On the Boundaries of Constructive Definability in Arithmetic — The Fundamental Limit of the Natural Number Sequence — Jonas M. Petrov. — Self-published, 2025, 6 p..pdf

This paper introduces the concept of a natural number ("Numerus Apoptosis" or "Apoptonumerus"), the attainment of which leads to a fundamental collapse of arithmetic properties. It is proven that any attempt to define a natural number exceeding this value results in a logical contradiction within the framework of standard set theory axioms. The proposed object establishes an absolute set-theoretical limit for the concept of a "natural number."