{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DPEZOO3D4LSXXVIAKNA6H437W2","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":"4e63665a65c9ec4f392306306706305d80186f790bf6465f017c1a908e54d99f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-24T16:48:06Z","title_canon_sha256":"cc1c396e34737418693fb2731dc39e20003b327fb87b6388bd926288ce25587c"},"schema_version":"1.0","source":{"id":"2401.13582","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.13582","created_at":"2026-07-05T10:13:38Z"},{"alias_kind":"arxiv_version","alias_value":"2401.13582v2","created_at":"2026-07-05T10:13:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.13582","created_at":"2026-07-05T10:13:38Z"},{"alias_kind":"pith_short_12","alias_value":"DPEZOO3D4LSX","created_at":"2026-07-05T10:13:38Z"},{"alias_kind":"pith_short_16","alias_value":"DPEZOO3D4LSXXVIA","created_at":"2026-07-05T10:13:38Z"},{"alias_kind":"pith_short_8","alias_value":"DPEZOO3D","created_at":"2026-07-05T10:13:38Z"}],"graph_snapshots":[{"event_id":"sha256:925cafb2b7fa9e358024f129d9f6901617dccf632e7ff12e245bd458a75e3935","target":"graph","created_at":"2026-07-05T10:13:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.13582/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $E_{/\\mathbb{Q}}$ be an elliptic curve with rank $E(\\mathbb{Q})=0$. Fix an odd prime $p$, a positive integer $n$ and a finite abelian extension $K/\\mathbb{Q}$ with rank $E(K) = 0$. In this paper, we show that there exist infinitely many extensions $L/K$ such that $L/\\mathbb{Q}$ is Galois with $\\operatorname{Gal}(L/\\mathbb{Q}) \\simeq \\operatorname{Gal}(K/\\mathbb{Q}) \\ltimes \\mathbb{Z}/p^n\\mathbb{Z}$, and rank $E(L)=0$. This is an extension of earlier results on rank stability of elliptic curves in cyclic extensions of prime power order to a non-abelian setting. We also obtain an asymptotic ","authors_text":"Anwesh Ray, Siddhi Pathak","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-24T16:48:06Z","title":"Rank stability of elliptic curves in certain non-abelian extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.13582","kind":"arxiv","version":2},"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":"sha256:7e332599ca632cb446842eb147b14d76675e3ce88ad53d1100ec87024dcd9892","target":"record","created_at":"2026-07-05T10:13:38Z","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":"4e63665a65c9ec4f392306306706305d80186f790bf6465f017c1a908e54d99f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-24T16:48:06Z","title_canon_sha256":"cc1c396e34737418693fb2731dc39e20003b327fb87b6388bd926288ce25587c"},"schema_version":"1.0","source":{"id":"2401.13582","kind":"arxiv","version":2}},"canonical_sha256":"1bc9973b63e2e57bd5005341e3f37fb6b64d643b599e1cbb2efae6b0ff977a87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bc9973b63e2e57bd5005341e3f37fb6b64d643b599e1cbb2efae6b0ff977a87","first_computed_at":"2026-07-05T10:13:38.317265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:38.317265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2FHBx0uISEr3e2uEwwcVia2oVHxgZfn2q7IFLTvIgFCxqDq+RxTruU1kXZMUiN5fNv3ytgFAHLffGGwR1eQaBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:38.317905Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.13582","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e332599ca632cb446842eb147b14d76675e3ce88ad53d1100ec87024dcd9892","sha256:925cafb2b7fa9e358024f129d9f6901617dccf632e7ff12e245bd458a75e3935"],"state_sha256":"858bcc28d563050511bae856e8247ed598c36877733cc4995b09b38cdae64aae"}