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2011.13240#0
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Blockchain mechanism and distributional characteristics of cryptos
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Blockchain mechanism and distributional characteristics of
cryptos∗
Min-Bin Lin†Kainat Khowaja‡Cathy Yi-Hsuan Chen§
Wolfgang Karl H ardle¶
Abstract
We investigate the relationship between underlying blockchain mechanism of cryptocurren-
cies and its distributional characteristics. In addition to price, we emphasise on using actual
block size and block time as the operational features of cryptos.
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2011.13240#1
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2011.13240
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2011.13240#1
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Blockchain mechanism and distributional characteristics of cryptos
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We use distributional charac-
teristics such as fourier power spectrum, moments, quantiles, global we optimums, as well as
the measures for long term dependencies, risk and noise to summarise the information from
crypto time series.
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2011.13240#0
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2011.13240#2
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2011.13240
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2011.13240#2
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Blockchain mechanism and distributional characteristics of cryptos
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With the hypothesis that the blockchain structure explains the distribu-
tional characteristics of cryptos, we use characteristic based spectral clustering to cluster the
selected cryptos into ve groups.
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2011.13240#1
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2011.13240#3
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2011.13240
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2011.13240#3
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Blockchain mechanism and distributional characteristics of cryptos
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We scrutinise these clusters and nd that indeed, the clus-
ters of cryptos share similar mechanism such as origin of fork, diculty adjustment frequency,
and the nature of block size.
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2011.13240#2
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2011.13240#4
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2011.13240
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2011.13240#4
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Blockchain mechanism and distributional characteristics of cryptos
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This paper provides crypto creators and users with a better un-
derstanding toward the connection between the blockchain protocol design and distributional
characteristics of cryptos.
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2011.13240#5
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2011.13240
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2011.13240#5
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Blockchain mechanism and distributional characteristics of cryptos
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Keywords: Cryptocurrency, price, blockchain mechanism, distributional characteristics,
clustering
JEL Classication: C00
∗Financial support of the European Union's Horizon 2020 research and innovation program \FIN- TECH: A Finan-
cial supervision and Technology compliance training programme" under the grant agreement No 825215 (Topic: ICT-
35-2018, Type of action: CSA), the European Cooperation in Science & Technology COST Action grant CA19130 -
Fintech and Articial Intelligence in Finance - Towards a transparent nancial industry, the Deutsche Forschungs-
gemeinschaft's IRTG 1792 grant, the Yushan Scholar Program of Taiwan and the Czech Science Foundation's grant
no.
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Blockchain mechanism and distributional characteristics of cryptos
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19-28231X / CAS: XDA 23020303 are greatly acknowledged.
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2011.13240#7
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Blockchain mechanism and distributional characteristics of cryptos
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†International Research Training Group 1792, Humboldt-Universit at zu Berlin, Spandauer Str.
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2011.13240#8
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Blockchain mechanism and distributional characteristics of cryptos
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1, 10178 Berlin,
Germany.
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2011.13240#9
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2011.13240#9
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Blockchain mechanism and distributional characteristics of cryptos
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Email: min-bin.lin@hu-berlin.de
‡International Research Training Group 1792, Humboldt-Universit at zu Berlin, Spandauer Str.
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2011.13240#8
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2011.13240
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Blockchain mechanism and distributional characteristics of cryptos
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1, 10178 Berlin,
Germany.
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2011.13240#11
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2011.13240
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2011.13240#11
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Blockchain mechanism and distributional characteristics of cryptos
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Email: kainat.khowaja@hu-berlin.de
§Adam Smith Business School, University of Glasgow, United Kingdom; IRTG 1792 High Dimensional Non
Stationary Time Series, Humboldt-Universit at zu Berlin. Email: cathyyi-hsuan.chen@glasgow.ac.uk
¶BRC Blockchain Research Center, Humboldt-Universit at zu Berlin, Berlin, Germany; Sim Kee Boon Institute,
Singapore Management University, Singapore; WISE Wang Yanan Institute for Studies in Economics, Xiamen Uni-
versity, Xiamen, China; Dept.
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Blockchain mechanism and distributional characteristics of cryptos
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Information Science and Finance, National Chiao Tung University, Hsinchu, Taiwan,
ROC; Dept.
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Blockchain mechanism and distributional characteristics of cryptos
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Mathematics and Physics, Charles University, Prague, Czech Republic, Grants{DFG IRTG 1792 grate-
fully acknowledged.
