Uniform projective Dimension Growth Conjecture

Let $V\subset\mathbb{P}^N$ be an irreducible projective variety, and let $C(V)$ and, where relevant, $\gamma(V)$ be the constants in the Projective Dimension Growth Conjecture. Uniform projective Dimension Growth Conjecture. The conjecture should hold with $C(V)$, and $\gamma(V)$ if relevant, depending on the degree and dimension of $V$ but not otherwise on $V$. This asks for uniformity across varieties with fixed degree and dimension, strengthening the non-uniform projective Dimension Growth Conjecture.