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Theorem

Kolmogorov-Arnold Representation Theorem

Analysis

The Kolmogorov-Arnold representation theorem, also called the superposition theorem, states that every continuous function of several real variables on the unit cube can be written as a finite composition of continuous functions of a single variable combined only by addition. Established through the work of Andrey Kolmogorov and Vladimir Arnold, it solved a more constrained form of Hilbert's thirteenth problem as a corollary, and in this representation the inner functions are universal and independent of the particular function being represented, while the outer functions depend on it. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Statement Form
Existence Theorem 1
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Has Statement Form

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Kolmogorov-Arnold Representation Theorem (Wikipedia)
Sources
1. Kolmogorov-Arnold Representation Theorem (Wikipedia)
In Branch: Real Analysis, Lead sentenceView the Source
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