ENTRO-OMEGA (E-LAB-10) is the tenth and culminating project of the EntropyLab decadal research programme — a unified theoretical and computational framework that fuses all prior entropic control protocols (E-LAB-01 through E-LAB-09) into a single self-governing engine designated OMEGA v1.0.
| Component | Full Name | Role |
|---|---|---|
| Ω_core(t) | Omega State Function | 5-component vector tracking dissipation, pulsation, memory, quantum probability, network coherence |
| UFE | Unified Field Equation | dΩ_core/dt = E(Ω_core,u,ε) - Λ·Ω_core + ξ(t) |
| UAS | Universal Adaptive Stabiliser | Closed-loop controller with ISS guarantee |
| H(t) | Composite Health Index | Weighted L²-norm complement with AEW adaptation |
| θ(t) | Breathing Threshold | Self-adaptive activation boundary |
| Metric | ENTRO-OMEGA | Target |
|---|---|---|
| Collapse rate | 0.0% | 0.0% ✅ |
| Peak load reduction | 91.3% | >90% ✅ |
| Throughput gain | 44.5% | >35% ✅ |
| Convergence index | 0.9987 | >0.99 ✅ |
| Convergence time | 2.87s | <4.0s ✅ |
pip install entro-omegaQuick Start
OMEGA v1.0 Engine
from entro_omega import OmegaCore
# Initialize OMEGA v1.0 engine
omega = OmegaCore(theta_base=0.55, gamma=0.40, delta=0.15)
# Observe environment and step
result = omega.step(env_snapshot)
print(f"Omega State: {result['omega']}")
print(f"Health Index: {result['H']:.3f}")
print(f"Control Vector: {result['u']}")Universal Adaptive Stabiliser (UAS)
from entro_omega import UASController
uas = UASController(alpha=[1.0]*5, beta=[0.8]*5)
control = uas.compute(omega_state, theta_threshold)Health Index with AEW Adaptation
from entro_omega import HealthIndex
health = HealthIndex(weights=[0.2, 0.2, 0.2, 0.2, 0.2])
H = health.compute(omega_state)
weights = health.update_weights(H, target=0.80)Documentation
Resource Link Website https://entro-omega.netlify.app Research Paper DOI: 10.5281/zenodo.19547863 API Reference https://entro-omega.readthedocs.io OSF Registration https://osf.io/6v4xt
Project Structure
ENTRO-OMEGA/
│
├── entro_omega/
│ ├── __init__.py
│ ├── omega_core.py # Omega State Function Ω_core(t)
│ ├── uas.py # Universal Adaptive Stabiliser
│ ├── health.py # Composite Health Index H(t)
│ ├── threshold.py # Breathing threshold θ(t)
│ └── utils.py # Simulation utilities
│
├── tests/
│ ├── test_omega_core.py
│ ├── test_uas.py
│ ├── test_health.py
│ └── test_utils.py
│
├── examples/
│ ├── example_omega.py
│ ├── example_uas.py
│ └── example_health.py
│
├── results/
│ ├── daily_report_2026-04-14.txt
│ ├── weekly_report_week16_2026.txt
│ ├── monthly_report_april_2026.txt
│ ├── alerts.log
│ └── coverage_report_2026-04-14.txt
│
├── docs/
│ ├── conf.py
│ ├── index.rst
│ └── api.rst
│
├── Netlify/
│ ├── index.html
│ ├── dashboard.html
│ ├── reports.html
│ └── documentation.html
│
├── bin/
│ └── run_simulation.py
│
├── scripts/
├── data/
├── dist/
│ └── entro-omega-1.0.0.tar.gz
│
├── pyproject.toml
├── requirements.txt
├── requirements-dev.txt
├── Dockerfile
├── Makefile
├── VERSION
├── CITATION.cff
├── AUTHORS.md
├── CHANGELOG.md
├── CONTRIBUTING.md
├── SECURITY.md
├── DEPLOY.md
├── INSTALL.md
└── COMPLETION.md
Codebase Statistics
Metric Value Python modules 5 Test files 4 Test cases (pending) Coverage (pending) Governing equations 12+
EntropyLab Research Program - COMPLETE
ENTRO-OMEGA is the tenth and final project in the EntropyLab series — a unified research program bridging thermodynamic entropy, Shannon information theory, and AI systems control.
E-LAB Project Focus Status 01 ENTROPIA Theoretical foundations ✅ 02 ENTRO-AI AI inference stability ✅ 03 ENTRO-CORE Core entropy measurement ✅ 04 ENTRO-ENGINE System coupling ✅ 05 ENTRO-EVO Adaptive weighting ✅ 06 ENTRO-NET Distributed synchronization ✅ 07 ENTRO-QUANTUM Probabilistic states ✅ 08 ENTRO-GHOST Entropic memory ✅ 09 ENTRO-PULSE Periodic pulsing ✅ 10 ENTRO-OMEGA Grand Unification ✅
→ Program home: entropia-lab.netlify.app
Integration of All Nine Predecessor Projects
Project Contribution to OMEGA v1.0 ENTROPIA (E-LAB-01) Thermodynamic foundation - Dissipation index ρ(t) ENTRO-AI (E-LAB-02) AI entropy throttling - Phase transition boundaries ENTRO-FLOW (E-LAB-03) Flow control - Routing backbone ENTRO-ENGINE (E-LAB-04) Coordination law - Control law substrate u_i(t) ENTRO-EVO (E-LAB-05) AEW adaptation - Weight updates w(t) ENTRO-NET (E-LAB-06) Network synchronisation - Coherence index N(t) ENTRO-QUANTUM (E-LAB-07) Quantum collapse - Probability Q(t) ENTRO-GHOST (E-LAB-08) Spectral memory - Recall fidelity G(t) ENTRO-PULSE (E-LAB-09) Rhythmic pulsation - Pulse phase P(t)
Citation
@software{baladi2026entromega,
author = {Samir Baladi},
title = {ENTRO-OMEGA: Grand Unification of Informational Entropy},
year = {2026},
publisher = {Zenodo},
doi = {10.5281/zenodo.19547863},
note = {EntropyLab E-LAB-10},
url = {https://doi.org/10.5281/zenodo.19547863}
}License
MIT License © 2026 Samir Baladi Ronin Institute / Rite of Renaissance · ORCID 0009-0003-8903-0029
"Stability is not a target to be reached but a mode of existence to be maintained — dynamically, adaptively, and in full awareness of both history and probability."
— EntropyLab Research Program