THE SILENT RADIX: Positional Notation as Ultrametric Tree and the Calculus of Indications as Remedy

DOI: 10.5281/zenodo.21148596 July 2, 2026
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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