{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P4PZWG7LS3BFA3LUIZACKGPZ3X","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":"acd10101b41934d9a27c7ce7bdb016de9e814dc078bf83008ab666963e371ec2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-15T00:16:37Z","title_canon_sha256":"dfd28cfb27b3bd366156c4b07f535fdc01b88703786f63f16c8e74396f7ef461"},"schema_version":"1.0","source":{"id":"1712.05484","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05484","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05484v2","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05484","created_at":"2026-05-18T00:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"P4PZWG7LS3BF","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P4PZWG7LS3BFA3LU","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P4PZWG7L","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:2f5817f5b8f3ab4e6f9edbabb708f393ef6f93e025a16ad57a8b600836bc64c7","target":"graph","created_at":"2026-05-18T00:10:47Z","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 extend the notion of semi-infinite cohomology of Lie algebras to include cases where the Lie algebra does not admit a semi-infinite structure but satisfies a mild condition. Our construction clarifies the definition of affine W-algebras in general nilpotent elements case given by V. Kac, S. Roan and M. Wakimoto. We will also give a characterization of admissible pairs with respect to a nilpotent element in a semisimple Lie algebra and define affine W-algebras associated to admissible pairs, while finite W-algebras associated to admissible pairs were already introduced before.","authors_text":"Xiao He","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-15T00:16:37Z","title":"A remark on semi-infinite cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05484","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:daaebf16461c231523a15de25b8d4d6908810ec180779f238966e87f381858f7","target":"record","created_at":"2026-05-18T00:10:47Z","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":"acd10101b41934d9a27c7ce7bdb016de9e814dc078bf83008ab666963e371ec2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-15T00:16:37Z","title_canon_sha256":"dfd28cfb27b3bd366156c4b07f535fdc01b88703786f63f16c8e74396f7ef461"},"schema_version":"1.0","source":{"id":"1712.05484","kind":"arxiv","version":2}},"canonical_sha256":"7f1f9b1beb96c2506d7446402519f9ddf7488076e9356343f3dbe8169906f9de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f1f9b1beb96c2506d7446402519f9ddf7488076e9356343f3dbe8169906f9de","first_computed_at":"2026-05-18T00:10:47.096812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:47.096812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mvwD7mh1t+vNq64oAS9G+2NWZhyEgOjNRB/gdQ1QAM49eQ0mRvLfQ89+XUmKr3gUtfIWexyzIZZdtqACb0gmBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:47.097484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05484","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daaebf16461c231523a15de25b8d4d6908810ec180779f238966e87f381858f7","sha256:2f5817f5b8f3ab4e6f9edbabb708f393ef6f93e025a16ad57a8b600836bc64c7"],"state_sha256":"c07061b3f0af73e330c91331a96ba2a82711075101e7303fab8ad17c5a848423"}