{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GT7MPPKBMO2S2GLPA5FWK2IEED","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":"d1b5055b8844f8706e509a6eb9edf4f8bada0295d633795b09ed1979fb835bef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-10-06T21:09:10Z","title_canon_sha256":"c781660edca008aa442cb16c438c12cf6a6e86409b096a0ae4cdde6c26460977"},"schema_version":"1.0","source":{"id":"1910.02525","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.02525","created_at":"2026-07-05T00:59:54Z"},{"alias_kind":"arxiv_version","alias_value":"1910.02525v3","created_at":"2026-07-05T00:59:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.02525","created_at":"2026-07-05T00:59:54Z"},{"alias_kind":"pith_short_12","alias_value":"GT7MPPKBMO2S","created_at":"2026-07-05T00:59:54Z"},{"alias_kind":"pith_short_16","alias_value":"GT7MPPKBMO2S2GLP","created_at":"2026-07-05T00:59:54Z"},{"alias_kind":"pith_short_8","alias_value":"GT7MPPKB","created_at":"2026-07-05T00:59:54Z"}],"graph_snapshots":[{"event_id":"sha256:c68fd3786846d6c4539a8db69c7e55e217a0abe2e03ff5aa40a1ac97be956501","target":"graph","created_at":"2026-07-05T00:59:54Z","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/1910.02525/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $F$ be a non-Archimedean local field. Let $\\mathcal{A}_n(F)$ be the set of equivalence classes of irreducible admissible representations of $\\textrm{GL}_n(F)$, and $\\mathcal{G}_n(F)$ be the set of equivalence classes of n-dimensional Frobenius semisimple Weil-Deligne representations of $W'_F$. The local Langlands correspondence(LLC) establishes the reciprocity maps $\\textrm{Rec}_{n,F}: \\mathcal{A}_n(F)\\longrightarrow \\mathcal{G}_n(F)$ , satisfying some nice properties. An important invariant under this correspondence is the L- and $\\epsilon$-factors. This is also expected to be true under ","authors_text":"Dongming She","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-10-06T21:09:10Z","title":"Local Langlands correspondence for the twisted exterior and symmetric square $\\epsilon$-factors of $\\textrm{GL}_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.02525","kind":"arxiv","version":3},"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:d062bdbde75a14c7c9193ab65dd3d8091779c217a3d1c1478c0daf0460aa7e48","target":"record","created_at":"2026-07-05T00:59:54Z","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":"d1b5055b8844f8706e509a6eb9edf4f8bada0295d633795b09ed1979fb835bef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-10-06T21:09:10Z","title_canon_sha256":"c781660edca008aa442cb16c438c12cf6a6e86409b096a0ae4cdde6c26460977"},"schema_version":"1.0","source":{"id":"1910.02525","kind":"arxiv","version":3}},"canonical_sha256":"34fec7bd4163b52d196f074b65690420f92e0625266dacd150cfbcfc541aa9e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34fec7bd4163b52d196f074b65690420f92e0625266dacd150cfbcfc541aa9e3","first_computed_at":"2026-07-05T00:59:54.241175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:59:54.241175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9IE1USOQt3qH+9LC0sLI1eWBJ7ipItvRVUd/quzmmIe5jMXwyQuSJqlqDIA/cEla5TtM7UR1d6+vZZXDDLcBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:59:54.241527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.02525","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d062bdbde75a14c7c9193ab65dd3d8091779c217a3d1c1478c0daf0460aa7e48","sha256:c68fd3786846d6c4539a8db69c7e55e217a0abe2e03ff5aa40a1ac97be956501"],"state_sha256":"231aafb435f6067da6574fef59403bb772d3600486079c694b7065d2cdc1b0c4"}