{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7YDWVALFKQEGNLQUVOITE4FRFS","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":"5dd15643d11d15f5f3c8357744ed434447c4c080fdfa5986d14ce948dc8f22c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-10T15:14:30Z","title_canon_sha256":"8c082ba35494da268192376c9eaa441a14a3a22c040da3cebccd9534d2d32bcc"},"schema_version":"1.0","source":{"id":"1511.03132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03132","created_at":"2026-05-18T01:27:16Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03132v1","created_at":"2026-05-18T01:27:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03132","created_at":"2026-05-18T01:27:16Z"},{"alias_kind":"pith_short_12","alias_value":"7YDWVALFKQEG","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7YDWVALFKQEGNLQU","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7YDWVALF","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:9c6950c549c03175dcef809895cfafe6bb8d3921e8efc7caa195efe62a327ef1","target":"graph","created_at":"2026-05-18T01:27:16Z","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":"An $n$-dimensional Lie algebra $\\mathfrak{g}$ over a field $\\mathbb{F}$ of characteristic two is said to be of Vergne type if there is a basis $e_1,\\dots,e_n$ such that $[e_1,e_i]=e_{i+1}$ for all $2\\leq i \\leq n-1$ and $[e_i,e_j] = c_{i,j}e_{i+j}$ for some $c_{i,j} \\in \\mathbb{F}$ for all $i,j \\ge 2$ with $i+j \\le n$. We define the algebra $\\mathfrak{m}_0$ by its nontrivial bracket relations: $[e_1,e_i]=e_{i+1}, 2\\leq i \\leq n-1$, and the algebra $\\mathfrak{m}_2$: $[e_1, e_i ]=e_{i+1}, 2 \\le i \\le n-1$, $[e_2, e_j ]=e_{j+2}, 3 \\le j \\le n-2$.\n  We show that, in contrast to the corresponding r","authors_text":"Ioannis Tsartsaflis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-10T15:14:30Z","title":"On the Betti numbers of filiform Lie algebras over fields of characteristic two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03132","kind":"arxiv","version":1},"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":"sha256:1a90f3e677f81b290d9c5a41fa9f209129f95963665575fc44fd777fe3d2b64a","target":"record","created_at":"2026-05-18T01:27:16Z","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":"5dd15643d11d15f5f3c8357744ed434447c4c080fdfa5986d14ce948dc8f22c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-10T15:14:30Z","title_canon_sha256":"8c082ba35494da268192376c9eaa441a14a3a22c040da3cebccd9534d2d32bcc"},"schema_version":"1.0","source":{"id":"1511.03132","kind":"arxiv","version":1}},"canonical_sha256":"fe076a8165540866ae14ab913270b12c98598eefcb2fb302a67c5c57d4b033ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe076a8165540866ae14ab913270b12c98598eefcb2fb302a67c5c57d4b033ca","first_computed_at":"2026-05-18T01:27:16.932456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:16.932456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1P8T+WPl5xcEjSD5zLHwzInBNt1iQmiBrf6HeCWNlkbioLqKUe1xeBVX5ZH3Uqyl1Z3VRu4T5kwI3zhylmrPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:16.932934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a90f3e677f81b290d9c5a41fa9f209129f95963665575fc44fd777fe3d2b64a","sha256:9c6950c549c03175dcef809895cfafe6bb8d3921e8efc7caa195efe62a327ef1"],"state_sha256":"929fdbe24c484955eca96d87724aaf04cde97ff9a6ffaf874e5d852222597ec5"}