The Grand Capstone of the EntropyLab Research Program
NEUROPIA is the tenth and final installment of the EntropyLab research program — the Grand Unification of all nine preceding Physics-Informed AI (PIAI) frameworks into a single, coherent neural field architecture.
Where each predecessor (E-LAB-01 through E-LAB-09) targeted entropy production within a single physical substrate — from quantum optical coherence to magnetohydrodynamic turbulence — NEUROPIA addresses the meta-problem: the nine dissipation channels are not independent phenomena requiring nine separate controllers; they are coupled subsystems of a single dissipative meta-system whose joint entropy production can be monitored, predicted, and suppressed by a unified learnable operator.
The answer is built on three mathematically rigorous constructs:
| Construct | Role |
|---|---|
| Omni-Spectral Fourier Operator (O-SFO) | 32×32 cross-domain spectral kernel solving coupled multi-physics evolution equations in unified frequency space |
| Grand Constraint Network (GCN) | Enforces all nine EntropyLab conservation laws as hard architectural priors — not soft penalty terms |
| Unified Flux Resolver (UFR) | Model-predictive control engine tracking the Generalized Stress-Energy Tensor across all coupled subsystems |
| Metric | Value |
|---|---|
| Mean Unified Efficiency Index (η_NEUROPIA) | 96.8% |
| Mean cross-domain dissipation reduction | 91.4% vs. uncontrolled baselines |
| Instability suppression factor | 12.3× vs. uncontrolled baselines |
| Unification Dividend (vs. 9 uncoupled specialists) | +7.5 pp |
| Approach to theoretical entropy floor | 3.2% gap |
| Inference latency — A100 FP32 (full 32-component) | 3.5 ms (286 Hz) |
| Inference latency — Orin INT8 (domain-selective) | 0.28 ms (3,571 Hz) |
| Unified State Vector components | 32 (9 domain blocks) |
| Hard-enforced conservation laws | 9 |
| Total parameters (O-SFO + GCN) | 312.6 M |
Input: 32-component Unified State Vector Ψ(r,t)
[Fluid | MHD | Gravitational | Thermal | Electrochemical |
Quantum | Chemical | Biological | Cognitive/AI | Control]
│
▼
┌──────────────────────────────────────────────────┐
│ Omni-Spectral Fourier Operator (O-SFO) │
│ L=12 spectral layers · k_max=96 · 32×32 kernel │
│ Ψ(r,t+dt) = W·Ψ + F⁻¹[ R_φ(k)·F[Ψ](k) ] │
│ Hard constraint projection P_HC (9 laws) │
└───────────────────┬──────────────────────────────┘
│
▼
┌──────────────────────────────────────────────────┐
│ Grand Constraint Network (GCN) │
│ L_GCN = Σ λᵢ · Lᵢ (i = 1…9) │
│ Cross-domain Onsager: L_ij = L_ji │
│ NTK-rebalanced adaptive weights (every 200 ep.) │
└───────────────────┬──────────────────────────────┘
│
▼
┌──────────────────────────────────────────────────┐
│ Unified Flux Resolver (UFR) │
│ T^μν_Σ = Σ T^μν_i (all 9 domains) │
│ min F_ctrl: ∫Φ(S,J,T) dr dt │
│ s.t. λ_min(T^μν_Σ) ≥ λ_safe │
│ MPC horizon: 800 µs · timestep: 40 µs │
└───────────────────┬──────────────────────────────┘
│
▼
Output: F_ctrl — coordinated actuator commands across all coupled domains
δλ_Σ(r,t) — unified cross-domain risk map
η_NEUROPIA — scalar efficiency index ∈ [0,1]
pip install neuropia-enginefrom neuropia import UnifiedStateTracker
# Initialize tracker with active domain configuration
tracker = UnifiedStateTracker(
spatial_dim=256,
k_max=96,
domains=['plasma', 'quantum', 'thermal']
)
# Execute a unified control step
tracker.step(
dt=1e-6,
multi_obs={'B_field': B, 'rho_q': rho, 'T_field': T},
actuator_schedule=None # UFR computes optimal schedule
