Conformal Cyclic Cosmology Under the Light of TNA: Realizability, Entropy Reset, and Failure of Local Closure in Cyclic Cosmology

This paper analyzes Roger Penrose’s Conformal Cyclic Cosmology (CCC) through the framework of the Theory of Non-Derivable Admissibility (TNA). It demonstrates that the conformal transition between aeons functions structurally as an implicit, non-local $N_1$ reset operator rather than a purely local $N_0$ derivation . By examining the core sequence of CCC—including the complete evaporation of black holes, the disappearance of physical scale, and the sudden restoration of a low-entropy state —we expose a systemic Failure of Local Closure. The model attempts to reduce cosmological closure entirely to internal physical dynamics ; however, the preservation of informational continuity across aeons without classical temporality introduces deep conceptual tensions. Furthermore, the empirical problem of infinite aeonic traces within the Cosmic Microwave Background (CMB) highlights the difficulty of stabilizing infinite cyclicity via local evolution alone. Ultimately, we argue that CCC does not eliminate external boundary conditions or transcendence, but instead geometrizes them. The theory reveals that local physical dynamics remain insufficient for self-derivability, positioning the conformal transition as a hidden $N_1$ realizability filter essential for structural renormalization