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

A consilient research program demonstrating that positional notation is an ultrametric tree whose radix encodes a chosen grouping cycle; that the systematic errors of silent radices, silent metrics, and assumed linearity arise from substituting a monocultural decimal default and flattening the tree into an Archimedean line; and that re-founding on Spencer-Brown's calculus of indications restores the observer, the ultrametric, and the self-measuring '10' as the seed of all self-aware quantity. v1.1 completes the Consequence Atlas with 142 expansion entries across 14 domains (207 total across 17 domains: healthcare, military, transportation, environmental systems, media & communications, education, history & archaeology, physics, biology & genetics, architecture & engineering).

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-30
DOI
https://doi.org/10.5281/zenodo.21052038
Primary Topic
advanced mathematical theories
Type
article
Field-Weighted Citation Impact
0.00
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article

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

QNFO Research
Zenodo (CERN European Organization for Nuclear Research)
advanced mathematical theories
article

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

QNFO Research
article en

Abstract

A consilient research program demonstrating that positional notation is an ultrametric tree whose radix encodes a chosen grouping cycle; that the systematic errors of silent radices, silent metrics, and assumed linearity arise from substituting a monocultural decimal default and flattening the tree into an Archimedean line; and that re-founding on Spencer-Brown's calculus of indications restores the observer, the ultrametric, and the self-measuring '10' as the seed of all self-aware quantity. v1.1 completes the Consequence Atlas with 142 expansion entries across 14 domains (207 total across 17 domains: healthcare, military, transportation, environmental systems, media & communications, education, history & archaeology, physics, biology & genetics, architecture & engineering).

Zenodo (CERN European Organization for Nuclear Research)
Q-Flex (United States) (US)
Openalex Percentile: Top 4%
advanced mathematical theories
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The Silent Radix: Positional Notation as Ultrametric Tree and the Calculus of Indications as Remedy — QNFO Research · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS