## 4 Discussion
A recent study from [PERSON] et al. [12] investigated the relationship between five core stability-related measurements and CMJ height. They reported that trunk extensor endurance, one-minute sit-up, and dominant leg standing time had no significant correlation with CMJ height, with or without arm-swing. Trunk flexion and extension range of motion and dominant leg hop distance had a significant correlation with CMJ height both with and without arm-swing. They concluded that \"specificity\" should be considered for core training to improve CMJ performance. Despite the inconsistent results, many elite athletes continue to perform core strength training as an essential part of their training program. The \"principle of dynamic correspondence\" should be considered to understand this confounding situation [20]. This principle states that special exercises must be in harmony with those parameters of movement that characterize the structure of competition technique. Thus, only when core strength training is consistent with the CMJ in kinetic and kinematic structures can strength training effectively improve CMJ performance [20; 21]. Therefore, the confounded conclusions of core strength are mainly due to the neglect of the \"specificity\" of core strength to the sporting event [6]. Different core exercises train the different core musculature in various forms, while performance mainly depends on the \"specificity\" of the core strength. Specific and targeted core strength training should be considered relevant research projects and training protocols [6; 22; 25]. Normalized peak torque during both dynamic flexion at 180\({}^{\circ}\) per second (NPDF180) and static flexion at 120\({}^{\circ}\) (NPSF120) shared 72.0% variance with CMJ height with arm-swing (H\({}_{\text{AS}}\)), while NPSF120 shared 57.0% variance with CMJ height without arm-swing (H\({}_{\text{NAS}}\)). Buffering and extension periods are included in the whole CMJ motion. The core is dominant and plays a major role in the buffering period but the dominant region moves to the lower limbs in the extension period, in which the lower limbs need to afford more load than body weight. Especially in the end of the extension period, the ankle contributes most of the push power. In the present study, trunk (lumbar-pelvic) muscle, not hip, contributed most of the power in the trunk strength test. Thus, trunk flexion strength plays an important role in the buffering period of the CMJ, but trunk extension strength in the extension period is not as important as trunk flexion strength in the buffering period. That could explain why all predictors of CMJ height with and without arm-swing were trunk flexion strength (NPDF180 and NPSF120) in the present study. Regarding the kinematic and kinetic structures of the core strength tests, NPDF180 was the fastest test in the dynamic core strength tests, in which core muscle contractions were fastest. It is necessary for the CMJ to yield maximum trunk flexion power, increasing the coming trunk extension power to promote CMJ performance. The NPSF120 test had the most similar posture (with the hip angle of about 120\({}^{\circ}\)) to the CMJ in the buffering period, which we observed in the video we captured. Thus, the kinematic and kinetic structures of the core test were vital to evaluate the correlation between core strength and CMJ performance [20]. Moreover, one static core strength could be used to explain the majority variance of CMJ height without arm-swing, but both static and dynamic core strength was needed to explain the variation of CMJ height with arm-swing. Thus, both static and dynamic core strength should be considered to study CMJ with arm-swing, but the dynamic core strength in CMJ without arm-swing is not as important as in CMJ with arm-swing. There is an active flexion period at the beginning of the CMJ. The dynamic core flexion strength plays an important role in the flexion period and makes the flexion more powerful. A faster and deeper active flexion period would lead to a more powerful backswing of the arm.