finite.works
Results · Quantum correlations

Proof-Carrying Exact Bounds for the I3322 Bell Inequality

Nidhal Mghirbi · release 2.0.0 · Zenodo, · a software record that carries the manuscript · doi:10.5281/zenodo.21462892

In plain wordsThe best quantum score in the well-known I3322 nonlocality test lies above 0.25087538451 and at most 0.2508753855, a window narrower than 10⁻⁹ and about 265 times narrower than the previous exact one, each end carried by a certificate that exact arithmetic checks.

The result

As the paper states it, in briefThe first proof-carrying release: a rational certificate on the full word space of length at most four and an explicit dimension-499 strategy prove 0.25087538451 < Qt≤Qc≤0.2508753855, an exact window narrower than 10−9, about 265 times narrower than the preceding exact level-three enclosure. The paper above is the later, sharper account.

How this was checked

The author’s own checks
The author’s own checks: two separately implemented standard-library verifiers, mutation and corruption tests, continuous integration. Supplementary material doi:10.5281/zenodo.21837049.
Lean
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Novelty and credit

Novelty
New, with named precedent: the lower strategy makes Pál and Vértesi’s ansatz exact.

Versionsone, each with its own DOI

Every archived version, newest first. Dates are Zenodo publication dates.
VersionDateDOINotes
2.0.010.5281/zenodo.21462892

Paper, code and links

Paper

On Zenodo: doi:10.5281/zenodo.21462892. No copy is hosted here.

Corrections

None so far.

All corrections, and what counts as one.

Cite

@misc{mghirbi2026proofcarrying,
  author  = {Mghirbi, Nidhal},
  title   = {Proof-Carrying {E}xact {B}ounds for the {I3322} {B}ell {I}nequality},
  year    = {2026},
  version = {2.0.0},
  doi     = {10.5281/zenodo.21462892},
  url     = {https://doi.org/10.5281/zenodo.21462892}
}

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