{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:N65FTVFQ62LUYJIMNBCYLOZ3DY","short_pith_number":"pith:N65FTVFQ","schema_version":"1.0","canonical_sha256":"6fba59d4b0f6974c250c684585bb3b1e2a7cd9305adcf5b5ce4926b45b128ec3","source":{"kind":"arxiv","id":"1903.01697","version":2},"attestation_state":"computed","paper":{"title":"Periods of automorphic forms over reductive subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Micha{\\l} Zydor","submitted_at":"2019-03-05T06:54:23Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1903.01697","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-05T06:54:23Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"63489fadf75b8b6816ca7cc9829f035df1b8937ceba0a648448ef31a315ddd6a","abstract_canon_sha256":"fbd27efcb8f5f36a47d16fd981dd21f2cd29ce1827608bbf5640394ef137a49b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:46.454277Z","signature_b64":"WThwTdbeq8LOgkNl4+sLkZCKuKHU/OCuEZk4oZPJ6WVSv48vVuiXf3kC8a9Gf+TESAmj5fQOP9+VMJpEgmyfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fba59d4b0f6974c250c684585bb3b1e2a7cd9305adcf5b5ce4926b45b128ec3","last_reissued_at":"2026-05-17T23:51:46.453702Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:46.453702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periods of automorphic forms over reductive subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Micha{\\l} Zydor","submitted_at":"2019-03-05T06:54:23Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01697","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1903.01697","created_at":"2026-05-17T23:51:46.453788+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.01697v2","created_at":"2026-05-17T23:51:46.453788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.01697","created_at":"2026-05-17T23:51:46.453788+00:00"},{"alias_kind":"pith_short_12","alias_value":"N65FTVFQ62LU","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"N65FTVFQ62LUYJIM","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"N65FTVFQ","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY","json":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY.json","graph_json":"https://pith.science/api/pith-number/N65FTVFQ62LUYJIMNBCYLOZ3DY/graph.json","events_json":"https://pith.science/api/pith-number/N65FTVFQ62LUYJIMNBCYLOZ3DY/events.json","paper":"https://pith.science/paper/N65FTVFQ"},"agent_actions":{"view_html":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY","download_json":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY.json","view_paper":"https://pith.science/paper/N65FTVFQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.01697&json=true","fetch_graph":"https://pith.science/api/pith-number/N65FTVFQ62LUYJIMNBCYLOZ3DY/graph.json","fetch_events":"https://pith.science/api/pith-number/N65FTVFQ62LUYJIMNBCYLOZ3DY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY/action/storage_attestation","attest_author":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY/action/author_attestation","sign_citation":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY/action/citation_signature","submit_replication":"https://pith.science/pith/N65FTVFQ62LUYJIMNBCYLOZ3DY/action/replication_record"}},"created_at":"2026-05-17T23:51:46.453788+00:00","updated_at":"2026-05-17T23:51:46.453788+00:00"}