In https://mathoverflow.net/questions/41414/boundedness-of-hilbert-polynomials-of-hypersurfaces Brian Conrad's comment says that if we fix $N$ and $d$, then the set of possible Hilbert polynomials of degree $d$ geometrically integral subschemes of $\mathbb{P}^N$ is finite, as we vary over all ground fields.
Is there a reference with a proof? When I searched, I found only something that stated it without proof and without a reference. I'm not looking for something expository, but rather something you might cite.