False Vacuum Decay as a Minimal Dynamical Completion of the CCC Crossover

Penrose's Conformal Cyclic Cosmology (CCC) requires the conformal factor Ω to vanish at the boundary between aeons, but provides no dynamical mechanism that drives it there. This paper proposes that false vacuum decay via the Coleman–De Luccia (CDL) mechanism fills exactly this role, and derives the functional form of Ω from within the CCC framework itself. Within the class of non-degenerate, scale-homogeneous CCC maps, the identification Ω² = V(φ)/V_f is the universal local representative to which every admissible map reduces at leading order near the crossover. Three conditions force this uniquely: CCC regularity enforces V_t = 0, the No-New-Scale principle restricts Ω² to a function of V/V_f, and non-degeneracy of the crossover map selects the unique local linear form n = 1. A functional dilatation-flow argument confirms n = 1 as an IR attractor. This identification implies a condition strictly stronger than Penrose's Weyl Curvature Hypothesis: not only the Weyl tensor but the full Kretschmann scalar must vanish at the crossover. This stronger condition constrains the scalar potential: V ~ ξ^(2k) near the true vacuum requires k ≥ 3 (sextic or higher minimum). The sufficiency k ≥ 3 ⟹ K̂ → 0 is proved as a theorem for the full O(4)-symmetric CDL geometry. The necessity remains an open conjecture supported by numerics and four robustness arguments. The framework yields three falsifiable consequences: V_t = 0 (reproduced as internal consistency), k ≥ 3 (derived, not assumed), and sub-exponential late-time expansion, ruling out eternal de Sitter. Present DESI DR2 constraints are consistent with the framework but do not yet decisively test the asymptotic regime.