Combining asynchronous Byzantine Fault Tolerant (BFT) consensus with Proof-of-Stake (PoS) creates a trilemma between Sybil resistance, reward distribution fairness, and protection against persistent plutocracy. Existing DAG-BFT approaches (Narwhal+Tusk, Bullshark, and Mysticeti) prioritize liveness over the fairness implications of stake-based selection, resulting in persistent longitudinal centralization. FairWave is a dual-channel DAG BFT protocol that separates anchor selection from reward distribution. The selection channel is super-linear in stake, guaranteeing Sybil gain < 1 for all split factors K > 1. The reward channel is sub-linear, using square-root stake normalization to mitigate rich-get-richer dynamics. The finalized DAG structure provides deterministic uptime and latency factors, allowing honest validators to agree on operational quality without any external oracle. To avoid circular dependency between selection outcomes and selection weights, reputation is used in a lagged form: the active value at epoch e equals the prior epoch's final value. We derive closed-form constraints for both channels and validate them through nine empirical analyses (approximately 550,000 Monte Carlo rounds) against eight baselines. FairWave achieves a Gini coefficient of 0.149 (vs. Pure-PoS's 0.488), a monotone HHI reduction from 0.039 to 0.021 over 50,000 epochs, an optimal-adversary Sybil split of K* = 1, and a success-rate coefficient of variation of 5.2% under +/-25% input perturbation. Safety (agreement and validity) is a formal consequence of the 2f+1 strong-support commit rule, holding unconditionally for f < n/3; the empirical differential is the monotone-continuous liveness-degradation curve, which decreases from 99.6% commit rate at b=0.20 to 71.1% at the theoretical bound b=1/3 without the discontinuous cliff characteristic of view-change-driven leader-BFT.

翻译：将异步拜占庭容错共识与权益证明相结合，会在女巫攻击抵抗性、奖励分配公平性以及对抗持续性财阀统治之间形成三元悖论。现有DAG-BFT方案（Narwhal+Tusk、Bullshark和Mysticeti）优先保证活跃性，却忽略了基于权益的选择机制带来的公平性问题，导致长期纵向中心化。FairWave是一种双通道DAG BFT协议，将锚定节点选择与奖励分配相分离。选择通道采用超线性权益机制，确保所有分裂因子K>1时女巫攻击收益小于1。奖励通道采用次线性机制，通过平方根权益归一化缓解富者愈富效应。最终DAG结构提供确定性运行时间与延迟系数，使诚实验证者无需任何外部预言机即可就操作质量达成共识。为避免选择结果与选择权重之间的循环依赖，声誉以滞后形式引入：第e个周期的活跃值等于前一周期最终值。我们推导出两个通道的闭式约束条件，并通过九项实证分析（约55万轮蒙特卡洛模拟）与八个基线方案进行验证。FairWave实现了0.149的基尼系数（对比纯权益证明的0.488）、经5万个周期后赫芬达尔指数从0.039单调递减至0.021、最优敌手女巫分裂因子K*=1，以及在±25%输入扰动下成功率变异系数为5.2%。安全性（协议一致性与有效性）是2f+1强支持提交规则的形式化推论，在f<n/3条件下无条件成立；其经验差分特征为单调连续活性衰减曲线，在b=0.20时提交率为99.6%，当逼近理论边界b=1/3时降至71.1%，且不存在视图转换驱动型领导者拜占庭容错协议特有的不连续悬崖式衰减。