Quantitative Morphological Isomorphism in Early Bronze Age Eurasian Administrative Scripts: A Topological Analysis of Ur III and Shang Royal Titularies

Abstract This study investigates the structural and semiotic correlations between pre-dynastic Shang epigraphy and the administrative matrices of the late Uruk and Ur III periods. Utilizing a quantitative morphometric framework and a Log-Confidence spatiotemporal model, we propose an objective topological mapping between Yellow River Oracle Bone Inscriptions (OBI) and Mesopotamian archaic cuneiform. Our analysis highlights notable structural homologies, exploring the potential morpho-semantic correlation of the Shang progenitor Shang Jia () with Ur-Nammu, Wang Hai () with Ur-Utu, and identifying the "Shang Wang" () logogram as a possible ligated structural equivalent to the Ur III imperial formula Lugal Ki-en-gi Ki-uri-ke₄ (King of Sumer and Akkad). Through systematic component ablation and algorithmic scoring, our analysis shows that these alignments achieve a structural similarity score above 62%, substantially exceeding the stochastic noise floor of <56% observed in control experiments, suggesting a non-random correspondence worthy of further investigation. Rather than asserting deterministic demographic migration, this research highlights a statistically significant correlation between the two epigraphic systems. These findings provide a novel quantitative framework, raising the possibility of a highly stabilized, trans-Eurasian diffusion of early statecraft taxonomies, spatial paradigms, and sovereign administrative morphologies during the Bronze Age. Keywords: Shang Dynasty, Sumerian King List, Oracle Bone Inscriptions, cross-cultural transmission, early state formation