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Paradigm-challenging assertions deserve equally challenging critique so that the lessons can be applied with confidence. Ascribing intent to placement of mounds of dirt five-thousand years and more old requires more than a leap of faith, so a mathematical test was applied to show that chance could not explain the number of points connected by relatively few straight lines. Beyond that, mound arrangements can be made to register by no more than the primary calendar numbers of 260 and 365 as scaling factors. The oldest mound pattern at Watson Brake, Louisiana could be made to register to a master grid from Caney mounds at each of three equiangular rotations. The same technique of geometry reoccurs in a chert eccentric from Copan, demonstrating that traits persist for thousand of years. Recovery of a standard unit of measure is a theoretically daunting task. Fortunately, a couple of chert artifacts provided sufficient context to eliminate ambiguity and link specific lengths to specific numbers. Analysis of a cache of chert eccentrics provided independent confirmation and quantified a tight enough range of variation to avoid ambiguity. As increasing examples of numbers encoded into artifacts are encountered, it becomes clear that rules of syntax, including redundant indications and symmetry clarify the distinction between coincidence and intent. It also is clear that sacred numbers were presented with great precision and accuracy while ordinary measures were applied by body-part equivalencies, such as 260 units for a foot and 1300 units for an outreached arm reach.
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