)
# Retrieve diagnostics
risk_map = tracker.get_unified_safety_margin() # δλ_Σ(r,t) across all domains
eta = tracker.get_neuropia_efficiency() # scalar η_NEUROPIA ∈ [0,1]
ctrl = tracker.get_control_history() # F_ctrl time seriesThe 32-component Unified State Vector Ψ(r,t) encodes the complete thermodynamic state of the coupled multi-physics system:
| Domain Block | Components | Field Variables | Source Project |
|---|---|---|---|
| Fluid Mechanics | 1–3 | Velocity field u(r,t) | MAGNA-FLOW |
| Magnetodynamics | 4–6 | Magnetic field B(r,t) | MAGNA-FLOW |
| Gravitational | 7–10 | Metric perturbation h_µν(r,t) | GRAVI-NEURAL |
| Thermal | 11–12 | Temperature T, heat flux q(r,t) | THERMO-NET |
| Electrochemical | 13–14 | Potential φ, current density J | ENTRO-ENGINE |
| Quantum Coherence | 15–18 | Density matrix ρ_ij (4 real dof) | PHOTON-Q |
| Chemical Reactive | 19–22 | Species concentration c_k (×4) | CHEM-ENTROPIA |
| Biological Metabolic | 23–26 | Metabolic flux J_met (×4) | BIO-ENTROPIA |
| Cognitive / AI | 27–30 | Info density ρ_I, entropy S_AI | ENTRO-AI |
| Control Actuation | 31–32 | External field F_ctrl (×2) | NEUROPIA (new) |
| # | Law | Expression |
|---|---|---|
| 1 | Gauss's Law for Magnetism | ∇·B = 0 |
| 2 | Incompressibility | ∇·u = 0 |
| 3 | Magnetic Helicity Conservation | dH_m/dt = −2η∫(J·B)dV |
| 4 | Second Law of Thermodynamics | dS/dt ≥ 0 |
| 5 | Onsager Reciprocity (cross-domain) | L_ij = L_ji |
| 6 | Bianchi Identity | ∇_µ G^µν = 0 |
| 7 | Quantum Unitarity | Tr(ρ) = 1, ρ ≥ 0 |
| 8 | Mass Conservation (stoichiometric) | Σ_k M_k Γ_k = 0 |
| 9 | ATP Balance (metabolic steady-state) | J_met steady-state flux balance |
| ID | Platform | Domains Coupled | Primary Instability | η_NEUROPIA | σ Reduction |
|---|---|---|---|---|---|
| V1 | ITER-class Tokamak + Thermal shield | MHD + Thermal | ELM + thermal runaway | 97.1% | 93.2% |
| V2 | Hall Thruster + Power electronics | MHD + AI | Breathing mode + logic error | 96.4% | 91.8% |
| V3 | Liquid PbBi Reactor + Neutron transport | MHD + Chemical | Hartmann + radiolysis | 96.9% | 92.6% |
| V4 | Planetary Dynamo + Seismic | MHD + Gravitational | Rotating MHD + core oscillation | 95.8% | 90.3% |
| V5 | Quantum Optical Network + Thermal bath | Quantum + Thermal | Decoherence + phonon cascade | 97.3% | 93.7% |
| V6 | Metabolic Reactor + Chemical network | Bio + Chemical | ATP depletion + pH collapse | 96.1% | 90.9% |
| V7 | AI Inference Engine + Power supply | AI + Thermal | Context collapse + thermal throttle | 97.8% | 94.2% |
| V8 | Full fusion power plant (all coupled) | All 9 domains | 6-link cross-domain cascade | 96.1% | 91.4% |
| Mean | — | — | — | 96.8% | 91.4% |
| Configuration | Mean η | Instab. Suppression |
|---|---|---|
| Uncontrolled baseline | 0.0% | 1.0× |
| Classical LQG (per domain) | 58.3% | 1.8× |
| 9× Specialist (no coupling) | 89.3% | 6.7× |
| O-SFO only (no GCN/UFR) | 91.2% | 7.4× |
| O-SFO + GCN (no UFR) | 94.1% | 9.8× |
| NEUROPIA v1.0.0 (Full) | 96.8% | 12.3× |
The 7.5 pp Unification Dividend — the performance gain attributable specifically to cross-domain coupling awareness — is the central quantitative contribution of NEUROPIA.
A supplementary stress test replacing the geometric gravitational sector (GRAVI-NEURAL metric perturbation block) with an Emergent Entropic Operator (EEO) derived from Verlinde's entropic gravity hypothesis and Jacobson's thermodynamic derivation of the Einstein equations.
