Let CSP Be Your ANCHOR: Adaptive Crystal Search over Frozen Structure Priors

De novo crystal generation (DNG) jointly learns where to search in composition space and how to generate structures. We argue that this coupling creates two limitations for discovery. First, we show that replacing DNG structure generation with crystal structure prediction (CSP) at fixed DNG-sampled compositions increases stability and SUN on both the MatterGen and LeMat-GenBench benchmarks, demonstrating that dedicated CSP is stronger when structure generation is isolated. Second, likelihood-trained DNG composition marginals reflect training distributions, not where discovery is most productive. Reward-guided DNG moves beyond this marginal, but directly fine-tuning DNG again couples composition search to structure generation. We take a more direct route and introduce ANCHOR, which learns a GRPO composition policy around a frozen CSP model acting as a strong physical prior. To sustain exploration, we introduce continuous adaptive novelty (CAN), scoring candidates against known structures and the growing discovery history. ANCHOR raises state-of-the-art SUN to 42.30% on the MatterGen evaluation pipeline and transfers without retraining to two additional CSP backbones, reaching 42.80% and 43.60%. Our results identify the DNG composition marginal as a discovery bottleneck that undersamples productive chemical regions.