{"paper":{"title":"An Improved Upper Bound for the Dirichlet Spectrum in Diophantine Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ethan Wang, Siyuan Wang, Zixuan Peng","submitted_at":"2026-05-20T15:06:06Z","abstract_excerpt":"We study the continuous part of the Dirichlet spectrum $\\mathbb{D}$ and improve the best previously published upper bound for the ray-origin constant $\\delta$. Building on and refining V. A. Ivanov's approach, we introduce a Cantor-type set $F_4^*$ defined by certain restrictions on partial quotients. For its thickness, we prove $\\tau(\\log(F_4^*))>1$, and apply sum-set results for Cantor sets to prove that the set $F_4^* \\cdot F_4^*$ is an interval. Finally, we establish a new upper bound $\\delta\\le \\frac{111(397+\\sqrt{26565})}{65522}\\approx0.94866$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21275","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/2605.21275/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"}