Verifier strength does not buy discovery quality: a pre-registered two-domain test of LLM-based automated research, with post-hoc evidence pointing to proposer-pool composition

Automated research pipelines pair an LLM proposer with a verifier on an implicit bet: discovery quality rises with verification strength. Under a pre-registered protocol we test this bet in two real-data domains -- job-shop scheduling and vehicular edge offloading on Beijing T-Drive trajectories -- across 100 matched LLM/random pairs per domain and three verifier tiers. The manipulation binds -- a 429-case mutation battery shows scores rising across tiers -- yet the paired LLM-over-random advantage does not scale with it (A, one-sided p=0.1115; D, p=0.9994), and in D shrinks under the strict tier (margin contrast -0.040, p=0.0013). The two lower gates promote identical candidates in 100/100 and 99/100 pairs, so the strict order is untestable when they coincide. Constructively, LLM proposals carry a real paired advantage over random controls, but a post-hoc union-pool analysis shows the fastest path to better discovery is widening the pool, not tightening the gate: mixing the two pools adds +1.52 holdout-value units in domain A (one-sided Wilcoxon, n=100, p=0.0002) -- evidence that pool composition, not verification strength, is the lever. Criteria, ledgers and scripts are archived on Zenodo (DOI: 10.5281/zenodo.23308866).