What question did this study set out to answer?

The aim is to explore the relationship between the Kakeya needle problem and cosmic growth theories using a topological reconstruction framework.

May 25, 2026Open Access

PFUSRC₁3 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

Key Points

The aim is to explore the relationship between the Kakeya needle problem and cosmic growth theories using a topological reconstruction framework.
Utilized the axiomatic framework of PFUSRC_01 and PFUSRC_04 for ontological basis.
Analyzed the Kakeya problem through topological equivalence and phase shifts.
Employed intrinsic scale constants to eliminate asymmetries in the ontological structure.
Established that area convergence in the Kakeya rotation is a topological shift rather than a return to the original state.
Demonstrated that intrinsic scale constant c0_1 = 12/11 supports cosmic expansion theories.
Found that two full rotation cycles are necessary for a genuine primitive return to the initial state.

Abstract

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 PFUSRC₀1 and PFUSRC₀4 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 ₁ = 12/11 rather than the geometric constant, 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.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper