{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GJPCS6SUGSVKZCHYJ37AZF36QR","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":"c37be57d5bed2281de84c523f10470456819fd59fe32a68e5b789946a46601d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-02T00:17:56Z","title_canon_sha256":"cb5d40b0ce44caf74a2b228c5f33143393ee2f9678af592e2338d0e342c0800a"},"schema_version":"1.0","source":{"id":"1407.0428","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0428","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0428v2","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0428","created_at":"2026-05-18T02:28:55Z"},{"alias_kind":"pith_short_12","alias_value":"GJPCS6SUGSVK","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GJPCS6SUGSVKZCHY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GJPCS6SU","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:b428515606a6b18ffd8aeaa5eaf96dbe682e114d319128429607c2c8e547b41e","target":"graph","created_at":"2026-05-18T02:28:55Z","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":"When $\\mathfrak h$ is a toral subalgebra of a Lie algebra $\\mathfrak g$ over a field $\\mathbf k$, and $M$ a $\\mathfrak g$-module on which $\\mathfrak h$ also acts torally, the Hochschild-Serre filtration of the Chevalley-Eilenberg cochain complex admits a stronger form than for an arbitrary subalgebra. For a semidirect product $\\mathfrak g = \\mathfrak h \\ltimes \\mathfrak k$ with $\\mathfrak h$ toral one has $H^*(\\mathfrak g, M) \\cong \\bigwedge\\mathfrak h^{\\vee} \\bigotimes H^*(\\mathfrak k,M)^{\\mathfrak h} = H^*(\\mathfrak h, \\mathbf k)\\bigotimes H^*(\\mathfrak k,M)^{\\mathfrak h}$, and for a Lie pos","authors_text":"Murray Gerstenhaber, Vincent E. Coll Jr.","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-02T00:17:56Z","title":"Cohomology of Lie semidirect products and poset algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0428","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":"sha256:595356c9a449be000ee97c77657f9cda1042571082c917e1d63edb972d377c64","target":"record","created_at":"2026-05-18T02:28:55Z","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":"c37be57d5bed2281de84c523f10470456819fd59fe32a68e5b789946a46601d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-02T00:17:56Z","title_canon_sha256":"cb5d40b0ce44caf74a2b228c5f33143393ee2f9678af592e2338d0e342c0800a"},"schema_version":"1.0","source":{"id":"1407.0428","kind":"arxiv","version":2}},"canonical_sha256":"325e297a5434aaac88f84efe0c977e8442a663857c0b52aefb5bef26518e9b72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"325e297a5434aaac88f84efe0c977e8442a663857c0b52aefb5bef26518e9b72","first_computed_at":"2026-05-18T02:28:55.091068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:55.091068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7btAzHNsNDMC+pstYWHxQcB+x/kQfNlwOz96gEd51FEdqSH8VuvBvNZpjuXh2Jm5RfLhCR+CHiP80JCqoHqmAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:55.091448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0428","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:595356c9a449be000ee97c77657f9cda1042571082c917e1d63edb972d377c64","sha256:b428515606a6b18ffd8aeaa5eaf96dbe682e114d319128429607c2c8e547b41e"],"state_sha256":"9ded7d8d42322fb782fc3bbd6e49985b6df9bafb52a53bf54eb72c25fdc3662c"}