{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4I2PS6JIX2AJISOGSGGJF4FRY7","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":"c45b88d1fca9bba0cdfaa43fa8c713aec333997982a527368771c21fc5f09b24","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-11T07:14:34Z","title_canon_sha256":"d45cb26c5c4cf4e0e85ae4a524be654b4aa65b2b1a64e56556c0a2a5d2b75e95"},"schema_version":"1.0","source":{"id":"2608.10585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10585","created_at":"2026-08-12T01:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10585v1","created_at":"2026-08-12T01:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10585","created_at":"2026-08-12T01:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"4I2PS6JIX2AJ","created_at":"2026-08-12T01:22:48Z"},{"alias_kind":"pith_short_16","alias_value":"4I2PS6JIX2AJISOG","created_at":"2026-08-12T01:22:48Z"},{"alias_kind":"pith_short_8","alias_value":"4I2PS6JI","created_at":"2026-08-12T01:22:48Z"}],"graph_snapshots":[{"event_id":"sha256:c32c10d34cb63e0639f9caad124abeb4dacbb70dc8364e59701f6276249034e9","target":"graph","created_at":"2026-08-12T01:22:48Z","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/2608.10585/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies simple Lie algebras in the Verlinde category, with canonical fundamental group action, using combinatorial methods. We give an exhaustive list of such Lie algebras which either have length at most 3, or appear as a subalgebra of the restriction of the Lie algebra of a simple algebraic group along a principal morphism. The results and exceptions answer several questions and conjectures regarding Verlinde categories of algebraic groups and their Lie algebras.","authors_text":"Joseph Newton","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-11T07:14:34Z","title":"Small Lie algebras in the Verlinde category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10585","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":"sha256:49ae3eb0929e1e10c4e1e079e5f5309ba7df3d24577f22f4df70c83ae821386d","target":"record","created_at":"2026-08-12T01:22:48Z","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":"c45b88d1fca9bba0cdfaa43fa8c713aec333997982a527368771c21fc5f09b24","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-11T07:14:34Z","title_canon_sha256":"d45cb26c5c4cf4e0e85ae4a524be654b4aa65b2b1a64e56556c0a2a5d2b75e95"},"schema_version":"1.0","source":{"id":"2608.10585","kind":"arxiv","version":1}},"canonical_sha256":"e234f97928be809449c6918c92f0b1c7d03abcde6238e95cd55837a68ccd99fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e234f97928be809449c6918c92f0b1c7d03abcde6238e95cd55837a68ccd99fc","first_computed_at":"2026-08-12T01:22:48.737374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T01:22:48.737374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3YC1ShZuCyW6Rj9RScOwWH5hKI12Pdz4nSGE5sNiJIbihoV0vTAZnRTgqja1egCJFpL/nYqafcW7REbauPDxBQ==","signature_status":"signed_v1","signed_at":"2026-08-12T01:22:48.738864Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.10585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49ae3eb0929e1e10c4e1e079e5f5309ba7df3d24577f22f4df70c83ae821386d","sha256:c32c10d34cb63e0639f9caad124abeb4dacbb70dc8364e59701f6276249034e9"],"state_sha256":"19492b3892e5228b3fee644db484c5c906895566c8b353e4dd824767343dfa05"}