MetaTime XIII: Embodied Scarcity Across Substrates as an Operational Multi-Agent Framework Low-Dissipation Coordination in Biological and Technological Transducers

MetaTime XIII extends the MetaTime framework toward a substrate-independent theory of biological and technological intelligence, treating both as instances of a single physical class: the transducer. In this formulation, carbon-based metabolism and silicon-based computation are interpreted as alternative implementations of the same constrained thermodynamic task: converting latent informational structure (rho_L) into executed structure (rho_I) under finite execution current and finite power budget. This revised version preserves the original emphasis on embodiment while making its empirical program more explicit and more careful. Landauer-type language is now treated as diagnostic bookkeeping rather than as a direct physical bound unless the relevant substrate and erasure mapping are independently specified. The manuscript also clarifies the status of the critical destructive scale Omega_c by recasting it as an operational crossover to be estimated in embodied multi-agent systems, swarm robotics, or MARL environments, rather than as a purely abstract threshold. The result is a more operational and more testable version of MetaTime XIII, preserving the original claim that low-dissipation coordination emerges as a favored solution under shared scarcity, while expressing that claim in more disciplined and experimentally addressable terms.