## 3 Results
### Cross-Domain Relationship Shifts  
In addition to univariate improvements, significant shifts in inter-variable correlations were observed in the HIIT group, suggesting enhanced physiological integration. Notably, the correlation between the lactate rise slope and the perceived exertion slope increased (\(\Delta\)r = +0.58, \(p\) < 0.01), as did the association between HR recovery and \(\Delta\)Base Excess (\(\Delta\)r = +0.54, \(p\) < 0.01). Strong statistical associations emerged between the cognitive load index and both the speed reserve (\(\Delta\)r = +0.61, \(p\) = 0.003) and the lactate threshold speed (\(\Delta\)r = +0.92, \(p\) = 0.014). These changes highlight emergent coordination between metabolic, cardiovascular, and cognitive domains in the HIIT group. By contrast, the control group did not show substantial shifts in inter-variable correlations, reinforcing the idea that multidomain integration was specific to the high-intensity intervention (Figure 3). Figure 3: Cross-Domain Correlation Shifts in the Control & HIIT Group from R1 to R3. Heatmap showing changes in Pearson correlation coefficients (\(\Delta\)r) between variables from different physiological domains (e.g., metabolic, neuromuscular, cognitive, physical) within the (**A**) Control and (**B**) HIIT group from pre- to post-intervention (R1 to R3). Only statistically significant changes (\(p\) < 0.05) are shown, as determined by Fisher r-to-z transformation. Cell borders are drawn around pairs where \(|\Delta\)r \(|>\) 0.5, indicating large shifts in connectivity. Color gradients represent the magnitude and direction of change (blue = decreased correlation, red = increased correlation). In the clustering analysis, we examined how physiological and cognitive variables clustered across test phases (R1-R3) in both the HIIT and control groups (Figure 4). Statistical tests of domain distributions within clusters using the Chi-square test revealed no significant deviation from randomness in either group or phase (all \(p>0.05\)). However, the control group in phase R1 showed a trend toward significance (\(\chi^{2}=17.28\), \(p=0.068\), df = 10), suggesting early, non-random clustering of domains under passive conditions. In contrast, the HIIT group remained more uniformly distributed across all phases (R1: \(\chi^{2}=11.61\), \(p=0.312\); R3: \(\chi^{2}=11.51\), \(p=0.174\)). Figure 4: Sankey diagram illustrating cluster transitions across phases (R1 \(\rightarrow\) R2 \(\rightarrow\) R3) in the (**A**) Control and (**B**) HIIT group. Each node represents a domain-cluster combination within a specific phase, and the width of each flow (link) denotes the number of variables transitioning between clusters. Variables are color-coded by their physiological domain (Cognitive, Metabolic, Physical). Cluster stability analysis, quantified as the number of transitions a variable made between clusters (range: 0 to 2), showed that variables from the cognitive domain in the control group remained entirely stable (mean = 0.00, SD = 0.00, \(n\) = 11), indicating persistent clustering patterns. Similarly, physical (mean = 0.00, \(n\) = 3) and metabolic (mean = 0.00, \(n\) = 1) variables in the HIIT group exhibited complete cluster stability. On the other hand, cardiovascular variables in the control group showed maximum instability (mean = 2.00, SD = 0.00, \(n\) = 4), indicating that without training intervention, these variables shifted clusters across all phases. Transition Matrix Analysis further emphasized these trends. In the HIIT group, anthropometric and cardiovascular domains demonstrated broader transitions between clusters (e.g., two transitions in 1\(\rightarrow\)2 and 2\(\rightarrow\)3 for the anthropometric domain; one transition each for 2\(\rightarrow\)1, 3\(\rightarrow\)1, and 3\(\rightarrow\)2 in the cardiovascular domain).