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Explore the mathematical foundations of Conscious Agent Theory in this 24-minute conference talk by Chetan Prakash at the Models of Consciousness Conference. Delve into the concept of consciousness as fundamental, examining how the experience of a physical world emerges from dynamics within consciousness. Learn about the probabilistic structure of conscious agents and the Markovian dynamics of conscious agent networks. Discover how the combination problem is addressed through the fusion of agents, represented by asymptotic "fusion" polytopes and the "Birkhoff polytope" within the agent dynamics described by the "Markov polytope." Investigate the mathematics of 3- or higher-agent processes and their potential connection to the emergence of space-time and quantum behavior. Examine the relationship between agent dynamics, fusion, and particle scattering in spacetime by exploring connections to particle physics research, particularly the work on Grassmanian Geometry of Scattering Amplitudes. Gain insights into a potential path for solving the mind-body problem by deriving physical reality as an interface representation of conscious dynamics.