Text Watermarking

Article 50 (2) of the EU Artificial Intelligence Act requires providers of generative systems to make synthetic outputs machine-readable and detectable, while qualifying the effectiveness, interoperability, robustness, and reliability by technical feasibility, cost, content-specific limits, and the state of the art. For free-form text, one important implementation route is the implementation of a generative watermarking procedure, which poses a compliance problem that is hard to address. Strong watermarking is impossible against adaptive removal, while ordinary edits attenuate statistical evidence, and unmarked human text may overlap distributionally with machine output. This article develops an auditable alternative. First, it defines a description-length robustness profile. A finite-sample bound shows that detectable bias decays and that the required sample size grows with the inverse square of the decay rate. This replaces an unidentified Shannon-entropy constant with collision entropy. Second, it constructs label-conditional conformal prediction sets with separate false-attribution and false-exclusion levels, reporting watermark supported,'' not supported,'' or ``inconclusive''. Coverage is obtained as a finite-sample result and is class-conditional under exchangeability. A small reproducible simulation of a tournament watermark confirms both claims and shows that the surviving-token rule overstates the tolerable edit rate roughly twofold. The resulting premarket certificate, signed detector report, and postmarket recalibration protocol operationalize the Commission's 2026 Code of Practice without claiming universal robustness.

We introduce a framework for multi-bit text watermarking with security defined directly through $f$-divergence from the base language model distribution. Unlike prior approaches that focus on average-key distortion-freeness or a particular statistical distance, our formulation supports general $f$-divergences, including total variation and KL divergence, and enforces the guarantee for each realized key and embedded message. We develop a coding-based watermarking scheme that optimally biases next-token distributions subject to a prescribed divergence budget, and characterize the resulting tradeoff between embedding rate, decoding reliability, and statistical security. Experimentally, we compare our method against prior multi-bit watermarking schemes across modern language models and payload regimes. Our approach achieves substantially lower watermark detectability while maintaining competitive message-recovery performance and generation quality. Our results provide a unified view of secure multi-bit watermarking and recover several commonly used security notions as special cases.

Large language model watermarking embeds detectable statistical signals during decoding, but the resulting changes to token probabilities can degrade generation quality. This trade-off is particularly important for code, where small changes in token selection can break syntax or alter program behavior. Existing code watermarking methods mitigate this risk through entropy-based insertion or syntax-aware token selection, but they do not directly construct the watermark over the set of continuations admitted by the current grammar state. We propose Grammar-Guided Code Watermarking with Green Temperature (GTCW), which integrates grammar-constrained decoding with probability-aware watermarking. At each decoding step, GTCW restricts the candidate set to grammar-admissible tokens and partitions this support into keyed green and red subsets. At eligible high-entropy positions, green temperature reweights the green tokens according to the model's relative preferences, strengthening the watermark signal while retaining the grammar constraint. Across five models and five benchmarks spanning four programming languages, GTCW achieves a mean AUROC of 73.61%, compared with 67.83% for the strongest baseline, while maintaining a mean Pass@1 of 59.18% versus 59.58% for unwatermarked generation. Our implementation is available at https://github.com/hyundong98/GTCW .

Text watermarking techniques have gained significant attention for identifying machine-generated text and mitigating risks from large language models (LLMs). Existing methods typically divide an LLM's vocabulary into green and red tokens, but encouraging generation toward green tokens can reduce text quality and naturalness. To address this, we propose TripPattern, a watermarking framework that formulates text watermarking as a pattern-based matching task using three vocabulary partitions. TripPattern divides the vocabulary into one neutral group and two pattern groups. During generation, the model alternates token selection between the two pattern groups to embed detectable patterns, while neutral tokens are selected independently to improve flexibility and preserve naturalness. For detection, TripPattern uses pattern-based statistical tests that provide interpretable p-values by measuring how often adjacent tokens alternate between the pattern groups. Theoretical analysis and empirical evaluations on four multilingual datasets show that TripPattern maintains LLM generation quality while achieving robust watermark detectability.

