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The uneven rise of AI-generated web content

Adam Visokay, Soumyakanti Pan, Molly Griston, Polina Iasakova, Mark Nepf, Denis Peskoff, Riya Sinha, Jikai Sun, Isabelle Thiara, Letao Wang, Yiwei Wu, Lauren Yan, Tyler H. McCormick

arXiv:2610.36631v1cs.AIcs.CYcs.NIstat.AP

TL;DR

The extent and distribution of AI-generated text across the public web remain uncertain because prior studies often focus on new pages or limited settings and detector errors vary by context. This paper estimates prevalence across a probability sample of crawlable pages using multiple detectors and a Bayesian model that accounts for those errors. It finds that AI-influenced text has risen substantially and unevenly, with much of the increase on peripheral pages.

  • Problem

    Prior studies often examine newly published pages or limited settings, leaving total prevalence and its distribution across languages and web centrality less established.

    Source: §1 · pp. 3–4

  • Method

    The authors analyze a probability sample of 5.1 million crawlable pages with multiple AI detectors and a Bayesian hierarchical model that adjusts for context-specific detector errors and their uncertainty.

    Source: §1 · p. 2

  • Results

    About 24 percent (95% credible interval 22.9-24.4) of crawlable webpages contained AI-generated or AI-edited text in August 2026; roughly four-fifths of the increase came from peripheral domains.

    Source: §1 · p. 2

  • Takeaways & Limitations

    AI-generated text increasingly shapes public-facing web communication and the conventions, style, and norms of future language models trained on web content.

    Source: §1 · p. 2

    The estimand excludes pages behind logins, inside apps, or on sites that block crawlers, as well as pages with fewer than 500 characters of extractable text.

    Source: §5 · p. 28

Abstract

from arXiv · show

In less than five years, generative artificial intelligence (AI) has dramatically reshaped the public-facing web. Using a sample of more than 5 million crawlable webpages, we demonstrate that the share containing AI-generated text has increased precipitously, but unevenly. Our analyses reveal substantial differences in AI composition across language and domain categories (e.g., .edu, .com, or .gov). A higher fraction of English-language webpages contain AI-generated text compared to pages in other languages, and prevalence is substantially lower on .gov and .edu domains compared to .com. These distinctions persist even after accounting for compositional effects. We also find heterogeneity based on a page's position in the connectivity structure of the web. AI-generated text is most common and has increased most rapidly in pages that are the least central in the graph, which drives much of the overall growth in AI-generated text. A slower increase has taken place for more central pages, with the most central tier emerging as the least likely to contain AI-generated text. Methodologically, we use multiple AI detection tools, and generate estimates using a Bayesian hierarchical model that incorporates corrections for the detectors' statistical properties (both false positives and false negatives) and allows for different detector performance across groups, while propagating uncertainty in detector error rates into prevalence estimates. Our work suggests that AI is a prominent, but varied, contributor to public information and internet-based communication.

1 Introduction

This study measures the changing prevalence of AI-generated text across the crawlable web and examines how it varies by network centrality, language, and domain type. It uses multiple detectors and a Bayesian model to account for context-specific measurement error.

1 Introduction

  • About 24 percent of crawlable webpages contained AI-generated or AI-edited text in August 2026, and the annual increase nearly doubled to 8.1 percentage points since early 2025.The estimated rate rose from 4.6 percentage points per year between early 2023 and early 2025.Source: §1 · p. 2
  • AI-generated text is most common and has grown fastest on peripheral pages, which account for about four-fifths of the overall increase.The most central domains are least likely to contain fully AI-generated or AI-edited text.Source: §1 · pp. 2–3
  • English-language pages and .com domains show faster AI spread, while differences across languages and domain types persist after accounting for page composition.The analysis considers language, text length, and centrality as possible contributors to observed domain differences.Source: §1 · pp. 2, 4
  • A Bayesian hierarchical model combines multiple detectors with labeled benchmarks and pre-2022 crawls, allowing error rates to vary across contexts and propagating their uncertainty into prevalence estimates.Specificity varies by detector, language, centrality tier, top-level domain, and text length; sensitivity varies by detector and language.Source: §1 · pp. 2–3
  • Earlier studies largely tracked new pages or specific settings, leaving total prevalence and cross-language trends with detector-error correction less established.Prior work also left open how AI-text growth is distributed across the web’s connectivity structure.Source: §1 · p. 3

2 Results

Across 71 Common Crawl snapshots, the estimated share of eligible pages containing fully AI-generated or AI-edited text rose substantially, with marked differences by network centrality, language, and domain category. These differences persist after accounting for page composition.

