CAJA CUSA: Certificación estructural de viabilidad clínica mediante proyección de dominio y estabilidad hessiana

This work introduces CAJA CUSA (Consciousness–Universal Structural Auditor), a formal mathematical framework for structural viability, stability certification, and automatic reconstruction of non-viable configurations in complex systems, with direct application to pharmacological design and biomedical optimization. The model defines a configuration space X in Rⁿ endowed with a potential V (X), whose second-order structure is characterized by the Hessian matrix H (X) = ∇²V (X). Structural stability is formally certified when H (X) is positive semidefinite, verified through its eigenvalue spectrum. A structural domain D is introduced as the intersection of multiple subdomains (physical, biological, toxicological, clinical, regulatory, or others), defined by constraint functions gᵢ (X) ≤ 0. The distance to the admissible domain is quantified by: d (X, D) = sum over i of max (0, gᵢ (X) ) ²providing a continuous measure of structural violation. Beyond diagnosis, CAJA CUSA implements a reconstruction operator (Regroctudie): ΠD (X) = argmin over Y in D of ||Y − X||²which projects any non-viable configuration onto the nearest admissible one. A corrective dynamic: dX/dt = −∇V (X) − α∇d (X) drives the system toward stable and domain-compliant solutions. The framework outputs a standardized certification report including final configuration, Hessian eigenvalues, stability flags, domain distance, projected solution, and global viability verdict. Validation examples, including pharmacological compounds such as cisplatin, demonstrate that CAJA CUSA not only detects structural infeasibility but automatically reconstructs clinically admissible configurations. This establishes CAJA CUSA as a general-purpose certifier and redesign engine for stability, coherence, and viability across scientific and engineering domains.