{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3GKG2M4ONCCJTOJM7EHGU7PRTC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4a9e5dfeebb0b28388e80de1009ff2a2d4d1740a48a526b9c7a901c92cdf824d","cross_cats_sorted":["math.AG","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T03:45:52Z","title_canon_sha256":"d5c37e3813d54d020582f59d1b9ad151b18bd7476bbd67960f620f9e9eba5b43"},"schema_version":"1.0","source":{"id":"2606.00983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00983","created_at":"2026-06-02T01:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00983v1","created_at":"2026-06-02T01:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00983","created_at":"2026-06-02T01:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"3GKG2M4ONCCJ","created_at":"2026-06-02T01:04:11Z"},{"alias_kind":"pith_short_16","alias_value":"3GKG2M4ONCCJTOJM","created_at":"2026-06-02T01:04:11Z"},{"alias_kind":"pith_short_8","alias_value":"3GKG2M4O","created_at":"2026-06-02T01:04:11Z"}],"graph_snapshots":[{"event_id":"sha256:5bd31108ad40295b3c4af05f0b7fe805b4c8491dd6badb8991c9014528a02923","target":"graph","created_at":"2026-06-02T01:04:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.00983/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"David Hansen, Lucas Mann","cross_cats":["math.AG","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T03:45:52Z","title":"The categorical local Langlands conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00983","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d7e369da28556e8b76d5ddfdcb5930bba4fb42049a1e32a9f48c3abac47bd7e6","target":"record","created_at":"2026-06-02T01:04:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4a9e5dfeebb0b28388e80de1009ff2a2d4d1740a48a526b9c7a901c92cdf824d","cross_cats_sorted":["math.AG","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-31T03:45:52Z","title_canon_sha256":"d5c37e3813d54d020582f59d1b9ad151b18bd7476bbd67960f620f9e9eba5b43"},"schema_version":"1.0","source":{"id":"2606.00983","kind":"arxiv","version":1}},"canonical_sha256":"d9946d338e688499b92cf90e6a7df198bc3c4cf8d10d4953878dd92eb699f97b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9946d338e688499b92cf90e6a7df198bc3c4cf8d10d4953878dd92eb699f97b","first_computed_at":"2026-06-02T01:04:11.195274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:11.195274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BOypwUWRzhAjxzLRa+6snVxRuzcG7LgxqrYFPkQsxzIfigAS2HAKNLdX8XTQfct6lWhzyrYxjsF7ewE9V7noBQ==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:11.195762Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7e369da28556e8b76d5ddfdcb5930bba4fb42049a1e32a9f48c3abac47bd7e6","sha256:5bd31108ad40295b3c4af05f0b7fe805b4c8491dd6badb8991c9014528a02923"],"state_sha256":"20a1b92e815be25d46b3cb0f616b78d571ef4b61063e9ba53e5b51f4070b833f"}