Gravitational Lensing as a Refractive Index Gradient in a Stationary Hexagonal Close-Packed Lattice

The deflection of light by massive astronomical bodies - conventionally interpreted within General Relativity as a geometric bending of a continuous spacetime manifold - is mathematically re-examined here within a strict discrete-mechanical framework. We model the spatial vacuum as a stationary, rigid Hexagonal Close-Packed (3HCP) discrete space crystal of an invariant coordination profile Z = 12. By replacing continuous metric tensors with a localized Dynamic Electro-Leeway Tensor Luv, we demonstrate that the presence of massive baryonic charge concentrations induces a hydrostatic compaction of the adjacent lattice cells, scaling their local capacity registers up toward the limit Llimit = 256. This localized density increase systematically contracts the sub-nodal clearance paths, causing a proportional decay in the propagation velocity of electromagnetic wave packets (clocal < c0). Through a multi-variable Taylor series expansion, we establish a rigorous mathematical bridge proving that this discrete node-shifting transport scheme converges identically onto the continuous Fermat principle and the classical Eikonal trajectory equations as the physical lattice parameter approaches zero (h -> 0). The apparent bending of light paths emerges not from a curved vacuum void, but as a physical, non-linear refraction gradient across the varying density sheets of the spatial crystal. This framework derives the exact Einstein deflection angle theta = 4GM/c2R purely from first-principles discrete optical mechanics, effectively stripping the geometric mystique from gravitational lensing.

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