🔴 ENTRO-CORE — Regime-Dependent Entropy-Augmented Control

"Intelligence by Design, Stability by Physics"

ENTRO-CORE is the third project of the EntropyLab research program (E-LAB-03). It investigates entropy-based control architectures for dynamical systems, introducing a hybrid regime-switching controller that combines PID with nonlinear entropy feedback.

Project Code: E-LAB-03 | Lab: Entropy Research Lab | Submitted: April 2026

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📋 Table of Contents

• Overview
• Key Finding
• Control Laws
• Experimental Results
• Project Structure
• Installation
• Quick Start
• Validation
• EntropyLab Roadmap
• Documentation
• Citation
• Author
• License

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🔭 Overview

Modern AI systems operate under high-dimensional feedback loops that can lead to instability, especially under long-context reasoning or recursive inference. ENTRO-CORE moves entropy control from an external monitoring layer (ENTRO-AI) into the core control architecture itself.

Instead of: Monitor → Detect → Intervene (reactive)
ENTRO-CORE does: Self-regulate internally (proactive)

Metric	Value
PID Final Ψ (stable regime)	0.017
ENTRO-CORE Final Ψ	-0.239
Hybrid Final Ψ	-0.012
Validation Runs	5 runs per controller
Noise Robustness	σ = 0.00 → 0.15

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🔬 Key Finding

Entropy-based control is regime-dependent, not universally superior.
PID remains optimal in stable linear systems, while entropy-based control provides benefits in near-critical regimes.

Regime	Optimal Controller
Stable linear	PID
Near-critical / nonlinear	ENTRO-CORE / Hybrid

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📐 Control Laws

PID Controller

u_PID(t) = K_p·e(t) + K_i·∫e(τ)dτ + K_d·ė(t)

with e(t) = -Ψ(t), K_p=0.8, K_i=0.2, K_d=0.3

Entropy-Based Controller (ENTRO-CORE v1)

u_ENTRO(t) = w₁·σ(Ψ_norm - θ) + w₂·tanh(Ψ̇) + w₃·tanh(Ψ̈)

with w₁=0.5, w₂=0.3, w₃=0.2, θ=1.4

Hybrid Regime-Switching Controller

u(t) = { u_PID(t)      if Ψ(t) < Ψ_th
{ u_ENTRO(t)    if Ψ(t) ≥ Ψ_th

with switching threshold Ψ_th = 1.7

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📊 Experimental Results

Under near-critical initial conditions (Ψ(0)=1.8, Ψ̇(0)=0.3):

Controller	Final Ψ (t=20s)	Outcome
Uncontrolled	0.053	Naturally stable
PID	0.017	Optimal convergence
ENTRO-CORE v1	-0.239	Mild overshoot
Hybrid (threshold=1.7)	-0.012	Robust performance

Noise Sensitivity (Hybrid Controller)

Noise σ	Final Ψ	Outcome
0.00	0.339	Stabilized
0.02	0.341	Stabilized
0.05	0.355	Stabilized
0.10	0.412	Stabilized
0.15	0.523	Stabilized

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🗂️ Project Structure

entro-core/
│
├── 📄 README.md                            # This file
├── 📄 LICENSE                              # MIT License
├── 📄 CHANGELOG.md                         # Version history
├── 📄 CONTRIBUTING.md                      # Contribution guidelines
├── 📄 CITATION.cff                         # Academic citation metadata
├── 📄 pyproject.toml                       # Build configuration
├── 📄 requirements.txt                     # Runtime dependencies
├── 📄 requirements-dev.txt                 # Development dependencies
│
├── 📁 entro_core/                          # Core Python package
│   ├── 📄 init.py                      # Package entry point
│   ├── 📄 controller.py                    # ENTRO-CORE v1 (original)
│   ├── 📄 controller_v2.py                 # ENTRO-CORE v2 (negative feedback)
│   ├── 📄 hybrid_controller.py             # Regime-switching controller
│   ├── 📄 actuator.py                      # Actuation strategies
│   ├── 📄 normalize.py                     # Logistic normalization (Eq. 4)
│   ├── 📄 state.py                         # State tracker (Ψ, Ψ̇, Ψ̈)
│   └── 📄 control_law.py                   # Control law u(t) (Eq. 5)
│
├── 📁 simulation/                          # Validation simulations
│   ├── 📄 generate_figures_fixed.py        # Trajectory generation
│   ├── 📄 validation_experiment.py         # Full validation suite
│   ├── 📄 hybrid_test.py                   # Hybrid controller test
│   └── 📁 results/
│       └── 📄 trajectories_fixed.csv       # Comparison data
│
├── 📁 tests/                               # Unit tests
│   ├── 📄 test_controller.py               # Controller tests (21 tests)
│   └── 📄 init.py
│
├── 📁 paper/                               # Research paper assets
│   └── 📁 arxiv/
│       └── 📄 entro_core_paper_revised.tex # LaTeX manuscript
│
└── 📁 docs/                                # Documentation
├── 📄 index.md
├── 📄 control_theory.md
└── 📄 api_reference.md

