The Swarm Simulator: A Dynamical Systems Model of Collective Intelligence Using the TO/TOGT Operator Pipeline

This paper introduces the Swarm Simulator, a multi‑agent dynamical system based on the generative operator pipeline G=U∘F∘K∘C from Topographical Orthogonal Generative Theory (TO/TOGT). Each agent undergoes local compression, curvature intensification, loss of injectivity, and stabilisation. At the collective level, four operators—shared‑intent stability It, coordination efficiency Ct, type‑propagation multiplier Mt, and diffusion factor Ft—govern the swarm’s evolution. All mathematical results in this paper follow directly from previously proved theorems in the Principia Orthogona series, including fixed‑point theory, contraction mapping, saturated pitchfork bifurcation, and the algebraic separation theorem (HAL hal‑05555216v1). No empirical claims, numerical simulations, or unverifiable assertions are made. All formulas are presented in a “do not trust, verify” manner. This work is mathematically independent of speculative physical or cosmological models that use similar terminology. Here, “orbit” refers strictly to operator‑generated identity trajectories in dynamical systems.