Applied Economics and Finance; Vol. 9, No. 3; 2022
ISSN 23327294 EISSN 23327308
Published by Redfame Publishing
102
A Review of the Anthropogenic Global Warming Consensus: An
Econometric Forecast Based on the ARIMA Model of Paleoclimate Series
Gilmar Veriato Fluzer Santos1, Lucas Gamalel Cordeiro1, Claudio Antonio Rojo1, & Edison Luiz Leismann1
1 PPGAdm, Universidade do Oeste do Paraná, Cascavel, Brasil
Correspondence: Gilmar Veriato Fluzer Santos, PPGAdm, Universidade do Oeste do Paraná, Cascavel, Brasil.
Received: July 19, 2022 Accepted: August 26, 2022 Available online: September 2, 2022
doi:10.11114/aef.v9i3.5703 URL: https://doi.org/10.11114/aef.v9i3.5703
Abstract
This paper projects a climate change scenario using a stochastic paleotemperature time series model and compares it to
the prevailing consensus using Autoregressive Integrated Moving Average Process Model (ARIMA). The parameter
estimates of the model were below that established by the anthropogenic experts and governmental organs, such as the
IPCC (UN) over a 100year scenario. Results from the ARIMA model suggest a current period of temperature reduction
and a probable cooling. The results from this study add a statistical element of paleoclimate to the debate that contradicts
the current scientific consensus.
Keywords: global warming, Paleoclimatology, time series, Arima model, climate scenarios, forecasting
1. Introduction
Controversies regarding global warming and its effects on the economy and the environment are the subject of global
discussion and debate. These controversies also partially determine how governments and companies develop their
policies and conduct their business.
Human action has been responsible for climate change and global warming (greenhouse effect) according to the followers
of anthropogeny and other international bodies such as the IPCC (Intergovernmental Panel on Climate Change  UN); as
echoed by most scientific publications (more than 90% of research studies) that show that global warming is
anthropogenic. This explanation has been established as the "official version" by IPCC advocates (Salzer, Neske & Rojo,
2019; Cook et al. 2013; Bray, 2010; Anderegg et al., 2010; Oreskes, 2004). The IPCC Working Group Chair, Jim Skea,
stated: "Limiting warming to 1.5°C is possible within the laws of chemistry and physics but doing so requires
unprecedented changes" (IPCC Special Report, 2019).
Nevertheless, assessing the state of scientific contestations on certain issues when the scientific community considers a
proposition a fact is essential as posited by Shwed and Bearman (2010). The authors also explain how internal dissent in
the face of consensus diminishes.
The defenders of the naturalistic cause present arguments that challenge published research studies by claiming that
anthropogenic global warming is theoretically fragile with calculated misinformation, and its historical sample of only
150 years is insufficient to establish a consensus often supported by agnotology and metric uncertainties (Molion, 2008;
Legates et al. 2015; Legates, Soon & Briggs, 2013; Reinsinger et al. 2010).
Notably, the more research explores the past, the more the anthropogenic thesis is weakened. Davis (2017) and Harde
(2019) found that changes in the atmospheric CO2 concentration did not cause changes in ancient climate temperature.
They also found that climate change was not related to the carbon cycle but to native impacts. Easterbrook (2016), in his
evidencebased book opposed CO2 emissions as the primary source of global warming; however, this thesis has been
captured by politics and dubious computer modeling.
Furthermore, other anthropogenic studies either ignore the paleoclimatology factor in research or factor it in as an element
of uncertainty, such as the research by Haustein et al. (2017), Cook et al. (2013), Mitchell et al. (2017), Medhaug et al.
(2017), similar to studies at the genesis of the IPCC studies (Solomon et al. 2007). However, scientists such as
Easterbrook (2016) and the arguments present in Koonin's book (2021), are increasingly pointing to data which suggests
that climate changes result from natural cycles that have been occurring for thousands of years,.
Thus, there is a gap in this debate which is the absence of a broader time horizon and statistical predictability to climate
change. This study, set out to establish a climate prediction scenario for the next 100 years based on a 12,000year
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paleotemperature series (Holocene Period) and the uncertainties within that the data were used to make this prediction.
