Class Topology Survives Corruption: Prior, Monitor, and Repair for 3D Continual Test-Time Adaptation

Continual test-time adaptation (CTTA) aims to adapt a source-trained model to continuously evolving target distributions without access to source data, target labels, or domain-boundary information. Most existing CTTA methods rely on computationally expensive mean-teacher frameworks. Moreover, they often require explicit distribution-shift detection and treat each target distribution independently, limiting their ability to exploit information shared across domains. In this work, we show that, despite substantial accuracy degradation, the relational topology among classes remains remarkably stable across diverse 3D corruptions. Motivated by this observation, we propose **To**pology-Anchored **Co**ntinual **T**est-**T**ime **A**daptation (ToCoTTA), which leverages this class topology as a stable structural anchor throughout continual adaptation. Specifically, ToCoTTA derives a reference class topology from the source classifier and uses it in three complementary ways: as a **prior** to refine noisy online class prototypes, as a **monitor** to quantify the reliability of ongoing adaptation, and as a **repair** signal to regulate updates and recover from accumulated parameter drift. By providing a unified structural signal for both prediction and adaptation, class topology enables ToCoTTA to remain robust under continually evolving target distributions. Extensive experiments on multiple 3D point cloud benchmarks demonstrate consistent improvements over existing CTTA methods with negligible computational overhead.