Pith. sign in

REVIEW 4 major objections 6 minor 100 references

Decentralization in PoS Blockchain Consensus: Quantification and Advancement

T0 review · 4 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Replacing linear stake weights with square-root or logarithmic weights improves measured decentralization of PoS blockchains by 51% and 132% respectively.

desk verdict Solid empirical measurements with a real Sybil-cost arithmetic error; the decentralization improvements are only established for a fixed validator set, not for permissionless systems. read the letter →

arxiv 2504.14351 v1 pith:DNKPSOSW submitted 2025-04-19 cs.DC cs.CYcs.ET

Shashank Motepalli , Hans-Arno Jacobsen This is my paper · ORCID
classification cs.DCcs.CYcs.ET
keywords proof-of-stakedecentralizationmetricsNakamotocoefficientGiniindexShapleyvaluesquare-rootstakeweightlogarithmicSybilcost
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to measure how decentralized proof-of-stake (PoS) blockchains actually are and to find a mechanism that makes them more so. Using a suite of metrics—Nakamoto coefficients, Gini index, Herfindahl-Hirschman index, Shapley-value Gini, and Zipf's coefficient—it finds that in ten major chains a small group of validators controls a disproportionate share of consensus weight. It then proposes two changes to how validator votes are weighted: square-root stake weight (SRSW) and logarithmic stake weight (LSW). The paper argues, and proves in formal lemmas, that both models yield higher Nakamoto coefficients and lower inequality metrics than today's linear weighting, with LSW strongest; average improvements are 51% and 132%. If true, a consensus protocol could become meaningfully more censorship-resistant and equitable without changing its underlying BFT algorithm.

What carries the argument

The load-bearing mechanism is the replacement of linear validator weight $w_i = s_i$ with concave functions of stake: $w_i^* = \sqrt{s_i}$ for SRSW and $w_i^\phi = \log(s_i)$ for LSW. These new weights enter the two-thirds quorum condition $Q \ge \frac{2}{3}\sum_i w_i$ and the per-epoch reward $r_{n_i} = \alpha w_i$. Because a concave function shrinks large stakes more than small ones, the weight distribution flattens, and by Jensen's inequality the smallest coalition able to reach one-third (for liveness) or two-thirds (for safety) of total weight must contain more validators. Thus Nakamoto coefficients rise; the same flattening lowers Gini, HHI, Zipf's coefficient, and the Gini of Shapley values.

What would settle it

Deploy SRSW or LSW on a live or testnet PoS chain and observe whether any validator rationally splits a large stake into $n$ small validators to gain extra voting weight; the model predicts no splitting when the Sybil cost $C$ exceeds the threshold derived in Section V-D, so systematic stake fragmentation across many validators would falsify the robustness claim.

Watch

Extended reading notes

Core claim

The central discovery is that the concentration of consensus influence in PoS chains is not a fixed property of having large validators; it is an artifact of the linear mapping from stake to voting power. By replacing $w_i = s_i$ with $w_i^* = \sqrt{s_i}$ or $w_i^\phi = \log(s_i)$ in the quorum-size computation, the authors show that Nakamoto coefficients (the percentage of validators needed to halt liveness or break safety) rise, while Gini, HHI, Zipf, and Shapley-value Gini all fall. Theorems 3 and 4 state the ordering: every decentralization metric under SRSW is at least as good as linear, and under LSW at least as good as SRSW, with the proofs relying on Jensen's inequality for concave functions. Empirically, across ten blockchains (Aptos, Axelar, BNB, Celestia, Celo, Cosmos, Injective, Osmosis, Polygon, Sui), the average metric improvement is 51% for SRSW and 132% for LSW.

Load-bearing premise

The paper's decentralization gains hold only if the system can enforce a Sybil cost high enough that validators do not split large stakes into many small identities, because concave weighting makes fragments collectively more powerful.

Editorial extensions

If this is right

  • A PoS chain adopting SRSW or LSW only needs to change how voting weights and rewards are computed at epoch boundaries; the underlying BFT consensus remains the same.
  • Liveness and safety Nakamoto coefficients increase substantially, so a would-be censoring or ledger-rewriting coalition must capture a larger fraction of the validator set.
  • Reward growth flattens for large stakeholders, slowing the rich-get-richer compounding that concentrates stake over time.
  • LSW consistently outperforms SRSW across all measured metrics, so protocols seeking maximum decentralization can choose LSW, while SRSW offers a computationally cheaper intermediate step.
  • The measured concentration in ten existing chains (Gini 0.35–0.8, liveness Nakamoto coefficients below 16%) indicates the problem is real and current, not hypothetical.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Concavity, not the specific square-root or log form, is what drives the improvement; any strictly concave weighting (e.g., cubic root, $\ln(1+s)$) would sit between linear and LSW, suggesting a tunable design space the paper does not explore.
  • The formal theorems assume validators do not fragment their stake; if the Sybil cost $C$ is not enforceable in practice, a rational large stakeholder could split into many identities and, under a concave weighting scheme, actually increase total voting power, undermining the claimed robustness. The paper acknowledges this socio-economic hurdle.
  • The near-perfect correlation between Shapley-value Gini and stake-weight Gini suggests Shapley metrics add little information, so a simpler index could monitor decentralization at lower computational cost.
  • The improvement numbers are computed on the same validator sets with weights recalculated; a real deployment would change staking incentives, so the measured 51% and 132% may not persist once validators adjust their behavior.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper studies decentralization of proof-of-stake consensus by measuring ten blockchains across several metrics (Nakamoto coefficients for liveness and safety, Gini index, HHI, Shapley-based Gini indices, and Zipf's coefficient). It reports significant stake concentration in existing systems and proposes two alternative stake-weighting schemes: Square Root Stake Weight (SRSW) and Logarithmic Stake Weight (LSW). Using the same validator sets, the paper recalculates weights and reports percentage improvements in decentralization metrics, with average improvements of 51% for SRSW and 132% for LSW across the seven metrics (Table IV). The authors also provide formal statements (Lemmas 1--2, Theorems 3--4) that these schemes improve decentralization, and discuss Sybil cost as a mechanism to prevent stake fragmentation.