Central finding: NEUROPIA's entropy-minimization architecture is theory-agnostic at the functional form level. Performance degrades by at most 1.7 pp under the extreme substitution of classical general relativity with emergent entropic gravity — and by only 0.1–0.3 pp in regimes where gravitational coupling is weak.
| Regime | Primary η (Geometric) | E-LAB-X η (Entropic) | Δη |
|---|---|---|---|
| V4 (Dynamo + Seismic) | 95.8% | 94.1% | −1.7 pp |
| V1 (Tokamak + Thermal) | 97.1% | 96.8% | −0.3 pp |
| V5 (Quantum + Thermal) | 97.3% | 97.1% | −0.2 pp |
| V7 (AI + Thermal) | 97.8% | 97.7% | −0.1 pp |
| Mean | 97.0% | 96.4% | −0.6 pp |
E-LAB-X also introduces the Processing Capacity Index (PCI):
PCI(t) = 1 − Σ_total(t) / Σ_max ∈ [0, 1]
Σ_max = (2π · E · k_B) / (ħ · ln 2) [Bekenstein bound]
PCI = 1 → full processing capacity (low entropy production)
PCI = 0 → thermodynamic saturation (maximum dissipation)
PCI will be implemented as a standard UnifiedStateTracker diagnostic output in NEUROPIA v2.0.
Generalized Dissipation Action:
S[Ψ] = ∫∫ { ½ ⟨∂ₜΨ, G⁻¹ ∂ₜΨ⟩ − V[Ψ] − Φ(S, J, T) } d³x dt
Generalized MGHDT Evolution Equation (Euler-Lagrange):
G⁻¹ ∂ₜΨ + C[Ψ, ∂ₜΨ] + δV/δΨ + δΦ/δΨ = F_ctrl(r, t)
O-SFO Forward Map:
Ψ(r, t+dt) = W·Ψ(r,t) + F⁻¹[ R_φ(k) · F[Ψ](k) ]
Generalized Stress-Energy Tensor:
T^μν_Σ = T^μν_MHD + T^μν_grav + T^μν_therm + T^μν_chem
+ T^μν_quant + T^μν_bio + T^μν_AI
Unified Entropy Production Rate:
dS_total/dt = σ_Ohm + σ_visc + σ_grav + σ_therm
+ σ_chem + σ_quant + σ_bio + σ_AI
Unified Efficiency Index:
η_NEUROPIA = 1 − (dS_total/dt)_controlled / (dS_total/dt)_uncontrolled
| Hyperparameter | Value |
|---|---|
| O-SFO layers (L) | 12 |
| Fourier modes (k_max) | 96 per dim |
| Hidden channels | 512 |
| GCN collocation points | 8,192 per batch |
| Loss weight schedule | Adaptive (NTK, every 200 epochs) |
| UFR MPC horizon | 800 µs |
| UFR control timestep | 40 µs |
| Training compute | 18,400 GPU-hours (8× A100) |
| Total parameters | 312.6 M (O-SFO + GCN) |
| Warm-start | 9 domain checkpoints (predecessor models) |
| Total training epochs | 8,500 |
| Phase | Epochs | Objective |
|---|---|---|
| 1 | 1–800 | Warm-start from 9 predecessor domain checkpoints (84% convergence speedup) |
| 2 | 801–2,500 | Train off-diagonal coupling blocks on synthetic coupled-domain data |
| 3 | 2,501–5,000 | GCN cross-domain Onsager + UFR end-to-end joint training |
| 4 | 5,001–8,500 | Adversarial cross-domain cascade scenarios |
| Hardware | Mode | Full Cycle | Max Hz |
|---|---|---|---|
| NVIDIA A100 (FP32) | Full 32-component | 3.5 ms | 286 Hz |
| NVIDIA A100 (FP16) | Full 32-component | 2.1 ms | 476 Hz |
| NVIDIA A100 | Domain-selective (2 domains) | 1.9 ms | 526 Hz |
| NVIDIA RTX 4090 | Full 32-component | 7.8 ms | 128 Hz |
| NVIDIA Orin (INT8) | Domain-selective | 0.28 ms | 3,571 Hz |
| Xilinx Versal (v2.0) | Domain-selective | < 0.04 ms | > 25,000 Hz |
NEUROPIA is the capstone of a ten-project unified research program. All projects share the ENTROPIA Unified Dissipation State Function Φ(S, J, T) as their thermodynamic foundation.
