in the geometric realization of the crystal graph.","authors_text":"Olivier Schiffmann","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-16T10:10:15Z","title":"On the number of points of the Lusztig nilpotent variety over a finite field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3772","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:ec50b3677e5739764732800216c6866ab4890014ecf9f491aea6001d4cfe5a29","target":"record","created_at":"2026-05-18T03:37:40Z","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":"794bdc607e5a4fd21966138340ac347441a173f8b1b399cffb3cf04280f29c6f","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-16T10:10:15Z","title_canon_sha256":"5abec1354a68d23773316fa3b6082ccd82a8353f6e8107b9e32a7c48a59df251"},"schema_version":"1.0","source":{"id":"1212.3772","kind":"arxiv","version":2}},"canonical_sha256":"831a013555bb53dcbece27a70045acf4a0e0ce1d8e5202a1dd6df8bcf6716552","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"831a013555bb53dcbece27a70045acf4a0e0ce1d8e5202a1dd6df8bcf6716552","first_computed_at":"2026-05-18T03:37:40.486281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:40.486281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GMWKJjjURfxK9VhMq4dXYUN4TiBvydgGzLkp4sb85h33yxIskqqzCe3wFGWmcerebt0w/PptHKWj72qG3WSMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:40.486763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec50b3677e5739764732800216c6866ab4890014ecf9f491aea6001d4cfe5a29","sha256:3eb17c8c0870b6b029a5955b3de5eac5f09de759f4ea9af27eccb9b694f8a8fe"],"state_sha256":"a3d38f5e75f2e8fbcd3ca028d027fe64fed4dffed9f55fa444384637ddc61645"}