possibly an easier entry point to the topic is herehttps://en.wikipedia.org/wiki/Chaitin%27s_constant
which is a specific construction that has some relation to the ideas OP has for a construction
possibly an easier entry point to the topic is here
https://en.wikipedia.org/wiki/Chaitin%27s_constant
which is a specific construction that has some relation to the ideas OP has for a construction