Scientific discovery saturates when new hypotheses cease to provide independent information, even if the nominal hypothesis space remains large. We study hybrid discovery systems that combine structured local search with LLM-generated non-local proposals and pose the Search Compression Hypothesis: non-local exploration helps only when three geometric conditions co-occur: spectral compression, orthogonal escape from the explored span, and residual signal alignment with the target. We formalize these conditions, derive necessary conditions for hybrid advantage, and test the mechanism in controlled synthetic environments, large-scale A-share factor discovery, and symbolic-regression benchmarks; a public tabular operational sanity check tests the associated budget-allocation implication. Signal-planting and directed-versus-random experiments show that novelty alone is insufficient: random orthogonal jumps expand coverage but do not improve yield without predictive alignment. Across compression sweeps, real factor archives, and LLM-SRBench tasks, hybrid gains concentrate in weakly represented but target-bearing directions and vanish as the hypothesis space approaches full rank. The framework turns LLM-guided discovery from generic novelty search into a diagnostic procedure for deciding when directed non-local exploration is warranted.

翻译：当新假说无法提供独立信息时，即使名义假说空间依然庞大，科学发现也会趋于饱和。我们研究结合结构化局部搜索与LLM生成非局部提议的混合发现系统，并提出搜索压缩假说：非局部探索仅在三个几何条件同时满足时发挥作用——谱压缩、从已探索张成空间的正交逃逸，以及残差信号与目标的对齐。我们形式化这些条件，推导混合优势的必要条件，并在受控合成环境、大规模A股因子发现及符号回归基准中验证该机制；一项公开表格化操作完整性检验测试了相关的预算分配影响。信号植入实验与定向/随机对比实验表明，新颖性本身并不足够：随机正交跳跃可扩大覆盖范围，但若无预测性对齐则无法提升产出。在压缩扫描、真实因子档案和LLM-SRBench任务的横跨实验中，混合增益集中于表征薄弱但携带目标的维度，并在假说空间趋近满秩时消失。该框架将LLM引导的发现从通用新颖性搜索转变为诊断程序，用于判定何时应用定向非局部探索。