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REVIEW 4 major objections 6 minor 2 cited by

Blockspace Under Pressure: An Analysis of Spam MEV on High-Throughput Blockchains

T0 review · 4 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The paper claims that spam MEV volume on high-throughput blockchains is determined by a zero-profit competitive equilibrium with closed-form solutions in block capacity and gas-price floor, and that capping capacity before the plateau remov

desk verdict A useful equilibrium framework for spam MEV, but the linear opportunity-scaling assumption is load-bearing and at best weakly confirmed on Arbitrum; still worth sending to referees. read the letter →

arxiv 2604.00234 v2 pith:B2A34HV7 submitted 2026-03-31 cs.GT

Wenhao Wang , Aditya Saraf , Lioba Heimbach , Kushal Babel , Fan Zhang This is my paper
classification cs.GT MSC 91A1091A80
keywords spamMEVmaximalextractablevaluecompetitiveequilibriumblockcapacityminimumgaspricepriorityfeeorderingnetworkexternalityrollupeconomics
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 argues that the flood of speculative 'spam' transactions on high-throughput, low-fee blockchains is not noise but an equilibrium outcome: free entry drives expected spam profits to zero, which pins down how much spam enters as a function of block capacity, the minimum gas price, and the fee-ordering rule. It derives closed-form equilibrium spam volumes in three regimes and shows that spam takes an increasing share of each marginal unit of capacity. That yields a concrete design rule: cap block capacity below the plateau threshold B_plat to eliminate a disproportionate amount of spam while giving up little user welfare, or raise the gas price floor. It extends the analysis to priority fee ordering and shows spam concentrates in later, cheaper positions. A sympathetic reader should care because it converts a reactive, chain-by-chain guessing game into a tunable economic model with parameter-level guidance.

What carries the argument

The workhorse is a zero-profit competitive equilibrium built on three components: the probability that a spam transaction captures a randomly positioned opportunity, S/(S+1) when S spammers are present; the clearing gas price g(S) = max(g_min, g1 + (s/beta) S) set by a linear demand curve D(g) = D0 - beta g; and the linear opportunity-scaling assumption r = r0 * Q_u / D0. Solving free entry (u(S) = 0) yields the closed-form equilibrium spam volume and a threshold B_plat = D(g_min) + (r0 D(g_min)/(D0 g_min) - s)_+ beyond which further capacity no longer helps users. The user-share derivative m_user = partial Q*_u / partial B_max is strictly decreasing in B_max, which is the mechanism behind t

What would settle it

Estimate the elasticity of realized MEV profit with respect to non-MEV volume on a chain where block capacity and gas-price floor are fixed; if the elasticity deviates substantially from 1, or if raising the gas-price floor by a known factor does not move spam volume according to the closed-form formula, the model's predictions fail. A cleaner test: make one exogenous step increase in block capacity and measure the spam share of the added capacity; the model predicts the user share of each marginal unit is strictly decreasing in B_max.

Watch

Extended reading notes

Core claim

The central claim is that in a competitive equilibrium where searchers' expected profits are driven to zero, equilibrium spam volume is a closed-form function of block capacity B_max, the minimum gas price g_min, and the linear opportunity-scaling parameter r0. Spam volume falls into one of three regimes: no entry when the opportunity value is below per-transaction cost; a slack-at-the-floor regime where spam is entirely determined by g_min; and a congested regime where spam is given by the closed-form expression S* = [sqrt((s - Delta + beta*r0/D0)^2 + 4 beta r0) - (s + Delta + beta*r0/D0)] / (2s), with Delta = D0 - B_max. Because the user share of marginal capacity m_user decreases in B_max

Load-bearing premise

The entire derivation rests on the assumption that arbitrage opportunity value scales linearly with included user gas (r = r0 * Q_u / D0); the paper's own data on one of its two rollup case studies fit this relationship poorly (elasticity ~0.82, R²=0.13).