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2011.13240#14
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2011.13240
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2011.13240#14
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Blockchain mechanism and distributional characteristics of cryptos
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Email: haerdle@hu-berlin.de
1arXiv:2011.13240v2 [cs.CR] 24 Aug 2021
1 Introduction
Cryptocurrency (crypto) is a digital asset designed to be as a medium of exchange wherein individual
coin ownership is recorded in a digital ledger or computerised database.
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2011.13240#13
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2011.13240#15
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2011.13240
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2011.13240#15
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Blockchain mechanism and distributional characteristics of cryptos
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Its creation of monetary
units and verication of fund transactions are secured using encryption techniques and distributed
across several nodes (devices) on a peer-to-peer network.
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2011.13240#14
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2011.13240#16
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2011.13240
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2011.13240#16
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Blockchain mechanism and distributional characteristics of cryptos
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Such technology-enhanced and privacy-
preserving features make it potentially dierent to other existing nancial instruments and has
attracted attention of many investors and researchers (H ardle et al., 2020).
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2011.13240#15
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2011.13240#17
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2011.13240
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2011.13240#17
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Blockchain mechanism and distributional characteristics of cryptos
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Many studies have
investigated the similarity between a pool of cryptocurrencies in order to classify the important
features of digital currencies.
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2011.13240#16
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2011.13240#18
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2011.13240
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2011.13240#18
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Blockchain mechanism and distributional characteristics of cryptos
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For example, Blau et al.
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2011.13240#17
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2011.13240#19
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2011.13240
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2011.13240#19
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Blockchain mechanism and distributional characteristics of cryptos
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(2020) has concluded that the top sixteen
most active cryptocurrencies co-move with bitcoin.
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2011.13240#18
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2011.13240#20
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2011.13240
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2011.13240#20
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Blockchain mechanism and distributional characteristics of cryptos
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Researchers have also focused on describing the
price behaviour of cryptos using economic factors (Ciaian et al., 2016; Sovbetov, 2018).
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2011.13240#19
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2011.13240#21
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2011.13240
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Blockchain mechanism and distributional characteristics of cryptos
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However,
owing to the unique technology of cryptocurrencies, there still exists a gap between the creators of
blockchain mechanism and users operating the nancial market of the crytocurrencies and through
this research, we aim to take a step towards mitigating that gap.
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2011.13240#20
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2011.13240#22
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2011.13240
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2011.13240#22
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Blockchain mechanism and distributional characteristics of cryptos
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We specialise our research on the following research questions.
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2011.13240#21
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2011.13240#23
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2011.13240
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2011.13240#23
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Blockchain mechanism and distributional characteristics of cryptos
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First, we characterise crypto
behaviour using distributional characteristics of time series data.
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2011.13240#22
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2011.13240#24
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2011.13240
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2011.13240#24
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Blockchain mechanism and distributional characteristics of cryptos
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Also, instead of using the prices
alone, we use actual block time and block size to incorporate the operational features of cryp-
tos.
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2011.13240#23
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2011.13240#25
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2011.13240
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2011.13240#25
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Blockchain mechanism and distributional characteristics of cryptos
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Second, we hypothesise that the blockchain structure that the coin attaches plays a pivotal
role in explaining the behaviour.
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2011.13240#24
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2011.13240#26
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2011.13240
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2011.13240#26
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Blockchain mechanism and distributional characteristics of cryptos
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More explicitly, we investigate the extent to which blockchain
structure leads to explain the distributional characteristics.
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2011.13240#25
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2011.13240#27
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2011.13240
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2011.13240#27
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Blockchain mechanism and distributional characteristics of cryptos
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Using a characteristic based clustering
coupled with spectral clustering technique, we group the selected cryptos into a number of clusters
and stratify the mechanisms that make the coins within the particular cluster showing the same
behaviour in price, actual block time, and actual block size, respectively.
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2011.13240#26
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2011.13240#28
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2011.13240
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2011.13240#28
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Blockchain mechanism and distributional characteristics of cryptos
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When studying cryptocurrencies, many researchers only focus on crypto price and daily returns
(Trimborn and H ardle, 2018; Hou et al., 2020).
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2011.13240#27
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2011.13240#29
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2011.13240
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2011.13240#29
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Blockchain mechanism and distributional characteristics of cryptos
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While price is important when cryptos are used
as a medium of payment, it is denitely not the only measure for evaluation of cryptocurrencies.
