Under Kirchenbauer et al., each previous token acts as a cryptographic seed to pseudo-randomly split the vocabulary into green and red lists. At generation time, green tokens receive a logit bias boost (+δ). As text length N increases, detection confidence scales rapidly: \(Z = \frac{|G| - \gamma N}{\sqrt{N\gamma(1-\gamma)}}\).
During text generation, each antecedent token hash splits the vocabulary into green and red partitions according to ratio gamma. Applying logit boost delta expands the sampling odds of green tokens, driving the observed green count well above the unwatermarked expectation. The detector computes a one-tailed z-score against the null binomial distribution. Crossing z greater than three confirms synthetic provenance. Clicking Synonym Perturbation substitutes words across the passage. While green count drops slightly, statistical confidence remains well within the verified watermark domain.