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We present PS4, a proxy-supervised training framework for TSE in real conversational mixtures, with two main contributions. First, we construct a large-scale corpus of 71,771 training samples derived from four public datasets, covering both Chinese and English scenarios. Each sample contains an overlapping speech mixture, per-speaker enrollment audio, a ground-truth transcript, and frame-level voice activity labels. Second, we propose a proxy-supervised joint training strategy that fine-tunes a BSRNN-based TSE model using four complementary differentiable objectives: ASR cross-entropy, speaker similarity, frame-level voice activity detection, and perceptual audio quality. 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