PFUSRC_13 Topological Reconstruction of Coupling Interface 0 and Global Equivalence Closure Direct Proof of Cosmic Growth Theory and Logical Origin Theory via 360° Rotation in the Kakeya Problem

The classical Kakeya needle problem interprets the statement that “the area swept by a unit line segment rotating 360° can approach zero” as measure vanishing and existential recovery, which has long led to a fundamental paradox between geometry and physics. Within the framework of the PFUSRC unified theory of the cosmos, this paper takes Coupling Interface 0 as its ontological basis and strictly aligns with the axiomatic system, symbolic conventions, and logical structure of PFUSRC_01 and PFUSRC_04 to accomplish a holistic reconstruction of zero. This paper proves that the area convergence in the Kakeya rotation is not a return to the original initial state, but a topological equivalent shift driven by phase closure, oscillation damping, and temporal closure. The final state converges to an Equivalent Coupling Interface 0 that is isomorphic to the initial state but ontologically updated. This process is rigidly supported by the intrinsic scale constant \pi_1 = 12/11 rather than the geometric constant \pi, which eliminates the ontological asymmetry caused by irreversible evolution. A single rotation corresponds to the minimal unit of cosmic helical growth, realizing the dynamic construction and derivation of space. Theoretically, two full cycles of forward and reverse rotation are required to achieve genuine global primitive return. The essence of the Kakeya rotation provides topological evidence for Cosmic Growth Theory, Logical Origin Theory, and Global Dynamic Space Generation Theory. This paper completes a paradigm shift at the holistic level and provides decisive microscopic support for the PFUSRC framework.