{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7DUU7WVX4YDXBHJJHDIK4XPDMM","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":"caeabd99c8770c1486c934612d920dc2e06ac1b1156dd97c3145b313f8768de9","cross_cats_sorted":["math.LO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-09T15:19:07Z","title_canon_sha256":"f5e2646ab6327c30955302fb42c3b75dc25111aedf0ed0849e14f1d367732993"},"schema_version":"1.0","source":{"id":"1208.1945","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1945","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1945v3","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1945","created_at":"2026-05-18T02:35:52Z"},{"alias_kind":"pith_short_12","alias_value":"7DUU7WVX4YDX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7DUU7WVX4YDXBHJJ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7DUU7WVX","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:e47c4684489246ccaa9866d20b900cc420893de0a570efecbbd30bef04d725b2","target":"graph","created_at":"2026-05-18T02:35:52Z","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"},"paper":{"abstract_excerpt":"We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let $G$ be a reductive group over a number field $F$ which admits discrete series representations at infinity. Let $^{L}G=\\hat G \\rtimes \\mathrm{Gal}(\\bar F/F)$ be the associated $L$-group and $r:{}^L G\\to \\mathrm{GL}(d,\\mathbb{C})$ a continuous homomorphism which is irreducible and does not factor through $\\mathrm{Gal}(\\bar F/F)$. The families under consideration consist of discrete automorphic representations of $G(\\mathbb{A}_F)$ of given weight and level a","authors_text":"Nicolas Templier, Sug Woo Shin","cross_cats":["math.LO","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-09T15:19:07Z","title":"Sato-Tate theorem for families and low-lying zeros of automorphic $L$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1945","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":"sha256:7a53a59cb726015b1f51233a4b78474149fe9aabef86d6cd659b9e82bf13663e","target":"record","created_at":"2026-05-18T02:35:52Z","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":"caeabd99c8770c1486c934612d920dc2e06ac1b1156dd97c3145b313f8768de9","cross_cats_sorted":["math.LO","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-09T15:19:07Z","title_canon_sha256":"f5e2646ab6327c30955302fb42c3b75dc25111aedf0ed0849e14f1d367732993"},"schema_version":"1.0","source":{"id":"1208.1945","kind":"arxiv","version":3}},"canonical_sha256":"f8e94fdab7e607709d2938d0ae5de36324f4fc6f277d963a803942ed2b9fc438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8e94fdab7e607709d2938d0ae5de36324f4fc6f277d963a803942ed2b9fc438","first_computed_at":"2026-05-18T02:35:52.665182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:52.665182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NbsmFsnl6c+BVyIP9MLz9lgOW4AphSP+LYmAtv53OVcO9qz+hPFDYozeBAaAZe4WsFdj5x/qhXzdIM5cBN/vAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:52.665716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1945","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a53a59cb726015b1f51233a4b78474149fe9aabef86d6cd659b9e82bf13663e","sha256:e47c4684489246ccaa9866d20b900cc420893de0a570efecbbd30bef04d725b2"],"state_sha256":"cb0bd9a876ebc99ffe7f2801469dda87c89af52c976e69450e55a1385500e2c5"}