During January 2026, this developer contributed foundational mathematical proofs to the HEPLean/PhysLean repository, focusing on the tight-binding chain model in quantum mechanics. They established the Hermiticity of the Hamiltonian and demonstrated the orthogonality of energy eigenstates for distinct wavenumbers, both essential properties for theoretical consistency and reliable simulation results. Their approach relied on formal verification and theorem proving, utilizing the Lean language to ensure rigor and correctness. The work addressed core quantum mechanical principles, enhancing the model’s reliability for downstream applications. Throughout the period, the developer emphasized mathematical precision and clear documentation, reflecting depth in both technical skill and domain knowledge.