2 Results

  • A Bayesian hierarchical model corrected detector errors across groups and propagated their uncertainty; poststratification weighted estimates to the population of eligible pages.The analysis covered 5,118,347 pages from 505,974 domains across 71 snapshots, with eligible pages defined as successfully captured pages containing at least 500 extracted main-text characters.Source: §2 · pp. 4–5

2.1 Overall prevalence and rate of change

  • About one in four eligible pages contained fully AI-generated or AI-edited text in August 2026, and prevalence growth accelerated to 8.1 percentage points per year.The increase was 0.2 percentage points per year from January 2019 to February 2023 and 4.6 from February 2023 to January 2025; the final rate exceeded the previous one by 3.6 points per year (95% credible interval 3.3 to 3.9).Source: §2.1 · p. 5, Figure 2.1 · p. 6

2.2 Increasing prevalence comes mostly from the least connected sites

  • By August 2026, estimated prevalence ranged from 11.6% in the most-central tier to 27.5% in the least-central tier, and the gap persisted after standardizing page composition.Standardized prevalence ranged from 11.1% in Top to 26.7% in Tail; no tier's standardized estimate differed from its original estimate by more than 1.2 percentage points.Source: §2.2 · p. 7
  • Bottom and Tail held 70.5% of eligible pages but accounted for 78.8% of the net prevalence increase; most of their contribution came from rising prevalence within those tiers.Of the 21.7-point overall increase, 15.7 points came from within-tier prevalence change in Bottom and Tail, versus 1.4 points from their changing page share.Source: §2.2 · pp. 7–9, Figure 2.2 · p. 8

2.3 AI-generated text is more common on English-language pages

  • In August 2026, prevalence was 32.8% for English-only pages and 17.0% for non-English-only pages; their gap widened over time and remained after standardization.At a common composition, prevalence was 32.5% for English-only, 16.8% for non-English-only, and 21.4% for bilingual pages; bilingual prevalence reached 20.2% in August 2026.Source: §2.3 · pp. 9–10, Figure 2.3 · p. 10

2.4 Prevalence of AI-generated text is lower on government and educational domains, but rising

  • In August 2026, estimated prevalence was 29.5% on .com pages, versus 6.1% on .edu and 5.8% on .gov; these differences narrowed but persisted after standardization.The common-composition estimates were 26.4% for .com, 7.0% for .edu, and 7.5% for .gov; the latter estimates rely on predictions for sparsely represented combinations.Source: Figure 2.4 · p. 11, §2.4 · pp. 11–12

3 Discussion

The public web shapes both the information people receive and the text used to train future language models. Because detector outputs are imperfect proxies for authorship, treating them as authoritative can lead to consequential judgments.

3 Discussion

  • The web’s changing composition can shape what people read and how future language models write and convey information.The public web serves as a channel for information and communication, and as training data for future models.Source: §3 · p. 12
  • Detector outputs are imperfect proxies for AI involvement, and each approach has blind spots, so any individual flag supports only a narrow claim about latent authorship.Detectors can miss fully AI-generated text and flag mostly human text, and different methods can do so for different reasons.Source: §3 · p. 12
  • Treating detector outputs with undue authority risks consequential judgments about authorship, reputation, and professional legitimacy.The Caine Prize-winning story was placed under review after a commercial detector flagged nearly all of it as AI-generated; the author denied using AI, and no conclusive determination had been issued.Source: §3 · p. 13

4 Methods

The methods use a stratified, longitudinal Common Crawl sample, calibrated complementary AI detectors, and Bayesian hierarchical modeling to estimate AI-text prevalence over time across page and domain groups. Estimates are poststratified to page-count and PageRank-weighted populations, with detector uncertainty and changes in page composition accounted for.

