A Metadeductive Principle for Detecting Retrodefinition in Mathematical Proofs

This work introduces a metadeductive principle aimed at detecting structural circularity in mathematical derivations. The proposed framework identifies situations in which a conclusion implicitly constrains the rules intended to generate it, a phenomenon referred to as retrodefinition. Rather than treating repeated non-deducible steps as isolated errors, the principle interprets their recurrence as evidence of framework insufficiency. The contribution is methodological and foundational in nature: it does not resolve any specific conjecture, nor does it claim impossibility in an absolute sense. Instead, it provides a falsifiable diagnostic criterion for determining when a deductive system cannot support a non-circular proof without explicit extension.