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arxiv: 2509.21475 · v3 · submitted 2025-09-25 · 💻 cs.CR · cs.CE· cs.GT

Geographical Centralization Resilience in Ethereum's Block-Building Paradigms

Sen Yang , Burak \"Oz , Fei Wu , Fan Zhang This is my paper

Pith reviewed 2026-05-18 13:39 UTC · model grok-4.3

classification 💻 cs.CR cs.CEcs.GT
keywords ethereumblock buildinggeographical centralizationdecentralizationlatencyvalidatorsproof of stakeresilience
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The pith

Ethereum's block-building paradigms create location-dependent incentives that encourage validators to geographically centralize.

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

The paper develops a formal model of how Ethereum validators decide where to locate under its two block-building approaches: local and external. Both approaches tie payoffs to proximity because shorter propagation delays improve a validator's chance of timely attestations or block inclusion. Using mean-field analysis plus simulations fed with real latency measurements, the work shows these rules push validators toward low-latency corridors and toward concentrations of information sources. Consensus settings such as slot duration and attestation thresholds change how strongly location matters. A reader should care because geographic spread is what gives the network resilience against regional outages or policy shocks, yet the protocol rules themselves erode that spread.

Core claim

Ethereum's block-building architecture is not geographically neutral. Both the local and external block-building paradigms generate location-dependent payoffs and create incentives for validators to position closer to payoff-relevant parties in order to reduce propagation delays, although the mechanisms differ between the paradigms. Asymmetric access to information sources further amplifies geographical centralization. Consensus parameters such as attestation thresholds and slot times modulate latency sensitivity and can intensify the centralizing pressure.

What carries the argument

Formal model of validators' geographical positioning incentives that links the interaction between local and external block-building paradigms to the spatial distribution of validators and information sources.

If this is right

  • Validators will cluster in regions with favorable latency to other validators and information sources.
  • Local block building and external block building each push centralization but operate through distinct delay-reduction channels.
  • Raising or lowering attestation thresholds and slot times will strengthen or weaken the pull toward geographic concentration.
  • Ignoring geography in protocol rules leaves the system more exposed to single-region disruptions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same latency-based incentives could appear in other proof-of-stake systems that separate block proposal from attestation.
  • Adding explicit geographic diversity bonuses or penalties to rewards might offset the centralizing force identified here.
  • Ongoing public mapping of validator IP locations against latency maps would provide an early warning of unintended clustering.

Load-bearing premise

Validator locations are chosen mainly to maximize expected rewards under the economic incentives created by the two block-building rules.

What would settle it

Direct measurements of current validator locations and their distances to major information sources or other validators that show no systematic preference for lower-latency sites once stake size is controlled for.

Figures

Figures reproduced from arXiv: 2509.21475 by Burak \"Oz, Fan Zhang, Fei Wu, Sen Yang.

