Cyclic Expansion Growth and Binary-Ternary Bidirectional Textural Mechanism of the PFUS-PFUSR Bicone Four-Dimensional Structure

This paper establishes a self-consistent, closed dynamic framework of the four-dimensional cosmic bicone based on the original PFUS (Pythagorean Frustum Unified System) and PFUSR recursion mechanism. The 11-dimensional apex acts as the primordial origin, the 5-dimensional waist as the global symmetric steady-state core, and the upper and lower bicone tips as dimensional coupling poles. Cosmic expansion is revealed as tip–waist–tip reciprocating pulsation with plant-like self-similarity, governed by the axial meridian operator \boldsymbol{\beta_1} and the dynamic scale parameter \boldsymbol{\pi_1}, which approaches \dfrac{12}{11} at the conical poles and converges to \pi in the waist region. A fundamental breakthrough is achieved in the definition of time: time is not an independent dimension, but the cumulative trace formed by photon propagation and cosmic spiral growth. Although the bicone structure can reciprocate bidirectionally, traces can only accumulate and cannot be reversed, providing a natural and definitive explanation for the unidirectionality of time. Meanwhile, the large-scale flat appearance of the universe arises from the fact that observers in the waist region cannot perceive the underlying conical geometry, resulting in smooth temporal perception consistent with spatial flatness. This unified system naturally explains cosmic accelerated expansion, large-scale flatness, dark energy as structural dynamics, singularity elimination, high-dimensional stability, the origin of physical constants, vacuum quantum fluctuations, and the origin and irreversibility of time without additional hypotheses. The model completes the cosmic growth dynamics of the PFUS‑PFUSR system and opens a new foundational perspective for theoretical physics and cosmology.