Certified exact identification of the I3322 quantum value
Abstract
We determine the quantum value of the three-setting, two-outcome Bell functional I3322. The value is the unique intersection q† of an analytic A-high stable curve of the exact Jacobi characteristic map with a central reverser curve. A computer-assisted proof isolates this intersection in a rational interval of width 10−55, beginning 0.2508753845139765356173366109459512989013219739714764755. We prove that the supremum over finite-dimensional tensor-product strategies, the unrestricted spatial value and the commuting-operator value all equal q†. No finite-dimensional strategy attains the value, whereas a normal infinite-dimensional spatial strategy and a commuting GNS strategy do. The proof combines an exact Bellman/path variational reduction, extraction of a positive bilateral calibrated Jacobi fibre from a maximizing weak-star state, a reflected-fibre central-incidence theorem and interval certificates for the unique stable/central intersection. A separate operator-positive three-remainder decomposition gives the commuting upper bound. The complete verification record is archived at DOI 10.5281/zenodo.22160086.
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BibTeX
@misc{krohngrimberghe2026certified,
title = {{Certified exact identification of the I3322 quantum value}},
author = {Artus Krohn-Grimberghe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29693},
eprint = {2609.29693},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29693},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Certified exact identification of the I3322 quantum value
AU - Artus Krohn-Grimberghe
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29693
UR - https://arxiv.org/abs/2609.29693
AB - We determine the quantum value of the three-setting, two-outcome Bell functional I3322. The value is the unique intersection q_† of an analytic A-high stable curve of the exact Jacobi characteristic map with a central reverser curve. A computer-assisted proof isolates this intersection in a rational interval of width 10^−55, beginning 0.2508753845139765356173366109459512989013219739714764755. We prove that the supremum over finite-dimensional tensor-product strategies, the unrestricted spatial value and the commuting-operator value all equal q_†. No finite-dimensional strategy attains the value, whereas a normal infinite-dimensional spatial strategy and a commuting GNS strategy do. The proof combines an exact Bellman/path variational reduction, extraction of a positive bilateral calibrated Jacobi fibre from a maximizing weak-star state, a reflected-fibre central-incidence theorem and interval certificates for the unique stable/central intersection. A separate operator-positive three-remainder decomposition gives the commuting upper bound. The complete verification record is archived at DOI 10.5281/zenodo.22160086.
ER -