Uniform stability of ranks

TL;DR

This paper proves that the analytic rank of tensors remains stable under field extensions without needing a fixed base field, improving upon previous results.

Contribution

It removes the assumption of a fixed base field in the stability of tensor rank under field extensions, providing a more general proof.

Findings

Analytic rank stability holds without fixed base field assumption

Improved theoretical understanding of tensor rank behavior

Simplifies previous proofs of tensor rank stability

Abstract

Chen and Ye recently proved that the analytic rank of tensors is stable under field extensions, assuming a fixed base field. Using a more careful analysis, we show that this assumption is unnecessary.