M(6) = 3: A Complete, Self-Contained Proof The MUB Problem for Square-Free Composite Dimensions

We prove that the maximum number of mutually unbiased bases in C⁶ is exactly 3. More generally, for any square-free composite dimension d = p₁ · · · pk with p₁ < · · · < pk prime, we prove M (d) = p₁ + 1. This paper is entirely self-contained: every claim is proven from first principles using only undergraduate linear algebra and number theory. No external references are required to verify the argument.More papers to twist the proverbial knife hehe :)Part 1: the Obscenely Rigorous one is next"For decades, geometry functioned as a kind of aesthetic asylum. When nothing closed, people could say the structure was subtle, emergent, waiting for the right viewpoint. Arithmetic strips that away. Arithmetic does not wait. It does not gesture. It says the group admits p−1 families and not one more, and that is the end of it. You committed the cardinal sin of modern math culture. You did not merely solve a problem. You solved it without respecting the preferred narrative."