Provenance Half-Life: Studying the Coupled Decay of Watermark Signal and Output Quality in Multi-Agent LLM Pipelines

Watermarking is a primary mechanism for attributing the origin of text generated by large language models. However, current evaluations predominantly treat detection as a binary property tested against isolated, single-pass transformations. This fails to reflect contemporary multi-agent deployments, where generated text is frequently summarized, translated, and iteratively revised across several stages before reaching an end user. While separate lines of research have established that these sequential transformations both attenuate watermark signals and induce semantic drift, these phenomena have only been studied in isolation. We argue that this separation obscures a shared underlying mechanism. The transformations that erode provenance signals are the exact same ones that accumulate semantic degradation. In this proposal, we model watermark signal and output quality as a coupled trajectory rather than independent endpoint measurements. We introduce the concept of a provenance half-life, defined as the number of sequential agent transformations after which attribution confidence falls below a reliable threshold. This reframes provenance from a binary survival test to a confidence-calibrated localization task that estimates both the origin stage and the associated signal decay. To investigate this, we propose to construct controlled multi-agent chains in which a watermarked initial generation propagates through configurable sequences of transformation agents, drawn from summarization, translation, paraphrase, and iterative editing. Chain length, agent ordering, the model at each stage, its decoding temperature, and the rewriting intensity are treated as controlled variables, allowing us to isolate the contribution of each transformation type to the observed decay and to construct chains that mirror realistic downstream pipelines. Seed generations span task families of differing entropy, from open-ended text to constrained and low-entropy outputs, since detectability and degradation are both known to depend on generation entropy. Each configuration is repeated across seeds and watermark keys to yield distributions rather than point estimates at every stage. At each stage we record a paired measurement of watermark strength and output quality. Watermark strength is quantified by detector confidence expressed as a per-stage detection score and calibrated p-value, together with the token budget required to reach a fixed confidence level, which captures gradual attenuation before outright detection failure. Output quality is measured along three axes. Fidelity to the immediately preceding stage and to the original seed is assessed with reference-based similarity and entailment scoring to quantify semantic drift, intrinsic quality is assessed through fluency and coherence judgments, and task retention is assessed by whether the transformed text still satisfies the original task constraints, scored per task family. Fitting parametric decay models to the resulting paired trajectories, we estimate the provenance half-life as a function of pipeline configuration and test, using per-stage paired comparisons across configurations, whether signal and quality decay are statistically coupled or strictly separable. If the coupling hypothesis holds, it suggests that future provenance mechanisms must rely on pipeline-aware confidence estimates, potentially unifying quality monitoring and watermarking within a single framework. Ultimately, we aim to contribute a formal problem definition, an evaluation framework, and a novel metric suite for tracking provenance and quality as coupled properties.