Burdick Crag Mass Paper B v1.0: Operator Decomposition of the Substrate Wave Manifold

Version 1.0: Six numerical probe experiments on the Burdick Crag Mass (BCM) substrate wave PDE characterize the control operators governing the four-field state tensor (λ_c, λ_fold, λ_cold, H). Perturbations along four axes — the nonlinear coupling coefficient ξ ∈ [0.005, 0.07], the Taylor source coefficient a with saturation b held fixed, the memory regularization α ∈ [0.0, 0.95], and the diffusion coefficient D ∈ [0.1, 2.0] — resolve a clear operator hierarchy. The spectral eigenvalue λ_c scales linearly with the ratio a/b (λ_c = 0.0592·(a/b), Pearson r = 0.99999 across five a values). In contrast, λ_c is invariant under ξ to within 10^-9 relative range across 14× variation, invariant under α to within 10^-4 relative range across the converged α subset, and exhibits only a weak shear under D (~1.9% relative range across 20× variation). The Jacobian ∂λ_c/∂(ξ,α,D,a/b) spans seven orders of magnitude. λ_fold and λ_cold are invariant under all four axes. The hysteresis loop H ≈ 0.05 is not reduced by any tested axis and is attributed by elimination to absorbing-state asymmetry of the cold-torus terminal phase. The framework is presented as a non-equilibrium effective-field reconstruction with emergent invariant spectrum; no phase transition or saddle-node fold bifurcation is claimed.