Multi-agent systems must coordinate despite heterogeneous preferences, asymmetric stakes, and imperfect information. When coordination fails, friction emerges: measurable resistance such as deadlock, thrashing, or conflict. We derive a formal framework for coordination friction from a single axiom: actions affecting agents require their authorization in proportion to stakes. From this axiom of consent we establish the kernel triple $(α, σ, \varepsilon)$ -- alignment, stake, and entropy -- as sufficient statistics for any resource-allocation configuration, and propose a friction functional whose simplest candidate form $F = σ(1+\varepsilon)/(1+α)$ predicts that friction rises with stakes and entropy and falls with alignment. We stress that this form is a phenomenological ansatz, not a theorem -- the simplest expression satisfying our desiderata -- whose empirical adequacy, in particular whether the alignment dependence is monotone, remains open. A companion study tests it in a multi-agent reinforcement-learning environment, finds the linear alignment dependence falsified by a U-shaped relationship, and motivates a quadratic form $F = σ(1+\varepsilon)/(1+α^2)$ that we characterize axiomatically as a refinement for future confirmation. The Replicator-Optimization Mechanism governs selection over coordination strategies: lower-friction configurations persist longer, making consent-respecting arrangements dynamical attractors rather than normative ideals. We give formal definitions for resource consent, coordination legitimacy, and friction-aware allocation, a measurement apparatus, and machine-checked Lean 4 proofs of the core comparative-statics. Illustrative applications to cryptocurrency governance and political legitimacy show one architecture spanning domains, offered as candidate unification, not established identity.