ADRIAN SHARMAN
For over a century, computational analyses of the Inca khipu have been constrained by what we term the "Spreadsheet Fallacy" — the attempt to computationally validate khipus primarily as flat, base-10 arithmetic ledgers. This model fails to account for the fact that only 4.6% of known cord clusters demonstrate valid summation. In this paper, we extend Metrological Domain Profiling (MDP) to analyse 54,403 cords across 619 khipus from the Open Khipu Repository, moving beyond one-dimensional colour profiling to reconstruct the full three-dimensional, tactile, and hierarchical ontology of the system. We demonstrate that the khipu possesses strict spatial and material structure operating across four distinct layers: (1) Material Metrology, where fiber type (cotton vs camelid) redefines numerical scale by up to 67×; (2) Topological Syntax, where administrative granularity is encoded in subsidiary cord depth and colour palette shifts systematically with hierarchical level; (3) Categorical Syntax, featuring statistically constrained colour sequences (p < 0.001) that demonstrate strict institutional sorting rules rather than random clustering, with same-colour run lengths spiking at decimal administrative units; and (4) Hardware Metadata, where physical features including canutito thread-wrappings (98.6% colour-independent from parent cords), primary cord construction, and cord termination types encode document-level metadata and institutional information. Three hypotheses were explicitly tested and falsified: cluster spacing as punctuation, Hanan/Hurin midpoint split, and cord thickness as domain marker. These findings suggest the khipu is not merely a mathematical ledger, but a multi-layered, tactile administrative system whose information is distributed across the material, spatial, and structural dimensions of the textile.