On August 2, 2026, the obligations of Article 50 of the EU AI Act took effect, requiring generative AI providers to mark the content their systems produce and ensure it can be detected as AI-generated. Days later, Anthropic disclosed that every Claude model released after that date embeds a watermark based on SynthID-Text in all generated text, enabled by default with no user opt-out; Google has deployed SynthID-Text in Gemini since 2024. Users objected that the watermark degrades quality, particularly for code, that it secretly encodes identifying information, and, in mutual contradiction, that it is easily removable and inescapable; the vendor answered with assurances of unchanged quality, no identifying information, and robustness to light editing. In this work, we argue that neither the objections nor the assurances can currently be verified and that this unverifiability, rather than watermarking itself, is the substantive governance failure. We sort the contested assertions by what it would take to settle each and evaluate the open-source SynthID-Text implementation on two open-weight models, because no public tool can test the deployed systems. On prose, the measured effect of the watermark does not exceed that of changing the sampling seed. On code, the cost is three points of correctness on one model and below measurement on the other, while detection remains near chance, a limitation of detectability rather than quality. The remaining gaps trace to withheld access or missing institutions and we map each to a requirement: release of matched outputs, configuration disclosure, accredited audits, a shared evaluation protocol, and interoperable detection.

Multi-bit watermarking for large language models enables content source tracing by embedding user-identifiable messages into generated text. Existing methods face a fundamental trade-off among extraction accuracy, text quality, and payload capacity. We propose WeaveMark, a robust and scalable multi-bit LLM watermarking scheme based on coded payload spreading. WeaveMark shifts this trade-off frontier by improving payload capacity through multi-bit-per-token spreading (weaving), improving extraction accuracy through soft-decision error-correcting codes, and preserving text quality through unbiased multilayer reweighting. It further introduces dedicated zero-bit layers for reliable watermark presence detection. Extensive experiments demonstrate substantial gains in extraction performance, especially for long messages and edited text, without degrading text quality. WeaveMark achieves an 89.8% match rate for 32-bit messages at 200 tokens, compared with 20.8% for BiMark. Under 10% substitution attacks on 16-bit messages at 200 tokens, it maintains 86.0% versus 30.7%. Code is available at https://anonymous.4open.science/r/WeaveMark-ED6F.

Regulatory regimes such as the EU AI Act mandate machine-readable marking of synthetic text, but existing watermark detectors rely on the generating LM and on heuristic thresholds with no closed-form calibration. We introduce ChainMark, an active watermark that partitions the vocabulary into S states via keyed SHA-256 and forces a hard Markov transition on a fraction rho of positions; the detector replays the partition from the same key in O(n) hash operations, with no LM access. We derive a closed-form S*(n, rho, alpha) mapping a target FPR, text length, and budget to the minimum state count (Theorem 1), prove a universal robustness threshold delta* = 1 - 1/sqrt(2) approximately 29.3% that is invariant in (S, rho, n) (Theorem 2), and generalise both to any k-regular transition topology (Theorem 3). Across three instruction-tuned LLMs and four domains, ChainMark strictly dominates KGW and SWEET under translation and random-substitution attacks at matched budget; a one-corpus empirical recalibration restores the 1% target FPR on natural-language text.

Governments are increasingly mandating that LLM-generated content carry watermarks. The EU AI Act calls for markings that are "sufficiently reliable and robust." California's SB 942 requires disclosure that is "permanent or extraordinarily difficult to remove." Both mandates rest on an untested assumption: that watermark detection yields evidence reliable enough for courts. This paper tests that assumption directly. We evaluate three representative LLM watermarking methods -- KGW, Unigram, and the MarkLLM implementation of SynthID-Text -- against the Daubert admissibility criteria and the NIST SP 800-86 digital forensic process. To structure this evaluation, we propose a Forensic Readiness Score (FRS) framework with 12 criteria, three mandatory gates, and a 60-point scoring system. We focus on meaning-preserving paraphrase as the attack vector, since it is both legally realistic and difficult to dismiss as evidence tampering. The results raise serious evidentiary concerns. Out of 846 valid paraphrase runs across 15 diverse prompts per method, every single initially-detected KGW and Unigram text lost its watermark after paraphrasing -- 100% conditional removal. SynthID fared only slightly better at 98.3%. Even before any attack, false-negative rates were already high: 70% for KGW, 83% for Unigram, 80% for SynthID. The SynthID configuration also flagged 5.4% of paraphrased human-written controls as AI-generated and showed an 18.6% paradox rate, with 80% of its own pristine watermarked output landing in the uncertainty deadband. None of the three methods satisfy more than two of five Daubert factors. We also find that the FRS point-based scoring system, despite working as designed, cannot fully capture forensic uselessness -- a limitation worth noting for future framework design. These configurations, as tested, do not meet the evidentiary bar that courts require.

