Prime Irregularity as a Projection Artifact from Curved Relational Geometry

This article presents a conceptual geometric framework for understanding the apparent irregularity of prime numbers. A concrete toy model based on curved relational geometry with exponential volume growth is introduced, together with an explicit projection onto the integer line that produces logarithmic thinning consistent with the Prime Number Theorem. The work is explanatory rather than foundational: no new arithmetic theorems are claimed, and no results concerning the truth of the Riemann Hypothesis are asserted. The paper is intended as a geometric perspective on why curvature and spectral methods repeatedly arise in successful approaches to prime statistics.