### Existing Research  
Solar flares are generally categorized into different levels based on the intensity of their X-ray flux. This study specifically focuses on C-class flares, which, despite their lower intensity compared to M-class and X-class flares, are more frequent and can have cumulative effects on the ionosphere. These rapid ionospheric variations directly impact communication, navigation systems, and high-frequency radio communications in polar regions [9; 10; 11; 12].  
[PERSON] et al. (2010) demonstrated that the propagation of low-frequency time-code sky waves is strongly dependent on the ionospheric reflection characteristics, meaning that ionospheric disturbances caused by solar flares often lead to issues such as signal offset, delay, and attenuation. These disturbances, in turn, affect the reliability and accuracy of these signals in critical applications [11]. Studies have shown [7; 8; 9; 10] that solar flares release high-energy X-ray radiation, which not only directly impacts signal propagation following flare events but may also induce precursor disturbances in signal propagation paths and phases through the ionosphere's anticipatory response. [PERSON] et al. (2021) and [PERSON] et al. (2020) pointed out that the ionosphere at mid- and low latitudes exhibits unique electron density variation characteristics during C-class solar flare events [4; 13]. [PERSON] et al. (2019) emphasized that studying how solar flares influence low-frequency time-code signals through ionospheric interactions is crucial for understanding this complex, indirect impact mechanism [6]. In this study, both the transmission station (Shangqiu, approximately 34.45\({}^{\circ}\) N latitude) and the reception station (Xi'an, approximately 34.34\({}^{\circ}\) N latitude) are located in the mid-latitude region, making them typical cases for analyzing the dynamic characteristics of the mid-latitude ionosphere.  
Although considerable progress has been made in investigating the relationship between solar flares, the ionosphere, and low-frequency signal propagation, most research has concentrated on the effects of intense flare events, such as M-class and X-class flares [14; 15; 16; 17; 18; 19]. In contrast, the impact of C-class flares, which are weaker but more frequent, on the ionosphere and low-frequency time-code signals has not been sufficiently explored. While the individual effects of these weaker flares may appear small, their frequent occurrence could lead to cumulative effects on ionospheric dynamics and long-term radio communication. However, research on C-class solar flares has largely been confined to case studies, with a notable lack of quantitative analysis regarding the changes in low-frequency time-code signal strength during such events. This study, therefore, aims to offer a new perspective on ionospheric response mechanisms by analyzing the lag time between low-frequency signal strength fluctuations and C-class flare events. Furthermore, the research seeks to assess the potential impact of C-class flares on low-frequency time-code signal propagation, providing scientific evidence to improve communication system stability and enhance resistance to interference. Additionally, by incorporating Granger causality testing, this study further validates and quantifies the causal relationship between C-class solar flares and changes in low-frequency signal strength, thereby offering a foundation for future early-warning and predictive models.