A watermark in a generative model's output is usually asked only whether a text is machine-made. The same mark can do more: attribute it to the user who produced it, extract a hidden payload, or localize the part that survives editing. These form a forensic ladder, and we ask what each rung costs in the sample length $n$. One object organizes the answers. Let $S$ be the secret the mark carries (a user's identity or payload), and let the information profile $ν(t)=I(S;X_t\mid X_{<t})$ record how much the $t$-th token reveals about $S$ given the earlier ones. Its total mass pays for attribution and extraction; how that mass is spread pays for localization; and detection alone is paid for not by information but by presence, the distance from the marked to the unmarked distribution. The literature's two quality models, a mark subtle on every token and one that stamps a few tokens loudly, are two incomparable ways of capping this profile. Our main theorem settles the ladder's entropy column. For statistically distortion-free schemes, attributing a text to one of $N$ users costs $Θ(\log N/h)$ tokens over every stationary-ergodic source of entropy rate $h$, sharp to a $(1+o(1))$ factor: to our knowledge the first tight entropy-rate law for multi-user attribution (via exact alignment). The natural collision-counting analysis overcharges without bound; only a decoder thresholding each candidate by its own realized surprisal attains the rate while almost never implicating an innocent user. A matching converse makes the law two-sided, and extraction of an $\ell$-bit payload costs $Θ(\ell/h)$. Two gaps are real, not modeling artifacts: a $Θ(\log N)$-token window in which a text is provably machine-made yet unattributable, and a footprint-resolution uncertainty principle. Experiments on GPT-2, Pythia-410M, and Qwen2.5 recover the predicted constants.

With the rapid development of Large Language Models (LLMs), text watermarking has emerged as a crucial technique for identifying machine-generated content. However, directly applying existing logits-based watermarking methods to code generation remains challenging, since the low-entropy nature of code exacerbates the trade-off between code quality and watermark detectability. In this paper, we propose a novel code watermarking approach called Grammar-Driven Watermark (GDW) for LLMs. GDW preserves syntactic validity through a grammar-guided three-level masking mechanism and injects watermark signals via structural role-aware modulation, assigning a stronger bias to content-bearing tokens while applying a more conservative bias to syntax-critical tokens. Aligning with the generation process, we further design a role-aware weighted detection statistic to improve detectability. Experiments across multiple programming languages, models, and decoding strategies show that GDW establishes a stronger quality-detectability trade-off frontier than existing methods, while maintaining robustness against variable-renaming attacks.

Attributing code to the large language model that produced it is essential for provenance, licensing, and misuse accountability, yet no deployed watermark meets this need. Generation-time schemes require access to the producing model and cannot be applied to third-party code, while post-hoc schemes work on any code but carry at most 4 bits of payload, far too few to distinguish the many deployed model configurations. We present multi-channel spread-spectrum watermarking, the first post-hoc, training-free code watermark with a 24-bit payload and formal robustness guarantees. The scheme encodes bits in variable naming conventions and in eight pairs of semantically equivalent code patterns, and a keyed pseudo-random permutation maps every site to a codeword bit so that each bit receives multiple independent votes. Majority voting absorbs distributed corruption, while an outer Reed-Solomon code recovers the identifier when concentrated channel attacks defeat the vote, yielding provable robustness bounds for formatting, syntactic, and structural attacks. Across 1,750 Python files from CodeNet and from GPT-4.1 and Llama-4 generations, the watermark achieves 100% clean-detection accuracy with zero false positives. Under 17 attack types, it recovers the identifier at 97.6% accuracy under 8 variable renames and 94.1% under 10% random per-site corruption, while the strongest post-hoc baseline collapses to 0% under any single-transform attack. Embedding and detection together take under 200 ms on CPU without training data or GPU.

Watermarking methods embed imperceptible and verifiable signals into text generated by large language models (LLMs). Existing approaches include zero-bit schemes for distinguishing synthetic text from human writing and multi-bit schemes for embedding metadata. However, current multi-bit watermarking methods do not allow selective disclosure: verifying any part of the watermark requires revealing the entire embedded message. This lack of control leads to unnecessary information exposure and raises privacy concerns. We propose Hierarchical Vocabulary Routing (HeRo), a watermarking framework that enables selective disclosure of embedded metadata. The method recursively partitions the vocabulary and distributes watermark information across hierarchical layers, so that different verifiers can decode only the portions of the payload corresponding to their access level. We show that the proposed scheme preserves the unbiasedness of the underlying sampling process and thus maintains text quality. Experiments demonstrate that our framework supports fine-grained access control while achieving high detection accuracy and low latency. Code is available at https://github.com/xuyangc03/hero-watermark.

