How do you calculate computing capacity? What is the output - AI gibberish? What guarantees that its generated by the official model? This only works with math

How do you calculate computing capacity? What is the output - AI gibberish? What guarantees that its generated by the official model? This only works with maths - that is SHA-256 or other hash algorithms in a Proof of Work manner. The only thing that can't be spoofed is maths.