PUMA PUNKU, TIWANAKU, AND IMPERIAL INCA ARCHITECTURE: Metrological Analysis, Statistical Quantogram Identification, and Euclidean Derivation of a Unified Canonical Module (B≈0.6235" m" )

This study investigates architectural modularity across major pre-Columbian megalithic complexes in the South-Central Andes, specifically focusing on the Tiwanaku/Puma Punku horizon (ca. 500–1000 CE) and Imperial Inca monumental architecture (ca. 1438–1532 CE). Utilizing published terrestrial laser scanning (TLS), close-range photogrammetry, and precision tachymetric datasets (), we isolate an invariant fundamental module () and its constitutive half-module, the canonical foot (). Rather than an arbitrary empirical convention, we demonstrate via Euclidean geometry that this system represents an exact trigonometric derivation: the projection of an equilateral triangle ( symmetry, factor ) constructed over an elementary stonecutting increment (, anchored in the base-81 geodetic fathom ). The system organically generates the classical cubic root constant , yielding the classical five-sixths royal cubit (). Kendall’s cosine quantogram independently confirms the existence of this quantum at () and (), rejecting the null hypothesis of unstandardized construction via Monte Carlo simulation (). The identification of this module resolves the long-standing lexicographical ambiguity in early Aymara ethnohistorical records regarding Luk'a as a "double foot" rather than an anatomical forearm.