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2011.13240#30
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2011.13240#30
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Blockchain mechanism and distributional characteristics of cryptos
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For example, many low price coins are highly traded and many coins that are not used as medium
2
of payment have low prices, e.g., XPR and Dogecoin.
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2011.13240#29
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2011.13240#31
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2011.13240
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2011.13240#31
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Cryptos were introduced to serve various
purposes and the purpose of the coin does matter.
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2011.13240#32
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2011.13240
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2011.13240#32
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This makes it necessary to use other time series
while studying crypto markets.
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2011.13240#33
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2011.13240#33
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In this research, we propose to use actual block size and actual
block time alongside price.
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2011.13240#32
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2011.13240#34
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2011.13240
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2011.13240#34
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Blockchain mechanism and distributional characteristics of cryptos
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Actual block size is the average actual size "usage" of a single block in data storage for one
day.
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2011.13240#33
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2011.13240#35
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2011.13240
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2011.13240#35
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Blockchain mechanism and distributional characteristics of cryptos
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Since a block comprises of transaction data, it can represent the status of how a blockchain
mechanism allocates transactions to a block.
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2011.13240#34
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2011.13240#36
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2011.13240
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2011.13240#36
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Blockchain mechanism and distributional characteristics of cryptos
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We consider it a measure of scalability of the system.
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2011.13240#37
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2011.13240
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2011.13240#37
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Blockchain mechanism and distributional characteristics of cryptos
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A
well-functioning blockchain should be able to level the transaction arrivals.
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2011.13240#36
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2011.13240#38
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2011.13240
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2011.13240#38
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Blockchain mechanism and distributional characteristics of cryptos
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Transaction distribution
within a day for any crypto needs such balancing because it aects miners rewards and hence the
demand of the coin.
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2011.13240#37
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2011.13240#39
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2011.13240
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2011.13240#39
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Blockchain mechanism and distributional characteristics of cryptos
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An ideal block size would keep conrmation times from ballooning while
keeping fees and security reasonable.
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2011.13240#38
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2011.13240#40
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2011.13240
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2011.13240#40
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Blockchain mechanism and distributional characteristics of cryptos
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Therefore, actual block size of cryptos can provide insight
into the behaviour of cryptos.
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2011.13240#39
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2011.13240#41
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2011.13240
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2011.13240#41
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Blockchain mechanism and distributional characteristics of cryptos
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Actual block time, on the other hand, measures the consistency and performance of the system.
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2011.13240#40
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2011.13240#42
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2011.13240
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2011.13240#42
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Blockchain mechanism and distributional characteristics of cryptos
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It is dened as the mean time required in minutes for each day to create the next block.
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2011.13240#41
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2011.13240#43
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2011.13240
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2011.13240#43
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Blockchain mechanism and distributional characteristics of cryptos
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In other
words, it is the average amount of time for the day a user has to wait, after broadcasting their
transaction, to see this transaction appear on the blockchain.
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2011.13240#42
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2011.13240#44
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2011.13240
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2011.13240#44
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Think of crypto markets as a fast
food franchise and miners as customers who have to wait a certain time to make the purchase.
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2011.13240#43
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2011.13240#45
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2011.13240
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2011.13240#45
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Blockchain mechanism and distributional characteristics of cryptos
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If
the waiting time is shorter on certain days while on other instances, the customers have to wait
much longer, there is a discrepancy in the system.
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2011.13240#44
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2011.13240#46
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2011.13240
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2011.13240#46
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Blockchain mechanism and distributional characteristics of cryptos
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Analogously, the time series of block time, which
is the distribution of waiting time, can be seen as a service level of the whole system and it is
necessary to maintain as the users' expectation or target block time set by the system depend on
it.
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2011.13240#45
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2011.13240#47
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2011.13240
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2011.13240#47
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Blockchain mechanism and distributional characteristics of cryptos
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The idea of investigating the underlying blockchain mechanism, a cornerstone of crypto technol-
ogy, and its connection to the crypto behaviour is still in its infancy.
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2011.13240#48
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2011.13240
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2011.13240#48
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Blockchain mechanism and distributional characteristics of cryptos
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One of the rst endeavours in
explaining this relationship was made by Guo et al.
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2011.13240#47
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2011.13240#49
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2011.13240
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2011.13240#49
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Blockchain mechanism and distributional characteristics of cryptos
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(2018) who highlight that the the fundamental
characteristics of cryptocurrencies (e.g., algorithm and proof type) have a vital role in dieren-
tiating the performance of cryptocurrencies.
