{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JC7SN5KYUPZFVII75T5GUIQGCH","short_pith_number":"pith:JC7SN5KY","schema_version":"1.0","canonical_sha256":"48bf26f558a3f25aa11fecfa6a220611f8723e5617dd147acf069589975f7530","source":{"kind":"arxiv","id":"1111.2002","version":1},"attestation_state":"computed","paper":{"title":"Maass spaces on U(2,2) and the Bloch-Kato conjecture for the symmetric square motive of a modular form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Krzysztof Klosin","submitted_at":"2011-11-08T18:15:42Z","abstract_excerpt":"Let K be an imaginary quadratic field of discriminant -D_K<0. We introduce a notion of an adelic Maass space S_{k, -k/2}^M for automorphic forms on the quasi-split unitary group U(2,2) associated with K and prove that it is stable under the action of all Hecke operators. When D_K is prime we obtain a Hecke-equivariant descent from S_{k,-k/2}^M to the space of elliptic cusp forms S_{k-1}(D_K, \\chi_K), where \\chi_K is the quadratic character of K. For a given \\phi \\in S_{k-1}(D_K, \\chi_K), a prime l >k, we then construct (mod l) congruences between the Maass form corresponding to \\phi and hermit"},"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":"1111.2002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-08T18:15:42Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"518ddf5c98f13fca0e553037b9199a7d4ffc9f880e4300e587c4a38047b45d52","abstract_canon_sha256":"ba4335926a893f9a369707749bac555d88e0d5b523946dcb5483df8fd9b62ba7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:03.614569Z","signature_b64":"NwZHV9YG+ZALoOF8w+Xnt5uPNneMhNLvaLXkIPaP/+hwpHSvvxPMR6fPSFoBScZFyEJ2dX6F7BcnsNzFekmBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48bf26f558a3f25aa11fecfa6a220611f8723e5617dd147acf069589975f7530","last_reissued_at":"2026-05-18T04:09:03.613978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:03.613978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maass spaces on U(2,2) and the Bloch-Kato conjecture for the symmetric square motive of a modular form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Krzysztof Klosin","submitted_at":"2011-11-08T18:15:42Z","abstract_excerpt":"Let K be an imaginary quadratic field of discriminant -D_K<0. We introduce a notion of an adelic Maass space S_{k, -k/2}^M for automorphic forms on the quasi-split unitary group U(2,2) associated with K and prove that it is stable under the action of all Hecke operators. When D_K is prime we obtain a Hecke-equivariant descent from S_{k,-k/2}^M to the space of elliptic cusp forms S_{k-1}(D_K, \\chi_K), where \\chi_K is the quadratic character of K. For a given \\phi \\in S_{k-1}(D_K, \\chi_K), a prime l >k, we then construct (mod l) congruences between the Maass form corresponding to \\phi and hermit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2002","kind":"arxiv","version":1},"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":"1111.2002","created_at":"2026-05-18T04:09:03.614077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.2002v1","created_at":"2026-05-18T04:09:03.614077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2002","created_at":"2026-05-18T04:09:03.614077+00:00"},{"alias_kind":"pith_short_12","alias_value":"JC7SN5KYUPZF","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JC7SN5KYUPZFVII7","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JC7SN5KY","created_at":"2026-05-18T12:26:32.869790+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/JC7SN5KYUPZFVII75T5GUIQGCH","json":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH.json","graph_json":"https://pith.science/api/pith-number/JC7SN5KYUPZFVII75T5GUIQGCH/graph.json","events_json":"https://pith.science/api/pith-number/JC7SN5KYUPZFVII75T5GUIQGCH/events.json","paper":"https://pith.science/paper/JC7SN5KY"},"agent_actions":{"view_html":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH","download_json":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH.json","view_paper":"https://pith.science/paper/JC7SN5KY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.2002&json=true","fetch_graph":"https://pith.science/api/pith-number/JC7SN5KYUPZFVII75T5GUIQGCH/graph.json","fetch_events":"https://pith.science/api/pith-number/JC7SN5KYUPZFVII75T5GUIQGCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH/action/storage_attestation","attest_author":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH/action/author_attestation","sign_citation":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH/action/citation_signature","submit_replication":"https://pith.science/pith/JC7SN5KYUPZFVII75T5GUIQGCH/action/replication_record"}},"created_at":"2026-05-18T04:09:03.614077+00:00","updated_at":"2026-05-18T04:09:03.614077+00:00"}