You probably don't want to use BLAKE as the poster child for this argument, since it uses two sets of constants of distinct provenance: the initialization vecto

You probably don't want to use BLAKE as the poster child for this argument, since it uses two sets of constants of distinct provenance: the initialization vector, which uses the same constants as SHA-2, i.e., the square roots of the first 8 primes, and the constants used in the compression function, which are indeed the expansion of pi. BLAKE2 got rid of the pi constants.