The DOI matches its Crossref record; 53 of the 54 references it cites were found in a registry or an index.
Deep learning for early warning signals of tipping points
Open accessAbstract
Significance: Early warning signals (EWS) of tipping points are vital to anticipate system collapse or other sudden shifts. However, existing generic early warning indicators designed to work across all systems do not provide information on the state that lies beyond the tipping point. Our results show how deep learning algorithms (artificial intelligence) can provide EWS of tipping points in real-world systems. The algorithm predicts certain qualitative aspects of the new state, and is also more sensitive and generates fewer false positives than generic indicators. We use theory about system behavior near tipping points so that the algorithm does not require data from the study system but instead learns from a universe of possible models.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Figures



Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Combine that with long-term soundscapes and mechanistic ecological models, and you get early-warning indicators that could outperform abundance-only monitoring (Bury et al. 2021; Rasmussen et al. 2024; Stowell and Sueur 2020).”
From Listening forward: emerging roles of bioacoustics in ecology, evolution, and conservation (2026) · cites this paper as Bury et al. 2021
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
SciPy 1.0: fundamental algorithms for scientific computing in Python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al. (2020) · Nature Methods · doi:10.1038/s41592-019-0686-2 · Cited by 38,430 · cited 1×
“The simulation uses the odeint function from the Python package Scipy (42) with a step size of 0.01.”
MethodInfluentialRobust Locally Weighted Regression and Smoothing Scatterplots
Cleveland, W. S. (1979) · Journal of the American Statistical Association · doi:10.1080/01621459.1979.10481038 · Cited by 11,594 · cited 1×
“This is done using Lowess smoothing (52) with span 0.”
MethodSciPy 1.0: fundamental algorithms for scientific computing in Python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al. (2019) · Apollo - University of Cambridge Repository · doi:10.17863/cam.64134 · Cited by 10,460
Elements of Applied Bifurcation Theory
Kuznetsov, Y. A. (2004) · Applied mathematical sciences · doi:10.1007/978-1-4757-3978-7 · Cited by 5,729
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
Strogatz, S. H., Friedman, M. J., Mallinckrodt, A. J., & McKay, S. R. (1994) · Computers in Physics · doi:10.1063/1.4823332 · Cited by 4,654
Deep learning for time series classification: a review
Ismail Fawaz, H., Forestier, G., Weber, J., Idoumghar, L., & Muller, P.-A. (2019) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-019-00619-1 · Cited by 3,342 · cited 1×
“Supervised DL algorithms can also detect patterns (features) in time series, and have achieved state of the art in time series classification (23)—the ability to classify time series based on characteristic features in the data.”
BackgroundNonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering
Strogatz, S. H., & Fox, R. F. (1995) · Physics Today · doi:10.1063/1.2807947 · Cited by 2,584
Anticipating Critical Transitions
Scheffer, M., Carpenter, S. R., Lenton, T. M., Bascompte, J., Brock, W., Dakos, V., van de Koppel, J., van de Leemput, I. A., Levin, S. A., van Nes, E. H., et al. (2012) · Science · doi:10.1126/science.1225244 · Cited by 2,208 · cited 1×
“This information is important to know for both theoretical and practical purposes, since tipping points in many systems can lead to undesirable collapse (14).”
BackgroundSelf-citationGraphical Representation and Stability Conditions of Predator-Prey Interactions
Rosenzweig, M. L., & MacArthur, R. H. (1963) · The American Naturalist · doi:10.1086/282272 · Cited by 2,057 · cited 2×
“To test the Hopf and transcritical bifurcations, we use the Rozenzweig−MacArthur consumer−resource model (29) with additive white noise.”
MethodThresholds and breakpoints in ecosystems with a multiplicity of stable states
May, R. M. (1977) · Nature · doi:10.1038/269471a0 · Cited by 1,743 · cited 2×
“The model systems included a simple harvesting model consisting of a single equation that exhibits a fold bifurcation (28); a system of two equations representing a consumer−resource (predator−prey) system exhibiting both Hopf and transcritical bifurcations (29); and a system of five equations representing the coupled…”
MethodAUTO-07p: Continuation and bifurcation software for ordinary differential equations
Doedel, E. J., CHAMPNEYS, A. R., Dercole, F., Fairgrieve, T. F., Kuznetsov, Y. A., Oldeman, B. E., Paffenroth, R. C., Sandstede, B., Wang, X. J., & Zhang, C. H. (2007) · Cited by 1,631
Selective review of offline change point detection methods
Truong, C., Oudre, L., & Vayatis, N. (2019) · Signal Processing · doi:10.1016/j.sigpro.2019.107299 · Cited by 1,594 · cited 1×
“Therefore, we use a change-point detection algorithm contained in the Python package ruptures (44) to locate a transition point if one exists.”
