Why Three Dimensions? Dimensional Uniqueness from Holography, Locality, and Finiteness

The present work develops an information-theoretic argument that three spatial dimensions are singled out among integer dimensions by the simultaneous requirements of holographic entropy bounds, local dynamics, and finite discrete structure. The reasoning does not rely on any specific microscopic model of quantum gravity; instead, it is formulated for a broad class of theories that are holographic, local, and of finite density. Within this class, it is shown that D = 1 is incompatible with a non-degenerate holographic bound, that D = 2 is marginal and cannot support robust propagating bulk degrees of freedom under natural scrambling assumptions, and that D ≥ 4 suffers from a bulk–boundary mismatch: bulk configurational complexity grows too quickly to be coordinatized by any boundary theory obeying holographic scaling and local information propagation, under mild assumptions about compression and coordination. Under these conditions, D = 3 emerges as the unique integer dimension in which holography, locality, and finiteness can jointly support stable, causally coherent macroscopic physics.