The mathematical UTAC logistic core — σ(β(R−Θ)), β-Fitting, Frame-Principle (σ_Φ ≈ 0.0625) and v_RIG for unified field emergence.
pip install utac-core
# with full GenesisAeon stack integration:
pip install "utac-core[stack]"utac fit --beta 0.0625
utac frame-principle
utac rig 10.0
utac logistic 1.618 --beta 0.0625 --theta 1.0from 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| 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 |
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
DOI: 10.5281/zenodo.19057365
PyPI: pip install utac-core (oder pip install "utac-core[stack]" für den vollen GenesisAeon-Stack)
