PAV (Process Advantage Verifiers)

Proves that a step-level reward should measure progress (the change in success probability induced by step $s_k$) rather than absolute state value: $R_{\text{PAV}}(s_k \mid s_{1:k-1}) = V^\mu(s_{1:k-1}) + \alpha \underbrace{\left(Q^\mu(s_{1:k-1}, s_k) - V^\mu(s_{1:k-1})\right)}_{\text{Process Advantage } A^\mu(s_{1:k-1}, s_k)}$ under a distinct prover policy $\mu$, preventing the policy from stalling on zero-progress tautological steps.