If I have a set of $N$-byte input values to be hashed using SHA-256, then what are the mapping functions for each of the 256 bits of the output?
It seems to me that hashes are one-way partially because we don't know the input size, but if we did know the size to be $N$, then I expect to find a generalized mapping functions for each of the 256 output bits as functions of the $N$ input bits.
To be clear, I am not trying to find an input for a given output - I am happy for a mapping to still be a 1-way function. Say, for 1000 bits of input, each output bit may be a function of all 1000 bits, or perhaps fewer, or perhaps with extra variables (S-box etc):
ox = f(i0, i1,...1N, s0, s1,...)
Xthoutput bit as a function of up to $N$ input bits and other variables.
In theory, should this be possible? If not, why not? If yes, what are some tips to learning all 256 mapping functions from the algorithm?