{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AK33D2R7PQWWJFWMGVTFBR5DOI","short_pith_number":"pith:AK33D2R7","schema_version":"1.0","canonical_sha256":"02b7b1ea3f7c2d6496cc356650c7a3720755f93c699f8f58193b9c0fbc30b3f2","source":{"kind":"arxiv","id":"1608.07645","version":1},"attestation_state":"computed","paper":{"title":"An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.QA"],"primary_cat":"math.AT","authors_text":"Masaaki Suzuki, Shigeyuki Morita, Takuya Sakasai","submitted_at":"2016-08-27T01:59:51Z","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."},"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":"1608.07645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-08-27T01:59:51Z","cross_cats_sorted":["math.GT","math.QA"],"title_canon_sha256":"16bbfce9d8996d1ebc6b08ede0ab7434d6612a8796ba91f0f4f66e5af3ca0735","abstract_canon_sha256":"ea068a2c42e808be94a755eacbbfdb5b6c619666ba97bbcc332e7843b8b45846"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:42.028291Z","signature_b64":"nXrABDxFXZBjkgG/sPJOi4Z/9EH57T7XbG6z9Yq5xNYTNh1K56C9AJDh4CCqoAxuwBLtPna1WRW0WMexCfITAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02b7b1ea3f7c2d6496cc356650c7a3720755f93c699f8f58193b9c0fbc30b3f2","last_reissued_at":"2026-05-18T00:04:42.027714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:42.027714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An abelian quotient of the symplectic derivation Lie algebra of the free Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.QA"],"primary_cat":"math.AT","authors_text":"Masaaki Suzuki, Shigeyuki Morita, Takuya Sakasai","submitted_at":"2016-08-27T01:59:51Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07645","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":"1608.07645","created_at":"2026-05-18T00:04:42.027807+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.07645v1","created_at":"2026-05-18T00:04:42.027807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07645","created_at":"2026-05-18T00:04:42.027807+00:00"},{"alias_kind":"pith_short_12","alias_value":"AK33D2R7PQWW","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AK33D2R7PQWWJFWM","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AK33D2R7","created_at":"2026-05-18T12:30:07.202191+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/AK33D2R7PQWWJFWMGVTFBR5DOI","json":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI.json","graph_json":"https://pith.science/api/pith-number/AK33D2R7PQWWJFWMGVTFBR5DOI/graph.json","events_json":"https://pith.science/api/pith-number/AK33D2R7PQWWJFWMGVTFBR5DOI/events.json","paper":"https://pith.science/paper/AK33D2R7"},"agent_actions":{"view_html":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI","download_json":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI.json","view_paper":"https://pith.science/paper/AK33D2R7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.07645&json=true","fetch_graph":"https://pith.science/api/pith-number/AK33D2R7PQWWJFWMGVTFBR5DOI/graph.json","fetch_events":"https://pith.science/api/pith-number/AK33D2R7PQWWJFWMGVTFBR5DOI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI/action/storage_attestation","attest_author":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI/action/author_attestation","sign_citation":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI/action/citation_signature","submit_replication":"https://pith.science/pith/AK33D2R7PQWWJFWMGVTFBR5DOI/action/replication_record"}},"created_at":"2026-05-18T00:04:42.027807+00:00","updated_at":"2026-05-18T00:04:42.027807+00:00"}