Significance. If the claims are established, the paper offers a simple, protocol-level intervention that reduces stake concentration in PoS consensus and provides a reproducible empirical dataset (public GitHub repository, defined metrics, and a comparison table that can be recalculated). The proposal is easy to state and the empirical evaluation covers a diverse set of chains. However, the significance is tempered by two issues: the improvements in inequality metrics are largely mechanical consequences of applying concave transformations to weights, and the practical guarantee in permissionless settings depends on an enforceable Sybil cost, which the paper does not establish. The formal analysis, as written, does not meet the standard of rigorous proof promised in the introduction.

major comments (4)
  1. [Section V-D, Eqs. (21)-(22) and Sybil cost derivation] The Sybil cost bounds are arithmetically incorrect. For SRSW, the no-split condition is sqrt(S) > n*sqrt(S/n) - C, which gives C > (sqrt(n)-1)*sqrt(S), not the paper's stated C >= (sqrt(n)-1)/(n-1)*sqrt(S); for n>2 the paper underestimates the required cost by a factor of n-1. For LSW, the condition ln(1+S) > n*ln(1+S/n) - C gives C > n*ln(1+S/n) - ln(1+S), which for large S behaves as (n-1)*ln S - n*ln n and thus grows without bound, whereas the paper states C >= ln(n)/(n-1), a constant independent of S. Because both weighting functions are subadditive, a rational validator with large stake increases its total weight by splitting, and without an enforceable, correctly bounded Sybil cost the decentralization improvements in Table IV cannot be guaranteed in permissionless settings. The paper's own admission in Section V-D that establishing Sybil costs is 'a complex socio-economic challenge' beyond scope directly conflicts with the abstract's claim that the models 'support more equitable and resilient blockchain systems.'
  2. [Section VI-A, Lemmas 1--2 and Theorems 3--4] The formal analysis is not rigorous. Lemma 1 asserts that Jensen's inequality 'necessitates' a larger subset K* for the square-root weights, but no majorization or ordering argument is provided; the proof is a sketch. Lemma 2 is a prose paragraph asserting that the square-root transformation yields a lower Gini index, which is plausible but not proven. Theorem 3 states that HHI, Shapley-Gini, and Zipf's coefficient all improve without any derivation, and Theorem 4 asserts that LSW dominates SRSW because 'log(s) is more concave than sqrt(s)', a claim that is not true on the entire positive domain (for large s, the second derivative of sqrt(s) has larger magnitude than that of ln(1+s)). Since the introduction promises 'rigorous proofs that justify the observed results,' these gaps must be filled or the statements should be reframed as conjectures supported solely by the empirical evaluation.
  3. [Section IV-B / Table IV (interpretation of improvements)] The reported improvements are to a significant extent by construction rather than empirical discovery. Gini, HHI, and Shapley-based Gini are inequality measures that decrease under any concave increasing transformation of weights, and Nakamoto coefficients increase because concave transformations reduce the top-k share of total weight. The paper should explicitly acknowledge this and clarify that the contribution is the specific proposal and its quantitative evaluation on real validator sets, not a new formal theorem about decentralization. Without this clarification, the formal analysis in Section VI-A overstates the novelty of the results.
  4. [Section IV-B / Table III and Table IV (Zipf coefficient)] The methodology for computing the Zipf coefficient Z is not described. The paper does not state whether Z is estimated by ordinary least squares on log-log ranked weights, which rank range is used, or how the 'Z (%)' improvements in Table IV are derived. The near-uniform values (approximately 50% for SRSW and 95% for LSW across all ten chains) suggest a deterministic transformation of the fitted exponent, but the reader cannot verify this without the estimation procedure. Please provide the exact calculation and, ideally, the fitted exponents for the linear, SRSW, and LSW models.
minor comments (6)
  1. [Table IV] The column headers 'GφL (%)' appear twice; the second occurrence should presumably be 'GφS (%)'.
  2. [Section V-C and Eq. (26)] The logarithm base is inconsistent: Section V-C defines w_i^φ = log(s_i), while Eq. (26) and the Sybil analysis use ln(1+s_i). Please specify the base and clarify whether the +1 is part of the proposed LSW weighting or only used in the calculations.
  3. [Table I] The table header contains a typo: 'Priniciple' should be 'Principle'.
  4. [Figure 3] The y-axis label reads 'Zipf's Coefficient ( )' with an empty placeholder; the symbol is missing.
  5. [References] Reference [18] for Celestia points to https://celo.org/, which appears to be a copy-paste error; it should point to the Celestia documentation.
  6. [Section IV-A] The statement that all examined blockchains 'employ DPoS for Sybil resistance' is a broad generalization; Aptos and Sui are commonly described as PoS with delegated staking rather than DPoS, and this distinction should be qualified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the decentralization improvements are derived from explicitly stated concave weight maps and externally defined metrics; the Sybil-cost caveat is an admitted robustness gap, not a circular step.

