Abstract: Addressing the scientific problem of the stochastic motion mechanism of trajectory jet splashing droplets under both initial condition randomness and process randomness excitation, this paper applies high-dimensional number-theoretic grading methods and fiber bundle structures to establish a double stochastic coupled number theory graded random splashing model of water droplets. The stochastic source phase space constructed by this model systematically integrates the initial randomness occurring when the water jet impacts the downstream water cushion, and the microscopic randomness generated by frequent collisions with air molecules during droplet motion. By assigning both initial randomness and Brownian motion process information to the graded phase points simultaneously, efficient modeling of the droplet motion process under dual random coupling effects is achieved. Comparison of numerical results shows that with the same number of graded phase points, this model has faster convergence speed, and the results are closest to the high-precision solution. Therefore, the number-theoretic graded model coupling initial and process randomness for water droplets can achieve higher-precision numerical simulation with fewer computational phase points, effectively reducing the dimensionality of the high-dimensional stochastic source term probability density space to a one-dimensional phase space, significantly improving computational efficiency.