## 4 Results and Interpretation
### Thermal History  
Based on the distribution of AFT lengths and age data, the HeFTy software (Version. 1.8.3, [PERSON], 2005) [34] was used to better constrain the exhumann history. The time-temperature (t-t) history was calculated using the multi-kinetic annealing model of [PERSON] et al. (2007a) [35] and the c-axis projected length of [PERSON] et al. (2007b) [36]. Samples were modeled with at least 100 track-length measurements. The inverse models were executed with 10,000 randomly chosen time-temperature histories for each sample, which in all cases resulted in N > 1000 acceptable paths. A goodness-of-fit parameter (GOF) estimated the degree to which modeled data matched measured values. A path was accepted if the GOF value was >0.05; a good fit was indicated if the GOF value was >0.5 [34]. The initial simulation temperature was set at 130 \({}^{\circ}\)C, which is slightly higher than the AFT annealing temperature (120-60 \({}^{\circ}\)C). The lower limit of simulation temperature was set at 15 \({}^{\circ}\)C, based on the present-day mean surface temperature in the Helanshan Mountains. Because the age of sample LS-97 is old, the fission-track simulation initial time is set at 170 Ma. Furthermore, to explicitly illustrate the temporal pattern of sample LS-98's t-t history spanning from 120 to 110 Ma, the initial time of sample LS-98 is established at 130 Ma, while the other samples start at 120 Ma. The modeling t-t paths of AFT samples from the central and southern HTB, cooling since 130 \({}^{\circ}\)C, are shown in Figure 7. Except for samples LS-82 and LS-86, the cooling paths for most samples share a three-stage cooling history. These three cooling paths include two episodes of rapid cooling that bracket an episode of slow cooling. Samples LS-94 and LS-95 share almost the same t-t history. They have the AFT ages of \(\sim\)120 Ma when they pass across the upper limit of the partial annealing zone. Samples LS-94 and LS-95 underwent the first rapid cooling until 95 Ma with a cooling rate of 1.6 \({}^{\circ}\)C/Ma. Following this rapid cooling stage, a relatively stable episode occurred from 95 Ma to 10-8 Ma at a rate of 0.12 \({}^{\circ}\)C/Ma. The third fast cooling existed from 10-8 Ma, which is almost the same time when they entered into the lower limit of partial annealing zone until the present with the rapid cooling rate of 4.5 \({}^{\circ}\)C/Ma. The first relatively fast cooling stage of sample LS-97 lasts from 170 Ma to 120 Ma with a cooling rate of 0.47 \({}^{\circ}\)C/Ma, and its second rapid cooling episode developed from 10-8 Ma until the present at a rate of 4.5 \({}^{\circ}\)C/Ma. The sample LS-98 exhibits two rapid cooling episodes: the first one occurs from 130 Ma to 105 Ma, during which the temperature decreases from 115 to 70 \({}^{\circ}\)C with a cooling rate of 1.8 \({}^{\circ}\)C/Ma; the second one occurs from \(\sim\)5 Ma to the present, recorded the temperature drop from 60 \({}^{\circ}\)C to 15 \({}^{\circ}\)C at a rate of 9 \({}^{\circ}\)C/Ma. The LS-82 and LS-86 samples have two- and four-stage cooling histories, respectively. Specifically, sample LS-82 experienced a period of stable cooling from 120 Ma to 60 Ma and entered the rapid cooling path from 60 Ma at a rapid cooling rate of 1.58 \({}^{\circ}\)C/Ma. Meanwhile, the sample LS-86 developed two rapid cooling histories from 66 to 60 Ma and from \(\sim\)8 Ma to the present at a rate of 6.67 \({}^{\circ}\)C/Ma and 6.87 \({}^{\circ}\)C/Ma, respectively. Overall, the inverse modeling of AFT revealed four rapid cooling episodes: 170-120 Ma, 120-95 Ma, 66-60 Ma, and \(\sim\)10-8 Ma to the present. The first episode is mainly developed in the sample LS-97. The second rapid cooling stage occurred between the samples LS-94, LS-95, and LS-97. The third one is derived from the sample LS-86, which aligns with the outcome of AFT obtained using the radial plot.