# SMT-Based Verification

Stability and safety of dynamical systems are usually guaranteed by Lyapunov functions and barrier certificates, yet the numerical, interval and SMT solvers used to check candidates often need relaxations, and standard test suites drifted toward low-dimensional polynomial systems. LLM2Cert has a language model propose candidate certificates and routes each proof obligation to an SMT solver or to the Lean proof assistant, allowing only proof repair and never a change to the theorem. On the 105-instance DynaCertBench, the full framework verifies 81 instances end to end, against 63 for one-shot proposal without feedback.

Stability and safety of dynamical systems are usually guaranteed by Lyapunov functions and barrier certificates, yet the numerical, interval and SMT solvers used to check candidates often need relaxations, and standard test suites drifted toward low-dimensional polynomial systems. LLM2Cert has a language model propose candidate certificates and routes each proof obligation to an SMT solver or to the Lean proof assistant, allowing only proof repair and never a change to the theorem. On the 105-instance DynaCertBench, the full framework verifies 81 instances end to end, against 63 for one-shot proposal without feedback.