{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LMVB4CLWJJHSRFEFXSSSWMAFYP","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":"7008466901418302f103acbdc685c88b16d275904752c9902445a6e062fd90e8","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-10-14T20:44:30Z","title_canon_sha256":"2b5b42b01bf351356762176fa7d80a55a451767598c3302416c4e7d09c4e61e8"},"schema_version":"1.0","source":{"id":"1010.3028","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.3028","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"1010.3028v1","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.3028","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"LMVB4CLWJJHS","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LMVB4CLWJJHSRFEF","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LMVB4CLW","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:269cc02cacb73c8cd41282e6e01e33b0405c668fa626220250f3c1325c9441ff","target":"graph","created_at":"2026-05-18T04:39:17Z","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":"In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller subalgebras. These results are used later to affirmatively answer questions, which were originally posed in \\cite{BKN1} and \\cite{BaKN}, about realizing support varieties for Lie superalgebras via rank varieties constructed for the smaller detecting subalgebras.","authors_text":"Daniel K. Nakano, Gustav I. Lehrer, Ruibin Zhang","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-10-14T20:44:30Z","title":"Detecting Cohomology for Lie Superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3028","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":"sha256:5bd31fb3fdc00ed3b5a3af94e024427c5819484cdad2a2e934f3964e0c2e6833","target":"record","created_at":"2026-05-18T04:39:17Z","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":"7008466901418302f103acbdc685c88b16d275904752c9902445a6e062fd90e8","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-10-14T20:44:30Z","title_canon_sha256":"2b5b42b01bf351356762176fa7d80a55a451767598c3302416c4e7d09c4e61e8"},"schema_version":"1.0","source":{"id":"1010.3028","kind":"arxiv","version":1}},"canonical_sha256":"5b2a1e09764a4f289485bca52b3005c3c7d67d9002a54c05cb0f165acfc1c222","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b2a1e09764a4f289485bca52b3005c3c7d67d9002a54c05cb0f165acfc1c222","first_computed_at":"2026-05-18T04:39:17.987495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:17.987495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sMd7jcwOqvS/455jic07hVsSLZGvmtf8kzM753TWYfzk2OMyfJrAeD6z83b2BlgiRVYLxh0NNum/wD0g7qS6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:17.988565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.3028","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bd31fb3fdc00ed3b5a3af94e024427c5819484cdad2a2e934f3964e0c2e6833","sha256:269cc02cacb73c8cd41282e6e01e33b0405c668fa626220250f3c1325c9441ff"],"state_sha256":"72b622353733cd752eba578add9a11734d1f3dc986b06ea38f7d8908bc4cd469"}