MethodPathak, J., Hunt, B. R., Girvan, M., Lu, Z., & Ott, E. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.024102 · Cited by 1,367 · cited 1×
“This limits its ability to detect features such as deterministic chaos (22), which require at least three state variables (40).”
BackgroundDakos, V., Carpenter, S. R., Brock, W. A., Ellison, A. M., Guttal, V., Ives, A. R., Kéfi, S., Livina, V., Seekell, D. A., van Nes, E. H., et al. (2012) · PLoS ONE · doi:10.1371/journal.pone.0041010 · Cited by 1,151 · cited 1×
“Generic early warning indicators are computed using the Python package ewstools (20) which implements established methods (51).”
MethodSelf-citationTime, structure, and fluctuations
Prigogine, I. (1978) · Science · doi:10.1126/science.201.4358.777 · Cited by 1,148 · cited 1×
“This has stimulated research in fields ranging from evolutionary biology (1) and statistical mechanics (2) to dynamical systems theory (3).”
BackgroundSlowing down as an early warning signal for abrupt climate change
Dakos, V., Scheffer, M., van Nes, E. H., Brovkin, V. A., Petoukhov, V. K., & Held, H. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0802430105 · Cited by 1,036 · cited 3×
“The three empirical datasets consisted of data from paleoclimate transitions (17), transitions to thermoacoustic instability in a horizontal Rijke tube which is a prototypical thermoacoustic system (30), and sedimentary archives capturing episodes of anoxia in the eastern Mediterranean (31) (see Materials and Methods).”
BackgroundSelf-citationPunctuated equilibrium comes of age
Gould, S. J., & Eldredge, N. (1993) · Nature · doi:10.1038/366223a0 · Cited by 957 · cited 8×
“Null time series of the same length are generated from an AR (1) (autoregressive lag 1) process fit to the initial 20% of the data.”
BackgroundMethodInfluentialTravelling waves and spatial hierarchies in measles epidemics
Grenfell, B. T., Bjørnstad, O. N., & Kappey, J. (2001) · Nature · doi:10.1038/414716a · Cited by 952 · cited 2×
“For the transcritical bifurcation, we simulate null trajectories with a = 2 and forced trajectories with a ∈ [ 2,6 ] ; for the Hopf bifurcation, we use a = 12 and a ∈ [ 12,16 ] , respectively.”
BackgroundMethodDynamical Systems in Cosmology
Böhmer, C. G., & Chan, N. (1997) · Cambridge University Press eBooks · doi:10.1017/cbo9780511524660 · Cited by 888
AI can be sexist and racist — it’s time to make it fair
Zou, J., & Schiebinger, L. (2018) · Nature · doi:10.1038/d41586-018-05707-8 · Cited by 765
One-Dimensional Schrödinger Equation with an Almost Periodic Potential
Ostlund, S. S., Pandit, R. A., Rand, D. A. J., et al. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.1873 · Cited by 731 · cited 1×
“Thus, dynamical systems are extremely diverse, ranging in spatial scale from the expanding universe (4) to quantum systems (5) and everything in between (6–8).”
BackgroundResilience indicators: prospects and limitations for early warnings of regime shifts
Dakos, V., Carpenter, S. R., van Nes, E. H., & Scheffer, M. (2014) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2013.0263 · Cited by 632 · cited 1×
“A clear trend in variance or lag-1 AC is taken to provide an early warning signal of an upcoming state transition (32).”
BackgroundSelf-citationTransient phenomena in ecology
Hastings, A., Abbott, K. C., Cuddington, K. M., Francis, T. B., Gellner, G., Lai, Y., Morozov, A. Y., Petrovskii, S., Scranton, K., & Zeeman, M. L. (2018) · Science · doi:10.1126/science.aat6412 · Cited by 599
Generic Indicators of Ecological Resilience: Inferring the Chance of a Critical Transition
Scheffer, M., Carpenter, S. R., Dakos, V., & van Nes, E. H. (2015) · Annual Review of Ecology Evolution and Systematics · doi:10.1146/annurev-ecolsys-112414-054242 · Cited by 575 · cited 1×
“However, supervised DL algorithms require many thousands of time series to learn classifications—something we do not have for many empirical systems (24).”
