{"id":"fedc0464-594e-457e-a499-19ba20393341","arxiv_id":"2604.00234","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"Equilibrium spam-MEV volume on high-throughput chains is derived in closed form as a function of block capacity, minimum gas price, and fee ordering, and is tested on Base and Arbitrum data.","lead":"An economic model predicts how much 'spam MEV' — speculative transactions that mostly fail — will occupy block space on high-throughput chains, based on block size, minimum fees, and ordering. Data from Base and Arbitrum give partial support, but the empirical evidence is mixed and not independently reproducible.","discovery_kind":"first_principles","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Closed-form equilibria and the marginal-spam-share result hinge on r ∝ Q_u linearity, which Appendix D supports only weakly (Arbitrum R²=0.13, γ=0.82).","rationale":"After checking the algebra in §3.1 and Appendix C, I found no internal mathematical error: the quadratic for S* is consistent with the model, and Theorem 3.3's condition on the demand curve is correctly derived given the linearity assumption. The most load-bearing step is the leap from arbitrary opportunity value to the specific functional form r = r0Q_u/D0. That is used in every closed-form equilibrium and in the monotonicity result that drives the paper's main policy guidance. The reader's weakest_assumption identifies exactly this. I also considered the zero-profit free-entry assumption; Section 7.4's dominant-operator observation is a concern for external validity, but the competitive benchmark is a standard modeling device and can be defended as a long-run/large-n limit, whereas the linearity assumption is directly contradicted by the low explanatory power in Appendix D. Therefore I agree with the reader's conditional verdict: the paper should be accepted only with the requirement that the authors either release the code/data and re-estimate γ with a better proxy, or explicitly acknowledge the sensitivity of the design conclusions to this assumption. My proposed analytical test would settle whether the qualitative insights survive with the measured γ.","tokens_in":33161,"tokens_out":10355,"duration_ms":89665,"concrete_test":"Re-derive the congested-regime equilibrium and m_user(B_max) for the generalized scaling r = r0·(Q_u/D0)^γ with γ ∈ {0.5, 0.82, 1, 1.08, 1.5}, keeping the rest of the model fixed. Specifically: (1) solve the zero-profit condition r0(Q_u/D0)^γ/(S+1) = s·g(S) together with Q_u = B_max − sS and g(S) = (D0 − Q_u)/β; (2) compute ∂m_user/∂B_max symbolically or numerically across the congested region. If for γ=0.82 the marginal share m_user is not strictly decreasing (or if the equilibrium S* has no closed form), then the design guidance in §3.3 and the demand-scaling plateau result in §5 fail under the empirically measured scaling, and the paper's claims must be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central equilibrium expressions (S* in §3.1, B_plat, the congested-regime formulas) and the key design conclusion that spam's share of marginal capacity rises (Theorem 3.3 and the MMUS rule in §3.3) all assume the opportunity value is exactly linear in included user gas: r = r0·Q_u/D0. The proof of Theorem 3.3 in Appendix C.2 uses the free-entry condition r0D(g*)/(D0(S*+1)) = s g*, which holds only for γ=1. If the true scaling were r = r0·(Q_u/D0)^γ with γ≠1, the quadratic for S* becomes a different nonlinear equation, the closed forms in §3.1 and §5 change, and the monotonicity of the marginal user share m_user (i.e., the 'increasing spam share of marginal capacity' insight) is not guaranteed. The empirical support is weak: Appendix D's log-log regression of realized net cyclic arbitrage profit on non-MEV volume yields γ̂=1.08 with R²=0.47 on Base and γ̂=0.82 with R²=0.13 on Arbitrum. The low R² on Arbitrum means the linearity is far from established, and the paper itself acknowledges this limitation. Moreover, realized profit is an equilibrium outcome that may be attenuated by competition, so it is a questionable proxy for the underlying opportunity value. Because the welfare trade-off advice (cap B_max below B_plat) relies on the marginal spam share being increasing, a sublinear or superlinear relationship could overturn the recommended policy. This is a load-bearing assumption, not merely a calibration detail.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":33618,"tokens_out":6219,"duration_ms":63855,"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":[{"comment":"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","section":"§3.1, §3.3, §5; Appendix D"},{"comment":"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.","section":"§7.4, Table 3"},{"comment":"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.","section":"§4, Figures 8–9"},{"comment":"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.","section":"§7.4, Table 3"}],"minor_comments":[{"comment":"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.","section":"§3.2, §A"},{"comment":"The symbol ∆ is used in the congested S* formula but defined only later; define ∆ = D0 − Bmax inline.","section":"§3.1"},{"comment":"The y-axis label 'Spam volume (gas), S s1' appears garbled; it should be 'S·s' or 'spam gas'.","section":"Figure 4"},{"comment":"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.","section":"§4.1"},{"comment":"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.","section":"§7.1"},{"comment":"The before-window dates are