Multi-Stage Sensitivity Analysis of Single Coin Finds: Challenging Central-Place Models in the Early and High Medieval Rhine-Meuse Delta

Traditional historical perspectives on early medieval urban developments regularly presuppose that elite administrative frameworks, including Carolingian and Ottonian palatia, automatically operated as primary catalysts for centralized, palace-driven trade network growth. However, investigating such top-down assumptions is heavily constrained by highly fragmented written records. This study implements an alternative mathematical framework by conducting a three-stage sensitivity evaluation of an expanding stray-coin dataset (N_A = 25, N_B = 97, and N_C = 116) distributed across four neighboring riverine zones: Neder-Betuwe, Overbetuwe, Tiel, and Nijmegen. Through the concurrent application of Pearson’s independence tests, cell-specific adjusted residuals, and sequential alpha corrections, we track the shifting structural relationship between chronological coin cohorts (450 - 1200 CE) and modern municipal boundaries. The statistical results demonstrate that while the broader delta landscape achieved macroeconomic uniformity from the Carolingian horizon onward, Nijmegen followed a highly idiosyncratic institutional trajectory during the post-Roman transition (450 - 600 CE). A significant, localized overrepresentation of early monetary losses consistently resisted all sample expansions. This robust data signature implies that, notwithstanding the proven absence of stable domestic settlement structures within the former Roman center, the site maintained a highly specialized, episodic, or institutional function. Conversely, the post-600 CE regional uniformity directly challenges the palace-centric market model, indicating that high-medieval monetization was propelled by regional ecclesiastical lords surfing upon collective riverine transport corridor dynamics.