{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:V75F66QNXEECCNA3FIO7377KYM","short_pith_number":"pith:V75F66QN","canonical_record":{"source":{"id":"1903.02544","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-06T18:47:41Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f65b01a2b30f7fde9e964b4a0e7800158303a05d3a9d1dde0159e1ef1edd1d28","abstract_canon_sha256":"aff771a31694bc13a81a27c83f561e3049dd39a3fdd0228d179c369014eabe30"},"schema_version":"1.0"},"canonical_sha256":"affa5f7a0db90821341b2a1dfdffeac325c7ea5cc5f7f4c091065b19bb243d6b","source":{"kind":"arxiv","id":"1903.02544","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:V75F66QNXEECCNA3FIO7377KYM","target":"record","payload":{"canonical_record":{"source":{"id":"1903.02544","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-06T18:47:41Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f65b01a2b30f7fde9e964b4a0e7800158303a05d3a9d1dde0159e1ef1edd1d28","abstract_canon_sha256":"aff771a31694bc13a81a27c83f561e3049dd39a3fdd0228d179c369014eabe30"},"schema_version":"1.0"},"canonical_sha256":"affa5f7a0db90821341b2a1dfdffeac325c7ea5cc5f7f4c091065b19bb243d6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:46.425814Z","signature_b64":"HkNAUSFu6JOSci1vam+0xpq+XY+5Xofxf2rlBfrRQKm1GpxnfNgIeF1eBt5RprnfzU+Eskjk2eW0CqHiryO3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"affa5f7a0db90821341b2a1dfdffeac325c7ea5cc5f7f4c091065b19bb243d6b","last_reissued_at":"2026-05-17T23:51:46.425209Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:46.425209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.02544","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u2gkcDVvpSENgzXm8yODKFq2A1rqi+akWIEtgMeoQGsGjhkmITby5k0jOPQ7EOKgq+k+mAYm+pc5w4PTCxDKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:19.693706Z"},"content_sha256":"5a7fb0027016db42ae6d878c9d19749a18f0f6d30121037ca98cdc53440eab0c","schema_version":"1.0","event_id":"sha256:5a7fb0027016db42ae6d878c9d19749a18f0f6d30121037ca98cdc53440eab0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:V75F66QNXEECCNA3FIO7377KYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the residue method for period integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Aaron Pollack, Chen Wan, Micha{\\l} Zydor","submitted_at":"2019-03-06T18:47:41Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02544","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PaHLovMl35z3AuriHYvxlOwk2Err6zd2uVxL2wsNIy/Y6I8dO8tvb+24U6YXF3W9d8Y3Bdat369vfeLkB+m9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:21:19.694379Z"},"content_sha256":"d16843cb26e5be591718f5d6ae87b988d9ed969415533c7cc4ba69a534524eac","schema_version":"1.0","event_id":"sha256:d16843cb26e5be591718f5d6ae87b988d9ed969415533c7cc4ba69a534524eac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V75F66QNXEECCNA3FIO7377KYM/bundle.json","state_url":"https://pith.science/pith/V75F66QNXEECCNA3FIO7377KYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V75F66QNXEECCNA3FIO7377KYM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T06:21:19Z","links":{"resolver":"https://pith.science/pith/V75F66QNXEECCNA3FIO7377KYM","bundle":"https://pith.science/pith/V75F66QNXEECCNA3FIO7377KYM/bundle.json","state":"https://pith.science/pith/V75F66QNXEECCNA3FIO7377KYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V75F66QNXEECCNA3FIO7377KYM/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4k2ln6+CgGxj5CpwnTXW3HLsfNuQ4mnpOSQ0l8fgDxe8QhJ/+T+7Ohs7vSE9+VvCdwhbHt4N8yEcrsm8HI0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:21:19.697456Z","bundle_sha256":"db4264fbe9744009bc6dd78d7226d84b6b77af1bd9db5f4a2a212228d011de88"}}