{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z4NL42V43RWATRP3QNACRSTLU7","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":"c975a06e10d93b48878f085007c31b3d0e6601958c911fbc3ea6e8b11fec3c46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-11T23:14:38Z","title_canon_sha256":"16cee41571699f4947477478047fc7ac6f52335e6b66db3b775b19ba6dae78c7"},"schema_version":"1.0","source":{"id":"1309.2998","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2998","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2998v2","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2998","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"Z4NL42V43RWA","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z4NL42V43RWATRP3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z4NL42V4","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:2a39e6a3ce9b902c14c6f9d387bf17fde1b02ab6cb478c4da54aefbe3ec7143c","target":"graph","created_at":"2026-05-18T00:44:58Z","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 algebraic extension K of the rationals has the Bogomolov property if the absolute logarithmic height of non-torsion points of K* is bounded away from 0. We define a relative extension L/K to be Bogomolov if this holds for points of L\\K. We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K, when K is Galois over Q.","authors_text":"Robert Grizzard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-11T23:14:38Z","title":"Relative Bogomolov extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2998","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:e81334c4a6bd6522d59ede6a40beafcccec36bbeff2f0f270f7242d73c57c9ea","target":"record","created_at":"2026-05-18T00:44:58Z","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":"c975a06e10d93b48878f085007c31b3d0e6601958c911fbc3ea6e8b11fec3c46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-11T23:14:38Z","title_canon_sha256":"16cee41571699f4947477478047fc7ac6f52335e6b66db3b775b19ba6dae78c7"},"schema_version":"1.0","source":{"id":"1309.2998","kind":"arxiv","version":2}},"canonical_sha256":"cf1abe6abcdc6c09c5fb834028ca6ba7e54fe8f45d0e620dc1241244f04a063e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf1abe6abcdc6c09c5fb834028ca6ba7e54fe8f45d0e620dc1241244f04a063e","first_computed_at":"2026-05-18T00:44:58.504261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:58.504261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9LtP+rxRv6bgUdpSQpEhOtCjWTxhq987Va4gvkH4rbR4fxc/YYFpc/pikQTdvAF3a0COnqDyQrt3LbGe+kJ6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:58.504813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2998","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e81334c4a6bd6522d59ede6a40beafcccec36bbeff2f0f270f7242d73c57c9ea","sha256:2a39e6a3ce9b902c14c6f9d387bf17fde1b02ab6cb478c4da54aefbe3ec7143c"],"state_sha256":"dbeb2104f9a2c61dc57675cf0bb42455e36664fd5691d17690519d3ae9b22369"}