Verifier-guided sampling: training-free reranking for scientific code generation without a learned reward model

When a language model writes scientific code, the result usually runs and returns a plausible number that can still be wrong by a sign, a unit, a factor, or a violated conservation law — and the model's own confidence does not tell you which. We study verification grounded independently in the underlying science: a declarative correctness checker, built from a public schema-validated knowledge corpus spanning physics, chemistry, biology, climate, mathematics, and numerical methods, and never trained on preference labels. Applied at sampling time as a best-of-N reranker over an un-tuned base model — an approach we call verifier-guided sampling — it supplies, without preference labels or training, the reranking signal that learned reward models (RLHF, DPO, RLVR) are used to provide. On a 73-prompt scientific-code benchmark and two open-weights model families (Llama 3. 1 8B and Mistral Nemo 12B), the deployable verification-only signal selects the same candidate as a functional ground-truth oracle on 97. 3% of prompts; across an N-sweep (N in 3, 5, 10, 20, 50) it raises the mean overall score by up to +0. 108 (Llama) and +0. 148 (Mistral Nemo) and captures at least 95% of the available rerank headroom at N=50, robustly across vendors. The contributions are (i) an information-theoretic analysis of what any post-hoc verifier can recover from a generation distribution, separating an outlier-rejection regime from a partial-credit regime; (ii) a sample-budget sweep characterising the diminishing-returns curve; and (iii) sampling-policy ablations (fixed-N, adaptive-N, and beam-with-verifier). A direct comparison against a trained reward model is left to dedicated follow-up work. The benchmark, the run records, and the open Lemma verification substrate are publicly released.