Figure 1
Figure 1. Figure 1: Validator distribution (a) and inter-region Internet latencies (b) highlight [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Setup: Homogeneous validators and information sources. Evolution of cen￾tralization metrics under SSP and MSP with varying costs c ∈ {0, 0.002}. information sources (see Section A). In the SSP setup, this reduces relay-attester propagation time, giving an edge in timing games. In the MSP setup, the same advantage applies, while proximity to multiple sources further increases expected payoff. With a migrati… view at source ↗
Figure 3
Figure 3. Figure 3: Setup: Homogeneous validators and information sources. Validator distri￾bution aggregated by macro-regions under SSP and MSP with c ∈ {0, 0.002}. Early termination of a line means no validators remain in that macro-region [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Setup: Homogeneous validators with heterogeneous information sources. Evolution of centralization metrics under SSP and MSP with latency-aligned vs. latency-misaligned source placement (c = 0.002). With a migration cost of c = 0.002, [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Setup: Heterogeneous validators with homogeneous information sources. Evolution of centralization metrics under SSP and MSP with a heterogeneous validator distribution and homogeneous information sources. with a high density of validators such as Europe and North America—briefly im￾proving geographical decentralization. However, over time, the system converges toward every validator moving to this region, … view at source ↗
Figure 6
Figure 6. Figure 6: Setup: Heterogeneous validators and information sources. Evolution of centralization metrics under SSP and MSP with latency-aligned vs. latency￾misaligned source placement (c = 0.002). posal (EIP)-7782 [1]. These results are presented in Section E.3 and Section E.4, respectively. 5 Discussion and Future Works Latency data. In our simulations, latency and region information are based solely on GCP data. Whi… view at source ↗
Figure 7
Figure 7. Figure 7: Heatmap of median latency between macro-regions. [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: CDF of marginal benefit in the first 1,000 slots of the baseline. from 0 to 0.003; at the upper end of this range, the cost eliminates over 70% of the typical marginal relocation gain in both SSP and MSP (see [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Setup: Homogeneous validators and information sources. Evolution of centralization metrics under SSP and MSP with varying migration costs c ∈ {0, 0.001, 0.002, 0.003}. E.2 Clustering in Real-World Validator Distribution [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Setup: Heterogeneous validators and information sources. Validator dis￾tribution aggregated by macro-regions under SSP and MSP in the latency￾aligned case and latency-misaligned case. E.3 Attestation Threshold We now study how the required attestation threshold γ (the quorum needed for a block to become canonical) shapes geographical centralization. Specifically, we set γ to different values ( 1 3 , 1 2 ,… view at source ↗
Figure 11
Figure 11. Figure 11: Setup: Homogeneous validators and information sources. Evolution of centralization metrics under SSP and MSP with different attestation threshold (γ ∈ { 1 3 , 1 2 , 2 3 , 4 5 }) when c = 0.002. Note that the orange solid line largely overlaps with the blue solid line. E.4 Shorter Slot Time Reducing Ethereum’s slot time has been recently discussed in the community through EIP-7782 [1], which proposes ∆ = 6… view at source ↗
Figure 12
Figure 12. Figure 12: Setup: Homogeneous validators and information sources. Evolution of centralization metrics under SSP and MSP with shorter (∆ = 6 s) versus current slot times (∆ = 12 s) when c = 0.002 [PITH_FULL_IMAGE:figures/full_fig_p029_12.png] view at source ↗
read the original abstract

Decentralization has an important geographic dimension that conventional metrics, such as stake distribution, often overlook. Validator location affects resilience to regional shocks (e.g., outages, natural disasters, or government intervention) as well as fairness in reward access. Yet major blockchain protocols do not encode geographical location in their rules; instead, validator locations emerge from a combination of economic incentives, regulatory constraints, infrastructure availability, and validator deployment choices. When some locations offer systematic advantages, validators may strategically co-locate to increase expected rewards, as in Ethereum, where validators cluster along the Atlantic corridor, which exhibits favorable latency. In this paper, we develop a formal model of validators' geographical positioning incentives under Ethereum's protocol design, capturing the interaction between its two block-building paradigms, local and external block building, and the distribution of validators and information sources. We analyze the model under a mean-field approximation and complement it with agent-based simulations calibrated with real-world latency data to quantify how these incentives translate into geographical concentration under heterogeneous geographic and infrastructural conditions. Our results show that Ethereum's block-building architecture is not geographically neutral. Both paradigms create location-dependent payoffs and incentives to move closer to payoff-relevant parties to reduce propagation delays, though through different mechanisms. Asymmetric access to information sources further increases geographical centralization. We also show that consensus parameters, including attestation thresholds and slot times, affect latency sensitivity and can strengthen these effects. Finally, we discuss implications for protocol design and possible mitigation directions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper develops a formal model of validators' geographical positioning incentives under Ethereum's two block-building paradigms (local and external). It analyzes the model via mean-field approximation and complements it with agent-based simulations calibrated to real-world latency data, claiming that both paradigms generate location-dependent payoffs that incentivize co-location to reduce propagation delays, producing geographical centralization (e.g., Atlantic corridor clustering). Asymmetric access to information sources amplifies this, and consensus parameters such as attestation thresholds and slot times modulate latency sensitivity.

