Despite decades of research, cardinality estimation remains the optimizer's Achilles heel, with industrial-strength systems exhibiting a systemic tendency toward underestimation. At cloud scale, this is a severe production vulnerability: in Microsoft's Fabric Data Warehouse (DW), a mere 0.05% of extreme underestimates account for 95% of all CPU under-allocation, causing preventable slowdowns for thousands of queries daily. Yet recent theoretical work on provable upper bounds only corrects overestimation, leaving the more harmful problem of underestimation unaddressed. We argue that closing this gap is an urgent priority for the database community. As a vital step toward this goal, we introduce xBound, the first theoretical framework for computing provable join size lower bounds. By clipping the optimizer's estimates from below, xBound offers strict mathematical safety nets demanded by production systems - using only a handful of lightweight base table statistics. We demonstrate xBound's practical impact on Fabric DW: on the StackOverflow-CEB benchmark, it corrects 23.6% of Fabric DW's underestimates, yielding end-to-end query speedups of up to 20.1x, demonstrating that even a first step toward provable lower bounds can deliver meaningful production gains and motivating the community to further pursue this critical, open direction.

翻译：尽管历经数十年研究，基数估计仍是查询优化器的致命弱点，工业级系统普遍存在系统性低估倾向。在云规模场景下，这构成严重生产隐患：在微软Fabric数据仓库（DW）中，仅0.05%的极端低估案例就导致95%的CPU资源分配不足，每日造成数千条查询遭遇本可避免的性能下降。然而近期关于可证明上界的理论研究仅能修正高估问题，对危害更大的低估问题却未提出解决方案。我们认为填补这一理论空白已成为数据库领域的紧迫任务。作为实现该目标的关键一步，我们提出xBound——首个用于计算可证明连接基数下界的理论框架。通过为优化器估计值提供下界截断，xBound仅需少量轻量级基表统计信息，即可构建生产系统所需的严格数学安全网。我们在Fabric DW上验证了xBound的实际影响：基于StackOverflow-CEB基准测试，该系统修正了Fabric DW中23.6%的低估案例，实现端到端查询速度最高提升20.1倍。这表明即使向可证明下界理论迈出的第一步，也能带来显著的生产效益，从而激励学界进一步探索这一关键而开放的研究方向。