🔴 Overview
From self-calibration to collective synchronization
"Stability is not an individual property — it is a collective effort." — Samir Baladi, April 2026
ENTRO-NET extends adaptive entropy weighting from individual systems to distributed networks. Multiple nodes physically share stability states through the Ψ-Sync protocol, preventing cascading failure via synchronized entropy flow. Built upon ENTRO-EVO (E-LAB-05), this work demonstrates that stability emerges from collective coordination.
0.0002
Min Variance (N=5)
Optimal stability regime
0.22
Saturation Ceiling
σ²_max at large N
57.1%
Variance Reduction
N=5 scraper regime
15
Max Validated N
Stable up to 50
🎯 Core Innovation
Entropy Sync · Collective AEW · θ_net
E_sync,i = Σ κ·(Ψ_j - Ψ_i)
∇L_collective = ∇L_local + β·∇L_network
θ_net = θ_base + γ·Var(Ψ_i)
🔄 Ψ-Sync Protocol
Entropy Exchange Law
Ψ_total(t) = Σ λ_i·Ψ_i(t) + C_sync(t)
E_sync,i = Σ κ·(Ψ_j - Ψ_i)
E_sync,i = Σ [α·κ·(Ψ_j - Ψ_i) + α²·(Ψ_j - Ψ_i)³]
| Parameter | Symbol | Value | Description |
|---|
| Synchronization constant | κ | 0.1-2.0 | Controls stability transfer speed |
| Coupling coefficient | C_sync | 0.05-0.9 | Network coupling strength |
| Node weights | λ_i | 1/N | Relative importance in network |
📐 Collective-AEW
Collaborative Weight Adaptation
∇L_local = 2·(Ψ_norm - Ψ*)·[1-Ψ_norm, dΨ/dt, d²Ψ/dt²]
∇L_network = f(network_errors, reward_signal)
∇L_collective = ∇L_local + β·∇L_network
w_new = w_old - η·∇L_collective
| Parameter | Symbol | Value | Description |
|---|
| Learning rate | η | 0.01 | Weight update speed |
| Cooperation coefficient | β | 0.3-1.0 | How much nodes learn from neighbors |
| Momentum | μ | 0.9 | Smoother weight updates |
🌡️ Networked Threshold
Variance-Sensitive Activation
θ_net = θ_base + γ·Var(Ψ_i)
📊 Scaling Results
Extended N = 20, 30, 50
| N | Variance (mean ± std) | Linear Prediction | Deviation |
|---|
| 20 | 0.165380 ± 0.002169 | 0.1689 | -0.0035 |
| 30 | 0.197713 ± 0.002204 | 0.2699 | -0.0722 |
| 50 | 0.221481 ± 0.000677 | 0.4719 | -0.2504 |
Linear (N≤15)
σ² = 0.0101·N - 0.0331
R² = 0.986
Saturation (N≥25)
σ² → 0.22
Variance ceiling
Crossover
N ≈ 15-25
Transition zone
📈 Saturation Model
Bounded Variance Growth
σ²(N) = σ²_max · (1 - e^{-N/N₀})
σ²_max = 0.228 (saturation ceiling)
N₀ = 16.2 (characteristic scale)
"ENTRO-NET does not exhibit unbounded variance growth under scaling. Instead, it transitions from linear accumulation to a saturation regime, indicating intrinsic regulation mechanisms."
📦 Installation
Quick setup
pip install entro-net
git clone https://github.com/gitdeeper10/ENTRO-NET.git
cd ENTRO-NET
pip install -r requirements.txt
pip install -e .
python -c "from entro_net import __version__; print(__version__)"
🔧 API Reference
Python interface
PsiSync
Ψ-Sync Protocol for entropy exchange between nodes
from entro_net import PsiSync
sync = PsiSync(n_nodes=5, kappa=1.0, aggression=1.0)
synced_states = sync.broadcast(psi_states)
CollectiveAEW
Collective Adaptive Entropy Weighting optimizer
from entro_net import CollectiveAEW
aew = CollectiveAEW(eta=0.01, target=0.339, beta=1.0)
weights = aew.step(avg_psi, avg_d_psi, avg_d2_psi, network_errors)
NetThreshold
Networked dynamic activation threshold
from entro_net import NetThreshold
threshold = NetThreshold(theta_base=1.4, gamma=10.0)
theta_net = threshold.update(psi_states)
FaultIsolation
Automatic node isolation for cascading failure prevention
from entro_net import FaultIsolation
iso = FaultIsolation(psi_critical=0.8)
iso.check_node(node_id, psi)
🧩 Core Modules
ENTRO-NET architecture
psi_sync.py
Ψ-Sync Protocol
Entropy exchange & coupling
collective_aew.py
Collective-AEW
Collaborative weight learning
net_threshold.py
Net Threshold
Variance-sensitive activation
fault_isolation.py
Fault Isolation
Cascading failure prevention
👤 Author
Principal investigator
🔴
Samir Baladi
Interdisciplinary AI Researcher — Theoretical Physics, Statistical Mechanics & Information Theory
Ronin Institute / Rite of Renaissance
Samir Baladi is an independent researcher affiliated with the Ronin Institute, developing the Rite of Renaissance interdisciplinary research program. ENTRO-NET is the sixth project (E-LAB-06) in a ten-project research program, building directly on ENTROPIA (E-LAB-01), ENTRO-AI (E-LAB-02), ENTRO-CORE (E-LAB-03), ENTRO-ENGINE (E-LAB-04) and ENTRO-EVO (E-LAB-05).
No conflicts of interest declared. All code and data are open-source under MIT License.
📝 Citation
How to cite
@software{baladi2026entronet,
author = {Samir Baladi},
title = {ENTRO-NET: Distributed Entropy Synchronization Protocols
for Collective Neural Networks},
year = {2026},
version = {1.0.0},
publisher = {Zenodo},
doi = {10.5281/zenodo.19474217},
url = {https://doi.org/10.5281/zenodo.19474217},
note = {E-LAB-06. Builds on E-LAB-01 through E-LAB-05}
}
@software{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}
}
@software{baladi2026entrocore,
author = {Samir Baladi},
title = {ENTRO-CORE: Self-Regulated Intelligence},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19431029},
note = {E-LAB-03}
}
@software{baladi2026entroengine,
author = {Samir Baladi},
title = {ENTRO-ENGINE: Entropy Flow Regulator},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19441032},
note = {E-LAB-04}
}
@software{baladi2026entrovevo,
author = {Samir Baladi},
title = {ENTRO-EVO: Adaptive Entropy Weighting for Self-Calibrating Systems},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19464489},
note = {E-LAB-05}
}
"Stability is not an individual property — it is a collective effort. ENTRO-NET proves that synchronized entropy flow prevents cascading failure and creates networks of physically honest intelligence."