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⚙️ Installation

Requirements

• Python 3.11+
• No external dependencies required (pure Python)

Via PyPI

pip install entro-core

From Source

git clone https://github.com/gitdeeper10/entro-core.git
cd entro-core
pip install -e ".[dev]"

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🚀 Quick Start

1. Import and Use Hybrid Controller

from entro_core.hybrid_controller import HybridController

# Create controller with threshold
controller = HybridController(threshold=1.7)

# Simulate a near-critical state
result = controller.step(psi=1.8)

print(f"u(t) = {result.u:.3f}")
print(f"Mode: {result.mode}")  # 'PID' or 'ENTRO-CORE'
print(f"Active: {result.is_active}")

u(t) = 0.423
Mode: ENTRO-CORE
Active: True

2. Run Validation Experiment

python simulation/validation_experiment.py

3. Generate Comparison Trajectories

python simulation/generate_figures_fixed.py

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📊 Validation Results

Test Suite (21 tests)

Category Passed Normalization 4/4 ✅ Sigmoid 3/3 ✅ Tanh 3/3 ✅ Control Law 3/3 ✅ Actuation 4/4 ✅ Controller 4/4 ✅ Total 21/21

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🗺️ EntropyLab Research Roadmap

E-LAB-01  ✅  ENTROPIA          — Thermodynamic unification
E-LAB-02  ✅  ENTRO-AI          — Entropy-resistant AI inference
E-LAB-03  ✅  ENTRO-CORE        — Regime-dependent control (this repository)
E-LAB-04  📅  ENTRO-ENGINE      — Generalized entropy control framework
E-LAB-05  📅  ENTRO-FIN         — Financial entropic dynamics
E-LAB-06  📅  ENTRO-SOCIAL      — Information cascades in networks
E-LAB-07  📅  ENTRO-QUANTUM     — Quantum entropy extension
E-LAB-08  📅  ENTRO-BIO         — Biological neural entropy systems
E-LAB-09  📅  ENTRO-CLIMATE     — Climate entropy modeling
E-LAB-10  📅  ENTRO-META        — Unified entropy control theory

✅ Complete | 🔄 In Progress | 📅 Planned

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📚 Documentation

Resource Link Full Documentation entropia-lab.netlify.app/entro-core/docs Research Paper (PDF) entropia-lab.netlify.app/entro-core/paper API Reference entropia-lab.netlify.app/entro-core/api Parent Project (ENTRO-AI) entro-ai.netlify.app Foundation (ENTROPIA) doi.org/10.5281/zenodo.19416737

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🤝 Contributing

git clone https://github.com/gitdeeper10/entro-core.git
cd entro-core
pip install -e ".[dev]"
pytest tests/

Priority contribution areas:

· Smooth switching (sigmoidal interpolation) · Additional system dynamics models · Real-world validation datasets

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📖 Citation

@software{baladi2026entrocore,
  author       = {Samir Baladi},
  title        = {ENTRO-CORE: Regime-Dependent Entropy-Augmented Control},
  year         = {2026},
  version      = {0.1.0},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.19431029},
  url          = {https://doi.org/10.5281/zenodo.19431029},
  note         = {E-LAB-03. Builds on E-LAB-01 and E-LAB-02}
}

Parent frameworks:

@article{baladi2026entropia,
  title        = {ENTROPIA: Statistical Dynamics of Information Dissipation},
  author       = {Samir Baladi},
  year         = {2026},
  doi          = {10.5281/zenodo.19416737},
  note         = {E-LAB-01}
}

@software{baladi2026entroai,
  author       = {Samir Baladi},
  title        = {ENTRO-AI: Entropy-Resistant Inference Architecture},
  year         = {2026},
  version      = {2.0.0},
  doi          = {10.5281/zenodo.19284086},
  note         = {E-LAB-02}
}

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👤 Author

Samir Baladi

· Role: Principal Investigator, Interdisciplinary AI Researcher · Affiliation: Ronin Institute / Rite of Renaissance · Email: gitdeeper@gmail.com · ORCID: 0009-0003-8903-0029 · GitHub: github.com/gitdeeper10 · GitLab: gitlab.com/gitdeeper10

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📜 License

MIT License — see LICENSE for details.

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