{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JFFLZAS43DHU3KOXY77JTY4XHL","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":"b67380c167f0f126108ce05023126509a6542a3c7badd39000ff91663315adfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-20T08:15:19Z","title_canon_sha256":"16de865b0a943d9811da1ac0b93203443a8b5f8374ceec18b67647ec4a4dd31c"},"schema_version":"1.0","source":{"id":"1403.5061","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5061","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5061v7","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5061","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"JFFLZAS43DHU","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JFFLZAS43DHU3KOX","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JFFLZAS4","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:0c590deb9fb1c35ab05de454ead05cba95b9f1ef85eb5f7dd42fc739b5d53c1f","target":"graph","created_at":"2026-05-18T01:23:33Z","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":"In \\cite{Ha}, Neal Harris has given a refined Gross-Prasad conjecture for unitary group as an analogue of Ichino and Ikeda's paper \\cite{Ich} concerning special orthogonal groups. In his paper, he stated a conjecture under the assumption that the pair of given representations should be tempered. In this paper, we consider a specific pair involving a non-tempered one. In this case, an analogous formula still exists but the central critical $L$-value is slightly different with the one in the conjecture. As a corollary, this verifies that the tempered condition is indispensable in formulating the","authors_text":"Jaeho Haan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-20T08:15:19Z","title":"The Bessel Period of U(3) and U(2) involving a non-tempered representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5061","kind":"arxiv","version":7},"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":"sha256:1e76169eeb83d3e25b246d987d2e77fee95e23b465d03b72e4ab30649a02d3e4","target":"record","created_at":"2026-05-18T01:23:33Z","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":"b67380c167f0f126108ce05023126509a6542a3c7badd39000ff91663315adfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-03-20T08:15:19Z","title_canon_sha256":"16de865b0a943d9811da1ac0b93203443a8b5f8374ceec18b67647ec4a4dd31c"},"schema_version":"1.0","source":{"id":"1403.5061","kind":"arxiv","version":7}},"canonical_sha256":"494abc825cd8cf4da9d7c7fe99e3973aff611f18fe802cd1f4b483f68c5f2eb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"494abc825cd8cf4da9d7c7fe99e3973aff611f18fe802cd1f4b483f68c5f2eb1","first_computed_at":"2026-05-18T01:23:33.805478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:33.805478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QLSOPxjLuYd+FcsPYX67y3ubJ6PdeLZebWWIjEuAd++BJFXbiUbfHEEPPc0wke4eFdh7w4rjad7cY37ZnXZDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:33.806260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5061","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e76169eeb83d3e25b246d987d2e77fee95e23b465d03b72e4ab30649a02d3e4","sha256:0c590deb9fb1c35ab05de454ead05cba95b9f1ef85eb5f7dd42fc739b5d53c1f"],"state_sha256":"74b69ebbe27049d814f1b850da3f94a4863ea22d0879a71ebda2b7ac5ce7ec3f"}