FissionGuard: Testing Local Watermark Proportions with FDR Control

A watermark detector can flag a text even when only a small fraction of its tokens are watermarked. We study sequential auditing to identify local passages whose watermark proportions exceed a prespecified threshold. Each alarm fixes a candidate passage's endpoint, while its start is chosen from earlier tokens. Reusing the same evidence to locate and test a passage can invalidate inference. We propose FissionGuard, which uses data fission to construct an alarm value and a validation value from each token-level $p$-value. The alarm values guide alarms and localization. The validation values yield passage-level $p$-values through partial conjunction, excluding as many of the strongest signals as the proportion null allows. These $p$-values are used to test the corresponding hypotheses at levels assigned by an online multiple-testing procedure. Under the stated watermark generation model, allowing dependence among token-level $p$-values at watermarked positions, we prove finite-sample false discovery rate (FDR) control among reported passages at every fixed finite horizon. We also derive a finite-sample lower bound on power for testing nonnull candidates. Experiments on synthetic streams and Mistral and Qwen generations across four marking layouts show gains in watermarked-token coverage over sample splitting, with empirical FDR below the target.