Utopreservation and the Relational Invariance of Physical Constants: From Conformal Fields to the Geometry of Pi

Here, I investigate the hypothesis that the numerical constants of physics, including the geometric ratio Pi, are not absolute quantities but invariant relationships emerging from the interaction between curvature, field dynamics, and local observation. Through analytical and numerical exploration of a conformal scalar model, I demonstrate that the system exhibits no scalar hair and that the scalar field stabilizes into a constant configuration. This result implies that Pi, and by extension, other fundamental constants appear fixed only within the locally flat frames defined by the observer’s own metric domain. I propose the Utopreservation Principle, the preservation of relational proportions under metric transformations, as a universal mechanism linking local flatness and the perceived constancy of physical laws.