VDE: Verifiable Dynamic Evaluation of Mathematical Reasoning via Typed Bipartite Graphs

Mathematical reasoning benchmarks are increasingly limited by static test sets, which are vulnerable to contamination and slow to adapt as models improve, while manually building fresh high-quality problems is expensive. We propose VDE (Verifiable Dynamic Evaluation), a dynamic evaluation framework that generates replay-verifiable math problems from typed value--theorem bipartite graphs. Each instance is an executable graph with model-independent ground truth recovered by deterministic replay rather than model-produced solutions. Beyond compositional depth, VDE supports explicit constraint injection and controlled branching to produce harder problems while preserving verifiability. We instantiate the same framework in analytic geometry and number theory, showing that a unified graph-based generation paradigm can cover structurally different domains. Experiments on frontier models show that performance remains far from saturation and degrades predictably as we increase construction depth, constraints, and branching, making VDE a scalable and trustworthy testbed for dynamic mathematical reasoning evaluation.