{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3LQMX5PXGFIAYJCWBH4FYOSZVV","short_pith_number":"pith:3LQMX5PX","schema_version":"1.0","canonical_sha256":"dae0cbf5f731500c245609f85c3a59ad78b90b0557b439e61c4aa321523499c3","source":{"kind":"arxiv","id":"1704.02995","version":1},"attestation_state":"computed","paper":{"title":"Lower Bounds for Heights in Relative Galois Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alia Hamieh, Kathleen Petersen, Kevser Akta\\c{s}, Kirsti Biggs, Lola Thompson, Shabnam Akhtari","submitted_at":"2017-04-10T18:03:41Z","abstract_excerpt":"The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic number $\\alpha$ when the base field $\\mathbb{K}$ is a number field and $\\mathbb{K}(\\alpha)/\\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any non-zero element $\\alpha$ which is not a root of unity in a Galois extension $\\mathbb{F}/\\mathbb{K}$, depending on the degree of $\\mathbb{K}/\\mathbb{Q}$ and the number of c"},"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":"1704.02995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-10T18:03:41Z","cross_cats_sorted":[],"title_canon_sha256":"246ea75973bf2251871f13de570b54687ba8e38c16b7c1256f95c7c2d9a20033","abstract_canon_sha256":"b3cec6e58f99c2a4ccda8914fb3bc6d19d2dfca65c4c0c826a7faf2846af9810"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:34.079336Z","signature_b64":"o09W0puTt2w7yP5HCD2TAVnXfR6hdPVcsCCnOY4TmfGFX8LESyu7g52c8JZg3oBGnCgKYMtgyKMKtyt3S+YgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dae0cbf5f731500c245609f85c3a59ad78b90b0557b439e61c4aa321523499c3","last_reissued_at":"2026-05-18T00:46:34.078565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:34.078565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower Bounds for Heights in Relative Galois Extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alia Hamieh, Kathleen Petersen, Kevser Akta\\c{s}, Kirsti Biggs, Lola Thompson, Shabnam Akhtari","submitted_at":"2017-04-10T18:03:41Z","abstract_excerpt":"The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic number $\\alpha$ when the base field $\\mathbb{K}$ is a number field and $\\mathbb{K}(\\alpha)/\\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any non-zero element $\\alpha$ which is not a root of unity in a Galois extension $\\mathbb{F}/\\mathbb{K}$, depending on the degree of $\\mathbb{K}/\\mathbb{Q}$ and the number of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02995","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":"1704.02995","created_at":"2026-05-18T00:46:34.078688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.02995v1","created_at":"2026-05-18T00:46:34.078688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02995","created_at":"2026-05-18T00:46:34.078688+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LQMX5PXGFIA","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LQMX5PXGFIAYJCW","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LQMX5PX","created_at":"2026-05-18T12:30:58.224056+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/3LQMX5PXGFIAYJCWBH4FYOSZVV","json":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV.json","graph_json":"https://pith.science/api/pith-number/3LQMX5PXGFIAYJCWBH4FYOSZVV/graph.json","events_json":"https://pith.science/api/pith-number/3LQMX5PXGFIAYJCWBH4FYOSZVV/events.json","paper":"https://pith.science/paper/3LQMX5PX"},"agent_actions":{"view_html":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV","download_json":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV.json","view_paper":"https://pith.science/paper/3LQMX5PX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.02995&json=true","fetch_graph":"https://pith.science/api/pith-number/3LQMX5PXGFIAYJCWBH4FYOSZVV/graph.json","fetch_events":"https://pith.science/api/pith-number/3LQMX5PXGFIAYJCWBH4FYOSZVV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/action/storage_attestation","attest_author":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/action/author_attestation","sign_citation":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/action/citation_signature","submit_replication":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/action/replication_record"}},"created_at":"2026-05-18T00:46:34.078688+00:00","updated_at":"2026-05-18T00:46:34.078688+00:00"}