{"paper":{"title":"El mar que envuelve a las piedras: espacios de Stone, profinitos y su papel en la aritm\\'etica contempor\\'anea","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.NT"],"primary_cat":"math.GN","authors_text":"J.R. P\\'erez-Buend\\'ia","submitted_at":"2025-11-26T07:25:44Z","abstract_excerpt":"Stone duality establishes a contravariant equivalence between the category of Boolean algebras and the category of compact, Hausdorff, totally disconnected topological spaces (Stone spaces). These spaces are precisely the profinite spaces and form the natural environment for arithmetic objects such as the $p$-adic integers, absolute Galois groups, and profinite completions. In this article we give a rigorous and self-contained development of the construction of the Stone space associated to a Boolean algebra, prove Stone's representation theorem, and describe profinite spaces as inverse limits"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.21128","kind":"arxiv","version":2},"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/2511.21128/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"}