{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3LQMX5PXGFIAYJCWBH4FYOSZVV","short_pith_number":"pith:3LQMX5PX","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"},"canonical_sha256":"dae0cbf5f731500c245609f85c3a59ad78b90b0557b439e61c4aa321523499c3","source":{"kind":"arxiv","id":"1704.02995","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02995","created_at":"2026-05-18T00:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02995v1","created_at":"2026-05-18T00:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02995","created_at":"2026-05-18T00:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"3LQMX5PXGFIA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LQMX5PXGFIAYJCW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LQMX5PX","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3LQMX5PXGFIAYJCWBH4FYOSZVV","target":"record","payload":{"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"},"canonical_sha256":"dae0cbf5f731500c245609f85c3a59ad78b90b0557b439e61c4aa321523499c3","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"},"source_kind":"arxiv","source_id":"1704.02995","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QcRUuo45fn2I86mFYHw8drP8nRutk0JgVV/4UWpXF4f4YrnndTJMxehuLMOvg3d1w4zVycmXFlQY4lrZrgX+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:03:51.944234Z"},"content_sha256":"4c3f8d4c943ec3628f76c2fe30819d8cfa3e8d99925602676976ec3b446f537c","schema_version":"1.0","event_id":"sha256:4c3f8d4c943ec3628f76c2fe30819d8cfa3e8d99925602676976ec3b446f537c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3LQMX5PXGFIAYJCWBH4FYOSZVV","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3QXW5tUIP0e157seU67TBR8OTYp45ZY6Ltchm4C20sINra0bjjJQSNVW/dyja4hRwYoUyGl6LhEsbMN9x+jDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:03:51.944935Z"},"content_sha256":"af1bf14aaef2da715791b31ae00a4826f33025e462bb21f982849168cdd28878","schema_version":"1.0","event_id":"sha256:af1bf14aaef2da715791b31ae00a4826f33025e462bb21f982849168cdd28878"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/bundle.json","state_url":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T19:03:51Z","links":{"resolver":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV","bundle":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/bundle.json","state":"https://pith.science/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LQMX5PXGFIAYJCWBH4FYOSZVV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3LQMX5PXGFIAYJCWBH4FYOSZVV","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":"b3cec6e58f99c2a4ccda8914fb3bc6d19d2dfca65c4c0c826a7faf2846af9810","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-10T18:03:41Z","title_canon_sha256":"246ea75973bf2251871f13de570b54687ba8e38c16b7c1256f95c7c2d9a20033"},"schema_version":"1.0","source":{"id":"1704.02995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02995","created_at":"2026-05-18T00:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02995v1","created_at":"2026-05-18T00:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02995","created_at":"2026-05-18T00:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"3LQMX5PXGFIA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LQMX5PXGFIAYJCW","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LQMX5PX","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:af1bf14aaef2da715791b31ae00a4826f33025e462bb21f982849168cdd28878","target":"graph","created_at":"2026-05-18T00:46:34Z","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":"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","authors_text":"Alia Hamieh, Kathleen Petersen, Kevser Akta\\c{s}, Kirsti Biggs, Lola Thompson, Shabnam Akhtari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-10T18:03:41Z","title":"Lower Bounds for Heights in Relative Galois Extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02995","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":"sha256:4c3f8d4c943ec3628f76c2fe30819d8cfa3e8d99925602676976ec3b446f537c","target":"record","created_at":"2026-05-18T00:46:34Z","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":"b3cec6e58f99c2a4ccda8914fb3bc6d19d2dfca65c4c0c826a7faf2846af9810","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-04-10T18:03:41Z","title_canon_sha256":"246ea75973bf2251871f13de570b54687ba8e38c16b7c1256f95c7c2d9a20033"},"schema_version":"1.0","source":{"id":"1704.02995","kind":"arxiv","version":1}},"canonical_sha256":"dae0cbf5f731500c245609f85c3a59ad78b90b0557b439e61c4aa321523499c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dae0cbf5f731500c245609f85c3a59ad78b90b0557b439e61c4aa321523499c3","first_computed_at":"2026-05-18T00:46:34.078565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:34.078565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o09W0puTt2w7yP5HCD2TAVnXfR6hdPVcsCCnOY4TmfGFX8LESyu7g52c8JZg3oBGnCgKYMtgyKMKtyt3S+YgAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:34.079336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c3f8d4c943ec3628f76c2fe30819d8cfa3e8d99925602676976ec3b446f537c","sha256:af1bf14aaef2da715791b31ae00a4826f33025e462bb21f982849168cdd28878"],"state_sha256":"04a391b51bf6e4fbd2d036daf8d292490eb0d100a9a7892623e63c35b07a0c10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9B5E3j7FH/oRILaKCv5x5zhsCEw0p19IqGB1bVDbqyMUoyQt27HszYO96WNEllWXBrm4ROZ/d8bGje9obEFbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:03:51.948679Z","bundle_sha256":"64b490ed5c8b210a7e574805176a25df8cc3e60fb7e188b059a55812a23480f6"}}