Emergent Dimensionality from History-Dependent Growth and Torsion Minimizatioñ

The dimensionality of spacetime is often treated as a fixed background assumption, despite the logical consistency of alternative dimensional configurations. In this work, we approach dimensionality from a growth-based perspective, in which dimensions emerge through a history-dependent generative process rather than being postulated a priori. We introduce dimensional growth vectors that encode generative histories and emphasize that identical vectors may arise from distinct growth processes. To compare alternative growth paths, we define a symbolic per-dimension density ρ = (Π + Σ)/D, consisting of a static configuration term Π and a history term Σ that counts coarse-grained degeneracy among mutually exclusive candidates. Growth proceeds by minimizing the stepwise increment ∆ρ. Within this framework, an abstract torsion language is introduced as a unifying interpretation tool, without fixing a unique functional form. Explicit discrete evaluations exhibit a qualitative transition around four dimensions: while dimensional extension is repeatedly se- lected in lower dimensions, beyond four independent directions extension ceases to reduce the incremental per-dimension density, and refinement becomes competitive. These results suggest that four dimensions arise as a structurally stable outcome of history-sensitive growth under minimal distortion.