Significance. If the central claim holds, the work provides a valuable formal and simulation-based lens on an under-studied dimension of blockchain decentralization—geographical resilience—beyond conventional stake metrics. The calibration against external real-world latency data and the use of agent-based simulations to quantify concentration under heterogeneous conditions are strengths that ground the analysis in observable network properties and offer falsifiable predictions for protocol designers.

major comments (1)
  1. [Model Analysis] Model section (mean-field analysis): The mean-field approximation averages validator locations into fields rather than modeling discrete positions on the latency graph. This risks suppressing the local feedback loops (e.g., one validator's relocation reducing delay for others via shared relays) that the paper identifies as drivers of clustering. The manuscript should include an explicit comparison showing that mean-field equilibria align with the clustered states found in the agent-based simulations; without this, the quantitative link between protocol design and observed centralization is weakened.
minor comments (1)
  1. [Introduction] The description of local vs. external block-building mechanisms could be expanded with a short diagram or pseudocode to clarify how each paradigm interacts with validator location and information sources.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and for recognizing the strengths of our calibration and simulation approach. We address the single major comment below and describe the revisions we will incorporate.

read point-by-point responses

  1. Referee: Model section (mean-field analysis): The mean-field approximation averages validator locations into fields rather than modeling discrete positions on the latency graph. This risks suppressing the local feedback loops (e.g., one validator's relocation reducing delay for others via shared relays) that the paper identifies as drivers of clustering. The manuscript should include an explicit comparison showing that mean-field equilibria align with the clustered states found in the agent-based simulations; without this, the quantitative link between protocol design and observed centralization is weakened.

    Authors: We appreciate the referee's point that the mean-field approximation, by construction, works with averaged location densities rather than tracking individual discrete positions and pairwise relay interactions. This averaging is intentional to obtain tractable equilibrium conditions for the two block-building paradigms, yet we agree it leaves open the question of whether the resulting density predictions reproduce the clustering observed in the discrete simulations. In the revised manuscript we will add a dedicated subsection (and associated figure) that extracts the mean-field equilibrium location densities for representative latency and parameter values and directly overlays them against the empirical location histograms obtained from the calibrated agent-based runs. The comparison will quantify the match in terms of concentration metrics (e.g., Gini coefficient on the latency graph and fraction of validators in the Atlantic corridor) and will discuss the residual discrepancy attributable to higher-order local feedback. This addition will make the quantitative bridge between the analytical model and the simulation results explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity: external latency calibration grounds the model independently

full rationale

The paper constructs a formal model of validator location incentives under Ethereum's local and external block-building paradigms, then analyzes it via mean-field approximation and agent-based simulations. The simulations are explicitly calibrated with real-world latency data, providing an external benchmark independent of the model's internal assumptions. No equations or claims reduce by construction to fitted parameters renamed as predictions, self-definitions, or load-bearing self-citations. The derivation chain remains self-contained against external data and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available; detailed free parameters, axioms, and entities cannot be extracted. The model relies on standard assumptions about rational validator behavior and latency effects.

axioms (2)
  • domain assumption Validators act strategically to maximize expected rewards by choosing locations that minimize propagation delays
    Invoked to explain emergence of geographical clustering under the two block-building paradigms.
  • domain assumption Mean-field approximation accurately captures aggregate validator distribution dynamics
    Used to analyze the formal model of positioning incentives.

pith-pipeline@v0.9.0 · 5802 in / 1190 out tokens · 42672 ms · 2026-05-18T13:39:43.133572+00:00 · methodology

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Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages

  1. [1]

    Ethereum Im- provement Proposals (7782) (October 2024), https://eips.ethereum.org/EIPS/eip- 7782, [Online serial]

    Adams, B., Feist, D.: EIP-7782: Reduce Block Latency [DRAFT]. Ethereum Im- provement Proposals (7782) (October 2024), https://eips.ethereum.org/EIPS/eip- 7782, [Online serial]

    work page 2024

  2. [2]

    https://aws.amazon.com/ about-aws/global-infrastructure/ (2025), accessed: 2025-09-17