This work presents Dual-Embedding Watermarking (DEW), a semantic watermarking scheme for large language models (LLMs) that leverages contextual and token-level embeddings to enhance robustness against paraphrasing and translation. DEW utilizes a signal-processing methodology, applying algebraic vector-space operations to token and context embeddings to derive a watermark signal that degrades gracefully under semantic shifts. The method obfuscates the watermark by projecting embedding vectors through pseudo-random matrices seeded with a secret key. Relevant distributions derived from the underlying algebra are evaluated and employed for statistical testing and benchmarking of DEW. Experimental results across multiple LLMs indicate that DEW improves post-paraphrase detection while maintaining competitive text quality, and remains detectable after translation, even when prior semantic watermarks degrade significantly. These findings position DEW as a practical and robust solution for safeguarding LLM-generated text and addressing critical issues in responsible AI deployment.

Reliable provenance for LLM outputs requires multi-bit watermarks that remain robust under editing while maintaining strict false-positive control. Existing ECC-based LLM watermarks rely largely on hard-decision decoding, discarding token-level reliability information. We propose CORE-BREW, a Constant-hit-Rate Embedding extension of block-wise BREW for robust multi-bit watermarking. CORE-BREW calibrates the watermark channel by targeting a fixed hit rate p-star, yielding closed-form per-token log-likelihood ratios (LLRs) for principled soft-decision decoding. It supports two detection modes: Strict-Safe, which preserves the bounded-distance designated-codeword acceptance region, and FPR-Calibrated, which uses likelihood-based scoring and lightweight list decoding to characterize the FPR-TPR trade-off. Experiments on open-source LLMs under token-level edits and paraphrasing demonstrate improved low-FPR discrimination and robustness over prior multi-bit watermarking baselines while maintaining comparable semantic quality.

Existing sentence-level watermarking methods enhance robustness to paraphrasing by anchoring watermarks in sentence semantics. However, their prefix-based designs remain vulnerable to structural perturbations, such as sentence splitting and merging, which commonly arise under strong paraphrasers like DIPPER and GPT-3.5. To mitigate this issue, we propose AliMark, a framework that reformulates sentence-level watermarking as a bit sequence encoding and alignment problem between a potentially watermarked text and a secret bit sequence. Notably, our approach adopts a two-stage detection strategy: we generate multiple restructured text variants and adaptively align their extracted bit sequences with the secret bit sequence to minimize alignment cost. This multi-candidate alignment design naturally improves robustness to sentence merges and splits. Extensive experiments demonstrate that AliMark substantially outperforms state-of-the-art baselines under diverse paraphrasing attacks.

The widespread deployment of generative artificial intelligence (AI) models has raised serious concerns about the proliferation of AI-generated content. This has led to a surge of interest in, and demand for, reliable tracking and detection mechanisms for content that is AI-generated, such as watermarking, metadata tagging, content tagging, and more. The problem has captured the attention of policymakers as well as the popular media, and a spate of recent bills in the US have sought to regulate the spread of AI content, and enforce or promote methods to track and label it. This work performs a critical analysis of the policy discourse surrounding generative AI content transparency in the US and EU. Through a broad document selection methodology, we first collect a broad corpus of documents containing legislative language and policy-relevant discourse on the topic. We then analyze these through inductive coding, and leverage our coding to systematize these documents, identifying key patterns, gaps, and open questions. We identify critical points of disconnect between policy and technological capabilities and practice, and we highlight and discuss potential ambiguities and pitfalls raised by the trends in our corpus.

Semantic-level watermarking (SWM) improves robustness against text modifications by treating sentences as the basic unit. However, robustness to paragraph-level paraphrasing remains difficult because such attacks globally disrupt watermark signals by changing sentence order. In this work, we propose SAMark, a self-anchored watermarking framework that removes the dependency on sentence order by establishing a step-independent green region in semantic space. To improve detectability, we introduce a multi-channel hyperbolic scoring mechanism that amplifies watermark signals while suppressing noise from weakly aligned candidates. We further propose a diversity-aware filtering strategy that combines hard filtering with soft regularization, extending beyond simple n-gram repetition filters to address semantic redundancy. Experimental results show that SAMark achieves up to 90.2% TP@FP1% under typical paragraph-level paraphrasing attacks, outperforming the strongest prior baseline by more than 30% on average, while maintaining generation quality competitive with unwatermarked text and breaking the robustness-quality trade-off that limits prior methods. Our code will be released at this URL.

