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Mathematical Conditions for Regime Failure
One of the recurring themes in science is the tendency to confuse the limits of our models with the limits of reality.
In a recent working paper, I explore a simple question:
What happens when a descriptive framework reaches the boundary of its validity?
In physics, singularities are often treated as endpoints. But another possibility is that they represent points where a particular description stops working, while the underlying reality continues in a form not yet captured by the model.
The paper develops a minimal framework built around three ideas:
Rather than viewing boundaries as proof of termination, the framework treats them as potential transitions between descriptive regimes.
This is an exploratory paper and does not make strong physical claims. Its goal is to provide a mathematical language for discussing regime failure, persistence, and structural boundaries.
One of the most interesting implications is that what we often call a "limit" may sometimes be a limit of description rather than a limit of existence.
Mathematical Conditions for Regime Failure in Relational Field
Theory: A Structural Framework for Descriptive Boundaries