4.1 Sampling

  • Across 71 crawls from January 2019 to August 2026, 112.7 billion of 194.9 billion captures (58%) met the denominator: successful pages yielding at least 500 cleaned text characters.Common Crawl provides a longitudinal frame with page indexes and a domain hyperlink graph; each crawl had a median duration of 13.1 days.Source: §4.1 · p. 13

4.1.1 Stratification and Sampling Allocation

  • Each crawl sampled 20,000 domains across six fixed PageRank-quantile strata, fully censusing the roughly 900-domain top tier; the tail held 38.0% of pages, while the top held 30.2% of PageRank mass.The design uses quantile cutoffs to cover consistent frame fractions over time and allocates draws to support comparisons across centrality levels.Source: §4.1.1 · p. 14, §4.1.2 · p. 15

4.1.2 Data Descriptives

  • English-classified pages, including bilingual pages, declined from 63.0% to 61.0%, while long pages rose from 49.1% to 54.3%, so the model conditions on length because detector sensitivity varies with it.The sample averaged 72,000 scored pages per crawl; longer-page drift would raise measured sensitivity independently of prevalence.Source: §4.1.2 · p. 15

4.2 AI Detection

  • The prevalence model uses open Pangram for all pages and English-only Binoculars-Falcon as a complementary zero-shot detector; RoBERTa, Binoculars-Qwen, and Pangram 4 were excluded.Open Pangram was chosen for its partial-AI and non-English detection, RAID ranking accuracy, and throughput; Binoculars-Falcon provides a detector with a different method and architecture.Source: §4.2.1 · p. 17, §4.2 · p. 17

4.2.2 Empirical overlap of detector errors

  • The deployed detectors’ false-positive flags were near-independent on control pages, but their misses correlated on AI text (r = 0.27 on RAID; r = 0.18 on AITDNA), potentially biasing prevalence downward; Pangram 4 was excluded because its errors overlap open Pangram’s.Pangram 4’s misses on AI-involved text were more correlated with open Pangram than with Binoculars-Falcon.Source: §4.2.2 · p. 18

4.2.3 Pangram 4 as a validation reference

  • Pangram 4 flagged only 2 of 20,100 control pages, neither among 1,593 open-model flags, and had non-English sensitivity 0.708 versus 0.363 for open Pangram.These results support treating control-period open-model flags as false positives and the open model’s non-English sensitivity as a floor.Source: §4.2.3 · pp. 18–19

4.2.4 Datasets for calibrating false-negative and false-positive rates

  • Pre-2022 crawls calibrate false positives, while EditLens, RAID, and multilingual benchmarks inform false negatives; non-English sensitivity is pooled at 0.363 because benchmark language coverage is limited.Open Pangram’s control false-positive rate was 4.5% on English-only pages and 28.5% on bilingual pages. The model excludes evaluation sets that overlap a detector’s training data and uses hierarchical priors to retain benchmark-level sensitivity differences.Source: §4.2.4 · pp. 19–20

4.3 Bayesian measurement error model

  • The Bayesian model jointly estimates detector operating characteristics and prevalence across cells defined by language, length, PageRank tier, and TLD; ordered centrality tiers receive a structured prior.Pre-2022 crawls serve as negative controls for specificity, and prevalence varies over time; the model’s baseline uses English-only, .com, and long-text pages.Source: §4.3 · pp. 20–21, §4.3.1 · p. 22

4.3.1 Hierarchical priors on cell attributes

  • Cell prevalences use shared attribute effects, with adjacent centrality tiers borrowing information while language, domain, and word-count effects are exchangeable.Cells sharing more attributes are more strongly correlated a priori.Source: §4.3.1 · p. 22

4.3.2 Modeling temporal inhomogeneity

  • A shared temporal trend and language-, tier-, and domain-specific monthly slopes model changes across crawls, with a penalized spline spanning the study period.The fixed knot scheme places knots at the first and last crawl midpoints, at 2022-01-01 and 2022-11-30, and every 10 crawls within each of the three resulting eras.Source: §4.3.2 · p. 23