full rationale

The paper's central derivation chain is self-contained rather than circular. The decentralization metrics (Gini, Nakamoto coefficients, HHI, Shapley-Gini, Zipf) are defined externally in Section III on validator weights, and the SRSW and LSW models are fixed transformations of stake (Eqs. 18 and 23). The claimed improvements are proved as mathematical consequences of concavity (Lemmas 1-2, Theorems 3-4, Eqs. 27-33), not obtained by fitting parameters to the data. No parameter is calibrated to the ten-blockchain dataset; Section VI-B simply recomputes the same externally defined metrics under the proposed weights. The self-citations to prior work [70] for SRSW and metric adaptation are not load-bearing, because the relevant inequalities are re-derived in this paper and the metrics are standard external tools. The paper explicitly acknowledges in Section V-D that establishing Sybil costs is 'a complex socio-economic challenge' and 'beyond the scope of this work'; that is a limitation of the permissionless robustness claim, not a reduction of the claimed result to its own inputs. Theorem 4's extension from Nakamoto coefficients to Shapley-Gini and Zipf is asserted more than proved, but that is an evidentiary gap, not a circularity.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No fitted constants are needed to produce the reported metric improvements; the transformation functions are fixed. The practical viability rests on the Sybil-cost and rationality assumptions above. SRSW and LSW are model families rather than new physical entities.

free parameters (2)
  • M (maximum validator set cardinality) = not prescribed
    Proposed design parameter for limiting validator count; no specific value is chosen, and the paper states it depends on algorithm and implementation (Section V-D).
  • Sybil cost C = no concrete implemented value
    Assumed sufficiently high to deter stake splitting; minimum expressions are derived but no deployment mechanism is selected (Section V-A, V-D).
assumptions (4)
  • domain assumption Validators are rational reward maximizers (Section V-A, Eq. 16).
    The Sybil-deterrence argument for SRSW/LSW relies on reward comparison; if validators pursue governance power or other objectives, the fragmentation equilibrium changes.
  • domain assumption Quorum thresholds remain 1/3 and 2/3 after nonlinear reweighting, with unchanged BFT fault-tolerance assumptions (Section II-B, Eq. 5; Section VI-A).
    The formal metrics and safety claims assume a 2/3 quorum and 1/3 adversary bound continue to hold when weights are transformed, but attack economics under reweighted stake are not re-derived.
  • standard math Jensen's inequality applied to concave transformations implies monotone increases in Nakamoto coefficients and monotone decreases in Gini, HHI, Shapley, and Zipf metrics (Section VI-A, Lemmas 1-2, Theorems 3-4).
    This is the mathematical engine of the formal analysis; the proof in the paper is only a sketch and does not actually demonstrate the required subset-cardinality inequalities.
  • ad hoc to paper A high Sybil cost C can be enforced in practice (Section V-A, V-D).
    This is the load-bearing practical assumption; the paper itself lists candidate mechanisms but says establishing Sybil costs is beyond its scope.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Decentralization in PoS Blockchain Consensus: Quantification and Advancement." pith.science (2026). https://pith.science/paper/DNKPSOSW

@misc{pith2026250414351,
  author       = {Pith},
  title        = {Pith review of: Decentralization in PoS Blockchain Consensus: Quantification and Advancement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DNKPSOSW}},
  note         = {Machine review of arXiv:2504.14351}
}
read the original abstract

Decentralization is a foundational principle of permissionless blockchains, with consensus mechanisms serving a critical role in its realization. This study quantifies the decentralization of consensus mechanisms in proof-of-stake (PoS) blockchains using a comprehensive set of metrics, including Nakamoto coefficients, Gini, Herfindahl Hirschman Index (HHI), Shapley values, and Zipfs coefficient. Our empirical analysis across ten prominent blockchains reveals significant concentration of stake among a few validators, posing challenges to fair consensus. To address this, we introduce two alternative weighting models for PoS consensus: Square Root Stake Weight (SRSW) and Logarithmic Stake Weight (LSW), which adjust validator influence through non-linear transformations. Results demonstrate that SRSW and LSW models improve decentralization metrics by an average of 51% and 132%, respectively, supporting more equitable and resilient blockchain systems.

Figures

Figures reproduced from arXiv: 2504.14351 by the authors.

Figure 1
Figure 1. Comparison of Nakamoto coefficients for safety and liveness in linear, SRSW and LSW weighting functions [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Comparison of Gini index Aptos Axelar Binance Celestia Celo Cosmos Injective Osmosis Polygon Sui 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Zip f's C o e f ficie n t ( ) 5.68 w = s SRSW * LSW [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Comparison of Zipf’s law coefficient B. Empirical Validation In this subsection, we use the validator set data outlined in Section IV to recalculate weights using SRSW and LSW func￾tions. We then compare decentralization metrics of the SRSW and LSW models against the linear stake weight model for specified validator sets. Our observations confirm the results of formal analysis. Our findings across the decentralizati… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Implications of updated weight on block proposals and rewards [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

100 extracted references · 66 canonical work pages

  1. [1]

    Proof-of-fee, part 2

    0L. Proof-of-fee, part 2. https://0l.network/2022/10/20/proof-of-fee- part-2-a-proposal/. Accessed: 2023-12-15

    2022

  2. [2]

    Re- fining jensen’s inequality

    Shoshana Abramovich, Graham Jameson, and Gord Sinnamon. Re- fining jensen’s inequality. Bulletin math ´ematique de la Soci ´et´e des Sciences Math ´ematiques de Roumanie , pages 3–14, 2004

