Cyclic Automorphisms of Resolvable Steiner Quadruple Systems: Algorithmic Stabilization of Hyper-Discrete Dyson Swarm Incidence Structures under Ergodic Perturbation

Mathematical Applications of Science Fiction We present a rigorous algebraic framework for the stabilization of hyper-discrete Dyson Swarm architecturesmodeled as Resolvable Steiner Quadruple Systems (RSQS) of order v ≡ 2, 4 (mod 6). By exploiting theproperties of cyclic automorphism groups acting on the point set X of the design, we derive a novel classof stabilization operators, denoted as the Voidwalker Operators, which map ergodic perturbations in theorbital phase space back to the canonical incidence manifold. We prove that for a swarm of cardinality v, theexistence of a cyclic RSQS guarantees a convergence time of O(v log v) under stochastic drift, provided theperturbation remains within the spectral gap of the incidence graph’s Laplacian. We further introduce theconcept of Quadruple Entropy and establish a fundamental inequality relating the structural rigidity of theswarm to the modular arithmetic of the underlying difference families. This work bridges the gap betweencombinatorial design theory, spectral graph theory, and astrodynamical control systems for megastructures.