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 with dedicated builders are analyzed in detail: C15 Laves phase, Weaire-Phelan, Kelvin (BCC foam), and FCC (control lattice). A landscape scan of 19 cubic crystal prototypes shows 13 satisfy the elastic isotropy bound, spanning 8 space groups and 2–58 sites per cell. 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 A_Z 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. Code: https://github.com/alex-toader/st_dec_foam_waves