Power Symmetry Breaking in Generalized Language Systems: An Inquiry into Relational Asymmetries and Convention Dynamics

This paper develops a conditional account of power-sensitive convention selection in generalized language systems. It distinguishes mathematical symmetry under specified group actions, historically situated selection among feasible alternatives, and asymmetric capacities to authorize, interpret, maintain, and revise conventions. Elementary finite-state results characterize equivariant deterministic selection, unique choice and reduced objective invariance under an explicit asymmetric perturbation, invariance of probability laws under equivariant stochastic dynamics, and directional changes in stationary convention probabilities. Constructed capacity and network models establish, under stated transition assumptions, adoption-conditioned persistence and a direct one-step intervention contrast, with an additional complete-mixing fixation result. The models distinguish conditional no-switch events, stationary occupancy, and network-mediated diffusion. These proofs define mathematical possibilities without identifying relational power as their empirical cause. A historical-institutional analysis distinguishes attested, accessible, and admissible alternatives and examines the activities through which conventions become authoritative. The paper then specifies prospective artificial-agent interventions, communication controls, competing causal explanations, and longitudinal evidence requirements. Its normative analysis separates influence, effective authority, and legitimacy; an outcome-equivalent construction shows that identical adoption distributions can coexist with different decision and revision rights. The conclusion integrates these results into a revisable research programme in which formal symmetry, causal mechanisms, historical evidence, and ethical assessment retain independent standards of justification. The general Power Symmetry-Breaking Theorem remains an open objective, and no new artificial-agent experiment or human-institutional causal estimate is reported.