{"paper":{"title":"Linked Fates: How Small of an Ambiguity Increase Can Make the Difference Between Equaling and Separating from P?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Benjamin Carleton, Conor Taliancich, David E. Narv\\'aez, Lane A. Hemaspaandra, Melissa Welsh, Michael C. Chavrimootoo","submitted_at":"2026-06-18T15:52:47Z","abstract_excerpt":"Ambiguity-bounded versions of $\\mathrm{NP}$, denoted $\\mathrm{UP}_{\\leq f(n)}$, bound by $f(n)$ the number of accepting paths the nondeterministic polynomial-time Turing machine can have on inputs of length $n$. Such classes range from Valiant's completely unambiguous ($f(n)=1$) class $\\mathrm{UP}$ to $\\mathrm{NP}$ itself, where there is no bound or, equivalently, there is the toothless exponential bound ($f(n) = 2^{n^{O(1)}}$).\n  This paper seeks to understand which of these classes stand and fall together as to whether they equal deterministic polynomial time. Informally put, what ranges of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20399","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/2606.20399/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"}