    2004

  3. [3]

    Injective tendermint core: A powerful consensus engine for decentralized finance

    Big Ace. Injective tendermint core: A powerful consensus engine for decentralized finance. https://medium.com/@charlesace/injective- tendermint-core-a-powerful-consensus-engine-for-decentralized- finance-a1db298b0b70. Accessed: 2023-12-14

    2023

  4. [4]

    Lazyledger: A distributed data availability ledger with client-side smart contracts

    Mustafa Al-Bassam. Lazyledger: A distributed data availability ledger with client-side smart contracts. arXiv preprint arXiv:1905.09274 , 2019

    arXiv 1905

  5. [5]

    On Finality in Blockchains

    Emmanuelle Anceaume, Antonella Pozzo, Thibault Rieutord, and Sara Tucci-Piergiovanni. On finality in blockchains. arXiv preprint arXiv:2012.10172, 2020

    work page Pith review arXiv 2012

  6. [6]

    https://aptosfoundation.org/

    Aptos. https://aptosfoundation.org/. Accessed: 2023-10-25

    2023

  7. [7]

    Dao decentralization: V oting-bloc entropy, bribery, and dark daos

    James Austgen, Andr ´es F´abrega, Sarah Allen, Kushal Babel, Mahimna Kelkar, and Ari Juels. Dao decentralization: V oting-bloc entropy, bribery, and dark daos. arXiv preprint arXiv:2311.03530 , 2023

    arXiv 2023

  8. [8]

    https://axelar.network/

    Axelar. https://axelar.network/. Accessed: 2023-10-25

    2023

Show all 100 references
  1. [9]

    Mysticeti: Reaching the limits of latency with uncertified dags

    Kushal Babel, Andrey Chursin, George Danezis, Anastasios Kichidis, Lefteris Kokoris-Kogias, Arun Koshy, Alberto Sonnino, and Mingwei Tian. Mysticeti: Reaching the limits of latency with uncertified dags. arXiv preprint arXiv:2310.14821 , 2023

  2. [10]

    State machine replication in the libra blockchain

    Mathieu Baudet, Avery Ching, Andrey Chursin, George Danezis, Franc ¸ois Garillot, Zekun Li, Dahlia Malkhi, Oded Naor, Dmitri Perel- man, and Alberto Sonnino. State machine replication in the libra blockchain. The Libra Assn., Tech. Rep , 7, 2019

    2019

  3. [11]

    A survey on blockchain interoperability: Past, present, and future trends

    Rafael Belchior, Andr ´e Vasconcelos, S ´ergio Guerreiro, and Miguel Correia. A survey on blockchain interoperability: Past, present, and future trends. ACM Computing Surveys (CSUR) , 54(8):1–41, 2021

    2021

  4. [12]

    Proof-of-personhood: Rede- mocratizing permissionless cryptocurrencies

    Maria Borge, Eleftherios Kokoris-Kogias, Philipp Jovanovic, Linus Gasser, Nicolas Gailly, and Bryan Ford. Proof-of-personhood: Rede- mocratizing permissionless cryptocurrencies. In 2017 IEEE European Symposium on Security and Privacy Workshops (EuroS&PW) , pages 23–26. IEEE, 2017

    2017

  5. [13]

    Reward sharing schemes for stake pools

    Lars Br ¨unjes, Aggelos Kiayias, Elias Koutsoupias, and Aikaterini- Panagiota Stouka. Reward sharing schemes for stake pools. In 2020 IEEE european symposium on security and privacy (EuroS&p) , pages 256–275. IEEE, 2020

    2020

  6. [14]

    Tendermint: Byzantine fault tolerance in the age of blockchains

    Ethan Buchman. Tendermint: Byzantine fault tolerance in the age of blockchains. PhD thesis, University of Guelph, 2016

    2016

  7. [15]

    The latest gossip on bft consensus

    Ethan Buchman, Jae Kwon, and Zarko Milosevic. The latest gossip on bft consensus. arXiv preprint arXiv:1807.04938 , 2018

    2018 arXiv

  8. [16]

    The new merger guidelines and the herfindahl- hirschman index

    Stephen Calkins. The new merger guidelines and the herfindahl- hirschman index. Calif. L. Rev., 71:402, 1983

    1983

  9. [17]

    Practical byzantine fault toler- ance

    Miguel Castro, Barbara Liskov, et al. Practical byzantine fault toler- ance. In OsDI, volume 99, pages 173–186, 1999

    1999

  10. [18]

    https://celo.org/

    Celestia. https://celo.org/. Accessed: 2023-12-14

    2023

  11. [19]

    https://celo.org/

    Celo. https://celo.org/. Accessed: 2023-12-14

    2023

  12. [20]

    The origins of the gini index: extracts from variabilit `a e mutabilit `a (1912) by corrado gini

    Lidia Ceriani and Paolo Verme. The origins of the gini index: extracts from variabilit `a e mutabilit `a (1912) by corrado gini. The Journal of Economic Inequality, 10:421–443, 2012

    1912

  13. [21]

    https://www.bnbchain.org/

    BNB Chain. https://www.bnbchain.org/. Accessed: 2023-10-25

    2023

  14. [22]

    White paper

    BNB Smart Chain. White paper. https://github.com/bnb-chain/whitep aper/blob/master/WHITEPAPER.md. Accessed: 2023-11-08

    2023

  15. [23]

    https://coinmarketcap.com/

    CoinMarketCap. https://coinmarketcap.com/. Accessed: 2023-12-14

    2023

  16. [24]

    https://cosmos.network/

    Cosmos. https://cosmos.network/. Accessed: 2023-10-25

    2023

  17. [25]

    Flash boys 2.0: Frontrunning in decentralized exchanges, miner extractable value, and consensus instability

    Philip Daian, Steven Goldfeder, Tyler Kell, Yunqi Li, Xueyuan Zhao, Iddo Bentov, Lorenz Breidenbach, and Ari Juels. Flash boys 2.0: Frontrunning in decentralized exchanges, miner extractable value, and consensus instability. In 2020 IEEE Symposium on Security and Privacy (SP),...

