Developing a Geometric Framework for Hilbert’s Sixth Problem

Develop a rigorous geometric framework for physical laws that complements Kolmogorov’s axiomatization of probability, thereby addressing the geometric component of Hilbert’s sixth problem and providing a precise mathematical setting in which geometry and probability are integrated.

Background

Hilbert’s sixth problem calls for the axiomatization of physics, emphasizing both probability theory and a geometric framework for physical laws. While Kolmogorov’s measure-theoretic foundations have addressed the probabilistic aspect, the geometric development remains unresolved.

This paper introduces Soft Logic and Soft Numbers and proposes a Möbius-strip-based geometric perspective as a potential step toward fulfilling the geometric aspect of Hilbert’s sixth problem, but it explicitly notes that the geometric framework component is still open.