Mathematical Structure of Exceptionally Compact Globular Proteins Containing a Large Internal Functional Cavity

The observation that some globular proteins exhibit hydrodynamic dimensions below the standard mass-dependent scaling law is recast as a scaling problem. We show that the total volume of a protein with a functional cavity is governed by the additive decomposition V'_tot(M) = V_prot(M) + V'_void(M) + V_cavity(M), and that the six structural scenarios previously described in qualitative terms correspond to explicit constraints on the scaling exponents of each term. Around this decomposition we identify three mathematical objects: an effective scaling exponent ν', a fractal dimension D_f = 1/ν', and a packing-density functional φ(M). Their composition yields a predictive map Ψ that converts measurable hydrodynamic data into a classification of compactness. The note argues that this mathematical profile, rather than the qualitative taxonomy, is what makes the phenomenon of exceptionally compact proteins operational and testable.