Effective Hausdorff and Spectral Dimensions in the Fractal Consistency Law

This paper presents a standalone dimensional module of the Fractal Consistency Law (FCL). Its aim is to derive the effective Hausdorff dimension and the spectral dimension from a balanced simplicial microfamily rather than to treat them as merely compatible with the theory. The paper introduces a texture-corrected combinatorial growth law, derives the effective Hausdorff dimension from covering growth, derives the spectral dimension from fractional diffusion, fixes the ultraviolet transport exponent through the Principle of Minimal Inconsistency, and makes the ultraviolet/infrarred crossover explicit through an interpolating operator. A toy model shows that the texture factor Theta_L is calculable rather than vacuous.