BackgroundSelf-citationFlickering gives early warning signals of a critical transition to a eutrophic lake state
Wang, R., Dearing, J. A., Langdon, P. G., Zhang, E., Yang, X., Dakos, V., & Scheffer, M. (2012) · Nature · doi:10.1038/nature11655 · Cited by 517 · cited 1×
“This task lies in the domain of time series forecasting instead of classification and is a difficult undertaking, given that stochasticity could cause a system to jump prematurely to a new basin of attraction even before the system has reached the tipping point (39).”
BackgroundSelf-citationA CNN-LSTM Approach to Human Activity Recognition
Mutegeki, R., & Han, D. S. (2020) · 2020 International Conference on Artificial Intelligence in Information and Communication (ICAIIC) · doi:10.1109/icaiic48513.2020.9065078 · Cited by 452 · cited 2×
“As a result, this approach excels at pattern recognition and sequence prediction (25, 26).”
BackgroundMethodA universal law of the characteristic return time near thresholds
Wissel, C. (1984) · Oecologia · doi:10.1007/bf00384470 · Cited by 422 · cited 1×
“For example, all local bifurcations, that is, those where eigenvalues of the respective matrices cross the imaginary axis, are accompanied by critical slowing down (3, 13).”
BackgroundBaurmann, M., Groß, T., & Feudel, U. (2006) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2006.09.036 · Cited by 366 · cited 1×
“State transitions may also occur through codimension-two bifurcations where two forcing parameters are varied simultaneously (16, 35, 36), or bifurcations of periodic orbits (22), for which EWS are more apparent.”
BackgroundWhat Do You Mean, ‘Tipping Point’?
van Nes, E. H., Arani, B. M. S., Staal, A., van der Bolt, B., Flores, B. M., Bathiany, S., & Scheffer, M. (2016) · Trends in Ecology & Evolution · doi:10.1016/j.tree.2016.09.011 · Cited by 297 · cited 1×
“Sometimes, a system that is close to equilibrium may experience slowly changing external conditions that move it toward a tipping point where its qualitative behavior changes (we note that “tipping point” has been used to refer to a variety of phenomena (9), but here we will treat it as being synonymous with a local b…”
BackgroundSelf-citationGold volatility prediction using a CNN-LSTM approach
Vidal, A., & Kristjanpoller, W. (2020) · Expert Systems with Applications · doi:10.1016/j.eswa.2020.113481 · Cited by 286 · cited 2×
“As a result, this approach excels at pattern recognition and sequence prediction (25, 26).”
BackgroundMethodEarly warning signals also precede non‐catastrophic transitions
Kéfi, S., Dakos, V., Scheffer, M., van Nes, E. H., & Rietkerk, M. (2012) · Oikos · doi:10.1111/j.1600-0706.2012.20838.x · Cited by 275 · cited 5×
“This happens for fold, Hopf, and transcritical bifurcations, and thus critical slowing down is manifested before these three bifurcations types (16).”
BackgroundMethodInfluentialSelf-citationEarly warning signals: the charted and uncharted territories
Boettiger, C., Ross, N., & Hastings, A. (2013) · Theoretical Ecology · doi:10.1007/s12080-013-0192-6 · Cited by 220
Early warning signals of regime shifts in coupled human–environment systems
Bauch, C. T., Sigdel, R. P., Pharaon, J., & Anand, M. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1604978113 · Cited by 187 · cited 2×
“Improved EWS can help us better prevent or prepare for such state transitions (41).”
BackgroundSelf-citationEarly warning signals and the prosecutor's fallacy
Boettiger, C., & Hastings, A. (2012) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2012.2085 · Cited by 167 · cited 1×
“These time series, however, do not address how the approaches might perform when faced with a neutral time series where no transition occurs, and whether they might mistakenly generate a false positive prediction of an oncoming state transition (33).”
BackgroundOraby, T. F., Thampi, V. A., & Bauch, C. T. (2014) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2013.3172 · Cited by 139 · cited 4×
“For the transcritical bifurcation, we simulate null trajectories with a = 2 and forced trajectories with a ∈ [ 2,6 ] ; for the Hopf bifurcation, we use a = 12 and a ∈ [ 12,16 ] , respectively.”
BackgroundMethodInfluentialSelf-citationEarly warning signals: The charted and uncharted territoriesPreprint
Boettiger, C., Ross, N., & Hastings, A. (2013) · Cited by 130
Early-warning signals for Dansgaard-Oeschger events in a high-resolution ice core record
Boers, N. (2018) · Nature Communications · doi:10.1038/s41467-018-04881-7 · Cited by 124 · cited 1×
“Early warning indicators generally require high-resolution data from a sufficiently long time series leading up to the tipping point (38).”
