{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:54Q6ZAK2VSBHKYIOAGQNUYPGD7","short_pith_number":"pith:54Q6ZAK2","schema_version":"1.0","canonical_sha256":"ef21ec815aac8275610e01a0da61e61fca7bf4e7e0f3ae4a4212febbd767b958","source":{"kind":"arxiv","id":"1208.3946","version":3},"attestation_state":"computed","paper":{"title":"Automorphy of Symm^5(GL(2)) and base change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Luis V. Dieulefait","submitted_at":"2012-08-20T08:50:11Z","abstract_excerpt":"We prove that for any Hecke eigenform f of level 1 and arbitrary weight there is a self-dual cuspidal automorphic form $\\pi$ of $GL_6(\\Q)$ corresponding to $\\Symm^5 (f)$, i.e., such that the system of Galois representations attached to $\\pi$ agrees with the 5-th symmetric power of the one attached to f. We also improve the base change result that we obtained in a previous work: for any newform f, and any totally real number field F (no extra assumptions on f or F), we prove the existence of base change relative to the extension $F/\\Q$. Finally, we combine the previous results to deduce that ba"},"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":"1208.3946","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-20T08:50:11Z","cross_cats_sorted":[],"title_canon_sha256":"8b02365be337e2084be4d4a9c6da5a8a37cda7af6409c2311e494f469fbcc9b6","abstract_canon_sha256":"9a0a08cdf6178b77457b20d7812e0b5492301e5b7ef8b586ad7a89b4ed809e39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:59.818108Z","signature_b64":"J+3cZetwraGzGtWMR26IFyfjpZdzKgQoazEPYlycaBjzBg0YWZ3JgBLmtUevk9tWaMrb6sVw5tEFQC9CNSRIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef21ec815aac8275610e01a0da61e61fca7bf4e7e0f3ae4a4212febbd767b958","last_reissued_at":"2026-05-18T02:41:59.817745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:59.817745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphy of Symm^5(GL(2)) and base change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Luis V. Dieulefait","submitted_at":"2012-08-20T08:50:11Z","abstract_excerpt":"We prove that for any Hecke eigenform f of level 1 and arbitrary weight there is a self-dual cuspidal automorphic form $\\pi$ of $GL_6(\\Q)$ corresponding to $\\Symm^5 (f)$, i.e., such that the system of Galois representations attached to $\\pi$ agrees with the 5-th symmetric power of the one attached to f. We also improve the base change result that we obtained in a previous work: for any newform f, and any totally real number field F (no extra assumptions on f or F), we prove the existence of base change relative to the extension $F/\\Q$. Finally, we combine the previous results to deduce that ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3946","kind":"arxiv","version":3},"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":"1208.3946","created_at":"2026-05-18T02:41:59.817794+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.3946v3","created_at":"2026-05-18T02:41:59.817794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3946","created_at":"2026-05-18T02:41:59.817794+00:00"},{"alias_kind":"pith_short_12","alias_value":"54Q6ZAK2VSBH","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"54Q6ZAK2VSBHKYIO","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"54Q6ZAK2","created_at":"2026-05-18T12:26:53.410803+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/54Q6ZAK2VSBHKYIOAGQNUYPGD7","json":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7.json","graph_json":"https://pith.science/api/pith-number/54Q6ZAK2VSBHKYIOAGQNUYPGD7/graph.json","events_json":"https://pith.science/api/pith-number/54Q6ZAK2VSBHKYIOAGQNUYPGD7/events.json","paper":"https://pith.science/paper/54Q6ZAK2"},"agent_actions":{"view_html":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7","download_json":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7.json","view_paper":"https://pith.science/paper/54Q6ZAK2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.3946&json=true","fetch_graph":"https://pith.science/api/pith-number/54Q6ZAK2VSBHKYIOAGQNUYPGD7/graph.json","fetch_events":"https://pith.science/api/pith-number/54Q6ZAK2VSBHKYIOAGQNUYPGD7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7/action/storage_attestation","attest_author":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7/action/author_attestation","sign_citation":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7/action/citation_signature","submit_replication":"https://pith.science/pith/54Q6ZAK2VSBHKYIOAGQNUYPGD7/action/replication_record"}},"created_at":"2026-05-18T02:41:59.817794+00:00","updated_at":"2026-05-18T02:41:59.817794+00:00"}