Structural Ruptures in Scientific Revolutions: A Formal Interpretation of Kuhnian Paradigm Shifts

The Kuhnian concept of scientific paradigms has traditionally been analyzed through sociological or epistemological lenses, often lacking a formal structural definition. In this work, we propose a formal interpretation of scientific revolutions within the framework of the Theory of Non-Derivability and Admissibility (TNA). We reinterpret a paradigm as a structural admissibility operator S that defines the domain of valid theoretical configurations. Periods of normal science correspond to internally derivable regimes (N₀), while scientific revolutions are modeled as structural ruptures S → S'. By introducing the Bresciano Metric to quantify the structural distance to the boundary of a paradigm, we provide a formal explanation for incommensurability: the transition between regimes is non-derivable, meaning theoretical trajectories in S cannot be extended into $S'$. This approach provides a unified formal language to describe the discontinuous nature of scientific progress across different scales of knowledge.