Vatayan: Computational Paleography and Geometric Equivalency between Indus and Vaigai Scripts

Comparative paleography has long depended on qualitative visual inspection to assess potential morpho-syntactic or graphical continuities between undeciphered and deciphered ancient scripts. This study introduces Vatayan, a computational framework designed to evaluate structural and geometric equivalencies between the undeciphered Indus Valley Script (IVS) and Tamil-Brahmi graphemes recovered from the Vaigai River basin (Keeladi corpus). I constructed a 5-tier waterfall pipeline comprising: (1) Directed Hausdorff Distance to evaluate spatial boundary alignment, (2) Graph Edit Distance (GED) for structural and topological skeleton matching, (3) Histogram of Oriented Gradients (HOG) to model local edge-orientation distributions, (4) Hu Moments for translation-, scale-, and rotation-invariant shape profiling, and (5) Topological Isomerism analysis to quantify loop density and junction configuration invariants. Evaluated across a standardized dataset comprising 641 Indus signs and 42 Vaigai base graphemes, Vatayan offers a formal metric for graphic affinity that mitigates subjective bias in comparative epigraphy.