Technical report accompanying OpenAI’s October 5, 2026 blog post on EU text provenance.
textGrain couples token generation to keyed randomness through an optimal transport problem with costs based on Gumbel random variables and KL regularization. The KL divergence from independence equals reduction in conditional entropy, giving the watermark strength parameter a direct information-theoretic interpretation.
Transport is applied to vocabulary blocks to reduce optimization dimension while preserving relative token probabilities within each block. The detector requires only generated text and the secret key, not the budget used during generation.
Detection reconstructs partition, cost table, and selected column at each scored position using the same tokenizer, block counts, context-window rule, and keyed pseudorandom construction as generation.