{"paper":{"title":"On the Approximate Non-Deterministic Degree of Total Boolean Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Samruddhi Pednekar, Supartha Podder","submitted_at":"2026-05-22T07:52:09Z","abstract_excerpt":"The approximate non-deterministic degree of a Boolean function $f$, denoted $\\mathsf{ndeg}_\\epsilon(f)$ (written $\\mathsf{N}_\\epsilon(f)$ for brevity), is the minimum degree of a real polynomial $p$ such that $0 \\le |p(x)| \\le \\epsilon$ whenever $f(x) = 0$, and $|p(x)| \\ge 1$ whenever $f(x) = 1$. Unlike exact non-deterministic degree, which only requires the polynomial to be nonzero on $1$-inputs, this measure enforces a uniform gap: the polynomial must stay close to zero on all $0$-inputs and bounded away from zero on all $1$-inputs.\n  The rational degree conjecture, open for over three decad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23336","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/2605.23336/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"}