Stateless Bernoulli watermarking drops green-list membership to O(1) and adds under 1% overhead.

SBW determines green-list membership through independent per-token Bernoulli trials rather than KGW's vocabulary permutation or SynthID's tournament, requiring one comparison per token against a counter-based RNG, which enables single-kernel execution with zero intermediate allocations. The z-score test stays N(0,1) under the null, preserving detection guarantees, and the stateless design enables full-vocabulary self-salt watermarking over 6000x faster than KGW's self-salt and 2x faster than SynthID. They also identify hash design as a new quality axis, with a GPU-native Jenkins hash improving null calibration 1.8x. arXiv 2609.03844