We adopted the Autoregressive Integrated Moving Average (ARIMA) model, also known as BoxJenkins. BoxJenkins
ARIMA model's objective is to provide a valid basis for forecasting, after all tests, parameters, and diagnostics have been
performed. We obtained the ARIMA database from the article by Kaufman et al. (2020), who applied five statistical
methods of thermal reconstruction to verify global mean surface temperature (GMST) to the present day.
Our results indicated the fragility of the anthropogenic thesis by showing significant divergence from the latest scenario
projected by the IPCC that predicted an increase of more than 1.5°C in the planet's temperature by 2050 (IPCC, 2019).
Therefore, we established an additional variable for the global warming debate to stimulate critical discussion about the
consensus that prevails today.
2. Data, Method, and Its Justification
The data used in this research were obtained from Kaufmann et al., (2020) unprecedented multimethod reconstruction
research of mean land surface temperature (GMST) during the Holocene era (12,000 years) to the present day, "whose
database is the most comprehensive global compilation of previously available published Holocene proxy temperature
time series" (Kaufman et al., 2020, p. 01).
Primary data from the current study is available as individual CSV files and merged as a netCDF file at figshare 35 and at
NOAA Palaeoclimatology 36 (https://www.ncdc.noaa.gov/paleo/study/29712). A CSV file with the multimethod joint
median and 5th and 95th percentiles is also available in both data repositories. All were used as input data to compose the
12k time series of paleotemperatures in the two variables (the median and the uncertainty set) and fed into IBM SPSS
Statistics software (v. 22). The data generated for the development of this research are available in supplementary file.
The Arima model is an established predictive tool, as demonstrated in the works of Babu & Reddy (2014), Valipour
(2015) and Katimon, Shahid & Mohsenipour (2018).
In this study, our methodology was based on the use of this model for longterm forecasting in time series, both in
economic and stochastic variables, such as temperatures for example suggested in the book by Gujarati & Porter (ch.
2122, 2011).
To respond to our research question, the data were represented graphically and fed into the software IBM  SPSS Statistics,
v. 22, for ARIMA  Box Jenkins methodology. Figure 1 shows the evolution of the 12k median of the data set extracted
from Kaufmann et al. (2020) on a 100year scale, with milestone "0" being the year 2019 (p. 8) calculated from the
different reconstruction methods.
Figure 1. Evolution of the Global Median 12k years temperature
Source: Author elaboration (adapted from Kaufman et al. (2020 p. 06) from CSV file data at
https://www.ncdc.noaa.gov/paleo/study/29712).
Figure 2 depicts the 5th and 95th percentile range of the set that takes into consideration various sources of uncertainty,
including proxy temperature, chronology, and methodological choices, as per Kaufman et al. (2020 p. 03).
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Figure 2. Evolution of the parameters 5th and 95th global percentiles (uncertainties)
Source: Author elaboration (adapted from CSV file data  temp 12K all methods percentiles at
https://www.ncdc.noaa.gov/paleo/study/29712).
The average temperature of the 18001900 period for each composite was used as the preindustrial reference period that
was defined by the authors as an anomaly of 0° C; an average which served as the reference for the IPCC (18501900).
Hence, this period was removed from each member of the ensemble to avoid issuing individual records and different
reconstructions (Kindly refer to page 04 of Kaufmann et al. (2020). The forecasts of the twotime series, median and
uncertainties, were generated in the IBM  SPSS Statistics software, version 22, in a specific session for ARIMA
modeling.
2.1 Stochastic Processes and the Stationarity Test
To introduce the forecast, we graphically and mathematically presented the results that the SPSS software generated for
the two variables of this study, the median and the uncertainty set. We presented the graphs in this section, the
mathematical formulation of their results and the structuring of the uncertainty set (same pattern) in a supplementary file.
Firstly, we applied two tests to verify the stationarity of the time series: (1) graphical analysis and (2) the correlogram
test; condition for using the ARIMA (BJ) model.