    Amazon Web Services, Inc.: Aws global infrastructure. https://aws.amazon.com/ about-aws/global-infrastructure/ (2025), accessed: 2025-09-17

    work page 2025

  3. [3]

    https://geo- decentralization.github.io/ (2025)

    Authors: Geographical decentralization simulation. https://geo- decentralization.github.io/ (2025)

    work page 2025

  4. [4]

    https://www.blockchain.com/ explorer/charts/pools (2025), accessed: 2025-09-09

    Blockchain.com: Hashrate distribution (pools). https://www.blockchain.com/ explorer/charts/pools (2025), accessed: 2025-09-09

    work page 2025

  5. [5]

    https: //ethresear.ch/t/estimating-validator-decentralization-using-p2p-data/19920 (June 27 2024)

    Bostoen, J., Garg, N.: Estimating validator decentralization using p2p data. https: //ethresear.ch/t/estimating-validator-decentralization-using-p2p-data/19920 (June 27 2024)

    work page 2024

  6. [6]

    arXiv preprint arXiv:2003.03052 (2020)

    Buterin, V., Hernandez, D., Kamphefner, T., Pham, K., Qiao, Z., Ryan, D., Sin, J., Wang, Y., Zhang, Y.X.: Combining ghost and casper. arXiv preprint arXiv:2003.03052 (2020)

    work page arXiv 2003

  7. [7]

    https://ccaf.io/cbnsi/ethereum/network_analytics (2025), accessed September 1, 2025 Designing Ethereum’s Geographical (De)Centralization Beyond the Atlantic 19

    Cambridge Centre for Alternative Finance (CCAF): Ethereum network analytics. https://ccaf.io/cbnsi/ethereum/network_analytics (2025), accessed September 1, 2025 Designing Ethereum’s Geographical (De)Centralization Beyond the Atlantic 19

    work page 2025

  8. [8]

    https://dune.com/chainbound/geolocating- validators (2024), accessed: 2025-08-18

    Chainbound: Geolocating validators. https://dune.com/chainbound/geolocating- validators (2024), accessed: 2025-08-18

    work page 2024

  9. [9]

    Available at SSRN 5171559 (2024)

    Cong, L.W., Dong, Y., Lu, Y., Ruan, Q., Wang, G.: Agent-based modeling for daos and defi. Available at SSRN 5171559 (2024)

    work page 2024

  10. [10]

    The Review of Financial Studies34(3), 1191–1235 (2021)

    Cong, L.W., He, Z., Li, J.: Decentralized mining in centralized pools. The Review of Financial Studies34(3), 1191–1235 (2021)

    work page 2021

  11. [11]

    In: 2020 IEEE symposium on security and privacy (SP)

    Daian, P., Goldfeder, S., Kell, T., Li, Y., Zhao, X., Bentov, I., Breidenbach, L., Juels, A.: Flash boys 2.0: Frontrunning in decentralized exchanges, miner ex- tractable value, and consensus instability. In: 2020 IEEE symposium on security and privacy (SP). pp. 910–927. IEEE (2020)

    work page 2020

  12. [12]

    The review of economics and statistics pp

    Dorfman, R.: A Formula for the Gini Coefficient. The review of economics and statistics pp. 146–149 (1979)

    work page 1979

  13. [13]

    https://www.ethernodes.org/countries (2025), accessed: 2025-09-01

    ethernodes.org: Ethernodes – countries. https://www.ethernodes.org/countries (2025), accessed: 2025-09-01

    work page 2025

  14. [14]

    https://docs.flashbots.net/flashbots-mev- boost/introduction (2025), accessed: 2025-08-03

    Flashbots: Overview – mev-boost. https://docs.flashbots.net/flashbots-mev- boost/introduction (2025), accessed: 2025-08-03

    work page 2025

  15. [15]

    https://ethereum.org/en/roadmap/ pbs/ (2024), accessed: 2025-08-13

    Foundation, E.: Proposer-builder separation. https://ethereum.org/en/roadmap/ pbs/ (2024), accessed: 2025-08-13

    work page 2024

  16. [16]

    https:// github.com/ethereum/consensus-specs (2025), accessed: 2025-09-09

    Foundation, E.: Ethereum proof-of-stake consensus specifications. https:// github.com/ethereum/consensus-specs (2025), accessed: 2025-09-09

    work page 2025

  17. [17]

    https://ethereum.org/en/roadmap/merge/ (2025)

