Respiratory sound classification distinguishes four categories: Normal, Crackle, Wheeze, and Both (crackle and wheeze). Existing knowledge distillation transfers four-class predictions without explicitly exploiting shared respiratory events, potentially limiting the transfer of event-specific knowledge across individual abnormal classes and the Both class. We propose PAC-KD, a pathology-aware compositional knowledge distillation framework that learns crackle and wheeze presence through two dedicated specialists. Their complementary knowledge is transferred to a unified four-class student, enabling it to effectively capture pathology-specific attributes while preserving class-level discrimination. Furthermore, stable conflict calibration adaptively regulates specialist guidance according to its consistency with classification supervision, mitigating potential supervision conflicts. Experiments on ICBHI and SPRSound achieve Scores of 65.28\% and 89.54\%, respectively, outperforming strong knowledge distillation baselines on both datasets.

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