Morphological Saturation in Positional Bases: Finiteness of Exceptions, Early Completion, and the Mixed-Form Bottleneck
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 bottleneck. Part of the sub-limit dynamics research series.
Fields of Study & Subjects
Theoretical and Computational Physics
Origins and Evolution of Life
Cellular Automata and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 23 February 2026
- Language
- EN
- Document type
- Preprint