🎬Comparative Analysis of Dimensional Scaling

The scaling constant observed in these transformations—ranging from 1 in 2D to 6 in 4D—serves as a geometric scaling factor determined by the number of valid index permutations in a given dimension. While 2D operations relate to simple vector projections and 3D contractions underpin the standard BAC-CAB vector identity, higher dimensions like 4D involve hyper-volume scaling determined by the $(n-1)!$ factorial growth. This progression highlights how antisymmetric tensor products consistently collapse into symmetric, manageable scales across different spatial complexities.