{"paper":{"title":"Optimal Proximity Gap for Folded Reed--Solomon Codes via Subspace Designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.IT"],"primary_cat":"cs.IT","authors_text":"Fernando Granha Jeronimo, Lenny Liu, Pranav Rajpal","submitted_at":"2026-01-15T03:53:19Z","abstract_excerpt":"A collection of sets satisfies a $(\\delta,\\varepsilon)$-proximity gap with respect to some property if for every set in the collection, either (i) all members of the set are $\\delta$-close to the property in (relative) Hamming distance, or (ii) only a small $\\varepsilon$-fraction of members are $\\delta$-close to the property.\n  In a seminal work, Ben-Sasson \\textit{et al.}\\ showed that the collection of affine subspaces exhibits a $(\\delta,\\varepsilon)$-proximity gap with respect to the property of being Reed--Solomon (RS) codewords with $\\delta$ up to the so-called Johnson bound for list deco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.10047","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/2601.10047/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"}