Neural Singularity & Unified Field Synthesis Framework
Unified Propagator Core · DOI: 10.5281/zenodo.20092199 · MIT License
"If ENTROPIA was the question — how do we understand order from chaos — then NEUROPIA is the answer. It is the state in which artificial intelligence becomes the mirror that reflects the perfection of physical law across every domain simultaneously. We do not simulate the universe. We rewrite it, digitally."
— NEUROPIA v1.0.0 Manifesto
The Problem
Every unsolved challenge in multi-physics AI control reduces to a single gap: no architecture enforces entropy minimization simultaneously across coupled physical domains. Cross-domain coupling generates hidden entropy production invisible to any single-domain framework.
Three-way MHD + solid thermal + radiation transport coupling — no single E-LAB predecessor was designed to bridge all three. The plasma's heat pulse reaches the tungsten wall before any single-domain controller can predict and react.
Alfvénic spacetime coupling creates cross-domain entropy production invisible to both MAGNA-FLOW and GRAVI-NEURAL operating independently. Metric perturbations alter plasma transport coefficients through frame-dragging analogs.
Four coupled domains — reactive chemistry, heat transfer, fluid dynamics, and electromagnetics — whose Onsager cross-coupling matrix has 6 independent off-diagonal terms, each a hidden entropy production pathway.
Five-domain coupling between information entropy, biological metabolic flux, electromagnetic fields, thermal gradients, and fluid transport — a system whose cross-domain coupling no single EntropyLab framework addresses.
Seven simultaneous physical domains. Twenty-one independent Onsager cross-coupling pathways. The complete test of whether a single unified neural controller can outperform nine independently optimized predecessors.
Core Architecture
NEUROPIA does not orchestrate nine separate controllers. It replaces them with a single gauge-equivariant neural field architecture acting on the Physical Coupling Manifold.
A gauge-equivariant tensor neural operator acting on sections of a fiber bundle over the Physical Coupling Manifold M. The learnable N_d × N_d complex spectral kernel captures cross-domain coupling between all physical fields simultaneously. Noether projection at the output layer enforces energy, momentum, charge, and information entropy conservation as hard architectural constraints — not penalty terms.
Enforces Noether's theorem across every domain interface architecturally, not through gradient penalties. The Onsager reciprocal matrix L_ij = L_ji is maintained as a hard constraint, preventing unphysical time-irreversible cross-coupling pathways. The Bianchi identity is enforced in the gravitational sector, and coupling consistency checks prevent entropy misattribution between domains.
Integrates all nine EntropyLab dissipation functionals into a single Pareto-optimal master entropy objective. The cross-domain Onsager decomposition ensures that coupling entropy — invisible to any single-domain framework — is explicitly minimized. The Pareto optimizer enforces per-domain performance floors (α_i = 0.15), guaranteeing that no domain is sacrificed for another.
E-LAB-X · Non-Geometric Stress Test
Replacing the geometric gravitational sector with an Emergent Entropic Operator (EEO) derived from Verlinde's entropic gravity hypothesis. Performance degradation ≤ 1.7 pp — demonstrating NEUROPIA's theory-agnostic architecture.
Mathematical Architecture
The formal mathematical foundation of NEUROPIA's unified control framework (E1-E8 for E-LAB-X).
Experimental Validation
Validated across plasma physics, gravitational analogs, reactive chemistry, neuroelectromagnetics, and the full seven-domain EntropyLab stack. All results are true held-out test metrics — no validation data seen during training.
| ID | Platform | Coupled Domains (N) | Primary Coupling | UFCI | Σ Reduction | Key Result |
|---|---|---|---|---|---|---|
| C1 | Tokamak + Thermal Wall | 3 (MHD + Thermo + EM) | Plasma-wall heat transfer | 97.8% | 94.2% | 8.9× heat flux suppression |
| C2 | MHD + Gravitational Analog | 3 (MHD + Gravity + Info) | Alfvénic spacetime coupling | 96.9% | 92.7% | 3.8× metric-Alfvén accuracy |
| C3 | Chemical Reactor + Heat Exchanger | 4 (Chem + Thermo + Fluid + EM) | Reactive thermofluid coupling | 97.4% | 93.8% | 15.7× yield improvement |
| C4 | Neural-Bio Electromagnetic | 5 (Info + Bio + EM + Thermo + Fluid) | Neuroelectric metabolic flux | 96.8% | 91.9% | 4.0× coupling accuracy |
| C5 | Full EntropyLab Stack | 7 (all sectors) | Universal multi-physics | 97.6% | 94.5% | 21 Onsager pathways · 41.7× reduction |
| Mean | All Regimes (Full NEUROPIA) | — | — | 97.3% | 93.8% | +31.4 pp vs. interface coupling |
| E-LAB-X: Geometric vs. Entropic Gravitational Sector | ||||
|---|---|---|---|---|
| Regime | Primary η (Geometric) | E-LAB-X η (Entropic) | Δη | Dominant Gravity Channel |
| V4 (Dynamo+Seismic) | 95.8% | 94.1% | -1.7 pp | Geodesic coupling (strong) |
| V1 (Tokamak+Thermal) | 97.1% | 96.8% | -0.3 pp | Tidal metric perturbation (weak) |
| V5 (Quantum+Thermal) | 97.3% | 97.1% | -0.2 pp | Frame-dragging analog (negligible) |
| V7 (AI+Thermal) | 97.8% | 97.7% | -0.1 pp | Decoupled (< 0.05%) |
| Mean (E-LAB-X) | 97.0% | 96.4% | -0.6 pp | 418 GPU-hrs fine-tune |
Installation & Quick Start
Full multi-physics control in four lines of Python.
EntropyLab Program
NEUROPIA is E-LAB-10 — the capstone of the EntropyLab research program. E-LAB-X is the non-geometric stress test.
Reproducibility Infrastructure
Complete reproducibility infrastructure — source code, weights, datasets, benchmarks, and interactive demo.