"Stability is not an individual property — it is a collective effort."
— Samir Baladi, April 2026
ENTROPY RESEARCH LAB · E-LAB-06 · v1.0.0
ENTRO-NET is the sixth project of the EntropyLab research program (E-LAB-06). It represents the leap from self-calibrating individual systems — mastered in ENTRO-EVO (E-LAB-05) — to distributed networked systems.
After successfully enabling a system to self-calibrate its weights via the Adaptive Entropy Weighting (AEW) algorithm with a 78.1% error reduction, this research builds a protocol that allows multiple nodes to physically share their stability states. The goal is to prevent cascading failure by synchronizing entropy flows across the network.
Extended empirical validation across N = 2 to N = 50 nodes reveals a non-trivial crossover from near-linear variance growth to a bounded saturation regime, with no catastrophic failure observed for any tested configuration.
| Component | Description |
|---|---|
| Ψ-Sync Protocol | Real-time sharing of the entropy state Ψ(t) between nodes — stable nodes absorb informational pressure from stressed nodes |
| Collective-AEW | Extension of the single-node AEW algorithm: each node learns from both its own experience and the collective stability history of the entire network |
| θ_net Threshold | Dynamic networked threshold elevated from local to global level, ensuring the system responds as a coherent single entity |
| Fault Isolation | Automatic isolation of nodes exceeding Ψ_critical to prevent entropic contagion from propagating to stable regions |
Collective State:
Ψ_net(t) = { Ψ_1(t), Ψ_2(t), ..., Ψ_N(t) }
Entropy Synchronization Signal:
δ_i_sync(t) = κ · Σ_{j ≠ i} [ Ψ_j(t) − Ψ_i(t) ]
Collective-AEW Weight Update:
w_i(t+1) = w_i(t) − η · [ ∇L_local(t) + β · ∇L_collective(t) ]
Networked Threshold:
θ_net(t) = θ_base + γ · Var[ Ψ_net(t) ]
Global Lyapunov Stability Candidate:
V_net(t) = (1/2) · Σ_{i=1}^{N} [ Ψ_i(t) − Ψ_target ]²
| Objective | Technical Description | Expected Outcome |
|---|---|---|
| Distributed Stability | Balance Ψ state across at least 3 distributed nodes | Reduce total entropy variance by > 50% |
| Networked Transfer | Instant transfer of optimal weights [w₁, w₂, w₃] between nodes | Reduce adaptation time for new nodes by > 70% |
| Fault Isolation | Isolate nodes exceeding Ψ_critical | 100% protection for remaining network members |
Systematic experiments under the scraper regime (800 steps, 4 repetitions per N):
| N | Variance (mean ± std) |
|---|---|
| 20 | 0.165380 ± 0.002169 |
| 30 | 0.197713 ± 0.002204 |
| 50 | 0.221481 ± 0.000677 |
Linear model fitted for N ≤ 15: σ² = 0.0101·N − 0.0331 (R² = 0.986)
| N | Linear Prediction | Actual Variance | Deviation |
|---|---|---|---|
| 20 | 0.1689 | 0.1654 | −2.1% |
| 30 | 0.2699 | 0.1977 | −26.7% |
| 50 | 0.4719 | 0.2215 | −53.1% |
Key finding: Linear scaling breaks down beyond N ≈ 20. The system enters a saturation regime where additional nodes contribute progressively less to global variance.
0.25 ┤
│ ★ N=50
0.20 ┤ ●
│ ●
│ ●
0.15 ┤ ●
│ ●
│ ●
0.10 ┤ ●
│ ●
│●
0.05 ┤●
│
0.00 ┼━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━→ N
0 5 10 15 20 25 30 35 40 45 50
● Empirical data points (mean variance)
── Linear fit (N ≤ 15): σ² = 0.0101·N − 0.0331
── Saturation fit: σ² = 0.228·(1 − e^{−N/16.2})
▒ Crossover region (N ≈ 15–25)
| Regime | N Range | Behavior | Description |
|---|---|---|---|
| Linear Accumulation | 2 – 15 | σ² ≈ 0.0101·N − 0.0331 | Near-linear growth, R² = 0.986 |
| Transition | 15 – 25 | Bending toward saturation | Crossover zone |
| Saturation | 25 – 50 | σ² → 0.22 | Variance ceiling observed |
σ²(N) = σ²_max · (1 − e^{−N/N₀})
| Parameter | Symbol | Value | Interpretation |
|---|---|---|---|
| Saturation ceiling | σ²_max | 0.228 | Maximum variance asymptote |
| Characteristic scale | N₀ | 16.2 | Crossover scale (nodes) |
| Goodness of fit | R² | 0.992 | — |
| Root mean square error | RMSE | 0.004 | — |
Asymptotic properties:
- For small N:
σ² ≈ (σ²_max / N₀) · N→ linear growth - For large N:
σ² → σ²_max→ bounded variance
1. No Catastrophic Failure
The system remains stable and operational for all tested configurations (N ≤ 50). Variance does not diverge.
