The Minimal Stability Theorem
Year: 2026
Type: article
Abstract: This paper presents the Minimal Stability Theorem, which shows that any coherent multi‑gradient system governed by a single invariant reference must resolve into a five‑layer structural configuration. The reduction sequence demonstrates that coherent evolution forces the system into five interacting domains, each containing five internal modes, coupled across five boundaries, and embedded within five nested shells. This structure is not descriptive or domain‑specific; it is the minimal configuration required for stability, controllability, and preservation of the invariant under perturbation.Systems with fewer than five layers lose coherence or controllability, while systems with more than five collapse into five effective components. The theorem establishes this five‑layer configuration as a universal stability requirement across physical, biological, and engineered systems. It provides the mathematical foundation for understanding why coherent multi‑gradient systems must adopt this structure and completes the formal statement of minimal stability.
Author: Rieckmann, Brian
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7119494482
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