{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7YDWVALFKQEGNLQUVOITE4FRFS","short_pith_number":"pith:7YDWVALF","schema_version":"1.0","canonical_sha256":"fe076a8165540866ae14ab913270b12c98598eefcb2fb302a67c5c57d4b033ca","source":{"kind":"arxiv","id":"1511.03132","version":1},"attestation_state":"computed","paper":{"title":"On the Betti numbers of filiform Lie algebras over fields of characteristic two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ioannis Tsartsaflis","submitted_at":"2015-11-10T15:14:30Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.03132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-10T15:14:30Z","cross_cats_sorted":[],"title_canon_sha256":"8c082ba35494da268192376c9eaa441a14a3a22c040da3cebccd9534d2d32bcc","abstract_canon_sha256":"5dd15643d11d15f5f3c8357744ed434447c4c080fdfa5986d14ce948dc8f22c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:16.932934Z","signature_b64":"1P8T+WPl5xcEjSD5zLHwzInBNt1iQmiBrf6HeCWNlkbioLqKUe1xeBVX5ZH3Uqyl1Z3VRu4T5kwI3zhylmrPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe076a8165540866ae14ab913270b12c98598eefcb2fb302a67c5c57d4b033ca","last_reissued_at":"2026-05-18T01:27:16.932456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:16.932456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Betti numbers of filiform Lie algebras over fields of characteristic two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ioannis Tsartsaflis","submitted_at":"2015-11-10T15:14:30Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03132","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.03132","created_at":"2026-05-18T01:27:16.932530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03132v1","created_at":"2026-05-18T01:27:16.932530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03132","created_at":"2026-05-18T01:27:16.932530+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YDWVALFKQEG","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YDWVALFKQEGNLQU","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YDWVALF","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS","json":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS.json","graph_json":"https://pith.science/api/pith-number/7YDWVALFKQEGNLQUVOITE4FRFS/graph.json","events_json":"https://pith.science/api/pith-number/7YDWVALFKQEGNLQUVOITE4FRFS/events.json","paper":"https://pith.science/paper/7YDWVALF"},"agent_actions":{"view_html":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS","download_json":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS.json","view_paper":"https://pith.science/paper/7YDWVALF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03132&json=true","fetch_graph":"https://pith.science/api/pith-number/7YDWVALFKQEGNLQUVOITE4FRFS/graph.json","fetch_events":"https://pith.science/api/pith-number/7YDWVALFKQEGNLQUVOITE4FRFS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS/action/storage_attestation","attest_author":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS/action/author_attestation","sign_citation":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS/action/citation_signature","submit_replication":"https://pith.science/pith/7YDWVALFKQEGNLQUVOITE4FRFS/action/replication_record"}},"created_at":"2026-05-18T01:27:16.932530+00:00","updated_at":"2026-05-18T01:27:16.932530+00:00"}