{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6QMBU7N5MH2QQFRNGZ7MZUOR2D","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":"55452b7108fdda23b8189de1bfae2f872f0b13ec7c0a46414c373a937364a89f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T16:42:31Z","title_canon_sha256":"d25d57d164122ea7f46a3ca2071535aaf41bf121b0b66708adecaedd32a1bf9b"},"schema_version":"1.0","source":{"id":"1302.6144","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6144","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6144v2","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6144","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"6QMBU7N5MH2Q","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6QMBU7N5MH2QQFRN","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6QMBU7N5","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:1d4ce28d67e85a3d6a519a78ed9ad48875e1feee70c682dada6bd3b589bb8604","target":"graph","created_at":"2026-05-17T23:53:35Z","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":"This paper proves two results on the field of rationality $\\Q(\\pi)$ for an automorphic representation $\\pi$, which is the subfield of $\\C$ fixed under the subgroup of $\\Aut(\\C)$ stabilizing the isomorphism class of the finite part of $\\pi$. For general linear groups and classical groups, our first main result is the finiteness of the set of discrete automorphic representations $\\pi$ such that $\\pi$ is unramified away from a fixed finite set of places, $\\pi_\\infty$ has a fixed infinitesimal character, and $[\\Q(\\pi):\\Q]$ is bounded. The second main result is that for classical groups, $[\\Q(\\pi):","authors_text":"Nicolas Templier, Sug Woo Shin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T16:42:31Z","title":"On Fields of rationality for automorphic representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6144","kind":"arxiv","version":2},"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:fbd7ca5b95fb2c8edce653f262f93aa98464f20551475e21a417354c937a49b3","target":"record","created_at":"2026-05-17T23:53:35Z","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":"55452b7108fdda23b8189de1bfae2f872f0b13ec7c0a46414c373a937364a89f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-25T16:42:31Z","title_canon_sha256":"d25d57d164122ea7f46a3ca2071535aaf41bf121b0b66708adecaedd32a1bf9b"},"schema_version":"1.0","source":{"id":"1302.6144","kind":"arxiv","version":2}},"canonical_sha256":"f4181a7dbd61f508162d367eccd1d1d0cb0f2e0fbc02f91a92c92aa848f36c2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4181a7dbd61f508162d367eccd1d1d0cb0f2e0fbc02f91a92c92aa848f36c2f","first_computed_at":"2026-05-17T23:53:35.745149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:35.745149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iSAGHT8jQwcARgLgfKBsDBdbxHNnCixm0YN66kbNse+LKaTlC9Hg1XoMdxyht1fKhOMEZhA0eJp1z6YVzlTnBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:35.745968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6144","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbd7ca5b95fb2c8edce653f262f93aa98464f20551475e21a417354c937a49b3","sha256:1d4ce28d67e85a3d6a519a78ed9ad48875e1feee70c682dada6bd3b589bb8604"],"state_sha256":"428c6e26804fbda9e4e1817a13f0428a2e01b28297f74837fae14fca0d437b8d"}