BackgroundCritical dynamics in population vaccinating behavior
Pananos, A. D., Bury, T. M., Wang, C., Schonfeld, J., Mohanty, S. P., Nyhan, B. J., Salathé, M., & Bauch, C. T. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1704093114 · Cited by 95 · cited 1×
“To test the DL algorithm on a model of higher dimensionality than the ecological models, we used a stochastic version of the SEIRx model that captures interactions between disease dynamics and population vaccinating behavior (12, 45) given by”
MethodSelf-citationDetecting and distinguishing tipping points using spectral early warning signals
Bury, T. M., Bauch, C. T., & Anand, M. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2020.0482 · Cited by 93 · cited 4×
“Other early warning approaches have been developed to predict the type of bifurcation (20, 22, 34).”
BackgroundMethodInfluentialSelf-citationVirtual Hopf phenomenon: A new precursor of period-doubling bifurcations
Wiesenfeld, K. A. (1985) · Physical Review A · doi:10.1103/physreva.32.1744 · Cited by 85 · cited 4×
“This limits its ability to detect features such as deterministic chaos (22), which require at least three state variables (40).”
BackgroundInfluentialScaling Effects and Spatio-Temporal Multilevel Dynamics in Epileptic Seizures
Meisel, C., & Kuehn, C. (2012) · PLoS ONE · doi:10.1371/journal.pone.0030371 · Cited by 82 · cited 1×
“These generic early warning indicators have been found to precede catastrophic regime shifts in systems including epileptic seizures, Earth’s paleoclimate system, and lake manipulation experiments (17–19).”
BackgroundCharting pathways to climate change mitigation in a coupled socio-climate model
Bury, T. M., Bauch, C. T., & Anand, M. (2019) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007000 · Cited by 79
Self-citationDYNAMICAL SYSTEMS IN COSMOLOGY
Nunes, N. J. (2001) · doi:10.1142/9789812811035_0023 · Cited by 70
Early warnings of regime shifts in spatial dynamics using the discrete Fourier transform
Carpenter, S. R., & Brock, W. A. (2010) · Ecosphere · doi:10.1890/es10-00016.1 · Cited by 67
Spatial early warning signals in a lake manipulation
Butitta, V. L., Carpenter, S. R., Loken, L. C., Pace, M. L., & Stanley, E. H. (2017) · Ecosphere · doi:10.1002/ecs2.1941 · Cited by 50
Effect of rate of change of parameter on early warning signals for critical transitions
Pavithran, I., & Sujith, R. I. (2021) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0025533 · Cited by 42 · cited 2×
“We perform experiments in a horizontal Rijke tube which consists of an electrically heated wire mesh in a rectangular duct (30).”
BackgroundMethodSelf-citationCalculating Centre Manifolds for Delay Differential Equations Using Maple™
Campbell, S. A. (2009) · Springer eBooks · doi:10.1007/978-0-387-85595-0_8 · Cited by 35 · cited 1×
“In these circumstances, dynamical systems theory predicts that even very high-dimensional systems will simplify to follow low-dimensional dynamics (10, 11).”
BackgroundDetection of bifurcations in noisy coupled systems from multiple time series
Williamson, M. S., & Lenton, T. M. (2015) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4908603 · Cited by 35 · cited 1×
“State transitions may also occur through codimension-two bifurcations where two forcing parameters are varied simultaneously (16, 35, 36), or bifurcations of periodic orbits (22), for which EWS are more apparent.”
BackgroundSelf-citationTransient indicators of tipping points in infectious diseases
O’Regan, S. M., O’Dea, E. B., Rohani, P., & Drake, J. M. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2020.0094 · Cited by 34 · cited 3×
“Other early warning approaches have been developed to predict the type of bifurcation (20, 22, 34).”
BackgroundEarly‐Warning Signals for Marine Anoxic Events
Hennekam, R., van der Bolt, B., van Nes, E. H., de Lange, G. J., Scheffer, M., & Reichart, G. (2020) · Geophysical Research Letters · doi:10.1029/2020gl089183 · Cited by 33 · cited 6×
“The three empirical datasets consisted of data from paleoclimate transitions (17), transitions to thermoacous-tic instability in a horizontal Rijke tube which is a prototypical thermoacoustic system (30), and sedimentary archives capturing episodes of anoxia in the eastern Mediterranean (31) (see Materials and Methods…”
BackgroundMethodInfluentialSelf-citationDelayed Random Walks: Investigating the Interplay Between Delay and Noise
Ohira, T., & MILTON, J. G. (2009) · Springer eBooks · doi:10.1007/978-0-387-85595-0_11 · Cited by 14
Forecasting resilience profiles of the run-up to regime shifts in nearly-one-dimensional systems
Adamson, M. W., Dawes, J., Hastings, A., et al. (2020) · Journal of The Royal Society Interface · doi:10.1098/rsif.2020.0566 · Cited by 10 · cited 2×
“However, other types of transitions are possible, such as global bifurcations that do not depend on changes to the local stability of equilibria (27).”
