Inverting the Dimensional Hierarchy: Advocating for a 4D-Native Framework for Quantum Geometry

The standard mathematical framework of differential topology reveals a profound peculiarity: smooth structures on 4-manifolds are wild, unclassifiable, and form an uncountably infinite set, while in all other dimensions they are either unique or finitely classifiable. This presents a fundamental obstacle to constructing a quantum theory of gravity via a path integral sum over geometries as the configuration space becomes intractably complex. Crucially, this mathematical wildness is not a mere curiosity but a diagnostic signal that our dimension-agnostic mathematical framework is fundamentally inadequate for describing quantum spacetime in our 4-dimensional universe. We argue that this impasse signals not a pathology of 4-dimensional spacetime, but a critical flaw in our mathematical starting point. We propose a radical inversion of priorities: instead of seeking to tame 4D wildness within a dimension-agnostic formalism, we should construct a new mathematical framework whose axioms are explicitly designed so that 4-dimensional spacetime emerges as its unique, natural, and tame solution. The price for this 4D simplicity is that other dimensionalities may appear ill-defined or trivial within the new framework, a price we argue is not only acceptable but necessary for a physical theory of our universe. We outline the philosophical and formal principles of such a 4D-native approach and discuss its embodiment in existing pre-geometric quantum gravity programs where smooth geometry emerges from more fundamental substrates.