{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DSWZEZGDKRM6BZCLYAPFJIS7IA","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":"ddf7a317861bb99ce434481f0c96249d3ddf7515ab66370e85d34ad2fb015fce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-21T13:43:50Z","title_canon_sha256":"0e9db31302ea03eb66213d2fd8b79f80e5ed771c1f2f03da81e3d71dbdc521b3"},"schema_version":"1.0","source":{"id":"1510.06249","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06249","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06249v3","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06249","created_at":"2026-05-18T00:08:46Z"},{"alias_kind":"pith_short_12","alias_value":"DSWZEZGDKRM6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DSWZEZGDKRM6BZCL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DSWZEZGD","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:5f325093f8db00adc4047a185a418b1001213eeb46dee95b3999d8ebf08d60fd","target":"graph","created_at":"2026-05-18T00:08:46Z","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":"An abelian surface $A_{/{\\mathbb Q}}$ of prime conductor $N$ is favorable if its 2-division field $F$ is an ${\\mathcal S}_5$-extension with ramification index 5 over ${\\mathbb Q}_2$. Let $A$ be favorable and let $B$ be any semistable abelian variety of dimension $2d$ and conductor $N^d$ such that $B[2]$ is filtered by copies of $A[2]$. We give a sufficient class field theoretic criterion on $F$ to guarantee that $B$ is isogenous to $A^d$.\n  As expected from our paramodular conjecture, we conclude that there is one isogeny class of abelian surfaces for each conductor in $\\{277, 349,461,797,971\\","authors_text":"Armand Brumer, Kenneth Kramer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-21T13:43:50Z","title":"Certain Abelian varieties bad at only one prime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06249","kind":"arxiv","version":3},"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":"sha256:77c7354f9e4e39a92bf99d3920f5d1ca3f766b2be17fd8fa9e1f6be69b3c13da","target":"record","created_at":"2026-05-18T00:08:46Z","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":"ddf7a317861bb99ce434481f0c96249d3ddf7515ab66370e85d34ad2fb015fce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-21T13:43:50Z","title_canon_sha256":"0e9db31302ea03eb66213d2fd8b79f80e5ed771c1f2f03da81e3d71dbdc521b3"},"schema_version":"1.0","source":{"id":"1510.06249","kind":"arxiv","version":3}},"canonical_sha256":"1cad9264c35459e0e44bc01e54a25f40205e64276df8c5dd1013ff4d0ae3c81d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cad9264c35459e0e44bc01e54a25f40205e64276df8c5dd1013ff4d0ae3c81d","first_computed_at":"2026-05-18T00:08:46.625622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:46.625622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+e0HRIQJ+4QFaIOJaW14D9OzRn3sTdcDi/RrGJ+ckt2RKJJO9d3ERATe9kyh2T669jneKV/2ar0GVhSFLFxABA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:46.626225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06249","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77c7354f9e4e39a92bf99d3920f5d1ca3f766b2be17fd8fa9e1f6be69b3c13da","sha256:5f325093f8db00adc4047a185a418b1001213eeb46dee95b3999d8ebf08d60fd"],"state_sha256":"eb98ccc76831d551e1ccc545df78d81e4b0df97b7c79a8d75ce00090c20c2331"}