Informational Set Theory

This paper introduces Informational Set Theory (IST), a foundational mathematical framework that treats set-theoretic identity through the lens of informational conservation. While standard Zermelo-Fraenkel Set Theory (ZFC) treats mathematical operations as costless mappings, IST establishes the Law of Kept Data (A_KD), an axiom requiring that the net change in information (Delta I) remains zero for any valid transformation.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-21
DOI
https://doi.org/10.5281/zenodo.19686310
Primary Topic
Topological and Geometric Data Analysis
Type
article
Field-Weighted Citation Impact
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article

Informational Set Theory

Asa Smith
Zenodo (CERN European Organization for Nuclear Research)
Topological and Geometric Data Analysis
article

Informational Set Theory

Asa Smith
article en

Abstract

This paper introduces Informational Set Theory (IST), a foundational mathematical framework that treats set-theoretic identity through the lens of informational conservation. While standard Zermelo-Fraenkel Set Theory (ZFC) treats mathematical operations as costless mappings, IST establishes the Law of Kept Data (A_KD), an axiom requiring that the net change in information (Delta I) remains zero for any valid transformation.

Zenodo (CERN European Organization for Nuclear Research)
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Topological and Geometric Data Analysis
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Informational Set Theory — Asa Smith · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS