On Abstract Universes and the Consequences of the Abstraction

The primary aim of this paper is to explore and comprehend the abstraction underlying the mechanisms of the universe. The central theme of this work revolves around two fundamental questions: What is truly meant when we invoke the concept of a “universe” and its subsequent evolution? And what underlying principles enable a universe to be structured with such precision down to its fundamental constants and intricate details—that it can sustain itself and evolve over billions of years? To address these questions, the paper examines two abstract universes: (A) the Fractal Universe, denoted as U3, and(B) the Abstract ζ-Function Universe, denoted as U4. The structural and cosmological evolution of these universes is described, followed by a comparative analysis and a discussion of the philosophical consequences of constructing such abstract mathematical models.