Dimensional Solvability Conjecture

We propose that the observed dimensionality of spacetime is limited by a fundamental algebraic solvability constraint analogous to the Abel–Ruffini theorem for polynomial equations. In algebra, generic equations of degree five or higher become non-solvable because the symmetry group of their roots is no longer decomposable into a hierarchical sequence of operations. We conjecture that an analogous transition occurs in geometry: beyond a critical dimension, the symmetry group of the space of physical configurations becomes non-solvable, preventing the existence of global coordinate systems, causal indexing, and dynamically coherent laws. As a result, only spacetimes up to four dimensions remain physically realizable, while higher dimensions, though possibly existent in an abstract sense, fail to contribute to observable physics due to algebraic non-coordinatizability and destructive interference of configurations. This provides a structural, non-anthropic explanation for the dimensionality of spacetime.