LatticeFit

Deterministic engine for discovering discrete multiplicative structure in positive real data.

Given measurements x_1, x_2, ..., x_n, LatticeFit tests whether they cluster near a geometric lattice:

x_i ~ A * r^(k_i/d),   k_i in Z

and quantifies whether the alignment is statistically non-accidental.

Installation

pip install latticefit            # core only
pip install "latticefit[plots]"   # with matplotlib

Quick start

import latticefit
import numpy as np

# Standard Model fermion masses (GeV)
masses = [5.11e-4, 0.1057, 1.777, 0.00216, 1.275, 172.76,
          0.00467, 0.0934, 4.18]
names  = ["e", "mu", "tau", "u", "c", "t", "d", "s", "b"]

result = latticefit.fit(masses, anchor=5.11e-4,
                        base=latticefit.PHI, denom=4, names=names)
print(result.summary())

Features

• Deterministic scan -- no random initialization, reproducible results
• Anchor-shift invariance -- fits relative ratios, not absolute scale
• Structure-preserving null hypothesis -- permutation test that preserves the multiplicative spread of the data
• Auto-discovery -- scans over base r and denominator d automatically
• CLI -- latticefit data.csv --base phi --denom 4
• Publication-quality plots -- ladder diagrams, residual histograms

Background

LatticeFit was developed as the core fitting engine for the Hyperbolic Flavour Geometry programme, which derives Standard Model flavor parameters from the arithmetic geometry of compact hyperbolic 3-manifolds.

The golden ratio base r = phi = (1+sqrt(5))/2 is motivated by the Lucas trace identity: closed geodesics of length 4m*log(phi) in hyperbolic 3-manifolds have integer holonomy traces equal to Lucas numbers.

Lucas mode

# Scan with golden ratio base (motivated by hyperbolic geometry)
result = latticefit.fit(masses, base=latticefit.PHI, lucas=True)

Citation

If you use LatticeFit in your research, please cite:

Gentry, M.L. (2026). LatticeFit v0.3.0.
GitHub: https://github.com/drmlgentry/latticefit
PyPI: https://pypi.org/project/latticefit/

License

MIT