{"paper":{"title":"Halving the original Kalton--Roberts upper bound for nearly additive set functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Boon Suan Ho, Tomasz Kania","submitted_at":"2026-06-05T01:21:10Z","abstract_excerpt":"Let $K_\\mathrm{KR}$ denote the optimal Kalton--Roberts constant for approximately additive real-valued set functions on algebras of sets. Kalton and Roberts proved $K_\\mathrm{KR}\\le89/2$, and Bondarenko, Prymak, and Radchenko improved the upper bound to $38.8$. We prove that $$K_\\mathrm{KR}\\le\\frac{694,198,146,664,396,294,486,127,753}{34,994,834,677,886,019,996,000,000}\\,\\approx 19.837.$$ Thus the original Kalton--Roberts upper bound is more than halved. The proof changes the source collections fed into the expander-recombination step however still uses expander graphs as the other proofs do. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06807","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/2606.06807/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"}