## 2 Materials and Methods
### Experimental Design  
One month prior to data collection, the runners were informed of the purposes of the study and were instructed to purchase a new pair of conventional mountain running shoes (CON). At the same time, a new pair of AFT mountain running shoes (AFT) was randomly provided to each runner (six different manufacturers). Participants were asked to use both pairs of shoes (i.e., CON and AFT) for a total of 50 to 100 km before the 3 rd day of testing (see Figure 1) to ensure appropriate familiarization and adaptation. To check that all pairs of shoes were similar, they were weighed (Portable Electronic Scale, MECO Co Ltd., Seoul, Republic of Korea) following a protocol described in a previous study [30]. Thus, the mass of the AFT shoes was similar to that of the CON shoes (296.3 \(\pm\) 20.3 vs. 295.3 \(\pm\) 28.6 g, \(p\) = 0.93 and \(\eta_{p}\)\({}^{2}\) = 0.001) for sizes between 8 and 11.5 USA. This is important because previous studies have shown that differences of up to 50 g do not affect running performance in high-intensity races [31]. As expected, the heel height (30.0 \(\pm\) 5.0 vs. 26.5 \(\pm\) 3.5 mm, \(p\) = 0.03 and \(\eta_{p}\)\({}^{2}\) = 0.354) and the forefoot height (24.4 \(\pm\) 4.4 vs. 20.0 \(\pm\) 4.1 mm, \(p\) = 0.01 and \(\eta_{p}\)\({}^{2}\) = 0.477) were higher in the AFT shoes than in the CON ones, without differences in the drop between shoe types (5.7 \(\pm\) 1.0 vs. 6.5 \(\pm\) 1.5 mm, \(p\) = 0.16 and \(\eta_{p}\)\({}^{2}\) = 0.017). This ensured the homogeneous characteristics of both types of shoes despite being acquired from different manufacturers. The experimental procedure was carried out over three days, with a 7-day interval between sessions (see Figure 1). On the 1 st day, the participants completed an incremental maximal test. On the 2 nd day, the participants previewed the mountain circuit, which was going to be used for the specific evaluation. On the 3 rd day, participants performed two running time trials on the mountain circuit using both types of shoes (CON and AFT) in a randomized order based on their performance in the incremental maximal test (i.e., AFT-CON for the runner with the lowest performance level, CON-AFT for the next participant, and so on). **Incremental maximal test (1 st Day). ** A standardized track test was used to determine MAS and estimate VO\({}_{2}\)max [32]. First, the participants completed a warm-up consisting of 5 min of continuous running, two 10 s progressive runs, and 3 min of walking. Following  
Figure 1: Overview of the experimental procedure performed over three days (incremental maximal test, circuit review and running time trials, respectively). Measurements were taken before (pre-) and after (post-) each time trial (Time Trial 1 and Time Trial 2). Rating of perceived exertion (RPE). the warm-up, they performed a maximal aerobic speed test on a track to assess their performance level. The test started at 8 km/h, with the speed increasing by 1 km/h every minute until exhaustion. The track was marked with cones every 25 m to control the speed, and the runners were required to reach a cone following an acoustic signal. The test ended when the runners achieved volitional exhaustion or failed to reach two consecutive cones. At this point, their total distance and maximum speed were recorded. Every runner used an HR monitor (Polar(r) Vantage V2, Polar Electro Oy, Kemblele, Finland) with an HR chest strap (Polar(r) H10, Polar Electro Oy, Finland). After the test, participants performed an easy 10 min jog to cool down. This testing day was also used to familiarize participants with both the rating of perceived exertion (RPE) scale [33; 34] and vertical stiffness tests [35], which are described below. **Circuit review (2 nd Day). ** After 7 days, the participants familiarized themselves with the mountain circuit (5.19 km) in preparation for the 3 rd day of testing.