VISCOSITY SOLUTIONS FOR HAMILTON-JACOBI-BELLMAN EQUATIONS IN PSYCHOHISTORICAL DYNAMICS: A TOPOS-THEORETIC APPROACH

Mathematical Applications of Science Fiction Abstract. We present a rigorous derivation of the existence and uniqueness of viscosity solutions for aclass of infinite-dimensional Hamilton-Jacobi-Bellman (HJB) equations governing the stochastic evolu-tion of psychohistorical dynamics. By embedding the sociopolitical state space into a non-Archimedeanperfectoid space P, we construct a value function associated with the optimal control of the SeldonOperator. We utilize the theory of Crandall-Lions viscosity solutions adapted to Hilbert-Schmidt oper-ators on derived stacks. Furthermore, we establish a comparison principle for the associated hypoellip-tic Hamiltonian H(x, p, X) involving a degenerate diffusion term driven by a motivic Wiener process.The convergence of the finite-difference approximation is proven via the method of half-relaxed limits,demonstrating topological stability of the predicted historical trajectory under small perturbations ofthe initial prime radiant flux.