I found the problem itself to be poorly defined. > What if we allow representations beyond plain data types? Since we want representations to remain computable

I found the problem itself to be poorly defined. > What if we allow representations beyond plain data types? Since we want representations to remain computable, the most general kind of representation would be a program in some programming language. But the program must be small enough to fit in 64 bits. If you bring in a whole programming language, you bring in a lot more than 64 bits. This all seems to be the math equivalent of saying you wrote a program in 2k when the first line is "import 'megalibrary'".