ψ-Biomedical Retention: A Threshold Framework for Pre-Clinical Structural Persistence

This work introduces ψ-Biomedical Retention, a theoretical framework extending the ψ-Architecture (Δψ, Ξ, Λψ) to biological and pre-biological systems. The paper formulates a retentive Lagrangian for structural stability and establishes a universal threshold triad — SNR* (minimal signal clarity), ε* (minimal asymmetry), and Rᶜ (critical nucleation radius) — that determines when a biological or proto-biological pattern can persist under noise and perturbation. ψ-Biomedical Retention does not propose diagnostics or clinical interventions. Instead, it provides a physics-based language for structural stability that complements systems biology, morphology, regenerative medicine, synthetic bio-architectures, and early-stage modeling. The framework positions ψ-Architecture as a foundational approach to understanding how biological form endures while remaining fully aligned with ethical boundaries and theoretical rigor.