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2011.13240#48
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2011.13240#50
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2011.13240
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2011.13240#50
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Blockchain mechanism and distributional characteristics of cryptos
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They develop a spectral clustering methodology to
3
group cryptos in a dynamic fashion, but their research is limited in the exploitation of blockchain
characteristics.
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2011.13240#49
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2011.13240#51
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2011.13240
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2011.13240#51
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Blockchain mechanism and distributional characteristics of cryptos
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With a similar spirit, Iwamura et al.
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2011.13240#50
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2011.13240#52
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2011.13240
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2011.13240#52
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Blockchain mechanism and distributional characteristics of cryptos
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(2019) start by claiming that high
uctuation
is a re
ection of the lack of
exibility in the Bitcoin supply schedule.
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2011.13240#51
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2011.13240#53
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2011.13240
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2011.13240#53
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Blockchain mechanism and distributional characteristics of cryptos
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They further strengthen their
arguments by considering the predetermined algorithm of cryptos (specically, the proof of work)
to explain the volatility in cryptocurrency market.
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2011.13240#52
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2011.13240#54
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2011.13240
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2011.13240#54
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Blockchain mechanism and distributional characteristics of cryptos
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Zimmerman (2020) argue in their work that the
higher congestion in blockchain technology leads to higher volatility in crypto prices.
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2011.13240#53
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2011.13240#55
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2011.13240
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2011.13240#55
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Blockchain mechanism and distributional characteristics of cryptos
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They claim
that the limited settlement space in blockchain architecture makes users compete with one another,
aecting the demand.
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2011.13240#54
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2011.13240#56
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2011.13240
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2011.13240#56
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Blockchain mechanism and distributional characteristics of cryptos
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In his model, the value of cryptos is governed by its demand, making the
price sensitive to blockchain capacity.
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2011.13240#55
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2011.13240#57
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2011.13240
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2011.13240#57
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Blockchain mechanism and distributional characteristics of cryptos
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These research results, albeit true, are limited to a particular set of cryptocurrency mechanism
and do not thoroughly explain the dynamics of cryptocurrencies.
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2011.13240#56
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2011.13240#58
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2011.13240
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2011.13240#58
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Blockchain mechanism and distributional characteristics of cryptos
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Also, most of the papers only
use price as a proxy of behaviour.
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2011.13240#57
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2011.13240#59
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2011.13240
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2011.13240#59
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Blockchain mechanism and distributional characteristics of cryptos
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We advance the previous ndings by incorporating a rich set
of underlying mechanisms and connecting them to multiple time series.
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2011.13240#58
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2011.13240#60
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2011.13240
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2011.13240#60
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Blockchain mechanism and distributional characteristics of cryptos
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We take a deep dive into
eighteen cryptos with a variety of mechanisms- concluded in Garriga et al.
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2011.13240#61
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2011.13240
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2011.13240#61
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Blockchain mechanism and distributional characteristics of cryptos
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(2020))- from a technical
perspective to summarise their mechanism and algorithm designs using variables, such as consensus
algorithm, type of hashing algorithm, diculty adjustment frequency and so on.
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2011.13240#60
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2011.13240#62
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2011.13240
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2011.13240#62
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Blockchain mechanism and distributional characteristics of cryptos
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We investigate a relationship between underlying blockchain mechanism of cryptocurrencies
and the distributional characteristics.
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2011.13240#61
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2011.13240#63
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2011.13240
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2011.13240#63
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Blockchain mechanism and distributional characteristics of cryptos
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Using the a characteristic-based clustering technique, we
cluster the selected coins into a number of clusters and scrutinise the compositions of fundamental
characteristics in each group.
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2011.13240#62
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2011.13240#64
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2011.13240
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2011.13240#64
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Blockchain mechanism and distributional characteristics of cryptos
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We observe that the clusters obtained from these time series indeed
share common underlying mechanism.
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2011.13240#63
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2011.13240#65
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2011.13240
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2011.13240#65
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Blockchain mechanism and distributional characteristics of cryptos
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Through empirical evidence, we show that the cryptos forked
from same origin and same consensus mechanism tend to become part of same clustering group.
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2011.13240#64
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2011.13240#66
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2011.13240
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2011.13240#66
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Blockchain mechanism and distributional characteristics of cryptos
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Furthermore, the clusters obtained by the time series of block time have same hashing algorithms
and diculty adjustment algorithms.
