{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:V75F66QNXEECCNA3FIO7377KYM","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":"aff771a31694bc13a81a27c83f561e3049dd39a3fdd0228d179c369014eabe30","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-06T18:47:41Z","title_canon_sha256":"f65b01a2b30f7fde9e964b4a0e7800158303a05d3a9d1dde0159e1ef1edd1d28"},"schema_version":"1.0","source":{"id":"1903.02544","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02544","created_at":"2026-05-17T23:51:46Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02544v2","created_at":"2026-05-17T23:51:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02544","created_at":"2026-05-17T23:51:46Z"},{"alias_kind":"pith_short_12","alias_value":"V75F66QNXEEC","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"V75F66QNXEECCNA3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"V75F66QN","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:d16843cb26e5be591718f5d6ae87b988d9ed969415533c7cc4ba69a534524eac","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":"By applying the residue method for period integrals and Langlands-Shahidi's theory for residues of Eisenstein series, we study the period integrals for six spherical varieties. For each spherical variety, we prove a relation between the period integrals and certain automorphic L-functions. In some cases, we also study the local multiplicity of the spherical varieties.","authors_text":"Aaron Pollack, Chen Wan, Micha{\\l} Zydor","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-06T18:47:41Z","title":"On the residue method for period integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02544","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":"sha256:5a7fb0027016db42ae6d878c9d19749a18f0f6d30121037ca98cdc53440eab0c","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":"aff771a31694bc13a81a27c83f561e3049dd39a3fdd0228d179c369014eabe30","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-06T18:47:41Z","title_canon_sha256":"f65b01a2b30f7fde9e964b4a0e7800158303a05d3a9d1dde0159e1ef1edd1d28"},"schema_version":"1.0","source":{"id":"1903.02544","kind":"arxiv","version":2}},"canonical_sha256":"affa5f7a0db90821341b2a1dfdffeac325c7ea5cc5f7f4c091065b19bb243d6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"affa5f7a0db90821341b2a1dfdffeac325c7ea5cc5f7f4c091065b19bb243d6b","first_computed_at":"2026-05-17T23:51:46.425209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:46.425209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HkNAUSFu6JOSci1vam+0xpq+XY+5Xofxf2rlBfrRQKm1GpxnfNgIeF1eBt5RprnfzU+Eskjk2eW0CqHiryO3Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:46.425814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.02544","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a7fb0027016db42ae6d878c9d19749a18f0f6d30121037ca98cdc53440eab0c","sha256:d16843cb26e5be591718f5d6ae87b988d9ed969415533c7cc4ba69a534524eac"],"state_sha256":"ab1f17badd88f665a8badc29d1249380c2ebf16a028487482eb96c82d5d16fe0"}