{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T52RTLSHXOTN3SWZAGB2UHJIZW","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":"5584271daf30d7dce19df1b9416297126e5395622da47dff1200e4d1b7297dce","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-04-13T07:26:44Z","title_canon_sha256":"b0c16ba042bd1dd776799d37d934eff9c7f933640649fc443db52b7186a2b2c9"},"schema_version":"1.0","source":{"id":"1404.3351","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3351","created_at":"2026-07-05T01:12:15Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3351v2","created_at":"2026-07-05T01:12:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3351","created_at":"2026-07-05T01:12:15Z"},{"alias_kind":"pith_short_12","alias_value":"T52RTLSHXOTN","created_at":"2026-07-05T01:12:15Z"},{"alias_kind":"pith_short_16","alias_value":"T52RTLSHXOTN3SWZ","created_at":"2026-07-05T01:12:15Z"},{"alias_kind":"pith_short_8","alias_value":"T52RTLSH","created_at":"2026-07-05T01:12:15Z"}],"graph_snapshots":[{"event_id":"sha256:36ddb660c1d73276134f3853f06bc3ded80d5cadd9fc2970f85e88d39d7174ce","target":"graph","created_at":"2026-07-05T01:12:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1404.3351/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the structure of the symplectic invariant part $\\mathfrak{h}_{g,1}^{\\mathrm{Sp}}$ of the Lie algebra $\\mathfrak{h}_{g,1}$ consisting of symplectic derivations of the free Lie algebra generated by the rational homology group of a closed oriented surface $\\Sigma_{g}$ of genus $g$.\n  First we describe the orthogonal direct sum decomposition of this space which is induced by the canonical metric on it and compute it explicitly up to degree $20$. In this framework, we give a general constraint which is imposed on the $\\mathrm{Sp}$-invariant component of the bracket of two elements in $\\mat","authors_text":"Masaaki Suzuki, Shigeyuki Morita, Takuya Sakasai","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-04-13T07:26:44Z","title":"Structure of symplectic invariant Lie subalgebras of symplectic derivation Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3351","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":"sha256:0139beaa67afae264a72e96b42dd3641dff8e6fae201d7da01eed82da3e37bfc","target":"record","created_at":"2026-07-05T01:12:15Z","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":"5584271daf30d7dce19df1b9416297126e5395622da47dff1200e4d1b7297dce","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-04-13T07:26:44Z","title_canon_sha256":"b0c16ba042bd1dd776799d37d934eff9c7f933640649fc443db52b7186a2b2c9"},"schema_version":"1.0","source":{"id":"1404.3351","kind":"arxiv","version":2}},"canonical_sha256":"9f7519ae47bba6ddcad90183aa1d28cdaded9fd560aebbc66e87b27512509f54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f7519ae47bba6ddcad90183aa1d28cdaded9fd560aebbc66e87b27512509f54","first_computed_at":"2026-07-05T01:12:15.992938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:12:15.992938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZqVR4VF+WROs+PO2JNwK7ttZLSpSbxkXrqaSOvYwZhNsY41YPcwSLRKjg7RlNnblih7NsiQVrS9ECtRpWa/9AA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:12:15.993312Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3351","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0139beaa67afae264a72e96b42dd3641dff8e6fae201d7da01eed82da3e37bfc","sha256:36ddb660c1d73276134f3853f06bc3ded80d5cadd9fc2970f85e88d39d7174ce"],"state_sha256":"0aa85e39fe72d2c9dfe47a29f751025afa7efc560d9a2fe3a59cc0f4c6613b12"}