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2011.13240#65
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2011.13240#67
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2011.13240
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2011.13240#67
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Blockchain mechanism and distributional characteristics of cryptos
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Also, a similar nature (static or dynamic) of block size was
observed within clusters obtained by the time series of actual block size.
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2011.13240#66
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2011.13240#68
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2011.13240
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2011.13240#68
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Blockchain mechanism and distributional characteristics of cryptos
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We conclude with empirical
evidence that the crypto behaviour is actually linked with their blockchain protocol architectures.
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2011.13240#67
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2011.13240#69
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2011.13240
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2011.13240#69
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Blockchain mechanism and distributional characteristics of cryptos
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The implications of this study are abundant.
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2011.13240#68
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2011.13240#70
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2011.13240
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2011.13240#70
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Blockchain mechanism and distributional characteristics of cryptos
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The creators of cryptocurrencies can manage the
4
impact of blockchain underlying mechanisms on the corresponding distributional characteristics, in
a consideration of adoption rate of invented coins.
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2011.13240#71
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2011.13240
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2011.13240#71
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Blockchain mechanism and distributional characteristics of cryptos
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From the users' perspective, they can make an
optimal decision in which coins should be adopted while concerning the price
uctuation.
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2011.13240#70
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2011.13240#72
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2011.13240
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2011.13240#72
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Blockchain mechanism and distributional characteristics of cryptos
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This paper proceeds as follows.
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2011.13240#73
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2011.13240
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2011.13240#73
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Blockchain mechanism and distributional characteristics of cryptos
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Section 2 discusses data source and the underlying mechanisms
of the cryptos.
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2011.13240#74
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2011.13240
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2011.13240#74
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Blockchain mechanism and distributional characteristics of cryptos
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Section 3 presents the methodology used for classifying characteristics of time series
and clustering algorithm.
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2011.13240#75
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2011.13240
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2011.13240#75
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Blockchain mechanism and distributional characteristics of cryptos
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Section 4 provides an illustration of analysis results.
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2011.13240#76
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2011.13240
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2011.13240#76
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Blockchain mechanism and distributional characteristics of cryptos
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Section 5 concludes
and provides several avenues for future research.
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2011.13240#77
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2011.13240
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2011.13240#77
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Blockchain mechanism and distributional characteristics of cryptos
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2 Data Source and Description
According to CoinMarketCap (https://coinmarketcap.com), currently there are over 7,000 cryp-
tocurrencies and their total market capitalisation has surpassed USD $400 billion as of November
09, 2020.
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2011.13240#76
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2011.13240#78
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2011.13240
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2011.13240#78
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Blockchain mechanism and distributional characteristics of cryptos
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Most of studies have focused on the mainstream coins (e.g., Bitcoin, Ethereum), and
little has been investigated on the coins which have been introduced and featured with a diverse
blockchain mechanisms and invented technologies.
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2011.13240#77
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2011.13240#79
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2011.13240
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2011.13240#79
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Blockchain mechanism and distributional characteristics of cryptos
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The work of Guo and Donev (2020) is one of
exceptions.
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2011.13240#78
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2011.13240#80
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2011.13240
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2011.13240#80
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Blockchain mechanism and distributional characteristics of cryptos
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In this study, 18 cryptos with dierent set of blockchain mechanisms have been ex-
amined {Bitcoin, Bitcoin Cash, Bitcoin Gold, Bitcoin SV, Blackcoin, Dash, Dogecoin, Ethereum,
Ethereum Classic, Feathercoin, Litecoin, Monero, Novacoin, Peercoin, Reddcoin, Vertcoin, XRP
(Ripple), and Zcash.
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2011.13240#79
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2011.13240#81
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2011.13240
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2011.13240#81
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Blockchain mechanism and distributional characteristics of cryptos
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We explore an interplay between distributional characteristics of crpytos and
blockchain mechanism.
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2011.13240#80
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2011.13240#82
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2011.13240
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2011.13240#82
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Blockchain mechanism and distributional characteristics of cryptos
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We discuss the key characteristics of blockchain mechanisms and the time
series data in this section.
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2011.13240#83
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2011.13240
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2011.13240#83
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Blockchain mechanism and distributional characteristics of cryptos
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2.1 Underlying Mechanism
Most of cryptos nowadays apply blockchain-based systems in which transactions are grouped into
blocks and cryptographically interlinked to form a back-linked list of blocks containing transactions.
