## 3 Results and Discussion
### Temperature Measurements
The temperature curves illustrated in Figure 5 exhibit consistent trends without significant variation in slope across the three measured locations (lower surface, core, and upper surface). This consistency under constant oven operating conditions justifies the development of empirical time-temperature relationships, as expressed in Equations (1)-(3), respectively, determined from the experimental plot:  
Figure 5: Dough lower, upper, and core temperature measurements. \[T_{LS}= 0.465\;t^{2}+6.66\;t+34.19 \tag{1}\] \[T_{C}= 0.0031\;t^{5}-0.1070\;t^{4}+1.1638\;t^{3}-3.95878\;t^{2}+5.2797\;t+ 31.589\] (2) \[T_{US}= 1.218\;t^{2}+3.14\;t+36.43 \tag{3}\]  
where \(T_{LS}\) is the lower surface temperature in \({}^{\circ}\)C, \(T_{C}\) the core temperature in \({}^{\circ}\)C, \(T_{US}\) the upper surface temperature in \({}^{\circ}\)C, and \(t\) the baking time in seconds. The empirical temperature fittings were developed to smooth measurement variability and provide a continuous, analytical representation of the thermal evolution at different depths of the dough. This allows for the estimation of instantaneous thermal gradients within the flathead thickness, which are otherwise difficult to extract directly from discrete experimental data. These fitted curves form the basis for comparing the rate and extent of heat penetration across the dough layers. Specifically, the regression analysis for the lower surface temperature (\(T_{LS}\)) yielded an \(R^{2}\) value of 0.9936 and a Residual Standard Error of 3.9, indicating a strong correlation between the modeled and observed temperatures. For the upper surface temperature (\(T_{US}\)), the \(R^{2}\) value was 0.9975 with a Residual Standard Error of 3.5, suggesting a very accurate prediction of the temperature changes on the upper surface exposed to direct heat. Finally, the core temperature analysis (\(T_{C}\)) demonstrated the highest accuracy, with an \(R^{2}\) value of 0.9994 and a Residual Standard Error of 0.7, reflecting a near-perfect alignment between the predicted and observed core temperatures. However, it is important to distinguish between good fitting and prediction ability. While high \(R^{2}\) values and low Residual Standard Errors indicate the model fits the observed data well, prediction ability refers to the model's ability to predict unseen data. In this study, the high \(R^{2}\) values suggest that the model fits the training data well, but further testing on new data is required to assess its predictive power. These findings contribute to understanding the thermal behavior during baking and provide insight into how different regions of the bread heat up, an aspect closely linked in the literature to pocket formation and crust development, which are key quality indicators in flathead. The results show a higher temperature on the upper surface than on the lower surface. Temperature plays a key role in browning, which occurs through the Maillard reaction and caramelization, heat-induced chemical reactions between sugars and proteins in the dough, contributing to the bread's flavor and aroma [50]. The Maillard reaction is optimal between 150 \({}^{\circ}\)C and 180 \({}^{\circ}\)C, while caramelization occurs around 170 \({}^{\circ}\)C to 190 \({}^{\circ}\)C. Browning can be influenced by baking time, temperature, and dough water, as demonstrated by [PERSON] and [PERSON] [23], who found a strong correlation between browning indices and Maillard reaction products, particularly under more intense thermal conditions. Thus, the temperature difference between the upper and lower surfaces contributes to the observed difference in browning, with the upper surface reaching 150 \({}^{\circ}\)C more quickly and achieving a higher temperature than the lower surface, which is associated with the bread's surface characteristics (Figure 6).