The Silent Radix: Positional Notation as Ultrametric Tree and the Calculus of Indications as Remedy

July 4, 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. --- *Published under QNFO-ULA. [legal.qnfo.org](https://legal.qnfo.org/)*

The Silent Radix: Positional Notation as Ultrametric Tree and the Calculus of Indications as Remedy

Authors: Rowan Brad Quni-Gudzinas

Published: 2026-07-04

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. --- Published under QNFO-ULA. [legal.qnfo.org](https://legal.qnfo.org/)

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