The Anta-Rai Stability Structure A Variational Operator Model for Centered Stability in Physical Systems

This paper presents the physical formulation of the Anta-Rai framework, a minimal operator-based model for stability in physical systems. The core of the framework is a centered deformation of the Hodge-Laplace operator, defined by LAR(σ)=ΔH+α(σ−c)2. The work analyzes the spectral and variational properties of this operator, establishing the conditions under which stable configurations emerge from the coincidence of geometric admissibility and spectral equilibrium. A key finding is the identification of a non-trivial harmonic stability sector (the "Stable Core") at the saturation point σ=c. By introducing a stability functional F(σ,ω), the study demonstrates how energetic minimization drives the system toward this centered state. The framework provides a structural description of resilience and stability that is independent of specific dynamical models, bridging the gap between differential geometry and theoretical systems physics.