Multi-Scale Negative Coupled Information Systems (MNCIS): A Unified Spectral Topology Framework for Stability in Turbulence, AI, and Biology

Abstract

Complex dynamical systems frequently encounter a recurrent structural instability: the collapse of the spectral gap, driving the system toward a low-dimensional "Zero-Mode Attractor" (e.g., spectral pile-up or over-smoothing). Building upon recent global well-posedness estimates [Hou, arXiv:2601.00638], this work generalizes the Multi-Scale Negative Coupled Information System (MNCIS) framework. We postulate that global stability requires an active topological operator - Adaptive Spectral Negative Coupling (ASNC) - functioning as a state-dependent high-pass filter that penalizes entropy accumulation at spectral boundaries. We validate this unified framework via three implementations: (1) Hydrodynamics: In 3D Navier-Stokes turbulence ($N=256^3$), ASNC acts as a global-enstrophy adaptive sub-grid scale (SGS) model, stabilizing the inviscid limit and preserving the Kolmogorov $-5/3$ inertial range without artificial hyper-viscosity. Crucially, we verify that the operator remains dormant (${\hat{I}}^3\approx 0$) during the linear growth phase of physical instabilities, functioning strictly as a conditional topological clamp. (2) Artificial Intelligence: Addressing Over-smoothing in Graph Neural Networks (GNNs), we implement ASNC as a parameter-free topological constraint. Unlike baselines (e.g., DeepGCNs) relying on dense residual connections, our framework enables the training of ultra-deep 64-layer networks without residual connections, maintaining perfectly stationary feature variance ($\ddot{I}{ƒ}^2\equiv 1.0$) on the ogbn-arxiv benchmark. (3) Biological Physics: In reaction-diffusion morphogenesis, it stabilizes Turing patterns against diffusive washout in high-entropy regimes. Our results suggest that the MNCIS framework provides a base-independent topological condition for distinguishing viable complex systems from those collapsing into thermal equilibrium.

Includes supplementary materials and code. Foundation and mathematical proofs can be found in the companion paper arXiv:2601.00638. V2: Significant theoretical expansion. Extended experimental validation to N=256^3 turbulence simulations