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

• URL: http://arxiv.org/abs/2601.11594v1
• Date: Tue, 06 Jan 2026 21:11:33 GMT
• Title: Multi-Scale Negative Coupled Information Systems (MNCIS): A Unified Spectral Topology Framework for Stability in Turbulence, AI, and Biology
• Authors: Pengyue Hou,
• Abstract summary: This work generalizes the Multi-Scale Negative Coupled Information System (MNCIS) framework.<n>Global stability requires an active topological operator -- Adaptive Spectral Negative Coupling (ASNC) -- functioning as a state-dependent high-pass filter.<n>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.<n>Our results suggest that the MNCIS framework provides a base-independent topological condition for distinguishing viable complex systems from those collapsing into thermal equilibrium
• Score: 1.4213973379473657
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.(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 to bypass signal decay, our framework enables the training of ultra-deep 64-layer networks without residual connections, maintaining perfectly stationary feature variance ($σ^2 \equiv 1.0$) 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, bridging physical stability and information persistence.

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