{"paper":{"title":"Statistical Estimation of higher Dedekind Numbers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Fihman, Christian Plessl, Lennart Van Hirtum","submitted_at":"2026-07-09T13:08:14Z","abstract_excerpt":"We provide highly accurate estimations of the 10th through 15th Dedekind Numbers, to a precision of 4 digits for $D(10)$, to 2 digits for $D(15)$. These estimates were obtained using three methods, including pair matching on large quantities of 9-dimensional monotone Boolean functions for $D(10)$, Reference Subsets for $D(10)$, $D(11)$, and $D(12)$. And our best method \"Weight Layer Branching\" which provided accurate estimates for all $D(10)$ through $D(15)$, strongly improving on the previous best known estimates by Korshunov and Tian-Shun Chen et al. arXiv:2606.09795"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08446","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/2607.08446/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"}