Hierarchical Self-Referential Reconstruction Cosmology G: Inter-Cosmic Universes: Branch Entanglement and Observational Residuals in the Self-Referential Hierarchy

Within the framework of ”Hierarchical Self-Referential Reconstruction Cosmology”, this paper proposes a theory of ”intertextuality” based on higher-order category theory to describe the weak interactions between cosmic branches with different levels of logical constraints. The theory rigorously defines the intertextuality measure I on the logical hypergraph and derives its numerical value fromfirst principles. The core conclusion indicates that in our information-conservationdominated branch (c=3), the quantum information leakage from neighboring highentropy branches (c=0, 1) accumulates into observable classical residuals throughout cosmological evolution. This provides a unified, principled explanation for twoprominent puzzles in current cosmology: the Hubble constant H0 tension (∼ 5%)and the cosmic microwave background (CMB) large angular scale anisotropy anomalies. The theory predicts that the H0 tension originates from the effective dark energy equation of state correction induced by the continuous leakage from the c=1branch (Ic=1 ∼ 10−5), while the CMB large-scale anomalies correspond to topological defects left by transient early contact with the c=0 branch, characterizedby parity-multipole-selective enhanced non-Gaussianity. The article further proposes specific joint testing schemes through CMB-S4’s EB polarization correlation,redshift-dependent measurements of H0, and the ”sawtooth” features in the 21cmpower spectrum, thereby transforming the multiverse conception into a computable,falsifiable working theory.