Detecting sparse anomalies in long time series is a fundamental challenge in time series anomaly detection, where anomalous events are extremely rare, subtle, and occupy only a minute fraction of the sequence. Excessive false positives in such sparse settings can severely undermine system usability and erode user trust. Most deep learning models are constrained by fixed window scopes and single-mode decision mechanisms, lacking explicit connections to historical windows and sufficient anomaly evaluation criteria, which leads to frequent false alarms. To tackle these limitations, we propose a self-supervised method named C \(^3\) DR (Cross-window Contrast and Cross-level Discriminative Reconstruction), which unifies representation quality and reconstruction deviation as joint multi-mode evaluation criteria within a single algorithm. Specifically, C \(^3\) DR models long-range cross-window consistency during encoding, and introduces a discriminative bidirectional cross-attention mechanism during decoding to mitigate overfitting on anomalous regions. On the high-quality UCR benchmark, four-protocol testing shows C \(^3\) DR reliably outperforms leading deep learning and distance-based detectors, achieving superior event-level accuracy, robust regional detection, and reduced false alarms.