The Shiwhare Cosmology: Emergent Spacetime, Stress-Energy, and the Arrow of Time from a Discrete Lattice

We present Shiwhare Cosmology, a fully discrete lattice framework in which spatial structure, stress, entropy, and cosmological time emerge from microscopic scalar-field interactions rather than being assumed as fundamental inputs. The model is defined on an infinite-dimensional integer lattice $\mathbb{Z}^d$ and does not require a pre-existing spacetime manifold, background metric, or fundamental time coordinate. Nearest-neighbour and higher-order couplings generate localized excitations, termed NB-entities, whose formation and interaction increase block entropy defined on finite lattice regions. We show that this entropy growth is monotonic under local relaxation dynamics, providing a natural ordering of configurations that plays the role of an emergent arrow of time. Mechanical equilibrium and anisotropic stress arise directly from asymmetric neighbour interactions. A symmetric stress tensor is constructed purely from lattice field differences and coupling strengths and is invariant under $\Phi \rightarrow -\Phi$, without reference to continuum geometry. Explicit numerical evaluation in a three-dimensional projection demonstrates relaxation toward unique equilibrium states and the emergence of compressive and shear stress patterns. Together, these results establish a self-consistent pre-geometric framework in which spacetime structure, stress–energy, and temporal directionality arise from discrete microscopic dynamics.