{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:M7VB3SEQYSSJYWKSKYBY6WHACP","short_pith_number":"pith:M7VB3SEQ","schema_version":"1.0","canonical_sha256":"67ea1dc890c4a49c595256038f58e013dcd7a22973e8f795c0dcf9e6a6d41f26","source":{"kind":"arxiv","id":"2505.13332","version":1},"attestation_state":"computed","paper":{"title":"Monoidal categorification of genus zero skein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT","math.QA"],"primary_cat":"math.RT","authors_text":"Dylan G. L. Allegretti, Hyun Kyu Kim, Peng Shan","submitted_at":"2025-05-19T16:44:26Z","abstract_excerpt":"We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima variety of triples with monoidal structure defined by the convolution product. We thus give a monoidal categorification of the skein algebra, partially answering a question posed by D. Thurston."},"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":"2505.13332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-05-19T16:44:26Z","cross_cats_sorted":["hep-th","math.GT","math.QA"],"title_canon_sha256":"ed977f9b20b5965bb196d8443ee003edffa1a0b60a3b2dcde8df9176316e174e","abstract_canon_sha256":"d53f196efacd04df4aa07024a3f74379ebcb2f3e59219f70dddc1353091d8709"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:28.689670Z","signature_b64":"Jh1YC9dYzJpMpvYrofi8W3MgRECA0kWFFI4d47oicRNuWQ6uHB8XRiw84Qf6IXvvBQejOs9ypt5SaSuJvZTCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ea1dc890c4a49c595256038f58e013dcd7a22973e8f795c0dcf9e6a6d41f26","last_reissued_at":"2026-07-05T11:05:28.689169Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:28.689169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monoidal categorification of genus zero skein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT","math.QA"],"primary_cat":"math.RT","authors_text":"Dylan G. L. Allegretti, Hyun Kyu Kim, Peng Shan","submitted_at":"2025-05-19T16:44:26Z","abstract_excerpt":"We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$-theoretic Coulomb branch. As a consequence, we see that our skein algebra arises as the Grothendieck ring of the bounded derived category of equivariant coherent sheaves on the Braverman-Finkelberg-Nakajima variety of triples with monoidal structure defined by the convolution product. We thus give a monoidal categorification of the skein algebra, partially answering a question posed by D. Thurston."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13332","kind":"arxiv","version":1},"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/2505.13332/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":"2505.13332","created_at":"2026-07-05T11:05:28.689226+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.13332v1","created_at":"2026-07-05T11:05:28.689226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13332","created_at":"2026-07-05T11:05:28.689226+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7VB3SEQYSSJ","created_at":"2026-07-05T11:05:28.689226+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7VB3SEQYSSJYWKS","created_at":"2026-07-05T11:05:28.689226+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7VB3SEQ","created_at":"2026-07-05T11:05:28.689226+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/M7VB3SEQYSSJYWKSKYBY6WHACP","json":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP.json","graph_json":"https://pith.science/api/pith-number/M7VB3SEQYSSJYWKSKYBY6WHACP/graph.json","events_json":"https://pith.science/api/pith-number/M7VB3SEQYSSJYWKSKYBY6WHACP/events.json","paper":"https://pith.science/paper/M7VB3SEQ"},"agent_actions":{"view_html":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP","download_json":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP.json","view_paper":"https://pith.science/paper/M7VB3SEQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.13332&json=true","fetch_graph":"https://pith.science/api/pith-number/M7VB3SEQYSSJYWKSKYBY6WHACP/graph.json","fetch_events":"https://pith.science/api/pith-number/M7VB3SEQYSSJYWKSKYBY6WHACP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP/action/storage_attestation","attest_author":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP/action/author_attestation","sign_citation":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP/action/citation_signature","submit_replication":"https://pith.science/pith/M7VB3SEQYSSJYWKSKYBY6WHACP/action/replication_record"}},"created_at":"2026-07-05T11:05:28.689226+00:00","updated_at":"2026-07-05T11:05:28.689226+00:00"}