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While token pruning reduces sequence length, prior methods rely on heuristics that break compatibility with hardware-efficient kernels like FlashAttention. In this work, we observe that tokens evolve toward \\textit{semantic fixing points}, making further processing redundant. To this end, we introduce Delta Attention Selective Halting (DASH), a training-free policy that monitors the layer-wise update dynamics of the self-attention mechanism to selectively halt stabilized tokens. Extensive evaluation confirms that DASH generalizes across language and vision benchmarks, delivering significant prefill speedups while preserving model accuracy and hardware efficiency. 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