Interactive world models must respond quickly to controls while preserving scene consistency. Existing acceleration methods can miss heterogeneous control responses and spatial transport when recovering skipped features. We observe that interaction-induced feature changes correlate with approximation error, while low-frequency interpolation errors are phase-sensitive and show more predictable phase progression. These findings motivate CAST, a reconstruction-coupled inference framework. CAST selects anchors by interaction sensitivity and cross-layer coverage, reconstructs skipped residuals with frequency- and confidence-aware Phase-Aware Reconstruction (PAR), and coordinates historical KV routing according to downstream reconstruction responsibility. On Matrix-Game 3.0 and HY-World 1.5, CAST achieves 2.15x and 3.48x speedups, respectively, while maintaining visual quality close to Native (Figure 1). It also attains the highest VBench scores among compared methods and leads non-native baselines on seven and six of thirteen WorldMark dimensions, demonstrating a balance of generation speed, visual quality, and interactive responsiveness under real-time control. Code is available at https://github.com/lokiniuniu/CAST.

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