The Essence of Geometry Is Measurement, and the Essence of Measurement Is Self-Consistency: A Unified Interpretation of Euclidean and Riemannian Geometry in Time Field Theory

Geometry is the fundamental language for physics to describe the world, but how does geometry itself acquire physical meaning? This paper points out a long-overlooked fact: Euclidean geometry can describe the physical world because it implies a physical premise — time flows uniformly; Riemannian geometry can describe gravitation because it can express the non-uniformity of time. The difference between the two lies not in whether space is curved, but in their corresponding temporal structures. Starting from the meta-axiom that "time is the only self-consistent measurement benchmark", Time Field Theory (TFT) proves that both Euclidean geometry and Riemannian geometry are projections of measurement self-consistency — the former corresponds to a uniform time field, and the latter corresponds to a non-uniform time field. The essence of geometry is measurement, and the essence of measurement is self-consistency. This is the most profound repositioning of geometry by TFT. This paper is a thematic work on the essence of geometry in the metretike series of Time Field Theory (TFT), and constitutes the complete philosophical foundation of TFT metretike together with other related papers.