    Foundation, E.: The merge. https://ethereum.org/en/roadmap/merge/ (2025)

    work page 2025

  18. [18]

    In: International conference on financial cryptog- raphy and data security

    Gencer, A.E., Basu, S., Eyal, I., Van Renesse, R., Sirer, E.G.: Decentralization in bitcoin and ethereum networks. In: International conference on financial cryptog- raphy and data security. pp. 439–457. Springer (2018)

    work page 2018

  19. [19]

    https://lookerstudio.google.com/reporting/fc733b10-9744-4a72- a502-92290f608571 (2025), accessed: 2025-09-11

    Google: Google looker studio dashboard: fc733b10-9744-4a72-a502- 92290f608571. https://lookerstudio.google.com/reporting/fc733b10-9744-4a72- a502-92290f608571 (2025), accessed: 2025-09-11

    work page 2025

  20. [20]

    In: International Conference on Financial Cryptography and Data Security

    Grandjean, D., Heimbach, L., Wattenhofer, R.: Ethereum proof-of-stake consensus layer: Participation and decentralization. In: International Conference on Financial Cryptography and Data Security. pp. 253–280. Springer (2024)

    work page 2024

  21. [21]

    In: 5th Workshop on Coordination of Decentralized Finance 2024 (2024)

    Grandjean, D., Heimbach, L., Wattenhofer, R.: Ethereum Proof-of-Stake Consen- sus Layer: Participation and Decentralization. In: 5th Workshop on Coordination of Decentralized Finance 2024 (2024)

    work page 2024

  22. [22]

    In: 2023 ACM Internet Measurement Conference (IMC), Montreal, QC, Canada (2023)

    Heimbach,L.,Kiffer,L.,FerreiraTorres,C.,Wattenhofer,R.:Ethereum’sproposer- builder separation: Promises and realities. In: 2023 ACM Internet Measurement Conference (IMC), Montreal, QC, Canada (2023)

    work page 2023

  23. [23]

    In: 34th USENIX Security Symposium, Seattle, WA, USA (2025)

    Heimbach, L., Vonlanthen, Y., Villacis, J., Kiffer, L., Wattenhofer, R.: Deanonymizing ethereum validators: The p2p network has a privacy issue. In: 34th USENIX Security Symposium, Seattle, WA, USA (2025)

    work page 2025

  24. [24]

    Journal of Open Source Software 10(107), 7668 (2025)

    ter Hoeven, E., Kwakkel, J., Hess, V., Pike, T., Wang, B., Kazil, J., et al.: Mesa 3: Agent-based modeling with python in 2025. Journal of Open Source Software 10(107), 7668 (2025)

    work page 2025

  25. [25]

    The Economic Journal39(153), 41–57 (1929)

    Hotelling, H.: Stability in competition. The Economic Journal39(153), 41–57 (1929). https://doi.org/10.2307/2224214

    work page doi:10.2307/2224214 1929

  26. [26]

    In: Proceedings of the Internet Measurement Conference

    Kim, S.K., Ma, Z., Murali, S., Mason, J., Miller, A., Bailey, M.: Measuring ethereum network peers. In: Proceedings of the Internet Measurement Conference

    work page

  27. [27]

    In: 2023 IEEE International Conference on Blockchain and Cryptocurrency (ICBC)

    Kraner, B., Vallarano, N., Schwarz-Schilling, C., Tessone, C.J.: Agent-based modelling of ethereum consensus. In: 2023 IEEE International Conference on Blockchain and Cryptocurrency (ICBC). pp. 1–8. IEEE (2023) 20 S. Yang et al

    work page 2023

  28. [28]

    In: Proceedings of the 1st Conference on Advances in Financial Technologies (AFT)

