Hierarchical Self-Referential Reconstruction Cosmology F: Physical Necessity in the Infinite Self-Referential Hierarchy: From the Selection Problem to Existence Theorems

This paper proposes a cosmological theoretical framework based on non-wellfounded set theory and infinite ordinal dynamics. By modeling the universe generation process as an infinite-order self-referential dynamical system, it is proven thatat strong limit ordinals, universe nodes satisfying specific physical conditions necessarily exist with uncountably infinite cardinality. This framework transforms thetraditional “fine-tuning” problem into an existence theorem of “observers necessarilyexist in a describable subset,” and derives three testable observational predictions:the non-Gaussianity of the primordial perturbation spectrum exhibits logarithmicscale dependence, the stochastic gravitational wave background exhibits an inverselogarithmic spectral feature, and the large-scale structure power spectrum exhibits acharacteristic cutoff in the ultraviolet band. These predictions can be jointly testedby next-generation multi-messenger astronomical observations, with the potentialto reach 5σ statistical significance within the next decade.