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arXiv · 2609.38539

UCP Extension in Dimension Three

James Tian
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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 $\sqrt{d}$, 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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James Tian. 2026-09-29. UCP Extension in Dimension Three. https://arxiv.org/abs/2609.38539

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