## 3 Results and Discussion
In contrast, the limited predictive capacity observed in more heterogeneous stones (like traverting) is consistent with known limitations of UPV in porous and anisotropic media, where wave propagation is highly influenced by structural irregularities that do not necessarily correlate with water transport. Still, the ability of UPV to integrate large volumes of material helps mitigate local inconsistencies, providing more robust results than surface-limited techniques such as Leeb hardness, especially in heterogeneous stones (like breccia). To complement the lithology-based assessment, an analysis segmented by thermal exposure (reference, 300 \({}^{\circ}\)C, and 600 \({}^{\circ}\)C) was conducted to explore how temperature influences the correlation between capillary coefficient and the two non-destructive techniques. This approach offers a broader view of method reliability across progressive stages of thermal degradation (Figure 6). It must be mentioned that the traverting (TV) was excluded from this analysis. As demonstrated in previous sections, both HL and UPV failed to show meaningful correlation with capillary behavior (R\({}^{2}\)\(\approx\) 0.13 and 0.09 correspondingly), which is attributed to its highly porous, anisotropic, and irregular internal structure. Thesefeatures disrupt ultrasonic wave transmission and mechanical rebound dynamics, leading to inconsistent readings that are not representative of internal hydric changes. In this context, traverting's unique fabric falls outside the sensitivity range of these methods. As illustrated in the plots (Figure 6), UPV exhibited a robust inverse correlation with the capillary coefficient across all temperature stages, with a global fit of R\({}^{2}\) = 0.71. When analyzing temperature ranges separately, it is visible that its predictive capacity improved with increasing temperature, reaching R\({}^{2}\) = 0.52 at 600 \({}^{\circ}\)C, still lower than the global fit, reflecting better results, when considering all the temperature conditions, than the individual analysis. HL, in contrast, displayed more modest global performance (R\({}^{2}\) = 0.52), with a lower fit at 300 \({}^{\circ}\)C (R\({}^{2}\) = 0.37) and reduced reliability also at 600 \({}^{\circ}\)C (R\({}^{2}\) = 0.43). These results reflect the underlying physical mechanisms governing each technique's response to thermal alteration. At reference conditions, the stone's internal cohesion and pore framework remain largely unaffected, and water movement is mostly controlled by intrinsic textural attributes such as grain size, porosity type, and mineral arrangement, rather than structural discontinuities [24; 65]. While both techniques apply to intact materials, their limited correlation with capillarity at this stage suggests that subtle textural variations are not effectively captured, particularly in the absence of thermally induced damage. Above 300 \({}^{\circ}\)C, the development of microcracking becomes more significant, mainly driven by calcite's anisotropic thermal expansion [66]. This microstructural evolution increases the interdependence between mechanical degradation and moisture transport. In this context,  
Figure 6: Relationship between capillary coefficient and non-destructive parameters: (**a**) global correlation with UPV; (**b**) UPV correlation segmented by temperature; (**c**) global correlation with HL; (**d**) HL correlation segmented by temperature. Colored points represent mean values per lithology and thermal condition. UPV gains relevance due to its volumetric measurement principle; the ultrasonic wave propagates through the specimen and integrates internal changes such as crack formation and pore network evolution, providing a broader representation of damage. HL, on the other hand, relies on surface rebound dynamics and is more affected by localized features, such as roughness, grain boundary exposure, or isolated voids, which may not correspond well to bulk structural changes [67].