{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N65FTVFQ62LUYJIMNBCYLOZ3DY","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":"fbd27efcb8f5f36a47d16fd981dd21f2cd29ce1827608bbf5640394ef137a49b","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-05T06:54:23Z","title_canon_sha256":"63489fadf75b8b6816ca7cc9829f035df1b8937ceba0a648448ef31a315ddd6a"},"schema_version":"1.0","source":{"id":"1903.01697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.01697","created_at":"2026-05-17T23:51:46Z"},{"alias_kind":"arxiv_version","alias_value":"1903.01697v2","created_at":"2026-05-17T23:51:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01697","created_at":"2026-05-17T23:51:46Z"},{"alias_kind":"pith_short_12","alias_value":"N65FTVFQ62LU","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N65FTVFQ62LUYJIM","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N65FTVFQ","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:bcc86d4711d21b26655d939f75999ab605ab6e4c00ff8699cff0f8782233005b","target":"graph","created_at":"2026-05-17T23:51:46Z","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 present a regularization procedure of period integrals of automorphic forms on a group $G$ over an arbitrary reductive subgroup $G' \\subset G$. As a consequence we obtain an explicit $G'(\\mathbb{A})$-invariant functional on the space of automorphic forms on $G$ whose exponents avoid certain prescribed hyperplanes. We also provide a necessary and sufficient condition for convergence of period integrals of automorphic forms in terms of their exponents.","authors_text":"Micha{\\l} Zydor","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-05T06:54:23Z","title":"Periods of automorphic forms over reductive subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01697","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":"sha256:932765c87b9236dc82b6bb7d431960d5b5971b8e5eb94a8052566f8bcefcc0ef","target":"record","created_at":"2026-05-17T23:51:46Z","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":"fbd27efcb8f5f36a47d16fd981dd21f2cd29ce1827608bbf5640394ef137a49b","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-05T06:54:23Z","title_canon_sha256":"63489fadf75b8b6816ca7cc9829f035df1b8937ceba0a648448ef31a315ddd6a"},"schema_version":"1.0","source":{"id":"1903.01697","kind":"arxiv","version":2}},"canonical_sha256":"6fba59d4b0f6974c250c684585bb3b1e2a7cd9305adcf5b5ce4926b45b128ec3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fba59d4b0f6974c250c684585bb3b1e2a7cd9305adcf5b5ce4926b45b128ec3","first_computed_at":"2026-05-17T23:51:46.453702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:46.453702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WThwTdbeq8LOgkNl4+sLkZCKuKHU/OCuEZk4oZPJ6WVSv48vVuiXf3kC8a9Gf+TESAmj5fQOP9+VMJpEgmyfCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:46.454277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.01697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:932765c87b9236dc82b6bb7d431960d5b5971b8e5eb94a8052566f8bcefcc0ef","sha256:bcc86d4711d21b26655d939f75999ab605ab6e4c00ff8699cff0f8782233005b"],"state_sha256":"0aae15942354e3cf5cbee10c43544f2bd5ff5ada346b097dc9224f40b338530d"}