## 2 Materials and Methods
### Data Analysis Procedures  
The top gymnast's motion was also calculated in relation to a LCS, defined as the mid-point between the base's hands. As such, the top LCS CoM position was calculated as the difference between the Top GCS CoM and the LCS position. The interaction between gymnasts was also analyzed as a system:  
\[\text{CoM}_{\text{sys}}=\frac{\text{CoM}_{\text{T}}\times\text{Mass}_{\text{T }}-\text{CoM}_{\text{B}}\times\text{Mass}_{\text{B}}}{\text{Mass}_{\text{T}} +\text{Mass}_{\text{B}}}, \tag{1}\]  
the system's CoM (CoM\({}_{\text{sys}}\)) was calculated using the CoM (GCS) of each gymnast (top: CoM\({}_{\text{T}}\); base: CoM\({}_{\text{B}}\)), and their contribution to the overall system mass (top: Mass\({}_{\text{T}}\); base: Mass\({}_{\text{B}}\)). The system's CoM velocity was calculated as the position's first derivative. Each trial began with the base gymnast standing while supporting the top gymnast, who was balanced on the base's hands and stabilized on their shoulders. The movement onset was detected as the first instant when the top gymnast's CoM presented a downward velocity. The take-off was detected through visual inspection of the last contact point between the base's hands and the top's feet. Two independent observers identified the take-off frame, and any discrepancies were discussed until a consensus was reached. For the characterization of each gymnast and the system's motion, two phases were established according to the directionality of the CoM velocity. For each curve analyzed, phase I started at the movement onset and finished at the CoM maximal downward position (MD Pos). This phase included the CoM maximum downward velocity (MD Vel) and continued until reaching zero velocity, which corresponded to the MD Pos [19; 23]. For the base gymnast, this motion is similar to the unweighting and eccentric braking of the push press [24]. Phase II began at the instant of zero velocity, at which Phase I ended, and finished at take-off. During this period, the CoM velocity increases in an upward direction [19], featuring the maximum CoM upward velocity (MU Vel) [23]. In the push press, this is defined as concentric propulsion [24]. After take-off, the top gymnast is in free flight, with gravity being the only force acting upon them [23], and the base's CoM movement becomes unrelated to the top's flight trajectory. Thus, the top's flight and the base's motion after take-off are not in the scope of this study. Four CoM position and velocity-time curves were analyzed for each trial: (1) the base gymnast; (2) the top gymnast; (3) the top gymnast from the LCS; and (4) the system. The following variables were extracted to characterize the movement: (i) the trial duration; (ii) each phase duration; (iii) the MD Pos and MD Vel; (iv) MU Vel; and (v) CoM position and velocity at take-off (TO Pos and TO Vel). A custom MATLAB, version R2023b (MathWorks, Natick, MA, USA) routine was used for the extraction of these variables. The initial position and velocity of each time curve was set to zero at the starting position, and the trial duration normalized. The position and velocity were analyzed as absolute values and normalized to the gymnasts' stature. For the system, the sum of the top and base gymnasts' height was considered. To study the interpersonal coordination, the time-normalized curves of the CoM position and velocity were analyzed using cross-correlation between the entire signals. This procedure was performed in MATLAB, allowing to quantify the similarity between the base and top gymnasts' curves (GCS and LCS) of different experience levels. The higher the cross-correlation between two signals at a given time lag, the higher their similarity [34]. The variables used for analysis were the zero-lag correlation index (r\({}_{0}\)), the maximal correlation index (r\({}_{\text{max}}\)), and its time lag [35].