{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FPVM4FH246B4MW6EWI53ECBC6R","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":"9f0b33070f5fe59fc18bda39f08f39ffdb430aa6cd714f414ef21ab8d0d0f468","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-03-31T18:30:04Z","title_canon_sha256":"a49026294c90a3a3ae43b90f7b38c4aaf2fd96368941fc847e5d0aa82fdccf98"},"schema_version":"1.0","source":{"id":"2604.00124","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.00124","created_at":"2026-06-19T16:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"2604.00124v2","created_at":"2026-06-19T16:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.00124","created_at":"2026-06-19T16:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"FPVM4FH246B4","created_at":"2026-06-19T16:12:19Z"},{"alias_kind":"pith_short_16","alias_value":"FPVM4FH246B4MW6E","created_at":"2026-06-19T16:12:19Z"},{"alias_kind":"pith_short_8","alias_value":"FPVM4FH2","created_at":"2026-06-19T16:12:19Z"}],"graph_snapshots":[{"event_id":"sha256:7d2c3e663eb94505c41299a2274837c0f21e0720c8bb5c93769765b4c670a54e","target":"graph","created_at":"2026-06-19T16:12:19Z","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/2604.00124/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an explicit description of the BPS Lie algebra of any quiver with zero potential, by relating the perverse filtration on the cohomological Hall algebra with certain limit conditions on polynomials. Our results also give a partial description of the perverse filtration for arbitrary potential, which we conjecture is complete in the case of tripled quivers with canonical cubic potential.","authors_text":"Andrei Negu\\c{t}, Shivang Jindal","cross_cats":["math.AG","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-03-31T18:30:04Z","title":"BPS Lie algebras, perverse filtrations and shuffle algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.00124","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":"sha256:3378ef8f89d850e8dc6c2c58511b807d725e2f26f70dc1a92b9ba46e84801587","target":"record","created_at":"2026-06-19T16:12:19Z","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":"9f0b33070f5fe59fc18bda39f08f39ffdb430aa6cd714f414ef21ab8d0d0f468","cross_cats_sorted":["math.AG","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-03-31T18:30:04Z","title_canon_sha256":"a49026294c90a3a3ae43b90f7b38c4aaf2fd96368941fc847e5d0aa82fdccf98"},"schema_version":"1.0","source":{"id":"2604.00124","kind":"arxiv","version":2}},"canonical_sha256":"2beace14fae783c65bc4b23bb20822f47807d408fc92cefc4ad9920f02f6a695","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2beace14fae783c65bc4b23bb20822f47807d408fc92cefc4ad9920f02f6a695","first_computed_at":"2026-06-19T16:12:19.881489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:19.881489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4jjzrcwOxAtRw8hRcfTkbPv2djTKtiEwjLADq9ckeigVqmUY1zOeSFCTCvGgCY4NsS0jd1/G121TQF5/dSh+AA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:19.881929Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.00124","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3378ef8f89d850e8dc6c2c58511b807d725e2f26f70dc1a92b9ba46e84801587","sha256:7d2c3e663eb94505c41299a2274837c0f21e0720c8bb5c93769765b4c670a54e"],"state_sha256":"009b84c12b06cd40e2867a9109b1063b9a4dc7a80b3581eac6c6612170d7f602"}