nfield
A tool for digit fields, alignment,
and collision arithmetic.
I wrote nfield to get the calculations out of one-off programs and into something I could query, sweep, test, and reuse. You can reproduce a calculation from a paper, change the base or denominator, and see what changes.
What you can investigate
Choose an example to runFractional fields and alignment
Study rational numbers as complete fractional fields. Compare their cycles, symmetries, and alignment across bases, then classify whole ranges of denominators by the structure they share.
three-tier classify 100 --base 10Compare alignment classes ↗The arithmetic of the golden ratio
Reproduce the exact threshold and polynomial calculations behind the golden-ratio paper. Change the prime, base, and resolution to examine when the golden ratio is selected.
reciprocal-square-selection scan 31Run the prime-selection scan ↗Collisions, primes, and spectra
Follow digit collisions into residue classes and character spectra. Compute exact collision tables, inspect the surviving frequencies, and evaluate their contributions over finite prime ranges.
collision-transform spectrum --base 10 --lag 1Compute a character spectrum ↗Papers and checks
If you came here from a paper, help reading-map identifies the relevant commands. You can inspect one case, scan a range, or run a verifier’s fixed checks.
The output distinguishes exact arithmetic, numerical results, and bounded searches. A verifier reports what it actually checked.
Open the reading mapRun locally
The program is written in C. Build it with Make, LAPACK, and BLAS. Running locally gives you larger inputs, shell completion, and the JSON/TCP daemon.
git clone https://github.com/alexspetty/nfield.git
cd nfield
make
./nfield field 7Build instructions