Morphological Saturation in Positional Bases: Finiteness of Exceptions, Early Completion, and the Mixed-Form Bottleneck

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Abstract

Building on the six-form classification of C1 Paper ("Morphological Completeness of Positional Bases: Classification, Minimum Threshold, and the Structural Obstruction of Historical Number Systems") , we resolve three open problems: the anomalous incomplete bases are exactly four (b ∈ {9, 10, 21, 25}), the intrinsic saturation threshold is always strictly less than b for every complete base (ratio N*(b)/b tends to zero), and the structural bottleneck is always a mixed form (F5 in 82.1% of cases). These results transform the completeness criterion from a static classification into a dynamic picture where the morphological vocabulary fills rapidly, saturates early, and is constrained by a single structural…

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Topics & keywords

Keywords
  • Completeness (order theory)
  • Saturation (graph theory)
  • Bottleneck
  • Base (topology)
  • Vocabulary
UN Sustainable Development Goals
  • Quality Education
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