The Molina Structural Conjecture: A Structural Signature Framework for Frontier Mathematical Problems

We propose the Molina Structural Conjecture: every mathematical system at the frontier of human knowledge — precisely stated, resistant to proof, and asking whether a property holds universally — exhibits three measurable structural signatures: (1) a forbidden transition, a structural state provably impossible given the system's defining rules; (2) a contraction/expansion distinction, two modes of behaviour where the conjecture in each case asks whether the contractive mode is universal; and (3) a power-law spectrum, a Zipf-type distribution in the appropriate representation space. A fourth computational signature — finite Hilbert complexity — confirms that no problem requires infinite-dimensional structure. The conjecture is tested on nine mathematical systems (all seven Clay Millennium Problems plus Fermat's Last Theorem and the Poincaré Conjecture) and passes without exception. No counterexample is found. Three falsifiable predictions are stated. The conjecture is identified and measured using the Formulametrics / MXG structural analysis framework, which embeds each system into a shared signature space Σ = HT, DI, β. A companion paper documents the full framework (Molina 2026b). SHA-256: 06ebbaaf1a2a781f4bbd10e623b3b00992095ad8879e5c1b86315cb516f0ad5b