An important condition for model reliability is the residuals of the ACF (Autocorrelation Function) and PACF (The partial
autocorrelation function) correlations, the white noise. For the model to be validated as the most adequate model, ACF
and PACF should be concentrated around the mean, and the degree of significance should be absolute (0 or close) as
represented in figure 3. (Note: Retardo means Lag; “de resíduo” means of waste)
Figure 3. Residuals of the ACF and PACF correlograms (White noise)
Source: prepared by the author (SPSS  Statistics v. 22)
6
5
4
3
2
1
0
1
2
12000
11500
11000
10500
10000
9500
9000
8500
8000
7500
7000
6500
6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
∆ global temperature 5th e 95th
percentis
HOLOCENE PERIOD
Global 12K GMS T temperature 5th and 95th percentis
global_5 global_95
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Thus, once stationarity was achieved (see p. 79), we could model it with an autoregressive process (AR), which we
represented by Yₜ the Median (Md) at period t (Holocene) as:
where δ is the mean of Y and ut is an uncorrelated random error with zero mean and constant variance ᾳ² (this is white
noise); thus Yt follows a firstorder stochastic autoregressive or AR process (1).
The AR process we have just discussed is not just a mechanism that may have generated Y. In this case, Y may evolve into
a first order moving average process, or an MA (1). If we model Y in as shown below:
Y + ß
(2)
where µ is a constant and u, as before, is a white noise stochastic error term. Here Y at period t is equal to a constant plus
a moving average of the current and past error terms. More generally, we can represent it like this
(3)
which is an MA(q) process. Briefly, a moving average process is a linear combination of white noise error terms.
Therefore Y, most likely has characteristics of both AR and MA and is therefore ARMA. Then Yt follows an ARMA (1,1)
process, and can be written as
(4)
because there is an autoregressive term and a moving average term. In the Equation, ɵ represents a constant term. In
general, in an ARMA (p, q) process, there will be p autoregressive terms and q moving average terms.
In the fit chart, shown in figure 4, the two lines coincide and almost overlap indicating that this is the best of the models
tested. The outliers present between 1 and 5 dates were retain to ensure the series is robust and to guarantee its impartiality
and uncertainty for future events (Stockinger & Dutter, 1987). Note: observado means observed; ajuste means adjust;
UCL: the upper control limit; LCL: the lower control limit.
Figure 4. Graph of the adjusted 12k median series
Source: elaborated by the author (SPSS Statistics)
Froom Figures 1, 2 and 4, the series are not stationary; the data do not circulate it and express a trend around a mean
line for the 12K global temperature median series (Figure 5) . Note: número de sequência means sequence number.
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Figure 5. Graphical test for stationarity
Next, we applied correlation tests, also known as "F" correlation function: ACF (automatic) and PACF (partial) to make
the series stationary, as shown in figures 6 and 7, and Table 1. Note: coeficiente means coefficient. Número de retardo
means Lag numbers.
Figure 6. Graphical test of autocorrelation (automatic)
Table 1. LJung Box statistical report (Ho and H₁ hypotheses)
Automatic correlations
Series: MdTempGlob
Lag
Autocorrelation
Standard
Errora
BoxLjung Statistics
Value
df
Sig.b
1
,956
,090
113,376
1
,000
2
,887
,089
211,775
2
,000
3
,821
,089
296,777
3
,000
4
,759
,089
370,121
4
,000
5
,702
,088
433,357
5
,000












16
,246
0,84
723,810
16
,000
a. The underlying process considered is independence (white noise).
b. Based on the asymptotic chisquare approximation.
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Figure 7. Graphical test of partial autocorrelation – PACF
Graphical and correlation analysis indicated that we had to normalize the series to make it stationary. The process
occured with the choice of the first lag (lag), which exceeded the confidence interval in both tests and whose degree of
graphical significance was higher, i.e., it had the highest correlation and the lowest value according to the LjungBox
statistic. The lag that met these criteria, therefore, was number 1, highlighted in Table 1.
From these results, we graphically represented (Figure 8) the stationarity adjusted, as a function of the first
differentiation (lag 1):
Figure 8. Adjusted stationarity as a function of lag 1
We then replicated this modeling for the probabilistic analysis of the uncertainties, represented by the 5th and 95th
percentiles, at a 90% confidence level, since it assumed the same stationarity criteria and tests (graph and correlogram)
of the median. The graphical representation of the uncertainty set is described in the supplementary file.
