In “How Can Spin, Ply, and Knot Direction Contribute to Understanding the Quipu Code?” (2005), mathematician Marcia Ascher referenced new data on 59 Andean khipus to assess the significance of their variable twists and knots. However, this aggregative, comparative impulse arose late in Ascher's khipu research; the mathematical relations she had identified among 200+ previously cataloged khipus were specified only at the level of individual specimens. This article pursues a new scale of analysis, generalizing the “Ascher relations” to recognize meaningful patterns in a 650-khipu corpus, the largest yet subjected to computational study. We find that Ascher formulae characterize at least 74% of khipus, which exhibit meaningful arrangements of internal sums. Top cords are shown to register a minority of sum relationships and are newly identified as markers of low-level, “working” khipus. We reunite two fragments of a broken khipu using arithmetic properties discovered between the strings. Finally, this analysis suggests a new khipu convention—the use of white pendant cords as boundary markers for clusters of sum cords. In their synthesis, exhaustive search, confirmatory study, mathematical rejoining, and hypothesis generation emerge as distinct contributions to khipu description, typology, and decipherment.
