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.

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