Digit Collisions and the Cubic Law
The collision energy is the cube of the base, split one third to two thirds between diagonal and off-diagonal poles. The cubic constant is unity.
boundary
The Orbit's Edge
The orbit is multiplicative. The boundary is additive. The Jacobi sum is the bridge. Two laws from the time of Gauss show up because the boundary forced the character to look at -2.
Carry Boundaries and Bernoulli Spectra
The collision invariant turned out to be a special case. This paper finds the source underneath it. The floor provides the weight. The boundary provides the geometry. The spectrum is their product.