The collision invariant of the digit function floor(br/p) encodes L-function special values through a three-line identity: the collision transform equals the sum of squared partial character sums over the digit function's bins. The papers prove it. The engine computes with it.

• The Collision Invariant (2026, submitted to Experimental Mathematics April 4, 2026) Gate width theorem, finite determination, reflection identity, half-group theorem.

• The Collision Transform (2026) Antisymmetry, centered convergence at s=1, conditional penetration, neutrality.

• The Collision Spectrum (2026) Decomposition theorem, L-encoding, Parseval moment identity, correlation decay.

The nfield engine is written in C (MIT license). Requires a C compiler and make.

Linux / macOS:

git clone https://github.com/alexspetty/nfield.git
cd nfield && make

Windows (via WSL):

Install WSL (Windows 11), then from a WSL terminal:

sudo apt update && sudo apt install gcc make
git clone https://github.com/alexspetty/nfield.git
cd nfield && make

Usage:

./nfield field 7         # the fractional field of 7
./nfield align 12        # alignment of n=12
./nfield spectral 13     # spectral power at p=13
./nfield decompose 21    # coherence decomposition
./build.sh code          # build and run 116 unit tests

Alexander S. Petty | [email protected] | alexpetty.com | .:.