{
  "abstract": "We show that a certified formalization of the hitting-set-existence axiom of Atserias and Tzameret, instantiated on the parity-based Nisan-Wigderson compression class of Khaniki, is independent of the two-sorted theory $V^0_1$ of $\\mathrm{AC}^0$-reasoning, unconditionally: $V^0_1$ proves neither it nor its negation. The same holds for the corresponding certified dual weak pigeonhole principle, whose refutation is witnessed by a single seed that certified-computes every string of the model simultaneously. The mechanism is a bounded-arithmetic transfer of Atserias-Tzameret's reduction from hitting sets to the dual weak pigeonhole principle: the amplification half of that reduction, the sole source of its NP-oracle, is unnecessary at the native stretch of the Nisan-Wigderson map, and the compression half becomes a $V^0_1$-provable implication once circuit evaluation is replaced by its certified $Σ^B_0$ unfolding. This is, to our knowledge, the first independence result for a derandomization-flavoured existence principle at the $\\mathrm{AC}^0$-reasoning level, and it makes explicit the bridge between the Khaniki Nisan-Wigderson line and the Atserias-Tzameret reverse mathematics of hitting sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28813",
  "author_total": 1,
  "authors": [
    {
      "name": "Martin Kolář"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/464n961hns05a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28813",
  "fulltext_url": null,
  "id": "464n961hns05a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28813",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7204873947",
  "pdf_url": "https://arxiv.org/pdf/2608.28813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/464n961hns05a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Unconditional $V^0_1$-independence of a certified hitting-set principle",
  "title_text": "Unconditional V^0_1-independence of a certified hitting-set principle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/464n961hns05a",
  "venue": "arXiv",
  "versions": []
}