{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IAVMNC36QM2AVBK7K5JA3IOIFF","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":"6a2e6dd15483be5c79d56b674fc59b4bb174694423b5658df77f3fd321b9f60c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-08T03:37:45Z","title_canon_sha256":"a1666582b67b4af517cf701b730dd7c98984b729fccff3fe4d500a7d62f5aafb"},"schema_version":"1.0","source":{"id":"2606.08990","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08990","created_at":"2026-06-09T02:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08990v1","created_at":"2026-06-09T02:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08990","created_at":"2026-06-09T02:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"IAVMNC36QM2A","created_at":"2026-06-09T02:07:52Z"},{"alias_kind":"pith_short_16","alias_value":"IAVMNC36QM2AVBK7","created_at":"2026-06-09T02:07:52Z"},{"alias_kind":"pith_short_8","alias_value":"IAVMNC36","created_at":"2026-06-09T02:07:52Z"}],"graph_snapshots":[{"event_id":"sha256:2c1bfe57d7f23aaa23af7794011c7070b931edbebd720a6eea713f3abccce4ed","target":"graph","created_at":"2026-06-09T02:07:52Z","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/2606.08990/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a conjecture for associated varieties of simple affine vertex algebras $L_k(\\mathfrak{g})$ attached to a simple Lie algebra $\\mathfrak{g}$ of simply-laced type and any rational level $k$ greater than the critical level. The key new ingredient compared to the integral case is the covering duality map introduced by Gao-Liu-Lo-Shahidi. We provide evidence for the conjecture.","authors_text":"Peng Shan, Qixian Zhao, WenBin Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-08T03:37:45Z","title":"Associated varieties of simple affine vertex algebras at rational levels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08990","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":"sha256:993fffe68609d7db37b74a71f5f212e9c3e58224507cc01c34af70be983ba55b","target":"record","created_at":"2026-06-09T02:07:52Z","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":"6a2e6dd15483be5c79d56b674fc59b4bb174694423b5658df77f3fd321b9f60c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-08T03:37:45Z","title_canon_sha256":"a1666582b67b4af517cf701b730dd7c98984b729fccff3fe4d500a7d62f5aafb"},"schema_version":"1.0","source":{"id":"2606.08990","kind":"arxiv","version":1}},"canonical_sha256":"402ac68b7e83340a855f57520da1c82957e311d6a0e2f2a7181f1f072544771b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"402ac68b7e83340a855f57520da1c82957e311d6a0e2f2a7181f1f072544771b","first_computed_at":"2026-06-09T02:07:52.274656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:52.274656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ntA9Q0uTc8Af8igDs7oOovFwqoRCiumIV80opp1x9poeTpUMILYYfAH4V7KaknT7rBvZ/Zw6W2JE8elreSePCA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:52.275393Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08990","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:993fffe68609d7db37b74a71f5f212e9c3e58224507cc01c34af70be983ba55b","sha256:2c1bfe57d7f23aaa23af7794011c7070b931edbebd720a6eea713f3abccce4ed"],"state_sha256":"7225d83ca48f44aa1b152d6d68696d7e931312c396b570b0faf368e5e19ddf7a"}