preprint

The Fourier coefficients factor through Bernoulli numbers and L-function values at s = 1.

The collision periodic table, centered and Fourier-transformed. It cancels at s = 1.

A finite signed table for every prime, built from the digit function. The collision invariant.

The primes that organize long division are the same primes that organize musical pitch. In base 30, the alignment deficit lattice produces the just major scale. In base 12, the Pythagorean comma.