PreprintCC BY 4.0arXiv
UCP Extension in Dimension Three
Abstract
We show that every UCP extension problem for a finite dimensional operator system can be reduced to three dimensions after finite matrix amplification. The set of extensions is preserved by an affine bijection. The matrix size is of order √d, where d is the dimension of the original system. This also gives a three dimensional (smallest) counterexample to Arveson's hyperrigidity conjecture.
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BibTeX
@misc{tian2026extension,
title = {{UCP Extension in Dimension Three}},
author = {James Tian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38539},
eprint = {2609.38539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38539},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - UCP Extension in Dimension Three
AU - James Tian
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38539
UR - https://arxiv.org/abs/2609.38539
AB - We show that every UCP extension problem for a finite dimensional operator system can be reduced to three dimensions after finite matrix amplification. The set of extensions is preserved by an affine bijection. The matrix size is of order √d, where d is the dimension of the original system. This also gives a three dimensional (smallest) counterexample to Arveson's hyperrigidity conjecture.
ER -