Legacy Constraints and Irreversible Path Dependence: A Formal Framework

We formalize how constraints accumulate over time to create path dependence, demon-strating that historical lock-in arises from structural necessity rather than contingent events.The legacy constraint load Llegacy(t) increases monotonically as systems activate compat-ibility constraints, shrinking feasible con guration spaces irreversibly. When legacy loadexceeds system-speci c thresholds, trajectories become locked into historical patterns inde-pendent of current incentives or information. This framework uni es technological lock-in(QWERTY), institutional persistence, and habit formation under a common geometric prin-ciple.Keywords: path dependence, legacy constraints, institutional persistence, technologicallock-in, irreversibility