Editorial extensions

If this is right

  • If the zero-profit equilibrium is right, a designer can compute the exact spam volume that will result from any (B_max, g_min) pair and choose parameters to cap it at a target level.
  • Capping block capacity slightly below B_plat is predicted to remove a disproportionate share of spam—and its network externality—while sacrificing only low-value users, a direct corollary of the decreasing marginal user share.
  • Priority fee ordering is predicted to reduce spam when a large fraction of users bid for priority, and to push remaining spam to late block positions; chains with weak priority participation may see little or no benefit.
  • Under demand scaling, spam's share of included gas approaches a positive plateau, so scaling alone will not dissolve the spam problem without parameter intervention.
  • Empirically, the model predicts spam should respond sharply to exogenous gas-target changes (the paper's case studies show a 70M-to-50M cut reduced spam 34% vs 24% for non-spam) and to gas-price floor increases.

Reading between the lines

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

  • A testable extension: the formula implies the marginal user share is monotone decreasing in B_max; a chain with repeated capacity steps could verify this slope directly, and if the linear opportunity-scaling elasticity is far from 1, the plateau prediction fails.
  • The framework suggests that raising g_min and capping B_max are substitutes with different incidence: g_min charges every probe, while a cap waives the fee but rations; the choice could depend on whether the bottleneck is execution or data availability.
  • If free entry is occasionally violated—as in the paper's observation of a single entrant accounting for 51% of spam on one rollup—the equilibrium bounds may still hold as a price floor but the closed-form may under-predict transient spikes; a concentration-aware extension would be a natural next step.
  • The model's externality term can be reused to price blockspace: a blockchain could set B_max where the marginal user-share equals a chosen target, turning an externality judgment into a single-parameter policy.
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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. This paper develops a competitive-equilibrium model of 'spam MEV' on high-throughput blockchains. Using a linear demand curve D(g)=D0−βg, a gas-limit fee mechanism, and a linear opportunity value r = r0·Q_u/D0, it derives closed-form equilibrium spam volume S* under random ordering as a function of block capacity Bmax and minimum gas price gmin, with three regimes (no entry, slack-at-floor, congested). It characterizes user welfare, validator revenue, and network externality relative to a spam-free counterfactual, and shows that the welfare loss peaks at Bmax=D(gmin). A marginal-user-share (MMUS) rule and the B_plat plateau are proposed as design guidance. The model is extended to an approximate priority-fee-ordering (PFO) setting with n sub-blocks and a fraction v of priority-bidding users. A demand-scaling analysis argues that under linear opportunity scaling, spam's share of included gas plateaus at a positive level rather than vanishing. Empirical case studies on Base and Arbitrum document spam's response to capacity changes and minimum-fee floors. Proofs are in Appendix C; the MEV-opportunity scaling regression is in Appendix D.

Significance. If the model's predictions hold, this is the first principled framework for a phenomenon that currently drives reactive protocol changes on Base, Arbitrum, and other chains. The closed-form equilibria and the B_plat and gmin design rules are concrete and falsifiable; the connection to Mazorra et al.'s timing-game lower bound in the slack regime is a strong external anchor. The empirical event studies around Base's capacity reduction and fee-floor introduction are valuable. The main weaknesses are the linear opportunity-scaling assumption (weakly supported, especially on Arbitrum), the free-entry premise (contradicted by observed concentration), and the mixed result from Arbitrum's fee-floor doubling. These are load-bearing for the design guidance, so the paper needs robustness analysis before the policy conclusions can be accepted.