    2020

  18. [26]

    Ouroboros praos: An adaptively-secure, semi-synchronous proof-of- stake blockchain

    Bernardo David, Peter Ga ˇzi, Aggelos Kiayias, and Alexander Russell. Ouroboros praos: An adaptively-secure, semi-synchronous proof-of- stake blockchain. In Advances in Cryptology–EUROCRYPT 2018: 37th Annual International Conference on the Theory and Applications of Cryptograp...

    2018

  19. [27]

    Pbft vs proof- of-authority: Applying the cap theorem to permissioned blockchain

    Stefano De Angelis, Leonardo Aniello, Roberto Baldoni, Federico Lombardi, Andrea Margheri, Vladimiro Sassone, et al. Pbft vs proof- of-authority: Applying the cap theorem to permissioned blockchain. In CEUR workshop proceedings , volume 2058. CEUR-WS, 2018

    2018

  20. [28]

    The aptos blockchain: Safe, scalable, and upgradeable web3 infrastructure

    Aptos Dev. The aptos blockchain: Safe, scalable, and upgradeable web3 infrastructure. https://aptos.dev/aptos-white-paper/. Published:2022- 08-11, v1.0

    2022

  21. [29]

    Celestia’s data availability layer

    Celestia Docs. Celestia’s data availability layer. https://docs.celesti a.org/learn/how-celestia-works/data-availability-layer. Accessed: 2023-12-14

    2023

  22. [30]

    Consensus

    Celo docs. Consensus. https://docs.celo.org/protocol/consensus. Accessed: 2023-11-26

    2023

  23. [31]

    A guide to stake-weighted quality of service on solana

    Solana Docs. A guide to stake-weighted quality of service on solana. https://solana.com/developers/guides/advanced/stake-weighted-qos. Accessed: 2025-27-03

    2025

  24. [32]

    The sybil attack

    John R Douceur. The sybil attack. In International workshop on peer- to-peer systems, pages 251–260. Springer, 2002

    2002

  25. [33]

    Foundations of dynamic bft

    Sisi Duan and Haibin Zhang. Foundations of dynamic bft. In 2022 IEEE Symposium on Security and Privacy (SP) , pages 1317–1334. IEEE, 2022

    2022

  26. [34]

    Analyzing voting power in decentralized governance: Who controls daos? arXiv preprint arXiv:2204.01176, 2022

    Robin Fritsch, Marino M ¨uller, and Roger Wattenhofer. Analyzing voting power in decentralized governance: Who controls daos? arXiv preprint arXiv:2204.01176, 2022

    2022 arXiv

  27. [35]

    The bitcoin backbone protocol: Analysis and applications

    Juan Garay, Aggelos Kiayias, and Nikos Leonardos. The bitcoin backbone protocol: Analysis and applications. In Annual international conference on the theory and applications of cryptographic techniques , pages 281–310. Springer, 2015

  28. [36]

    The estimation of the lorenz curve and gini index

    Joseph L Gastwirth. The estimation of the lorenz curve and gini index. The review of economics and statistics , pages 306–316, 1972

    1972

  29. [37]

    Jolteon and ditto: Network-adaptive efficient consensus with asynchronous fallback

    Rati Gelashvili, Lefteris Kokoris-Kogias, Alberto Sonnino, Alexander Spiegelman, and Zhuolun Xiang. Jolteon and ditto: Network-adaptive efficient consensus with asynchronous fallback. In International conference on financial cryptography and data security , pages 296–

  30. [38]

    Algorand: Scaling byzantine agreements for cryptocurrencies

    Yossi Gilad, Rotem Hemo, Silvio Micali, Georgios Vlachos, and Nickolai Zeldovich. Algorand: Scaling byzantine agreements for cryptocurrencies. In Proceedings of the 26th symposium on operating systems principles, pages 51–68, 2017

    2017

  31. [39]

    Measurement of inequality of incomes

    Corrado Gini. Measurement of inequality of incomes. The economic journal, 31(121):124–125, 1921

    1921

  32. [40]

    Axelar core

    GitHub. Axelar core. https://github.com/axelarnetwork/axelar- core/blob/main/docs/cli/axelard tendermint version.md. Accessed: 2023-11-26

    2023

  33. [41]

    know your customer

    Damian Hodgson. “know your customer”: marketing, governmentality and the “new consumer” of financial services. Management Decision, 40(4):318–328, 2002

    2002

  34. [42]

    https://injective.com/

    Injective. https://injective.com/. Accessed: 2023-12-14

    2023

  35. [43]

    Centralized decentralization: Does voting matter? simple economics of the dpos blockchain governance

    Seungwon Eugene Jeong. Centralized decentralization: Does voting matter? simple economics of the dpos blockchain governance. Simple Economics of the DPoS Blockchain Governance (April 21, 2020), 2020

    2020

  36. [44]

