THE SILENT RADIX: Positional Notation as Ultrametric Tree and the Calculus of Indications as Remedy
Positional notation is not merely a convention for writing numbers - it is an ultrametric tree whose place-value columns encode a hierarchical distance function. The base (radix) is the structural parameter that determines the tree topology, yet in everyday practice it goes unstated and unexamined: a silent radix.
THE SILENT RADIX: Positional Notation as Ultrametric Tree and the Calculus of Indications as Remedy
Authors: QNFO Research
Published: 2026-07-02
DOI: [10.5281/zenodo.21148596](https://doi.org/10.5281%2Fzenodo.21148596)
Abstract
Positional notation is not merely a convention for writing numbers - it is an ultrametric tree whose place-value columns encode a hierarchical distance function. The base (radix) is the structural parameter that determines the tree topology, yet in everyday practice it goes unstated and unexamined: a silent radix.
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This paper is part of the QNFO research corpus.