{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:7OCFXTPDCDJ6YYXQL3PKRPKDKV","short_pith_number":"pith:7OCFXTPD","schema_version":"1.0","canonical_sha256":"fb845bcde310d3ec62f05edea8bd435556f679f3e8a1c6194ed8231c88bc44c8","source":{"kind":"arxiv","id":"1504.00994","version":1},"attestation_state":"computed","paper":{"title":"Automorphy of some residually dihedral Galois representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack A. Thorne","submitted_at":"2015-04-04T09:04:25Z","abstract_excerpt":"We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called `Taylor--Wiles hypothesis'. We apply this to the problem of the modularity of elliptic curves over totally real fields"},"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":"1504.00994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-04T09:04:25Z","cross_cats_sorted":[],"title_canon_sha256":"fab6becd6952a4c59137027baf85ad9499a4b6254115400ff85853f0626a9b88","abstract_canon_sha256":"6334c72cc68c33f632f1c537868842bb53128dc68df9d624fbe6cf449d05399c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:35.419071Z","signature_b64":"6m7jFbpFwOTtlnRQf8xH62od79GgM5fHL184JFBgfAu/Lmg21l4k4KKtA17JJbwCPEkstk/JjpDCyR+6jMwVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb845bcde310d3ec62f05edea8bd435556f679f3e8a1c6194ed8231c88bc44c8","last_reissued_at":"2026-05-18T02:19:35.418562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:35.418562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphy of some residually dihedral Galois representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack A. Thorne","submitted_at":"2015-04-04T09:04:25Z","abstract_excerpt":"We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called `Taylor--Wiles hypothesis'. We apply this to the problem of the modularity of elliptic curves over totally real fields"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00994","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":"1504.00994","created_at":"2026-05-18T02:19:35.418640+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00994v1","created_at":"2026-05-18T02:19:35.418640+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00994","created_at":"2026-05-18T02:19:35.418640+00:00"},{"alias_kind":"pith_short_12","alias_value":"7OCFXTPDCDJ6","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"7OCFXTPDCDJ6YYXQ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"7OCFXTPD","created_at":"2026-05-18T12:29:10.953037+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/7OCFXTPDCDJ6YYXQL3PKRPKDKV","json":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV.json","graph_json":"https://pith.science/api/pith-number/7OCFXTPDCDJ6YYXQL3PKRPKDKV/graph.json","events_json":"https://pith.science/api/pith-number/7OCFXTPDCDJ6YYXQL3PKRPKDKV/events.json","paper":"https://pith.science/paper/7OCFXTPD"},"agent_actions":{"view_html":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV","download_json":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV.json","view_paper":"https://pith.science/paper/7OCFXTPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00994&json=true","fetch_graph":"https://pith.science/api/pith-number/7OCFXTPDCDJ6YYXQL3PKRPKDKV/graph.json","fetch_events":"https://pith.science/api/pith-number/7OCFXTPDCDJ6YYXQL3PKRPKDKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV/action/storage_attestation","attest_author":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV/action/author_attestation","sign_citation":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV/action/citation_signature","submit_replication":"https://pith.science/pith/7OCFXTPDCDJ6YYXQL3PKRPKDKV/action/replication_record"}},"created_at":"2026-05-18T02:19:35.418640+00:00","updated_at":"2026-05-18T02:19:35.418640+00:00"}