FFC's Expanded Formal Derivations #54 and #55: Emergence of Cyclic Cosmology (Recursive Entropic Bounce, No Singularity)

Cyclic cosmology arises from recursive minimization of entropy (S) in fractal hierarchies without singularities (Axiom: seamless continuum, no voids/abrupts). Universe cycles as density reconfigurations via dilution/contraction; derives bounce at high where , resetting via φ-branching (unifying low initial (S) from prior min with dynamic Λ). No big bang: Nondiff paths ) smooth , preventing curvature blowup. The time to entropy maxima is derived internally from dilution thresholds where dispersion maximizes S, leading to ∇S reversal.