Background Curvature and Untracked Populations

Background Curvature and Untracked Populations formalizes the role of hidden mass, unresolved dynamics, and unobserved populations as geometric curvature terms in near-critical systems. The paper shows that background curvature acts as a continuous spectral load that consumes margin even in the absence of explicit control actions. By modeling untracked populations as curvature operators added to system dynamics, the theory explains silent instability, unexpected drift, and failure modes that evade conventional instrumentation. The framework establishes that stability must be evaluated on the effective operator A+UA+UA+U, not on the nominal system alone, completing the curvature theory of the Einsteinian Stack.