{"paper":{"title":"Limit Laws for Consensus Protocols on the Complete Graph","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Julian Becker, Konstantinos Panagiotou","submitted_at":"2026-05-18T21:31:12Z","abstract_excerpt":"We study a distributed consensus problem on a complete communication network of $n$ vertices, each holding one of two opinions. The vertices communicate in rounds, possibly in the presence of adversarial noise, and exchange information until they all agree on a single opinion. We consider a general class of protocols, where the vertices randomly sample neighbors and update their own opinion according to an update function $f$ depending on the sampled opinions. A prominent example is the $k$-maj protocol, where every vertex adopts the majority opinion of $k$ randomly sampled neighbors.\n  We con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19131","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/2605.19131/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"}