The Collision Periodic Table

In 1869, Mendeleev arranged the known elements into a grid. Each element

The Collision Spectrum

Here is a sentence I would not have believed five years ago.

The Collision Transform

Take the collision periodic table. Forty signed integers in base 10, computed

The Collision Invariant

Take a prime, any prime. Do long division by it in some

Phase-Filtered Ramanujan Sums and the Spectral Gate

The autocorrelation formula closed the chain. The self-match count $R(\ell)$ at

The Autocorrelation Formula

There was one place in the chain where the gears didn'

The Spectral Power of the Digit Function

Every prime in base $10$ has a fingerprint, and the fingerprint is

The Spectral Structure of Fractional Fields

A matrix has a voice. You hear it in its eigenvalues. The

The Cross-Alignment Matrix

What if you could see the inside of an integer? Not its

The Coherence Decomposition

Walk into a room where everyone is singing the same note. Now

The Three-Tier Theorem

Divide $1$ by $7$ in base $10$ and you get the famous

The Alignment Limit for All Primes

The digit-partitioning primes are the easy ones. Three of them in base