Critical Bellman–Jacobi dynamics for reversible Bell functionals

As the paper states it, in briefFor a parameterized class of three-setting binary Bell functionals, a strict wall gap and an exactly certifiable endpoint barrier give finite-dimensional nonattainment, attainment by an infinite-dimensional spatial strategy, and nonclosure; for I₃₃₂₂ this proves the Pál–Vértesi nonattainment conjecture. The theory also gives the constructive bound $D(\epsilon )=O(\log (1/\epsilon ))$.

• Answered Does any finite-dimensional strategy reach the quantum maximum of the I₃₃₂₂ Bell inequality? posed by others
• Answered Which three-setting binary Bell functionals reach their quantum maximum only in infinite dimension?

The author’s own checks

The author’s own checks: exact certificates and independent algebraic verification programs. Reproducibility package doi:10.5281/zenodo.21910110; verification archive doi:10.5281/zenodo.22801636.

Lean

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Peer review

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Label checked 30 October 2026.

Novelty

Concurrent with named independent work: in the paper’s words, “in contemporaneous independent work, Douglas established the overlapping I3322-specific finite-nonattainment and spatial-attainment conclusions”; the parameter-general critical theory is the paper’s own. For I₃₃₂₂ alone, Pauwels and Coladangelo also proved nonattainment independently (see the I₃₃₂₂ entry above).

Paper

On Zenodo: doi:10.5281/zenodo.22688831. No copy is hosted here.

DOI

10.5281/zenodo.22688831; all versions 10.5281/zenodo.21910040

None so far.

All corrections, and what counts as one.

@misc{mghirbi2026criticalbellmanjacobi,
  author = {Mghirbi, Nidhal},
  title  = {Critical {Bellman}–Jacobi dynamics for reversible {B}ell functionals},
  year   = {2026},
  doi    = {10.5281/zenodo.22688831},
  url    = {https://doi.org/10.5281/zenodo.22688831}
}

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