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Reconstructing dense 3D geometry from continuous video streams requires stable inference under a constant memory budget. Existing $O(1)$ frameworks primarily rely on a ``pure eviction'' paradigm, which suffers from significant information destruction due to binary token deletion and evaluation noise from localized, single-layer scoring. To address these bottlenecks, we propose StreamCacheVGGT, a training-free framework that reimagines cache management through two synergistic modules: Cross-Layer Consistency-Enhanced Scoring (CLCES) and Hybrid Cache Compression (HCC). CLCES mitigates activation noise by tracking token importance trajectories across the Transformer hierarchy, employing order-statistical analysis to identify sustained geometric salience. Leveraging these robust scores, HCC transcends simple eviction by introducing a three-tier triage strategy that merges moderately important tokens into retained anchors via nearest-neighbor assignment on the key-vector manifold. This approach preserves essential geometric context that would otherwise be lost. Extensive evaluations on five benchmarks (7-Scenes, NRGBD, ETH3D, Bonn, and KITTI) demonstrate that StreamCacheVGGT sets a new state-of-the-art, delivering superior reconstruction accuracy and long-term stability while strictly adhering to constant-cost constraints.