Reliable causal discovery in time series depends on whether the conditioning set adequately represents the system state. If relevant history or unobserved processes are omitted, residual dependence can appear as direct causal links. We study this failure mode on promnient constraint-based causal discovery methods through a simple premise: how much does the inferred graph change as conditioning depth increases? When the observed process is described approximately by a finite-order Markovian representation, inferred graphs should stabilize once sufficient past observations are observed. Hidden confounding and other hidden-memory mechanisms should remain sensitive to depth when the observed state is incomplete. We formalise this behavior with graph instability statistics computed over the conditioning-depth grid. The empirical study covers synthetic systems with known ground truth and calcium imaging recordings with unknown causal structure. In simulations, both Markovian and non-Markovian systems relatively upheld our premise. With known ground truth, we evaluate recovery using confusion matrix metrics; while in real data without ground truth, we use descriptive graph instability summaries. Across synthetic Markovian and hidden memory systems, c-GC variants give the clearest separation, while PCMCI variants show weaker compatible trends. In real data, inferred connectivity drops sharply with conditioning depths and then levels off. This method, however, does not recover latent graphs, nor does it clearly separate latent confounding from lag-order misspecification, non-stationarity, measurement error. Its contribution is more modest and practical: and explicit model-checking tool for deciding when causal claims are stable and when they should be treated caustiosly.

翻译：时间序列中的可靠因果发现取决于条件集是否充分表征系统状态。若遗漏相关历史信息或未观测过程，残差依赖性可能表现为直接因果联系。我们通过一个简单前提研究这一失效模式对主流基于约束的因果发现方法的影响：当增加条件深度时，推断图的变化程度如何？当观测过程可近似由有限阶马尔可夫表示描述时，若纳入足够的过去观测，推断图应趋于稳定。当观测状态不完整时，隐藏混杂因素及其他隐藏记忆机制应保持对条件深度的敏感性。我们通过条件深度网格上计算的图不稳定性统计量来形式化这一行为。实证研究涵盖具有已知真实地标的合成系统与因果结构未知的钙成像记录。在模拟实验中，马尔可夫与非马尔可夫系统均相对支持我们的前提。对于已知真实地标的情况，我们使用混淆矩阵指标评估恢复效果；而在无真实地标的真实数据中，我们采用描述性图不稳定性摘要。在合成马尔可夫与隐藏记忆系统上，c-GC变体表现出最清晰的区分度，而PCMCI变体仅呈现较弱的相容趋势。在真实数据中，推断连接性随条件深度增加急剧下降后趋于平稳。然而，该方法既无法恢复潜在图结构，也无法清晰区分潜在混杂因素与滞后阶数误设、非平稳性、测量误差。其贡献更为适度且实用：作为一种显式模型检验工具，用于判断因果主张何时稳定、何时应谨慎对待。