Open Source

omni_toolkit

Python package for symmetric space geometry. Parametric Riemannian computations on GL+(n)/SO(p,q) with applications across all five domains.

v0.1.0
Quick Start

Installation

Terminal 
# Clone and install in editable mode
git clone https://github.com/sausterm/OmniSciences.git
cd OmniSciences/omni_toolkit
pip install -e ".[dev]"

# Run tests
make test
Architecture

Module Overview

core/symmetric_space.py SymmetricSpace, DeWittMetric — parametric GL+(n)/SO(p,q) with geodesic distance, log/exp maps, Fréchet mean
core/lie_algebra.py LieAlgebra — structure constants, Killing form, adjoint representation, root systems
core/curvature.py RicciTensor — Ricci curvature, scalar curvature, sectional curvature on symmetric spaces
core/representations.py EigenDecomposition — eigenvalue decomposition, V+/V- splitting, spectral analysis
dynamics/rg_running.py RGRunner, BetaSystem — renormalization group running, coupling evolution
dynamics/effective_potential.py ColemanWeinberg, Particle — one-loop effective potentials, symmetry breaking
topology/complex_structures.py QuaternionicStructure — complex/quaternionic structures, Ja endomorphisms
topology/index_theorem.py GenerationCounter — index theorem computations, generation counting
applications/pati_salam.py PatiSalam — Weinberg angle, gauge coupling, fermion content, proton lifetime
applications/condensed_matter.py GL+(3)/SO(3) elasticity — strain tensors, elastic moduli, deformation geometry
applications/catalysis.py GL+(2)/SO(2) surface deformations — adsorption geometry, strain catalysis
applications/topological_qc.py Topological quantum computing — anyonic braiding, non-Abelian statistics
applications/eeg_bci.py DeWittBCIClassifier — EEG motor imagery, curvature features, SPD classification
applications/dti_analysis.py DTI metrics — FA, MD, curvature anisotropy, geodesic interpolation
Examples

Cross-Domain Usage

Physics — Gauge Unification 
from omni_toolkit.core import SymmetricSpace
from omni_toolkit.applications import PatiSalam

space = SymmetricSpace(4, (3,1))
ps = PatiSalam()

print(space.dewitt_signature())
# (6, 4)
print(ps.weinberg_angle())
# 0.2312
Medical — DTI Analysis 
from omni_toolkit.applications import dti_analysis
import numpy as np

D = np.diag([1.7e-3, 0.3e-3, 0.3e-3])

result = dti_analysis.analyze(D)
print(result['fa'])
# 0.8165
print(result['tissue_type'])
# 'white_matter'
Neuro — BCI Classification 
from omni_toolkit.applications.eeg_bci import (
    DeWittBCIClassifier
)

clf = DeWittBCIClassifier(
    n_channels=8, n_classes=4
)
clf.fit(X_train, y_train)
acc = clf.score(X_test, y_test)
# ~75% on BCI-IV-2a
Materials — Elasticity 
from omni_toolkit.core import SymmetricSpace

# GL+(3)/SO(3) for strain tensors
space = SymmetricSpace(3, (3,0))

# Geodesic distance between strains
d = space.distance(strain_A, strain_B)
# Affine-invariant, no swelling
Technical

Requirements

Python

≥ 3.10

NumPy

Required

SciPy

Required