{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GCKOXAL7V22IIE5GU5S2O2HPQQ","short_pith_number":"pith:GCKOXAL7","schema_version":"1.0","canonical_sha256":"3094eb817faeb48413a6a765a768ef840e8172e151b3c275d22e13758b1276bb","source":{"kind":"arxiv","id":"1509.00900","version":2},"attestation_state":"computed","paper":{"title":"A local converse Theorem for U(2,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qing Zhang","submitted_at":"2015-09-02T23:26:39Z","abstract_excerpt":"Let $F$ be a $p$-adic field and $E/F$ be a quadratic extension. In this paper, we prove the local converse theorem for generic representations of $\\textrm{U}_{E/F}(2,2)$ if $E/F$ is unramified or the residue characteristic of $F$ is odd. Our method is purely local and analytic, and the same method also gives the local converse theorem for $\\textrm{Sp}_4(F)$ and $\\widetilde {\\textrm{Sp}}_4(F)$ if the residue characteristic of $F$ is odd."},"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":"1509.00900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-02T23:26:39Z","cross_cats_sorted":[],"title_canon_sha256":"e927bdf217a0905c96f3cb70f0dc5440d627fbe7cf06044591c7ccacc3cc5a8a","abstract_canon_sha256":"3d2258b839a79ec772f1c165dbc075be2f5f439b0b71356158a27c9f2fc0a71d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:10.009443Z","signature_b64":"gaGtqXW96bOpPO5mWd1zos7+Kg6d+qDRqOjnmxo0Mbu8GFspS2UrkA470WJ95mZXTQn8c4p7XOlSArj0qakTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3094eb817faeb48413a6a765a768ef840e8172e151b3c275d22e13758b1276bb","last_reissued_at":"2026-05-18T00:44:10.008961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:10.008961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A local converse Theorem for U(2,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qing Zhang","submitted_at":"2015-09-02T23:26:39Z","abstract_excerpt":"Let $F$ be a $p$-adic field and $E/F$ be a quadratic extension. In this paper, we prove the local converse theorem for generic representations of $\\textrm{U}_{E/F}(2,2)$ if $E/F$ is unramified or the residue characteristic of $F$ is odd. Our method is purely local and analytic, and the same method also gives the local converse theorem for $\\textrm{Sp}_4(F)$ and $\\widetilde {\\textrm{Sp}}_4(F)$ if the residue characteristic of $F$ is odd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00900","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":"1509.00900","created_at":"2026-05-18T00:44:10.009031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00900v2","created_at":"2026-05-18T00:44:10.009031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00900","created_at":"2026-05-18T00:44:10.009031+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCKOXAL7V22I","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCKOXAL7V22IIE5G","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCKOXAL7","created_at":"2026-05-18T12:29:22.688609+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/GCKOXAL7V22IIE5GU5S2O2HPQQ","json":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ.json","graph_json":"https://pith.science/api/pith-number/GCKOXAL7V22IIE5GU5S2O2HPQQ/graph.json","events_json":"https://pith.science/api/pith-number/GCKOXAL7V22IIE5GU5S2O2HPQQ/events.json","paper":"https://pith.science/paper/GCKOXAL7"},"agent_actions":{"view_html":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ","download_json":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ.json","view_paper":"https://pith.science/paper/GCKOXAL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00900&json=true","fetch_graph":"https://pith.science/api/pith-number/GCKOXAL7V22IIE5GU5S2O2HPQQ/graph.json","fetch_events":"https://pith.science/api/pith-number/GCKOXAL7V22IIE5GU5S2O2HPQQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ/action/storage_attestation","attest_author":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ/action/author_attestation","sign_citation":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ/action/citation_signature","submit_replication":"https://pith.science/pith/GCKOXAL7V22IIE5GU5S2O2HPQQ/action/replication_record"}},"created_at":"2026-05-18T00:44:10.009031+00:00","updated_at":"2026-05-18T00:44:10.009031+00:00"}