{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AK33D2R7PQWWJFWMGVTFBR5DOI","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":"ea068a2c42e808be94a755eacbbfdb5b6c619666ba97bbcc332e7843b8b45846","cross_cats_sorted":["math.GT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-27T01:59:51Z","title_canon_sha256":"16bbfce9d8996d1ebc6b08ede0ab7434d6612a8796ba91f0f4f66e5af3ca0735"},"schema_version":"1.0","source":{"id":"1608.07645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07645","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07645v1","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07645","created_at":"2026-05-18T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"AK33D2R7PQWW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AK33D2R7PQWWJFWM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AK33D2R7","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:785c827c982cd28e25f76938fd536179a7466b894d36a9fde33e406c47dca1d4","target":"graph","created_at":"2026-05-18T00:04:42Z","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":"We construct an abelian quotient of the symplectic derivation Lie algebra $\\mathfrak{h}_{g,1}$ of the free Lie algebra generated by the fundamental representation of $\\mathrm{Sp}(2g,\\mathbb{Q})$. More specifically, we show that the weight $12$ part of the abelianization of $\\mathfrak{h}_{g,1}$ is $1$-dimensional for $g \\ge 8$. The computation is done with the aid of computers.","authors_text":"Masaaki Suzuki, Shigeyuki Morita, Takuya Sakasai","cross_cats":["math.GT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-27T01:59:51Z","title":"An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07645","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:d9e524bb3731108d5b1182abbef3ae10b3222593d744cd674ef15b69dea8613a","target":"record","created_at":"2026-05-18T00:04:42Z","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":"ea068a2c42e808be94a755eacbbfdb5b6c619666ba97bbcc332e7843b8b45846","cross_cats_sorted":["math.GT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-27T01:59:51Z","title_canon_sha256":"16bbfce9d8996d1ebc6b08ede0ab7434d6612a8796ba91f0f4f66e5af3ca0735"},"schema_version":"1.0","source":{"id":"1608.07645","kind":"arxiv","version":1}},"canonical_sha256":"02b7b1ea3f7c2d6496cc356650c7a3720755f93c699f8f58193b9c0fbc30b3f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02b7b1ea3f7c2d6496cc356650c7a3720755f93c699f8f58193b9c0fbc30b3f2","first_computed_at":"2026-05-18T00:04:42.027714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:42.027714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nXrABDxFXZBjkgG/sPJOi4Z/9EH57T7XbG6z9Yq5xNYTNh1K56C9AJDh4CCqoAxuwBLtPna1WRW0WMexCfITAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:42.028291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9e524bb3731108d5b1182abbef3ae10b3222593d744cd674ef15b69dea8613a","sha256:785c827c982cd28e25f76938fd536179a7466b894d36a9fde33e406c47dca1d4"],"state_sha256":"14c8cb5e1a78c06b77938699efaadb069b00261262fa1a5c19318860a102e290"}