Hierarchical Self-Referential Reconstruction Cosmology C: Qualitative Inference on the Proportions of Four Universe Types Based on Constraint Strength and Measure Concentration

Hierarchical self-referential cosmology regards ”computability” and ”information conservation” as emergent constraints at the middle layer, rather than axioms at the bottom layer. This paper, within a common framework of topologicalmeasure theory and computational complexity theory, makes qualitative inferencesabout the relative abundances of four types of universes in the underlying logical space: (1) information-conserving and computable, (2) information-conservingbut non-computable, (3) non-information-conserving but computable, and (4) noninformation-conserving and non-computable. The core hypothesis is: the strongerthe constraint, the higher the codimension of the corresponding parameter submanifold, and its measure decays at a double-exponential rate. The results show thatthe ”doubly infinite” universes (type 4) dominate absolutely, the ”doubly finite”universes (type 1) constitute an extremely scarce null set, and the two ”singleconstraint” universes (types 2 and 3) exhibit an asymmetric intermediate distribution. This conclusion is compatible with anthropic observations and leads totestable predictions such as a decay in the primordial gravitational wave powerspectrum and a step-like feature in the 21-cm background temperature.