4.3.3 Prior for calibration of detectors

  • Specificity is informed by control crawls, sensitivity by benchmark corpora, and detector operating characteristics are allowed to shift after the control period.The shift is static after the control period; the primary transport scales are 0.5 for specificity and 0.25 for sensitivity.Source: §4.3.3 · pp. 24–25
  • Pangram’s Youden index posterior means were 0.58 to 0.97 for English-stratum pages and 0.37 for non-English pages; Binoculars’ means were −0.06 to 0.04 and positive in every draw for 68% of pages.The authors assess the fitted control-period calibration rather than imposing a positive Youden-index constraint.Source: §4.3.3 · p. 25

4.3.4 Posterior inference

  • Marginalizing latent page status enables gradient-based Hamiltonian Monte Carlo and reduces likelihood evaluation from about 5 million pages to about 50 thousand unique cell-crawl-detector combinations.Poststratification reweights cell-level estimates to the target population, using eligible-page counts or PageRank mass; it assumes known cell composition and within-cell sample representativeness.Source: §4.3.4 · pp. 26–27
  • Tier-growth contributions are calculated as each tier’s share of the net prevalence increase, while a symmetric Kitagawa decomposition separates prevalence change from page-share change.The fixed-page-distribution comparison does not track the same pages or domains over time or identify a causal effect of centrality.Source: §4.3.4 · p. 27

5 Limitations

The estimates describe crawler-reachable, long-form web text, with pages scored as whole documents. The model also omits domain-level random effects because they would make estimation computationally prohibitive.

5 Limitations

  • The estimand excludes pages crawlers cannot reach and standalone text shorter than 500 characters, including many social-media posts, comments, and reviews.Short texts collected together on a page are scored as one document, so results describe the page rather than individual posts.Source: §5 · p. 28
  • The analysis omits domain-level random effects, which would model similarity among pages from the same domain beyond language, centrality tier, TLD, and page length.Including one effect for each of 505,974 sampled domains would prevent the page aggregation used for efficient likelihood evaluation and make estimation computationally prohibitive.Source: §5 · pp. 28–29
  • Common Crawl’s changing policy to combat link spam caused substantial variation in unique domain nodes across crawls, though uncrawled link-farm domains do not affect the analysis.A domain’s presence in the web graph does not itself mean it was crawled.Source: §5 · p. 28
  • The authors expect prevalence estimates by group to be little affected because centrality tier and TLD absorb part of the unmodeled domain heterogeneity.The median domain has six sampled pages; 38% have at most four, and 14% have one, leaving domain-specific effects weakly informed and difficult to separate from detector misclassification.Source: §5 · p. 29

Conflict of interest

Pangram provided API credits, but did not direct the research decisions or review materials before release.

Conflict of interest

AI Use Statement

The authors used AI tools across implementation, analysis support, and manuscript preparation, and say they reviewed and validated the AI-assisted work.

AI Use Statement

  • AI coding agents supported Common Crawl sampling and WARC extraction, Slurm job management for GPU-based detection, and modeling software.Source: AI Use Statement · p. 30
  • Other AI tools helped design tables and figures, provide project feedback, identify literature, and edit the manuscript for readability.Source: AI Use Statement · p. 30
  • The authors say they reviewed and validated all AI-assisted work and take full responsibility for the final content, including text, claims, code, and figures.Source: AI Use Statement · p. 30

Ethics Statement

The authors state that detection-tool outputs are not intended as conclusive evidence of authorship and that the data were public and used with license permissions followed.

Ethics Statement

A Related work

Prior web-prevalence studies address sampling frames or detector error in narrower settings; this study combines both in a statistical estimate for English and non-English pages. It treats detector outputs as noisy measurements and uses the model to estimate prevalence and its distribution across groups over time.