major comments (4)
  1. [§3.1, §3.3, §5; Appendix D] The model's closed forms all assume r = r0·Q_u/D0 (γ=1). This is load-bearing: Theorem 3.3's proof (Appendix C.2) uses the free-entry condition r0D(g*)/(D0(S*+1)) = s g*, which is exactly the linear case; with r ∝ (Q_u/D0)^γ, the quadratic for S* becomes another nonlinear equation and the monotonicity of m_user is not established. The empirical support is weak: Appendix D reports γ̂ = 1.08 (R²=0.47) on Base and γ̂=0.82 (R²=0.13) on Arbitrum, and the text itself acknowledges the Arbitrum relationship is 'considerably weaker and less reliable.' Moreover, realized net cyclic arbitrage profit is an equilibrium outcome that may be attenuated by competition, so it is not a clean proxy for the primitive opportunity value. Please provide a robustness analysis for γ≠1, or at least derive the sign of m_user's derivative for γ in an empirically plausible range, and qualify the §3.3 and §5 takeaways
  2. [§7.4, Table 3] The competitive equilibrium assumes free entry drives spam profits to zero. Section 7.4 reports that three new contracts accounted for 51% of all Arbitrum spam gas in February 2026, going offline together, suggesting a single operator. A market where one entity controls half the spam is far from competitive, and in such periods the zero-profit condition is unlikely to hold. The paper should state the domain of validity of the free-entry assumption, describe how the number of active spam operators varies across the sample, or add a concentrated-entry model. As is, the central equilibrium may not describe the very episodes in which spam is most severe.
  3. [§4, Figures 8–9] The second main insight is that priority fee ordering reduces spam. But Figure 8 shows that for v=0 PFO can increase spam relative to random ordering; the text dismisses this as an artifact of the approximate model. Since v (the fraction of users who bid for priority) is not estimated, the policy conclusion is not unconditional. The n=500 sub-block discretization is also an approximation with no convergence analysis. Please characterize the (v, parameter) region in which PFO reduces spam, report sensitivity to n, and restate the takeaway as conditional on a sufficient share of users participating in the priority market.
  4. [§7.4, Table 3] The minimum gas price is presented as a key lever against spam, but the cleanest quasi-experiment in the paper cuts the other way. On Arbitrum, doubling gmin from 0.01 to 0.02 gwei produced a +8.6% change in spam gas and a +6.4% change in spam share (Table 3). The paper explains this as 'too small relative to spam profitability,' but no calibration is provided to support that claim. Without a quantitative reconciliation using the model's parameters, the empirical support for the gmin lever is mixed. Please derive or estimate the model's predicted effect for the Arbitrum change and discuss why the observation deviates.
minor comments (6)
  1. [§3.2, §A] The text refers to 'Theorem 3.2' and 'Theorem 3.3', but the displayed statements are 'Proposition 3.2' and 'Proposition 3.3'; the same issue occurs with 'Theorem A.1' versus 'Proposition A.1' in Appendix A. Please unify the numbering.
  2. [§3.1] The symbol ∆ is used in the congested S* formula but defined only later; define ∆ = D0 − Bmax inline.
  3. [Figure 4] The y-axis label 'Spam volume (gas), S s1' appears garbled; it should be 'S·s' or 'spam gas'.
  4. [§4.1] The main text defers the equilibrium derivation to Section B.1 but does not state the fixed-point condition for ḡ*; please include at least the equilibrium condition so the PFO equilibrium concept does not require the appendix.
  5. [§7.1] The spam classification heuristic depends on a 50% transfer-rate threshold and a top-100-per-month cutoff. A sensitivity analysis for these thresholds would increase confidence in the empirical results.
  6. [Table 2] The before-window dates are not shown in the table; adding the exact calendar dates for each window would improve reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: equilibrium formulas are derived from explicit primitives; the linear opportunity-scaling assumption is an empirical input, not a quantity fitted to the claimed predictions.

full rationale

The derivation chain is self-contained. Section 3.1 states the primitives r = r0*Q_u/D0, the clearing price g(S) = max(gmin, (D0-Bmax)/beta + sS/beta), and spam utility u(S) = S/(S+1)*r - S*s*g(S); setting u(S)=0 yields all three S* branches, with the congested case solving the resulting quadratic. No observed spam volume is used to fit r0 or the functional form; r0 remains a free parameter. Theorem 3.3 and the MMUS marginal-share rule are proven in Appendix C.2 from the same free-entry condition and block-full equation, not read off data. The slack-regime formula independently matches Mazorra et al. [40] (Remark 3.1), providing an external anchor. The demand-scaling section (Section 5) assumes linear opportunity growth based on Appendix D's log-log regressions (gamma-hat=1.08, R^2=0.47 on Base; gamma-hat=0.82, R^2=0.13 on Arbitrum). This is an input assumption, not a fitted version of the target prediction: the plateau result is a conditional theorem, and the paper does not estimate S* or the spam share from that same regression. The low R^2 on Arbitrum and the use of realized profit as a proxy for opportunity value are genuine robustness concerns (Appendix D explicitly says the relationship is 'considerably weaker and less reliable' on Arbitrum), but they are correctness risks, not circularity. Self-citations ([48], [16], [31]-[34], etc.) support contextual, empirical, or related-work claims; none carries the central derivation. No uniqueness theorem is imported from the authors' prior work to force the model choice. Section 7's capacity and fee-floor tests are independent observations and are not used as fitting data for the central equations. Thus no load-bearing step reduces to its own input by construction.

