Standard sequential inference architectures are compromised by a normalizability crisis when confronted with extreme, structured outliers. By operating on unbounded parameter spaces, state-of-the-art estimators lack the intrinsic geometry required to appropriately sever anomalies, resulting in unbounded covariance inflation and mean divergence. This paper resolves this structural failure by analyzing the abstraction sequence of inference at the meta-prior level (S_2). We demonstrate that extremizing the action over an infinite-dimensional space requires a non-parametric field anchored by a pre-prior, as a uniform volume element mathematically does not exist. By utilizing strictly invariant Delta (or ν) Information Separations on the statistical manifold, we physically truncate the infinite tails of the spatial distribution. When evaluated as a Radon-Nikodym derivative against the base measure, the active parameter space compresses into a strictly finite, normalizable probability droplet. Empirical benchmarks across three domains--LiDAR maneuvering target tracking, high-frequency cryptocurrency order flow, and quantum state tomography--demonstrate that this bounded information geometry analytically truncates outliers, ensuring robust estimation without relying on infinite-tailed distributional assumptions.

翻译：标准序列推理架构在遭遇极端结构化异常值时，会因可归一化危机而失效。由于在无界参数空间上运行，现有最优估计器缺乏适当分离异常值所需的内在几何结构，导致协方差无限膨胀与均值发散。本文通过分析元先验层面（S_2）的推理抽象序列，解决了这一结构缺陷。我们证明：在无限维空间上对作用量进行极值化时，需要以预先验为锚点的非参数场，因为数学上不存在均匀的体积元。通过在统计流形上应用严格不变的Δ（或ν）信息分离，我们在物理层面截断了空间分布的无限尾部。当作为Radon-Nikodym导数相对于基测度进行评估时，活动参数空间被压缩为严格有限、可归一化的概率液滴。在三个领域——LiDAR机动目标跟踪、高频加密货币订单流及量子态层析——的实证基准测试表明，这种有界信息几何能解析截断异常值，确保在不依赖无限尾部分布假设的前提下实现鲁棒估计。