2.2 Applying the Box Jenkins Model
BoxJenkins’s method aims (Figure 9) is to estimate a statistical model and interpret it according to the sample data. If
this estimated model is used for forecasting, we should assume that its characteristics are constant over the period and
particularly in future periods. Any model that is inferred based on stationary data can be interpreted as stationary or
stable and therefore provides a valid basis for prediction (Pokorny, 1987, Gujarati and Porter, 2011).
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Figure 9. The Box–Jenkins methodology
Step 1: Identification. We concluded this step by finding the appropriate values of p, d and q. We also showed how the
correlogram and the partial correlogram facilitated this task.
Step 2: Estimation. We identified the appropriate p and q values and estimated the parameters of the autoregressive and
moving average terms included in the model.
Step 3: Diagnostic check. Having chosen a particular ARIMA model and estimated its parameters, the chosen model
fitted the data perfectly as attested by the white noise of the residuals.
Step 4, Forecasting: One of the reasons why ARIMA modeling is popular is due to its success in forecasting. In many
cases, ARIMA forecasts for both long and shortterm variables,are more reliable than those obtained from traditional
econometric modeling (Gujarati and Porter, 2011, p. 762;778).
We concluded that the MedTempGlobal (as described in the data/figures) time series model was not stationary and we
had to normalize it, making it stationary with constant mean and variance and its covariance invariant over time.
Therefore, it is an integrated time series, i.e., it combines the two autoregressive processes (AR and MA) in the same set.
An important point to note is that when using the Box Jenkins methodology, we must have both a stationary time series
and a time series that is stationary after one or more differentiations (Gujarati and Porter, 2011).
Then, we can state that if a time series is integrated of order 1, therefore, it is I (1), after differentiating it becomes I (0),
that is, stationary. In general, if a time series is I (d), after differentiating it d times, we get an I (0) series.
If one has to differentiate a time series d times to make it stationary and apply the ARMA (p, q) model to it, one will say
that the original time series is ARIMA (p, d, q), that is, it is a moving average integrated autoregressive time series,
where p denotes the numbers of the autoregressive terms, d the number of times the series must be differentiated before it
becomes stationary, and q the number of moving average terms.
We, therefore, have in this time series an ARIMA (1,0,1) model, as it was differentiated once (d = 1) before becoming
stationary (of first difference), and can be modeled as an ARMA (1,1) process, as it has an AR term and an MA post
stationarity.
Finally, it is important to emphasize that to optimize the results, it was necessary to run in the software SPSS  Statistics all
the possible combinations of the ARIMA model (p,d,q) in the two parameters, to arrive at the statistically optimal model
after the decomposition of the data and meeting the criteria of analysis and execution.
3. Results
The parameters used in this study were the median and the 5th and 95th percentiles representing the estimate of
uncertainties with 90% confidence, as recommended by authors below:
“Future users of this reconstruction use the full ensemble when considering
the plausible Holocene GMST evolution. By representing the multimethod
reconstruction as a single time series, the median of the ensemble may be best
along with the 90% range of the ensemble to represent uncertainty."
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(Kaufman et al., 2020, p.04).
As per the model parameters, predictions for the median were expressed as temperature estimates for the next 100 years
represented by AR and MA. For statistical reliability, the degree of significance (Marôco, 2018) of the measured
parameters must be extremely significant in AR and very significant in MA, as shown on the output of table 2.
Table 2. 100year scale temperature estimates of AR and MA parameters
Arima model parameters
Estimate
SE
t
Sig.
MdTempGlobModel_1
MdTempGlob
No transformation
Constant
,191
,129
1,489
,139
AR
Lag 1
,932
,032
28,799
,000
MA
Lag 1
,266
,099
2,695
,008
Source: Author elaboration with Software SPSS  Statistics v. 22.
(URL: https://www.ibm.com/support/pages/spssstatistics220availabledownload).
For the uncertainty results, the 5th and 95th percentiles, a similar to that used for the median, whose configuration is
described in a supplementary file, was used. The following parameters were generated for the uncertainty results as
shown in table 3:
Table 3. Output of the parameters of the 5th and 95th percentile temperatures (model uncertainty)
ARIMA model parameters
Estimate
SE
t
Sig.
