{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ILJLZTONMGM7FJTU4HWVGNIYIK","short_pith_number":"pith:ILJLZTON","schema_version":"1.0","canonical_sha256":"42d2bccdcd6199f2a674e1ed53351842a42faac6d137a0fdbb3bd6ff9d2be6e5","source":{"kind":"arxiv","id":"2602.09359","version":3},"attestation_state":"computed","paper":{"title":"A proof of Dolbeault geometric Langlands for $\\mathrm{GL}_2$ with reduced spectral curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Yukinobu Toda","submitted_at":"2026-02-10T03:09:15Z","abstract_excerpt":"In our previous paper with Tudor P\\u{a}durariu, we introduced the notion of limit categories for moduli stacks of Higgs bundles and formulated the Dolbeault geometric Langlands correspondence. These limit categories are expected to provide an effective ``classical limit'' of the categories of D-modules on the moduli stack of bundles, and our formulation links categorical Donaldson-Thomas theory with the geometric Langlands correspondence.\n  In this paper, we prove the above Dolbeault geometric Langlands correspondence for $\\mathrm{GL}_2$ over the locus in the Hitchin base where the spectral cu"},"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":"2602.09359","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-02-10T03:09:15Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"391e07403211c39033cb591f132070e8bba2e648766234230dbee6940e792ba3","abstract_canon_sha256":"c782279016cb6349b5641727afd2c2e15a0ab00daec2fb39a6a92b646000ec88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:08:22.448648Z","signature_b64":"SA0HeJgsjnZvJHLfeEix0rNb+ofyTpXytSL/OsH4CbRZiCGvmMY6tl009lOInALZjKOLqmucyVv72aeljD3pAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42d2bccdcd6199f2a674e1ed53351842a42faac6d137a0fdbb3bd6ff9d2be6e5","last_reissued_at":"2026-06-12T01:08:22.447722Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:08:22.447722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A proof of Dolbeault geometric Langlands for $\\mathrm{GL}_2$ with reduced spectral curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Yukinobu Toda","submitted_at":"2026-02-10T03:09:15Z","abstract_excerpt":"In our previous paper with Tudor P\\u{a}durariu, we introduced the notion of limit categories for moduli stacks of Higgs bundles and formulated the Dolbeault geometric Langlands correspondence. These limit categories are expected to provide an effective ``classical limit'' of the categories of D-modules on the moduli stack of bundles, and our formulation links categorical Donaldson-Thomas theory with the geometric Langlands correspondence.\n  In this paper, we prove the above Dolbeault geometric Langlands correspondence for $\\mathrm{GL}_2$ over the locus in the Hitchin base where the spectral cu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.09359","kind":"arxiv","version":3},"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/2602.09359/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":"2602.09359","created_at":"2026-06-12T01:08:22.447841+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.09359v3","created_at":"2026-06-12T01:08:22.447841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.09359","created_at":"2026-06-12T01:08:22.447841+00:00"},{"alias_kind":"pith_short_12","alias_value":"ILJLZTONMGM7","created_at":"2026-06-12T01:08:22.447841+00:00"},{"alias_kind":"pith_short_16","alias_value":"ILJLZTONMGM7FJTU","created_at":"2026-06-12T01:08:22.447841+00:00"},{"alias_kind":"pith_short_8","alias_value":"ILJLZTON","created_at":"2026-06-12T01:08:22.447841+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2606.28878","citing_title":"The Dolbeault geometric Langlands correspondence for type A groups beyond the elliptic locus","ref_index":14,"is_internal_anchor":true},{"citing_arxiv_id":"2605.25976","citing_title":"Semiorthogonal decompositions for stacks","ref_index":88,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK","json":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK.json","graph_json":"https://pith.science/api/pith-number/ILJLZTONMGM7FJTU4HWVGNIYIK/graph.json","events_json":"https://pith.science/api/pith-number/ILJLZTONMGM7FJTU4HWVGNIYIK/events.json","paper":"https://pith.science/paper/ILJLZTON"},"agent_actions":{"view_html":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK","download_json":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK.json","view_paper":"https://pith.science/paper/ILJLZTON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.09359&json=true","fetch_graph":"https://pith.science/api/pith-number/ILJLZTONMGM7FJTU4HWVGNIYIK/graph.json","fetch_events":"https://pith.science/api/pith-number/ILJLZTONMGM7FJTU4HWVGNIYIK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK/action/storage_attestation","attest_author":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK/action/author_attestation","sign_citation":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK/action/citation_signature","submit_replication":"https://pith.science/pith/ILJLZTONMGM7FJTU4HWVGNIYIK/action/replication_record"}},"created_at":"2026-06-12T01:08:22.447841+00:00","updated_at":"2026-06-12T01:08:22.447841+00:00"}