We develop the linear and spectral stability analysis for the coherence field χ in the MINT framework, a model of modified gravity in which spacetime admits two interwoven temporal foliations. The spatial operator ℒ is shown to be self-adjoint and coercive in the weighted Hilbert space L²_ξ (Ω), restricted to the zero-ξ-mean subspace V_ξ. We establish asymptotic stability conditions and derive rigorous non-autonomous energy estimates under an explicit quantitative adiabatic bound. Furthermore, we show that ℒ acts as a drift-diffusion (Witten-type) operator associated with the measure ξ dV, connecting naturally with the MINT Kernel Theorem T*. Under the conditions λ₁^ξ > κ Rₘax and |ξ̇/ξ| ≤ Γ/2, all linear perturbations decay exponentially in the L²_ξ norm. Physical interpretations regarding vacuum energy and black hole thermodynamics are presented as heuristic consequences of this geometric structure, with full derivations reserved for companion works.
M. de Paz (Sat,) studied this question.