Spectral Selection of the Recursion Manifold Under Strong Positivity in Structured Vacuum Field Theory

This paper establishes a spectral selection principle within the operator framework of Structured Vacuum Field Theory (SVFT). Let K be a compact, self-adjoint, strongly positive operator acting on a real Hilbert space ℋ with dominant eigenvalue λ₀ = 1 simple and subdominant spectral radius |λ₁| < 1. Under the nontriviality condition C_total = ⟨Ψ, Ψ⟩ > 0, the recursion update map Ψₙ₊₁ = KΨₙ is analyzed to determine the asymptotic behavior of the iterates KⁿΨ. Using spectral decomposition, exponential norm bounds, and projective convergence estimates, it is shown that for all initial configurations satisfying ⟨Ψ, Ψ₀⟩ ≠ 0 the normalized iterates converge in projective Hilbert space to the dominant eigenspace ℰ₁. The exceptional set is characterized as a closed codimension-1 subspace and is shown to be structurally unstable under perturbation. The selection mechanism is further proven to be robust under compact self-adjoint perturbations of K that preserve a positive spectral gap. The analysis is strictly operator-theoretic and does not invoke geometric interpretation, activation dynamics, or cosmological assumptions. The result identifies the recursion manifold as the unique nontrivial asymptotically stable invariant set of the recursion update map within the declared operator discipline.