{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QNGL5FCZNWPXQ74JVQLKAWDN4S","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":"d7e8954198286dbc25c1b020b371a02a03d516b6a64db951ecca1cceeb8b5b29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-20T21:29:12Z","title_canon_sha256":"3d395b5dc603e59ab974158ad7344ffd7cea8a8787d567865f984387eed5705c"},"schema_version":"1.0","source":{"id":"1308.4438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4438","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4438v2","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4438","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"QNGL5FCZNWPX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QNGL5FCZNWPXQ74J","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QNGL5FCZ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:14103e23419188fa3bb7db6505f522e6ea4a344fc50707b28ae9c2c70878c549","target":"graph","created_at":"2026-05-18T02:55:27Z","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 $N(d,n)$ be the variety of all $d$-tuples of commuting nilpotent $n\\times n$ matrices. It is well-known that $N(d,n)$ is irreducible if $d=2$, if $n\\le 3$ or if $d=3$ and $n=4$. On the other hand $N(3,n)$ is known to be reducible for $n\\ge 13$. We study in this paper the reducibility of $N(d,n)$ for various values of $d$ and $n$. In particular, we prove that $N(d,n)$ is reducible for all $d,n\\ge 4$. In the case $d=3$, we show that it is irreducible for $n\\le 6$.","authors_text":"Klemen \\v{S}ivic, Nham V. Ngo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-20T21:29:12Z","title":"On varieties of commuting nilpotent matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4438","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":"sha256:8457d1693b52b1ba87d4541fdc2338c90627447dfcc516e96d9b967e75c86e02","target":"record","created_at":"2026-05-18T02:55:27Z","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":"d7e8954198286dbc25c1b020b371a02a03d516b6a64db951ecca1cceeb8b5b29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-20T21:29:12Z","title_canon_sha256":"3d395b5dc603e59ab974158ad7344ffd7cea8a8787d567865f984387eed5705c"},"schema_version":"1.0","source":{"id":"1308.4438","kind":"arxiv","version":2}},"canonical_sha256":"834cbe94596d9f787f89ac16a0586de4850e490948d4baf7ede1d523003657a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"834cbe94596d9f787f89ac16a0586de4850e490948d4baf7ede1d523003657a9","first_computed_at":"2026-05-18T02:55:27.551736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:27.551736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pQM1crI2Cow5UGW2egaVPElSSVkmp7MgB+29sgYPeqLBCI9fBgRPac4JKzKRQekdpWSlM+k7sJFr2Bsh2oS5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:27.552344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8457d1693b52b1ba87d4541fdc2338c90627447dfcc516e96d9b967e75c86e02","sha256:14103e23419188fa3bb7db6505f522e6ea4a344fc50707b28ae9c2c70878c549"],"state_sha256":"c1d7a40ce3fde57496342f6f8e52b0944e87b2a34861b65328af3322efa179e8"}