The Collision Spectrum

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

The Collision Transform

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

The Collision Invariant

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

The Collision Spectrum and the L-Function Landscape

The coefficients factored. The digit function encodes L-function values at s = 1.

The Spectral Repulsion

Forty percent of the expected overlap is missing. The ratio is stable across every tested base.

The Double Transversality

The collision invariant and the prime distribution avoid each other across the spectrum.

The General Neutrality Theorem

Neutrality holds at every odd prime, not just 3. The same reflection, at every scale.

The Neutrality Theorem

The mod-3 structure holds the penetration together. Remove it and the sum explodes.

The Collision Transform and the Critical Strip

The centered sum converges at s = 1. Push it below. How far does it survive?

The Collision Periodic Table

Forty integers, determined by the last two digits of every prime past 100. Every pair sums to -1.

The Centered Collision Sum

Subtract the family bias and the divergence vanishes. The centered sum converges at s = 1.

The Collision Fluctuation Sum

I added up the collision deviations. The sum drifted downward, and the drift had a shape.