{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7HESPKH43TYSESEES664Q4S7CI","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":"0b39aaceafb35add5ae09f1b4bff92e4a311757f32c71034b233f5fb5d8bc980","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:37:07Z","title_canon_sha256":"83515184f83ecc25de96c4f319c92ababa9a664cc72287b1bcfd17394ee1b03d"},"schema_version":"1.0","source":{"id":"1207.4641","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4641","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4641v2","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4641","created_at":"2026-05-18T03:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"7HESPKH43TYS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7HESPKH43TYSESEE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7HESPKH4","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:23adca510fa3c3b87cfd5cffd2d2fcb7d2423279583435925591678adef95300","target":"graph","created_at":"2026-05-18T03:40:02Z","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":"A cuspidal automorphic representation \\pi of a group G is said to to be distinguished with respect to a subgroup H if the integral of f along H is nonzero for a cusp form f in the space of \\pi. Such period integrals are related to (non)vanishing of interesting L-values and also to Langlands functoriality. This article discusses a general principle, labelled arithmeticity, which roughly states that \"\\pi is H-distinguished if and only if any Galois conjugate of \\pi is H-distinguished.\" We study this principle via several examples; starting with GL(2) and leading up to more complicated situations","authors_text":"A. Raghuram, Wee Teck Gan","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:37:07Z","title":"Arithmeticity for periods of automorphic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4641","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:dd54349f139f907ba0af20b8ad18b64a188715ff8eea26541152f18cb0246c29","target":"record","created_at":"2026-05-18T03:40:02Z","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":"0b39aaceafb35add5ae09f1b4bff92e4a311757f32c71034b233f5fb5d8bc980","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:37:07Z","title_canon_sha256":"83515184f83ecc25de96c4f319c92ababa9a664cc72287b1bcfd17394ee1b03d"},"schema_version":"1.0","source":{"id":"1207.4641","kind":"arxiv","version":2}},"canonical_sha256":"f9c927a8fcdcf122488497bdc8725f122caed05f0fa7aa8ac56f780217fc5b85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9c927a8fcdcf122488497bdc8725f122caed05f0fa7aa8ac56f780217fc5b85","first_computed_at":"2026-05-18T03:40:02.864489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:02.864489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T7tZ3wosEkf+y3vBRvY/Px5+YD7nX4iLEJWe5t7LfwUOpYSpSgXzRLt5SiRnwcx+MvTwGTSTpeBxr9SGkSFgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:02.865061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4641","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd54349f139f907ba0af20b8ad18b64a188715ff8eea26541152f18cb0246c29","sha256:23adca510fa3c3b87cfd5cffd2d2fcb7d2423279583435925591678adef95300"],"state_sha256":"3f33d64188078ce9132aa5e6e31dd8b4029fe1d9932e59afeb90fec17953ef7a"}