Free-Probability Stability of Three-Dimensional Spatial Spectral Dimension and Clifford Principal-Symbol Closure A Conditional Theorem from Three-Step Condensation Spectral Shells to dspace = 3

This paper establishes a conditionally rigorous closure theorem for the low-energy spatial spectral dimension dspace = 3 in Algebraic Quan tum Morphogenesis (AQM). Earlier AQM material proposed a dimensional emergence argument based on nested Dirac recursion and a free-convolution attractor. The present paper makes a rigorous correction to that argu ment: free probability is no longer used as the primary criterion that by itself derives d = 3. Instead, it is used as an auxiliary mechanism for th