{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:UTZ5FBDOFK4IBT3VOG5H5VWKSA","short_pith_number":"pith:UTZ5FBDO","schema_version":"1.0","canonical_sha256":"a4f3d2846e2ab880cf7571ba7ed6ca90262e1146a3ae479a0ddda5cd6d08890d","source":{"kind":"arxiv","id":"2209.05971","version":6},"attestation_state":"computed","paper":{"title":"Affine BPS algebras, W algebras, and the cohomological Hall algebra of $\\mathbb{A}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.RT","authors_text":"Ben Davison","submitted_at":"2022-09-13T13:09:21Z","abstract_excerpt":"We introduce affinizations and deformations of the BPS Lie algebra associated to a tripled quiver with potential, and use them to precisely determine the $T$-equivariant cohomological Hall algebra $\\mathcal{H}_{\\mathbb{A}^2}^T$ of compactly supported coherent sheaves on $\\mathbb{A}^2$, acted on by a torus $T$. In particular we show that this algebra is spherically generated for all $T$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2209.05971","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-09-13T13:09:21Z","cross_cats_sorted":["hep-th","math.AG"],"title_canon_sha256":"1faeaebdb08848b1d9337b71b76c79513512b2f4e01b21184b25745d88b68534","abstract_canon_sha256":"e79c631784f73428e69585ff85985b7f429249c19888685ae5ffcdc4b200fc0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:06.280720Z","signature_b64":"TOvWnJ4v75a5b6K30dUJBV1ogcITOLWtxn1XWk6O78cua3tDd/0+Jr/1WyXyansiOQDkufsR+RA75S3J50RnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4f3d2846e2ab880cf7571ba7ed6ca90262e1146a3ae479a0ddda5cd6d08890d","last_reissued_at":"2026-07-05T11:37:06.280275Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:06.280275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine BPS algebras, W algebras, and the cohomological Hall algebra of $\\mathbb{A}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math.AG"],"primary_cat":"math.RT","authors_text":"Ben Davison","submitted_at":"2022-09-13T13:09:21Z","abstract_excerpt":"We introduce affinizations and deformations of the BPS Lie algebra associated to a tripled quiver with potential, and use them to precisely determine the $T$-equivariant cohomological Hall algebra $\\mathcal{H}_{\\mathbb{A}^2}^T$ of compactly supported coherent sheaves on $\\mathbb{A}^2$, acted on by a torus $T$. In particular we show that this algebra is spherically generated for all $T$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.05971","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.05971/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2209.05971","created_at":"2026-07-05T11:37:06.280338+00:00"},{"alias_kind":"arxiv_version","alias_value":"2209.05971v6","created_at":"2026-07-05T11:37:06.280338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.05971","created_at":"2026-07-05T11:37:06.280338+00:00"},{"alias_kind":"pith_short_12","alias_value":"UTZ5FBDOFK4I","created_at":"2026-07-05T11:37:06.280338+00:00"},{"alias_kind":"pith_short_16","alias_value":"UTZ5FBDOFK4IBT3V","created_at":"2026-07-05T11:37:06.280338+00:00"},{"alias_kind":"pith_short_8","alias_value":"UTZ5FBDO","created_at":"2026-07-05T11:37:06.280338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA","json":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA.json","graph_json":"https://pith.science/api/pith-number/UTZ5FBDOFK4IBT3VOG5H5VWKSA/graph.json","events_json":"https://pith.science/api/pith-number/UTZ5FBDOFK4IBT3VOG5H5VWKSA/events.json","paper":"https://pith.science/paper/UTZ5FBDO"},"agent_actions":{"view_html":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA","download_json":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA.json","view_paper":"https://pith.science/paper/UTZ5FBDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2209.05971&json=true","fetch_graph":"https://pith.science/api/pith-number/UTZ5FBDOFK4IBT3VOG5H5VWKSA/graph.json","fetch_events":"https://pith.science/api/pith-number/UTZ5FBDOFK4IBT3VOG5H5VWKSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA/action/storage_attestation","attest_author":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA/action/author_attestation","sign_citation":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA/action/citation_signature","submit_replication":"https://pith.science/pith/UTZ5FBDOFK4IBT3VOG5H5VWKSA/action/replication_record"}},"created_at":"2026-07-05T11:37:06.280338+00:00","updated_at":"2026-07-05T11:37:06.280338+00:00"}