    Sok: blockchain governance

    Aggelos Kiayias and Philip Lazos. Sok: blockchain governance. arXiv preprint arXiv:2201.07188, 2022. 13

    2022 arXiv

  37. [45]

    The most pressing issue on ethereum is validator size growth

    Christine Kim. The most pressing issue on ethereum is validator size growth. https://www.coindesk.com/consensus-magazine/2023/09/2 9/the-most-pressing-issue-on-ethereum-is-validator-size-growth/. Accessed: 2023-12-14

    2023

  38. [46]

    A taxonomic hierarchy of blockchain consensus algorithms: An evolutionary phylogeny approach

    Heesang Kim and Dohoon Kim. A taxonomic hierarchy of blockchain consensus algorithms: An evolutionary phylogeny approach. Sensors, 23(5):2739, 2023

    2023

  39. [47]

    Is stellar as secure as you think? In 2019 IEEE European Symposium on Security and Privacy Workshops (EuroS&PW), pages 377–385

    Minjeong Kim, Yujin Kwon, and Yongdae Kim. Is stellar as secure as you think? In 2019 IEEE European Symposium on Security and Privacy Workshops (EuroS&PW), pages 377–385. IEEE, 2019

    2019

  40. [48]

    Impossibility of full decentralization in permissionless blockchains

    Yujin Kwon, Jian Liu, Minjeong Kim, Dawn Song, and Yongdae Kim. Impossibility of full decentralization in permissionless blockchains. In Proceedings of the 1st ACM Conference on Advances in Financial Technologies, pages 110–123, 2019

    2019

  41. [49]

    The byzantine generals problem

    Leslie Lamport, Robert Shostak, and Marshall Pease. The byzantine generals problem. In Concurrency: the works of leslie lamport , pages 203–226. ACM, 2019

    2019

  42. [50]

    Decentralized exchanges

    Alfred Lehar and Christine A Parlour. Decentralized exchanges. Available at SSRN 3905316 , 2021

    2021

  43. [51]

    How does blockchain security dictate blockchain implementation? In Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, pages 1006–1019, 2021

    Andrew Lewis-Pye and Tim Roughgarden. How does blockchain security dictate blockchain implementation? In Proceedings of the 2021 ACM SIGSAC Conference on Computer and Communications Security, pages 1006–1019, 2021

    2021

  44. [52]

    Comparison of decentralization in dpos and pow blockchains

    Chao Li and Balaji Palanisamy. Comparison of decentralization in dpos and pow blockchains. In Blockchain–ICBC 2020: Third International Conference, Held as Part of the Services Conference Federation, SCF 2020, Honolulu, HI, USA, September 18-20, 2020, Proceedings 3 , pages 18–...

    2020

  45. [53]

    Cross-consensus measurement of individual-level decentralization in blockchains

    Chao Li, Balaji Palanisamy, Runhua Xu, and Li Duan. Cross-consensus measurement of individual-level decentralization in blockchains. In 2023 IEEE 9th Intl Conference on Big Data Security on Cloud (BigDataSecurity), IEEE Intl Conference on High Performance and Smart Computing,(...

    2023

  46. [54]

    How hard is takeover in dpos blockchains? understand- ing the security of coin-based voting governance

    Chao Li, Balaji Palanisamy, Runhua Xu, Li Duan, Jiqiang Liu, and Wei Wang. How hard is takeover in dpos blockchains? understand- ing the security of coin-based voting governance. arXiv preprint arXiv:2310.18596, 2023

    2023 arXiv

  47. [55]

    Liquid democracy in dpos blockchains

    Chao Li, Runhua Xu, and Li Duan. Liquid democracy in dpos blockchains. In Proceedings of the 5th ACM International Symposium on Blockchain and Secure Critical Infrastructure , pages 25–33, 2023

    2023

  48. [56]

    Measuring decentralization in bitcoin and ethereum using multiple metrics and granularities

    Qinwei Lin, Chao Li, Xifeng Zhao, and Xianhai Chen. Measuring decentralization in bitcoin and ethereum using multiple metrics and granularities. In 2021 IEEE 37th International Conference on Data Engineering Workshops (ICDEW), pages 80–87. IEEE, 2021

    2021

  49. [57]

    From decentralization to oligopoly: A data-driven analysis of decen- tralization evolution and voting behaviors on eosio

    Jieli Liu, Weilin Zheng, Dingyuan Lu, Jiajing Wu, and Zibin Zheng. From decentralization to oligopoly: A data-driven analysis of decen- tralization evolution and voting behaviors on eosio. IEEE Transactions on Computational Social Systems , 2022

    2022

  50. [58]

    Understanding the decentralization of dpos: perspectives from data- driven analysis on eosio

    Jieli Liu, Weilin Zheng, Dingyuan Lu, Jiajing Wu, and Zibin Zheng. Understanding the decentralization of dpos: perspectives from data- driven analysis on eosio. arXiv preprint arXiv:2201.06187 , 2022

    2022 arXiv

  51. [59]

    Sok: Validating bridges as a scaling solution for blockchains

    Patrick McCorry, Chris Buckland, Bennet Yee, and Dawn Song. Sok: Validating bridges as a scaling solution for blockchains. Cryptology ePrint Archive, 2021

    2021

  52. [60]

    Understanding blockchain governance: Analyzing decentralized voting to amend defi smart con- tracts

    Johnnatan Messias, Vabuk Pahari, Balakrishnan Chandrasekaran, Kr- ishna P Gummadi, and Patrick Loiseau. Understanding blockchain governance: Analyzing decentralized voting to amend defi smart con- tracts. arXiv preprint arXiv:2305.17655 , 2023