A Related work

  • The study jointly models sampling and detector error to estimate prevalence of fully AI-generated or AI-edited text on English and non-English pages, with uncertainty.Earlier approaches include Rogan–Gladen corrections, false-positive subtraction, and population-level word-frequency shifts.Source: A Related work · p. 36
  • Detector scores are treated as noisy measurements of an unobserved page-level status, not as labels of text origin.The model combines a population frame, labeled benchmarks for detector error, and statistical estimation with uncertainty.Source: A Related work · p. 36
  • The model supports error-corrected estimates by network position, domain type, and language, and decomposes temporal change into within-group shifts and changing group weights.The study also estimates detector sensitivity and specificity separately for English and non-English text and by text length.Source: A Related work · p. 36

B AI Detector Benchmarks

The appendix describes benchmark evaluations used to calibrate detector sensitivity and specificity for the measurement model. It also notes that overlapping training-data rows are excluded from calibration and explains how error corrections are represented in the study comparison.

B AI Detector Benchmarks

  • Benchmark evaluations calibrate detector sensitivity and specificity for the measurement model.Figure B.1 reports AI-text flag rates and human-text flag rates, including pre-2022 Common Crawl pages as an in-domain negative control.Source: B AI Detector Benchmarks · p. 36
  • Table A.2 compares existing studies with this study.The supplied caption identifies the comparison’s scope but does not provide the table’s specific entries.Source: Table A.2 · p. 37
  • The study comparison distinguishes error handled within the estimator from separate corrections, and notes propagation of sampling and detector-error uncertainty.It also identifies Rogan–Gladen adjustment, false-positive subtraction, and thresholds set to a 1% false-positive rate as approaches used in the compared studies.Source: B AI Detector Benchmarks · p. 37
  • Rows overlapping a detector’s training data are excluded from calibration.These are marked by hollow indicators in Figure B.1.Source: B AI Detector Benchmarks · pp. 36–37

B.1 Empirical overlap between AI-detectors

Detector errors vary across contexts, and the two detectors used together are nearly independent on human control pages but positively dependent on AI-involved text. In the August 2026 snapshot, long pages have higher estimated AI-text prevalence than short or medium pages, even after standardizing group composition.

B.1 Empirical overlap between AI-detectors

  • Neither Open Pangram nor Binoculars-Falcon performs best across all contexts; their relative false-positive rates reverse between .gov/.edu and .com pages.On RAID fully AI-generated text, their sensitivities were similar (0.720 and 0.727), while for co-written text Open Pangram flagged 94% versus 34% for Binoculars.Source: §B.1 · p. 37
  • Among 1.77 million English control pages, 5,278 were flagged by both open Pangram and Binoculars-Falcon versus 5,422 expected under independence, with ϕ = −0.002.On AI-involved benchmarks, the detector flags were positively dependent, with ϕ between 0.18 and 0.56; for the modeled pair, values were 0.27 on RAID, 0.48 on the English multilingual set, and 0.18 on AITDNA co-written texts.Source: §B.1 · p. 42
  • The model’s conditional-independence assumption holds for human-side errors but not AI-side errors, where it underpredicts joint flags and overpredicts single-detector flags.The authors expect a limited prevalence effect because Pangram scores every page and carries most information, but have not quantified it; modeling AI-side dependence is future work.Source: §B.1 · pp. 42–43

C.1 Prevalence pattern by text length

  • 30.2% of long pages were estimated to contain fully AI-generated or AI-edited text in August 2026, versus 15.2% of short and 16.7% of medium pages.After assigning each length group the same centrality, TLD, and language distribution, estimates were 29.4% for long, 15.7% for short, and 17.4% for medium pages.Source: §C.1 · p. 43
  • Figure C.1 separates overall prevalence growth into within-tier prevalence change and changes in the shares of pages across tiers.The caption defines the contributions in percentage points, but the supplied passage does not provide the plotted values.Source: Figure C.1 · p. 44, §C.1 · p. 44
  • Long pages had the highest prevalence at every crawl, and their gap from short and medium pages widened after 2023.The length comparison assumes detector sensitivity is constant across word-count levels, although specificity is modeled to vary with word count.Source: §C.1 · p. 45

C.2 Additional results by language

English-only pages’ growth advantage over non-English-only pages increased between the two calendar intervals, while language differences persist after composition standardization. The appendix describes model variants used for sensitivity analysis but the supplied passages do not report their comparative results.

