{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GT3VRPK4RHDQWJJDLYPSJHD76L","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":"f934e053063eeee6c5b57a931332ab8f48ed69aa2f10ffe107b8f036439fe8ed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-11-13T01:05:15Z","title_canon_sha256":"ac60c118e395db4087231c468bb25441891e4ff7b2971d8a04517c7203da82d0"},"schema_version":"1.0","source":{"id":"2211.06776","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.06776","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"2211.06776v4","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.06776","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"GT3VRPK4RHDQ","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_16","alias_value":"GT3VRPK4RHDQWJJD","created_at":"2026-05-20T14:03:16Z"},{"alias_kind":"pith_short_8","alias_value":"GT3VRPK4","created_at":"2026-05-20T14:03:16Z"}],"graph_snapshots":[{"event_id":"sha256:2c28e02f63f968b3aeaeb9bf1e796d96dffd2e70a9468581581541543c3556c6","target":"graph","created_at":"2026-05-20T14:03:16Z","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/2211.06776/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend results of Looijenga--Lunts and Verbitsky and show that the total Lie algebra $\\mathfrak g$ for the intersection cohomology of a primitive symplectic variety $X$ with isolated singularities is isomorphic to $$\\mathfrak g \\cong \\mathfrak{so}\\left(\\left(IH^2(X, \\mathbb Q), Q_X\\right)\\oplus \\mathfrak h\\right),$$ where $Q_X$ is the intersection Beauville--Bogomolov--Fujiki form and $\\mathfrak h$ is a hyperbolic plane. This gives a new, algebraic proof for irreducible holomorphic symplectic manifolds which does not rely on the hyperk\\\"ahler metric.\n  Along the way, we study the structure ","authors_text":"Benjamin Tighe","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-11-13T01:05:15Z","title":"The LLV Algebra for Primitive Symplectic Varieties with Isolated Singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.06776","kind":"arxiv","version":4},"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":"sha256:4d844c3275d927e71c5f23ad3451ea11787841c68b155cb3d8d004911e16a615","target":"record","created_at":"2026-05-20T14:03:16Z","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":"f934e053063eeee6c5b57a931332ab8f48ed69aa2f10ffe107b8f036439fe8ed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2022-11-13T01:05:15Z","title_canon_sha256":"ac60c118e395db4087231c468bb25441891e4ff7b2971d8a04517c7203da82d0"},"schema_version":"1.0","source":{"id":"2211.06776","kind":"arxiv","version":4}},"canonical_sha256":"34f758bd5c89c70b25235e1f249c7ff2e07d38f07dba31b5dbbf08b13a1a5b4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34f758bd5c89c70b25235e1f249c7ff2e07d38f07dba31b5dbbf08b13a1a5b4e","first_computed_at":"2026-05-20T14:03:16.060398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T14:03:16.060398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhJdSfj252IH2cFu/GDSumbvJT+Qo2zyCzKLpT/OfF37GSTXH8DZCUyyCAxL9nqQ3bcqTMeCi+Pd48CQqYKYAA==","signature_status":"signed_v1","signed_at":"2026-05-20T14:03:16.060873Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.06776","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d844c3275d927e71c5f23ad3451ea11787841c68b155cb3d8d004911e16a615","sha256:2c28e02f63f968b3aeaeb9bf1e796d96dffd2e70a9468581581541543c3556c6"],"state_sha256":"ded9bcaf9fb6f125786faf246d848da6f1d877557e36ca0dabfc91323fce1fba"}