Wave Propagation on Discrete Foam Complexes: A DEC Framework with Isotropy Analysis

We compute elastic wave propagation on periodic foam cell complexes using Discrete Exterior Calculus (DEC). Four structures are analyzed: C15 Laves phase, Weaire-Phelan, Kelvin (BCC foam), and FCC (control lattice). The C15 structure exhibits the lowest directional anisotropy (δv/v = 0. 93%) among candidates tested. A cross-validation shows that the geometric moment I₄ of edge directions predicts the Zener anisotropy AZ with Pearson r = -0. 996, confirming pipeline consistency. The gauge (Maxwell-like) sector shows ~60× stronger isotropy than the elastic sector on the same geometry (α ≈ 0. 015). Under statistical averaging over M ~ 10³⁴ grains per meter, predicted anisotropy is compatible with cavity Lorentz bounds (10⁻¹⁸) with 27× margin. The discrete structure produces n=2 (quadratic) dispersion, consistent with GRB time-of-flight constraints that exclude n=1.