Prevalence Bounds for Edited Watermarked Text: Power Envelopes and Calibration Sensitivity

Summary

This paper estimates the share of a document corpus produced by a watermarked language model, not just whether one document is watermarked, for Gumbel-max and green-list (KGW) watermarks under unknown edits. It derives a power envelope over retention, entropy and in-place substitution budgets, giving finite-sample bounds on the share. On OPT-1.3B and Qwen3-1.7B text, the exact-null bound at a share of 0.2 is about [0.14,0.38], and the bounds are fragile to LLM paraphrasing and to small null-calibration errors at large corpus sizes.