Alternating Bellman–Jacobi duality for three-setting binary Bell functionals

As the paper states it, in briefAn exact reduction, for a six-parameter class of three-setting binary Bell functionals that contains I₃₃₂₂ and the Gigena–Kaniewski family, of the operator optimization to an alternating one-dimensional Jacobi problem with a Bellman storage dual. It gives the exact rational bound $\omega (I_{3322})\le 0.250875384626$, a two-sided window of width about $1.12\times {10}^{-10}$ with an independent lower certificate.

• Answered How tightly can exact rational arithmetic enclose the I₃₃₂₂ quantum value?

The author’s own checks

The author’s own checks: two independent exact-arithmetic implementations and an exhaustive 204,801-node audit of the storage certificate. Reproducibility package doi:10.5281/zenodo.22237093 (version 1.3.1).

Lean

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Peer review

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Label checked 30 October 2026.

Novelty

Extends named prior work: Pál and Vértesi’s carrier, whose global exhaustiveness the paper proves for the six-parameter family, and Gigena and Kaniewski’s certificate, recast in its Proposition 48. In the paper’s words there is “genuine overlap” with Douglas’s independent I₃₃₂₂ work at the path/storage principle.

Paper

On Zenodo: doi:10.5281/zenodo.22688911. No copy is hosted here.

DOI

10.5281/zenodo.22688911; all versions 10.5281/zenodo.21879015

None so far.

All corrections, and what counts as one.

@misc{mghirbi2026alternatingbellmanjacobi,
  author = {Mghirbi, Nidhal},
  title  = {Alternating {Bellman}–Jacobi duality for three-setting binary {B}ell functionals},
  year   = {2026},
  doi    = {10.5281/zenodo.22688911},
  url    = {https://doi.org/10.5281/zenodo.22688911}
}

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