PreprintCC BY 4.0arXiv
Certified Fourier rounding for the real Grothendieck inequality
Abstract
We give a computer-assisted proof that the real Grothendieck constant is strictly smaller than $1.77987164$. The proof provides a complete interval-arithmetic realization of Ren's five-variable construction. A finite Fourier calculation encloses every scalar coefficient through degree $403$; a fourth-derivative estimate on the entire unit circle bounds the remaining coefficient sum by 10−4. Exact rational arithmetic then certifies the final inequality. We include the transfer to all finite real matrices and arbitrary vector dimensions, the analytic quadrature errors, the rational parameters, and source code for checking and regenerating the certificate.
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BibTeX
@misc{peng2026certified,
title = {{Certified Fourier rounding for the real Grothendieck inequality}},
author = {Bo Peng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24417},
eprint = {2610.24417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24417},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Certified Fourier rounding for the real Grothendieck inequality
AU - Bo Peng
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24417
UR - https://arxiv.org/abs/2610.24417
AB - We give a computer-assisted proof that the real Grothendieck constant is strictly smaller than $1.77987164$. The proof provides a complete interval-arithmetic realization of Ren's five-variable construction. A finite Fourier calculation encloses every scalar coefficient through degree $403$; a fourth-derivative estimate on the entire unit circle bounds the remaining coefficient sum by 10^−4. Exact rational arithmetic then certifies the final inequality. We include the transfer to all finite real matrices and arbitrary vector dimensions, the analytic quadrature errors, the rational parameters, and source code for checking and regenerating the certificate.
ER -