utac-core 1.0.0

The mathematical UTAC logistic core - sigma(beta(R-Theta)), beta-Fitting, Frame-Principle and v_RIG for the GenesisAeon stack.

utac-core

The mathematical UTAC logistic core — σ(β(R−Θ)), β-Fitting, Frame-Principle (σ_Φ ≈ 0.0625) and v_RIG for unified field emergence.

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Installation

pip install utac-core
# with full GenesisAeon stack integration:
pip install "utac-core[stack]"

Quick start

utac fit --beta 0.0625
utac frame-principle
utac rig 10.0
utac logistic 1.618 --beta 0.0625 --theta 1.0

Python API

from utac_core import beta_fit, v_rig, frame_principle
from utac_core.core import utac_logistic, SIGMA_PHI

# Fit β from field data
beta = beta_fit([1.0, 1.618, 2.718], [0.618, 1.0, 1.618])

# Evaluate UTAC logistic σ(β(x − Θ))
sigma = utac_logistic(1.618, beta=SIGMA_PHI, theta=1.0)

# Recursive implosive growth
growth = v_rig(t=10.0)

# Symbolic Frame-Principle equation
print(frame_principle())   # sigma(beta*(R - Theta)) = 0.0625

Mathematics

Symbol	Meaning
σ(β(R−Θ))	UTAC logistic function
σ_Φ ≈ 0.0625	Frame-Principle constant (1/16)
β	Logistic steepness / fitting parameter
R	Field resonance value
Θ	Logistic threshold
v_RIG	Recursive implosive growth: β·ln(t+1)·σ_Φ

Structure

utac-core/
├── src/utac_core/
│   ├── __init__.py
│   ├── core.py                  # σ(β(R−Θ)), β-Fit, Frame-Principle, v_RIG
│   ├── cli.py                   # utac CLI (Typer + Rich)
│   └── entropy_table_bridge.py  # optional [stack] bridge
├── tests/
│   ├── test_core.py
│   └── test_cli.py
├── domains.yaml
└── pyproject.toml

Citation

If you use utac-core in research, please cite it via its Zenodo DOI:

DOI: 10.5281/zenodo.19057365 PyPI: pip install utac-core (or pip install "utac-core[stack]" for the full GenesisAeon stack)

Role in the GenesisAeon Ecosystem

utac-core (P-CORE) is the UTAC base engine of the GenesisAeon ecosystem, providing the logistic ODE / CREP tensor core that downstream packages (sigillin, mandala-visualize, sonification, aeon-ai, and others) build on.

License

Source code is licensed under GPL-3.0-or-later. Documentation is licensed under CC BY 4.0.

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Built with SymPy · NumPy · Typer · Rich