Jard Nijholt developed a formal proof component for the HEPLean/PhysLean repository, focusing on the Harmonic Oscillator model. Using Lean and expertise in formal verification and classical mechanics, Jard formalized a lemma that rigorously ties a trajectory’s zero velocity to a position magnitude derived from initial conditions, grounded in energy conservation principles. This work enhanced the model’s validation by enabling more robust scenario testing and reducing simulation risk. Jard also updated model checks to leverage the new proof, and improved documentation and traceability, ensuring the feature’s maintainability and auditability. The contribution demonstrated depth in mathematical proof and formal methods.