The Topology of Tokens

This note formalizes the operational layer developed after The Dynamical Topology of Mind and The Architecture of ASI. The original ontology supplied attractors, basins, affinity, persistent homology, and agency as topology-reading. The present addendum supplies the dual program required for implementation: the topology already latent in tokens, and the tokenization of topology as an explicit handle. Because full-resolution topology is computationally inadmissible, navigation proceeds by coarse-graining with acceptable resolution loss across interconnected layers, in the same sense that a pharmacological cascade is examined through coupled reduced manifolds rather than a complete molecular state space. Navigational capability and navigational understanding are distinguished and made measurable. The first empirical gate remains affinity-aware control on current residual-stream infrastructure, augmented by compact token identifier nodes.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-04
DOI
https://doi.org/10.5281/zenodo.22309244
Primary Topic
Topological and Geometric Data Analysis
Type
preprint
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preprint

The Topology of Tokens

César Castro
Zenodo (CERN European Organization for Nuclear Research)
Topological and Geometric Data Analysis
preprint

The Topology of Tokens

César Castro
preprint en

Abstract

This note formalizes the operational layer developed after The Dynamical Topology of Mind and The Architecture of ASI. The original ontology supplied attractors, basins, affinity, persistent homology, and agency as topology-reading. The present addendum supplies the dual program required for implementation: the topology already latent in tokens, and the tokenization of topology as an explicit handle. Because full-resolution topology is computationally inadmissible, navigation proceeds by coarse-graining with acceptable resolution loss across interconnected layers, in the same sense that a pharmacological cascade is examined through coupled reduced manifolds rather than a complete molecular state space. Navigational capability and navigational understanding are distinguished and made measurable. The first empirical gate remains affinity-aware control on current residual-stream infrastructure, augmented by compact token identifier nodes.

Zenodo (CERN European Organization for Nuclear Research)
Industry, innovation and infrastructure
Topological and Geometric Data Analysis
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