The Inward Structural Dimension Hypothesis: Scale-Extended Objects, Perceptual Compression, and Dimensional Access

Abstract

The Inward Structural Dimension Hypothesis (ISDH) proposes a formal representation of physical objects using three ordinary spatial coordinates and an additional coordinate of inward structural depth. The coordinate I orders the progression from macroscopic form through progressively finer structural levels, while time remains separate. The framework represents an object as a multiscale field Phi(x, y, z, I; t) and proposes human perception as a lossy projection that combines effects from multiple inward levels into one effective three-dimensional percept. The work distinguishes three evidential layers. The mathematical layer treats I as a coordinate of multiscale representation. The perceptual layer introduces observer kernels and a 3D-to-4D reconstruction analogy. The stronger physical layer asks whether I has independent dynamics that cannot be reduced to ordinary three-dimensional evolution, latent state, measurement response, and coarse-graining. An explicit independence test, candidate cross-scale dynamics, a structural metric, a toy model, falsification criteria, and a staged research program are provided. The paper also states why predictive improvement alone would be insufficient to establish a new physical dimension. The paper does not claim experimental detection of a fourth physical dimension and does not claim historical priority for the general scale-as-coordinate idea. It acknowledges related work in scale-space theory, renormalization-group methods, scale relativity, holographic renormalization, S. A. Stewart's length-scale proposal, and Donald G. Palmer's scale-space formulation.