## 1 Introduction  
In weightlifting, an athlete's performance is determined by the sum of their heaviest successful competitive lifts: snatch and clean and jerk [1]. The snatch and clean and jerk are complex multi-joint movements, performed by a series of high-intensity muscular contractions [1, 2, 3]. Weightlifters must generate impulse, which is the product of force and time, to increase the momentum of the system mass (the lifter's bodyweight plus the barbell) and ultimately transfer it to the barbell to result in a sufficient displacement to complete the lift. Weightlifting performance is therefore largely determined by the lower body maximum strength and ballistic neuromuscular capabilities because weightlifters are required to generate a high magnitude of force within the technical and time constraints imposed by the competitive lifts [1, 4, 5]. The assessment of lower body neuromuscular capabilities in weightlifters is of interest to researchers and practitioners [4, 6, 7]. Previously reported by [PERSON] et al. [8], and recently reviewed by [PERSON] et al. [4], incorporating multi-joint performance tests that have similar mechanics to the snatch and clean and jerk, such as squats and vertical jumps, can provide valuable information and enable practitioners to effectively evaluate the neuromuscular capabilities that underpin weightlifting performance. For example, the foundation strength exercises front and back squat one-repetition maximums (1 RMs), as a measure of weightlifters' maximum strength capacity, have high to nearly perfect associations with the snatch and clean and jerk (r = 0.73-0.95) [4; 9; 10; 11; 12; 13]. Moreover, strong associations have been identified between the countermovement jump (CMJ) and deep squat jump (DSJ) peak displacement (jump height), as a measure of weightlifters' rapid force production and ballistic capabilities, and weightlifting performance (r = 0.59-0.93) [4; 6; 14]. These findings suggest that adequately incorporating tests to evaluate maximum strength and ballistic capabilities can serve as a valuable method for assessing weightlifters' neuromuscular function and subsequently monitoring performance. Vertical jumps, such as the CMJ and DSJ, are ballistic actions that share similar mechanics with weightlifting snatch and clean and jerk exercises and are frequently used to evaluate the rapid force production and ballistic capabilities of weightlifters by means of the jump height [4; 8; 12; 15; 16]. However, researchers have recommended to not only report jump height but also other force-time metrics such as propulsive impulse and peak power to monitor weightlifters' neuromuscular capabilities [4; 7]. For example, [PERSON] et al. [7] investigated a broad range of CMJ force-time metrics and their relationship with weightlifting performance and documented that reporting propulsive impulse may better reflect any alterations in the neuromuscular capabilities of weightlifters. Similarly, [PERSON] et al. [12] demonstrated that adding the countermovement jump peak power in addition to the isometric mid-thigh peak force (i.e., ballistic and maximum strength capabilities) increased the explained variance in the snatch and clean and jerk performance up to 95 and 92%, respectively. To the best of our knowledge, researchers have not studied the force-time metrics during the DSJ and their relationship with weightlifting performance to date. Furthermore, only a few researchers have evaluated the relationships between weightlifting performance, maximum strength in foundation exercises, and ballistic capabilities (i.e., jump height, propulsive impulse, and peak power) during vertical jump tests in top-level weightlifters competing at international tournaments [12; 17; 18]. The primary objective of this study was therefore to determine the associations between maximum strength in foundation exercises (i.e., front and back squat), ballistic capabilities in vertical jumps (i.e., CMJ and DSJ), and performance in snatch and clean and jerk in top-level weightlifters.