C.2 Additional results by language

  • The English-only growth advantage increased by 3.0 (2.8–3.2) percentage points per year between the two intervals, reflecting faster English-only growth than non-English-only growth.The corresponding growth-rate acceleration was 4.1 (3.7–4.5) points per year for English-only pages and 1.1 (0.8–1.4) for non-English-only pages; intervals are fixed by calendar date and no change point is estimated.Source: §C.2 · p. 45
  • Bilingual-page prevalence remained below English-only prevalence, with the gap increasing from 2.2 points in February 2023 to 12.7 in August 2026.As a fraction of English-only prevalence, however, it rose from 0.18 to 0.61; language tags do not establish bilingual authorship.Source: §C.2 · pp. 45–46
  • The non-English-only category pools many languages and is only a reference for comparison with English-only estimates, not an estimate for any individual non-English language.Non-English levels carry more calibration uncertainty because sensitivity calibration uses machine text from 2023-era generators in only some languages.Source: §C.2 · p. 46
  • Standardizing centrality, TLD, or length separately shifts no known-language prevalence estimate by more than 1.0 percentage point; joint standardization shifts the three plotted groups by 0.3, 0.2, and 1.2 points.Unknown-language estimates shift more because they are imprecise.Source: §C.2 · p. 47, Table C.5 · p. 47

D Sensitivity analysis

  • The sensitivity analysis compares 16 variants with the reported model, varying specificity structure, spline basis count, drift scales, and the early-prevalence prior.The reported model uses 12 spline basis functions and no interactions; the variants and their estimates are listed in Table D.6 and compared by WAIC in Table D.7.Source: D Sensitivity analysis · p. 47, §D.1 · pp. 47–49

D.1 Model variants

  • Other variants remove temporal effects or drift, use dynamic drift, constrain the control-period Youden index to be positive, or add interactions among centrality, TLD, and language.The dynamic-drift model was estimated only on a pilot subsample; the supplied passages describe these variants without reporting their comparative results.Source: §D.1 · pp. 48–49

D.2 Model comparison

Across specifications that allow detector drift and include a temporal effect, the August 2026 prevalence estimate remains between 22.3% and 24.2%. Removing either component fits substantially worse, while a more flexible specificity drift makes the end-of-series estimate assumption-sensitive.

D.2 Model comparison

  • 22.3–24.2% is the August 2026 prevalence range across specifications that allow drift and include a temporal effect, compared with 23.6% in the reported model.Removing drift gives 27.7%; removing the temporal effect gives 5.2%, and both alternatives fit worse.Source: §D.2 · p. 49, Table D.6 · p. 50
  • Allowing specificity to vary with word count, centrality tier, and TLD lowers WAIC by 2,380 relative to the reduced structure.The model adds cell-level specificity effects for both detectors.Source: §D.2 · pp. 50–51
  • Removing the temporal effect raises WAIC by 72,639 and lowers the August 2026 estimate to 5.2%, while removing drift raises the estimate to 27.7% and fits much worse.Without a temporal effect, detector drift alone explains flag-rate growth and yields meaningless Pangram calibration.Source: §D.2 · pp. 49, 51
  • Adding interactions improves WAIC by 1,662 relative to the reported model but changes overall prevalence by only 0.3 percentage points and reduces the smallest tail ESS to 215.The additive model is reported because the WAIC gain is small per page and the interaction fit has lower effective sample sizes.Source: §D.2 · p. 52
  • A pilot Gaussian random walk produced an August 2026 prevalence level between 9% and 22%, so the reported end-of-series estimate is conditional on specificity changing only once.The random walk and single-drift models were not distinguishable by WAIC in the pilot; specificity drift can absorb flag-rate growth otherwise attributed to prevalence.Source: §D.2 · p. 52

D.3 Robustness of the main findings

The main centrality and domain patterns persist across alternative model specifications that include drift and a temporal effect. Language comparisons and the timing of the bilingual crossing are also examined, with the non-English level and crossing date more sensitive to calibration and model assumptions.

