{"paper":{"title":"A Colombeau--Beurling criterion for the Riemann hypothesis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Amaury Alvarez Cruz, Esteban A Alvarez Gutierrez","submitted_at":"2026-06-21T15:41:53Z","abstract_excerpt":"This paper establishes an equivalence between the Riemann hypothesis and the association of a single moderate net in the Colombeau algebra G(0,1), constructed from damped Baez-Duarte sums. Two explicit damping strategies are introduced: an exponential damping exp(-k eps^2) combined with super-exponential truncation, and a polynomial damping k^(-delta(eps)), where delta(eps) = (log(1/eps))^(-alpha), combined with polynomial truncation. Assuming the Riemann hypothesis, the corresponding nets are shown to be moderate and associated with the negative characteristic function of (0,1). Conversely, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22562","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/2606.22562/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"}