{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BIFCCV3CVJNDJ2KAWHYA3S62SV","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":"cbc4eac11b24bf06685a2b7255f0520a61f46d97f16ff34fe83d26f5c21baaef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-04T18:49:37Z","title_canon_sha256":"25ed683eb4a4d1c40a8d38fb034be351e4f83b27a98d3b1ec28fd0422ab51aa0"},"schema_version":"1.0","source":{"id":"1502.01288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01288","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01288v1","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01288","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"BIFCCV3CVJND","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BIFCCV3CVJNDJ2KA","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BIFCCV3C","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:bb3a95ec9fb7c9e4a7c4f2e1b0657eb237d505ee5728b13775466f8e8aba1def","target":"graph","created_at":"2026-05-18T02:27:57Z","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":"Let $K$ be a number field and let $E/K$ be an elliptic curve whose mod $\\ell$ Galois representation locally has image contained in a group $G$, up to conjugacy. We classify the possible images for the global Galois representation in the case where $G$ is a Cartan subgroup or the normalizer of a Cartan subgroup. When $K = \\mathbf{Q}$, we deduce a counterexample to the local-global principle in the case where $G$ is the normalizer of a split Cartan and $\\ell = 13$. In particular, there are at least three elliptic curves (up to twist) over $\\mathbf{Q}$ whose mod $13$ image of Galois is locally co","authors_text":"Anastassia Etropolski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-04T18:49:37Z","title":"Local-Global principles for certain images of Galois representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01288","kind":"arxiv","version":1},"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":"sha256:41929c1f79ddbdd676b3d5398b46342fcc3e35f91aa9b09cae2bd42bdc39168e","target":"record","created_at":"2026-05-18T02:27:57Z","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":"cbc4eac11b24bf06685a2b7255f0520a61f46d97f16ff34fe83d26f5c21baaef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-04T18:49:37Z","title_canon_sha256":"25ed683eb4a4d1c40a8d38fb034be351e4f83b27a98d3b1ec28fd0422ab51aa0"},"schema_version":"1.0","source":{"id":"1502.01288","kind":"arxiv","version":1}},"canonical_sha256":"0a0a215762aa5a34e940b1f00dcbda955cbb2ea62d38d729709ac869d0bbc3eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a0a215762aa5a34e940b1f00dcbda955cbb2ea62d38d729709ac869d0bbc3eb","first_computed_at":"2026-05-18T02:27:57.636440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:57.636440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQ6G/IrekJ8kbb5UKsy0Mw3fv6xWcbN9x80DfQM9DIJxoo5EBr3JZEY2edNZB0o5wTUHNu4O9qN/6bkurWgwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:57.636887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41929c1f79ddbdd676b3d5398b46342fcc3e35f91aa9b09cae2bd42bdc39168e","sha256:bb3a95ec9fb7c9e4a7c4f2e1b0657eb237d505ee5728b13775466f8e8aba1def"],"state_sha256":"f739918ff8fa975435713fc12eb3e4ac1498bca59d2a1d9d276ba0ab6384c405"}