A 24 point Atiyah singular configuration in hyperbolic 3-space

We construct a configuration of 24 distinct, noncoplanar points in hyperbolic 3-space whose Atiyah polynomial coefficient matrix has rank exactly 23. In the curvature -1 Beltrami-Klein ball, the points are q_i = (s_*/10000)v_i, with explicitly listed integer vectors v_i. A rational interval of width 10^{-30} isolates a unique zero s_* of a real analytic determinant. Reflection symmetry reduces the complex coefficient matrix to a real matrix. Outward-rounded interval arithmetic certifies opposite endpoint signs and a strictly negative derivative throughout the interval, proving existence, uniqueness, and simplicity of the zero. A second implementation, using a different arithmetic backend, polynomial basis, and pivot strategy, reproduces these bounds. The construction gives the upper bound 24 for the least cardinality of a singular hyperbolic Atiyah configuration.