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This work explores generativity as the process that precedes and shapes mathematical structures and reality.

May 25, 2026Open Access

Generativity as the Foundation of Mathematics and Reality

Key Points

This work explores generativity as the process that precedes and shapes mathematical structures and reality.
Theoretical exploration of generativity as minimal, assumption-free iteration.
Analysis of the relationship between ontology and mathematics.
Development of a coherent framework unifying structure and conceptual systems.
Generativity is proposed as the origin of mathematical and physical structures.
Mathematics stabilizes generative patterns rather than originating order.
A new framework posits ontology as the basis for mathematics.

Abstract

This work presents generativity as the foundational process underlying the emergence of mathematicsand physical reality. It addresses a core paradox in contemporary science: the expectation that mathematics must describe stages of reality that existed before mathematics itself. The paper argues that generativity—understood as minimal, assumption free iteration—precedes and gives rise to mathematical structures, logical relations, and physical laws. Mathematics is interpreted not as the origin of order but as a stabilization of generative patterns. This perspective reverses the traditional epistemological direction: ontology explains mathematics, not the other way around. The result is a coherent framework that unifies the genesisof structure, invariants, and conceptual systems, offering a deeper understanding of how reality can arise from pre mathematical processes. Related works: Why Mathematics Must Have a Beginning Why Mathematics Needs a Generative Foundation Generativity as the Foundation of Mathematics and RealityAuthor: Waldemar Superson

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