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2011.13240#84
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2011.13240
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2011.13240#84
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Blockchain mechanism and distributional characteristics of cryptos
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The transactions are validated using the nodes within the crypto peer-to-peer network through
a majority consensus directed by algorithms instead of a central authority's approval.
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2011.13240#85
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2011.13240
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2011.13240#85
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Blockchain mechanism and distributional characteristics of cryptos
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In such
an operation process, many algorithmic mechanisms are required to govern the performance and
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outcome of a crypto system.
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2011.13240#84
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2011.13240#86
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2011.13240
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2011.13240#86
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Blockchain mechanism and distributional characteristics of cryptos
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Some key blockchain-based characteristics are discussed below:
Fork: It occurs as user base or developers conduct a fundamental or signicant software change,
see as in Figure 1.
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2011.13240#85
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2011.13240#87
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2011.13240
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2011.13240#87
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Blockchain mechanism and distributional characteristics of cryptos
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There are two types of forks { soft and hard forks.
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2011.13240#86
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2011.13240#88
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2011.13240
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2011.13240#88
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Blockchain mechanism and distributional characteristics of cryptos
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The former is an update
to the protocol architecture and then all the nodes are enforced to follow in order to proceed with
the operations of a crypto.
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2011.13240#89
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2011.13240
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2011.13240#89
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Blockchain mechanism and distributional characteristics of cryptos
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The latter one creates a duplicate copy of the origin blockchain and
modies the copy to meet the desired quality (e.g., safety, scalability).
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2011.13240#90
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2011.13240
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2011.13240#90
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Blockchain mechanism and distributional characteristics of cryptos
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In this case, a new crypto
can be generated accordingly.
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2011.13240#91
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2011.13240
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2011.13240#91
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Blockchain mechanism and distributional characteristics of cryptos
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For example, Peercoin network facilitates an alternative consensus
mechanism {proof-of-stake (PoS) to Bitcoin's proof-of-work (PoW) system for reducing dependency
on energy consumption from mining process (King and Nadal, 2012).
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2011.13240#92
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2011.13240
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2011.13240#92
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Blockchain mechanism and distributional characteristics of cryptos
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Going beyond a digital currency, Ethereum establishes an open-ended decentralised platform
for diverse applications such as decentralised applications (dapps) and smart contracts (Buterin,
2014).
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2011.13240#93
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2011.13240
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2011.13240#93
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Blockchain mechanism and distributional characteristics of cryptos
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Consensus mechanism: In order to establish an agreement on a specic subset of the candi-
date transactions, consensus mechanism provides a protocol for a large number of trust-less nodes
in a decentralised blockchain network.
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2011.13240#94
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2011.13240
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2011.13240#94
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Blockchain mechanism and distributional characteristics of cryptos
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For instance, PoW (Proof-of-Work, as adopted by e.g.,
Bitcoin, Litecoin) achieves consensus with a competition among miners on solving computational
puzzles, which consume numerous computational resources; and PoS (Proof-of-Stake, as adopted by
e.g., Peercoin, Blackcoin) randomly assigns a block creator (transaction validator) with probability
proportional to their coins staked.
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2011.13240#95
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2011.13240
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2011.13240#95
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Blockchain mechanism and distributional characteristics of cryptos
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Hashing algorithm: It is a mathematical algorithm that encrypts a new transaction (or a new
block) into a xed length character string, known as hash value, and later interlinks this string with
a given blockchain to ensure the security and immutability of a crypto.
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2011.13240#94
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2011.13240#96
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2011.13240
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2011.13240#96
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Blockchain mechanism and distributional characteristics of cryptos
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Various hashing algorithms
are implemented in cryptos such as SHA-256, Scrypt and Equihash.
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2011.13240#95
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2011.13240#97
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2011.13240
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2011.13240#97
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Blockchain mechanism and distributional characteristics of cryptos
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These provide dierent degree
of complexity to blockchain operations.
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2011.13240#98
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2011.13240
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2011.13240#98
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Blockchain mechanism and distributional characteristics of cryptos
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Diculty adjustment algorithm: It is an adaptive mechanism which periodically adjusts the
diculty toward hashrate to target an average time interval between blocks, known as target block
6
Figure 1: Blockchain software forks in cryptocurrency.
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2011.13240
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Blockchain mechanism and distributional characteristics of cryptos
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time or target conrmation time.
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2011.13240#100
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2011.13240
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