This article introduces a structural selection principle for spacetime dimensionality based on finite-time maintainability. Rather than treating the number of spacetime dimensions as a fundamental input or an anthropic outcome, dimensionality is approached as an emergent property determined by the ability of a physical regime to preserve its defining structure over a finite temporal horizon. The central idea is that mathematical consistency alone is insufficient to characterize physical existence. A regime may be internally consistent yet fail to persist as a coherent universe over cosmological timescales. To capture this distinction, the article formulates a finite-time maintenance invariant Y, combining effective energetic capacity, finite-time coherence, and the temporal cost of persistence. This quantity is not proposed as a conserved charge, but as a viability functional ordering physical regimes according to their capacity for autonomous persistence. Applying this criterion to spacetime dimensionality yields two generic failure modes. Spacetimes with more than four large, non-compact dimensions fail by dimensional dilution: interactions and restoring mechanisms weaken with scale, causing coherence to decay over long horizons. Spacetimes with fewer than four dimensions fail by overconstraint: the reduction of propagating degrees of freedom leads either to trivial, non-informative persistence or to instability once interactions are introduced. Four-dimensional spacetime emerges as a critical regime in which nontrivial interacting dynamics coexist with marginal, dynamically sustained coherence. The analysis is reinforced by an independent mathematical signal: the unique existence of exotic smooth structures on R4. These are interpreted as signatures of conditional global coherence at the critical dimension, where local consistency no longer uniquely fixes global differentiable structure. Their role is structural rather than dynamical. Overall, the article does not propose a new physical theory, modify existing frameworks, or introduce new ontological claims about time or spacetime. It provides a meta-structural filter applicable to any candidate theory, clarifying which regimes can persist as physical universes and why four effective dimensions are generically selected. This work is part of the Ranesis framework, which develops finite-time maintainability and coherence as pre-dynamical organizing principles underlying effective physical descriptions.
Alexandre Ramakers (Thu,) studied this question.