GLOBAL5Model_1
GLOBAL5
No transformation
Constant
2,403
3,490
,688
,493
AR
Lag 1
,999
,003
291,464
,000
MA
Lag 1
,700
,069
10,111
,000
GLOBAL95Model_2
GLOBAL95
No transformation
Constant
,149
,684
,218
,828
AR
Lag 1
,996
,006
179,006
,000
MA
Lag 1
,382
,106
3,593
,000
Source: Author elaboration (SPSS  Statistics v. 22).
We then had a set of six different extremely significant temperature results for the estimates of the two models: 0.932℃;
0.266℃ (Tab. 2) and 0.999℃; 0.70℃; 0.996℃; 0.382℃ (Tab. 3). The median, extracted from the set of estimates of
the two models, whose result was 0.333℃, was the most appropriate statistical measure in this case to fulfill the
objective of this study to calculate and adopt a reference standard measure. Based on our results, by the end of this
millennium we will have an average global temperature below the 1.50°C to 2.00°C projected by the IPCC. Thus, our
results indicate that, contrary to warming, the world may experience a period of decreasing temperatures over the next
hundred years.
4. Discussion
Why there is so much consensus around a scenario that leaves much room for doubt? Why there is so much scientific
unanimity around anthropogenic warming (97.2% according to Cook et al., 2013), now called "climate change"?
When comparing recent temperatures to the distribution of global maximum temperatures during the Holocene, on
average there has been a 1℃ increment over the preindustrial period (18501900) and for most members of the ensemble.
Furthermore, no 200year interval during these series exceeded the warmth of the most recent decade (Kaufman et al., p.
5, 2000). The time horizon of the anthropogenic thesis is more recent when compared to the time of man's existence on
earth (Holocene) and when the time of the anthropogenic thesis is compared to the results of this research, it lacks
substantiation if analyzed in the light of statistical science.
On the other hand, Kaufman et al., (2020), who relied on the IPCC projections, admit that this century’s temperatures are
likely to exceed 1℃ when compared to those of the preindustrial era (18001900), which they considered as an anomaly
of 0℃. Although the authors claim that the Holocene GMST reconstruction is comparable to the IPCC longterm
projections and those seen in the last decade, the results presented here show a different and antagonistic scenario
especially if one considers a hundredyear scale and the historical temporality present in the statistical series.
Furthermore, in the graphical temporal observations of the studies by Kaufman et al. (2020, p.6, fig. 3), Davis (2017, p. 6,
fig. 5) and Moberg et al. (2005, p. 3, fig. 2), there is significant climate variability every 2K years casting doubt on
establishing anthropogenicity as a criterion for the last 150 years. These observations are confirmed by Moberg et al.
(2005) who conclude that "The resulting model reconstruction supports the case that multicentennial natural variability
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has been larger than is commonly thought, and that considerable natural climate variation can be expected in future." One
of the villains of anthropogenic genesis, the greenhouse effect, was unveiled in 1896 by Arrhenius as a natural
phenomenon beneficial to the development of biological life on the earth's surface (troposphere). Arrhenius’ studies were
subsequently confirmed by Miller & Spoolman (2016), who stated that, "Our climate, lives, and economies depend on the
natural greenhouse effect. Greenhouse gases absorb heat radiated by the earth and the gases then emit infrared radiation
that warms the atmosphere. Without the natural greenhouse effect, the earth would become cold and uninhabitable." On
the contrary, other studies on the threat of the manmade greenhouse effect, such as those by Gillett & Matthews (2010)
and Anderson, Hawkins & Jones (2016), are inconclusive regarding the magnitude of these effects and demonstrate
uncertainty when set against the complexity of the earth's geophysical and climate systems. Therefore, reinventing this
evidence as the proponents of anthropogeny orthodoxly claim, is something that does not hold up considering the
historical veracity of science.
