This paper proposes a generalised cosmological conjecture in which successive universes are structured via conformal boundary matching, extending the framework of Penrose’s Conformal Cyclic Cosmology (CCC). Rather than assuming asymptotic future infinity as the launch point for a subsequent aeon, this model introduces a tiled structure of conformally compactified spacetime regions—each bounded by lightlike and spacelike conformal boundaries—stitched together in a higher-order topological fabric. We explore the theoretical implications of such a structure on information propagation, entropy scaling, and the global arrow of time. The work builds on existing conformal techniques in general relativity while incorporating heuristic arguments motivated by causal set theory and holographic encoding across null boundaries.