    Kwon, Y., Liu, J., Kim, M., Song, D., Kim, Y.: Impossibility of Full Decentral- ization in Permissionless Blockchains. In: Proceedings of the 1st Conference on Advances in Financial Technologies (AFT). pp. 110–123 (2019)

    work page 2019

  29. [29]

    IEEE Transactions on Information Theory37(1), 145–151 (1991)

    Lin, J.: Divergence Measures Based on the Shannon Entropy. IEEE Transactions on Information Theory37(1), 145–151 (1991)

    work page 1991

  30. [30]

    In: 2021 IEEE 37th Interna- tional Conference on Data Engineering Workshops (ICDEW)

    Lin, Q., Li, C., Zhao, X., Chen, X.: Measuring Decentralization in Bitcoin and Ethereum using Multiple Metrics and Granularities. In: 2021 IEEE 37th Interna- tional Conference on Data Engineering Workshops (ICDEW). pp. 80–87. IEEE (2021)

    work page 2021

  31. [31]

    In: Proceedings of the Winter Simulation Conference, 2005

    Macal, C.M., North, M.J.: Tutorial on agent-based modeling and simulation. In: Proceedings of the Winter Simulation Conference, 2005. pp. 14–pp. IEEE (2005)

    work page 2005

  32. [32]

    https://learn.microsoft.com/en-us/ azure/reliability/regions-list (2025), accessed: 2025-09-17

    Microsoft Corporation: Azure regions list. https://learn.microsoft.com/en-us/ azure/reliability/regions-list (2025), accessed: 2025-09-17

    work page 2025

  33. [33]

    Available at SSRN 3440802 (2008)

    Nakamoto, S.: Bitcoin: A peer-to-peer electronic cash system. Available at SSRN 3440802 (2008)

    work page 2008

  34. [34]

    https:// ethresear.ch/t/concurrent-block-proposers-in-ethereum/18777 (2024)

    Neuder, M., Resnick, M.: Concurrent Block Proposers in Ethereum. https:// ethresear.ch/t/concurrent-block-proposers-in-ethereum/18777 (2024)

    work page 2024

  35. [35]

    https:// us.ovhcloud.com/about/global-infrastructure/locations/ (2025), accessed: 2025- 09-17

    OVHcloud: Ovhcloud locations: Global infrastructure locations. https:// us.ovhcloud.com/about/global-infrastructure/locations/ (2025), accessed: 2025- 09-17

    work page 2025

  36. [36]

    In: Proceedings of the 2023 Workshop on Decentralized Finance and Se- curity

    Öz, B., Kraner, B., Vallarano, N., Kruger, B.S., Matthes, F., Tessone, C.J.: Time moves faster when there is nothing you anticipate: The role of time in mev re- wards. In: Proceedings of the 2023 Workshop on Decentralized Finance and Se- curity. p. 1–8. DeFi ’23, Association for Computing Machinery, New York, NY, USA (2023). https://doi.org/10.1145/360576...

    work page doi:10.1145/3605768.3623563 2023

  37. [37]

    Öz,B.,Sui,D.,Thiery,T.,Matthes,F.:Whowinsethereumblockbuildingauctions and why? In: 6th Conference on Advances in Financial Technologies. p. 1 (2024)

    work page 2024

  38. [38]

    Rhoades, S.A.: The Herfindahl–Hirschman Index. Fed. Res. Bull.79, 188 (1993)

    work page 1993

  39. [39]

    In: 5th Conference on Advances in Financial Technologies (2023)

    Schwarz-Schilling, C., Saleh, F., Thiery, T., Pan, J., Shah, N., Monnot, B.: Time is money: Strategic timing games in proof-of-stake protocols. In: 5th Conference on Advances in Financial Technologies (2023)

    work page 2023

  40. [40]

    https://https: //ethresear.ch/t/an-analysis-of-attestation-timings-in-a-6-s-slot/23016 (2025)

    Silva, M.I.: An analysis of attestation timings in a 6-s slot . https://https: //ethresear.ch/t/an-analysis-of-attestation-timings-in-a-6-s-slot/23016 (2025)

    work page 2025

  41. [41]

    news.earn.com (2017)

