{
  "abstract": "A recent OpenAI preprint claims a deterministic algorithm that counts the satisfying assignments of a $k$-CNF formula in time $2^{O_k(n\\log\\log n/\\sqrt{\\log n})}$, and $2^{O(n/\\sqrt{\\log n})}$ at bounded clause density, which would refute the Exponential Time Hypothesis. The headline bound is proved by tensor contraction; the body develops an interpolation algorithm with the weaker exponent $n(\\log\\log n)^2/\\sqrt{\\log n}$. This note does four things. First, it explains the interpolation algorithm in plain terms. Second, it asks how large $n$ must be for the bounds to bite. The preprint states no constants, so we treat the hidden constant $C$ as a parameter: the general bound beats the $2^n$ of brute force only beyond $n\\approx 10^{32}$ for $C=2$, $10^{126}$ for $C=3$ and $10^{3517}$ for $C=10$. We then extract the constants from the tensor-contraction proof: for every input with $m$ clauses at bounded density, the running time it certifies stays above $2^n$ unless $\\log_2(n+m)>10^9$, and on random 3-CNF at the satisfiability threshold unless $\\log_2 n>5\\times10^{11}$. So the bounds are subexponential as $n\\to\\infty$, but the proof certifies no speed-up over brute force for any input of bounded density that could ever be written down. Third, for the clause-product form of the interpolation algorithm we prove limits in a cost model matching the preprint's evaluation. By a short algebraic lemma, polynomial cost needs components of $O(\\log^3 n)$ variables with per-point evaluation, or primal treewidth $O(\\log^2 n)$ with dynamic programming over the groups. So the scheme costs $2^{Ω(\\sqrt{\\mathrm{tw}})}$ at treewidth $\\mathrm{tw}$, $2^{Ω(\\sqrt n)}$ with high probability on random 3-CNF above clause density 3, and $2^{Ω(n^{1/3})}$ even on trivially countable path formulas. We explain why the preprint's sharper routes escape these limits. Fourth, we report experiments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00517",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabio Dias"
    },
    {
      "name": "Yvens Lima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fgw187z7y4jd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00517",
  "fulltext_url": null,
  "id": "0fgw187z7y4jd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00517",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00517",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fgw187z7y4jd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00517",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00517"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Limits and Constants of OpenAI's Claimed ETH Refutation",
  "title_text": "Limits and Constants of OpenAI's Claimed ETH Refutation",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0fgw187z7y4jd",
  "venue": "arXiv",
  "versions": []
}