{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:APHHMD2XXXOTUSTILLNRULCFLV","short_pith_number":"pith:APHHMD2X","schema_version":"1.0","canonical_sha256":"03ce760f57bddd3a4a685adb1a2c455d75552dd4e815e8b1896ac7935e545bfd","source":{"kind":"arxiv","id":"2311.13415","version":2},"attestation_state":"computed","paper":{"title":"Coherent sheaves on surfaces, COHAs and deformed $W_{1+\\infty}$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexandre Minets, Anton Mellit, Eric Vasserot, Olivier Schiffmann","submitted_at":"2023-11-22T14:25:26Z","abstract_excerpt":"We compute the cohomological Hall algebra of zero-dimensional sheaves on an arbitrary smooth quasi-projective surface $S$ with pure cohomology, deriving an explicit presentation by generators and relations. When $S$ has trivial canonical bundle, this COHA is isomorphic to the enveloping algebra of deformed trigonometric $W_{1+\\infty}$-algebra associated to the ring $H^*(S,\\mathbb{Q})$. We also define a double of this COHA, show that it acts on the homology of various moduli stacks of sheaves on $S$ and explicitly describe this action on the products of tautological classes. Examples include Hi"},"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":"2311.13415","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-11-22T14:25:26Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6f1035f7e0566ac6eb95976ee9afd3a16aaaaa2428668f252633540fb1501a28","abstract_canon_sha256":"2824da3172700b50bafde03db6db9d2caa2e90349244b389de6584cef1d93d34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:03:45.028415Z","signature_b64":"FLOU12Jzvlm3fxs7hx7Ur/t7yXZxrvXiR98HMdPxyG6FivtW7XK453EfgxA+UBqlzebvidJ/Ry9ERnr5U1j5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03ce760f57bddd3a4a685adb1a2c455d75552dd4e815e8b1896ac7935e545bfd","last_reissued_at":"2026-05-26T02:03:45.027583Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:03:45.027583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coherent sheaves on surfaces, COHAs and deformed $W_{1+\\infty}$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexandre Minets, Anton Mellit, Eric Vasserot, Olivier Schiffmann","submitted_at":"2023-11-22T14:25:26Z","abstract_excerpt":"We compute the cohomological Hall algebra of zero-dimensional sheaves on an arbitrary smooth quasi-projective surface $S$ with pure cohomology, deriving an explicit presentation by generators and relations. When $S$ has trivial canonical bundle, this COHA is isomorphic to the enveloping algebra of deformed trigonometric $W_{1+\\infty}$-algebra associated to the ring $H^*(S,\\mathbb{Q})$. We also define a double of this COHA, show that it acts on the homology of various moduli stacks of sheaves on $S$ and explicitly describe this action on the products of tautological classes. Examples include Hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.13415","kind":"arxiv","version":2},"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/2311.13415/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":"2311.13415","created_at":"2026-05-26T02:03:45.027721+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.13415v2","created_at":"2026-05-26T02:03:45.027721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.13415","created_at":"2026-05-26T02:03:45.027721+00:00"},{"alias_kind":"pith_short_12","alias_value":"APHHMD2XXXOT","created_at":"2026-05-26T02:03:45.027721+00:00"},{"alias_kind":"pith_short_16","alias_value":"APHHMD2XXXOTUSTI","created_at":"2026-05-26T02:03:45.027721+00:00"},{"alias_kind":"pith_short_8","alias_value":"APHHMD2X","created_at":"2026-05-26T02:03:45.027721+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/APHHMD2XXXOTUSTILLNRULCFLV","json":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV.json","graph_json":"https://pith.science/api/pith-number/APHHMD2XXXOTUSTILLNRULCFLV/graph.json","events_json":"https://pith.science/api/pith-number/APHHMD2XXXOTUSTILLNRULCFLV/events.json","paper":"https://pith.science/paper/APHHMD2X"},"agent_actions":{"view_html":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV","download_json":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV.json","view_paper":"https://pith.science/paper/APHHMD2X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.13415&json=true","fetch_graph":"https://pith.science/api/pith-number/APHHMD2XXXOTUSTILLNRULCFLV/graph.json","fetch_events":"https://pith.science/api/pith-number/APHHMD2XXXOTUSTILLNRULCFLV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV/action/storage_attestation","attest_author":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV/action/author_attestation","sign_citation":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV/action/citation_signature","submit_replication":"https://pith.science/pith/APHHMD2XXXOTUSTILLNRULCFLV/action/replication_record"}},"created_at":"2026-05-26T02:03:45.027721+00:00","updated_at":"2026-05-26T02:03:45.027721+00:00"}