Dual Asymptotic Structure in Relativistic Proper-Time Geometry: A Minimal Necessity Argument

Special relativity is commonly interpreted as possessing a single asymptotic limit associated with lightlike motion. This work re-expresses that limit as a property of proper-time response rather than a kinematic boundary and examines the consequences of relational comparison between worldlines. The existence of an asymptotic suppression of proper time implies, under the assumption of relational closure, a complementary asymptotic structure when defined globally. Enforcing symmetry and consistency yields a minimal deformation of the clock law introducing a new scale βf . The resulting form χ(β) = 1 + (βf /β)2 defines a lower asymptote in proper-time response. The deformation, its uniqueness, and its empirical consequences are analyzed. The scale βf admits extraction from precision experiments, providing a direct empirical anchor.