Cosmological Universality in Quantum Gravity: Interface Entanglement, CPT-Admissible Continuation, and a Projected Geometric-Trinity Bridge

This is Part III of a trilogy that addresses a central question in quantum gravity: whether apparently distinct microscopic approaches can nevertheless share universal projected structures at the level of observable gravitational data. The guiding claim is not a microscopic equivalence between string-theoretic and loop/group-field-theoretic variables. Instead, the papers develop a restricted universality program in which only carefully projected interface data are compared. Part III applies the projected-interface framework to cosmology. It compares KFT-inspired holographic admissibility data with a restricted class of pair-correlated GFT condensate states. The core result is a conditional area-law-type scaling of interface entanglement across a graph cut, together with a CPT-admissible paired continuation and a restricted affine/geometric-trinity bridge near the cosmological interface. Phenomenological topics such as dark energy, dark-sector scales, tensor signatures, and transport estimates are separated from the core claim and treated only as conditional outlook-level extensions.