2. Intrinsic Self-Regulation
Variance growth is actively constrained by three emergent internal mechanisms:
- Adaptive aggression auto-tuning (α self-adjusts)
- Collective-AEW weight redistribution
- Networked threshold elevation (θ_net)
3. Smooth Crossover
The transition from linear growth to saturation is gradual — a soft scaling crossover rather than a sharp phase transition.
4. Bounded Variance Ceiling
The system approaches a natural ceiling σ² ≈ 0.23, independent of further node addition beyond N ≈ 30.
| Use Case | Recommended N | Expected Variance | Reliability |
|---|---|---|---|
| Production (critical) | 2 – 5 | < 0.05 | 🟢 Excellent |
| Production (standard) | 6 – 12 | 0.05 – 0.09 | 🟢 Good |
| Experimental | 13 – 20 | 0.09 – 0.17 | 🟡 Acceptable |
| Research / Development | 21 – 30 | 0.17 – 0.20 | 🔴 Degraded |
| Not recommended | > 30 | > 0.20 |
ENTRO-NET/
│
├── entro_net/ # Core library
│ ├── __init__.py
│ ├── psi_sync.py # Ψ-Sync protocol
│ ├── collective_aew.py # Collective-AEW optimizer
│ ├── net_threshold.py # θ_net dynamic threshold
│ ├── fault_isolation.py # Cascading failure prevention
│ └── simulator.py # Distributed simulation engine
│
├── bin/ # Executables
│ └── run_simulation.py
│
├── tests/ # Unit and integration tests
├── examples/ # Usage examples
├── scripts/ # Utility scripts
├── docs/ # Documentation
├── results/ # Simulation outputs
└── Netlify/ # Static website
from entro_net import PsiSync, CollectiveAEW, NetThreshold
# Initialize 3-node network
sync = PsiSync(n_nodes=3)
collective = CollectiveAEW(eta=0.01, target=0.339)
threshold = NetThreshold(theta_base=1.2)
# Run distributed control loop
for t in range(500):
psi_states = [node.observe() for node in nodes]
# Synchronize entropy states across network
synced_psi = sync.broadcast(psi_states)
# Collective weight adaptation
weights = collective.step(synced_psi)
# Apply global networked threshold
theta = threshold.update(synced_psi)
# Isolate faulty nodes if needed
if sync.detect_fault(psi_states):
sync.isolate_node(faulty_id)Reproduce all experiments:
python bin/run_simulation.py \
--nodes N \
--steps 800 \
--regime scraper \
--repeats 4| Project | Code | Contribution to ENTRO-NET |
|---|---|---|
| ENTROPIA | E-LAB-01 | Unified Dissipation State Function — foundational entropy formalism |
| ENTRO-AI | E-LAB-02 | AI risk monitoring — dynamic entropy threshold design |
| ENTRO-CORE | E-LAB-03 | Singular system will — local AEW weight architecture |
| ENTRO-ENGINE | E-LAB-04 | Budget distribution between coupled systems |
| ENTRO-EVO | E-LAB-05 | Self-learning AEW — 78.1% error reduction baseline |
| ENTRO-NET | E-LAB-06 | Collective Ψ-Sync — distributed stability (this work) |
| Resource | URL |
|---|---|
| 📄 Paper (Zenodo) | 10.5281/zenodo.19474217 |
| 📋 OSF Preregistration | 10.17605/OSF.IO/9Y7RX |
| 💻 GitLab | gitlab.com/gitdeeper10/ENTRO-NET |
| 💻 GitHub | github.com/gitdeeper10/ENTRO-NET |
| 💻 Bitbucket | bitbucket.org/gitdeeper-10/entro-net |
| 💻 Codeberg | codeberg.org/gitdeeper10/entro-net |
| 📦 PyPI | pypi.org/project/entro-net |
| 🌐 Website | entro-net.netlify.app |
@software{baladi2026entronet,
author = {Baladi, Samir},
title = {ENTRO-NET: Distributed Entropy Synchronization Protocols
for Collective Neural Networks},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19474217},
url = {https://github.com/gitdeeper10/ENTRO-NET},
note = {E-LAB-06. Builds on E-LAB-01 through E-LAB-05.
EntropyLab Research Program.
OSF Preregistration: 10.17605/OSF.IO/9Y7RX}
}Samir Baladi
Interdisciplinary AI & Theoretical Physics Researcher
Ronin Institute / Rite of Renaissance
- 📧 gitdeeper@gmail.com
- 🆔 ORCID: 0009-0003-8903-0029
- 💻 GitLab / GitHub / Codeberg: @gitdeeper10
MIT License — see LICENSE file for details.
Part of the EntropyLab ten-project research program · E-LAB-06 ✅ Complete
"Intelligence by Design, Stability by Physics, Evolution by Learning, Harmony by Network"