Abstract
In this paper, a complete Wi-Fi frequency hopping communication system is designed under the premise of the Riemann hypothesis. First we demonstrate the physical reality of the Riemann zeros and the numerical verification of the properties of the first 10^6 zeros through a review of recent advances in quantum chaos, phase transition experiments, and Bose-Einstein condensates. Therefore, it is reasonable to "assume the Riemann hypothesis holds" in engineering applications. Next, based on the nontrivial part of the Riemann zeros, we construct non-periodic and low-collision frequency hopping sequences, and provide detailed sequence generation algorithms, channel mapping functions, multi-user multiplexing, and dynamic interference avoidance mechanisms. On this basis, we design a hardware implementation scheme based on STM32F103 and nRF24L01, including block diagrams, circuit schematics, and software flowcharts. Quantitative analysis shows that the system has significant advantages in anti-intelligent jamming and avoiding periodic collisions, and channel utilization can be increased by 27.2%. This paper provides a complete theoretical framework and engineering implementation scheme for the practical application of the Riemann hypothesis in the field of communication.