{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JJNHEGGHIV5KLUW4SYXTOYL5LS","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":"5a161feae7fe03e2f47d3bba636dc1fc95cb5d255da0fe8eb78bdb2083c570a3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-02T20:55:51Z","title_canon_sha256":"42cf5106704a233dbad1bde347190c6f471b494b08dadd6b15535632453f7f19"},"schema_version":"1.0","source":{"id":"1710.00905","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00905","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00905v2","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00905","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"pith_short_12","alias_value":"JJNHEGGHIV5K","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JJNHEGGHIV5KLUW4","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JJNHEGGH","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:975817b17b0fac16635b90fc4e025a886220a919af4b664ad5b087c6f47c4aa8","target":"graph","created_at":"2026-05-18T00:09:05Z","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 an integral representation for the tensor product $L$-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and local) model, which generalizes the Whittaker model.\n  This is the first in a series of papers, treati","authors_text":"David Ginzburg, Eyal Kaplan, Solomon Friedberg, Yuanqing Cai","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-02T20:55:51Z","title":"Doubling Constructions and Tensor Product ${L}$-Functions: the linear case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00905","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":"sha256:2a4030c23b9330875c45cd7a9bebf8a7384f67ff08dae46fd70dc4c2dece4d35","target":"record","created_at":"2026-05-18T00:09:05Z","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":"5a161feae7fe03e2f47d3bba636dc1fc95cb5d255da0fe8eb78bdb2083c570a3","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-02T20:55:51Z","title_canon_sha256":"42cf5106704a233dbad1bde347190c6f471b494b08dadd6b15535632453f7f19"},"schema_version":"1.0","source":{"id":"1710.00905","kind":"arxiv","version":2}},"canonical_sha256":"4a5a7218c7457aa5d2dc962f37617d5ca020c35394403c314160c847e59da0d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a5a7218c7457aa5d2dc962f37617d5ca020c35394403c314160c847e59da0d3","first_computed_at":"2026-05-18T00:09:05.713858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:05.713858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KL7GneC1vOs/z6v0gsY22WyNtF5mf70gs87w+GU0HyWvSztQUYEDRCcNPUCOeD1n03bJA99OxyuYfePm4yGMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:05.714357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00905","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a4030c23b9330875c45cd7a9bebf8a7384f67ff08dae46fd70dc4c2dece4d35","sha256:975817b17b0fac16635b90fc4e025a886220a919af4b664ad5b087c6f47c4aa8"],"state_sha256":"89f389530feb1ef9a77aea562e36b5e411d650c848ba30a654f4d918ee382dff"}