Proprietary large language models (LLMs) face risks of intellectual property (IP) violation, as adversaries can replicate an LLM by collecting input-output pairs to train a surrogate model, causing financial setbacks. Watermarks offer a promising defense to verify ownership, but existing methods often struggle with semantic distortion, factual inconsistency, and adversarial attacks. In addition, key-conditioned watermarks for provider-specific detection, especially in cross-provider and multi-user scenarios, remain largely underexplored. To address these challenges, we propose SAFESEAL, a novel key-conditioned watermarking framework that achieves strong detectability with minimal impact on model utility, effectively balancing detectability, utility, and robustness. SAFESEAL preserves named entities while substituting linguistic terms with context-aware synonyms through a key-conditioned Tournament sampling mechanism, maintaining semantic fidelity and factual consistency. For detection, we introduce a key-conditioned contrastive detector that jointly encodes the text and key, enabling provider-specific and robust watermark verification. We derive theoretical bounds on the utility-detectability trade-off and significantly reduce latency through lightweight models, batching, and parallelism. Extensive experiments show that SAFESEAL outperforms baselines in utility, detectability, and robustness, achieving a BERTScore of 0.983, entity similarity of 0.963, a 98.2% detection rate, and the highest human ratings for text quality and content preservation, with latency comparable to the fastest baseline. To promote transparency and community-driven progress, we release the first public watermark leaderboard and an interactive demo.

Watermarking is widely proposed for provenance, attribution, and safety monitoring in generative models, yet is typically evaluated only under adversaries who attempt to evade detection or induce false positives at the level of individual samples. We argue that watermarking should be treated as a monitoring primitive, and that internal monitoring is unavoidable given per-entity attribution keys and messages, as well as detector access. We introduce an observer-based threat model in which observers can aggregate watermark signals across outputs to infer entity-level information, showing that even zero-bit watermarking enables attribution under multi-key settings. We further show that external monitoring can emerge over time from persistent, key-dependent statistical structure, although this depends on watermark design and may be mitigated by distribution-preserving or undetectable schemes. Our findings reveal a fundamental dual-use tension between attribution and monitoring, motivating evaluation of watermarking beyond per-sample robustness to account for aggregation and observer-based capabilities.

With LLM watermarking already being deployed commercially, practical applications increasingly require multibit watermarks that encode more complex payloads, such as user IDs or timestamps, into the generated text. In this work, we propose a fundamentally new approach for multibit watermarking: introducing binomial encoding to directly encode every bit of the payload at every token position. We complement our approach with a stateful encoder that during generation dynamically redirects encoding pressure toward underencoded bits. Our evaluation against 8 baselines on up to 64-bit payloads shows that our scheme achieves superior message accuracy and robustness, with the gap to baseline methods widening in more relevant settings (i.e., large payloads and low-distortion regimes). At the same time, we challenge prior works' evaluation metrics, highlighting their lack of practical insights, and introduce per-bit confidence scoring as a practically relevant metric for evaluating multibit LLM watermarks.

Large language models (LLMs) have made fluent essay writing, code drafting, and quiz answering instantly available to students at every level, from secondary school through graduate study. Many educators do not object to LLM use \emph{per~se}; what they need to detect is the case in which a student pastes the assignment prompt into a chatbot and submits the model's reply verbatim, without engaging with the work. Existing post-hoc AI-text detectors remain unreliable and have been shown to penalise non-native English writers, while output-side watermarks require cooperation from the model provider. We propose an alternative that the educator controls directly: an input-side watermark in which an invisible instruction is embedded inside the visible assignment prompt itself. An LLM that ingests the prompt verbatim quietly reads the hidden instruction and writes a tell-tale signature into its reply, exposing the copy-and-paste pathway specifically. We describe SteganoPrompt, a single-page, zero-dependency web tool that encodes an arbitrary printable-ASCII payload into the deprecated Unicode Tags block (\texttt{U+E0000}--\texttt{U+E007F}). The encoded string is visually identical to the original, survives common copy-paste channels (Word, Google Docs, PDF, Markdown, Slack, e-mail, the major learning-management systems), and is reliably tokenized by frontier models. We evaluate compliance across seven LLM families and a representative set of educational content channels. The work is informed by my experience as a graduate teaching assistant for an undergraduate software engineering course at the George Washington University. The tool is released under the MIT licence at https://ezharjan.github.io/SteganoPrompt/.

