{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3GKG2M4ONCCJTOJM7EHGU7PRTC","short_pith_number":"pith:3GKG2M4O","schema_version":"1.0","canonical_sha256":"d9946d338e688499b92cf90e6a7df198bc3c4cf8d10d4953878dd92eb699f97b","source":{"kind":"arxiv","id":"2606.00983","version":1},"attestation_state":"computed","paper":{"title":"The categorical local Langlands conjecture","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.NT","authors_text":"David Hansen, Lucas Mann","submitted_at":"2026-05-31T03:45:52Z","abstract_excerpt":"We formulate a program to prove the categorical local Langlands conjecture (CLLC) of Fargues-Scholze, for all quasisplit $p$-adic groups where the Fargues-Scholze $L$-parameters agree with the semisimplification of a known \"automorphic\" local Langlands parametrization. A key working hypothesis - which we expect to prove elsewhere jointly with Hamann - is the compatibility of the enhanced Whittaker coefficient functor $c_\\psi$ with Eisenstein series. For $\\mathrm{GL}_n$, we show that this hypothesis alone implies the full CLLC. For more general groups $G$, we prove an induction principle which "},"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":"2606.00983","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T03:45:52Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"d5c37e3813d54d020582f59d1b9ad151b18bd7476bbd67960f620f9e9eba5b43","abstract_canon_sha256":"4a9e5dfeebb0b28388e80de1009ff2a2d4d1740a48a526b9c7a901c92cdf824d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:11.195762Z","signature_b64":"BOypwUWRzhAjxzLRa+6snVxRuzcG7LgxqrYFPkQsxzIfigAS2HAKNLdX8XTQfct6lWhzyrYxjsF7ewE9V7noBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9946d338e688499b92cf90e6a7df198bc3c4cf8d10d4953878dd92eb699f97b","last_reissued_at":"2026-06-02T01:04:11.195274Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:11.195274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The categorical local Langlands conjecture","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.NT","authors_text":"David Hansen, Lucas Mann","submitted_at":"2026-05-31T03:45:52Z","abstract_excerpt":"We formulate a program to prove the categorical local Langlands conjecture (CLLC) of Fargues-Scholze, for all quasisplit $p$-adic groups where the Fargues-Scholze $L$-parameters agree with the semisimplification of a known \"automorphic\" local Langlands parametrization. A key working hypothesis - which we expect to prove elsewhere jointly with Hamann - is the compatibility of the enhanced Whittaker coefficient functor $c_\\psi$ with Eisenstein series. For $\\mathrm{GL}_n$, we show that this hypothesis alone implies the full CLLC. For more general groups $G$, we prove an induction principle which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00983","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/2606.00983/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":"2606.00983","created_at":"2026-06-02T01:04:11.195345+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.00983v1","created_at":"2026-06-02T01:04:11.195345+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00983","created_at":"2026-06-02T01:04:11.195345+00:00"},{"alias_kind":"pith_short_12","alias_value":"3GKG2M4ONCCJ","created_at":"2026-06-02T01:04:11.195345+00:00"},{"alias_kind":"pith_short_16","alias_value":"3GKG2M4ONCCJTOJM","created_at":"2026-06-02T01:04:11.195345+00:00"},{"alias_kind":"pith_short_8","alias_value":"3GKG2M4O","created_at":"2026-06-02T01:04:11.195345+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/3GKG2M4ONCCJTOJM7EHGU7PRTC","json":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC.json","graph_json":"https://pith.science/api/pith-number/3GKG2M4ONCCJTOJM7EHGU7PRTC/graph.json","events_json":"https://pith.science/api/pith-number/3GKG2M4ONCCJTOJM7EHGU7PRTC/events.json","paper":"https://pith.science/paper/3GKG2M4O"},"agent_actions":{"view_html":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC","download_json":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC.json","view_paper":"https://pith.science/paper/3GKG2M4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.00983&json=true","fetch_graph":"https://pith.science/api/pith-number/3GKG2M4ONCCJTOJM7EHGU7PRTC/graph.json","fetch_events":"https://pith.science/api/pith-number/3GKG2M4ONCCJTOJM7EHGU7PRTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC/action/storage_attestation","attest_author":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC/action/author_attestation","sign_citation":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC/action/citation_signature","submit_replication":"https://pith.science/pith/3GKG2M4ONCCJTOJM7EHGU7PRTC/action/replication_record"}},"created_at":"2026-06-02T01:04:11.195345+00:00","updated_at":"2026-06-02T01:04:11.195345+00:00"}