Hangzhou: A Triple-Seed Pseudo-Random Number Generator Based on Chaotic Trigonometric Maps

In this technical note, we introduce Hangzhou, a novel pseudo-random number generator (PRNG) whose design is directly inspired by the Victoria-Nash Asymmetric Equilibrium (VNAE) geometry and the classical three-body problem. Hangzhou employs three independent chaotic maps driven by mutually incommensurable transcendental frequencies $(\pi, e, \sqrt{2})$. Unlike conventional generators that rely on modular arithmetic, Hangzhou uses trigonometric functions (sine, cosine) together with an absolute-value-free chaotic recurrence. The three seeds evolve through a coupled nonlinear map, and the final integer output is obtained by summing the three states modulo~1, then scaling to $[0,N-1]$. This architecture mirrors the VNAE framework, where three asymmetric agents produce a curved Riemannian manifold whose Ricci curvature governs stability. Moreover, the three-body analogy ensures analytic non-invertibility: recovering the initial seeds from the output stream is as intractable as solving the three-body problem in reverse time. The generator passes standard statistical tests (chi-square, runs, autocorrelation, Shannon entropy, for example) and exhibits an enormous theoretical period $(2^{192}\approx 10^{57.8})$, making it suitable for high-performance simulations and as a building block for future cryptographic extensions.