    Srinivasan, B.S., Lee, L.: Quantifying Decentralization. news.earn.com (2017)

    work page 2017

  42. [42]

    Stichler,P.:Galaxyera:Agent-basedsimulationofexecutiontickets.arXivpreprint arXiv:2501.16090 (2025)

    work page arXiv 2025

  43. [43]

    Thorn, A., Fabiano, A., Helmy, K.: Examining the latest china bit- coin ban (May 2021), https://www.galaxy.com/insights/research/examining-the- latest-china-bitcoin-ban, research article

    work page 2021

  44. [44]

    In: Proceedings of the ACM Web Conference 2024

    Wahrstätter, A., Ernstberger, J., Yaish, A., Zhou, L., Qin, K., Tsuchiya, T., Stein- horst, S., Svetinovic, D., Christin, N., Barczentewicz, M., et al.: Blockchain cen- sorship. In: Proceedings of the ACM Web Conference 2024. pp. 1632–1643 (2024)

    work page 2024

  45. [45]

    arXiv preprint arXiv:2305.16468 (2023)

    Wahrstätter, A., Zhou, L., Qin, K., Svetinovic, D., Gervais, A.: Time to bribe: Measuring block construction market. arXiv preprint arXiv:2305.16468 (2023)

    work page arXiv 2023

  46. [46]

    Wu, F., Sui, D., Thiery, T., Pai, M.: Measuring cex-dex extracted value and searcher profitability: The darkest of the mev dark forest (2025), https://arxiv.org/ abs/2507.13023

    work page arXiv 2025

  47. [47]

    In: 2024 IEEE International Conference on Blockchain and Cryptocur- rency (ICBC)

    Wu, F., Thiery, T., Leonardos, S., Ventre, C.: Strategic bidding wars in on-chain auctions. In: 2024 IEEE International Conference on Blockchain and Cryptocur- rency (ICBC). pp. 503–511. IEEE (2024) Designing Ethereum’s Geographical (De)Centralization Beyond the Atlantic 21

    work page 2024

  48. [48]

    In: 28th European Conference on Artificial Intelligence (ECAI) (2025)

    Wu, F., Thiery, T., Leonardos, S., Ventre, C.: From competition to centralization: The oligopoly in ethereum block building auctions. In: 28th European Conference on Artificial Intelligence (ECAI) (2025)

    work page 2025

  49. [49]

    In: 2019 IEEE 9th Inter- national Conference on Electronics Information and Emergency Communication (ICEIEC)

    Wu, K., Peng, B., Xie, H., Huang, Z.: An Information Entropy Method to Quantify the Degrees of Decentralization for Blockchain Systems. In: 2019 IEEE 9th Inter- national Conference on Electronics Information and Emergency Communication (ICEIEC). pp. 1–6. IEEE (2019)

    work page 2019

  50. [50]

    In: 2025 IEEE Symposium on Security and Privacy (SP)

    Yang, S., Nayak, K., Zhang, F.: Decentralization of ethereum’s builder market. In: 2025 IEEE Symposium on Security and Privacy (SP). pp. 1512–1530. IEEE (2025)

    work page 2025

  51. [51]

    Yang, S., Öz, B.: syang-ng/geographical-decentralization-simulation (Sep 2025), https://github.com/syang-ng/geographical-decentralization-simulation, original- date: 2025-06-09T13:40:22Z A List of Google Cloud Platform Regions In this section, we present the list of Google Cloud Platform (GCP) regions used in our paper, along with their physical locations...

    work page 2025

  52. [52]

    Intuitively, a largerγtightens the effective timing window, increasing the value of low-latency placement and thus strengthening co-location incentives

    and run the homogeneous baseline of Section 4.2 under bothSSPandMSP. Intuitively, a largerγtightens the effective timing window, increasing the value of low-latency placement and thus strengthening co-location incentives. Figure 11 confirms this intuition forSSP: whenγ≤1 2, validators rarely migrate at costc= 0.002, as reflected in both Gini and HHI indic...

    work page 2000