D.3 Robustness of the main findings

  • Across 15 fits with drift and a temporal effect, August 2026 prevalence rises from 10.4–12.0% in the Top tier to 25.8–28.3% in the Tail, while .com remains highest and .edu and .gov lowest.The findings do not hold when drift or the temporal effect is removed; estimates describe pages with at least 500 characters of extracted text.Source: §D.3 · p. 52
  • The English-only prevalence advantage remains positive across temporal-effect fits, but the no-English estimate ranges from 13.3% to 18.4% and the advantage ranges from 14.6 to 19.9 percentage points.The English advantage's annual growth increase is 1.5 to 3.1 percentage points per year across fits with a temporal effect.Source: §D.3 · pp. 52–53

D.4 The level of non-English prevalence

  • The no-English prevalence estimate is most affected by calibration: it ranges from 13.3% to 18.4% across drift-and-temporal-effect fits, while English-only prevalence stays at 33.0–33.1% under the reduced specificity structure.No-English pages use Pangram alone, and non-English sensitivity is calibrated on 2023-era generators and treated as a lower bound; the English–no-English gap remains positive and growing, but its magnitude is conditional on these assumptions.Source: §D.4 · p. 54

D.5 Timing of the bilingual crossing

  • The posterior-mean bilingual-minus-no-English difference crosses zero between August 2025 and April 2026 across specifications, and never becomes non-negative without a temporal effect.The reported model's first non-negative difference is in February 2026, while specification changes shift the timing; the authors do not attribute the crossing to an event.Source: §D.5 · p. 54

D.6 Positive Youden index constraint

Imposing a positive Youden index changes some prevalence estimates and worsens fit, particularly for Binoculars, whose constrained sensitivity is held at the boundary. The authors retain the unconstrained model because the constraint does not remove an implausible mode and the data prefer the unconstrained fit.

D.6 Positive Youden index constraint

  • For Binoculars, the constraint binds at the boundary and raises control-period sensitivity from 4.6% to 7.6%, although benchmark true-positive rates range from 34% to 73%.The web data place Binoculars at or just below chance in the least specific cell; the constraint does not bind for Pangram.Source: §D.6 · p. 55
  • 544 higher WAIC accompanies the positive-Youden-index constraint; it changes August 2026 prevalence from 23.6% to 22.6% and no-English prevalence from 17.0% to 14.5%.All qualitative findings of Section D.3 hold under the constraint.Source: §D.6 · pp. 55–57
  • The authors do not impose the constraint because the mirror mode is not a concern, it moves Binoculars to a boundary estimate, and the unconstrained model has better WAIC.The constraint also makes sensitivity a non-smooth function of specificity effects, letting the least-specific cell's flag rates determine a parameter otherwise informed by benchmarks and webpages.Source: §D.6 · pp. 56–57

D.7 Convergence Diagnostics

The alternative fits generally pass the reported convergence checks, although a few derived early non-English prevalences have low tail effective sample sizes. The reported diagnostics also show Binoculars' Youden index near or below zero in the unconstrained drift fits.

D.7 Convergence Diagnostics

  • All seventeen fits have no divergent transitions, maximum-tree-depth transitions, or low energy Bayesian fraction of missing information; the largest split- bR is 1.011.Two fits have tail ESS below 400, for derived non-English prevalences in early crawls.Source: §D.7 · p. 57, Table D.10 · p. 61
  • Binoculars' Youden index is negative in every draw of each drift fit without the constraint, while Pangram's 95% interval is above zero in every fit except the one without a temporal effect.Table D.10 reports the index at the control-period calibration in the least-specific observed cell of each stratum.Source: §D.7 · p. 57, Table D.10 · p. 61
  • The constrained fit's smallest tail ESS is 1,399 versus 736 for the reported model, but its mean leapfrog steps rise from 431 to 541.The longer trajectories are attributed to the boundary and the minimum-over-cells constraint.Source: §D.7 · pp. 57–58

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