    2023 arXiv

  53. [61]

    The honey badger of bft protocols

    Andrew Miller, Yu Xia, Kyle Croman, Elaine Shi, and Dawn Song. The honey badger of bft protocols. In Proceedings of the 2016 ACM SIGSAC conference on computer and communications security , pages 31–42, 2016

    2016

  54. [62]

    Towards decen- tralization in dpos systems: election, voting and leader selection using virtual stake

    Jelena Mi ˇsi´c, V ojislav B Miˇsi´c, and Xiaolin Chang. Towards decen- tralization in dpos systems: election, voting and leader selection using virtual stake. IEEE Transactions on Network and Service Management, 2023

    2023

  55. [63]

    The istanbul bft consensus algorithm

    Henrique Moniz. The istanbul bft consensus algorithm. arXiv preprint arXiv:2002.03613, 2020

    2002 arXiv

  56. [64]

    Lido dominance prompts warnings about liquid staking derivatives

    Nicholas Morgan. Lido dominance prompts warnings about liquid staking derivatives. https://decrypt.co/154804/lido-lsd-liquid-staking- decentralization. Accessed: 2023-11-29

    2023

  57. [65]

    Sok: Decentralized sequencers for rollups

    Shashank Motepalli, Luciano Freitas, and Benjamin Livshits. Sok: Decentralized sequencers for rollups. arXiv preprint arXiv:2310.03616, 2023

    2023 arXiv

  58. [66]

    Reward mechanism for blockchains using evolutionary game theory

    Shashank Motepalli and Hans-Arno Jacobsen. Reward mechanism for blockchains using evolutionary game theory. In 2021 3rd Conference on Blockchain Research & Applications for Innovative Networks and Services (BRAINS), pages 217–224. IEEE, 2021

    2021

  59. [67]

    Decentralizing permis- sioned blockchain with delay towers

    Shashank Motepalli and Hans-Arno Jacobsen. Decentralizing permis- sioned blockchain with delay towers. arXiv preprint arXiv:2203.09714, 2022

    2022 arXiv

  60. [68]

    Analyzing geospatial distribution in blockchains

    Shashank Motepalli and Hans-Arno Jacobsen. Analyzing geospatial distribution in blockchains. arXiv preprint arXiv:2305.17771 , 2023

    2023 arXiv

  61. [69]

    Delay towers to bootstrap blockchains

    Shashank Motepalli and Hans-Arno Jacobsen. Delay towers to bootstrap blockchains. In 2024 IEEE International Conference on Blockchain and Cryptocurrency (ICBC) , pages 397–399. IEEE, 2024

    2024

  62. [70]

    How does stake dis- tribution influence consensus? analyzing blockchain decentralization

    Shashank Motepalli and Hans-Arno Jacobsen. How does stake dis- tribution influence consensus? analyzing blockchain decentralization. In 2024 IEEE International Conference on Blockchain and Cryptocur- rency (ICBC), pages 343–352. IEEE, 2024

    2024

  63. [71]

    Bitcoin: A peer-to-peer electronic cash system

    Satoshi Nakamoto. Bitcoin: A peer-to-peer electronic cash system. Decentralized business review, 2008

    2008

  64. [72]

    Power laws, pareto distributions and zipf’s law

    Mark EJ Newman. Power laws, pareto distributions and zipf’s law. Contemporary physics, 46(5):323–351, 2005

    2005

  65. [73]

    In search of an understandable consensus algorithm

    Diego Ongaro and John Ousterhout. In search of an understandable consensus algorithm. In 2014 USENIX annual technical conference (USENIX ATC 14) , pages 305–319, 2014

    2014

  66. [74]

    https://osmosis.zone/

    Osmosis. https://osmosis.zone/. Accessed: 2023-10-25

    2023

  67. [75]

    Analysis of the blockchain protocol in asynchronous networks

    Rafael Pass, Lior Seeman, and Abhi Shelat. Analysis of the blockchain protocol in asynchronous networks. In Annual international conference on the theory and applications of cryptographic techniques, pages 643–

  68. [76]

    Zipf’s word frequency law in natural language: A critical review and future directions

    Steven T Piantadosi. Zipf’s word frequency law in natural language: A critical review and future directions. Psychonomic bulletin & review , 21:1112–1130, 2014

    2014

  69. [77]

    https://polygon.technology/

    Polygon. https://polygon.technology/. Accessed: 2023-10-25

    2023

  70. [78]

    Proof of stake

    Staking Rewards. Proof of stake. https://www.stakingrewards.com/ass ets/proof-of-stake. Accessed: 2023-12-03

    2023

  71. [79]

    Compar- ative review of the blockchain consensus algorithm between proof of stake (pos) and delegated proof of stake (dpos)

    Sheikh Munir Skh Saad and Raja Zahilah Raja Mohd Radzi. Compar- ative review of the blockchain consensus algorithm between proof of stake (pos) and delegated proof of stake (dpos). International Journal of Innovative Computing , 10(2), 2020

    2020

  72. [80]

    Decentralization: Conceptualization and measure- ment

    Aaron Schneider. Decentralization: Conceptualization and measure- ment. Studies in comparative international development , 38:32–56, 2003

    2003

  73. [81]

    Unpacking how de- centralized autonomous organizations (daos) work in practice

    Tanusree Sharma, Yujin Kwon, Kornrapat Pongmala, Henry Wang, Andrew Miller, Dawn Song, and Yang Wang. Unpacking how de- centralized autonomous organizations (daos) work in practice. arXiv preprint arXiv:2304.09822, 2023

