On Biological States Admitting Repair Relations: With an Application to Long-Term Biological Deterioration

This preprint proposes a foundational framework for describing biological repair as a relation between a disturbed biological state, a causally relevant corrective process, an admissible transition, and the restoration or sufficient improvement of a declared structure or function. It distinguishes restoration, compensation, stabilization, replacement, support-dependent preservation, and autonomous repair. The framework introduces repair-state configurations, repair trajectories, repair-reachability, and repair capacity. It also distinguishes acceptable present function, self-maintained function, and retained capacity to respond to declared future disturbances. Long-term biological deterioration is examined as a possible transition from endogenous containment and recovery toward increasing external dependence, propagation of dysfunction, multi-system deterioration, and loss of self-maintained biological stability. The paper presents a minimal formal specification, testable consequences, empirical comparison strategies, and explicit failure conditions. It does not claim to provide a clinically validated diagnostic or predictive tool. Its purpose is to establish a conceptual and formal basis for later biological instantiation, longitudinal testing, and the study of how repair pathways may be preserved, lost, or reopened. AI-use disclosure: Artificial intelligence tools were used to assist with drafting, language refinement, structural organisation, formalisation, critical review, and PDF LaTeX document preparation. The conceptual direction, selection of claims, and final revisions remain the intellectual property of the author.