| Code | Title | DOI | Connection to NEUROPIA |
|---|---|---|---|
| E-LAB-01 | ENTROPIA | 10.5281/zenodo.19416737 | Entropy foundation; dS/dt objective; Φ(S,J,T) |
| E-LAB-02 | ENTRO-AI | 10.5281/zenodo.19551614 | AI-thermodynamic coupling block (components 27–30) |
| E-LAB-03 | PHOTON-Q | 10.5281/zenodo.19729926 | Quantum coherence domain block (components 15–18) |
| E-LAB-04 | ENTRO-ENGINE | 10.5281/zenodo.19740081 | Multi-channel σ decomposition (components 13–14) |
| E-LAB-05 | CHEM-ENTROPIA | 10.5281/zenodo.19749613 | Chemical reactive domain block (components 19–22) |
| E-LAB-06 | BIO-ENTROPIA | 10.5281/zenodo.19754893 | Biological metabolic domain block (components 23–26) |
| E-LAB-07 | THERMO-NET | 10.5281/zenodo.19760903 | Thermal domain block; LEPM design (components 11–12) |
| E-LAB-08 | GRAVI-NEURAL | 10.5281/zenodo.19875543 | Gravitational tensor block (components 7–10) |
| E-LAB-09 | MAGNA-FLOW | 10.5281/zenodo.19893462 | MHD domain blocks; M-FNO kernel basis (components 1–6) |
| E-LAB-10 | NEUROPIA | 10.5281/zenodo.20092199 | This work — program completion |
| E-LAB-X | Stress Test (EEO) | — | Non-geometric gravitational sector; PCI diagnostic |
| Milestone | Target | Platform | Status |
|---|---|---|---|
| v1.0.0 release + PyPI | May 2026 | All GPUs | ✅ Complete |
| ITER integration planning | Q3 2026 | ITER PCS | 🔄 In progress |
| v2.0 R-O-SFO + PCI output | Q2 2027 | A100 cluster | 📐 Design phase |
| v2.0 FPGA deployment | Q4 2027 | Xilinx Versal | 📋 Planned |
| v3.0 compressible MHD (40-component) | Q1 2028 | A100 cluster | 📋 Planned |
| v3.0 astrophysical validation | Q3 2028 | Observatory data | 📋 Planned |
| Full ITER operational deployment | Q4 2028 | ITER device | 📋 Planned |
| Platform | Identifier / URL | Content |
|---|---|---|
| Zenodo | 10.5281/zenodo.20092199 | Archived release, DOI, datasets, paper PDF |
| GitLab (Primary) | gitlab.com/gitdeeper11/NEUROPIA | Primary repo, CI/CD pipelines |
| GitHub (Mirror) | github.com/gitdeeper11/NEUROPIA | Community mirror |
| Bitbucket (Mirror) | bitbucket.org/gitdeeper-11/neuropia | Backup mirror |
| Codeberg (Mirror) | codeberg.org/gitdeeper11/NEUROPIA | European mirror |
| PyPI | pip install neuropia-engine |
Python library (v1.0.0) |
| Netlify | neuropia-v1.netlify.app | Interactive demo + docs |
| OSF Project | osf.io/7pyn9 | Research project data |
| OSF Preregistration | 10.17605/OSF.IO/A4W8Z | Registered study protocol |
| Internet Archive | archive.org/details/osf-registrations-a4w8z-v1 | Permanent archive |
| ORCID | 0009-0003-8903-0029 | Author identifier |
| Resource | Link |
|---|---|
| GitLab ZIP | NEUROPIA-main.zip |
| GitHub ZIP | main.zip |
| Bitbucket ZIP | main.zip |
| Codeberg ZIP | main.zip |
| Zenodo Archive | NEUROPIA.zip |
| Paper PDF | NEUROPIA_Research_Paper_v2.pdf |
# Primary
git clone https://gitlab.com/gitdeeper11/NEUROPIA.git
# Mirrors
git clone https://github.com/gitdeeper11/NEUROPIA.git
git clone https://bitbucket.org/gitdeeper-11/neuropia.git
git clone https://codeberg.org/gitdeeper11/NEUROPIA.gitpip install neuropia-engine
pip install neuropia-engine[cuda] # CUDA-accelerated FFT
cd NEUROPIA && pip install -e . # Development install
python benchmarks/run_all_regimes.py # Run V1–V8 validation suite
python examples/quick_start.py # Minimal working example
python bin/unified_control.py --regime full_fusion_plant@software{baladi2026neuropia,
author = {Baladi, Samir},
title = {NEUROPIA v1.0.0: Neural Cognitive Field Unification
for Cross-Domain Dissipative Intelligence},
year = {2026},
publisher = {Zenodo},
doi = {10.5281/zenodo.20092199},
url = {https://doi.org/10.5281/zenodo.20092199},
note = {E-LAB-10, EntropyLab Program.
Ronin Institute / Rite of Renaissance.}
}Samir Baladi Independent Researcher — Ronin Institute / Rite of Renaissance EntropyLab Research Program gitdeeper@gmail.com | ORCID: 0009-0003-8903-0029
"The universe does not dissipate in nine separate languages. NEUROPIA learns the one language they all speak — entropy — and answers in the only dialect that matters: control."
— NEUROPIA v1.0.0 Manifesto
© 2026 Samir Baladi. Licensed under the MIT License.