Assumptions & free parameters 8 free parameters · 8 assumptions · 0 invented entities

The framework's predictions are built on stylized primitives — linear demand, a single arbitrage opportunity whose value is proportional to user gas, zero-profit free entry, and random or approximately priority-ordered placement. These are standard economic simplifications rather than derived results, and the empirical support for the linear opportunity-scaling assumption is limited (R²≤0.47). The empirical validation also relies on a heuristic spam classifier. No new physical or economic objects are postulated beyond these modeling abstractions.

free parameters (8)
  • D0 = 1200 in figures
    Intercept of the linear demand function D(g)=D0-beta*g. It is a model primitive, chosen by hand for illustrations and used throughout the closed-form equilibria.
  • beta = 6 in figures
    Price sensitivity of the linear demand curve. A model primitive; the design-guidance rules in Section 3.3 depend on it.
  • s = 20 in figures
    Gas reserved by each spam transaction. A model primitive; equilibrium spam volume scales with s in the zero-profit condition.
  • r0 = 6000 in figures
    Scaling constant for opportunity value, r = r0*Q_u/D0. It is not fitted to data in the model; equilibrium spam formulas depend directly on it.
  • v = explored over {0,0.25,0.5,0.75,1}
    Fraction of users who opt into the priority-fee market in the PFO model. It is not estimated from data; PFO results depend critically on it.
  • n = 500 for PFO figures
    Number of equal sub-blocks in the approximate priority-fee-ordering model. A discretization choice; finer or coarser n may change quantitative spam levels.
  • c1, c2 = not assigned
    Per-unit capacity and execution cost coefficients in the network externality function E=c1*Bmax+c2*B. They are structural parameters; the trade-off conclusions assume they are positive.
  • gamma (opportunity elasticity) = 1.08 (Base), 0.82 (Arbitrum)
    Estimated elasticity of daily cyclic-arbitrage profit with respect to non-MEV trading volume in Appendix D. It is used to justify the linear opportunity-scaling assumption but is not itself inserted into the equilibrium equations.
assumptions (8)
  • domain assumption Linear demand function D(g)=D0-beta*g for non-spam users.
    Used throughout Section 3 for closed forms, welfare, and design rules; Proposition 3.3 extends some results to a broader class, but the main guidance is linear.
  • domain assumption Opportunity value scales linearly with included user gas: r = r0*Q_u/D0.
    Introduced in Section 3 and used again in Section 5. Appendix D gives only partial empirical support (R²=0.47 Base, R²=0.13 Arbitrum).
  • domain assumption Competitive zero-profit free entry: u(S)=0 determines equilibrium spam volume.
    Section 3.1 solves the zero-profit condition directly. Real spam markets can be concentrated, as Section 7.4's three-contract episode shows.
  • domain assumption A single arbitrage opportunity is placed uniformly at random among S+1 relative positions, giving success probability S/(S+1).
    Section 3.1 uses this combinatorial argument for the random-ordering benchmark; PFO replaces it with the approximate sub-block spillover model.
  • domain assumption The TFM charges for gas limit rather than gas used, and all included transactions pay a uniform clearing price in the random-ordering model.
    Stated in Section 2 as modeling a Monad/Solana-style mechanism. Results are claimed to adapt to gas-used charging, but the formal analysis is for gas-limit charging.
  • ad hoc to paper Approximate priority fee ordering: block split into n equal sub-blocks, random within each sub-block, and a fraction v of users bid honestly for priority.
    Section 4 and Appendix B.1 introduce this as a tractable approximation; n and v are not estimated from data, and the equilibrium is computed iteratively rather than proven unique.
  • domain assumption Externalities are linear in provisioned and used gas: E=c1*Bmax+c2*B.
    Definition 2.3 and the welfare/externality trade-offs depend on this linear form; c1 and c2 are never measured.
  • ad hoc to paper Spam classification heuristic: contracts with DEX interactions but <50% ERC-20 transfer rate, with at least 10 interactions, are spam; only top 100 by gas per month are retained.
    Section 7.1 uses this heuristic for empirical validation. It is arbitrary at the threshold and truncation level, and no ground-truth validation is provided.