BackgroundHennekam, R., van der Bolt, B., van Nes, E. H., et al. (2020) · Socio-Environmental Systems Modeling · doi:10.1594/pangaea.923197 · Cited by 2
Self-citation
Cited by
Sorted by citations
Exceeding 1.5°C global warming could trigger multiple climate tipping points
Armstrong McKay, D. I., Staal, A., Abrams, J. F., Winkelmann, R., Sakschewski, B., Loriani, S., Fetzer, I., Cornell, S. E., Rockström, J., & Lenton, T. M. (2022) · Science · doi:10.1126/science.abn7950 · Cited by 1,931
“These could be augmented with deep learning techniques (99).”
Self-citationCheng, S. L., Quilodrán-Casas, C., Ouala, S., Farchi, A., Liu, C., Tandeo, P., Fablet, R., Lucor, D., Iooss, B., Brajard, J., et al. (2023) · IEEE/CAA Journal of Automatica Sinica · doi:10.1109/jas.2023.123537 · Cited by 351
“finding canonical bifurcations of dynamical systems from toy examples [301].”
BackgroundA 1 km daily soil moisture dataset over China using in situ measurement and machine learning
Li, Q., Shi, G., Shangguan, W., Nourani, V., Li, J., Li, L., Huang, F., Zhang, Y., Wang, C., Wang, D., et al. (2022) · Earth system science data · doi:10.5194/essd-14-5267-2022 · Cited by 292
Earlier collapse of Anthropocene ecosystems driven by multiple faster and noisier drivers
Willcock, S., Cooper, G. S., Addy, J., & Dearing, J. A. (2023) · Nature Sustainability · doi:10.1038/s41893-023-01157-x · Cited by 150
“…useful simplification for theoretical understanding, risks https://doi.org/10.1038/s41893-023-01157-x creating a false sense of security by overestimating the distance remaining before critical thresholds are breached in the real world where multiple drivers and noise are abundant 27,52 .”
InfluentialImpacts of climate change on vegetation pattern: Mathematical modeling and data analysis
Sun, G., Li, L., Li, J., Liu, C., Wu, Y.-P., Gao, S., Wang, Z., & Feng, G. (2022) · Physics of Life Reviews · doi:10.1016/j.plrev.2022.09.005 · Cited by 115
Metadata
- Authors
- Bury, T. M., Sujith, R. I., Pavithran, I., Scheffer, M., Lenton, T. M., Anand, M., & Bauch, C. T.
- Affiliations
- University of Waterloo (CA)
- Indian Institute of Technology Madras (IN)
- Wageningen University & Research (NL)
- University of Exeter (GB)
- University of Guelph (CA)
- Corresponding author
- Bauch, Chris T.
- ORCID
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2021-09-20
- Volume
- 118
- Issue
- 39
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC8488604
- OpenAlex
- W3200303296
- Semantic Scholar
- 91c6031240527a1cdba25aef61bdf5a3cf767498
- Cited by
- 284
- References
- 54
- Citations by year
- 2026: 61 · 2025: 59 · 2024: 67 · 2023: 51 · 2022: 44 · 2021: 2
- FWCI
- 16.80
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion, cc-by-nc-nd)
- Europe PMC (PubMed Central) (publishedVersion, other-oa)
- PubMed Central (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Socio-Environmental Systems Modeling (submittedVersion, cc-by-nc-nd)
- Data Archiving and Networked Services (DANS) (submittedVersion, cc-by-nc-nd)
- Funders
- Gouvernement du Canada | Natural Sciences and Engineering Research Council of Canada (RGPIN 2019, RGPIN 2020)
- Topics
- Physical Sciences › Environmental Science › Global and Planetary Change › Ecosystem dynamics and resilience
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical and Theoretical Epidemiology and Ecology Models
- Keywords
- tipping points, early warning indicators, normal forms, dynamical systems, deep learning, state transitions, lag-1 autocorrelation, variance, scaling behavior, model-free prediction, ecological tipping points, thermoacoustics, climate tipping points
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review