Structural Residual Compensation (SRC): A Framework for High-Order Acceleration of Slowly Converging Series

We present Structural Residual Compensation (SRC), a framework for accelerating the conver- gence of slowly converging series by designing symbolic compensators to cancel dominant asymptotic residual terms. Applied to the Leibniz series for π and the Riemann zeta function ζ(2), SRC achieves ninth- and seventh-order convergence, respectively. By treating errors as structurally predictable rather than random, SRC integrates symbolic asymptotic analysis with high-precision numerical val- idation to systematically suppress residuals, enabling efficient, high-order approximations of series sums.