{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FDOWGDS6VM5TYRISZGHUKTI5V6","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":"ba7c8fb0f85d034847288405b925f866a3d7543c879aecf06c88ac313aabfdc5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-28T19:58:33Z","title_canon_sha256":"3ce634fc97dfcba1bef641ad23bcabeae5a9f8fb51bf64f566678cab6e0a578d"},"schema_version":"1.0","source":{"id":"2606.29585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29585","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29585v1","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29585","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"FDOWGDS6VM5T","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"FDOWGDS6VM5TYRIS","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"FDOWGDS6","created_at":"2026-06-30T01:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:2c56e5a516880e4d8e16dbc4a7e6ad9125595e4f383a598e3790923c8d0f37f4","target":"graph","created_at":"2026-06-30T01:18:13Z","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/2606.29585/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct the quantum geometric Langlands functor in the Betti setting via Whittaker coefficients. We show that the functor is compatible with the 2-Fourier-Mukai equivalence between sheaves of categories over 2-stacks $\\operatorname{Ge}_{Z_G}$ and $\\operatorname{Ge}_{\\pi_1(\\check{G})}$, which classify gerbes on $X$ with respect to the center $Z_G$ of $G$ and algebraic fundamental group $\\pi_1(\\check{G})$ of $\\check{G}$.","authors_text":"Ekaterina Bogdanova","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-28T19:58:33Z","title":"Quantum Betti geometric Langlands functor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29585","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":"sha256:6cc3814cc5b62aaebb709516634825ff69e4a655d3d49d25f2bb4f6828195b09","target":"record","created_at":"2026-06-30T01:18:13Z","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":"ba7c8fb0f85d034847288405b925f866a3d7543c879aecf06c88ac313aabfdc5","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-06-28T19:58:33Z","title_canon_sha256":"3ce634fc97dfcba1bef641ad23bcabeae5a9f8fb51bf64f566678cab6e0a578d"},"schema_version":"1.0","source":{"id":"2606.29585","kind":"arxiv","version":1}},"canonical_sha256":"28dd630e5eab3b3c4512c98f454d1daf85f8ff51364079a501a0ad7b499ca06e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28dd630e5eab3b3c4512c98f454d1daf85f8ff51364079a501a0ad7b499ca06e","first_computed_at":"2026-06-30T01:18:13.133512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:18:13.133512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AAaVt/Sml/J0YkxAF9IW1nxFGI+3GCpRaIz8J6/HFdw1fFYuZGqYpGMY4JQ8jr/i3gqIYBT3ymWce/98FN4TDQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:18:13.134167Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cc3814cc5b62aaebb709516634825ff69e4a655d3d49d25f2bb4f6828195b09","sha256:2c56e5a516880e4d8e16dbc4a7e6ad9125595e4f383a598e3790923c8d0f37f4"],"state_sha256":"bd394f2803195a99e06a9a9e7c754fb8572f60436dd577d4934155110c8ee538"}