Scale-Dependent Dimensionality Profiles Across Neural and Synthetic Representations

We analyzed effective dimensionality as a function of neighborhood scale across five rep-resentational systems. Effective dimensionality follows a consistent growth–saturation profile:locally low-dimensional structure expands with increasing neighborhood size before reachinga bounded plateau. After within-system normalization, dimensionality curves exhibit strongcross-domain alignment (mean Pearson r ≈ 0.90, corresponding to approximately 81% sharedvariance). Systems differ quantitatively in growth rate (range: 0.23–0.82) and saturation behav-ior. Model-derived cortical representations (TRIBE) show pronounced compression (Deff ≈ 3–5,compression ratio = 0.49) and early saturation relative to synthetic systems.Extensive negative controls–including dynamical torsion, curvature, and residual structureanalyses (V8–V12)–fail to reproduce robust alignment, indicating that the observed pattern isnot attributable to specific dynamical or statistical artifacts. A null model with matched eigen-value spectrum partially reproduces the growth–saturation profile but shows weaker alignmentwith other systems, suggesting some aspects may reflect general statistical structure while othersremain system-specific. These findings are descriptive and do not establish a mechanistic originor generalize beyond the systems analyzed.