The Dimensional Visualization and Interaction Theory: Observation as Dimensional Projection and the Affine-Span Origin of Space

This work presents a parameter-free geometric framework in which observation is an act of dimensional projection. The Visualization Function V(n, x) = max(0, min(n, x) − 1) quantifies the reduction in spatial degrees of freedom when an n-dimensional observer measures an x-dimensional object. The companion Interaction principle establishes, by affine geometry, that space is generated by the interaction of entities according to the general affine-span law dim(A ⊕ B) = a + b − s + ε, whose fundamental base case is the interaction of two one-dimensional entities spanning exactly three dimensions (1D ⊕ 1D → 3D, rank-verified). The framework is applied to reinterpret wave–particle duality and geometric-optics phenomena as predictable consequences of projection geometry. This version corrects the interaction law to its general affine-span form and supersedes earlier drafts.Supersedes earlier drafts. Claims appearing in earlier versions regarding lossless geometric compression ratios and an nD⊕nD→(n+2)D interaction rule have been withdrawn by the author and are corrected in this version.