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Emergence of Massive Equilibrium States from Fully Connected Stochastic Substitution Systems
Thomas L. Wood

This article investigates the properties and emergent behaviour of a new kind of discrete substitution system. The micro-states of these systems are modelled as complete weighted graphs over \mathbb{N}, the weights of which are stored in a state matrix St = {sij}t, and evolve via a set of constituent specific, independent probabilistic substitution rules. The state is then embedded in \mathbb{R}n by treating flat space geometrical violations as internal curvature within the system that may be minimized via a process of stress minimization. This paper gives arguments for a definition of energy within the system, observes an emergent intrinsic inertia affecting vertex clusters, and shows the emergence of particle like massive equilibrium states. An retentive effect due to clustering is also observed within this system.

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