The Axiom of Consent: Friction Dynamics in Multi-Agent Coordination

Multi-agent systems face a fundamental coordination problem: agents must coordinate despite heterogeneous preferences, asymmetric stakes, and imperfect information. When coordination fails, friction emerges -- measurable resistance manifesting as deadlock, thrashing, communication overhead, or conflict. This paper derives a formal framework for analyzing coordination friction from a single axiom: actions affecting agents require authorization in proportion to stakes. From this axiom of consent we establish the kernel triple (alpha, sigma, epsilon) -- alignment, stake, and entropy -- as sufficient statistics for a resource-allocation configuration, and propose a friction functional whose simplest form is F = sigma(1+epsilon)/(1+alpha): friction rises in stakes and entropy and falls in alignment. This form is a phenomenological ansatz, not a theorem, and its empirical adequacy is left open. The Replicator-Optimization Mechanism governs selection over strategies: lower-friction configurations persist longer, making consent-respecting arrangements dynamical attractors rather than normative ideals. We give formal definitions, a measurement apparatus, and machine-checked Lean 4 proofs of the core comparative-statics, with illustrative applications to cryptocurrency governance and political legitimacy.