    2023 arXiv

  74. [82]

    Fault-tolerant architectures for space and avionics applications

    Daniel P Siewiorek and Priya Narasimhan. Fault-tolerant architectures for space and avionics applications. NASA Ames Research http://ic. arc. nasa. gov/projects/ishem/Papers/Siewi, 2005

    2005

  75. [83]

    A simple method for measuring inequality

    Thitithep Sitthiyot and Kanyarat Holasut. A simple method for measuring inequality. Palgrave Communications, 6(1):1–9, 2020

    2020

  76. [84]

    A simple method for estimat- ing the lorenz curve

    Thitithep Sitthiyot and Kanyarat Holasut. A simple method for estimat- ing the lorenz curve. Humanities and Social Sciences Communications, 8(1):1–9, 2021

    2021

  77. [85]

    Better safe than sorry: Recovering after adversarial majority

    Srivatsan Sridhar, Dionysis Zindros, and David Tse. Better safe than sorry: Recovering after adversarial majority. arXiv preprint arXiv:2310.06338, 2023

    2023 arXiv

  78. [86]

    Srinivasan and Leland Lee

    Balaji S. Srinivasan and Leland Lee. Quantifying decentralization. https://news.earn.com/quantifying-decentralization-e39db233c28e. Accessed: 2023-11-05

    2023

  79. [87]

    https://sui.io/

    Sui. https://sui.io/. Accessed: 2023-10-25

    2023

  80. [88]

    Open problems in daos

    Joshua Z Tan, Tara Merk, Sarah Hubbard, Eliza R Oak, Joni Pirovich, Ellie Rennie, Rolf Hoefer, Michael Zargham, Jason Potts, Chris Berg, et al. Open problems in daos. arXiv preprint arXiv:2310.19201, 2023

    2023 arXiv

  81. [89]

    Tendermint explained — bringing bft-based pos to the public blockchain domain

    Chjango Unchained. Tendermint explained — bringing bft-based pos to the public blockchain domain. https://blog.cosmos.network/tendermint- explained-bringing-bft-based-pos-to-the-public-blockchain-domain- f22e274a0fdb. Accessed: 2023-11-26

    2023

  82. [90]

    Ethereum censorship dashboard

    Toni Wahrst ¨atter. Ethereum censorship dashboard. https://censorship.p ics/. Accessed: 2023-12-17

    2023

  83. [91]

    Ethereum smart contract security research: survey and future research opportunities

    Zeli Wang, Hai Jin, Weiqi Dai, Kim-Kwang Raymond Choo, and Deqing Zou. Ethereum smart contract security research: survey and future research opportunities. Frontiers of Computer Science, 15:1–18, 2021

    2021

  84. [92]

    Sift: Design and analysis of a fault-tolerant computer for aircraft control

    John H Wensley, Leslie Lamport, Jack Goldberg, Milton W Green, Karl N Levitt, Po Mo Melliar-Smith, Robert E Shostak, and Charles B Weinstock. Sift: Design and analysis of a fault-tolerant computer for aircraft control. Proceedings of the IEEE , 66(10):1240–1255, 1978

    1978

  85. [93]

    Peppermint

    Polygon wiki. Peppermint. https://wiki.polygon.technology/docs/pos/d esign/heimdall/peppermint. Accessed: 2023-11-26. 14

    2023

  86. [94]

    The shapley value

    Eyal Winter. The shapley value. Handbook of game theory with economic applications, 3:2025–2054, 2002

    2025

  87. [95]

    A new identity and financial network

    Worldcoin. A new identity and financial network. https://whitepap er.worldcoin.org/#a-new-identity-and-financial-network. Accessed: 2023-12-16

    2023

  88. [96]

    Hotstuff: Bft consensus with linearity and responsive- ness

    Maofan Yin, Dahlia Malkhi, Michael K Reiter, Guy Golan Gueta, and Ittai Abraham. Hotstuff: Bft consensus with linearity and responsive- ness. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, pages 347–356, 2019

    2019

  89. [97]

    Towards More Efficient and Scalable Consensus Algorithms

    Gengrui Zhang. Towards More Efficient and Scalable Consensus Algorithms. PhD thesis, University of Toronto, 2023

    2023

  90. [98]

    Reaching consen- sus in the byzantine empire: A comprehensive review of bft consensus algorithms

    Gengrui Zhang, Fei Pan, Michael Dang’ana, Yunhao Mao, Shashank Motepalli, Shiquan Zhang, and Hans-Arno Jacobsen. Reaching consen- sus in the byzantine empire: A comprehensive review of bft consensus algorithms. arXiv preprint arXiv:2204.03181 , 2022

    2022 arXiv

  91. [99]

    Prestigebft: Revolutionizing view changes in bft consensus algorithms with reputation mechanisms

    Gengrui Zhang, Fei Pan, Sofia Tijanic, and Hans-Arno Jacobsen. Prestigebft: Revolutionizing view changes in bft consensus algorithms with reputation mechanisms. arXiv preprint arXiv:2307.08154 , 2023

    2023 arXiv

  92. [100]

    Human behavior and the principle of least effort: An introduction to human ecology

    George Kingsley Zipf. Human behavior and the principle of least effort: An introduction to human ecology . Ravenio books, 2016. Shashank Motepalli Motepalli is a PhD Candi- date at the Sr. Rogers Department of Electrical and Computer Engineering, University of Toronto. His res...

    2016

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.