{"paper":{"title":"Integer points close to a transcendental curve: an algorithmic approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.NT","authors_text":"Guillaume Hanrot, Nicolas Brisebarre","submitted_at":"2026-06-03T13:25:50Z","abstract_excerpt":"In this article, we propose an algorithmic approach to determine the integer points located near a transcendental curve. This approach is closely related to a celebrated work by Bombieri and Pila and to the so-called Coppersmith's method. We establish the underlying theoretical foundations, prove the algorithms, study their complexity and present practical experiments; we also compare our approach with previously existing ones. From a practical point of view, we focus on an instance of our general problem, called the Table Maker's Dilemma, whose solving makes it possible to evaluate a given fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04858","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04858/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}