Koku Universe v3.1 and Penrose's Conformal Cyclic Cosmology: A Structural Comparison

This paper systematically compares Penrose's Conformal Cyclic Cosmology (CCC) with the Koku Universe v3.1 model. Both frameworks independently arrive at the same geometric insight: the topological boundary of the universe and its origin are the same point, expressed through conformal geometry. CCC identifies future infinity (scri+) with the Big Bang singularity of the next aeon via conformal rescaling. Koku Universe v3.1 identifies center C with circumference C on the Riemann Koku-face. Three critical divergences are identified and formulated as falsifiable predictions: (1) CCC is cyclic; Koku Universe is layered — discriminated by CMB Hawking point periodicity; (2) CCC derives gravity from GR curvature; Koku v3.1 from temporal pressure gradient — discriminated by discrete vs. smooth time dilation near black holes; (3) CCC treats c as empirical; Koku v3.1 derives c as a geometric invariant — discriminated by precision c-measurement at cosmological scales. The two frameworks are complementary, not competing.