The Hub of the Cosmic Cycle: Inflation, Bounce, and Cross-Cycle Information Transfer — SGCU Theory Version 2.7

This paper connects two previous discoveries: Version 2.4 identified black holes as carriers of cross-cycle memory; Version 2.6 traced large-scale structure to the evolution of primordial seeds. Version 2.7 provides the missing link between them. It shows that inflation is not driven by an external inflaton field, but is the natural relaxation of the Ψ field after the bounce. It also shows that the bounce is not a boundary where information is lost: under the CPT mirror condition, the topological information of the previous cycle is mapped as geometric entropy into the new cycle. The causal chain is now complete: black hole memory → geometric entropy at the bounce → initial conditions of inflation → primordial perturbations → large-scale structure. Without this link, SGCU would be a set of separate insights. With it, the theory becomes a closed cycle — a universe that remembers.