Proper Time Is Not Sufficient Statistic for Biological Aging A Sufficiency No-Go, Exact Closure Criterion, and Observable Trilemma

AbstractThis paper argues that proper time, although an exact geometric invariant of relativistic duration, is not in general a constitutively sufficient statistic for biological aging. It establishes three core results. First, a minimal factorization no-go theorem shows that if two admissible biological histories share the same proper time but differ in aging outcome, then no universal scalar law of the form A = Φ(τ) can exist on that class. Second, an exact scalar-time closure criterion proves that such a reduction exists if and only if the aging observable is constant on every equal-proper-time fiber; when this fails, any scalar approximation incurs irreducible error. Third, an observable sufficiency trilemma shows that any attempt to preserve a universal scalar-time law must either restrict the admissible class, deny the biological relevance of observed differences, or introduce additional constitutive variables through a bridge law. The paper does not challenge relativity. Its claim is narrower: relativity determines elapsed duration exactly, but it does not by itself supply a constitutive law for biological aging. This clarifies the biological reading of the twin paradox and identifies the logical need for an explicit constitutive bridge.