{"paper":{"title":"Blocks in Finite Hyperfields","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Hobby","submitted_at":"2025-07-25T03:00:54Z","abstract_excerpt":"This paper studies the structure of finite hyperfields $H$, and finds a subtle pattern in their addition operation. Consider the class $\\mathcal{H}$ of all hyperfields with a given multiplicative group on $H^\\times = H - \\{0\\}$ and given value of $-1$. Then the addition of hyperfields in this class is determined by the set of pairs $(x,y)$ with $y \\in x+1$ for $x,y \\in H^\\times$. There are blocks of such pairs, where $(x_0,y_0)$ and $(x_1,y_1)$ are in the same block iff every hyperfield with $y_0 \\in x_0 + 1$ also has $y_1 \\in x_1 + 1$. The theory of these blocks is developed, they can easily "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.18908","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/2507.18908/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"}