We introduce SWAN (Semantic Watermarking with Abstract Meaning Representation), a novel framework that embeds watermark signatures into the semantic structure of a sentence using Abstract Meaning Representation (AMR). In contrast to existing watermarking methods, which typically encode signatures by adjusting token selection preferences during text generation, SWAN embeds the signature directly in the sentence's semantic representation. As the signature is encoded at the semantic structure level, any paraphrase that preserves meaning automatically preserves the signature. SWAN is training-free: watermark injection is achieved by prompting an LLM to generate sentences guided by a selected AMR template while maintaining contextual coherence, and detection uses an off-the-shelf AMR parser followed by a simple one-proportion z-test. Empirical evaluation on the RealNews benchmark shows SWAN matches state-of-the-art detection performance on unaltered watermarked text, while significantly improving robustness against paraphrasing, increasing detection AUC by up to 13.9 percentage points compared to prior methods. These results demonstrate that SWAN's approach of anchoring watermarks in AMR semantic structures provides a simple, effective, and prompt-based method for robust text provenance verification under paraphrasing, opening new avenues for semantic-level watermarking research.

Recent multi-bit watermarking methods for large language models (LLMs) prioritize capacity over reliability, often conflating decoding with detection. Our analysis reveals that existing ECC-based extractors suffer from catastrophic false positive rates (FPR), and applying rejection thresholds merely collapses detection sensitivity (TPR) to random guessing. To resolve this structural limitation, we propose BREW (Block-wise Reliable Embedding for Watermarking), a framework shifting the paradigm to designated verification. BREW employs a two-stage mechanism: (i) blind message estimation via independent block voting, followed by (ii) window-shifting verification that rigorously validates the payload against local edits. Experiments demonstrate that BREW achieves a TPR of 0.965 with an FPR of 0.02 under 10% synonym substitution, demonstrating that the high-FPR issue is not an inherent trade-off of multi-bit watermarking, but a solvable structural flaw of prior decoding-centric designs. Our framework is model-agnostic and theoretically grounded, providing a scalable solution for reliable forensic deployment.

With the growing use of large language models, concerns over content authenticity have spurred a variety of watermarking schemes. These schemes use secret keys to detect machine-generated text while remaining imperceptible to readers. Detection typically reduces to statistical hypothesis testing for the presence of watermarks, a topic that is now well studied. In contrast, the finer-grained task of localizing which segments of a text are watermarked is much less explored; existing approaches often lack scalability or guarantees robust to paraphrasing and post-editing. We bring a new perspective to this segmentation problem through the lens of epidemic change-points and, by exploiting this connection, propose WISER, a novel and computationally efficient watermark segmentation algorithm. We establish finite-sample error bounds and consistency for detecting multiple watermarked segments in a single text. Complementing these theoretical results, our extensive numerical experiments show that WISER outperforms state-of-the-art baseline methods, both in terms of computational speed as well as accuracy, on various benchmark datasets embedded with diverse watermarking schemes. Together, these theoretical and empirical results position WISER as an effective tool for watermark localization and illustrate how classical statistical ideas can yield theoretically valid and computationally efficient solutions to a modern problem of immediate importance.

Text watermarks in large language models (LLMs) are an increasingly important tool for detecting synthetic text and distinguishing human-written content from LLM-generated text. While most existing studies focus on determining whether entire texts are watermarked, many real-world scenarios involve mixed-source texts, which blend human-written and watermarked content. In this paper, we address the problem of optimally estimating the watermark proportion in mixed-source texts. We cast this problem as estimating the proportion parameter in a mixture model based on \emph{pivotal statistics}. First, we show that this parameter is not even identifiable in certain watermarking schemes, let alone consistently estimable. In stark contrast, for watermarking methods that employ continuous pivotal statistics for detection, we demonstrate that the proportion parameter is identifiable under mild conditions. We propose efficient estimators for this class of methods, which include several popular unbiased watermarks as examples, and derive minimax lower bounds for any measurable estimator based on pivotal statistics, showing that our estimators achieve these lower bounds. Through evaluations on both synthetic data and mixed-source text generated by open-source models, we demonstrate that our proposed estimators consistently achieve high estimation accuracy.