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Cite this review

Pith. "Pith review of Blockspace Under Pressure: An Analysis of Spam MEV on High-Throughput Blockchains." pith.science (2026). https://pith.science/paper/B2A34HV7

@misc{pith2026260400234,
  author       = {Pith},
  title        = {Pith review of: Blockspace Under Pressure: An Analysis of Spam MEV on High-Throughput Blockchains},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B2A34HV7}},
  note         = {Machine review of arXiv:2604.00234}
}
read the original abstract

On high-throughput, low-fee blockchains, a qualitatively new form of maximal extractable value (MEV) has emerged: searchers submit large volumes of speculative transactions, whose profitability is resolved only at execution time. We refer to this as spam MEV. On major rollups, it can at times consume more than half of block gas, even though only a small fraction of probes ultimately results in a trade. Despite growing awareness of this phenomenon, there is no principled framework for understanding how blockchain design parameters shape its prevalence and impact. We develop such a framework, modeling spam transactions competing for on-chain opportunities under a competitive equilibrium that drives their profits to zero, and deriving equilibrium spam volumes as a function of block capacity, minimum gas price, and the transaction fee mechanism. Empirical evidence from Base and Arbitrum supports the model: spam grew sharply as block capacity was scaled up and fell when minimum gas prices were introduced. Our analysis yields three main insights. First, spam is always costly: when block capacity is scarce, it displaces users and drives up gas prices; as block capacity grows, it increasingly consumes execution resources, raising network externality, i.e., the cost of provisioning and processing blocks. We show that spam takes an increasing share of each additional unit of block capacity, so capping it before all users are included creates a favorable trade-off: forgoing a small amount of user welfare eliminates disproportionate spam and externality. Second, we extend the analysis to priority fee ordering and show that ordering transactions by gas price helps reduce spam, as spammers must pay more to reach early block positions. Third, as user demand grows and blockspace is scaled accordingly, spam's share of block capacity plateaus rather than growing indefinitely.

Figures

Figures reproduced from arXiv: 2604.00234 by the authors.

Figure 2
Figure 2. Daily spam gas on Base and Arbitrum (7-day [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Linear demand curve D(g) = D0 − βg. At clearing price g ∗ , the shaded triangle is the user welfare (aggregate surplus of included users). transaction carries a gas limit of s, such that the number of spam transactions S = (B − Qu)/s. The TFM gives a clearing price g ∗ ≥ gmin that is paid by all the trans￾actions included in the block. A single arbitrage oppor￾tunity worth r is created by some user transaction and c… view at source ↗
Figure 4
Figure 4. Equilibrium spam volume as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (10 more)
Figure 5
Figure 5. Figure 5: Levels of user welfare, validator revenue, and externality, with and without spam, as functions of block size. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Impact due to spam as functions of block size. Negative [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Design rule for choosing the block size as a function of the gas price floor and the user-share target [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Equilibrium spam volume under approximate [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Location of spam within the block under ap [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: User welfare, validator revenue, and externality under approximate priority fee ordering. The solid curves [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Impact of demand scaling on the spam share [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 13
Figure 13. Figure 13: Spam’s share of total gas on Base (7-day mov [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 14
Figure 14. Figure 14: Spam’s share of total gas on Arbitrum (7- [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]
Figure 16
Figure 16. Figure 16: Daily net cyclic arbitrage profit versus daily non-MEV trading volume on log-log scales. [PITH_FULL_IMAGE:figures/full_fig_p026_16.png]

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Forward citations

Cited by 2 Pith papers

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    2024

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