not shown in the table; adding the exact calendar dates for each window would improve reproducibility.","section":"Table 2"}],"recommendation":"major_revision","confidential_remarks":"This is a borderline case. The theoretical core is algebraically coherent and the model is novel; the main risk is the unverified linearity assumption and the mixed empirical support. I do not think the paper should be rejected, because the framework can be reframed as conditional and supplemented with robustness analysis. The issues are fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know the core of this paper: it gives protocol designers a quantitative handle on spam MEV instead of just documenting it. The model derives closed-form equilibrium spam volume as a function of block capacity, gas-price floor, and TFM, and it connects welfare, validator revenue, and externality to those design parameters. The proof of Theorem 3.3, showing that spam takes an increasing share of marginal capacity, is the kind of result you can actually use. It also matches Mazorra et al. in the slack regime, which is a good external anchor. I credit the paper for shipping a coherent theoretical core, with proofs in appendices, and for testing its predictions with real Base and Arbitrum data. The Base elasticity of 2.27 for spam vs. gas target and the documented later-in-block spam distribution both fit the model's story.\n\nNow the soft spots, in proportion. The stress-test note is right: the closed forms and the marginal-share theorem all rest on the exact linear assumption r = r0 * Q_u / D0. Appendix D tries to support it with a log-log regression of realized net cyclic arbitrage profit on non-MEV volume. On Base you get gamma = 1.08 with R² = 0.47; on Arbitrum it's gamma = 0.82 with R² = 0.13. That is not a foundation. Realized profit is an equilibrium outcome, so it's also not a clean proxy for the underlying opportunity value. The paper explicitly acknowledges the low R², which is honest, but the assumption is load-bearing, so this is a serious limitation rather than a calibration detail. The empirical validation also has other known weaknesses: no code or data release, a spam-classification heuristic that isn't independently validated, before/after windows without uncertainty quantification, and an Arbitrum fee-doubling result that showed no durable reduction. The paper attributes the rebound to three transient contracts, which is plausible but is exactly the kind of story that needs more than 50-day windows to support.\n\nStill, I didn't find a load-bearing mathematical error. The model is coherent on its own terms, and the design guidance is conditional on the linearity assumption being true. A careful referee should push on that condition hard.\n\nWho is this for? Protocol designers and MEV researchers who want a first-principles model of how blockspace and fee floors interact with spam. It deserves a serious referee. My recommendation: send it to peer review, and require the authors to release their Dune queries and classification code, revisit the linearity assumption with better data or at least bound the gamma range over which the main conclusions survive, and add uncertainty to the before/after comparisons. If those land, this becomes a solid, often-cited paper.","headline":"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.","tokens_in":34058,"tokens_out":1595,"would_cite":true,"duration_ms":19302,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["91A10","91A80"],"pacs":[],"model":"deepseek-v4-flash","headline":"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","keywords":["spam MEV","maximal extractable value","competitive equilibrium","block capacity","minimum gas price","priority fee ordering","network externality","rollup economics"],"falsifier":"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.","tokens_in":33021,"feed_emoji":"🧮","tokens_out":6136,"duration_ms":61832,"temperature":0.7,"pith_summary":"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.","feed_headline":"Closed-form model sets spam MEV volume by block size and fee floor","feed_subtitle":"Designers can pick a cap below the plateau and shed most spam while giving up little user welfare.","key_machinery":"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","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Spam MEV volume pinned down by block size and fee floor","Capping blockspace cuts spam MEV with minimal user cost","Spam MEV share plateaus as blockchains scale","Priority fees slash spam MEV on high-throughput chains","Model predicts spam MEV from block size and gas price"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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).","fun_headline_variants_meta":{"raw":{"variants":["Spam MEV volume pinned down by block size and fee floor","Capping blockspace cuts spam MEV with minimal user cost","Spam MEV share plateaus as blockchains scale","Priority fees slash spam MEV on high-throughput chains","Model predicts spam MEV from block size and gas price"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000233,"raw_usage":{"total_tokens":1398,"prompt_tokens":881,"completion_tokens":517,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":625,"completion_tokens_details":{"reasoning_tokens":434}},"tokens_in":625,"tokens_out":517,"duration_ms":5297,"temperature":1.0,"reasoning_tokens":434,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T16:59:12.538205+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}