Paper 33B: Operator-Level Triadic Anisotropy and Source-Coupled Coherence-Wave Propagation in the Holosphere Lattice

Paper 33B develops a classical lattice model for studying gravitational-wave–like propagation within the Holosphere framework. Instead of treating gravitational waves as perturbations of spacetime geometry, the model represents them as coherence disturbances moving through a discrete network of coupled Holosphere elements. Each lattice site carries a real angular alignment variable that interacts with its neighbors through a nearest-neighbor Hamiltonian defined on a cuboctahedral (FCC) graph. The propagation operator is extended by introducing triadic anisotropy directly into the lattice connections. This is implemented through direction-dependent weights on the 12-neighbor stencil, producing a modified Laplacian that allows wave speeds to vary with direction. The field evolution is integrated using a second-order symplectic velocity-Verlet scheme, enabling energy audits that verify correct Hamiltonian behavior in the unforced isotropic limit. Numerical experiments include a solver contract test, an isotropic dispersion validation, an anisotropic dispersion sweep, and a fixed-magnitude directional scan. The solver passes the contract test with relative energy drift on the order of 10−510^{-5}10−5. Dispersion measurements match the discrete isotropic baseline within expected numerical tolerance. When triadic anisotropy is enabled, the propagation speed develops a measurable directional dependence. A three-fold directional fit yields an anisotropy amplitude that increases by roughly a factor of seven between the isotropic and anisotropic runs. A compact quadrupole-like source is also used to generate outward-propagating lattice disturbances. These simulations produce structured wavefronts and a directional orientation signal in the transverse estimator, while remaining below the admissibility threshold that would trigger transport dropout. The main contribution of Paper 33B is therefore mechanical: it establishes a reproducible classical lattice framework in which operator-level anisotropy, source coupling, and discrete dispersion can be explicitly defined, simulated, and tested. Within the reported parameter regime the model supports anisotropic propagation but does not yet activate threshold-collapse dynamics.