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Exact rational certification of upper and lower quantum bounds for the I3322 Bell inequality

Nidhal Mghirbi · Zenodo, ; first version , titled “Proof-carrying exact quantum bounds for the I3322 Bell inequality” · doi:10.5281/zenodo.21891897

In plain wordsThe best quantum score in the well-known I3322 nonlocality test is pinned, by finite certificates checked in exact arithmetic, between 0.2508753845139… and 0.250875385012, a window narrower than 5×10⁻¹⁰; the lower end comes from an explicit 499-dimensional strategy.

The result

As the paper states it, in briefFinite rational proof objects for both sides of the I3322 quantum value: a Gram certificate on all words of length at most four proves Qc≤0.250875385012, and an explicit strategy of local dimension 499 with rational projectors has exact value 0.25087538451397653548…, so the two ends differ by less than 5×10−10. The lower certificate also proves Qt>1/4.

Questionson the index

How this was checked

The author’s own checks
The author’s own checks: in the abstract’s words, “every theorem is checked using exact rational or integer arithmetic; floating-point computation is used only to discover candidates.” Reproducibility package: the proof-carrying release below.
Lean
None.
Peer review
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Novelty and credit

Novelty
New, with named precedent: Pál and Vértesi’s numerical value and high-dimensional strategies, and the rational certification methods of Cafuta, Klep and Povh, of Hrga, Klep and Povh, and of Naceur and coauthors, which the paper names as antecedents.

Versionstwo, each with its own DOI

Every archived version, newest first. Dates are Zenodo publication dates. All versions: 10.5281/zenodo.21477900, which always resolves to the newest.
VersionDateDOINotes
—10.5281/zenodo.21891897
first10.5281/zenodo.21477901Titled “Proof-carrying exact quantum bounds for the I3322 Bell inequality”.

Paper, code and links

Paper

On Zenodo: doi:10.5281/zenodo.21891897. No copy is hosted here.

Corrections

None so far.

All corrections, and what counts as one.

Cite

@misc{mghirbi2026exactbounds,
  author = {Mghirbi, Nidhal},
  title  = {Exact rational certification of upper and lower quantum bounds for the {I3322} {B}ell inequality},
  year   = {2026},
  doi    = {10.5281/zenodo.21891897},
  url    = {https://doi.org/10.5281/zenodo.21891897}
}

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