MetaRepair: A Unified Formal Framework for Constrained Protein Sequence Repair Optimization Grounded in F-Theory Meta-Axioms

MetaRepair is a unified formal framework for constrained protein sequence repair optimization, grounded in the four meta-axioms of F-Theory and formalized in Lean 4. It generalizes previous disease-specific formalizations—including DMD, schizophrenia, sickle cell disease, and cancer—into a single parametric framework.The framework introduces three key advancements: position-weighted amino acid distance, a three-component total cost functional (covering distance, efficiency, and safety), and a continuous $\epsilon$-feasibility constraint. Two existence theorems are proven in Lean 4 and verified via CI, establishing that any finite non-empty candidate set contains a constrained optimal element. MetaRepair provides the mathematical foundation for the F-Theory disease repair series.