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.

翻译：多智能体系统必须在异质偏好、非对称利益和不完全信息的条件下实现协调。当协调失败时，摩擦便产生：表现为死锁、颠簸或冲突等可测量的阻力。我们从单一公理出发推导出协调摩擦的形式化框架：影响智能体的行动需根据其利益比例获得授权。基于这一同意公理，我们建立了核心三元组 $(α, σ, \varepsilon)$——对齐度、利益与熵——作为任何资源配置构型的充分统计量，并提出摩擦泛函，其最简候选形式 $F = σ(1+\varepsilon)/(1+α)$ 预测摩擦随利益和熵的增加而增加，随对齐度的增加而减少。需强调的是，该形式是一个现象学假设而非定理——仅是我们满足要求的最简表达式——其经验充分性（特别是对齐依赖性是否为单调）仍有待验证。一项配套研究在多智能体强化学习环境中对其进行了检验，发现基于线性对齐依赖性的假设被U型关系所证伪，并由此推导出二次形式 $F = σ(1+\varepsilon)/(1+α^2)$，我们将其公理化地刻画为有待未来验证的改进方案。复制器-优化机制主导着协调策略的选择过程：低摩擦构型持续更久，从而使尊重同意的安排成为动态吸引子而非规范性理想。我们给出了资源同意、协调合法性和摩擦感知分配的形式化定义、一套测量体系，以及核心比较静态分析的机器验证Lean 4证明。对加密货币治理与政治合法性的示例性应用表明，单一架构可跨越不同领域，这里将其作为候选统一框架提出，而非已确立的同一性。