It is important to say our results do not ignore the impact that human action has brought to recent climate change which
however appears insignificant in the face of the millennial variability of the climate, the size and complexity of the
universe, and all the natural and astronomical phenomena that interact with the earth in the planetary system. Lastly, our
predicted climate scenario cannot determine what are the true causes of recent climate change, whether natural or
anthropogenic, since the two may be complementary, not divergent. Further studies on paleoclimate and its variability
are needed to corroborate the estimates resulting from this research and to avail more evidence in the search for scientific
truth.Therefore, reinventing this evidence as the proponents of anthropogeny orthodoxly claim, is something that does not
hold up considering the historical veracity of science. However, our results do not ignore the impact that human action has
brought to recent climate change which however appears insignificant in the face of the millennial variability of the
climate, the size and complexity of the universe, and all the natural and astronomical phenomena that interact with the
earth in the planetary system. Lastly, our predicted climate scenario cannot determine what are the true causes of recent
climate change, whether natural or anthropogenic, since the two may be complementary, not divergent. Further studies
on paleoclimate and its variability are needed to corroborate the estimates resulting from this research and to avail more
evidence in the search for scientific truth.
5. Conclusion and Policy Recommendation
In view of our findings, it is unreasonable to subject governments and organizations to be hostages of a doubtful thesis
with all its consequences in the face of scientific relativity. Subjecting government organizations and governments to the
current consensus may condemn humanity to unjustifiable climate catastrophism.
All actors involved in the global climate change movement ought to be heard and their opinions taken into consideration
especially when it comes to phenomena not yet proven by time and human experimentation. Every scientific consensus
should not be treated as absolute truth; one of the pillars of science, which has always thrived on seeking truth through doubt.
Nevertheless, this article does not belittle the public, governmental and corporate policies in relation to the alarmism that is
being given to climate change. Any public or private initiative to mitigate the impact that the planet suffers due to human
action is laudable and necessary. But the future and the progress of the next generations, especially in third world countries,
should be compromised by an ‘official’ scientific narrative that has become official; a narrative that is to the detriment of a
minority that thinks and researches differently, but with foundations and arguments as important or equal to it.
Data Records
The data collected for this research were extracted from Kaufman et al., 2020, as referenced in the text. After processing,
the data were fed into IBMSPSS Statistics v. 22, at
https://www.ibm.com/docs/en/spssstatistics/SaaS?topic=referencearima, for analysis and the of results’ generation.
These data are avaiable in the figshare repository:
https://figshare.com/articles/dataset/ArimaMedTempGlobal_spv/14429006;https://figshare.com/articles/dataset/Spreads
heet_for_entering_and_processing_paleoclimate_data_and_graphs_with_the_results_of_the_model_/14429273;https://f
igshare.com/articles/dataset/Mathematical_and_operational_foundations_of_the_model_mediana_and_uncertainties_/1
4442701.
Technical Validation
All data validation were done on the ARIMA platform of SPSSStatistics as described in the body of the manuscript and
in the data repository. For logistical reasons, only the data that satisfied the criterial for the research methodology is
available in the repository.
Acknowledgements
Special thanks and recognition to professors Claudio Antonio Rojo and Edison Luiz Leismann, who provided all the
support required to carry out this research. We also wish to acknowledge the legacy left behind by the authors cited in
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this paper, besides Kaufman et al. (2020): Routson et al. (2019), Cook et al. (2013), PAGES 2k Consortium, Marcott et
al. (2013), Harde (2019), Box & Jenkins (1978), Gujarati & Porter (2011), to whom we am indebted for the knowledge
acquired.
Author contributions statement
G. V. F. S. and L.G.C designed the experiment (s), C. A. R. and E. L. L. conducted the experiments, E. L. L. and C. A.
R. analyzed the results. All authors reviewed the manuscript and approved the final version for publication.
Competing interests and funding sources
The authors declare no competing interests. The authors did not receive any grants from funding agencies in the public,
commercial, or nonprofit sectors to do this research.
Additional information
Correspondence and requests for materials should be addressed to G.V. F. S.
Author’s information
G.V.F.S: https://orcid.org/0000000162162126
L.G.C: https://orcid.org/0000000290437024
C. A. R: https://orcid.org/0000000344849033
E. L. L: https://orcid.org/0000000241128241
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