{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MN3HALYKRHI2KF2YRYQOUZOCUX","short_pith_number":"pith:MN3HALYK","schema_version":"1.0","canonical_sha256":"6376702f0a89d1a517588e20ea65c2a5dc27ed9184841ff126bedcd7706e0e9e","source":{"kind":"arxiv","id":"1707.04355","version":1},"attestation_state":"computed","paper":{"title":"On the arithmetic of simple singularities of type E","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Beth Romano, Jack A. Thorne","submitted_at":"2017-07-13T23:45:07Z","abstract_excerpt":"An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exceptional diagrams $E_6, E_7$, $E_8$. These curves are non-hyperelliptic of genus 3 or 4. We prove that a positive proportion of each family consists of curves with integral points everywhere locally but no integral points globally."},"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":"1707.04355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-07-13T23:45:07Z","cross_cats_sorted":[],"title_canon_sha256":"62fca431576970c9c3b53dd03c7eac01796d7b7d0ba1f8b926812d991b6a8a91","abstract_canon_sha256":"1d4b30bf05c3630b26d1c2f3361b54855b5385bf1a34db8829067e84491521c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:18.503999Z","signature_b64":"n1jekAdfs1MEHM2eOm7C5jx+drvjK3xpRTNHuN3KNSqD1YUC0P5692BpDQ0VNyDGKgH78GV8KgGM3B8rsAdlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6376702f0a89d1a517588e20ea65c2a5dc27ed9184841ff126bedcd7706e0e9e","last_reissued_at":"2026-05-18T00:40:18.503296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:18.503296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the arithmetic of simple singularities of type E","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Beth Romano, Jack A. Thorne","submitted_at":"2017-07-13T23:45:07Z","abstract_excerpt":"An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exceptional diagrams $E_6, E_7$, $E_8$. These curves are non-hyperelliptic of genus 3 or 4. We prove that a positive proportion of each family consists of curves with integral points everywhere locally but no integral points globally."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04355","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":"1707.04355","created_at":"2026-05-18T00:40:18.503415+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04355v1","created_at":"2026-05-18T00:40:18.503415+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04355","created_at":"2026-05-18T00:40:18.503415+00:00"},{"alias_kind":"pith_short_12","alias_value":"MN3HALYKRHI2","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MN3HALYKRHI2KF2Y","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MN3HALYK","created_at":"2026-05-18T12:31:31.346846+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/MN3HALYKRHI2KF2YRYQOUZOCUX","json":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX.json","graph_json":"https://pith.science/api/pith-number/MN3HALYKRHI2KF2YRYQOUZOCUX/graph.json","events_json":"https://pith.science/api/pith-number/MN3HALYKRHI2KF2YRYQOUZOCUX/events.json","paper":"https://pith.science/paper/MN3HALYK"},"agent_actions":{"view_html":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX","download_json":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX.json","view_paper":"https://pith.science/paper/MN3HALYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04355&json=true","fetch_graph":"https://pith.science/api/pith-number/MN3HALYKRHI2KF2YRYQOUZOCUX/graph.json","fetch_events":"https://pith.science/api/pith-number/MN3HALYKRHI2KF2YRYQOUZOCUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX/action/storage_attestation","attest_author":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX/action/author_attestation","sign_citation":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX/action/citation_signature","submit_replication":"https://pith.science/pith/MN3HALYKRHI2KF2YRYQOUZOCUX/action/replication_record"}},"created_at":"2026-05-18T00:40:18.503415+00:00","updated_at":"2026-05-18T00:40:18.503415+00:00"}